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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS -1963
ORAL-P_3228
Conf.670812--/
MASTER
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AUG 22 1967.
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DEPENDENCE OF THE MÖSSBAUER ISOMER SHIFT ON THE DEGREE OF SPATIAL
ORDER FOR COPPER GOLD ALLOYS**
P. G. Huray, Louis D. Roberts, J. 0. Thorson.
Oak Ridge National Laboratory
stir
and
80
13.00, MA 165
University of Tennessee
Many experimental investigations have been made which show that the
spatial ordering of atoms in alloys has a great influence on the alloy
properties.
It has been shown that ordering can induce changes in the mag-
netic, electrical and mechanical alloy properties, for example. Consequently,
both experimental and theoretical studies of the ordering process and about
how it affects the physical properties of a system are of much practical
interest. The study of the order-disorder transformation is also.of impor-
tance from the point of view of theoretical solid state physics in develop-
ing a better understanding of the nature of the interactions between atoms
and electrons in solids.
Thus far no detailed studies of the electronic charge of the indi-
vidual alloy atoms as a function of the degree of order have been made. It
is now possible to make studies of the charge density near the nucleus by
the use of the isomer shift AE of the Mössbauer effect. Several years ago
preliminary measurements of AE for Cu,Au indicated that the charge at the
19 Au nucleus became slightly more negative as the alloy was ordered. In
this paper we present a more detailed study of this effect. Figures 1 and
2 show the results of these investigations to date. Figure 1 gives the
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isoner shift of several ordered and disoriered alloys as a function of com-
position. Figure 2 shows the data of Fig. I from which the straight line
h e
c
has been subtracted in order to more easily demonstrate the isomer shift
changes involved.
i malno recimo vietoverende menina de
We will define
DE as
n
13 = ken Flv a110210312 - 11 Au(0,12}
mi
(1)
my
bonnements on
where k is a calculable constant, n is a factor which depends only on nuclear
parameters, and lv alloy(0)12 ana lv Au (0) 12 represent the charge density
at the gold nucleus in the alloy and in pure gold respectively." One would
then expect a difference in the isomer shift for the ordered and disordered
alloys if there is a difference in the charge densities at the gold nucleus
for these two cases.
(2a)
(2a)
Skord. = xin {10aw.ora. (09 je lauros, e}
Bate. = kx í Waz.die.(osje. lix au copif}
(20)
SO
( AEord. - AEgis.) = kn ( 1 Va2.oxa. (0)12 -
147. dis.(0)2}
(3)
From the experimental evidence given in Figs. 1 and 2, herefore,
one can conclude that there is in fact a difference in the charge density
at the gold nucleus for the ordered and disordered cases.
In the theory of metals, it is often convenient to think of a pure
metallic sample as a single potential well for the conduction electrons.
The Bloch wave functions, Vk (r), which give a solution to the correspond-
ing quantum-mechanical problem extend throughout the entire sample. To make
a first order correction to this treatment in order to obtain a description
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of an alloy instead of a pure metal, we shall assume that the charge density
at a point in space is composed of a uniform charge density plus an
additional term which accounts for the modification of this screening charge
density due to the two different kinds of atoms (Au and Cu) in the alioy.
In this sense one could say
(4)
where
is the charge distribution associated with the screening
of the ion at the yon lattice site.
This type of treatment assunes that
the electron scattering or screening effects may be considered as perturba-
tions on a uniform charge density distribution. In a quantum mechanical
treatment starting from first principles, one would consider the charge
dersity as resultir.g from che square of the sum of a set of wave function
amplitudes. We suggest that our model is qualitatively that which would
arise from this squared sum if the cross terras between these amplitudes
are neglected.
The charge density at a specific gola nucleus located at F
is
then expressible as
P (FA) = P + § Pau Fau - 7:) + Poul Pau - Pre (5)
where F, and 7, denote Au and Cu ion positions art: Pau and Pcu are the
screening charge distributions surrounding the Au or Cu ions. By adding
and subtracting on the right hand side ? Pour - 7), & tern which
woulè correspond to putting Au atoms at Cu positions, we obtain
EGAL NOTICE
W
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States, nor the Commission, nor any person acung on behalf of the Commission:
A. Makou any warranty or representation, expressed or impiled, with respect to the accu-
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printely owned rights; or
B. Asnumos uy llabilities with respect to the use of, or for damages resulting from the
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with the Commission, or his employment with such contractor.
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WW.
otrau) = 80+ C
Pau Fau-) + De Pau Gau-FI +
Pau
. O
' AU
AU J
K
DP (Faux)
(6)
where
AP (FA4 - Ex = cuffau - -
P Au Au - Fred
.
The term in parentheses of Eq. (6) is now just the sum over all lattice
sites p of Auran - 7). We shall denote the sum of the first three-
terms on the R.H.S. of Eq. (6) as IV Auro) * In the limit of pure gola
this is the charge density seen by the gold nucleus.
Thus Eq. (6) becomes
pliab) = lv Au (osia + Ap (Eau
(7)
If now we consider the sum over all Cu lattice sites, Ike as being
carried out by summing over the n, cu atoms in the 1" shell of neighbors
about the gold nucleus at Fan we obtain
th
Therefore
D E ad = lv ru (0) 18 + g soliau - 73). (8)
I a1204(0)2 = (PLEAU? = IN AU (OTS + f (n. } AP EN - E37
(80)
The local order of a given alioy is usually described by the short range
order parameters a, for which
Kris = mcu ºs (1 - «?
where man is the atomic fraction of Cu atons in the alloy and c, is the
total number of atoms in the ith shell. Thus Eq. (86) becomes
th
IV 41209(0)12 = laurosiat şi cu ºs (1 - az) ap (FA- 7). (9)
Comoining Eqs. I and 9 we obtain
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}
c.
n
o
to kn
Cuina
* Au i
na iya (0)2}.
(10)
In the limit of complete disorder, all of the Q, are equal to zero
for all alloy compositions and in the limit of pure gold i laurosia
VAGO) 13} is equal to zero. If we assume that the latter quantity
remains small or equal to zero for all compositions, Eq. 10 has the form, a: = 0,
of a straight line with AE 700 ~ man,' This is the straight line
shown in Fig. 1. „Then, within this model the points shown in Fig. 2 (i.e.
the experimental data from which this straight line has been subtracted)
are described by
8 AE 1107 = - cu km
cez sp (Pau - Fig
.
(11)
This expression and Fig. 2 then explicitly display the dependence of the
isomer shift on the order parameters.
e mes
Approximate values for the order parameters , and , have 'been
obtained by X-ray methods for the compositions CuAu and Cuau. Cowley has
used a theoretical model to obtain values for , and , as a function of
composition which agrees reasonably with these measured values. These cal-
culations were made for disordered alloys at 770°C whereas our disordered
samples were annealed at 600°c and then quencheå. Our measurements were
made at 4.2°K The solid line in Fig. 2 is a plot of Eq. 1.1 using the
values for Q, and Q, at 770°C as a function of composition as given by
Cowley and neglecting all higher terms in Q. The parameters kn 0 ? (FA-F)
and kn Op (Fau-) for this line were obtained by fitting Eq. 410) to the
AE 70 values determined experimentally for the case of ordered Cu,Au
80
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(cy = 12, Q = -, ca = 6, Q2 = ?) ana for 1 atomic percent Au in Cu
(cy = 12, Q2 = 0, ca = 6, Q2 = 0). The calculated values for these two cor-
stants (in terms of an isomer shift, mm/sec) are
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In Ap tau - 7,) = 0.296 mm/sec
an sp (Tau - ) = 0.079 mm/sec
.
The values for Q, and dy given by Cowley should apply qualitatively
to our discrdered alloys. This disorder curve derived from parameters
determined from our measurements of ordered alloys, fits nicely to the
ooserved Edis, value at the composition Cu Au but does not show the
structure exhibited by the measured Eais as a function of composition.
Whether this deviation is due to the oversimplicity of our model for
DE 24 or to the approximate nature of the model for the short range
order parameters ay is not clear. We note, however, that the theoretical
model of Cowley for Q, and ~, gives only a smooth behavior for these parane-
ters as a function of composition.
The model used here implies that there are radial charge distribu-
tions surrounding each gold or copper atom in the alloy Pau or D cu
which are at least approximately independent of alloy composition and
state of order. When the composition or state of order is changed, the
change of E, or equivalently of lv 200101, is due to the change
of the relative number of P Au and cy charge distributions and to the
changes of their relative positions in space.
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REFERENCES
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Research sponsored by the V. S. Atomic Energy Commission uncer contract
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with the Union Carbide Corporation.
Oak Ridge Graduate Fellow from the University of Tennessee appointed by
Oak Ridge Associated Universities.
es
Consultant, now at Memphis State University, Memphis, Tennessee.
1. Roberts, I. D., Becier, R. I., Obenshain, F. E., and Thomson, J. O.,
Phys. Rev. 137, A895 (1965).
2. Cowley, J. M., Phys. Rev. 77, 669 (1950).
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FIGURE CAPTIONS
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z'ig. 1. Mössbauer isomer shift of the 77.4 kev samma ray of the 'Au
nucleus in several Cu-Au alloys which have various degrees or
spatial order. The isomer shirt relative to pure gold is
A E = isomer shift (relative to golå in Pt) + 1.204 = 0.020 m/sec.
The straight line represents the isomer shift expected for totally
disordered alloys according to a simple model. The other solid
line is the isomer shift dependence calculated for partially
disordered alloys. Eq. (10), text,
7is. 2. Mössbauer isomer shift data of Fig. I from which the straight
line shown there has been subtracted.
This line corresponds to
complete disorder. Thus AE corresponds to that part of the
i somer shift due to spatial order of the alloy. The solid line
is the isomer shift dependence calculated for partially äisorderea
alloys. Eq. (11), text.
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3.0
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- CALCULATED FROM
SHORT RANGE ORDER
PARAMETERS
ISOMER SHIFT (mm/sec) RELATIVE TO AU IN PI
W DISORDERED POINT
(QUENCHED FROM 600°C)
O ORDERED POINT
(SLOW COOLED FROM 410°C)
Još
THE ERROR BAR IS THE SIZE OF THE POINT.
20 40 60 80
100
Au
100
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ATOMIC % AU IN Cu
.
.
.
1
.
Fig. 1
.
1.5
i will entertainment
int
nsielle mani theo
i
..
--
-
-
-
8(DE)= AELOY-14
Fo% AU-DEPURE AUIX
IN CU
(AE) (mm/sec)
0 ORDERED: SLOW COOLED FROM 400°C
O DISORDERED: QUENCHED FROM 600°C
ok
-
--
0
0.05
0.100.150.200.25
X, (atomic fraction Au in Cu)
0.30

END

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DATE FILMED
9 / 29 / 67
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