FORM FACTOR MEASUREMENTS IN CeTe

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FORM FACTOR MEASUREMENTS IN CeTe

J. Boucherle, D. Ravot, J. Schweizer

To cite this version:

J. Boucherle, D. Ravot, J. Schweizer. FORM FACTOR MEASUREMENTS IN CeTe. Journal de

Physique Colloques, 1982, 43 (C7), pp.C7-263-C7-271. �10.1051/jphyscol:1982738�. �jpa-00222345�

Colloque C7, supplément au n°12, Tome 42, décembre 1982 page C7-263

FORM FACTOR MEASUREMENTS IN CeTe

J.X. Boucherle* D. Ravot* and J. Schweizer*

*DRF/DN, CEN-G, 85 X, 28041 Grenoble Cedex, France

*'*CSRS, ER 60-209, 1, Place A. Briand, 92190 Meudon, France +ILL, 156 X, 28042 Grenoble Cedex, France

Résumé. - Les mesures de facteur de forme ont été faites à T = 1,5 K et T = 12,8 K pour la composante ferromagnétique induite par un champ appliqué de 4,65 T. Aux deux températures, l'anisotropie du facteur de forme est importante et caractéristique d'un niveau fondamental de champ cristallin YT. Les résultats sont discutés à l'aide du modèle habituel de champ cristallin et d'interactions d'échange.

Abstract. - Form factor measurements have been performed at T = 1.5 K and T = 12.8K on the ferromagnetic component induced by an applied field of 4.65 T. At the two temperatures the anisotropy of the form factor is important and characteristic of a Tj ground state. The results are discussed in terms of the usual model involving crystal field and exchange interactions.

1. Introduction. - The magnetic properties of cerium monochalcogenides in general, and in particular of CeTe, have been very little investigated. In these compounds, which crystallize in the NaCl type structure, the cerium is trivalent and the ground state is 2Fs/2 (1). From the magnetic susceptibility, measured at low tempe- rature by Loginov et al. (2) CeTe was thought to be an antiferromagnet. A discre- pancy existed between the ordering temperature reported by Loginov et al. (2) and Hullinger et al. (3). Later, neutron diffraction experiments (4,5) have clearly established that below T^ = 2 K, CeTe orders into a type II antiferromagnetic structure, with a [111] easy axis. The magnetic moment, 0.2 uR per cerium atom, is very small, much less than the value expected for a T7 ground state. However, high field investigations of the magnetization (2) have shown the occurence of a meta- magnetic transition at 20 kOe : for higher fields, the moment reaches values as large as 0.75 uB/Ce.

The very low value of the cerium moment in the antiferromagnetic state is puzzling and unexplained. It may be related to some interaction between the 4f electrons and the conduction band as expected in Kondo compounds. In order to get more infor- mations on that problem, pnd with the hope to shed some light on the cerium ground state, we have performed form factor measurements on a CeTe single crystal with polarized neutrons.

2. Experimental. - a/ Sample_grep_aration. Single crystals were obtained by direct reaction between cerium and tellurium. The required amounts of materials were melted together in a sealed molybdenum crucible. They were rapidly heated to 2 000° C and then slowly cooled with a rate of 4° C/h. The purities of the starting elements were 6N for tellurium and 3N for cerium. All the handling of materials was performed in a purified argon atmosphere, to avoid cerium oxidation in air.

Single crystals of some mm3 were cleaved from the crystallized mass. They appeared to be single phase by X ray measurements, with a lattice constant 6.361 (4) A. From microprobe analysis and spectrographic emission they were found to be stoechiometric with a 2 % uncertainty.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982738

C7-264 JOURNAL DE PHYSIQUE

b / Neutron d i f f r a c t i o n experiment. The measurements were performed on t h e d i f f r a c t o - meter D3 of t h e ILL. The s i n g l e c r y s t a l (2.66 x 2.12 x 1.08 m3) was a l i g n e d w i t h a

twofold a x i s along t h e a p p l i e d f i e d (H = 46.5 kOe).

The magnetic s t r u c t u r e f a c t o r s were measured by t h e f l i p p i n g r a t i o technique (R = I+/I-) a t two temperaturgs. A t T = 12.8 K , 29 r e f l e x i o n s w e r e c o l l e c t e d i n t h e h o r i z o n t a l p l a n e a t

X

= 0.90 A. A t t h e lowest temperature (T = 1.5 K), 33 r e f l e c - t i o n s wer& measured i n t h e h o r i z o n t a l p l a n e and 24 o u t s i d g t h i s p l a n e a t

X

= 0.90 A. 8 r e f l e c t i o n s were a l s o measured a t

X

= 0.72 A i n o r d e r t o perform e x t i n c t i o n c o r r e c t i o n s .

Moreover i n t e g r a t e d i n t e n s i t i e s were a l s o measured a t t h i s temperature i n o r d e r t o check t h e n u c l e a r s t r u c t u r e : 48 r e f l e c t i o n s corresponding t o 14 independent s t r u c - t u r e f a c t o r s have been c o l l e c t e d .

C / E x t i n c t i o n c o r r e c t i o n . The comparison of t h e f l i p p i n g r a t i o s measured f o r t h e same r e f l e c t i o n a t d i f f e r e n t wavelengths a l l o w s a good d e t e r m i n a t i o n of t h e e x t i n c - t i o n phenomena. We have r e f i n e d t h e two parameters which c h a r a c t e r i z e t h e mosaic c r y s t a l : dimension of p e r f e c t b l o c k s ( t = 16 ( 4 ) p ) and mosaIc spread (11 = 2.8 (6)').

d / Nuclear s t r u c t u r e f a c t o r : Fenni l e n g t h of t e l l u r i u m . To perform t h e c a l c u l a t i o n of t h e n u c l e a r s t r u c t u r e f a c t o r s , t h e main problem concerns t h e s c a t t e r i n g l e n g t h of t e l l u r i u m . Several v a l u e s have been published : 0 . 5 6 ( 2 ) . 1 0 - ~ ' cm by a m i r r o r technique ( 6 ) , 0.543(4). lo-'' cm f rorn t h e C h r i s t i a n s e n f i l t e r method (7) and 0.580(6). 10-I' cm from d i f f r a c t i o n measurements on t e l l u r i c a c i d (Te(0H) ^{6 )} ( 8 ) . A s t h e s c a t t e r i n g l e n g t h of cerium i s r a t h e r w e l l known (9,101 a refinement of t h e n u c l e a r s t r u c t u r e h a s been undertaken a t T = 1.5 K, i n v o l v i n g t h e s c a t t e r i n g l e n g t h

of Te and t h e thermal v i b r a t i o n parameters of t h e two Ce and Te atoms. A s measured i n t e n s i t i e s i n c l u d e b o t h magnetic and n u c l e a r c o n t r i b u t i o n s , t h e s e p a r a t i o n of t h e n u s l e a r s t r u c t u r e f a c t o r s i m p l i e s combiging both unpolarized ( i n t e g r a t e d i n t e n s i t i e s

Z ( H ) ) and p o l a r i z e d n e u t r o n r e s u l t s (y(H) r a t i o s ) ( s e e f o r example ( 1 1 ) ) :

-+

-

where y(H), t h e e x t i n c t i o n c o r r e c t i o n , i s c a l c u l a t e d u s i n g t h e parameters p r e v i o u s l y determined. The r e s u l t s corresponding t o a r e l i a b i l i t y f a c t o r R = 1.9 % a r e :

We have used bCe = 0.476. lo-'' cm ( 9 ) . The f i t t e d v a l u e f o r bTe i s i n e x c e l l e n t agreement w i t h t h a t of r e f . ( 8 ) . Moreover i n r e f . (7) t h e small v a l u e 0.543.10-~' cm was obtained a f t e r a l a r g e water contamination c o r r e c t i o n which d e c r e a s e s d r a s t i c a l - l y t h e v a l u e f o r bTe. Moreover t h e v a l u e 0.580. cm h a s been confirmed r e c e n t l y on PbTe (1 2 ) . We have a l s o v e r i g i e d t h a t t h e resonance peak of t h e 3 ~ e ( n a t u r a l abondance 0.87 %) a t = 0.187 A does n o t e x p l a i n t h e d i f f e r e n c e s due t o resonance terms (Ab' and iAb").

Using t h e v a l u e bTe = 0.580 (5).10-" cm we o b t a i n t h e magnetic s t r u c t u r e f a c t o r s . The main p a r t of t h e r e s u l t s concerns s t r o n g n u c l e a r r e f l e c t i o n s (h,k,& even).

However some r e f l e c t i o n s w i t h small n u c l e a r s t r u c t u r e f a c t o r s have a l s o been measured.

3 . Data a n a l y s i s .

-

The magnetic s t r u c t u r e f a c t o r s FM(hkL) a r e t h e F o u r i e r c o e f f i - c i e n t s of t h e m a g n e t i z a t i o n d e n s i t y i n CeTe. I n t u r n , t h i s magnetization d e n s i t y r e f l e c t s t h e s t a t e of cerium i n t h i s compound. The a n a l y s i s of t h e d a t a w i l l t h u s p r o v i d e information on t h i s s t a t e . P r a c t i c a l l y , two approaches a r e p o s s i b l e :

mine directly the ground state wave function by comparing the shape of the corres- ponding magnetization density to that of the experimental density.

-

At temperatures where several levels are populated the former approach is unrea- listic due to the large number of coefficients to be determined. In such a case it is preferable to check a model for the cerium atom and to determine the best parameters of the corresponding Hamiltonian, that is those which provide, at the temperature of the experiment, a magnetization density as close as possible to the experimental density.

a/ Ground state wave function. The experimental magnetic amplitudes, measured at T = 1.5 K, are far from lying on a monotonic curve, indicating a strong anisotropy of the magnetic distribution (see figure

1).

The (hOO) reflections lie above the (Okk) reflections, all the other points being scattered between these two extremes.

In a cubic symmetry, the J = 512 ground multiplet is split into a doublet r7 and a quartet

Ts.

These two states present a very different form factor anisotropy (13).

The type of anisotropy observed for CeTe corresponds to the T 7 case. However the amplitude of this anisotropy is smaller than for the pure r7.

With a magnetic field applied along a twofold axis, the ground state wave function can be written as :

I@>

= C aM1.JM> with

AM

= 2

M

In particular the 2 states of r 7 are :

One may calculate the form factor of such a

4f

level using the tensor operator method ( 1 4 ) :

11

-

where Y$,(H) are spherical harmonics of the scattering vector, <jK' (H)> radial integrals taken from a Dirac-Fock calculation (1 5) and C K I I Q I I K I ~ I coefficients calculated from values tabulated for rare earth (16).

On the other hand it has been shown (17) that it is possible to use expression (1) to determine the ground state wave function coefficients aM. In the case of CeTe, a reduction factor k has been introduced in the procedure, which accounts for a possible non alignement of the magnetic moments (CeTe is antiferromagnetically ordered at T = 1.5 K) or any other moment reduction.

The ground state determined this way is (table

1)

:

This wave function, close to r7, has nevertheless a fair amount of

re

admixture.

The agreement between observed and calculated magnetic amplitudes is excellent as shown in figure 1 and table 3. In particular the extrapolated value of F(000) is very close to the bulk magnetic moment (18). There is almost no magnetic contribu- tion other than that of the 4f electrons of the ce3+ ions.

Table 1 : Ground state wave function : refinement parameters.

R

I I I I

x

Ground state wave function

T(K) k

C7-266 JOURNAL DE PHYSIQUE

Fig. 1 : Magnetic amplitudes at T = 1.5

K

: observations (full symbols), calcula- tions with the fitted ground state wave function (open symbols). (For more clarity, only the reflections in the horizontal plane have been included).

1.00

Fig. 2 : Magnetic amplitudes at T = 1.5 K : observations (full symbols), calculations with the C.E.F. and exchange Hamiltonian

(A

= 8 K, A = -2.8 K) (open

symbols).

-

r

0

*

<

C e T e T=1.5K HzL.65T ( G r o u n d S t a t e )

- .. -

.. .. ^- 1

(k :

moment reduction factor;A

= 360 BI, :

crystal field splitting

;

X

:

exchange parameter

; X2,

R

:

reliability factors).

Table

3 :

Observed and calculated magnetic amplitudes at T

= 1.5

K.

h k 1

0 0 0 1 1 1 2 0 0 0 2 2 3 1 1 2 2 2 4 0 0 1 3 3 4 0 2 0 2 4 4 2 2 5 1 1 3 3 3 0 4 4 6 0 0 2 4 4 6 0 2 5 3 3 6 2 2 4 4 4 -6 0 4 0 4 6 6 2 4 2 4 6 8 0 0 8 0 2 6 4 4 8 2 2 0 6 6 2 6 6 -8 0 4 0 4 8 8 2 4 4 6 6 8 4 4 10 0 0 0 6 8 10 0 2 2 6 8 -8 2 6 10 2 2 6 6 6 -10 -4 0 4 6 8 8 4 6 10 2 4 0 8 8 10 4 4 2 8 8 8 6 6 0 6 10 -10 2 6 2 6 10 12 0 0 4

a

8 12 0 2 10 4 6 12 2 2 L

Calculations Oround State 0.7283 0.6760 0.6793 0.5792 0.5910 0.5438 0.5563 0.4336 0.5045 0.4366 0.4553 0.4618 0.3910 0.3054 0.4133 0.2938 0.3784 0.3225 0.3488 0.2617 0.2964 0.1962 0.2738 0.1901 0.2892 0.2679 0.2171 0.2516 0.1178 0.1170 0.2147 0.1162 0.2043 0.1138 0.1693 0.1954 0.0632 0.1829 0.0641 0.1453 0.1746 0.1052 0.1505 0.0654 0.1228 0.1462 0.0290 0.1257 0.0310 0.0916 0.0278 0.1080 0.0287 0.1297 0.0356 0.1225 0.0955 0.1181 sine/l

0.000 0.136 0.158 0.223 0.261 0.273 0.315 0.343 0.352 0.352 0.386 0.409 0.409 0.446 0.473 0.473 0.498 0.516 0.522 0.546 0.568 0.568 0.589 0.589 0.630 0.649 0.649 0.668 0,668 0.687 0.704 0.704 0.722 0.739 0.772 0.788 0.788 0.803 0.803 0.803 0.818 0.818 0.848 0.848 0.848 0.863 0.891 0.905 0.905 0.918 0.918 0.932 0.932 0.945 0.945 0.958 0.971 0.971

A m8K 1 =-2.8K

0.7281 0.6760 0.6791 0.5796 0.5912 0.5445 0.5557 0.4341 0.5044 0.4371 0.4563 0.4612 0.3926 0.3049 0.4113 0.2943 0.3775 0.3247 0.3491 0.2640 0.2969 0.1952 0.2757 0.1900 0.2856 0.2655 0.2202 0.2504 0.1148 0.1151 0.2147 0.1161 0.2053 0.1144 0.1719 0.1906 0.0598 0.1793 0.0616 0.1476 0.1719 0.1080 0.1493 0.0651 0.1263 0.1458 0.0239 0.1270 0.0269 0.0954 0.0255 0.1095 0.0270 0.1242 0.0339 0.1180 0.0983 0.1145 Obervations

0.7650 (300) 0.6682(397) 0.6922 ( 72) 0.5819 ( 52) 0.5751 (444) 0.5394(50) 0.5469 ( 51) 0.4237(1000) 0.5009(50) 0.4373 ( 47) 0.4542 ( 52) 0.3818(1088) 0.3067 (706) 0.3093(43) 0.4092 ( 64) 0.2949 ( 58) 0.3661(99) 0.2799 (563) 0.3462 ( 80) 0.2733 ( 78) 0.2904(111) 0.2022 ( 64) 0.2822 (104) 0.1890 ( 85) 0.2995 (152) 0.2890(105) 0.2236 (102) 0.2472 (186) 0.1092(87) 0.1349 (219) 0.1992 (370) 0.1224(250) 0.2092 (135) 0.1229 (171) 0.1799 ( 99) 0.1965 ( 96) 0.0507 (106) 0.2081 (146) 0.0781 (114) 0.1314 (187) 0.1865(183) 0.1198(131) 0.1285 (207) 0.0764 (214) 0.0920(179) 0.1354 (175) 0.0097 (101) 0.1417 (151) 0.0315 ( 95) 0.1039 (132) -0.0422 (481) 0.1382(310) 0.0673(472) 0.1207 (211) 0.0167 (211) 0.1710 (314) 0.1337 (577) 0.0887 (397)

C7-268 JOURNAL DE PHYSIQUE

b/ Crystal field and exchange model. To analyse the neutron data at 12.8

K,

as well as to look for a model of cerium which is valid at both temperatures (in the anti- ferromagnetic state and in the paramagnetic state), we have tried to optimize an Hamiltonian which represents the crystalline electric field, the exchange interac- tions and the applied field :

For the ce3+ ion, this Hamiltonian depends on 3 parameters : the crystal field parameter B4 (for J = 5/2, the sixt order parameter Bg is irrelevant and B4 is proportional to the crystal field T7-Ts splitting

A

: BI, = A/360), the exchange parameter

A

and the applied field H

ap'

The Hamiltoniar. (2) has bee used to fit the neutron data at each temperature. For

$

a given set of parameters, has been diagonalized, and the magnetic amplitudes of the tbcrmally averaged populated states have been compared to the experimental amplitudes. The set of parameters which fits best the data has been determined.

Inelastic neutron scattering measurements (18) have shown the existence of an inelastic contribution. This contribution was attributed to a crystal field transi- tion

r7-r8

with a splitting

A

of about 30

K.

Further, as CeTe orders antiferromagne- tically at low temperature (TN = 2 K) a negative and small value for the parameter 1 is expected.

The results of the determination of

A

and

A

by comparison with the polarized neutron data are summarized in table 2.

At

T

= 1.5

K,

a refinement which imposes

A

= 30 K ends up with a positive value A = 8

K

not compatible with the antiferromagnetic structure. The best refinement has been obtained for A = 8

K

and

X

= - 2.8

K.

The agreement between observed and calcu- lated amplitudes is excellent (see figure 2 and table 3).This model yields exactly the same form factor as that previously calculated for the best ground state.

However it is important to notice that the two calculations correspond to rather different schemes. In the first case the form factor was based on the ground state wave function only. Here, the two states of the r7 level, separated by 1.56

K

only, are populated, which implies a reduction of the magnetic moment and a slight modifi- cation of the ground state wnve function. This model is probably more realistic.

The two wave functions of the

r7

level are now :

At T = 12.8 K, the best refinement provides

A

= 40 K and

X

almost zero. Imposing

A

= 30

K

fits the experimental data very well also, with a value

X

=

-1 K

(see f.igure 3 and table 4 ) . However if one fixes

A

= 8

K,

the value which fits best the low temperature data, the agreement is not as good : the magnetization anisotropy which has been observed experimentally is poorly represented (see figure 4 and table

4).

In summary it is possible to find for each experimental temperature a set of para- meters for which the crystal field and exchange Hamiltonian (2) fits very well the data, but the 2 sets of parameters are different. The set of parameters which best accounts for the experimental data at both temperatures is

A

= 8 K, A = -2.5 K,but the agreement with the high temperature results is not really satisfactory.

Fig. 3 : Magnetic amplitudes at T = 12.8 K :observations (full symbols), calculations with the C.E.F. and exchange Hamiltonian

(A

= 30 K, 1 = -1.0 K) (open

symbcls)

.

2

-

0

.. -

," G 2 ⁰

- -

^{N C}

-

⁰

^-

^"

0 0 w

-

^"

- -

_{" G}

-

_{N 2}

- - ^-

⁰

N N

m N

-

O

- -

0 5:

-

^rn _m ^E!

-

0

-

_(D ^N

- -

^{Y m;}

-

-

_N

^L

"

- "

^{(D w}

" ^{- --}

^{iD m m}

- w

N

a -

w

-

(D ^{w -}

- m a "

N (D

iD

-

-

Fig. 4 : Magnetic amplitudes at T = 12.8 K : observations (full symbols), calculations with the C.E.F. and exchange Hamiltonian

(A

= 8 K,

X

= -2.5.K) (open

symbols).

1

- -

-

JOURNAL DE PHYSIQUE

Table 4 :

h k 1

4.

Conclusions.

-

The polarized neutron experiment has clearly shown that the magnetization of CeTe arises from the

4f

electrons of the cerium atom. The anisotro- py of the magnetization density has the same features as the

r7

state but the ground state of cerium is not pure r 7 and contains a large amount of

T*

admixture.

An

attempt to fit a crystal field and exchange Hamiltonian with a unique set of parameters A and A, does not fit well the current results and, is not in agreement with the crystal field parameter deduced from inelastic neutron measurements. In any case, such a model does not explain the low moment of cerium in the antiferro- magnetic ordered state and the other cerium properties in this compound.

0 0 0 1 1 1 2 0 0 0 2 2 3 1 1 2 2 2 4 0 0 4 2 2 0 4 4 2 4 4

6

0 0

a 2 2 4 4 4 8 0 0 6 IJ 4 0 6 6 8 2 2 2 6 6 4 6 6 8 4 4 10 0 0 6 6 6 10 2 2 0 8 8 2 8 8 10 4 4 8 6 6 4 8 8 12 0 0 12 2 2

Acknowledgments

-

We wish to thank

F.

Tasset for his help during the experiment and J. Rossat-Mignod for helpful discussions.

sinB/X

References.

Calculations Observations

I

^{1 =-1.0.} A =30K

¹

ⁱ A =8K ^i-2.5K

Observed and calculated magnetic amplitudes at T 0.000

0.136 0.158 0.223 0.261 0.273 0.315 0.386 0.446 0.473 0.473 0.522 0.546 0.630 0.649 0.668 0.668 0.687 0.739 0.772 0.788 0.818 0.818 0.891 0.905 0.905 0.918 0.945 0.945 0.971

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11

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0.4030 (300) 0.3038 (238) 0.3370 ( 58) 0.2969(41) 0.2755 (226) 0.2709 ( 46) 0.2696 ( 37) 0.2228(59) 0.1662(138) 0.1594 ( 88) 0.1979 ( 86) 0.1751(73) 0.1337(56) 0.1505 (106) 0.1105 ( 65) 0.0888 (225) 0.1175 (124) 0.0636 (103) 0.0511 (181) 0.0755(251) 0.0626(150) 0.0553 (160) 0.0970 (124) 0.0063 (217) 3.0261 (521) 0.0534(208) 0.0764 (314)

(3)

F.

Hullinger,

B.

Natterer, H.R. Ott, 3 . Mag. Mag. Mat.

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(1978) 87.

( 4 ) H.R. Ott, J.K. Kjems,

F.

Hullinger, Phys. Rev. Lett.

42

(1979) 1378.

0.3618 0.3374 0.3351 0.2957 0.2907 0.2753 0.2686 0.2247 0.1706 0.1617 0.1929 0.1656 0.1384 0.1290 0.1086 0.0791 0.1136 0.0764 0.0691 0.0793 0.0824 0.0582 0.0742 0.0311 0.0307 0.0548 0.0460

(5)

D.

Ravot, P. Burlet, J. Rossat-Mignod, J.L. Tholence, J. Phys. 4J (1980) 1117.

0.3614 0.3383 0.3323 0.3022 0.2871 0.2789 0.2609 0.2223 0.1865 0.1746 0.1821 0.1584 0.1444 0.1179 0.1081 0.0967 0.1047 0.0918 0.0789 0.0749 0.0727 0.0621 0.0657 0.0456 0.0437 0.0489 0.0454

(6)

C.J. Heidl, I.W. Ruderman,

J.M.

Ostrowski, J.R. Ligenza, D.M. Gardner, Rev. Sci. Inst.

7

(1956) 620.

0.0387 0.0434 0.0396 0.0267 (443)

1

^0.0293

0.0864 (298) 0.0510

(7) L. Koester, K. Knopf, Zeit. f. Naturf.

26a

(1971) 361.

0.0242 (569) 0.0467

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(10)

L.

Koester, Neutron Physics, ed., Springer Verlag (1977).

(11) J . X . Boucherle, J . Schweizer, J. Mag. Mag. Mat. (1981) 308.

(12) A. Delapalme, J.Y. Henry, private communication.

(13) J . X . Boucherle, Valence Inctabilities, ed.

P.

Wachter (North ~olland) (1982), in press.

(14) S.W. Lovesey, D.E. Rimer, Rep. Prog. Phys.

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(1969) 333.

(15) A.J. Freeman, J . P . Desclaux, J. Mag. Mag. Mat.

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