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MICROCOPY RESOLUTION TEST CHART
NATIONAL BUREAU OF STANDARDS - 1963
les
66-90
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Conf-660924-1
NOTE: This is a draft of a paper being submitted for publication. Con- .
tents of this paper should not be quoted nor referred to without
permission of the authors.
· SEP 2 8 1966

MASTER CESTI PRICES
HC. $ 7.00 MN_50
CFSTI PRICES
ELECTEON SPIN RESONANCE SPECTRA OF Dy 3* In Tho, AND Ceo,
..*.*
.-
M.
M. M. Abraham, C. B. Finch, L. J. Raubenheimer,
2. M. El Saffar, and R. A. Weeks
*
*.
*
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RELEASED FOR ANNOUNCEMENT
IN WUCIEAR SCIENCE ABSTRACTS
LEGAL NOTICE
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The report wus prepared as an account of Government sponsored work. Noier the United
States, bor the Commission, por may person acting on behalf of the Comalaston:
A. Makes way warranty or representation, expressed or implied, with respect to the accu-
racy, completeness, or wefulness of the information contained in this reports or that the use
of any information, apparatus, mothod, or procou: daclound in this report may not infringe
privately owned rights; or
B. Asames way liabludes with respect to the use of, or for damages remulting from the
use of any information, apparatus, method, ar process disclosed in this report,
As used in the above, "per on acttag on behalf of the Commission" includes wy om-
ployee or coatractor of the Commission, or employbe of such contructor, to the extent that
such employs or contractor of the Commission of employee of such matractor prepares,
disseminatos, or provides accou to, way information purkuat to his employmeat or contract
wila the Commission, or his omployment with such contractor.
.
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SOLID STATE DIVISION
OAK RIDGE NATIONAL LABORATORY
Operated by
UNION CARBIDE CORPORATION
for the
U. S. Atomic Energy Commission
Oak Ridge, Tennessee
* August 1966
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ELECTRON SPIN RESONANCE SPECTRA OF Dy S* IN THO, AND
M. M. Abraham, C. B. Finch, L. J. Raubenheimer,
2. M. El Saffar, and R. À. Weeks
Solid State Division, Oak Ridge National Laboratory
Oak Ridge, Tennessee
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Single crystals of Tho, and Ceo, (fluorite structure) doped with
0.5 atomic weight percent impurities of isotopically enriched Dy?
(94% even-even isotopes) were grown. Electron spin resonance (ESR) .
measurements at -10 Gcps and liquid helium temperatures reveal spectra
with symmetry axes along the 4 crystal (111) axes. For Tho, 84 = 1.625
+ 0.002, 8. = 9.95 + 0.05 and for CeO2 811 = 1.632 + 0.002, 8. = 9.98 g.
0.05. An additional line is observed and attributed to a 11 >+1- >
transition between the levels of a ground state le quartet in a cubic'::.:.
crystal field. For Thoz, 85100) = 4.566, 8111] = 4.323, 8[110] =
4.386, and for Ceoz: 811001 4.433, 811111 = 4.401, 85110) * 4.411. with
0.1% error. These data are sufficient for a calculation of the ratio ".
of the cubic crystal field 4th and 6th order parameters. At 20°K no .
spectra were observed, which made it impossible to detect a low lying
Ty doublet as observed in the case of the isomorphous Cafy. All line
widths were larger than those for other rare-earth ions in these crystals
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and were 20 to 40 gauss.
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*Research sponsored by the U. S. Atomic Energy Commission under contract
with the Union Carbide Corporation.
SEZ
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INTRODUCTION
· The electron spin resonance (ESR) spectra of rare earth ions incor.
porated into the fluorite structures of thorium (1) and cerium dioxides (2)
... have furnished information about local crystal field symmetries. The
trivalent rare earths replace the tet ravalent thorium or cerium ions, and
cubic local fields may occur whenever the necessary charge compensation
is far removed. The presence of nearby charge compensation would add an
axial component to the crystal field, which would lower the syminetry. In
general, different types of charge compensation mechanisms give rise to
different local crystal fields, and all may be present in the same single
crystal.
|
2.
EXPERIMENTAL
Single crystals of Tho, and Ceo, doped with 0.5 atòmic weight percent
impurities of isotopically enriched Dy 4* (94% even-even isotopes) were
grown by a solution technique. () (The hyperfine structure of the Dys
and Dyos isotopes would make the interpretation of the data more dif- ' :
ficult.) ESR measurements at : 10 Gcps and at liquid helium temperatures
reveal spectra with symmetry axes along the four crystal (111) axes. .
For Thoz, 8,1 = 1.625 + 0.002, 8. = 9.95 + 0.05, and for Ce0g, 811 = .
1.632 0.002, 8. = 9.98 1 0.05.
An additional line is observed and attributed
transition between the levels of a ground state in quartet in a cubic
crystal field. For Thoz, 811001 - 4.566, 81111 = 4.323, 81101 = 4.386,
and for CeO2, 8[100] 4.433, 8[111] • 4.401, 8(110) = 4.411 with 0.1%
error: . . ..
error.
-3-
THEORY
.':
The J = 15/2 ground state for the trivalent dysprosium ion is split
by the cubic crystal field into two doublets and three quartets. A point
.
charge model predicts that either a I, doublet or a s quartet would lie
lowest. In isomorphous Cafy, Bierig and Weber (4) showed the 18 quartet. ·
is lowest with the s'y doublet about 8 cm-- higher. Using the formalism
of Lea, Leask and Wolf(5) (Fig. 1), the parameter x is defined to measure
the relative importance of the fourth and sixth order terms in the ex- .
pansion of the cubic crystal field potential. In Figure 2 (from Lea,
Leask and Wolf), the energy eigenvalues for J = 15/2 in a cubic crystal
field are plotted as a function of the parameter x. The Zeeman splitting
for 'a 1doublet is isotropic, while for a 88 quartet, the Zeeman split- .
ting is not isotropic and depends upon the direction cosines of the
magnetic field relative to the cubic axes. Bleaney () has formulated a
spin Hamiltonian (Fig. 3) to describe such a situation in terms of the
parameters 8 and f. Using Ayant's equivalent notation, the energies
are expressed in terms of the parameters P and Q for the magnetic field
along the [100], [111], and [110] directions. Some special cases for :
particular values of P and Q are also given. With the magnetic field
in a (111) plane, ce4 + m4 + n 4) = 5, and the fg energy levels are in-
variant to magnetic field rotation. Therefore in this plane, transitions
between the rg levels are isotropic and easy to identify. Using the
Landé g-factor of 4/3 for Ny *, we may equate the experimental g-values
to transitions betwee
evels of the 18 quartet and
arrive at values for P and Q. Since the P and Q values are functions
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of the parameter x we may the: caicu ate x. Unfortunate y, p gives one
value for x while Q gives ano:ler va le for x. This inconsistency may
be removed by adjusting the Lardé g-actor to obtain different P and Q
T:02; A = 1.3111, P = 5.0386, C = 1. 413, x = 0.6833, and for CeO2; A =.
1.3115, P = 5.0456, Q = 1.6900, and ; = 0.6764.
DISCUSSION
The effective Landé g-factors, ., for the two dioxides may be com-
pared with the Tb free ion vallie of :.3225(8) and the intermediate
coupling value of 1.312. (%) Similar reductions of the free ion Landé
g-factor(10) calculated for simple Rissell-Saunders coupling have been
attributed to effects of covalency o: the inability to calculate pro-
perly tie admixture of higher states.
The x-values are slightly large : than the 0.6 value obtained for
Dy** in CaF, (4) and are comparable with x-values for other rare earth
doped crystais obtained from sit:er SR or optical measurements.110
At 20°K, no spectra were observed, which made it: impossible to
detect a low lying r7 doublet as observed in the case of the isomorphous
Caf. (4) The average g-tensors (8, * 29_)/3 for the axial sites of
7.18 for Tho, and 7.20 for Ce), are rery close to the expected g-value
of 7.43 for the 17 doublet. Spectra observed with a spectrometer
operating at 24 Gcps were identical ith the 10 Gcps spectra and no
additior.al lines were observed. All line widths were larger than those
for other rare earth ions ir ti.ese crystals("? (2) and were 20 to 40 gauss.
WWW W
WWLWRthew
91
1
RI.FERE.
VES
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.
?
--
1. M. Abraham, R. A. Kieeks, Ci. W. Clark and C. B. Finch, Phys. Rev.
23?, A138 (1965); M. M. Alraham, E. J. Lee and R. A. l'eeks, J. Phys.
Chem. Solius 26, 1249 (1965).
2. .1. Abranar., R. A. leeks, G. i. Clark and C. B. Finch, Phys. Rev.
(in ress); 1. 1. Abraha-, I. d. Boatner; C. B. Finch, E. J. Lee,
and R. A. leeks, J. Phys. C:em. Solids (in press).
3. C. B. Finch and G. Wayne Clark, J. Appl. Phys. 36, 2143 (1965);
C. B. Finch and G. Wayne Clark, J. Appl. Phys. (in press).
R. 1. Bierig and M. J. Keber, Piys. Rev. 132, 164 (1963); k. Low,
Phys. Rev. 134, A1479 (1964).
5. . R. Lea, N. J. M. Leask and X. P. Holi, J. Phys. Chem. Solids 23,
2581 (1962).
6. B. Bleaney, Proc. Phys. Soc. (London) 73, 939 (1959).
7. Y. Ayant, Paramagnetic fiecorac , Vol. I, p. 267 (edited by W. Low,
Academic Press, New York, 1963).
3. S. Penselin and ä. Schilprann, woted by B. f. Judd and I. Lindgren,
Phys. Rev. 122, 1802 (1961).
9. B. G. Wybourne, J. Chem. Phys. 56, 2301 (1962).
10. See for example, D. Descamps and Y. Nerle d'Aubigne, Phys. Let. 8,
5 (1964); I. C. Chang and N. W. Anderson, Phys. Let. 13, ,112 (1964);
1. Low and R. S. Rubins, Phys. Rev. 131, 2527 (1963).
E. S. Sabisky, Phys. Rev. 141, 352 (1966) and references therein:
F. R. Merritt, H. Gugger.nei. ani C. G. B. Garrett, Phys. Rev. 145,
11.
wa
2
18
(1966) and references therein.
ht
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FICURE C. PTICIS
Fig. 1.
Hamiltonian for cubic czys' al field. Tie O's are operators
whose transformatio: prope:ties are similar to spherical
harmonics. The B's determ: ne the strength of tlie crystal field.
231x
B4
tlia
For J = 15/2, F(4) = 60, F 6) = 13860, so
Energy eigenvalues for J = 15/2 in a cubic crystal field as a
Fig. 2.
function of the parameter ::.
Fig. 3
a) Spin liamiltonian for i& quartet according to Bleaney with
energy levels as a functio. of the direction cosines. Ayant's
notation is used to expres: the energy levels in three major
crystal directions. A is the Landé g-factor. b) The relation
between Bleaney's and Ayant's parameters with some special
cases as shown.

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ORNL-DWG 66-6958
Cubic Crystal Field Hamiltonian
*4 = ,10% + 5 0) + B,(09 – 21 04)
04 = (09 + 5 09) 06 = 0; – 21 0
. F(4) and F(5) are factors common to all the matrix elements
..
... Wx = B. F(4) W (1 – [x]) = B, F(6)
* BA F(4)
1 - [x] BF(6)
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ORNL-DWG 66-6918
*
(3)
N
100
af.0
GB
-0.6
-0.%
-0,2
s
7
tion
-200 Fy
4-300 .J = 23
Energy eigenvalues for J = 15/2 in a cubic crystal
field as a function of the parameter X.

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ORNL-DWG 66-6959
Spin Hamiltonian for r; Quartet
W = g BH. S + BĦ.53
"
()=1659 +389= {* * * c*1900* + a* *a*) – ]"}}
Denoting the ', quartet as a
P=(!) e-(K)
E
= IP ABH and † Q ABH
E, - A$[} vcp? +Q%) + PⓇ) and Age [ce - or]
Lee = ABH
2 + 02) +
and ABH
(P-
2
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[daz – (zət qable to ta] uøv=olla
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[oar –(40+ pal1
and ABH
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ORNL-DWG 66-6960
3g 27f
AP= td
2 , 8
1Q=-t-
con
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/ Р
not
g
12
Special Cases
P - 3Q = 0 The S3 term vanishes and the energy levels are
equally spaced for all directions of the magnetic field
E = 3Q ABH and I QABH
(2)
P=- The levels degenerate into two doublets with
E = IPABH which are also invariant to the magnetic field di-
rection
PE+Q
E100 = 1 PABH
Eu = IV PABH and O
:: 8,0 - [145]pXpu ont [ 1 ] Papu
0
1
*
*

•
END
VE,
DATE FILMED
10/25 /66






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