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[AA ^^ r DIGITAL COMPUTER LABORATORY UNIA^ERSITY OF ILLINOIS URBANA, ILLINOIS REPORT NO. li^4 THE ELECTROCHEMICAL CELL AS A BINARY MEMORY ELEMENT by Bruce Edwin Briley August 9, 1963 (This work is being submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Electrical Engineering, August 19^3^ and was supported in part by the Atomic Energy Commission under contract No. AT(ll-l)-i+15). DIGITAL COMPUTER LABORATORY UNIVERSITY OF ILLINOIS URBANA, ILLINOIS REPORT NO. 144 THE ELECTROCHEMICAL CELL AS A BINARY MEMORY ELEMENT by Bruce Edwin Briley August 9, 1963 (This work is being submitted in partial fulfillment of the requirements for the Degree of Doctor of Philosophy in Electrical Engineering^ August 19^3^ and was supported in part by the Atomic Energy Commission under contract No. AT(11-1)-415). Digitized by the Internet Archive in 2013 http://archive.org/details/electrochemicalc144bril ACKNOWLEDC^ffilTTS The author wishes to gratefully acknowledge the guidance of his advisor. Professor James E. Robertson, the encouragement and many helpful suggestions of Professor Kenneth C. Smith who acted as advisor in the absence of Professor Robertson, the services of Professor Thomas A. Murrell as official substitute chairman, the critical reading of the first draft of this dissertation by Professors Herbert A. Laitinen and Sylvian S. Ray, the many discussions with members of the staff of the Digital Computer Laboratory at the University of Illinois, in particular, William D. Frazer and Dr. Sergio T. Ribeiro, the services of Mrs. Anna Rita Ferris, who typed the manuscript in its final form. the forbearance, encouragement, and aid of his wife, Marilyn. IV TABLE OF CONTENTS Page I. INTRODUCTION 1 II. HISTORICAL BACKGROUND 5 2.1 Introduction 5 2.2 Relay Memories 5 2.3 Active-Element Memories 6 2.k Circulation Memories 7 2.i^-.l Acoustic Memories 7 2.i4-.2 Magnetic Drum Memories 8 2.5 Electrostatic Memories 9 2.6 Magnetic Core Memories 10 2.7 Diode-Capacitor Memories 12 2.8 Ferroelectric Memories I3 2.9 Thin-Film Memories Ik 2.10 Cryogenic Memories Ik 2.11 Other Memories I6 III. PROPOSED MEMORY I8 3.1 Introduction I8 3-2 Properties Conducive to Memory I8 3.2.1 Energy Density I8 3.2.2 Change in Electromotive Force 21 A. Magnitude 21 B. Polarity 21 3.2.3 Change in Internal Resistance 21 3.2.4 Change in Internal Capacitance 22 3.3 Writing Scheme 22 3.3.1 Constant Voltage 23 3.3.2 Constant Current 2k 3.4 Energy Considerations 25 IV. CELL CHOICE 3I k.l Introduction 3I k.2 Idealized Properties 5I i4-.2.1 General 3I if. 2. 2 For Polarity Discrimination Reading 31 k.2.^ For Magnitude Discrimination Reading .... 32 k.2.k For Resistance Discrimination Reading. ... 32 if. 2. 5 For Capacitance Discrimination Reading ... 32 if. 3 Compromisable Properties. . . , 32 k.k Realizable Properties ^k k.^ Cell Comparison J,k if. 5.1 The Lead Acid Cell 35 if. 5.2 The Nickel-Iron Cell 35 if. 5.3 The Nickel-Cadmium Cell 36 if. 6 Cell Choice 37 TABLE OF CONTENTS (Cont'd) Page V. SELECTION SYSTEM kl 5.1 Introduction, 14-1 5.2 Orientation kl 5.3 Requirements kl '^.k Selection System Choice k2 5.5 Reading kk VI. EQUIVALENT CIRCUIT k6 6.1 Introduction k6 6.2 General Equivalent Circuit k6 6.3 Specific Equivalent Circuit 52 6.k Approximate Equivalent Circuit 55 VII. CIRCUITRY 59 7.1 Introduction 59 7.2 Counter 59 7.3 Logic 59 7.U Bit Write Driver 62 7.5 Word Write Driver 62 7.6 Read Circuitry 62 7.6.1 Magnitude Discrimination 66 7.6.2 Other Discrimination Methods 66 7.7 Comments 66 VIII. EXPERIMENTAL RESULTS 69 8.1 Introduction , 69 8.2 Common Electrolyte Experiment 69 8.2.1 Purpose 69 8.2.2 Procedure 70 8.2.3 Results 70 8.2.i4- Conclusions 70 8.3 Charge Rate Test 7I 8.3.1 Purpose 71 8.3.2 Procedure 7I 8.3.3 Results 71 S.^.k Conclusions 72 8,k Charge Rate Test Extension 78 8.i4-.l Purpose 78 8.^4-. 2 Procedure 78 8.i^.3 Results 79 8.4.^ Conclusions 79 8.5 Life Test I 8I 8.5.1 Purpose 81 8.5.2 Procedure 8I 8.5.3 Results 82 Q.^.k Conclusions 82 VI TABLE OF CONTENTS (Cont'd) Page 8.6 Life Test II 83 8.6.1 Purpose 83 8.6.2 Procedure 83 8.6.3 Results 8k 8.6. J+ Conclusions 85 8.7 Determination of Impedance as a Function of Frequency 86 8.7.1 Purpose 86 8.7.2 Procedure 87 8.7.3 Results 87 8.7.ij- Conclusions 88 8.8 Determination of Double-Layer Capacitance 100 8.8.1 Purpose 100 8.8.2 Procedure 100 8.8.3 Results 101 8.8.^4- Conclusions 101 8.9 Element Delay Test 102 8.9.1 Purpose 102 8.9.2 Procedure 102 8.9.3 Results 103 8.9.i^ Conclusions IO3 8.10 Two Word, Four Bit System Test IO9 8.10.1 Purpose 109 8.10.2 Procedure IO9 8.10.3 Results Ill 8.10. i| Conclusions. II3 8.11 Discharge-Voltage Drift Inhibition II3 8.11.1 Purpose 113 8.11.2 Procedure 113 8.11.3 Results 114 8.11.4- Conclusions Il4 IX. SOME PRACTICAL DESIGN CONSIDERATIONS II7 9.1 Introduction II7 9.2 Preliminary Considerations II7 9.3 A CD-I Chemory 121 9.k Extension 122 9.5 Limit . 125 X. CONCLUSIONS 126 10.1 General 126 10.2 Economic Feasibility 128 10.3 Recommended Cell Modifications for Chemistor Use. . . 129 10. i4- Further Study I30 BIBLIOGRAPHY I32 THE ELECTROCHEMICAL CELL AS A BINARY MEMORY ELEMENT Bruce Edwin Briley, Ph.D. Department of Electrical Engineering University of Illinois, 19^3 A memory (chemory) utilizing electrochemical cells for its binary- memory elements is proposed. The properties peculiar to cells and conducive to their use as memory elements are considered. Three cell parameters which are sensitive to the state of charge of a cell prove to be electrically monitorable • A chemory is shown to lend itself most readily to a pseudo-read- only memory system due to a great discrepancy between possible read and write time in a pseudo-nondestructive-read mode. An idealized cell is described, and the degree to which its properties may be compromised in a practical cell is discussed. Of those presently available, the nickel-cadmium cell is shown to approach most closely the ideal. A constant-current writing scheme is shown to have advantages over a constant -voltage scheme. The selection system chosen employs two diodes per bit and is word-oriented. A two-word, four -bit chemory was built and tested with excellent results. A general equivalent circuit is developed, particularized for the nickel -cadmiiom cell, and then approximated. Many experiments were perfonned; some of the conclusions based on the results follow: lo A common electrolyte chemory is unfeasible. -1- 2. The time to fully charge a sealed, pressed-plate nickel- cadmium cell is inversely proportional to the two-thirds power of the normalized charging current. 5. Capacitance discrimination reading is not practical for a nickel- cadmium cell, nor is resistance discrimination except for very small sizes; e.m.f. discrimination is practical for any size nickel- cadmium cell. k. The faradaic impedances of sealed pressed-plate nickel- cadmium cells behave in an anomalous fashion. 5. No delay is contributed by a nickel-cadmium cell "chemistor" during read because it behaves essentially like an immense charged capacitor. 6. A thousand word chemory is probably feasible. 7. Access time for a thousand word chemory would be approximately 70 ns, and cycle time, around l40 ns. 8. Structurally robust containers and means to prevent reversed polarity are necessary to successful use of chemistors. 9. Magnitude discrimination can be greatly improved by introducing a very small quiescent drain. 10. The minimimi write-time for a nickel- cadmium chemistor is of the order of one microsecond due to reaction-speed limitations. The advantages of a chemory are: a. Very fast read b. Effectively nondestructive read c. Existence of information in a salient form d. Large read-voltage magnitude e. Electrically alterable read-only operation. A historical review of memory developments is included. I. INTRO mCTION A digital computer is a device which automatically performs manipu- lations analogous to mathematical operations upon representations of numbers according to a pre-planned scheme, usually with the ability of maRing decisions depending upon the results of its calculations and of altering its instructions. The means of number representation used are many: the physical position of a switch contact; the presence or absence of a hole in a strip of paper; the magnitude or polarity of a voltage or current; etc. Almost all high-speed computers use a binary representation internally because multi- state circuits cannot be economically or reliably built. The necessary manipulations are performed by logic elements which take forms dependent upon the taste, philosophy, and budget allowance of the designer. Implicit in the definition given above is a need for storage facilities to preserve intermediate results and for input and output buffering. It is possible to imagine a digital computer which would have no need for memory of any kind: a real-time computer whose input would be a digitized version of the output of a transducer sensing some physical time- vaiying phenomenon; a wired-in program would cycle through arithmetic opera- tions, and the output would be digested immediately. Such a computer system is obviously far-fetched, and serves to illustrate how difficult it would be to build a general -purpose computer which did not have any memory. For several years a need for new and better memories has made itself felt in the field of digital computers . This need has fostered efforts along widely differing fronts; this dissertation in one such effort. Speed limiting characteristics of some present-day memories are as follows : (1) Totally destructive readout (requiring the rewriting of the information lost, lengthening the memory cycle by about a factor of two) (2) The need for large currents to effect readout (the production of large currents is a time consioming process) (3) Dependence upon a change of state of the memory element to produce the read information (state changes cannot take place instantaneously, so that a delay is introduced which will tend to vary from element to element) . The class of memories proposed in this dissertation eliminates two or more of the above limitations in each variation. Electrochemical cells have been used for many years as temporary energy-storage devices. The differences in energy stored upon charge and dis- charge (or in the case of a symmetrical cell, charge to either of two polarities) can be regarded as corresponding to the two binary states, and 1 (not necessarily respectively). At least three physically perceivable phenomena can herald a change in the stored energy of an electrochemical cell: electromotive force (magni- tude or polarity), resistance, and capacitance. Each of these lends itself admirably to electronic sensing. Electrochemical cells have found very limited use as electronic components thus far. Components used or proposed are: (1) The electrolytic capacitor--a capacitor formed by producing an oxide layer upon one or both electrodes of an electro- chemical cell, the extreme thinness of the oxide dielectric producing a large capacitance. (2) The electrolytic diode — certain films formed on the surface of an electrode of an electrochemical cell produce an insulating layer for one voltage polarity, but strip off when the polarity is reversed, producing 1* a relatively low impedance. (3) The memistor--a three terminal device which produces upon a relatively high impedance substrate, by means of two of its electrodes, a conducting layer proportional to the time integral of the current allowed to flow through them, the resistance of the conducting layer monitorable 2 through one of these electrodes and the third. {k). The electrolytic transistor- -an electrochemical cell employing a polarizable electrolyte containing ions of two possible ionization states, and three electrodes, which behaves in a manner analogous to that of a transistor. The use proposed in this dissertation is as a binary memory element. The term "Chemory" is hereby coined to denote a memory using electrochemical cells for its binary memory elements, and the term "Chemistor" to denote the memory element, regardless of the reading scheme used. References are listed at the end of each chapter. CHA.PTER I Footnotes 1. 5yron 0. Marshall, Jr., "Electrolytic Diodes/' Quarterly Report No. 1 of the Computer Components Fellowship , No. ^k'J (Oct. 11, I95O to Jan. 11, 1951}, pp. i.i-i.io. 2, M. E. Hoff, Jr., "Learning Phenomena in Networks of Adaptive Switching Circuits," Technical Report No. l^^^-l of Stanford Electronics Laboratories (July 1962), pp. kk-k^. 5. W. J. Poppelbaum and H. Letaw, an as yet unpublished report. II. HISTORICAL MCKGEOUND 2.1 Introduction Since 19^^^ when the first large-scale computer was built, there has been a mushrooming Interest In the field of memory devices. Though the number of methods of storage which have been used Is considerable, the number which are In favor at any given time Is small, because, as soon as a new and better method Is discovered, the old methods are abandoned on a wholesale scale. 2.2 Relay Memories In 19^^ Bell Telephone Laboratories completed their Model I relay 2 computing system. It was the first of a series of computing machines which used relays for their memory. The electromechanical relay is such a dependable, durable, flexible device, that when the best of all possible memory elements is about to eliminate all others, the relay may well be the sole survivor -with- tenure. Memory is obtained with relays either by employing a mechanical latching arrangement (a scheme of limited importance) or by causing an alter- nate sustaining- current path to come into being as a consequence of the relay's activation, guaranteeing the state of the device Independent of the original activating current. The advantages of relay memories are: (1) The input impedance can be almost arbitrarily high, depending only upon the construction of the relay. (2) The ratio between the output impedance for the inactivated and activated states of the relay is about as close to infinity as it is possible for any physically realizable device to attain. (5) There is no coupling between input and output. (k) Many mutually independent outputs can be used. (5) They are very reliable. The disadvantages are: (1) high cost per bit, (2) high power dissipation since (in general) current must flow to preserve the memory state, (3) great bulk per bit, (k) slow speed. The relay has long since been abandoned as much too slow for high speed computer memories. 2.5 Active -Element Memories In 19^6, the Eniac, built at the University of Pennsylvania, was completed; it was the first computer to use an active-element memory. Active-element memories, in their most common form, use two triodes or transistors coupled so that either of two states (one element conducting, the other cut off, and the reverse situation) can be induced, and will be preserved so long as power is not interrupted. Though other types such as the point-contact transistor and the tunnel diode are capable of holding Information with only one active element, the former has been abandoned due to unavailability of \iniform units, and the latter has not yet met with great success because of problems inherent to a two terminal memory element. The advantages of active-element memories are: (1) very fast write (set) times, (2) read times limited only "by the selection system. The disadvantages are: (1) very high cost per bit, (2) low bit density, (5) power dissipation required to retain memory, (k) power-dependent volatility. While active-element memories are by far the fastest, their high cost and bulk have limited their use to internal arithmetic registers, small "fa,st memories," and the like. 2.k Circulation Memories 2.4.1 Acoustic Memories In 1949? "the Edsac, built at Cambridge University, was completed; it was the first computer to use acoustic delay lines for memory (though patterned after Edvac, Edsac was completed three years ahead of it;. Acoustic memories use a delay -line type of memory element. These elements employ a substance such as mercury which conducts mechanical dis- turbances initiated by a transducer at one extremity down its length to a sensing transducer at its other end. The duration of its memory is extended to an arbitrary value by feeding the sensed, amplified information back to the element's input, causing the information to "circulate." There are a number of variations on this theme, but the basic principle employed is the same . The number of bits which may be stored in an acoustic memory element is limited by two factors: 8 (1) Due to resolution problems, the packing density of the "bits is limited. (2) The length of the delay-line is limited by the time one is willing to wait for a chosen bit to be accessed. The advantages of acoustic memories are barely perceptible in comparison to modern memories, but they were much faster than the relay memories they replaced. Their disadvantages are: (1) high cost per bit, (2) limited capacity, (3) non-random access, (k) temperature sensitivity. Most delay -line memories which were used on computers still running have been replaced with newer memory types. 2.4.2 Magnetic Drum Memories In 1950, the Mark III computer built at Harvard University was completed; it was the first computer to employ a magnetic drum memory. Magnetic drum memories use a rotating metal cylinder coated with a magnetic material. Bits are represented by the magnetic state of localized portions of the drum surface. Magnetic fields induced by currents in station- ary heads perform the writing function, inducing, in turn, magnetic fields in the portion of the surface under them. Reading is effected by monitoring the e.m.f. produced in a head by the moving magnetic field of the drum surface. Average random-access time for a drum with a single double-duty set of heads is one-half the time for one revolution. Mechanical difficulties encovmtered in attempting speeds much above 10,000 r.p.m. limit the ultimate average random-access time severely. The advantages of magnetic drum memories are: (1) high "bit density (volume as well as surface), (2) relatively low cost per bit, (3) non-volatility of information. Their main disadvantage is their large average random-access time. The magnetic dnam is still held in favor as an excellent memory for low-speed machines, and as a large capacity backing-store for high-speed machines. 2.5 Electrostatic Memories In March 19^9^ ?• C. Williams and T. Kilburn described in the Proc. I.E.E. an electrostatic-storage type of memory popularly known as a "Williams -tube memory." It proved to be such an elegant system that com- puters all over the world were soon employing it. The Williams -tube memory employs a cathode-ray tube with a metal pick-up plate against its outer face. If a small spot on the phosphor -coated screen is bombarded with electrons which have a velocity such that the coefficient of secondary electron emission is greater than one, the spot will acquire a positive charge. This positive charge can be intentionally removed by bombarding a closely adjacent spot so that secondary electrons from it fill the electrostatic "well" of the first spot and make its charge more-or- less neutral. The presence or absence of a well can be detected by interrogating a spot with the electron beam. If no well exists, one is formed, and the change in potential can be detected on the metal face-plate. If a well exists. 10 essentially no change takes place, and no signal is detected on the face-plate. Unfortunately, the electrostatic wells are extremely volatile, lasting for only tenths of a second, so that the information must be renewed often to prevent loss . A figure of merit for a Williams -tube memory is the "read-around ratio," the number of times neighbors of a given spot may be referenced before the spot is affected « The value of this figure of merit determines the degree to which a programmer may be restricted in the frequency with which he may reference the same word. The advantages of the Williams-tube memory are: (1) relatively fast read and write times, (2) random access (also fast). The disadvantages are s (1) the need for frequent periodic regeneration, (2) the need for an almost unreasonable amount of shielding to avoid spurious signals, (3) large bulk, (h) the fundamental limitation put upon the programmer by the read-aro"und ratio. Electrostatic memories have been nearly pushed out of existence by the adi'-ent of magnetic-core memories. 2.6 Magnetic Core Memories Soon after the completion of Whirlwind I at the Massachusetts Institute of Technology in 1950 ^ Its electrostatic store was replaced by a 7 magnetic core memory. It was tne first computer to employ such a memory. 11 The magnetic core memory makes use of tiny (as small as O.OI3 in. I.D., 0.018 in. O.D.) magnetic cores (usually of ferrite) which have a "square" hysteresis loop. One or two cores per bit are used, arranged in a three- dimensional matrix. Writing is accomplished by bringing about coincidence of two or more currents in the selected cores such that their sum produces a magneto- motive force greater than the threshold value. Reading is accomplished either by a coincident -current method like that used in writing (bit oriented), or by a single wire through all the cores of a word carrying a greater-than-threshold current (word oriented) . The information is sensed by monitoring the e.m.f. induced in a sense-wire thread- ing the same bit in each word. The change of state produced by the read-current is not instantaneous However, the speed with which the state-change occurs can be increased some- what by increasing the difference between the read-current and the threshold current . The above-mentioned reading schemes (which are, by far, the most used) are destructive. However, multi-aperatured cores have been developed which allow non-destructive readout. The possession by magnetic cores of hysteresis loops with finite area indicates that hysteresis losses will be non-zero. Indeed, the high currents and great repetition rates used make heating a serious problem. The advantages of the magnetic core memory are: (1) relatively high volume density of bits, (2) random access, (3) relatively low cost, (k) relatively high speed, (5) non -volatile information. 12 The disadvantages are : (1) destructive readout, (2) need for high speed, high current circuitry, (3) considerable power dissipation within the memory element. The magnetic core memory is the most popular and widely used memory for high speed machines at this time. 2.7 Diode -Capacitor Memories In late 1952, the National Bureau of Standards began reporting on 8 a new memory type, the diode-capacitor memory. This memory employs a capacitor as its memory element, the magnitude or polarity of the capacitor voltage being interpreted as binary states. The diodes (two per bit) are necessary to allow the passage of current in either direction through the capacitor during selection and yet present a high impedance between selections. The reverse-biased impedance, while large, is finite, so that the capacitor charge leaks away and must be replenished periodically; the intervals between regenerations are of the 9 order of 1 millisecond. The main advantage of the diode -capacitor memory is the short cycle time (a one microsecond cycle is obtainable). The disadvantages are: (1) volatility of information, (2) low bit -density, (3) high cost per bit. '^ Though moderate size arrays (256, ^4-5 bit words) have been built and operated successfully, the diode capacitor memory has essentially been abandoned . 13 2.8 Ferroelectric Memories In the middle of 1951^ the ferroelectric memory "began to be mentioned In the literature. Certain dielectric materials such as barium tltanate exhibit residual electric polarization. This is the electric analog of residual magnetization taken advantage of in magnetic core memories. A ferroelectric cell is written into by applying a voltage of sufficient magnitude to guarantee the polarity of the residual polarization. Reading is accomplished by applying a voltage of opposite polarity and sufficient magnitude to change the sign of the polarization. The capacitance exhibited by the cell upon reading is a function of the slope of the portion of the material's hysteresis loop which is traversed, the slope being largest if the sign of the polarization is altered. The magni- tude of the dynamic capacitance of the cell is sensed by making the cell a part of a capacitance voltage-divider which, in effect, compares it with a constant capacitor. The energy dissipated by ferroelectric materials is some two orders of magnitude greater than that of ferrltes, making cooling a very severe problem. The volatility of the information stored is dependent upon the magnitude of the voltages used, the lifetimes varying by a factor of nearly one hundred. The advantages of the ferroelectric memory are : (1) relatively high speed, (2) low information volatility (potentially), (3) possibility of high read voltages, 12 {h) high discrimination ratio (greater than I4-O). 11^ The disadvantages are: (1) difficulty in manufacture, (2) extreme dissipation. The ferroelectric memory has not yet left the experimental stage. 2.9 Thin-Film Memories Since 1955^ there has heen much interest in thin-film memories. These memories make use of vacuum evaporated, very thin layers of magnetic materials deposited on nonconducting plates. By any one of several techniques, the film is made uniaxially anisotropic. Memory cells are formed either as individual dots of magnetic material or by the proximity effect of orthogonal wires on a continuous sheet of fiLno States of a cell correspond to directions of magnetization. Memory cycle times as low as O.5 microseconds seem feasible. The advantages of thin-film memories should be: (1) high speed, (2) low cost per bit. The disadvantages are: (1) difficulty in producing uniform cells, (2) fundamental minimum size limitations. At the time of this writing, a small (128 word) thin-film control memory is being used in a commercially available computer, the Univac 1107» In 1956, the use of cryogenic techniques to produce computer canponents was first discussed; these novel devices have prompted a great deal of interest and study. 15 Cryogenic memories make use of certain peculiar properties exhibited by some materials when they are sufficiently cooled: (1) their resistance becomes zero, (2) the above property is temporarily negated if the magnetic fields penetrating the material are sufficiently great. An additional property made use of Is that the flux linking a super-conducting loop cannot change. Film cryotrons are constructed of a pair of orthogonal, super- conducting strips insulated from each other and a superconducting ground plane; one of the strips is designated as the gate and the other as the control. The materials are so chosen that the control strip can carry a current great enough to destroy the superconductance of the portion of the gate strip near it without destroying its own or that of the ground plane. A memory cell may be constructed as follows : a datum current has a choice of two parallel paths, one through a cryotron gate, the other through a superconducting wire; a write current path is through the cryotron's control. During write, the write current is always present, destroying the gate super- conductivity. If a zero is to be written, no datum current is turned on, so that after the write current is removed, no currents flow. If a one is to be written, datum current is turned on, all of which flows through the super- conducting wire (none through the ciyotron) . The write current is then removed and the cryotron becomes superconducting. When the datum current is then removed, the flux linking the loop made up of the wire and the ciyotron gate must be preserved, so a current equal to the datum current circulates within It Indefinitely. The state of the element may be detected by causing the wire path to be the control of a second cryotron. A read current passed 16 through the gate of this cryotron will produce no voltage or a finite voltage across the gate depending on whether the current through its control is zero 1 ry 1 Q or finite, respectively. ' The advantages of a cryotron memory are: (1) very fast switching time, (2) vanishingly small internal electrical power dissipation, (3) very small sizeo The disadvantages are: (1) the large power requirement for refrigerating equipment, (2) the great bulk of the above equipment, (3) difficulties in fabricating uniformly thick, multiple layers of very thin films, {h) conversion of signals to normal levels. 2.11 Other Memories Certain other memories are not considered either because they are not sufficiently unique (e<.g., the twistor) or do not contribute to the dis- cussion (e.g«, phase-lock oscillators). 17 CHAPTER II Footnotes 1. Staff, Engineering Research Associates, Inc., High Speed Computing Devices (New York: McGraw-Hill Book Co., Inc., 1950), p. l82. 2. Ibid ., p. 187. 3. Franz L. Alt, Electronic Digital Computers (New York and London: Academic Press, Inc., 1958), p. I8. k. Ibid., p. 20. 5- Ibid. , p. 19. 6. F. C. Williams and T. Kilburn, "A Storage System for Use with Binary- Digital Computing Machines," Proc. Inst. E.E ., (March 19^9), I^rt III, pp. 81-100. 7. Alt, p. 25. 8. A. W. Holt, "An Experimental Rapid Access Memory Using Diodes and Capacitors," Proc. ACM Toronto Meeting , (September 1952). 9. Charles V. L. Smith, Electronic Digital Computers (New York: McGraw- Hill Book Co., Inc., 1959)^ P- 1367 10. Ibid , , p. 302. 11. C. F. Pulvari, "An Electrostatically Induced Permanent Memory," Jour. Appl. Phys. , Vol. 22 No. 8 (August 1951), PP- 1059-lOlfi^. 12. Smith, p. 132. 13. Jan A. Rajchman, "Computer Memories — A Survey of the State of the Art," Proc. I.R.E. , Vol. 49 No. 1 (January I961), p. II9. Ik. Ibid . , p. 120. 15. Datamation , (November I962), p. I7. 16. D. A. Buck, "The Cryotron-Superconductive Computer Component," Proc . I.R.E. , Vol. kk (April 1956), pp. lj-82-if93. 17. William B. Ittner III and C. J. Kraus, "Superconducting Computers," Scientific American , (July I961), pp. I25-I36. 18. L. L. Burns, et al., "Coincident-Current Superconductive Memory," I.R.E . Trans. Elec. Comp ., Vol. EC-10 No. 3 (September I961), pp. kk2-kk6. 18 III. PROPOSED MEMORY 3.1 Introduction It is saying very little to state that many electrochemical cells meet the "basic requirements for memory elements because these requirements are not difficult to satisfy o They are: (1) ability to undergo a change of state in some sense (not necessarily more than once), (2) the existence of a technique for detecting the state of the element. It is saying a great deal, however, to state that certain electrochemical cells meet more than the basic requirements for a modern, fast, reasonably general-purpose memory. In addition to those stated above, they are: (1) ability to be incorporated in a random-access selection system, (2) ability to yield information very quickly upon interrogation, (3) ability to store information quickly. It will be shown that with the possible exception of the last stated, the above requirements are met by certain electrochemical cells. 3.2 Properties Conducive to Memory The properties exhibited by electrochemical cells in general are so many and varied that it is not surprising that some of these would be conducive to use as a memory element. 'J 3.2.1 Energy Density The diode-capacitor memory makes use of the ability of a capacitor to store energy in an electrostatic field. This energy is given by the relation 19 W = 1/2 CV^ where W = energy in joules C = capacity in farads V = voltage across the capacitor in volts The energy density achievable in capacitors is relatively small at the present state of the art. The greatest densities are found with electrolytic capacitors, where, for example, a 10,000 [if, 10 v unit would have a volume of about p 10 cm.x jric(5cm.) « 270 c.c, and the energy stored at the highest allowable voltage (lO v) would be W = 1/2 X 10"^(lO)^ = 1/2 joule, yielding an energy density of Wd = '-^ — r ~ 2 X 10^ joules/meter^. 270 X 10" The best known secondary cell is the lead-acid storage battery used for starting automobiles. A calculation of the energy density attainable in a commercially available battery will now be made: Voltage: 12 v Dimensions: about 25 cm. on a side Capacity: about 100 ampere-hours ■=/ VI dt « VI t = 12 X 100 X 3600 = 4.32 X 10 joules Vol. = 25^ = 1.56 X 10^ c.c. T.7^ ^-32 X 10° ^ ^ ,^8 . , / ^ 3 Wd = =^ — r z- ~ 3 X 10 joules/meter . 1.56 X 10 X 10 20 The ratio between the energy densities easily attainable in a capacitor and a secondary battery is then MdB ^ 3 X IqQ _ 1 5 X io5 ^"^^ 2 X 10^ The figure arrived at above can hardly be said to apply to all variations of capacitors and batteries, but even if it were two orders of magnitude too great, it would still be a striking comparison (actually, this ratio is pessimistic as a comparison for capacitors of diode-capacitor memories; these capacitors are typically from 2,000 to 10,000 |J.|J.f, so that electrolytic capacitors are not used) . The great density with which energy can be stored in a secondary- battery could be utilized in at least two ways: (1) A cell could serve the purpose of the capacitor memory, but with a great diminution in size. (2) A cell could be either charged or discharged to indicate a binary state, and interrogation could be performed with (a) direct-coupled circuitry which would drain energy from the cell, creating a pseudo- nondestructive readout system in which, though the number of possible interrogations per regeneration would be finite, could be quite large, or (b) capac it ively- coupled circuitry which would create a nondestructive readout system, assuming the volatility of the energy to be low. 21 5.2.2 Change In Electromotive Force A. Magnitude It is a well known property of secondary batteries that the closed-circuit e.m.f . measured when a battery is fully charged differs fraa that when it is discharged. This effect is usually attributed to an increase in internal resistance when a cell is discharged, not to a change in the e.m.f. produced by the cell. Seme cells, however, are observed to change their open circuit e.m.f. appreciably as a function of their state of charge . This property could be exploited to detect the state of charge of a cell without requiring the use of large currents. B. Polarity If a secondary cell of a symmetrical character were built, the polarity of its e.m.f. would provide a very easy means for sensing the state of the element. The cell would need electrodes of identical material, severely limiting the choice of possible cells . The advantages of such a memory elanent would be: i. ease of discrimination. ii. reliability of discrimination. 3.2.3 Change in Internal Resistance The internal resistance of an electrochemical cell is a combination of the ohmic resistance of metal conductors inside the cell and the resistance of the electrolyte, which is a function of ion densities for short times, and ion mobilities for long times. 22 ^.2.k Change in Internal Capacitance The nonfaradaic portion of the internal capacitances of an electro- lytic cell may have two constituents: (1) the double -layer capacitance formed by the charge 2 separation predicted by Coehn's rule at the inter- face between an electrolyte and a conducting electrode. (2) the capacitance formed by a film of oxide or other low- conductivity material on a conducting electrode. 3.3 Writing Scheme The method of writing will be fairly independent of the reading scheme, but will be very dependent, system-wise, upon the selection method, which will be discussed in Chapter V. Writing into a cell will require the removal or storage of energy in the cell. It is instinictive to compare the physics of energy storage in a secondary cell with that in a capacitor: assume the cell has a constant e.m.f. E: comparison will be made with a capacitor of value C. t Wg = j v(t) i(t) dt where W = stored energy in joules i(t) = current in amperes v(t) - voltage across element in volts Let i = I, a constant t t then W cell = / E • I dt = IE / dt 25 W cap. s t t I dt dt = i2 c t / t / dt dt dW cell s I E dt dW cap . ■;. dt (assuming W (O) = O) o Thus it can be seen that, while the rate of energy storage in a constant e.m.f. cell is a constant, it is proportional to time in the case of a capacitor. Since some resistance is always present in a circuit, it is important to consider the ratio of the amount of energy lost in dissipation to that stored. 5. 3*1 Constant Voltage By the way of comparison, it is interesting to note that it can be easily shown that one half the energy supplied to an RC series circuit by a constant voltage source is dissipated independent of the values of R and C. For a cell, V - E W = E i t where i = — ;- — s R = ^ " — '- t V = applied voltage (a constant) K W = i2 R t . iL^ R t = il^ t d j^2 R ^ = (V - E)^R t ^ (V - E) ^ W E(V- E) R t E V s ^ Thus, the ratio of energy dissipated to energy stored is dependent only on the applied voltage (assuming E to be unalterable). 2k 3.3.2 Constant Current W = E I t as has been shown s W^ = I^ R t d W 2 2d ^ I R t ^ I_R W"EIt E~i s The ratios a. and a contain all the information pertaining to the mode of charging because a general expression can be written which applies to both cases: tE^ ^sk = — \' A close look at these ratios is in order: a. q; -- the sign of this ratio is sensitive to the V magnitude of V, that is, it is negative for V < E; if when V is applied, its excursion begins at 0, energy- will be taken from the cell until it reaches E. b. Q;. -- the magnitude of this ratio is proportional to R; the portion of R contributed by the resistance of the electrolyte will decrease as the cell becomes charged, so that a. will decrease. 1 The fundamental limitation upon the value of the current which may be used in charging is the current density. If the current density is greater than a critical value, gas is evolved. In order to minimize charging time, if a constant voltage scheme is used, V would be chosen so that V - E — =; — = I crit. Re is R at completion of charge. Re X- o 25 Similarly, if a constant current scheme is used, I woiild 'be chosen to be equal to I crit. rr^ ^ Re I crit. Then a V E ' R I crit. and a^ = , . * . since R > Re, a. > Q! where equality only applies when charging reaches completion. That is, the loss-to-storage ratio for maximum constant-current is greater than that for maximum constant-voltage. More important, however, it should be noted that the current in the constant current case is greater than that for the constant voltage case, causing the energy stored per unit time (iE) to be greater in the former than in the latter case. The above result, coupled with the previous conclusion concerning the possibility of a negative, transient a , indicates that a constant current writing scheme would be best; this scheme, therefore, will be adopted. 5.4 Energy Considerations The problem of designing a chemistor reduces to balancing an energy budget. In the case of a pseudo-nondestructive scheme, the budget becomes W write > W read + W circuit loss + W self -discharge where W read = energy removed by each read W circuit loss = energy loss due to the finite impedance of the selection circuit between selections W self-discharge = energy lost due to the self -discharging property present to some degree in all cells. Assuming that W self -discharge is negligible, the inequality becomes 26 (1 - i) I^ E t^ > n Ig E tg . IE t where I^ = write current E = cell voltage (a constant) t-| = write time n = number of reads demanded before cell energy drops to l/e of its full charge value I = current drawn during a read tp = read time I = leakage current t = longest time chemory must retain information before cell energy drops to l/e of its full charge value (The use of the Napierian base may seem out of place here, but it is convenient for comparative purposes.) Assuming E = 1 v. I = 0.1 ma. t = 0.1 lis. I = O.OOliaa. (e.g. Fairchild's FD3OO diodes) t^ = 10 hours n = 10 0.63 I^ t^ > 10 X 10" X 10"''' + 10"^ X 3.6 X 10 > 10"^ + 3.6 X 10"^ = k.6 X 10"^. Assi;miing cell efficiency = 50/^^ I.-tn > r!^'^t ^ ^^c = 1-^6 X 10"^ coulombs. 11— 0. 63 X 0.5 If I is about 0.5 ampere, t^ > 292 \xs. 27 This is such a long time that the future of the chemory as any- thing but a slow-speed memory appears dim except for the following possibilities (1) Use of a periodic regeneration scheme — if replenish- ment were performed say once each minute, the maximum energy, and therefore the write (or replenishment) time would be diminished by a factor of 600, the latter to a value of O.kQ^ microseconds; for a four thousand word memory, regeneration would occupy 4 X 10^ X (0.1 + O.kS-j) X 10 = 2.55 X lO'^ sec. or 0.00592^ of the time. (2) Limitation to use as a pseudo-read-only memory — read-only memories are becoming increasingly popular; the ability to change their contents occasionally in a few seconds would almost surely make them more popular. For reasons which will later become clear, use as a pseudo-read- only memory appears to be the most fruitful prospect for the chemory, and will therefore receive the major emphasis in this dissertation. Read-only memories are still somewhat of a rarity. Probably the best known example is that developed for use with the Ferranti Atlas 5 computer. In this version, ferrite slugs are placed between orthogonal loops at their crosspoints in bit positions desired to correspond to one binary state while copper slugs are placed in those positions desired to correspond to the other. The ferrite slugs, being ferromagnetic, provide much better magnetic coupling between the loops than does air, while the copper slugs, being diamagnetic, provide somewhat less than would air. Thus a read pulse applied to a word wire will produce a much larger disturbance 28 in those bit wires coupled to it by ferrite slugs than those coupled to it by copper slugs . This memory is quite fast and very satisfactory, its only drawback being that it lives up so well to its name--it is indeed a read-only memory; that is, its contents are Tinchangeable by any but physical means (as opposed to electrical means) « Read-only memories are used for storage of standard subroutines, compilers, tables (for special purpose computers), and ''logic" for stored logic computers all of which are subject to occasional changes. There is an unfulfilled need then, for a nominally read-only memory which could have its contents changed occasionally in a relatively short time (implying electrical means) o A pseudo- read-only chemory might fill this need. It is very important to note that the loss through the selection circuitry is a constant for alL cell sizes, and, for cells with energy capacities much in excess of the numerical example just given, this loss will be negligibly small c The pseudo-read-only chemory must have its energy replenished from time to time. There are several possible techniques: 1. A periodic regeneration scheme which A. replenishes the entire chemory during regular maintenance periods spaced such that i. the worst-case interrogation rate cannot deplete the cell energy below a readable level, or ii. a limitation must be placed upon the programmer's interrogation rate for any one word B, replenishes the words one -by -one in a cyclic fashion at intervals spaced such that i above is not violated. 29 A periodic checking scheme which replenishes only when necessary, This checking may he performed in a cyclic manner such that l.A.i above is not violated, or by the rather interesting alternative of random sampling. There are two methods of effecting the checking: A. Provide for two discrimination circuits following the linear amplifier in each sense amplifier; the dis- criminator with the lower threshold would be the one which supplies the information contents of its bit of a selected word, while the discriminator with the some- what higher threshold would monitor the energy level of the same bit. The exclusive-or of these outputs would be "ored" with the exclusive-ors of the other bits of the selected word; if the result were a one, it would indicate a need for regeneration (this circuitry would also allow the use of a scheme which would check only during normal interrogations). B. Provide a "model" noninformation bit in each word which would be made a "one" every time the word was written into, and would suffer all the effects of interrogation and quiescent drain depletion, but would either have a lower energy capacity or an additional quiescent drain so that it would be guaranteed to lose energy at a rate greater than any other bit in its word. Checking would then be confined to this bit only. 30 CHAPTER III Footnotes 1. S. Uno Falk, "Investigations on the Reaction Mechanism of the Nickel Cadmium Cell," Jour. Electrochem. Soc , Vol. IO7 No. 8 (196O), p. GGG. 2. H. Jermain Creighton, Principles of Electrochemistry (New York: John Wiley and Sons, Inc., 19^?)/ P- 1^5- 3. Christie George Enke, The Formation and Dissolution of Surface Oxides on Platinum (University of Illinois: Ph.D. Thesis, 1959), p. 76. h. Rajchman, p. II8. 5. Ferranti Ltd., List DC. kG (Bradford, England: Limd. Humphries, I962), p. 1+. 51 IV. CELL CHOICE k.l Introduction Of the thousands of possible electrochemical cells, only a very- few exhibit properties desirable from the point of view of the memory- designer. It is therefore necessary to sort out the desirable and undesirable properties and pick those cells which have most of the former and least of the latter. k.2 Idealized Properties it. 2.1 General The general properties which an ideal cell would possess are as follows : (1) self-limiting energy capacity, (2) ability to be placed in a sealed con-tainer, (3) infinite life, (k) ability to be charged and discharged at arbitrarily great rates (i.e., fast charge and discharge), (5) no volatility (absence of a self -discharging mechanism), (6) small size, (7) absence of a recovery property. In addition to these general properties, individual reading methods foster preference for other properties. if. 2. 2 For Polarity Discrimination Reading (8) symmetry (9) large voltage 32 k.2,^ For Magnitude Discrimination Reading (10) large voltage variation as a function of charge k-.2.k For Resistance Discrimination Reading (11) large resistance variation as a function of charge k.2.'^ For Capacitance Discrimination Reading (12) large capacitance variation as a function of charge. k.J) Compromisable Properties In a practical system, some of the above properties can he dispensed with, and most of them can he compromised somewhat. The above properties will be considered in order: (1) Self -limiting energy capacity is a desirable property because, if the cell's state is to be changed, the amount of energy necessary to change it in the worst case must be known. Since it is convenient to be able to guarantee a certain state after writing without having to know the state of the element before writing, either the above property must exist, or an external limiting device must be used, otherwise successive writings of the same state may make it very difficult to write the opposite state. (2) The ability to be placed in a sealed container is important in a practical system. If unsealed containers were used, the electrolyte would tend to evaporate, and replenishment would become a nearly insurmountable difficulty in a large scale memory. 35 (3) Infinite life, though a desirable property, is not a necessary one. It is sufficient for the life of the element to be long compared with the expected life-span of the computer employing it. (k) The ability to be charged and discharged at arbitrarily great rates is desirable, but, so long as the allowable rates are great enough for the speed desired, it is sufficient. (5) The property of no volatility is very desirable. However, if the volatility is such that the energy change is small during the time the element is expected to retain its information, it is sufficient. (Volatility in a system will be very dependent on the circuitry of the selection scheme. ) Reasonable volatility can be tolerated if a periodic regeneration scheme such as that used with William's tube memories is employed. (6) Small size is an absolute, uncompromisable must in any large-scale memory. (7) The absence of a recovery property is very desirable, because recovery can cause information loss. (8) Perfect symmetry is not necessary. (9), (10), (11), (12) The adjective "large" may be replaced with "large enough to be electronically sensed without noise difficulties." i<-.U Realizable Properties Fortunately, every property listed above is to some degree realizable. if. 5 Cell Comparison It is perhaps not too surprising that a survey of possible reversible-reaction cells soon leads to the conclusion that probably the only cells approaching suitability for use as chemistors are the three most well known secondary cells, (1) the lead-acid cell, (2) the nickel-iron alkaline cell, (3) the nickel-cadmium alkaline cell. This result becomes even less surprising when it is noted that most of the ideal chemistor properties which have been postulated are also regarded as highly desirable properties for commercial batteries. The properties, the possession of which rendered most of the other considered cells unsuitable, are: (1) a self-destruction mechanism, (2) inadequate energy density. Cells whose reactions include the dissolution and subsequent replating of metal electrodes generally display a self-destruction mechanism because the replated metal rarely is as dense as the original electrode material, so that the shape of the electrode changes over a number of charge-discharge cycles, not only altering the properties of the cell, but eventually shorting it with metallic whiskers which tend to grow out from the electrode. Of the three cells mentioned above, one stands head and shoulders above the others, but this will be shown by means of a comparison. 35 if. 5-1 The Lead-Acid Cell The lead-acid cell was discovered in l859 ^Y Plante. It has beyond question commanded more scientific attention over the years than any other secondary cell. The exhaustively confirmed double -sulphate theory gives for the reaction equation PbOg + Pb + 2H2S0j^^ 2FbS0^ + 2H2O, where the reaction goes from left to right for discharge, and from right to 2 left for charge. Although special cells can be made which have relatively little self -discharge (l5^ per year), such cells have extremely low cycle life. A more typical self -discharge rate would be about ^0% per month. Repeated overcharge or overdischarge will utterly ruin a cell, as will long unattended storage (excepting so called dry charge batteries when left dry). Batteries may be charged at quite high rates, but some damage is done due to heating and excessive gassing. It is impossible to seal cells because they evolve copious quantities of gas during charge and discharge. The open circuit e.m.f. of a cell is given approximately by E = 1.85 + 0.917 (G - 1) volts where G is the specific gravity of the electrolyte. It is also a function of temperature. The cell is ruined by temperatures as high as I50 F. k.^.2 The Nickel-Iron Cell The nickel- iron or Edison cell was invented by Edison in I908. It is a cell superior in a number of respects to the lead-acid cell. 36 Only the general character of the reactions which take place in 7 this cell is known. At least five different equations have been proposed, one of the more popular of which being 2Ni(0H)^ + Fe zz± 2Ni(0H)^ + Fe(OH)^, where left to right is discharge, and right to left is charge. The electro- lyte, potassuim hydroxide plus a small quantity of lithium hydroxide, acts as a conveyer-belt for oxygen, carrying it from one electrode to the other, so that the cell is essentially independent of the electrolyte (unlike the lead-acid cell) . Gassing takes place during charging and discharging as is true of the lead-acid cell. The cell may not be sealed because of this gassing. Repeated overcharge and overdischarge do not harm this cell, and it may be stored for very long periods without damage . The self -discharging properties of this cell are comparable with that of the lead-acid battery i.e., it cannot hold a charge more than a few weeks. Its open-circuit voltage is 1.^+8 volts immediately after charging, but it drops to 1.55 volts after standing. Its terminal voltage collapses under sudden heavy-current load. The cell is damaged by temperatures as high as I50 F. i4-.5.5 The Nickel-Cadmium Cell o The nickel-cadmium cell was invented by Jungner in about I9OO. It has been manufactured in Europe since that time, but not in the United States until 19^6.^ This cell is very similar to the nickel- iron cell in that it uses the same electrolyte (performing the same oxygen conveying task) and one of the same electrodes. Even less is known of the actual reactions of this 37 cell than of the nickel- iron cell. More than ten equations have been proposed, one of the more popular being 2Ni(0H), • 5H^0 + Cd f* 2Ni(0H)^ • 6E = G C (x> + 1. s s s '" R is known as the polarization resistance, C as the s s pseudocapacity, and co = 2Jtf . k9 When the reaction is very fast, tends toward zero, and R C =i S S CO and, in fact s ^72 ' ^s ^72 03 ' Oi ' Class III This class of substances contributes an impedance given by a parallel RC circuit with component values E "I = J/G C I" - 1/j where J is a constant G is the product of the reaction rate constant for the combination reaction and the steady state concentration of the initial product. Class IV This class of substances contributes an impedance given by a parallel RC circuit with component values IV ^1 R •^ voo + _ IV ^1 ^ = n /p where k, r, , and c are constants, ^ CD ' ^ ^ Class V This class of substances contributes an impedance given by a series RC circuit with ccxnponent values 50 R = ^4^ / k„ + 2. ' ""^l ' ^ .(a^ . l)(Va^ . 1 ■ a) ' 1 \ C CO ' s 2 ^V 2(a2 + 1) 1/2' k where a = — and k's are constants. CO Class VI This class of substances contributes an impedance consisting of a capacitor with value 1 cW —^ = •^ , a constant with respect to frequency, where E is the potential across the entire double layer exclusive of any IR drop that may occur if the layer is very thick, and y is the substance concentration at the interface. The solution resistance is a function of the concentration of the electrolyte, in general decreasing as the concentration increases. The specific resistance of a solution is defined as the resistance measured between opposite faces of a cube of the solution one centimeter on a side. The equivalent resistance is defined as the resistance measured between two electrodes one centimeter apart, with area sufficient to contain one gram-equivalent of solute. When the concentration of a solution decreases, the specific resistance increases, while the equivalent resistance decreases (slightly). The first mentioned phenomenon is explainable by consideration of the fact that the conductance depends upon the number of ions present and must decrease as the number of ions is diminished. The second mentioned phenomenon is 51 explainable as the result of a diminishing of the electrostatic forces retarding complete independence of ion movement when the same amount of k solute is placed in a larger voliome. Kohlrausch's law of the independent migration of ions relates the conductivity of a solution with the mobilities of the individual ions. This relation may be written as A = ) n. |j. jq f mho/ cm. th P where [i. is the mobility of the i ion type in cm /volt sec. n. is the density of the i ion type in ions/cc. q. is the charge on an ion of the i type in coulombs. The double^layer capacitance Cdl is a consequence of the existence of an electrical double layer thought to exist at every interface. The double-layer is an array of charged particles and oriented dipoles which "... may consist of a layer of electrons..., a layer of adsorbed ions, and a diffuse double-layer consisting of an ionic atmosphere in which ions of one sign are in excess of their normal concentration, whereas those of the other sign are in defect." This capacitance is dependent upon applied voltage, and, for oxide 7 layers, exhibits a remarkable hysteretic effect. A distinction must be made between the latter two components and those previously discussed. The double-layer capacity and the solution resistance are essentially independent of the nature of an applied periodic forcing function (so long as its amplitude is not too great and its frequency is not too low) and of the electrochemical reaction which takes place as a result of the forcing function. The other components mentioned, however, UNIVERSITY Of ILUNOIS LIBRARY 52 are vitally concerned with the electrochemical reaction, and therefore with the nature of the forcing function; these components are given the name "faradaic iramittances" to distinguish them from the others. The assumptions made in the derivations of the faradaic immit- tances are of importance, as they place limitations on the utility of the results. They are that the electrodes are smooth and homogeneous, and that the current density at the electrodes is unifonn. To complete the equivalent circuit, a voltage source whose voltage is, in general, a function of the state of charge of the electrode, must "be added in parallel with Cdl. 6.3 Specific Equivalent Circuit In Chapter IV, the nickel- cadmium cell was chosen to be used as a chemistor, and the details of the construction of the commercially available cell were described. These details, and the nature of the reaction mechanisms, must be considered in arriving at the specific equivalent circuit. The assumptions made in the derivations of the faradaic impedances are all violated by the construction details of the cell. The porous nature of the electrodes, by definition, violates the assumption of smoothness, and by the same token, current density cannot be uniform over the entire active areas of the electrodes; the nonuniform current density, in turn, will cause different portions of the active areas of the electrodes to differ in character at any time, so that the assumption of homogeneity is violated. Thus it would seem that an attempt to apply the faradaic impedances would be futile. However, considered "in the small" the assiomptions are not violated severely, so that it might be expected that the macroscopic violations would merely act as "noise," and cloud somewhat the results, while not obliterating them. 55 The substance types will be considered in turn. Type I: Though the reaction equations proposed by some investigators appear to indicate that the nicad cell belongs in category lb (because, though the electrolyte enters into the reaction, o its concentration does not change) , others have shown that the concentration does change, so that the nicad cell does not belong to Type I. Type II: The statement made above concerning the change in concentra- tion would appear to place the nicad cell in this category but, according to Grahame, the Warburg (Type II) Impedance will not be observable in alkaline aqueous solutions, which woTild obviate the potassium hydroxide and water electrolyte of the nicad cell (actually, the Warburg Impedance is absent chiefly because the concentration of electrolyte changes so little) . Type III: A nicad cell might fall into this category in the latter stages of charging when atomic oxygen is evolved, if it combined with itself to form molecular oxygen; however, though the atomic oxygen does become molecular oxygen, the reaction is more complicated than simple self -combination, so Type III does not apply. Type IV: This category might apply when the evolved oxygen combines with the already reduced portion of the cathodic material. Type V: This category does not apply to the nicad cell. Type VI: The small quantity of lithium hydroxide which is added to the electrolyte would cause this category to apply to the nicad cell. 5^ Thus, the only two types which are not eliminated for the nicad cell are Types IV and VI (the solution resistance and double-layer capacitance are present in all cells) . It should be noted that the faradaic portion of the equivalent circuit impedance will not apply over the entire frequency spectrum. When the implicit assumption that the reaction rate is greater than the rate of change of the forcing function is violated, a relaxation phenomenon may be expected, and distortion will be observed over a range where the rates are nearly equal. When the frequency of the applied voltage or current is very great, the faradaic impedances will be unobservable. It should also be noted that, since both of the electrodes of a nickel-cadmium cell are capable of polarization, the total equivalent circuit comprises the series combination of two circuits such as the one discussed, but with differing parameters. As may have been noticed, the impedances just considered assimie a sinusoidal forcing function and steady-state conditions, and some are not immediately applicable to other waveforms. A variety of techniques exist for finding the complex frequency behavior of functions of co from either their real or imaginary parts and, indeed, simple analytic continuation will yield the forthcoming result. It is more enlightening to notice, however, that the Warburg Impedance is of the same form as the input impedance of an infinitely long transmission line with distributed series resistance and shunt capacitance only. This result is a consequence of the identity of form of the partial differential equations governing the two systems: o ^G (x,t) ^ ^ a^G (x,t) ^t hx^ where, for the transmission line. 55 G = V, A = RC and, for the electrochemical cell, G = concentration, A = diffusion coefficient . 12 For the latter case, the equation is a statement of Fick's first law. Employing the expression for the input impedance of an infinite transmission line, I — 15 _ |5 vhere Z is the series in V Y impedance per unit length, and Y is the shunt admit- tance per unit length. The aperiodic form of the Warburg Impedance becomes ZL^ = J-p where s = o + jco, s The experimentally observed behavior of the faradaic impedances is displayed and discussed in Section S.T- Though it is certainly possible to consider the e.m.f.'s produced by the individual electrode voltage sources, it is more convenient to consider their sum which is measurable at the cell's terminals (see Section 6 .k) . 6.h Approximate Equivalent Circuit Although the impedances discussed above were considered with an eye toward utility as well as completeness, experimental results indicate that for most practical purposes (including use as a chemistor) , a much simpler equivalent circuit suffices for the nickel-cadmium cell. This 56 clrciiit consists of the solution resistance in series with a voltage source whose e.m.f. is given by E = u(q.)(a q + I.IO) volts (see Section 8.6.4) where q. is the stored charge in coulombs, a is a constant inversely proportional to the energy capacity of a cell, and u(q) is the unit step function. It should be remarked that a voltage source whose e.m.f. is relatively insensitive to charge appears to be an immense charged capacitor in the same sense that a short circuit appears to be an infinite uncharged capacitor. 4o The solution resistance at full charge is given approximately by R = -rr ohms, where K is the cell's energy capacity in mah. (see Section 4-6), and increases by about a factor of two at total discharge (see Section 8.6.4) . Though it was observed that very low open circuit voltages could be obtained by prolonged discharge, there is a marked tendency to drift toward an upper limit of 1.10 volts. Fortunately, however, it is possible to prevent the discharged voltage from creeping above any desired value without much difficulty (see Section 8.1l). Justification for the choice of components in the approximate equivalent circuit follows: A. The actual faradaic impedances are shown by experiment (see Section 8.7) to be 1. low order effects, 2. low frequency effects, 3. in poor agreement with theoretical impedances. They would have little or no effect during charging (constant current) or reading (high frequency) and none at all in the 57 quiescent state. Thus, since their effects are negligible, and in fact, no satisfactory equivalent circuit for them exists, they do not appear in the approximate equivalent circuit for a nicad cell (this may not apply to other cells) . B. The double -layer capacitance exists and is quite large; however, the voltage source which it shunts acts like a huge capacitor, so that the effects of Cdl are negligible by comparison (and, in fact, are impossible to distinguish) and can therefore be deleted from the approximate equivalent circuit . C. The solution resistance is of importance chiefly for dissipation considerations and is therefore not deleted. D. The voltage soixrce is of great importance and therefore remains . The range of applicability of the approximate equivalent circuit must, be discussed. It may be used without reservation (other than minor inaccuracies) for 1. D.C. discharge at any current, 2. current or voltage pulses (or steps) of arbitrarily fast rise time and arbitrary duration. It may be used for charging at any current with the following reservation: energy considerations are more complicated than is implied by the circuit; for currents much above 2 ma, gross inaccioracies in energy storage calcula- tions will result from use of the equivalent circuit; the relations evolved in Sections 8.3 and 8.^ must be used for accurate calculations. 58 CHAPTER VI Footnotes 1. David C. Grahame, "Mathematical Theory of the Faradaic Admittance/' Jour. Electrochem. Soc . , Vol. 99 No. 12 (December 1952), pp. 370C- 385c. 7 8 9 10 11 12 13 Ibid ., p. 87. Creighton, pp. 67-68. Ibid ., p. 87. Herbert S. Harned and Benton B. Owen, The Physical Chemistry of Electrolytic Solutions (New York: Reinhold Publishing Co., 19^3) • David C. Grahame, "The Electrical Double Layer and the Theory of Electrocapillarity," Chem. Revs ., ^1 (19^7), pp. UJ+2-UU3. Enke, pp. 7^-80. Salkind, p. 6. Grahame , Jour. Electrochem. Soc . , p . 382C . Ernst a Guillemin, Synthesis of Passive Networks (New York: John Wiley and Sons, Inc., 1957)^ p. 279ff- G. C. Barker and I. L. Jenkins, "Square -Wave Polarography, " Analyst , 77 (1952), p. 686. Paul Delahay, New Instrumental Methods in Electrochemistry (New York: Interscience Publishers, Inc., 195^)^ P* ^8. W. L. Ever it t and G. E. Anner, Communication Engineering (New York: McGraw-Hill Book Co., Inc., 1956), p. 50^. 59 VTI. CIRCUITRY 7.1 Introduction In order to test the feasibility of the chemory proposed in Chapter III, it is necessary to synthesize some hardware circuitry. The system which was "built consists of two words of two bits each. The chemory cycles automatically, but has provision for several manual alterations of the cycle. The control of the memory is a four bit counter driven by a square wave generator which is controlled by an audio oscillator. The counter feeds a minute amount of logic circuitry which, in turn, feeds the write and read drivers . 7.2 Counter The functions of the counter stages (numbered in order of decreasing frequency) are Stage 1 Stage 2 Stage 3 Stage k address register (word or l) function register (read or write) write information for bit write information for bit 1. The circuit for the i counter stage is shown in Figure 3' 7.3 Logic The logic necessary to decode the counter information is very slight. A simple time-sequence logic diagram is shown in Figure h. 60 +25 V TO i+iS* STAGE 390/i/if: 9.1k > rtl 390^/tf T 470^/if FROM i-is* STAGE. FIGURE 3: t^^ STAGE OF THE COUNTER. 61 oJTloJTloJTloJTloITlojTlolTlol^ a: stage 1 w nn w m w mw mw b stage 2 c; STAGE 3 d; STAGE 4 "L _J n J L a «» b ^- FOR WORD WRITE J^ "U" U n r~ fl.h U L a-bl avbj FOR WORD 1 WRITE bvc b-c - FOR BIT (WRITE) FOR BIT 1 (WRITE) b-d a • b FOR WORD READ a • b FOR WORD 1 READ FIGURE 4: TIME- SEQUENCE LOGIC 62 In Figure 5 is shown the application of the logic to the boxes shown in Figure 1; to understand this diagram, it is necessary to know that the write drivers are inverting. The actual logic elements used were of the simple diode-resistor type. 7.^1- Bit Write Driver The purpose of this circuit is to provide a current source for writing one chemistor state, and a current sink for writing the other. The circuit is designed to cause only one of the auxiliary diodes to become forward biased at a time when fed by the proper logic circuitiy. The circuitry is shown in Figure 6. 7.5 Word Write Driver The purpose of this circuit is to provide a low impedance source- sink for current during writing. The strategy used is to forward bias both of each bit's diode-pairs; see Figure "J. "J. 6 Read Circuitry Two circuits are necessary to effect reading, a read driver and an amplifier. One half of the word write driver can be used for a read driver, causing only one diode of each chemistor 's pair to be forward biased, pro- ducing (depending upon the reading scheme) either a known increment in the voltage, or a known magnitude of voltage at one of the terminals of each chemistor in the selected word. '^ The read amplifiers will vary in character depending upon the reading scheme. They will, however, have certain features in common: a single 65 ADDRESS WORD I FUNCTION WRITE/READ b INFORMATION BIT BIT 1 Si i^ bb b L FIGURE 5: LOGIC. o 6k > lO CM O CVJ CVJ > in CO O CM CM 00 O CM r +' > CM + -nA— |f' ro CM CM DC O O OC UJ £ o UJ t IT ffi Ul o: O o > 65 a: q: > o UJ cc o q: o UJ a: S2 > 66 linear amplifier stage followed by a strobe circuit to block spurious signals, followed by a switching amplifier. 7.6.1 Magnitude Discrimination For magnitude sensing, the discrimination is performed by a dif- ference amplifier which compares the amplified algebraic sum of the selected chemistor's voltage and the voltage guaranteed by the read driver with a voltage determined by a potentiometer. The amplifier and strobe circuit are shown in Figure 8. 7-6.2 Other Discrimination Methods At the end of Chapter IV, it is shown that, for the kind and size cell chosen for experimental purposes, magnitude discrimination is the only practical sensing scheme. Circuit modifications necessary for the other methods will be briefly outlined: A. The amplifier circuit of Figure 8 may be used without modifi- cation for polarity discrimination. B. It would be necessary to add a capacitor between the base of the input transistor of the amplifier circuit and ground to form a capacitive voltage divider for capacitance discrimination . C. Adding a resistor in place of the capacitor in B would form a resistive voltage divider for resistance discrimination. 7.7 Comments The use of only positive voltage sources was a matter of convenience and would not be recommended for a large scale system. No claim other than adequacy is made for the circuits used. INPUT »■ tl5v Ik + I5v A <) 6F450II i220 ^7.5k QF450II (2) it S577G +I5v A >5I0 GF450I1 STFK)BE o 5 6? +I5v i / 6E342 I 250 FIGURE 8: AMPLIFIER AND STROBE CIRCUIT FOR MAGNITUDE DISCRIMINATION READING. 68 The chief aim of the amplifier design was to prove the sufficiency of a single unsophisticated stage of amplification for sensing purposes (see Section 8.IO) . 69 VIII. EXPERIMENTA.L RESULTS 8.1 Introduction A number of experiments of differing aims were performed, some to test the feasibility of an entire system, some to learn the character- istics of a single component. The presentation will be in rough chronological order . 8.2 Common Electrolyte Experiment 8.2.1 Purpose As originally conceived, the chemory was to consist of a tank of electrolyte containing many equally spaced wires lying in one plane, with wires orthogonal to these lying in a very close parallel plane. The chemistors would be "proximity elements" formed by portions of the wires near their crosspoints. The hoped-for advantages of such a scheme were: 1. The common electrolyte could be replenished and kept at constant temperature and concentration by a recirculating device. 2. Evolution of gas would not constitute a problem as it would for sealed cells because the gas could be drawn off, and tenacious bubbles could be removed by fluid motion or even by cavitation induced by the constant application of ultra- sonic power. 3. The chemory contents could be rendered permanent during power shut-down by draining the electrolyte before removing power . 70 k. The comparative initial cost would certainly be low, though maintenance might be costly. Since there was some question about the possibility of creating proximity elements and the degree of independence they might enjoy if they could be created, an experiment was performed to shed light upon it. 8.2.2 Procedure A cylindrical cell was fashioned of rubber (so that puncture holes made by skewering it with wires would be self -sealing) 1 cm. in diameter, and 2 cm. high. Two parallel wires were placed about l/2 cm. apart in a horizontal plane, a single horizontal wire was placed about l/lO cm. beneath them and orthogonal to them. The wires were Sn coated brass, B and S gauge 21. The electrolyte was a saturated aqueous solution of NaCl. An attempt was made to form two proximity cells at the inter- sections of the wires by applying + 1.2v. to the top two wires relative to the bottom wire. 8.2.3 Results Proximity cells of like and opposite polarity were successfully formed and made to coexist. However, the open-circuit-potential-decay time- constant for opposite polarity was much greater than for like polarity, and continued charging of one cell eventually changed the polarity of the other cell to its own. 8.2.J+ Conclusions A common electrolyte chemory is probably unfeasible because of the unwanted conducting paths provided by the surrounding electrolyte. Certain 71 aspects of such a system are so attractive, however, that further study may be warranted. 8.3 Charge Rate Test 8.5'1 Purpose The currents envisaged for writing into a chemory are of the order of half an ampere. This is some 25O times the current rating of the CD-I cell, so it behooves the entire project to ascertain whether the cell will tolerate currents of this magnitude, and what current (if any) would be optimism for charging. Using 250 times rated current might seem foolhardy, 125 but nickel-cadmium cells are noted for their stultifying ruggedness. ' ' The main difficulty expected woiild be the possibility of gas evolution at a rate greater than could be coped with by the cell's mechanism, inevitably causing rupture of the cell container. 8.3-2 Procedure A cell was charged at a specified rate for a specified time, then discharged through a standard resistor (5OO ohms) until the voltage slumped. The specified rate was, of course, changed each time, and the specified time was chosen as that time in which the specified current would bring the cell to its fully charged state if current efficiency were 100^. Thus for I in ma . , ^ ^ 20 X 60 1200 t chg. = = = — rr — min. 8.3.3 Results The data was digested in the following manner: the ratio of the discharge time for a fully charged cell to the discharge time for a specified charging time was multiplied by that charging time, yielding the time necessary 72 to charge a cell fully at the rate corresponding to the specified charging time (see Table l), assuming current efficiency constant for a specified current . The times necessary for full charging as a function of charging rate are displayed in Figure 9 iri a log -log plot. Catastrophic failure occurred at 560 ma. 8.3-^ Conclusions Figure 9 reveals that the logarithm of full charging time versus the logarithm of charging current approximately obeys a linear relationship. Thus, log T^ = k^ log I + log k^ ^1 or T^ = kg I . For I in ma . , these constants are k^ = -0.678 ~ -2/3 k = 850 min. ma.^/^ . The accuracy of the linear approximation is attested to by the results of extrapolating to 2 ma . , where the corresponding ordinate is found to be 602 min., or 10 hours and 2 minutes, very close to the rated time. Except for the attendant rise in temperature, for constant current the rate of energy storage is independent of the power dissipated in the cell resistance. Thus, P. = P^ + P = I^R + IE in d s assuming E and R constant. The question arises then: why is the observed full charging time so much in excess of the theoretical 100^ efficiency time 75 Table 1 Results of Charge Rate Test Charge Rate (ma . ) Charge Time Full Charge Discharge Rate (ohms) 500 Discharge Time ^ of Full Charge 100 Full Charge Time -- 8;58 — 20 1:00 500 i^:55 52.7 ]:5i<- ko 0:50 500 5:17 kk.k 1:08 80 0;15 500 2:17 52,8 0:i^5.8 120 0:10 500 2:05 25.8 0:14-2.0 i6o 0:07.5 500 1:55 21.9 0:514-. 2 200 0:06 5Q0 1:50 17.4 0:5^.5 21+0 0:05 500 1:55 22.2 0:22.5 280 0:04.29 500 2:09 2U.8 0:17.5 520 0:05.75 500 1:5U 22.0 0:17.05 360 0:05.55 500 1:51 21. i^ 0:15.60 llOO 0:05.00 500 l:i^2 19.7 0:15.25 i^i^ 0:02.75 500 1:^7 20.8 0:15.10 k&O 0:02.50 500 1:55 18. i+ 0:15.60 520 0:02.51 500 1:21 15.6 0:14. 80 560 0:02. U 500 Catastrophic i^ilure 7^ 9 8 7 6 K A 3 2.5 2 1.5 KMINJ 102 _ \ , N K 9 8 7 ft N N, X Sc 41 » Ss s. 5 4 v \ '"^ K s • 3 2.5 2 1.5 10 • i ► "X S s. • k __ L. % '^ N N K ' 5 2 . 2 Si 4 ^ t » < » 7 ' C )S 'i! 02 '• 9 2 t 2 .8 2 i A \ S > c i 7 ' c \ i V Kma) FIGURE 9: FULL CHARGING TIME vs. CURRENT 75 if the resistive losses do not influence this efficiency? The answer is that a mechanism other than resistive losses is lowering the efficiency. The most likely side-reaction mechanism is the evolution of oxygen. The equilibrium potential for O^/H is given hy E = 1.229 - 0.059 PH + O.Oli^S log pCOg) volts, where p(0„) is the oxygen pressure in atmospheres. Since any alkaline aqueous solution must have a pH greater than 7, for p(0 ) = 1 atm., E < 1.229 - 0.14-13 = 0.816 volts. Thus, for a solution-electrode interface potential at least as anodic as the above value, oxygen may be evolved. If the current -efficiency were 100^, the charge time would be given by T = "Y^ where k = 1200 ma. min. It is of interest to know the dependence upon current of the ratio between actual full-charge time and the time for 100^ efficiency: -2/3 '^0" k T-1 ~S . _850 1/3 ^^ ,1/3 1200 ' It now becomes possible to find the relation between current efficiency and charging current : W_ EI T^ -, , W. EI T_ 7173 • xn f I ' 76 In turn, the loss ratio may be calculated: L = 1 - Eff . = 1 - ^ = -^575- . Since it is important to know whether the cell failure was the result of light construction (the seal failed), the force causing the failure will be calculated. The assumptions will be made that the rate of gas evolution is so great that catalytic recombination is negligible by com- parison, and that oxygen behaves like an ideal gas. Then the energy employed in evolving oxygen was w = L Wq = f^ — i/r^ ) ^^'^ = ^^'^ j°^^^^ and Q = — = ., 'i, - 59' 8 coulombs. E 1.2 The electrochemical equivalent for oxygen is O.298 gms. /ampere hour or — ^'^^ = 8.28 X 10"^ gms. /coulomb, 3.6 X 10^ -5 -3 therefore 8.28 x 10 x 59-8 = ^-95 x 10 gms. of oxygen were produced. Now employing the equation of state for an ideal gas, nRT ^ p = — rr- where p = pressure m atm. n = no. of gm. moles T = temp, m K V = vol. in liters 6 R = 0.082 lit. atm. /mole K° ^•9^,; ^Q"^ X 0.082 X 300 p = ^^—^ — = 6.1 atm. it(0.59) X 0.572 X 10 ^ 77 According to Dalton's Law of Partial Pressures, the pressure inside the cell will now be 7-1 atm., taking into account the air originally in the cell. The net pressure exerted against the cell walls will therefore be 6.1 atm. The force on the cell end will be F = pA = 6.1 X 1.01 X 10 X Jt X (0.59)^ = 6.73 X 10 dynes = ^^11^^ = 15.1 lbs. k.h"^ X 10-^ Since this is a rather moderate value, it is reasonable to conclude that a more sturdy mode of construction (e.g., epoxy resin instead of rubber sealing) would allow greater currents. The average resistive dissipation taking place in the cell for R = ^'75 ohms (see Section 8.6. ij-) is av. W^ = I^R = (0.52)^ X i4-.75 = 1.28 watts d av. V " / at the maximum safe current value measured, therefore adequate provision for cooling would be necessary in a large-scale system. It should be remarked that dissipation could be the most fundamental limitation upon the allowable write current, for if the limit of one watt is arbitrarily placed upon the chemistor resistive dissipation, I R < 1 but R = -TT ohms, K in mah. (see Chapter IV) — Jl .-. ! this becomes 79 -2/5 T = 572 I' ' ^ min, Two values of charging current were used for each of 4 cells of capacities 50, I50, 225, and h^O mah. The values of full charge time yielded were compared with the values predicted by the above expression. 8.^4-. 3 Results The results are displayed in Table 2. 8.4.4 Conclusions The generalized expression for full charge time as a function of charging current yields good results over a range of capacities from 20 to 450 mah. There is a strong indication, therefore, that similar results may be expected over a range from 20 to O.89 mah, and order of magnitude or better accuracy for further extensions. It now becomes possible to calculate the minim\jm write time for a given energy capacity assuming dissipation as the limitation. From 8. 3 -4, ^<'[¥o^"'- Substituting into the generalized expression for T , T^ > 572 This result indicates that the write time diminishes slowly as K is reduced. Thus, dissipation should not be allowed to be limiting at a high value of T^. Fortunately, it can be removed from consideration by the Table 2 Results of Charge Rate Tests on Several Cell Sizes 80 Cell Capacity (mah) Discharge R (ohms) A 50 200 B 150 68 C 225 h3 D k^O 22 Charge Rate (ma) I' Charge Time Discharge Time ^ of Full Charge ; Exp. Calc. Diff. Cell A - - Full Chg. 7:28 100 - - - 50 10 1:00 3:13 h3-l 2:19 2:03 11.5 150 30 0:20 2:lif 27.7 1:12 0:59.2 17.8 Cell _B - - Full Chg. 8:08 100 - - - 75 5 2:00 5:07 63.0 3:10 3:16 3.2 300 20 0:30 3:37 hk.-^ 1:07.5 1:17.6 15.0 Cell _C - - Full Chg. 9:06 100 - - - 150 6.67 1:30 4:13 i+6.5 3:li^ 2:i^2 16.5 i400 17.8 0:33-5 2:1^0 29.3 l:5i^ l:2i^.2 26.2 Cell _D ' - Full Chg. 9:15 100 - - - 150 3-33 3:00 i^:57 53.5 5:36 4:16.3 23.7 1000 22.2 0:27 3:i^3 i40.2 1:07.2 1:12.5 7.5 81 expedient of providing sufficient cooling (this is probably always possible, though not necessarily easy). 8.5 Life Test I 8.5'1 Purpose As mentioned in Chapter IV, a carefully constructed cell should have an unlimited life. It is of interest, however, for economic reasons, to know how closely a commercially available cell approaches the ideal (manufacturers are unwilling to make any but vague statements concerning life). Life Test I investigates this aspect. The term "life" as used here is in no way related to the same term used with reference to primary cells, but refers to the number of charge-discharge cycles to which a cell may be subjected before its character- istics become so altered as to render the cell no longer useful. To avoid confusion, the term "cycle-life" will be used. 8.5-2 Procedure Since it would take nearly three years to cycle a cell a thousand times at rated current, a subterfuge was resorted to in order to accelerate the cycling. The current used was a 20 ma. peak-to-peak square wave provided by a pair of emitter followers driven by a multivibrator at a frequency of 1 cps., and the quiescent state of charge was allowed to drift from full charge to no charge and back at the rate of about one excursion every four hours . The reasoning employed is as follows: if for any quiescent state of charge, there corresponds a portion of the active material such that, if a small perturbation is impressed upon the quiescent state, only this portion will be affected, then the cycle-life of this portion will be no greater for 82 a number of shallow cycles centered around this quiescent point than for an equal number of deep cycles. Since chemical states are by nature discrete (a continuum of states cannot exist), then adjacent states must coexist in the active material except at the end -points, otherwise all of the material would have to change state at once, causing instantaneous changes in the state of charge, an as yet unobserved phenomenon. For any state of charge then, which exists during charge or discharge, the next molecule to change state, while not necessarily always the same one, is one of an exclusive group of limited size determined chiefly by the cell's geometry. It is, therefore, a matter of indifference to this molecule whether it is induced to change its state by a small localized influence, or a large general one. The criterion used to determine how much the cell had changed was the energy storage capability of the cell. This was determined by charging the cell for more than the rated time at the rated current, and then dis- charging the cell through a standard resistor (500 ohms). A pen recording voltmeter was used, so that a simple comparison of discharge time to voltage slump before and after the life test was tantamount to comparing the energy stored. 8.5.3 Results After subjecting the cell to 2.1 million shallow cycles, the energy storage capacity dropped by about 5^' 8.5.^ Conclusions It is necessary to convert the number of shallow cycles to an equivalent number of deep cycles. A number of symbols will be defined: R = rate of traverse of the quiescent point in ma. w = peak-to-peak width of a perturbation cycle in mclmbs. t = -x2f R = W X 2F, N F n ~ f ' 85 W - charge capacity of CD-I cell in mclmbs. f = perturbation frequency in cps. F = frequency of quiescent point shift in cps. t = number of transitions experienced by a vanishingly small portion of the active material for a single quiescent state traverse T = total number of transitions n = number of perturbation cycles N = number of quiescent state cycles. it- wfN and T = t X 2N = Zf K U-wfN w f but R = W X 2F. . . T = |j^ = 2 ^ X - X N and t..^, .♦. T=fxn= 2_x_20 ^ 2.1 x 10^ 20 X 3.6 X 10^ - 1168 transitions. This is twice the number of equivalent deep cycles . It is clear, then, that while the CD-I cell does not have infinite cycle-life, its vitality wanes slowly when small currents are used. 8.6 Life Test II 8.6.1 Purpose No matter how carefully a cell may be constructed, there is surely some current which will cause cell failure. What is of interest from the point of view of use as a chemistor is the effect upon cycle-life of currents which, though abusive, do not cause immediate failure. 8.6.2 Procedure The CD-I cell (as well as most other commonly made sealed nickel- cadmium cells) possesses an Achilles heel: if the voltage across the cell 81+ is made negative by prolonged force -discharging, hydrogen gas is evolved. If this condition is left unchecked, the cell will be ruptured. Fortunately, there are two elegant solutions to this problem which will be discussed in Chapter X. However, a stop-gap measure is necessary to allow the use of the available CD-I cell. To this end, a diode was used in parallel with the series combination of the cell and a 1.1 ohm resistor, anode to cathode. A i+OO ma. peak-to-peak square wave current with a period of 12 min. was applied. To obtain this long period, a relay was controlled by an RC circuit adjusted so that there was a 30 sec. delay between brief relay closures; a relay closure triggered a twelve position motorized switch. When the contact of the twelfth position was closed, it triggered another twelve position motorized switch wired to behave like a two position switch. Thus, a contact was made to alternate between two switch positions every six minutes . The behavior of the cell voltage was recorded on a pen recording voltmeter . As before, the charge storage ability of the cell was determined before and after the test. 8.6.3 Results The cell was subjected to 127 full cycles. The most negative voltage across the cell was -O.k^ volt, and the voltage across the cell jiaaped 2.k- volts when the current direction was changed from discharge to charge, while it changed by l.U volts when the opposite current change took place. After the test, the cell capacity dropped to 91-^^ of its pretest value . 85 8.6.^ Conclusions High-current cycling, while more destructive to CD-I cell life than low-current cycling, Is only moderately destructive. Moreover, small, short-term negative cell voltages are tolerable. Noting the voltage changes resulting from changes In current polarity permits calculation of the cell resistance when discharged and at a moderate state of charge . The voltage change is the product of the resistance at the moment of change and twice the current magnitude. Thus, Rj • u J = 77"V = 7^ TTt; - o ohms discharged 2 1 2 x 0.2 R i„ J = TTT =3-5 ohms, charged 0.4 •p The ratio — r; — ^ — = 1.72 is close to the value of 2 quoted by Krugman charged for all nonvented nickel-cadmi\;im cells. For this experiment as well as the experiment described in Section 8.5, voltage-time curves were obtained for cells discharging through a standard resistor. Since the resistor used was 500 ohms, the maximum current drawn was about 2.6 ma., which, in view of the values obtained above for the internal resistance, would cause a negligible voltage drop. In each case, the cell voltage dropped approximately linearly from 1.3 to 1.1 volts, then abruptly drooped to 0.5 volts and then proceeded in a leisurely exponential toward volts. The droop takes about 10 minutes out of a total discharge time of nearly 9 hours, less than 2% of the time. A voltage source approximating the important features of this behavior would have an e.m.f. given by E = u(q)(2.6 X lO"^ q + I.IO) volts 86 where q is the stored charge in coulombs, and u(q) is the unit step function defined by u(x) =0, X < u(x) =1, X > 0. It should be observed that the approximate equivalent voltage source for a cell with k times the energy capacity of a CD-I cell should be given by E = u(q)(2.6 X 10"^ q/k + I.IO) volts A conjecture will now be made as a possible explanation for the increased loss in cell capacity as a result of high-current cycling: the culprit may be the formation (on overcharge at high currents) of bubbles within the pores of the anode which become so large that they are trapped and effectively insulate the portion of the anode that they touch from the electrolyte, and present so little area relative to their volume that re- combination on standing is negligibly small, thus reducing the usable volume of active anode material. A descriptive name for such an effect would be the "bends." Sintered plate electrodes, due to their larger pore size, could probably never contract the bends. 8.7 Determination of Impedance as a Function of Frequency 8.7-1 Purpose In order to make effective use of a physical device, it is necessary to know its measurable characteristics, which, not infrequently, are at odds with theoretical behavior. In particular, the magnitudes of the faradaic impedances of the nickel-cac3mi\ffli cell, and the frequency at which they disappear, are of interest. 87 8.7-2 Procedure A cell was placed in series with a 10 microfarad capacitor (aluminum foil electolytic shunted by a 0.05 ceramic) and a 500 ohm resistor; across this series arrangement was impressed a 10 volt peak-to-peak sinusoidal voltage of variable frequency. The capacitor was used to prevent flow of any direct current, and its size was chosen so that its impedance would have influence only at low frequencies. The large voltage and resistor assured essentially constant current. Data was taken for two cells at frequencies chosen to provide good coverage on a logarithmic plot. Data taking consisted of measuring, with an oscilloscope, the magnitude of the voltage across the cell, and the phase shift of this voltage relative to the applied current; for reasons of ease in procuring data, the actual phase difference measured was between the applied voltage and the cell voltage. Data was taken for both the charged and discharged state. The charged e.m.f. of both cells was 1.26 v, about midway between a fully charged state and l/e of full charge. The discharged voltage of cell no. 1 was 1.10 v, that of cell no. 2 was 1.02 v. 8.7.3 Results The data was corrected, then the resistive and reactive components were calculated. Correction was performed as follows: recognizing that the cell drop (never greater than O.I3 volts) may be neglected, the current phase and magnitude are dependent only upon the series R and C, so that |Z'| =,Jvr + .±- = a/2.5 X 10^ + CJD C 4n f X 10 2 1 10 and 6 - arctan -r—r = arctan — - ; coRC Jt f ' 88 thus, must be added to the data phase shift, and Z' must be employed (rather than 500 ohms) to calculate the current used in arriving at the cell impedance (see Tables 3^ ^> 5^ 6 and 7 (9 is corrected phase) and Figures 10, 11, 12 and 13). Slightly above a megacycle, severe distortion set in and continued until about 9 megacycles. It ranged through every conceivable form, in- cluding really excellent (for the circumstances) square and isosceles triangular waves. 8.7.^ Conclusions The logarithm of the real part of the charged cell impedance plotted in Figure 10 can be seen to be a reasonably linear function of log f . The slope of the line is -0.125 or -I/8; this translates on a log-db plot to -2.5 db per decade, as compared with -10 db per decade for the Warburg Impedance, and or -20 db per decade, the closest values obtainable with elements independent of frequency. No rational, theoretical explanation for this behavior offers itself. An even greater anomaly is presented by the log-log plot of the imaginary part of the charged cell impedance in Figure 11. At about 125 cps., there appears to be a zero redolent of LC series resonance. A study of Tables k and 5^ however, reveals that this is not the case, for the reactance must change sign in passing through a zero resulting from LC resonance, while the cell reactance does not. Another argument against LC resonance calls attention to the large LC product necessary for such low frequency resonance; this argument is somewhat weakened by recognition of the rather startling fact that one of the electrodes is a ferromagnetic material, nickel. It will now be shown that the inductance due to the nickel electrode is inadequate to permit LC resonance at this frequency: Assuming uniform 89 Table 5 Current -Determining Impedance f (cps.) |Z' (ohms) 9 (degrees) 50 727 k6.6 60 566 28.0 100 52i^ 17.6 150 511 12.0 300 502 6.0 600 501 3.0 1000 500 1.8 Table k 90 Results of Z (f) Test Charged State Cell No . 1 f(cps.) ^C) V (mv.) I (ma.) ^c(°) Z (fi) R(n) x(a) 30 +27 60 13.8 -20 i^.35 i^.07 -1.1+9 60 +18 60 IT. 7 -10 3.39 3.3^^ -0.59 100 +15 60 19.1 -3. ^•ik 3-lk -0.16 150 +9 60 19.6 -3 5.06 3.1^ -0.16 300 56 19.9 -6 2.82 2.80 -0.30 6oo -9 53 20 -12 2.65 2.59 -0.55 Ik -9 50 20 -11 2.50 2.1+6 -0.1+8 1.5k -15 50 20 -15 2.50 2.1+2 -0.65 3k -18 ^5 20 -18 2.25 2.11+ -0.70 6k -18 k2 20 -18 2.10 2.00 -0.65 10k -20 39 20 -20 1.95 1.81+ -0.67 15k -2k 38 20 -2k 1.90 1.7^ -0.78 30k -20 32 20 -20 1.60 1.51 -0.55 60k -18 30 20 -18 1.50 l-k3 -0.1+7 100k -18 28 20 -18 l.i+O 1.33 -0.1+1+ 150k -18 26 20 -18 1.30 1.21+ -0.140 200k -9 25 20 -9 1.25 I.2I+ -0.20 91 Table 5 Results of Zi (f) Test Charged i State Cell No . 2 f(cps.) fO V (mv.) I (ma.) 9,(°) z (a) R(n) x(n) 50 +27 kS 15.8 -20 5.i^8 3.27 -1.19 60 +18 50 17.7 -10 2.83 2.79 -o.i+9 100 +9 50 19.1 -9 2.62 2.59 -0.1+1 150 +9 50 19.6 -5 2.55 2.55 -0.13 300 h9 19.9 -6 2.1+6 2.i+5 -0.26 600 -5 kS 20 -8 2. to 2.58 -0.31+ Ik -5 h3 20 -7 2.25 2.23 -0.28 1.5k -9 h5 20 -9 2.25 2.23 -0.35 3k -15 ko 20 -15 2.00 1.94 -0.52 6k -18 59 20 -18 1.95 1.85 -0.60 10k -18 37 20 -18 1.85 1.76 -0.57 15k -18 55 20 -18 1.75 1.67 -0.51+ 50k -18 53 20 -18 1.65 1.57 -0.51 60k -18 50 20 -18 1.50 1-^3 -0.1+7 100k -18 28 20 -18 i.to 1.33 -0.i+i+ 150k '9 26 20 -9 1.30 1.29 -0.23 200k -9 25 20 -9 1.25 1.2i+ -0.20 92 O O S s 8 ' 9i C9 / Z^' th tfA _ V T / // lO ♦ // V CO 1 / / J / ^ ^» <0 jj ' T 1 1/ 1 lO ♦ J/ J ^% Al 7 m 1 1 lO — — ( ^ ' i 1 1 p — r^ 1 0» VD / / J ^ ^ <0 T ;■ y 7 / lO ^' y^ / M m 10 W <0 6 lO d CD 3 o lO d d o Ul o LiJ O q: < X o 3 > Q UJ q: O f 93 • A f c^ k p* • CELL NO 1 ■ CELL NO 2 I • 1 * ' P A O f f K J i f lA f V A M% ml n r* V- 1 t4- t 0) w II ' II ■ ^ ^ n» Cir W 1 M % « •«? \ I'^j ^ \ >- k — ^^ "ca ^ 1 ,. 7" o> / i^_ d w T lA ^ > *!• ^^'^ *^ M« M N. <:^ ;::«*^ n* >- — ;!" — - »— — ^ :--. A « -— — . SZ^= &-=— * = ■^ ♦^ r^ n* to ^^ M ^ ^. ^ ^"^ ♦ <^'' ,-*- Al • w )_ a § ^ o s S S UJ I o UJ CD < 5 Q (0 > X o* CD O -I UJ a: CD Table 6 9h Results of Z( ;f) Test Discharged State Cell No. , 1 f(cps.) cp(°) V (mv.) I (ma.) cPe(°) z {^) R(Q) X (n) 30 +22 120 13.8 -25 8.70 7.87 -3.67 60 115 17.7 -28 6.50 5.7^ -3.05 100 -9 110 19.1 -27 5.76 5.13 -2.62 150 -13 100 19.6 -25 5.10 4.62 -2.16 300 -18 85 19.9 -24 4.27 3.90 -1.74 600 -22 70 20 -25 3.50 3.17 -1.48 Ik -22 65 20 -24 3.25 2.97 -1.32 1.5k -22 60 20 -22 3.00 2.78 -1.13 3k -18 50 20 -18 2.50 2.38 -0.77 6k -18 45 20 -18 2.25 2.14 -0.70 10k -14 42 20 -14 2.10 2.04 -0.51 15k -±k 40 20 -14 2.00 1.94 -0.48 30k -13 40 20 -13 2.00 1.95 -0.45 60k -13 35 20 -13 1.75 1.70 -0.39 100k -13 30 20 -13 1.75 1.70 -0.39 150k -13 30 20 -13 1.75 1.70 -0.39 200k -13 30 20 -13 1.75 1.70 -0.39 95 Table 7 Results of Z( ;f) Test Discharged State Cell No. , 2 f(cps.) ^O |V (mv.) I (ma.) ^c( ) z («) R(fi) X(fi) 50 +18 150 13.8 -29 9.i^5 8.21^ -i+.57 60 155 17.7 -28 7.63 6.75 -3.5i^ 100 -9 120 19.1 -27 6.28 5.59 -2.85 150 -.18 105 19.6 -30 5.56 k.6k -2.68 300 -27 90 19.9 -55 I1.52 5.79 -2.1^6 600 -31 70 20 -3h 3.50 2.90 -1.96 Ik -27 60 20 -29 3.00 2.62 -l.k5 1.5k -27 50 20 -27 2.50 2.23 -i.li^ 5k -27 h3 20 -27 2.25 2.00 -1.02 6k -27 ko 20 -27 2.00 1.78 -0 . 91 10k -27 55 20 -27 1.75 1.56 -0.80 15k -27 52 20 -27 1.60 l.i^5 -0.73 50k -25 50 20 -23 1.50 1.38 -0.59 60k -18 25 20 -18 1.25 1.19 -0.39 100k -18 25 20 -18 1.15 1.09 -0.36 150k -18 22 20 -18 1.10 1.05 -0.3^ 200k -15 20 20 -15 1.00 0.97 -0.26 96 (0 O 01 %U I*" U# %f\ j ^ 1 ■A r CM O OO A •y-^ k <0 ^ lO LijUJ / ▼ oo y / ^ K^ ' 1 « / .^^ 1 p* (O ^y^. ^ ^^^ ^ IP V *^ r 1 1 lO j^i >-/ f^ 1 CM o * ■<.^ ^ / ^^ OV _^>' yy^ 00 r^ ^^ / K. 9^ ^i r <0 r ^ .^ K> rx^ ^ ♦ ^ r^ n* o ' c < 3 ^ < IB > c \ ' < 5 ^ > 1 i 3 s C9 97 LtJ ifi O < b 3 o CO Lju o_j o ..J 98 current density, the self inductance of a two wire transmission line is given by L^K u. , D ^=— + In — henries per meter 8 for cylindrical wires of equal radii, where |j. = permeability of free space |j. = permeability of wires D = wire separation (center-to-center) r = wire radius . ^ for nickel is < 1200, o D < 1 meter, r = 0.59 cm. .*. L < hn X 10 -7 1200 , 100 + In 1+ 0.59 =0.12 mh. /meter. This is twice the inductance for one line, therefore the inductance for a 0.29 cm. length of nickel wire is - -? -h L < 0.06 X 0.29 X 10 = 1.7i+ X 10 mh. The condition for resonance is LC = ^ = 1.62 X 10" for 125 cps CO therefore, for LC resonance, the capacitance would have to satisfy the condition ^ . 1.62 X 10" n :t ^ C > = 9-3 farads 1.7!^ X 10 ■7 Actually, the inductance would be somewhat less than that calculated above due to skin effect and the porous nature of the electrode. 99 An even more fundamental deviation of the data from theory should "be mentioned. According to Bode, if the slope of the log-db plot of the real part of a network function is a constant k, the phase shift is given by e = k ^ . Thus, for a real part of the form R = R co , 9 = a — . Therefore since X = R tan 0, X = R„a) tan It «2 = X CO (a not necessarily an integer) . Thus, the reactive portion must have the same frequency dependence as the real part. It may be observed that the Warburg Impedance obeys this rule, but the observed data shown above does not begin to adhere to it. It may be argued that, since the faradaic impedances cease to exist above a certain frequency, the slope of the real-part is not constant for all frequencies and the above conclusions are invalid. It may be pointed out, however, that there is nothing in the low frequency behavior of the faradaic impedance which portends the relaxation phenomenon, and the above conclusions are therefore applicable. From Figure 12, it can be seen that the behavior of Log R vs. Log f is not as linear for the discharged state as it was for the charged state, and, as would be expected, the values are generally higher. For low frequencies, the slope is about -0.l6 ~ -l/6. Figure 13 shows a much better behaved reactance for the discharged state than was observed for the charged state. In particular, the "zero" observed in Figure 11 is conspicuously absent. The slope of this plot is about -O.32 ~ -I/3 over a wide range of frequencies. The faradaic impedances, by definition, arise from the electro- chemical reactions within a cell. Relaxation takes place when the reactions 100 can no longer follow the forcing function., Since relaxation was observed to take place at about one megacycle, the lower limit on write time would be of the order of a microsecond. The "zero" observed above for charged cells appears to be a one- port analog to a twin-T, RC null network. One possible application would be as a low frequency "tuned" filter. Another would be as an electro- chemical analog to a magnetic amplifier, since the magnitude of an AC voltage could be controlled by a DC current. Fortunately, the faradaic effects prove to be negligible at frequencies of interest for reading. 8.8 Determination of Double-Layer Capacitance 8.8.1 Purpose Since no capacitance-producing film is formed in a nickel- cadmium cell, the only state-of-charge dependent capacitance remaining is the double-layer capacitance; its dependence upon the state of charge is solely by virtue of its dependence upon the cell's open circuit voltage, which is a function of the state of charge. Capacitance sensing requires the existence of a state-dependent capacitance, therefore it is necessary to learn the characteristics of the double-layer capacitance of the CD-I cell. 8.8.2 Procedure A method normally used to eliminate the effect of the double-layer capacity will be used instead to determine the value of this capacity. This technique makes use of the fact that, when a step of voltage is applied across a cell, the current due to the double-layer capacity will decay with a time constant determined by the product of its own value and the resistance of the external circuit (neglecting internal resistance), while the faradaic 101 current decreases very slowly because a diffusion process is involved. Thus, by adjusting the resistance of the external circuit, the two currents can usually be easily distinguished. Since the value of the double-layer capacity was unknown, an assumption of the possible range of values had to be made, and appropriate values of resistance had to be used to cause the corresponding time constants to be in a perceptible range. It was assumed that the capacity would be not less than one micromicrofarad; resistances used were between twenty megohms and ten ohms. The square wave voltage used was about I50 mv. peak-to-peak, with a rise time less than one-half microsecond, and a period up to sixty milliseconds. Both a charged cell (I.26 v) and an uncharged cell {O.kk v) were used. 8,8.3 Results No overshoot (or droop) in the current was found for the entire range of resistors for either the charged or the uncharged cell. 8. 8. if Conclusions Since the lowest value of resistance was of the order of magnitude of the internal resistance, both resistances must be considered. No droop was observed for the entire range of resistances used, therefore in particular, for the ten ohm, sixty millisecond period case, -2 R C » 3 X 10 where R is the sum of the ten ohm external resistance and the internal resistance. From the results of Section 8.6, R < I6 ohms, ,-2 C > > ^ "".Y^ ~ 1,800 taf . IZ 102 Measured values of double-layer capacity for other kinds of cells are 12 around 50 to 60 microfarads per square centimeter, therefore an approxi- mate lower limit for the active electrode area can be calculated. Assuming the capacities of the two electrodes are about equal, 1800 X 2 ^^ 2 . ^ ^ XOUU X d. ^_ A > > tt; = 60 cm. The current necessary to cause a change of voltage of say one hundred millivolts in one tenth of a microsecond will be calculated : Av i " C xf At .'. i > > 1.8 X 10'^ i^ = 1.8 X 10^ amperes. 10"' Capacitance discrimination is thus obviated as a means of sensing. 8.9 Element -Delay Test 8.9'1 Purpose Since it is of vital interest to know what reading speed is physically possible with a chemory, it is necessary to measure the delay introduced by the element . 8.9-2 Procedure The sense amplifier in Figure 8 was used with the strobe disabled to prevent mistaking a strobe transient for a read pulse. The output of a read driver using a GFU5OII transistor was connected to the positive terminals of two cell holders, the negative terminals were connected to the input of the sense amplifier through a switch which allowed selection of one or the other of the cells. In one cell holder was placed a fully charged cell with 103 an open circuit e.m.f. of 1.26 volts, in the other was placed a discharged cell with an open circuit e.m.f. of O.7 volts. The discrimination-level-adjustment potentiometer was then set so that interrogation of the discharged cell produced essentially no output change; interrogation of the charged cell then produced an output change of about k- volts . 8.9.3 Results The delay between the start of the read drive pulse and the start of the realistically loaded input to the sense amplifier was imperceptible on an oscilloscope screen using a sweep speed of fifty nanoseconds per centimeter. The screen scale is provided with five divisions per centi- meter, and the resolution is about plus or minus one quarter of a division. Thus the delay was less than or equal to about 2.5 nanoseconds. 8. 9-^ Conclusions The fact that the delay through the cell was imperceptible indicates that, for pulse purposes, a cell acts like a charged capacitor. It should be possible at this point to draw some conclusions regarding the projected attainable reading speed for a practical chemory. Rajchman expresses the cycle time for a destructive read memory as T=2t +t^ + t +t + t ,^^ s t g a n' where t = switching time s ° t, = transmission time t = amplification time t = addressing time a ^ t = preread delay. lOi^- This expression will be modified to apply to a chemory of N vords of m bits each. t : since no switching takes place in a chemory, this term will be replaced by t , element delay time, and the factor 2 will be dropped because the read is nondestructive. 4- ^u- ,. -u (N + m)d . ,, , 4^ 4.L, t^i this term becomes -^— r— — — m the worst case for a three- t 2pc dimensional, equispaced array, where p = the fraction of the speed of light at which transmission occurs c = speed of light in cm. /sec. d = spacing between elements in cm. t : this temi changes character greatly for a chemory, becoming independent of the number of words; if Rajchman's assumption is made that the ratio of amplification to the time to obtain it may be regarded as a constant B, this term becomes V /BV where ^ a' r V - desired voltage a ^ V = unamplified, available read voltage. t : this term will remain unchanged. a ^ t : this term is present only after a write has been n performed, and only then if a word is interrogated within a post write delay time t' of being written into; if this delay is averaged over the total number of reads per write r, the tenri which will replace t is the average preread time t'- P r 105 The average read time for a chemory is then (N + tn)d \ ^ "^n c e 2pc BV a r •^ r The following values will be used: t < 2.5 X 10'^ sec. e — m = 50 bits d = 1 cm. P = 1/2 c = 3 X 10 cm. /sec V„ = 2 volts a V =0.25 volts r B = 10^ sec.""^ t = 0.02 X 10" sec. a t' = 10" sec n r = 10^ 3 N = 10 words. Substituting, T < 2.5x10-9 + ^050ij^ c — 10 Q 2 X 0.5 X 3 X 10 10^ X 0.25 -6 + 0.02 X 10' + i^ 10^ < 2.5 X 10"^ + 35 X 10'^ + 8 X 10"^ + 20 X 10'^ + 0.001 X lO'^ < Gd nanosec. This is a rather remarkable speed '. 106 The above number is the access time; certain considerations not included above enter into calculations of a cycle time, that is, the time which must elapse after one interrogation has begun before another inter- rogation can begin. These considerations have to do with the settling time after a read. The read-current path is rather complicated. It consists of a short "tap-root" with many long branch roots of equal length and roughly equal separation (the connections between planes will, in general, be greater than the element spacing) . A current path must be regarded as a tiransmission line for steps whenever the rise-time is small compared with the temporal length (t.l.) of the wire. The t.l. of the tap root (word line) is — which is about three nanoseconds for the values assumed above. Since the rise-time of the read step will probably be greater than this value, this portion of wire can be regarded as a liomped terminal rather than a transmission line. The branch roots (bit lines) have a t.l. given by — , about 70 nanoseconds for pc the above assumed values. They must, therefore, be regarded as transmission lines. Thus, the situation reduces to n transmission lines of equal length, connected in parallel at one end. One consequence of the need for application of transmission line considerations is the increase in the current drain from a chemistor during interrogation due to the low impedances involved (the current which must flow to establish a voltage on a transmission line is governed at first by the characteristic impedance of the line, and only somewhat later by the termination). There is the (expensive) possibility of providing separate amplifiers and bit drivers for small portions of a chemory to keep the sense lines short enough to act l\amped. 107 The lines can either be left unterminated (essentially open circuited due to the high input impedance of the amplifier) or terminated with their characteristic impedance. There are arguments for and against "both of these choices because a high impedance is desirable to reduce leakage during quiescent periods (though there is, of course, the reverse resistance of a diode in the circuit), while a match is desirable to prevent excessive settling times. The action of interrogation can be approximated by the closing of a switch connecting the previously open-circuited source end of the bit line with a zero impedance voltage source of or 1 volt e.m.f. depending on the state of the bit selected (the 15 v D,C. level may be ignored). Usually, the sensing strobe is made as narrow as possible to avoid spurious noise signals. If such a scheme were adopted here, it would be necessary to maintain read current for at least the time necessary for a signal to propagate from the furthest word to the amplifier at the midpoint of the bit line; this is necessary to sustain the signal until the strobe occurs even if it is from a word adjacent to the sense amplifier. Since energy is at a premium in a chemory, it would be preferable to have a wide strobe so that a short pulse occurring anytime within its bounds will be recognized. For a characteristic impedance of 100 ohms, a pulse lasting 10 ns would deplete 2 W = = — t = 2 X 10 joules per interrogation ^0 for the one state. If the line is terminated with an open circuit, the pulses (in general, two) will take a long time to decay to a level such that it 108 would "be safe to allow another interrogation because the series R and shunt G are usually quite small. The possibility of using resistive wire offers itself as a means of reducing the decay time. However, since the attenuation is an exponential function of the distance traversed, in order to prevent excessive drop in the sensed signal, the line resistance must be set at a level which requires an intolerable decay time (if a maximum sensed-signal drop of Wfo is specified, then about eleven traverses of the line are necessary for the signal to decay 90^) • If the line is terminated in its characteristic impedance, a settling time equal to twice the temporal length of the line must be allowed (all of this time is not wasted, as some of it is accountable in the access time). Thus, for this system (which appears best), and for the values previously assumed, the access time is 66 ns, and the cycle time is 1^^-0.5 ns, allowing for overlap. As a check on the validity of the assumptions of one-half the speed of light propagation time and 100 ohm characteristic impedance for the bit line, the capacitance per unit length will be calculated from these values . The delay per unit length T, and the characteristic impedance Z^ are given by T^-nr^ , Zo = '/| for negligible series resistance and shunt conductances where L and C are the series inductance and shunt capacitance per unit length. T ? X lO" Then C = ^ = , _;: = 20 pf per foot Zi_ lOu 109 Since the reverse biased diodes are one cm. apart, this would indicate a capacitance of l/2 pf per diode allowing 5 pf pe^r foot for the line. From Fairchild Semiconductor Bulletin SL201/2, this is close to typically- obtainable values for a reverse biased FDIOO diode. 8.10 Two Word, Four Bit System Test 8 . 10 . 1 Purpose This experiment might well be termed the piece de resistance of this dissertation, for it embodies a test of all the principles necessary for a full scale chemory. Its purpose then, is to experimentally verify the behavior theorized upon in the preceding chapters; upon its success or failure depends, to a great extent, the success or failure of the entire chemory proposition. 8.10.2 Procedure A four stage counter (Figure J)), two bit drivers (Figure 6), two word drivers (Figure ^) , and two sense amplifiers (Figure 8) were connected as shown in Chapter VII, with the following exceptions: 1. an emitter follower was placed between each counter output and its associated diode logic, 2. instead of the signals a • b and a • b going to the sides of the word drivers serving the cathodes of the bit diodes (Figure 5)^ the signals a and a, respectively, were used, allowing that side of the word-^write drivers to serve as read drivers as well. A protective diode (normally reverse biased) was placed across each of the CD-I cells for protection against over-discharge. A manual control was provided which allowed over-riding of the counter's normal 110 sequence^ permitting selection of a read or write function and the state to Toe written. The write-one current was set at the modest value of 200 ma., while the write-zero current was about 3OO ma.; a small change in the 15 volt supply causes an increase in one of the above currents and a decrease in the other, allowing a fine adjustment of their ratio. While it might normally be expected that any state of charge brought about by a given charge current would be easily within the reach of an equal discharge current due to the charging inefficiency, the addition of the protective diode reduces the effective discharge current, so that an increase in its nominal value appeared prudent , The first stage of the counter was run with a basic cycle time of 6.0 minutes (a 6.0 minute half -cycle time was used when two ones or two zeros were being written); thus the time for a complete sequence of events was one hour^ The sequence of events consisted of writing a pattern of informa- tion first into word zero and then into word one, then reading in the same order for the same time. Bit zero in each word was made to change state each time it was written into, while bit one in each word was made to change state every second time, thus testing the ability of a single write to change the state of a chemistor whose opposite state has been fortified by a double write; this choice also avoided a Gray code. Since, in a practical system, writing would be the exception rather than the rule, it is of particular interest to examine the more usual situations, i.e., reading and neither reading nor writing. Each information pattern was checked for longevity for quiescent and reading state-retention. The pattern was written into both words, and one word was then interrogated Ill continuously while the other was untouched. A dynamic read test was made for a particular pattern (word zero: 11; word one: 00). Read delay measurements were also made. In Figure Ik is shown the circuitry used in this experiment. The O/l and read/write switches on the control box were so arranged that they had no effect when in the center position, so that a square-wave could be applied, The cell holders were made from a type not intended for use with CD-I size cells, and are therefore considerably larger than is necessary. In the lower left-hand corner is shown a CD-I cell next to a penny for size comparison. The voltage supplies and other necessary pieces of equipment are not shown. 8.10.3 Results The chemory performed exactly as planned. The information was written and read in sequence with no difficulty for a total of 10 cycles, representing kO writes, corresponding to a change every ten days for more than a year. The patterns were checked for quiescent state-retention for 2k- hours with no measurable change in voltage for ones (I.3 v) and no zero which rose above 1.0 v. The results were the same under continuous interrogation for 24 hours. This time corresponded to 7 11 2k X 5600 X 10' = 8.614- X 10 interrogations. The same results were obtained (for the pattern described above) for 2k hours of 250 microsecond reads alternating between the two words. The delay measured between the beginning of a read command and the beginning of the output rise for a one (there is, of course, no output rise for a zero) was 100 nanoseconds. The delay was accountable as follows: 112 ^1 ■III I ■ m i ■■ i FIGURE Ik: TWO WORD, TWO BIT PER WORD CHEMORY 113 Write Driver (doubling as read driver) 70 ns . Chemistor ns . Linear Amplifier Stage 20 ns. Discrimination Circuit 10 ns. 100 ns. 8 . 10 . ^ Conclusions The chemory system used is basically sound. It is fairly obvious that, in a large, practical system, each bit line would have to be a current source or sink during write to guarantee the bit current, and the word lines could not be current sources or sinks. 8.11 Discharged-Voltage Drift Inhibition 8.11.1 Purpose Since discrimination becomes easier the greater the difference in voltage between the charged and discharged state, it is of interest to attempt to increase this difference. Since the value (l.lO v) to which the open-circuit discharged-state voltage drifts appears to stem from a very- weak source, it follows that for each value of resistor, there is a corre- sponding maximum discharged-state voltage. This experiment endeavors to test the feasibility of using an intentional quiescent leakage to aid voltage discrimination. 8 . 11 . 2 Procedure Seven cells were thoroughly discharged by placing 100 ohm resistors across their terminals for at least 2k hours. Resistors ranging in value from 100 thousand ohms to 5 megohms were systematically placed across their terminals to find the maximum value to which the cell voltage would drift over a period of 10 hours. 8.11.3 Results No cell was observed to have a voltage greater than I.05, O.8O, 0.60, 0.50 volts when shunted by resistors of values, respectively, 5, 1, 0.5^ 0.1 megohms . 8 . 11 . ^4- Conclusions For applications where an intentional quiescent leakage of the necessary size can be tolerated, the discharged state voltage can be held arbitrarily low. It is reasonable to assume that the leakage current necessary to guarantee a given voltage will be directly proportional to the cell's energy capacity. An interesting alternate method of preventing discharged-voltage drift would be to systematically interrogate each word often enough to cause the average equivalent leakage to be equal to the required value. It should be stressed that a periodic depletion referencing scheme need not obey most of the usual rules. That is, since the information is of no interest, more than one word could be interrogated at once (in the limiting case, all at once) if a few circuit modifications were made. Such a scheme would contribute a measure of flexibility to a chemoiy in the sense that the voltage difference between a one and a zero at the chemistor could be varied at will. Thus, for example, a chemory might have three possible modes of operation: 1. A "normal" mode maximizing the number of useful inter- rogations between regenerations to a degree consistent with good reliability. 'J 2. An "extranormal" mode yielding greater reliability while limiting somewhat the number of useful interrogations between regenerations (useful in a case where, for example, the 115 ambient noise level is unusually high or a problem requiring extraordinary reliability must be run). 3. A "supernormal" mode yielding ultrahigh reliability while limiting still more (possibly severely) the number of useful interrogations between regenerations (useful, for example, for allowing a chemory to limp along until the next scheduled maintenance period in spite of certain malfunctions such as a drop in amplifier gain). 116 CHAPTER VIII Footnotes 1. Koehler, p. 88. 2. Bergstrom, p. 2^4-80, 3. Salkind, p. Ij-, i+. Delahay, p. 268. 5. Encyclopedia Americana (196O Edition), Vol. 10, p. I85J. 6. F. W. Sears and M. W. Zemansky, University Physics (Cambridge: Addison- Wesley Publishing Co., 1953), p. 301. 7. Krugman, p. I30. 8. Walter E. Rogers, Electric Fields (New York: McGraw-Hill Book Co., Inc., 195^), P» 3iH7 9. Standard Handbook for Electrical Engineers (6th Edition; New York: McGraw-Hill Book Co., Inc., I933 ) , ~p7~U0^ 10. Hendrik W. Bode, Network Analysis and Feedback Amplifier Design (New York: D. Von Nostrand Co., Inc., 1957), pp. 31^^-315- 11. Barker and Jenkins, p. 687. 12. Salkind, p. 51. 13. Jan A. Rajchman, "A Survey of Computer Memories," Datamation , (December I962), p. 26. 117 IX. SOME PRACTICAL DESIGN CONSIDERATIONS 9.1 Introduction In this chapter some practical considerations of chemory design will be illustrated by means of examples. Since actual data is available for the CD-I cell^ a chemory using this cell and of a size within its range of applicability will be considered first, followed by an extension to a thousand words using smaller cells. Design from two points of view will thus be considered: that of a specified chemory size with a specified chemistor size, and that of a chemory of specified size and characteristics, but unspecified chemistor size. 9.2 Preliminary Considerations The voltage ranges to be interpreted as the binary states must be chosen. Suppose that leakage is provided of sufficient magnitude to guarantee that the voltage of a cell in the discharged state will be less than 0.80 volts (see Section 8.II). Suppose further that the selection circuitry does not differ materially from that used in Section 8.10. Then the components whose characteristics must be considered in a tolerance analysis are the read driver transistor, one of the element diodes, the element, and the amplifier transistor and resistors. A sense amplifier and its associated discrimination circuit must serve many chemistor s; it must reliably recognize the state of each of these chemistors when it is selected. The emitter-base drops of the discrimination transistors and the amplifier transistor may be removed from consideration if a potentiometer is allowed to adjust the reference voltage about which 118 discrimination is to be performed. This statement is based on two premises: 1. The emitter-base voltages will not drift appreciably with time; 2. The change in the emitter -base voltage of the amplifier transistor resulting from the small differences in emitter current corresponding to the two possible chemistor states is negligible i.e., < 0.01 v. Data taken for 100, 2N967 transistors from Motorola and Texas Instruments revealed that the greatest difference in emitter-base voltage between the values corresponding to 0-5 and 1.0 ma. emitter current was 0.022 volt, and the greatest difference between the values corresponding to 1.0 and I.5 ma. was O.OI6 volt; as will be seen, this data substantiates the above assumption. The alpha of the amplifier transistor and its associated resistors must, however, be considered in the tolerance analysis. The worst one and zero voltages (necessarily from different chem- istors utilizing different read driver circuits) which could be presented to the base of the amplifier transistor will be found, and then the worst voltage difference presented to the discrimination circuit will be calculated. During read, the read drive transistor is saturated; it is reason- able to assume that transistors can be readily obtained (or hand picked with a reasonable yield from obtainable transistors) whose emitter- collector saturation voltages lie within a 0.20 volt range about some center voltage. One of the element diodes is slightly forward biased during read. ■X- From data taken for 35^ RD75O diodes, the forward voltage drops at 100 micro- amps were such that 29 of the units were with a range of O.O38 volts around ■^ by staff members at the University of Illinois Digital Computer Laboratory 119 a center value of 0.^^67 volts. Probably, then, in a larger batch, some 80/0 of the units would lie within a O.O5 volt range. According to Burgess Battery Form No. 1228(821), the full charge voltage of a nickel-cadmium cell is greater than or equal to I.30 volts over the temperature range from +k^ C to -I5 C. A value of 1.27 volts will be chosen as the most pessimistic value which may be expected due to variations in manufacture. Assuming that leakage may be neglected, let 0.04 volts be invested in read depletion and aging. Since the "center" values of the voltages mentioned above apply for all cases, they will not be explicitly shown. Therefore, the worst voltages applied to the base of the amplifier transistor would be: Worst 0: V = O.8O + 0.10 + 0.025 = 0.925 volts Worst 1: V = 1.27 - 0.10 - 0.025 - 0.04 = 1.105 volts worst difference: AV = I.IO5 - O.925 = O.I8O volt. The least difference in emitter current would correspond to the largest emitter resistor. Assuming I'fo resistors, AI min. = ?-^^^ = 0.178 ma. e 1.01 Assuming a worst case alpha of 0.95 (of over 7OO, 2N711A.'s (from Motorola Raythron and Texas Instr\aments) tested, none had an alpha less than 0.955 for 10 ma. emitter current), the minimum collector current difference would be AI min. = O.I78 x O.95 = O.16O ma. * by staff members at the University of Illinois Digital Computer Laboratory 120 The least voltage difference at the collector would then be AV mln. = 0.160 X 7-^^25 = I.I8 volts, c Since + 0.10 v about a discrimination point is sufficient to switch a switching amplifier^ + 0.59 ^ should be more than adequate. The discrimination levels for the cell were set, in effect, above : corresponds to cell voltage < O.8O volts; 1 corresponds to cell voltage > 1.23 volts. Another choice of discrimination levels is possible. The energy- associated with voltage changes above 1.1 v is large while that associated with voltage changes below this value is small. Therefore, the choice of 1.1 V as the lower limit for a 1 roughly doubles the amount of energy which is available. To maintain the voltage difference found to be adequate above, a resistor of about 0.75 megohms would have to be used (see Section 8. 11. 5); thus, though the energy available has been doubled relative to that for the previous choice, the quiescent drain has been increased by only 33^^ increasing the allowable time between replenishments. However, while the voltage difference between a one and a zero is preserved by this choice, the voltage magnitude of a minimum 1 is reduced, which is undesirable. Calculations which follow will be in terms of the first -mentioned discrimination levels. It will be noted that the tolerances on supply voltages were not considered above. If the same supply is used for all voltages of interest during reading (as was done in Chapter VIl), long term drift should have no effect. There are any number of variations which could improve the above results, for example: 121 1. Increase the cell leakage to obtain a lower "O" voltage (at the cost of available energy for reading the "l" state), 2. Use two cells in series for each chemistor to double the magnitude of the voltage difference. 3. Use two cells anode to anode to double the magnitude of the voltage difference and allow polarity discrimination, k. Increase the gain of the single stage amplifier, 5. Increase the number of amplifier stages. It should be noted that the above will apply for any cell size, and in particular, to the two sizes which will be considered below. 9.3 A CD-I Chemoiy Consider a sixteen word, thirteen bit per word chemory which could serve as sixteen special registers addressable by the Advanced Control of the new University of Illinois computer Illiac II. A write current of ^00 ma would be a reasonably safe value. From Figure 9 'the corresponding write time for a CD-I cell is 15 minutes. Thus, the time necessary to change the entire contents of the chemory would be 16 X 15 = 2U0 minutes, although such total changes would seem unlikely. For the quiescent drain of about one microampere necessary to guarantee a discharged state voltage less than O.8O volts, the time necessary to deplete the 0.0^ volt allowance (neglecting the aging allowance for this calculation) would be t = r^ X -T——- = l.kk X 10' sec. 1.2 X 10-^ °-20 Y = '■ ^ = 166.8 days = O.h'^6 year, 2^4- X 3.6 X 10^ 122 thus this drain is negligible for most purposes. Allowing, say, 15^ of the depletion allowance for aging, the numher of interrogations possible before replenishment became necessary would be 1.2 X 10 X 10 ' The word drivers would have to accept or deliver between and 13 X O.k - 5 '2 amperes. The number of diodes, including a protective one for each bit and those in the driver circuits and strobe, would be 13 X 16 X 3 + 13 X 2 + 13 X 2 + 16 + 15 = 62i+ + 26 + 26 + 29 = 705. The number of power transistors necessary would be 2(13 + I6) = 58; an equal numiber of low power transistors would be necessary to drive them. Thirteen amplifier and twenty-six discriminator transistors would be necessary. The number of cells necessary would, of course, be I3 x 16 = 208. 9. 4 Extension Extension to larger chemories necessitates reduction in the energy capacity of the cells used, for the practical reason that the time necessary to change the contents of the entire chemory must be reasonable. The question arises: is it realistic to assume that the same current magnitudes can be sustained independent of cell capacity, or must the current be scaled down with the capacity? Consider the only limitations imposed by the current magnitude: 123 1. Cell rupture due to a. weak cell construction or b. inadequate ability to reabsorb evolved gas 2. Resistive dissipation. Item 1-a is probably not a practical limitation, nor should it become a more severe problem for cells of low capacity. Item 1-b arises only if the excess of cathodic material over that necessary to match the anode size is not sufficient. Suppose, for example, a nominal 20 mah cell has the size of its anode reduced while the cathode remains the same size. In Section 8.5-^^ the fractional current efficiency for a CD-I cell was shown to be given by Eff. = ^ which, for i^-00 ma, becomes 0.19- Thus, the recombination mechanism for the CD-I cell is capable of handling the gas evolution corresponding to 8l^ of the energy that was input (aside from resistive losses). Therefore, any anode size such that the total energy input to charge it is less than or equal to ^ ' ' -^ X 0.8l = 368 joules can be tolerated (even at zero efficiency). From Section 8.^^, T^ = 572 ' "f ^' I 10 I so that for an anode of capacity aK, W = 1.2 I T^ = 1.2 X O.lf X 60 X 572 X /^^^^-Q^l < 368 2/3 or a < 0.662. 124 Thus any anode of capacity less than 0.662 x 20 = 13.2^4- raah would, when coupled with the cathode of a 20 mah cell, be incapable of producing harmful gas pressures while being fully charged at i^OO ma or less. Item 2 should also present no insurmountable problems, since almost arbitrarily much cooling is possible. The answer to the above question is therefore: it is realistic to assume that the same current magnitudes can be used independent of the cell size (and with consequent reduction in charging time) . Assume a thousand word chemory, and allow four hours for a total change of contents. Then the write time for each word is ^4- x 10 hour. Using the results of Section Q.k, -. / K ^ 2/3 if X 10 ^ = 572 ' ,10 I If I, for example, is UOO ma, K = 0.03^4- mah. Since the quiescent drain necessary to guarantee 0.80 volts for the discharged state is proportional to K, it would be 0.03if „ „,„ . — ;r^ = 0.017 microamps. and would again be negligible (the bit diodes would, however, have to have a reverse leakage some two orders of magnitude less than for the CD-I example, a requirement which could fortunately be easily satisfied). The number of interrogations possible between replenishments for a system of this size for the same assumptions as were made in the above section, but with recognition that transmission line considerations become involved (see Section Q.'^.k), and assuming 100 ohm bit lines terminated in their characteristic impedance, and 10 ns read pulses, would be 125 0.03^ X 3-6 X 10 ^ 0.85 X O.Qii , ^^ ,_8 ^ = — ^3——^ ^ 0720— = i-^^ ^ 10 . — ^ X 10 X 10 10 The read drive current would be I = iti ^ X 10^ = 50 X T^r X 10^ = 500 ma for the case of all hits being one. It should be noted that, unlike a core memory, this current is proportional to the ni^mber of bits. Since cells of this size would be made specifically for use as chemistors, it is reasonable to assume that one of the devices described in Section 10.3 would be included, eliminating the need for a protective diode. Except for this detail, component calculations for this chemory are exactly like those for the above section. 9.5 Limit There must of course exist some limiting size (expressed in number of words) of chemory beyond which it is not practical or practicable to go. Cycle time is probably the most fundamental practical limitation to size. If, as appears to be true (see Section 10.2), a chemory will be more expensive than a core memory of the same size, it must have a shorter cycle time to justify its existence. RCA is currently advertising core memories with cycle times of 3OO ns . Since cycle time for a chemory is roughly proportional to size (most of the delay is propagation time), then from the results of Section 8.9.14-, two-thousand (2048) words would be the limiting size for the assumptions made in that section, subject to a cycle time less than 3OO ns. Of course, a chemory system made up of any number of two-thousand word cheraories could be used. 126 X. CONCLUSIONS 10.1 General 1. A carefully constructed _, ruggedly encased, sealed nickel- cadmiiom cell could probably be used as the chemistor for a sub-one-tenth microsecond chemory of 1000 words or less. 2. Though capacitance discrimination reading is theoretically possible, it is not practical for a nickel -cadmium cell; resistance discrimination might be possible for very small cells; e.m.f. magnitude discrimination is possible for all nicad cells. 5. A common electrolyte chemory is impractical. k. The full charging time for a nickel-cadmium cell adhering to the construction details of a CD-I cell may be expected to obey the following relation with good accuracy for about an order of magnitude above or below 20 mah, and order of magni- tude or better accuracy somewhat beyond these ranges: T^ - 572 I'"^/5 min. where I' is charging current normalized to the cell's 10 hour rate. 5. Currently available minimum size sealed nicad cells have a finite cycle life which is reduced as the current used is increased. 6. The faradaic portion of the impedance of a CD-I cell does not adhere well to theory, chiefly because of the porous, non- planar nature of the electrodes . I 127 7. The properties which a cell must have to make it attractive for use as a chemistor are: a. sealability, b. high current efficiency, c. low self -discharge, d. large dependence of sensed parameter upon state of charge. 8. The limiting competitive size for a chemory is 20kS words. 9. The advantages of a chemory are: a. very fast read, due to very low read current and lack of need to change state, b. effectively nondestructive read, c. reduction in peripheral equipment (one ampli- fication stage suffices), d. ability to have its information content altered quickly, by electrical means, e. existence of information in a salient form, aiding maintenance and allowing the possibility of use as an associative memory, f . random access, g. primary read voltage well above noise level, h. low internal noise production due to very low read current. The main disadvantage of this memory would be cost (see Section 10.2) 128 10.2 Economic Feasibility Unfortunately, economic considerations play an important role in feasibility studies. The cost of a device must be balanced by the need for its services before the device may be termed economically feasible. Cost has an interesting way of changing with the passage of time, chiefly due to improved methods of manufacture. Transistors, for example, have dropped about two orders of magnitude in price in the last decade. Indeed, it is predicted that within a short time, the price of transistors and diodes will be comparable to that at present of diodes and resistors, respectively. Projected, rather than present costs should be considered. Perhaps the best basis for cost comparison would be the magnetic core memory, because of its great present (and probably continuing) popularity, and because this popularity has driven the cost of these memories down to a value near their fundamental minimum price. This price is around $0.60 per bit including electronics for a thousand word memory. The CD-I cells used for chemistors in this study cost $0.77 in lots of a hundred thousand. If the diodes were only $0.10 (projected), the cost would be about $0.97 per bit excluding electronics. Recognizing that the cost of a magnetic core memory is roughly evenly divided between the core stack and its associated circuitry, and that this circuitry is nearly identical to that necessary for a chemory of equal size, the circuitry cost for a thousand word chemory would be about $0-30 per bit. The reduction in the number of transistors and attached components must also be considered. Two out of the fairly common three amplification stages may be omitted in a chemory sense amplifier. The price of these stages, including labor, could be $25-00 each. For an m bit word, the saving would be 50 m dollars. The saving per bit would be 129 •2-—— = $0.05 for a thousand word memory. io\ Thus, the cost for a 1000 word chemory would be about $0.97 + $0.30 - $0.05 = $1.22 per bit. Still other considerations affecting cost would be 1. reduction in cell size, 2. special additional cell features (see Section 10.5)^ 3. increased production if the chemory became popular, k. the possibility of building a chemistor with integrated electrolytic diodes sharing a common electrolyte. Initially then, the cost of a chemory might be two or more times that of a core memory; the cost would almost certainly drop in time, however (if there were enough interest), possibly to a comparable value. 10 . 3 Recommended Cell Modifications for Chemistor Use 1. Construction employing sintered plates with a Polypor separator. 2. Use of structurally robust containers. 3. Employment of one of the following devices to prevent excessive over-discharge hydrogen pressures: A. Make the negative electrode capacity the 3 limiting value. 130 B. Place between the electrodes a separator containing a nonconductive metallic compound so that, when the polarity is reversed, the compound is reduced to k metal and connects the electrodes. C. Make one end of the cell flexible so that extreme internal pressure would cause it to flex and temporarily break electrical contact with one of the electrodes; the contact would be reestablished when the gases were reabsorbed (this means could also be used to prevent failure due to excessive gas pressure resulting from overcharge). 10. ij- Further Study Further study could be directed toward: 1. Discovering a symmetrical cell so that polarity discrimination could be used, 2. Constructing a chemistor integral with its diodes, 3. Finding a way to use a common electrolyte for an entire chemory, h. Building a large scale chemory, 5. Finding the reasons for the anomalous behavior of the faradaic impedances, 6. 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