Neutron diffraction studies at the Puerto Rico Nuclear center

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Neutron diffraction studies at the Puerto Rico Nuclear center

I. Almodovar, H.J. Bielen, B.C. Frazer, M.I. Kay

To cite this version:

I. Almodovar, H.J. Bielen, B.C. Frazer, M.I. Kay. Neutron diffraction studies at the Puerto Rico Nuclear center. Journal de Physique, 1964, 25 (5), pp.442-446. �10.1051/jphys:01964002505044200�.

�jpa-00205801�

442.

NEUTRON DIFFRACTION STUDIES AT THE PUERTO RICO NUCLEAR CENTER (1)

By ^I. ALMODUVAR, H. J. BIELEN (2), ^B. C. FRAZER (2) ^and M. I. KAY (2),

The Puerto Rico Nuclear Center, Mayaguez, Puerto Rico.

Résumé. 2014 Un programme ^de diffraction neutronique ^a été récemment établi au Centre d’Études Nucléaires de Puerto Rico. Les deux diffractomètres utilisés ont été assemblés avec l’aide de membres du Laboratoire National de Brookhaven.

Le premier ^programme de recherche était l’achèvement de l’analyse de la structure d’un mono-

cristal de CaWO4. ^En choisissant l’origine ^{au site} 4a) des atomes W dans la maille quadratique,

groupe I41/a, ^{on trouve les} paramètres ^{suivants de} l’oxygène dans les sites 16(f) :

x ⁼

0,2413 ^± 0,0005, y

0,1511 ^± 0,0006,

0,0861 ^± 0,0001.

Les paramètres anisotropes ^{de vibration ont été} également déterminés pour ^tous les atomes dans

l’analyse ^aux moindres carrés de la structure.

La structure magnétique ^de CuSO4 ^a été déterminée en continuation d’une étude, commencee à Brookhaven en collaboration avec le Dr P. J. Brown. Dans la notation de Wollan-Koehler-Bertaut,

le mode de l’ordre antiferromagnétique ^des spins dans la maille orthorhombique ^du groupe Pbnm est Ax, c’est-à-dire sur les sites 0 0 0, ⁰ 0 1/2 ; 1/2 1/2 0, 1/2 1/2 1/2, ^{les spins se succèdent dans} la suite + - +

leur axe étant selon

Un moment d’environ _{1 03BCB} a été trouvé pour l’ion Cu2+.

La structure cristalline de BaNiO2 ^a été réexaminée et le résultat obtenu par Lander ^aux rayons X d’une coordination carré coplanaire ^{de Ni2+ a} été confirmé. On a également ^{cherché un ordre} magnétique ^dans BaNiO2 ^à 4,2 °K, ^{mais aucun} résultat concluant n’a été obtenu.

Une transition magnétique ^{a été trouvée dans} Fe2SiO4 ^au voisinage de 30 °K. Ce composé ^{a une}

structure du type ^{olivine avec huit ions} Fe2+ dans les positions 4(a) ^et 4(c) ^du groupe d’espace

Pbnm. L’analyse ^{de la structure} magnétique continue, mais le mode dominant est C dans la notation W.-K.-B.

Abstract.

A neutron diffraction program ^was initiated recently ^{at the} Puerto Rico Nuclear Center. The two double crystal spectrometers ^{in use were assembled} with the aid of staff mem-

bers of the Brookhaven National Laboratory.

The first research problem ^{to be} completed ^{was a} single crystal ^structure analysis ^of CaWO4.

Choosing ^the origin ^{at the} 4(a) tungsten ^{site in the} tetragonal I41/a cell, ^the 16(f) oxygen para- meters were found to be as follows :

0.2413 ± 0.0005, y = ^{0.1511 ±} 0.0006,

z ⁼

0.0861 ± ^0.0001. Anisotropic temperature parameters ^{were also} determined for all atoms in the least squares analysis of the structure.

The magnetic ^{structure of} CuSO4 ^has been determined in a continuation of a study ^{started at}

Brookhaven in collaboration with Dr. P. J. Brown. Using ^the Wollan-Koehler-Bertaut notation,

the antiferromagnetic spin ordering ^{mode in the} orthorhombic Pbnm cell is Ax, i.e., + - +

on the 0 0 0, 0 0 1/2, 1/2 1/2 0, 1/2 1/2 1/2 sites, with ^the spin ^axis parallel ^to

^{A moment of} approximately

1 03BCB ^was found for the Cu2+ ion.

The crystal structure of BaNiO2 ^was re-examined in a neutron powder diffraction study ^and

Lander’s _x-ray result of a coplanar square coordination of Ni2+ was confirmed. BaNiO2 ^{was also} investigated ^for magnetic ^{order at} 4,2 ^°K but conclusive results have not been obtained.

A magnetic transition has been found in Fe2SiO4 ^{in the} neighborhood ^{of 30 °K. This} compound

has an olivine type structure with eight ^{Fe2+ ions in the} 4(a) ^and 4(c) positions of the Pbnm space group. Analysis ^{of the} magnetic structure is still in progress, but the dominant mode is C in the W.-K.-B. notation.

PHYSIQUE 25, 1964,

History of neutron diffraction at the Puerto Rico Nuclear Center and technique employed.

^While

definite plans ^{for a neutron} diffraction program ^{at the} Puerto Rico Nuclear Center began ^{to take} shape ^about

one and a half years ago, the first actual research ^measu- rcments were not made until January, 1963. ^{At that}

(1) ^Work performed under the auspices of the U. S.

Atomic Energy Commission.

(2) Guest scientists : H. J. Bielen from the University ^of Frankfurt, Frankfurt, Germany ; B. C. Frazer from Brook- haven National Laboratory, Upton, ^New York, ^{U. S.} A. ; I. Kay ^from Georgia Institute of Technology, Atlanta, Georgia, ^{U. S. A.}

time the installation and testing ^{of a rather} simple spec- trometer was completed ^{at the Center’s one} megawatt swimming pool type ^{reactor. The} in-pile collimation,

water shutter, monochromator mount, ^{and shield for} this first machine were all patterned ^{after some of the}

less elaborate installations at the graphite ^{reactor of}

the Brookhaven National Laboratory. ^{The diffrac-}

tometer was an old instrument that had been used ^at Brookhaven for several years until it ^was replaced by

one of more advanced design. ^{It was} literally

rescued from the scrap heap ^and rehabilitated for use

in Puerto Rico. In June the Westhinghouse ^Research

Laboratories donated ^an excellent diffractometer and

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01964002505044200

443

several items of _accessory equipment, including ^a

modified Varian magnet, ^{to the} University ^{of Puerto}

Rico. The original design ^{for this machine was made}

at Brookhaven by B. C. Frazer and T. Mullaney, ^but

modifications were made at Westinghouse by ^{G. Shi-}

rane, W. Takei, ^{and R. Stuart. The} old Brookhaven diffractometer was replaced by ^{this fine} piece ^of equip-

ment.

In July, installation was started of a second spec- trometer. This versatile and highly ^{accurate instru-}

ment is almost identical with the new U. S. I units

designed by ^A. Kevey ^for the Brookhaven High ^Flux

Beam Reactor. The cylindrical monochromator shield rests on a gun ^mount (obtained ^as surplus equipment

from the U. S. Navy) ^{which can} be rotated to permit

continuous angular settings ^for wavelength ^selection

over a range of approximately

^{500 to} + ^{900. The} diffractometer is on a cantilevered mount which is bolted to the gun mount, ^{and hence remains} in proper

alignment ^if changes ^{are made in} 20 of the mono-

chromator. The monochromator itself is 1 : 2 cou-

pled ^{to the} gun ^mount hy ^{means of an} angle ^divider

so that the crystal stays ⁱⁿ reflecting position ^{if a} change ⁱⁿ wavelength ^{is made. It is} possible ^to change

the collimation of the primary ^{beam from the reactor} by turning ^a crank. This rotates a steel cylinder

which has positions ^for three collimators and has a

fourth closed, ^or shutter, position. ^At present only

one collimator is mounted. This has 24’ soller slits.

A single crystal collimator and one with 18’ soller slits will be installed _very soon. In addition to the mechan- ical shutter on the rotating collimator changer, ^which puts three feet of steel in the beam, ^{an in-pile water}

shutter is also available.

The U. S. I diffractometer _{is very} similar ^to the

Westinghouse machine, since it is also an improved

version of the original Frazer and Mullaney design.

Both are very sturdy ^machines capable ^of taking ^over

2 000 pounds ^{of direct} loading, ^and have maximum accumulated angular ^errors of less than I’ of arc.

Data are collected semi-automatically by pre-deter-

mined count monitor controlled step scanning. ^Data output ^is printed ^on adding ^machine tape. ^{All elec-}

tronic components ^are transistorized. Eventually ^the spectrometers ^will be controlled by automatic pro- grammers, probably ^{of the} Brookhaven type, ^but

because of the reactor operating ^{schedule semi-auto-}

inatic operation ^is adequate ^for present ^{work. The}

reactor now operates ^{on an 8-hour} day ^and 5-day ^week

schedule. A 16-hour day ^{and an increase in} power ^to two megawatts ^is expected. ^{Plans are} being ^made

for 24-hour operation ^{at five} megawatts ^{some time in} 1965. The efficiency ^of data collection can be increased

greatly ^{at that time} by converting ^to fully ^automatic systems.

~

CaW04

’

The first neutron diffractioll problem ^under-

taken was a single crystal ^structure analysis ^of CaW04 (scheelite). ^{While this structure is} usually

considered to be typical ^{of that} adopted by ^an important ^{series of} AB04 compounds, the oxygen coordinates have been known with an accuracy of

only ^{about ~.1} A [1]. ^{The reason} for this is that the B atom is always ^{one of rather} high ^atomic number, ^{relative to} oxygen, and hence the oxygen contributions to x-ray ^structure f actors are compar-

atively ^{small. In the neutron case the oxygen} scattering length ^{does not differ} greatly ^{from those}

of the other atoms. For CaWO4 ^{the neutron} scattering lengths ^{are :}

Accordingly, ^{the structure} analysis briefly ^desc-

ribed here was undertaken. In the course of this

analysis ^{it was found} that Zalkin and Tem-

pleton [2] ^were engaged ^{in an} independent study

of the structure using very ^accurate x-ray data and modern refinement techniques. Their results

are in excellent agreement ^{with those} reported

here.

CaWO4 crystallizes ^{in the} tetragonal space group

I41 la and has cell dimensions a = 5 . 243 -+- 0. 002~.

and c

11.376 ± ^0.003 A[2]. ^{The Ca and W}

atoms are in the four-fold symmetry-fixed posi-

tions 4(b) ^and 4(a), respectively, and oxygen is in the 16( f ) general position.

Least squares refinement calculations, ^carried

out on (h ⁰ 1) ^and (h ^h l) data collected from sam-

ples ^{cut from a} large synthetic crystal, ^{led to a}

final I~ value of 0.041. The oxygen parameters (with ^{the cell} origin ^{chosen at the} tungsten site) ^are

These yield ^a nearly regular, ^but measurably distorted, WO’4 group with a W-0 distance of 1.784 ~ ^0.003 A. The latter has been corrected

by ^{0.003 A for} vibrational motion. Anisotropic temperature parameters ^were determined for all atoms, ^{as will be} reported elsewhere in a detailed

publication of results.

Cuss 4

The anhydrous sulfates of the divalent transi- tion elements form a very interesting group of

magnetic compounds. Magnetic structures have

already ^been determined for FeSÛ4, NiSO~,

and [3-5]. ^{Discussed here are}

the results of a neutron diffraction study of CUS04-

This has been ^a continuation of a study begun by

two of the present ^authors (I. A. and B. C. F.) ^at

Brookhaven with Dr P. J. Brown, ^{and a full}

account of this work is to be published ^{later under} joint ^author ship.

Because of the low Cu2+ moment, ^{and because}

of troublesome peak overlaps ^{in a neutron} powder

pattern, ^the magnetic ^{structure of} CuSO4 ^should

really ^be investigated using single crystals. Single

444

crystals of suitable size are not easily grown,

however, ^{so an} attempt ^{has been made to solve the} problem using powder ^{data. What can be said} directly ^{from the neutron data is not} very satis-

fying, but if these data are considered along ^with

the magnetic measurements of Kreines [6] ^{a struc-}

ture can be proposed that is almost certainly

correct.

CUS04 ^{has the} orthorhombic ZnS04 type crystal

structure with space group Pbnm [7]. ^{The four} crystallographically equivalent ^{ions are loca-}

ted on the 0 0 0 0 1 11 I

0 I 11

sites. For

’ 2 22 ’ 222 2

the case where the magnetic ^{cell is identical with}

the chemical cell the possible ^collinear spin config-

urations for antiferromagnetic ordering ^are +20132013+,++2013-2013, and -~-- -- ~- -. ^{In the} Wollan-Koehler-Bertaut notation these arrange- ments are labeled G, ^{C and} A, respectively [8].

Each of these leads to a distinct set of magnetic

reflections.

.

In comparing diffraction patterns ^{taken at} 4.2 OK and 77 ~K only ^one clearly ^{resolved new} peak ^{was found in the low} temperature pattern.

This indexed as the (0 01 ) reflection, ^{which is char-}

acteristic of type ^A ordering. ^A small but defi-

nitely measurable change ⁱⁿ intensity ^{was also}

found for the combination (0 2 1), (1 1 1) peak, again characteristic of type ^A. No other inten-

sity changes ^were statistically significant.

This small amount of information is sufficient to

identify ^the ordering ^scheme (although ^{a multi-}

axis spin ^structure with small cant angles ^cannot

be directly ^ruled out), ^{but it is} insufficient to yield

reliable information ^on the magnitude ^{and orien-}

tation of the Cu2+ moment. Here it is useful to consider the magnetic measurements of Kreines [6].

Kreines used ^small single crystals ^{which were}

oriented by morphology and x-rays. While the

setting ^{was not} specified ^{in her} paper, ^{it can} be identified from the cell dimensions as Pbmn. Her

figure ^{4 is drawn} incorrectly, ^{since the Cu sites are} improperly assigned ^{for this} setting, ^{but this does}

not affect the conclusions which may be drawn from the measurements. According ^{to Kreines}

xl

xd

Xc and _{ZI, = xa.} This of course sug-

gests ^{a collinear} spin ^{structure with the} spin ^axis parallel ^{to a.} With this assumption ^{the CU2 +}

moment calculated from the neutron diffraction data is 1 as expected for this ion. The spin ordering ^{mode is} Ax, i.e., ^{+ - + - on the} 0 0 0,.

001 110, 111 sites, with the moment orienta- 2 22 ’222

tions along the a axis of the Pbnm cell.

BaNi02

While the results obtained on BaNiO2 ^{have been} largely negative ⁱⁿ character, ^it still may be worth-

while to make a few remarks on this rather unusual

compound. ^{There were several reasons} why ^it

was chosen for study. In the first place ^Lander’s

trial-and-error determination of the oxygen posi-

tions from visually ^estimated x-ray data did not

seem overly convincing since the atomic number of Ba is quite high ^{and even} that of Ni is relatively high ^{[9]. Some} preliminary packing calculations revealed other possible structures which were not mentioned by Lander, ^{and one of these in} parti-

cular seemed more logical ^{than the one he} reported.

Also the square planar oxygen coordination by

Ni2+ was most unusual in view of Lander’s obser- vation of a nearly " normal " paramagnetic

moment corresponding ^{to 1.8} unpaired ^electrons.

The explanation suggested byLander ^{for the observ-}

ed moment is that there are additional bonds between neighboring ^nickel ions, ^{as evidenced} by

the very short Ni-Ni distance of 2.36 A. Finally,

the orthorhombic Cmcm structure is similar in many respects ^{to the} anhydrous ^sulfate structures, and it was of interest to investigate possible magnetic ordering ^{at low} temperatures.

Essentially ^{the structure} investigation ^{led to}

confirmation of Lander’s structure. The refine- ment is still in progress, and it may be that some

significant parameter changes will be found (this

seems to be the case with the oxygen y parameter),

but there is no doubt that Lander’s general config-

uration is correct.

The magnetic studies have not been so conclu- sive. In a separate paper from his report ^{on the} DalVi02 structure, ^Lander quotes unpublished ^sus- ceptibility measurements of F. Morin [10]. ^The temperature range is ^not given, but it is stated that the Curie-Weiss law is obeyed ^{with A}

1.80~,

and that the calculated number of unpaired ^elec-

trons per nickel ^ion is 1.83. From this one might expect ^{to find a Neel} point well above the temper-

ature of liquid ^helium. However, ^{there are no}

obvious changes ^{in the neutron} powder patterns ⁱⁿ going ^{down to this} temperature. Through ^the courtesy ^{of Drs} W. J. Takei and D. E. Cox [11], ^of

the Westinghouse ^Research Laboratories, ^the

authors were able to obtain magnetic susceptibility

data down to 4.2 OK. These data disagreed ^some-

what with Morin’s in giving A

^{720 and} approxi- mately ^one unpaired ^electron per nickel ion. The Curie-Weiss law was obeyed ^{very well down to} liquid N~, ^{but the} 1 jx ^curve began ^to fall off from

a straight ^{line at lower} temperatures, suggestive ^of

an approaching transition. Unf ortunately, ^Takei

and Cox were unable to take data between 4.2 OK and approximately ⁵⁰ °K, ^{so there was no definite}

evidence of a transition. Also unfortunately, ^the magnetic sample ^{was found to} be somewhat contam- inated with impurities, ^{so not too much faith can}

be placed ^{in the} differences from Morin’s measure-

ments. If the Ni moment is as low as 1 as

445

indicated by ^{the data of Takei and} Cox, ^{it is} possible ^{that the neutron} diffraction statistics were

not sufficiently good ^{to observe} ordering. ^This

would be particularly ^{true if the} ordering ^is type A,

since peak overlaps happen ^to be very bad for this

case.

This is as much as can be said on this problem

for the moment. Further magnetic measurements must be made at low temperatures ^{on a} pure

sample ^before continuing ^{with neutron} diffraction work.

Fe2SiO 4

Until _very recently very little has been known about the magnetic properties ^{of the transition}

metal olivine type compounds. Early ^{in this} year Kondo and Miyahara [12] published magnetic ^sus- ceptibility ^{data on the} orthosilicates of divalent

Mn, Fe, Co, and Ni between 77 oK and 300 OK.

The curves suggest ^that magnetic transitions will be found in all of these compounds ^{at lower} temper-

atures. A transition in Fe2SiO 4 has been found

by ^the present ^authors by ^neutron diffraction ^mea- surements, and by Takei ^{and Cox} [11.] by magnetic susceptibility measurements. Fayalite ^mineral samples kindly supplied by ^Dr Clifford Frondel of

Harvard~University, ^were used for both measure-

ments. The Néel point ^{is not known} accurately,

but it is in the vicinity of 30 OK. The magnetic

measurements also showed some evidence of weak

ferromagnetism, with about 0.05 although

this may ^not be real since the mineral sample ^was

rather impure.

The first diffraction data were taken using ^the powdered ^mineral sample. ^Several single crystals

which appeared ^{to be of} fairly good quality ^were

removed from the bulk material before grinding

the sample. ^The purity ^{of the} crystals ^{should be} considerably ^{better than the} powdered material,

and one of these has been cut and mounted for

study. ^{So far the} only measurements made have been of powder, samples. ^While this showed

only very small percentages ^of substitutional

impurities ^{in a chemical} analysis, ^{the diffrac-}

tion patterns ^{disclosed an} appreciable ^contami-

nation of FeSiO,. The latter material also has a

magnetic transition at low temperatures, ^{so its}

effects on the data cannot be completely ^eliminated by subtraction of liquid N2 ^and liquid ^He patterns.

This should not be a problem ^{in the} future, ^how-

ever, for in addition ^to the natural single crystals already mentioned, ^some very good synthetic powder samples ^have been obtained.

In the orthorhombic olivine structure [131, space group Pbnm(D§g), ^{there are four} formula units _per iinit cell. The cell of Fe2SIO, has dimensions (14]

There are two four-fold sets of Fe2+ ions :

In the ideal olivine structure x

0 and y ^{= 1} /4,

but the values observed [13] ⁱⁿ olivine itself are

0.99 and 0.281, respectively. ^{Each of the Fe 2+}

ions is in octahedral coordination with oxygen, and

one may expect magnetic interactions of the same

nature as the B-B interaction in spinel structures.

In addition there are superexchange paths ^avail-

able via the covalent Si01+ groups.

If the magnetic and chemical cells are identical,

as proves ^{to be the case in} Fe2S’01, ^{there are} eight spin ^{vectors in the} cell, ^and hence there are very many possible antif erromagnetic configurations.

These can be reduced considerably by symmetry considerations, ^{but even} then there are 19 possible

collinear spin ordering modes, ^{and of course there}

are many ^more combination modes that become

possible ^{for canted} spin structures. The problem

of sorting through ^{all of these} possibilities ^to satisfy ^{observed neutron} intensities is complicated by ^{the f ree x and y} parameters ^{of Fell. For one} thing ^these parameters ^{must be} accurately ^deter-

mined as part ^{of the} analysis, ^{but a more} important difficulty ^{is that the} magnetic extinction rules which would apply ^{for Feri} spins in the ideal olivine structure are no longer ^{valid. In this} preli- minary stage ^{of the} problem, however, ^{the ideal}

structure is being assumed. This should be reason-

ably ^{safe in} determining the ,principal features of the magnetic structure, ^{since the} intensity ^contri-

butions arising ^from non-ideal shifts should be small.

Let the spins ^{on the Fei} 4(a) ^{sites be numbered}

1 through ^{4 in the same order as} given ^above.

Assuming ^ideal positions ^for Fell, ^{let the} spins ^on

the 4(c) ^sites be numbered 5 through ^{8 in the} following ^{order :}

If one calculates magnetic extinction conditions

for the various possible ^coliinear antiferromagnetic spin configurations ^{it is found that none of these}

can account for the observed data. Hence there must be at least two spin directions in the struc- ture. The proper spin ^vectors may be constructed from their components by using combinations of the collinear ordering ^modes.

The most intense reflection in the pattern ^is

the (100). ^This peak ^can arise from ^two different

modes but only ^{one of these can} yield ^a high ^inten-

sity :

ⁱ

1 2 3 4 5 6 7 8

446

In this ordering ^{scheme the} spin components

°

form alternating parallel ^{sheets on the} (200) planes.

This mode, wich is the dominent one in the

structure, ^is associated with the cristallo-

graphic b ^axis. Analysis ^{of the} data indicates a + - + - + - + - arrangement ^of spin components parallel ^{to a. The} components ⁱⁿ

the c direction are small, if indeed they ^{exist at}

all. The Fe2+ moment was found to be approxi- mately ⁴ ~B for both Fei and Fell. In both cases

the spin ^{vectors are} approximately parallel ^to

the XY plane ^{and are tilted from} the b axis by

about 300, ^{with the tilt} alternating ⁱⁿ sign ^as prescribed by the a axis ordering ^mode.

Acknowledgements.

^In closing, the authors would like to acknowledge ^the valuable assistance and advice of the Brookhaven National Laboratory

staff members in starting this program.

Discussion

Pr JAMES.

Pouvez-vous ^me pr6ciser l’impor-

tance de l’impuret6 FeSi03 ^{dans votre} Fe2SiO4 ^et

comment la d6terminez-vous ?

Dr KAY. - Environ 15 % ^et peut-être ²⁰ %,

par diagrammes ^aux neutrons et aux rayons ^X.

Pr BERTAUT.

11 _y a des tables des repr6sen-

tations irr6ductibles pour les sites b) ^et c) ^{dans le}

groupe Pbnm qui ^est aussi le groupe des p6rovskites

des terres rares FeR03 ~R

^terre rare). ^Avez-vous

6tudl6 si les configurations ^{de FeI et Fei, sont} eoupl6es ^en quel ^cas elles doivent appartenir ^{a la}

même representation ?

Dr KAY. - Jusqu’ici nous avons suppose lay eompatibilité ^{avec les} repr6sentations de groupes pour ^trouver la structure approch6e. ^{Mais nous}

devrons d’abord raffiner la structure avec des donn6es meilleures avant de r6pondre ^d6finiti-

vement a la question.

,

REFERENCES

[1] ^SILLEN (L. G.) and NYLANDER (A.), ^{Arkiv Kemi Min.}

Geol., 1943, 17 A, ^{n° 4.}

[2] ^ZALKIN (A.) and TEMPLETON (D. H.), ^{Private commu-}

nication.

[3] ^FRAZER (B. C.) ^{and BROWN} (P. J.), Phys. Rev., 1962, 125, 1283.

[4] ^BROWN (P. J.) and FRAZER (B. C.), Phys. ^Rev. 1963, 129, 1145.

[5] ^BERTAUT (E. F.), COING-BOYAT (J.) and DELAPALME

(A.), Phys. Letters, 1963, 3, 178.

[6] ^KREINES (N. M.), ^Zhur. Eksp. ⁱ Teoret., Fiz., 1958, 35, ¹³⁹¹ (Eng. transl : Sov. Phys., JETP, 1959, 8, 972).

[7] ^KOKKOROS (P. A.) ^and RENTZPERIS (P. J.), ^Acta Cryst., 1958, 11, ^361.

[8] ^BERTAUT (E. F.), ^J. Appl. Phys., Suppl., 1962, 33,

1138.

[9] ^LANDER (J. J.), ^Acta Cryst., 1951, 4, 148.

[10] ^LANDER (J. J.), J. Am. Chem. Soc., 1951, 73, 2450.

[11] ^TAKEI (W. J.) ^{and Cox} (D. E.), Unpublished ^data.

[12] ^KONDO (H.) and MIYAHARA (S.), ^J. Phys. ^Soc. Japan, 1963, 18, 305.

[13] ^BELOV (N. V.), ^BELOVA (E. N.), ANDRIANOVA (N. H.) and SMIRNOVA (P. F.), Dokl. Akad. Nauk, SSSR, 1951, 81, ^399.

[14] ^WINCHELL (H.), ^Amer. Cryst. ^Assoc. Meeting Abstr.,

p.14 (April 10-12, 1950).