Atomic disorder and canted ferrimagnetism in the TbCr6Ge6 compound. A neutron study

Jouraml of

AHD ~ ELSEVIER

~

~

Journal of Alloys and Compounds 255 (1997) 67-73

Atomic disorder and canted ferrimagnetism in the TbCr6Ge 6 compound. A neutron study P. S c h o b i n g e r - P a p a m a n t e l l o s a'*, J. R o d r f g u e z - C a r v a j a l b, K.H.J. B u s c h o w ¢ "Laboratorium fiir Kristallographie, ETHZ, CH-8092 Ziirich, Switzerland "Laboratoire IMon Briilouin (CEA-CNRS), Centre d'Etudes de Saclay, 91191. Gif-sur-¥vette. France "Van tier Waals-Zeeman Institute. University ~ Amsterdam, 1018 XE Amsterdam. The Netherlands

Received 4 October 1996

Abstract A structure determination using high resolution neutron powder data (difference Fourier maps) has shown that the hexagonal compound TbCr~,Ger, (P61nunm) is a partly disordered derivative of the HfFe6Ge~,-type structure where a part of the Tb atoms at l(a) (0,0,0) and a part of the Ge~ atoms at 2(e) (0,0,0,347) populate intermediate lattice positions which are shifted by cl2. The observed atomic disorder modifies the R-R interactions as well as the crystal field, leading to an ordered state and easy axis for the Tb moments different from that found for the (fully ordered) isomorphic TbMn~,Ge~,compound. As the Cr-Cr interaction is very weak the ordering is dominated by the R-R interaction. TbCr~,Ge¢~orde~ below T¢= 10.3 K with a canted ferrimagnetic moment arrangement where the moments of the Tb and Cr sublattices have different orientations making an angle of 25(2) deg. and 143(7) deg. with the c-axis respectively. The ordered moment values of the two sublattices at 1.5 K are 8.74( I ) i~.lTb and 0.48(10) ~.lCr. The net magnetic moment of the structural model proposed is found to be in :;atisfactory agreement with results of magnetic measurements reported earlier.

1. Introduction Recently several reports of investigations have appeared dealing with the magnetic behaviour [I-3] of the heavy rare earth RMn~,_xCrxGe 6 compounds (R=Tb, Dy, Ho, Er, and Y) crystallising with the HfFe6Ge6-type of structure (P61mmm space group) [4,5]. The pure Mn compounds were reported to order antiferromagnetically at elevated temperatures ranging from 400-500 K and to undergo at lower temperatures several magnetic phase transitions. These high ordering temperatures are associated with a dominant Mn-Mn interaction while the R-R interaction sets in at temperatures below 100 K. Contrary to the Mn compouLds the bulk magnetic properties of the RCr6Ge~, compounds, with the exception of R=Tb, show that no magnetic order could be found down to 5 K [3]. The compound TbCrt, Ge 6 showed a modest ordering below 12 K. From the magnetic isotherms at 1.5 K and 5 K of the compound formed with non-magnetic Y it was concluded

*Corresponding author. 0925-8388/97/$17.00 © 1997 Elsevier Science S.A. All right-,, reserved Pll S0925-8388(96~02872- I

that a very weak moment of 0.2 ~a is present, which was attributed to the Cr sublattice. The magnetic structures and phase transitions of the Mn compounds, studied extensive° ly by Venturini et al. [6,7] and the present authors [81, have shown the existence of complex ordering mechanisms and various spin reorientation phenomena in the low temperao ture region depending on the nature of the rare earth ion. in view of all these results it is of interest to extend the neutron study to the magnetic ordering of the RCr~Ge6 (R=Th, Dy, Ho, Er. and Y) compounds, in the present paper we will report on the structure and the magnetic ordering of the TbCroGe~, compound, having the highest ordering temperature in the RCr~,Ge~, series.

2. Experimental and results The TbCr6Ge 6 powder sample was prepared by arc melting from starting materials of at least 99% purity. The sample was wrapped in Ta foil and araealed at 800 °C for 4 weeks ia an evacuated quartz tube. After vacuum

68

P. Schobinger.Papcmumtellos el al, I Jom'nal of Alloys and Compomuls 255 (1997) 67-73

annealing, the sample was investigated by X-ray diffraction and found to be single phase (HfFe6Ge~, structure type) [4,51.

background at selected (hki) reciprocal lattice positions in particular around the (103) reflection whose intensity was found to be reduced by 20% from the value expected for the prototype structure. Introducing individual isotropic temperature factors in the refinement of the high-resolution data, resulted in quite large values for the atomic displacements of the Tb and the Ge 3 sites. This prompted us to calculate the difference Fourier neutron density maps from the fitted profile of the 293 K data using the Xtal programm [101. Fig. 2 shows the difference Fourier density layers, at heights z=0.15 and 1/2 where positive density (full contours) was found for the (0,0,1/2) and (0,0,0.15) positions. The dashed contours correspond to zero density while the dotted densities reflect negative values. Subsequently two additional atomic positions were introduced in the refinement of the 293 K data, which converged when the (0.0,1/2) site was occupied by 18% Tb and the (0,0.0.15) site by 10% Ge.~. Results are summarised in Table I Table 2 and in Fig. I. The resulting structure shown in Fig. 3 is a disordered derivative of the llfFe,Ge 6 structure type. It can be regarded as an intermediate structure between the prototype structure (HfFe,Ge6) and the fully disordered type of the structure (YCo,Ge,). In the TbCr,Ge, structure the atomic disorder affects only the atomic distribution of atoms located on chains along the ¢°axis, as it will be discussed in more detail below. The introduced new atomic R and Ge positions correspond to those of YCo,Ge, (see Fig. 3) but with different occupancy ratios, which has as a consequence a 2xe cell enlargement, leading to the same dimensions as in the I*itFe,Ge, unit cell.

3. N e u t r o n d i f f r a c t i o n

Neutron diffraction experiments were carried out at the facilities of the Orphic reactor (LLB-Saclay). The 293 K data, u~d for a structure determination, were collected with the 2-axes high resolution instrument 31"2 (20 detectors, A= 1.227~ with a 0.05 deg. step increment in 20 in the 20 angle 2-125 deg.). The data between 1.5-20 K were collected on the G4.1 diffractometer (800 cells multidetector, A=2.426/i, with a 0.1 deg. step increment in 20 in the 20 range 12-92 deg.). The data analysis was performed with the Fullprof 191 and Xtai computer programs [10l. 3. I. The nuclear structure

The 293 K high-resolution neutron patterns (Fig. I) as well as the 20 K data collected in the paramagnetic state can _be indexed with the hexagonal cell of the HfFe,Ge, lattice, similarly to the ThMn,Ge, compound. Furthermore, the patterns entail weak additional lines of a non identified foreign phase, labeled with (i) in the ton'e+ ~ponding figure,% that have been excluded from the calculations. The refinement, however indicated a strong deviation tTom the HfFeJ3e, ba,~ic model. The main characteristics of the TbCr.Oe, patterns is the presence of a wavy

+~-

-"

i

; ........ •

-"

U

-,

•

~l

" ....

'

•

'i-

• ........ ,

7 .....

I

"

+

"'I

200-

+

"

+

:

1

®.-.1

:,

.'-

Ill

20

1

~

+o._

,,

;

ql'iT t ~ +NQl l l',,ll ,M ~ ~ , + ~° qt~pb~plb . + . , , , + . Nqip . , . . ~ _qt ~

°0 °-- ° ,N + . ~

0

+ L t I

,,

~.

i

!

+-

"

....

~.+'1.224

eel

.-,

: '.

•

|

•

i -:~

TbCr oGe 6 293 K

" "

®

-

,

l N M

A

.

" it, b, ---t.

f--.,..,

I

Clll

" i

|

I

"

40

60 20 deg.

80

100

120

Fig. I+ Ob.scrved. calculated and dil+t'crence high resohJtion neutron diagram of TbCr~G% nmasured in the paramagnctic state at 293 K showing a deviation from

the Hfl:e.Ge.

structure.

Ea,~ily v i s i b l e

is t h e s t r o n g l y

reduced

(103)

intensity

(i)

stays for an unidentified

impurity

phase.

P. Schobinger-Papamantellos et al. I Journal o f Alloys and Compounds 25.5 (1997) 6 7 - 73

~ ; : ~:::.......-,,..::::<.. ~ , : . > ....., { ~',

~ _ ' , . ,

,

.... •. " . ' - " i

::

,

D",7"";.'T)", _l"-"~...'""...'~..".

,,

" *

i .."

~ ,#-

I

i

Zjt,t,_

-

a/.:,

~'"

•

"'. .

-,,._

.

.

J

~

~

""' r--\'"°..'.-:-" "-, ..".. t

/

~

.

_....-

•

I

~

%.

"

-.,,._

:

,.,

•

"

%I

.. .,,,-""

•

=""

,, /

:

I

,,

J ~ivl

[

I

l

~

C/

•

i I I ~

". ~

l

':Z

.'

_..

,, ",t~"

,, I

I t %

, .,"~/

~

•

•

I

, =.i ,"7

~

Ii

~

-. : . , - . , , , ~ :" .

f

-". $ i X

I 'II % ~, "

I

l

,:',..

,-... "~ :

,,/If

",,%~bi : I

v_.-:.>., ,-/) - - .

.

~ I..." , ' 1 1 I ' - - ~ \ \ ~

e

. .._'-,,._/.,'._ .._, ~I

.

1, - . , , , / ~ x ' , "

~

i " ..... .-"- ~. . _-"........." s

....

..-...

69

-., .4= _ .,,. ,.- ,,.,

f

0.5

(b)

;

/WJJJJIJ: . ~ ,'," ~ ..... "

/'-.-"~.-'"

1 772/

,

..'

# /'.

-,..

..}...-

/ 1 f,~

', ' )

." l ; :

f

I

.

.

.

.

.,....

)

.

i .

.'"

,', I

-

/ .......

\ "", .

," ...... "t

? , -, -' - - . . /

.... . .

.d'

,." ',

% X Y "~...~ I

/ ,..-."'

",

.'"

_" "

........

,, j,l,

r , ',~kkkk~ b

!

,b -- ....

,

.

•

, -. . . . . #,. . . . . %

" .... "

e

/ .

: t ) :

",, ",,..... . . . . . .

II

•

j i v

,

- .....

, \

/',, ',._.,' i ' x , ',._.,' / £ .... ""

",,

.,,c

..

•

', \

'

/

II

.

, .

.

",

;

,

/

(" 7 "

-

.

7

0.5 Fig. 2, Difference Fourier neutron density maps for : = 112 (top part) and ;=0.15 (bottom pan)calculated directly horn profileofitted high remflution powder data tit" ThCr.Ge~ at 2q3 K, The positive density is in both cases concentrated to the point (O,O,g),

Table I Relined parameters of TbCr,,Ge~, from neutron data (a) at 2q3 K (hi#t resolution) a,d (b) at 20 K , , d I.S K (G4~I ~pecimmeter) Paran~ter oe,(: ~ 0), B,, (nm: ) oc,(.: = I 12 ), El,, (tim")

293 K (high resolution)

20 K

1.5 K

0.810( I ), 0.(X)64( 5 ) O. 184( I ), 0.0064(5 )

0.816. = O. 135(2)

z~,,~ at 2(e)

0.3479(2)

0.3458(5 )

0,3479(9)

~n'~,,~,,,, El,, (nm:)

0.888( I ), 0.0091(2) O. 108(I), 0.0091(2) 0.2489(5).0.0079(3) =o ~ -

0.888( I ), 0.108(I ). 0.2533(6), 0.014(2)

0.888( I ). = 0.108(I), = 0.2534(9), 0.010(3)

-

8,74(14)

=

r~%~

=

25( I ) 0.48(I0) 143(7) 0.51018(4 ) 0.82854(0)

, , : , , B,, (nm;) =c, at 6(i), B,. (mu;) El,,, (am") V, Ip..I. ~'tl,,,,,.

4*,r,,(deg.)

~-, Ip,.I 4~,c, (deg.I

a (rim), c (ran) R,(%),

0.517(Y)( 2 ) 0.82817(3) R.,(~; ')

R.I,(%). R,.~t,(~)

0.51607( 7 ) 0.82822(9)

0.810, = 0.135(2 ), =

6.4. =

3.0, =

3.2. 6.1

16.0, 10

11.8, 3.2

I1.0, 1.0

The R and Ge~ ulonts partly occupy two siles eadl. Tb: I(a) (000), I(b) (00112) and Ge, 2(e): (0.0.z) and (0.0.= * 112). The Cr atoms =ire at 0(iL t i/2,0,~L and the Ge~ and G% atoms are ut 2(d). ( I / 3 . 2 1 3 . 1 / 2 ) and 2(e). (I/3.213.0) sites respectively./~ is the ordered luomen! value ~, its angle witll Ihe e axis, B,. are the isotropie atomic displacem~.ts mid B,,, the overall. R.. R,,,. R,~. are the reliability factors for the integrated nuclear, magnetic and wdghled pmlile intensities respectively.

P. Schobinger-Papamantelios el al. I Jounud ,~f AIIo.vs and Compounds 255 (1997) 67-73

70

Table 2 A part of ob~rved and calculated integrated neutron intensities of TbCr,,G% at 1.8 K (nuclear and ferromagnetic contributions) .

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

.

H

g

L

20 deg

Icalcnucl.

Icalcmag.

Icalctotal

lobstotal

0 I 0 ! I 0 I 1 l 2 I 0 2 ! I 2

0 O 0 0 0 0 I I 0 0 I 0 0 I 0 0

I 0 2 i 2 3 0 1 3 0 2 4 2 3 4 3

16.837 31.489 34.052 35.917 47.057 52.106 56.067 58.979 62.164 65.735 67.248 71.692 76.144 80.072 80.394 88.559

231 0.2 965 182 886 902 14458 75 3119 3990 16730 3992 10379 2119 6927 2329

816 8459 163 3786 3690 82 2320 1921 622 1076 2068 159 2250 508 690 428

IO47 8459.2 1128 3968 4576 984 16778 1996 3741 5066 18970 4151 12629 2627 7617 2757

1268 8404 848 4440 4465 1443 16752 1912 4037 5246 18761 4277 12850 2728 7316 2616

(q=0). This is indicative of a ferromag.cdc moment arrangement of both sublattiees~ if both would order. Their positions and their relative intensities remain unchanged over the entire magnetically ordered regime. The reflection close to 18 deg. as well as a part of the 001 reflection (see Table 2) apparently pertain to the magnetic impurity

3.2. Magnetic ordering The 1.5 K neutron pattern, in the magnetically ordered state, displays the same peak topology as that of 20 K (paramagnetic state), cf. Fig. 4. All magnetic reflections appear at reciprocal lattice positions of the chemical cell

p ...........

4., . . . . . . . . . . . ¢ . . . . . . . . . . .

/

", t~

t

~

~, ,

~

,,-,

I",.

,

.. ®

/' /

:

°o

0

/

~

¢~

/

,t,

o

,,

,. ®

I",

0

.'

0)

,,

°

'

,, 0

.

®

/"

', ,,

® ~

o~,

~

/

',

,'

k.J

/ ", ¢~

',, ,;

,~ ',. 0

", tgJ /

t

,,

/

',. @ / ,,./

•

',,/

',, /

.~ . . .

®

°

/

0, . . . . . . . . . . . . . ¢

',, t~ /'

,,,'~, - ~ ~

,/

/

/

4. .......... .~ ...........

/

,'

()

',, ,:

...

.

_..

".. 0

/"

,, ,'

@ :...." ~

',

12%

¢

..'

...........~ ..........~ ..........: ~ ..........~ ..........:~ ...........~.-

) z-oq Cr

Geb Ge~

Ge3

(a)

(b)

(c)

Fig. 3. ~hematic repre~ntation of the TbCr,,G% disordered structure at 293 K when viewed along [001 l. The insets a-c display the Tb and Ge~ distribution along the hexagonal prisms (channels) of (a) YCo¢,Ge,,, (b) TbCr,,G%, and (c) the prototype structure Hfl:e,,G%.

71

P. Schobinger-Papamantellos et al. / Journal of Alloys and Compounds 255 (1997) 67-73

.

30

.

.

•

i

•

.

•

.

i

.

.

•

,

u .

|

•

•

i

. . . .

.

•

•

.

i

•

•

TbCrsG% 20K

•

•

~.2A26~k

.

i

. . . .

lob.

~I~

m 1o ~ . . . . . . . . . .

.

. . . . .

,,_ _ ~ .

4~ .,,.,,.:;.,,;.i;:i:,..~,;-.".

r

I'

.... "--"~-,,=...-,,....

o:o °

""

I

6--,,

I I

m l e

i

20

,,b ,,,, ,~

...... aL .. ,4 ~

.....

....

,,-,,-- D" oJ I'I~

s l

Tb18% A

ur

lunl

u:... ~ "

i,

10

l.~-i~, Io~'imkl

30

i,, n

n,

i,

0, ~, o,

50

n,, i

70

i,

~

,,

90

p,, U .. P ..:O "t-'t---,.,. . . . . . -;-;¢'~--'" "l~~ II i i ",,,,4 II

I I

i

El

IS

i

II

I

o

OL

nJ

"

| I

I

.~,.~

an_

r~aq~o ugg.

20(deg.) Fig. 4. Ob~rved, calculated and difference neutron diagram of TbCr,~Ge,, measured iu the paramagnetic state at 20 K (top part) and in the magnetically ordered state at 1.5 K (bottom part). (i) Stays for an unidentified impurity phase.

mentioned in the previous section as they correspond to magnetic ordering taking place at of 16 K, which is different from the ordering temperature of the main phase. From the observation that the (001) reflection (only Tb contributions) has a very small intensity, one may draw the conclusion that the Tb moments are oriented in a direction close to the e axis. The refined moment values 8.74(10) ~,l'l'b and 0.48(12) p~ICr show that the Tb moment value is close to the Tb~+ free ion value of (gJ[p,,l--9lp,,]. The Cr has only a very small moment value. It is difficult to determine the latter accurately from powder data. However, within the 3o" limit the value obtained is in good agreement with the value of 0.2 p,~ derived from the magnetic measurements on YCr~,Ge~, [3]. The Tb moments make an angle of 25 deg with the e-axis while the Cr moments make an angle of about 143(7) deg with it (see Fig. 5). The moment values at the two Tb sites of different population were constrained to the same value. Here we would like to point out that due to the very small moment value the error in the corresponding orientational angle is also very large. We therefore prefer to restrict ourselves to a qualitative result by stating that within the 3o" limit the two ferromagnetic sublattices have a different easy axis of moment orientation. Because the canting angle between the two sublattices is larger than 90 deg. their coupling is most likely antiferromagnetic. The temperature dependence of the magnetic intensities and the corresponding moment values is shown in Fig. 6a.

Fig. 5. Schematic repre~ntation of the canted ferromagnetic moment arrangement of the TbCr,~Ge~ compound.

The two sublattices order simultaneously below T~= 10.3 K. The intensities of the (100) and the (101) reflections show a different behaviour. This can be explained by the fact that the fomler has only To contributions while the latter has contributions of both sublattices. The tempera° ture dependence of the Yo and Cr moments displayed in Fig. 6b shows that the ordering is clearly dominated by the ferromagnetic R-R interaction. At 4 K Tb has already reached the saturation value of 8.7 p,~ while the Cr value still increases.

4. Discussion The novel derivative of the HIFec,Ge~-type of structure found in ThC%Ge¢, adds a further member to the large family of RMoX~, (M=Fe. Mn, Cr, Co, and X~Ge0 Sn) compounds. The Mn compounds order with either the HfFec~Ge~, or the YCo6Ge~, types of structures. The Fe compounds display a much more complex ordering behaviour due to the presence of atomic density modulations mainly in the distribution of the R atoms and the X~ atoms along the e-axis. In some cases the atomic density modulation leads to long range ordering which comprises superstructures with various wave vectors as reported in [1] or to a complete disorder of the rare earth atoms at the I (a)

P. Schobinger.Pap, mumtello,s et al, / Jourtml ,!/" Alloys w.I Cw,lmumh 255 (1997) 07-Z~

72

TbCr~G% ; '~' ",.~"

. a

W

I

"

"

"

|''

~' 'U' i' 'I

i % I

"

'

i'l

'~-'-

~0@

®

p

lu ql ql

o.s

%

-

"u6

".

}

a..,

-

a

0.3 4

0

xbcr, ' " ' "

{'i""

80

T[K] a

4

®®

.

12

""

"

.... "

® ®

60

. m

I

@

o

.....

®

40

'q..,

t

20

"~,,!

• 100 L ...,o... 101

JLJJJ_a_LLL.a__t2

0

4

T[K]

$

12

Fig, O, Tem~ralure dependence of the moment value of the Tb and Cr ~tlbJatlit:e~ in ~r,~Ge,~, Also showl} is file thermal variation of the inlegrated intensity of several magnetic reflections (bottom pan) showing the ~totn of ferromagnetic order at T ~ 10.3 K,

tensions in the lattice which might relax by realizing a less rigid atomic distribution along the c axis. This is probably the reason why the lattice constant in the e direction of the Cr compound (0.82817(3) nm) is larger than that of the Mn compound (0.8181 ( 1)nm). Alternatively one may consider the structure of RCr6Ge 6 compounds as containing chains along the c direction consisting of R and Ge atoms. As can be seen in Fig. 3c, in the fully ordered HfFe6Ge 6 structure these chains consist of Hf(R) atoms at site I (z=O) alternated with a pair of dumbbell Ge atoms, the center of which is located at site II (z=l/2) in Fig. 3c. In the fully disordered YCo6Ge ~ structure sites I and il are statistically occupied by either Y atoms or a dumbbell pair of Ge atoms. The structure of TbCrt,Ge 6 represents an intermediate case. Here site I is occupied by 82% of Y atoms and site I1 by only 18% of Y atoms. As seen from the occupation numbers given in Fig. 3b for the Ge atoms, this substitution scheme is fairly well obeyed. The accommodation of more than I/6 of the R atoms into intermediate positions along the e chain greatly modifies the magnetic behaviour of the Tb moments in TbC%Ge~, compared to TbMn~Ge~ as it introduces additional R-R interactions at el2 distances and may also modify the crystal field interaction. Although TbMn~Ge(, has a much more complex magnetic structure than TbCrc,Geo, it is interesting to note that also the Mn compound displays a small ferromagnetic /x,te, moment component coupled antil~rromagnetically with the Mn moments in the low temperature region. The main difference between both compounds is that the spiral part observed in the Mn compound is missing in the Cr compound. The proposed model Ibr the magnetic structure is in concord with the results of magnetic measurements made at 5 K 131. If one takes the algebraic sum of the values presented in Fig. 6b at the same temperature one finds (8.2 p,a-6x0,4 p,a)~5.8 p,,. This value is in satisfactory agreement with the spontaneous moment of 6.2 P,, obtained ~y extrapolation of the data reported in Ret: 131 for fields below 20 T.

References

( ~ ) sites and the Ge2 atoms at the 2(c) (0,0.z) sites, as tbund in YCo,Ge,,. The atomic disorder lbund in TbC%G% relates to the smaller size of the Cr atoms and consequently to the rigid honeycomb part of the HfFef,Ge(, structure consisting of the Cr triangular prisms centred by the Gel and Ge2 sites. This is reflected also by the smaller size of the a lattice constant (0,517~(2) nm) compared to that of the fully ordered TbMn~G% structure (0.52412(6) rim). The inclu)ion of" ihe laigel tale eartll atOillb, such tits Tb, creates

III G. Venturini. R. Welter and B. Malama,. J. AIIoy.~ ('omp.. 183 (1~2) '(~, (21 ].H.VJ. Brabers,v.HM. buijl~, F.R. de B~r and K.HJ. Buschow, J. Alloys Comp.. 198 (1993) 127, 131 J.It.VJ. Brabers. K.H.J. B,aschow and F.R. de Bt~:r. J. AIh~ys (.~,,p.. 20.¢ (1994) 77, 14] R,R, Olentich. L.G. Akselrud and Ya.P. Yarmoliuk. Dopm'. Akad. Nauk. Ukr, RSR Ser. A. 2 (1981) 84, 151 E. Panh~ and B. Chabot. in K.A. Gschneidncr. Jr. and L. Eyring (Eds.), Handtmok an the Physics and Chemistr)" of Rare Earths. Vol. 6. Notth-ii~iiattd, Amsterdam. 19~4, p. 113.

P. Schobinger-Papomantellos et al. I Journal of Alloys and Compounds 255 (1997) 67-73 [6] G. Venturini, R. Welter and B. Malaman, J. Alloys Comp., 200 (1993) 51. [7] G. Venturini, B. Chafik E! irdissi, E. Ressouche and B. Malaman, J. Alloys Comp., 216 (1994) 243. |8] P. Schobinger-Papamantellos, J. Rodriguez-Carvajal, G. Andr~ and K.H.J. Buschow, Workshop on application of symmetr)." analysis to

73

diffraction investigations. Krak6w, July 6-9, 1996, p. 31 and references therein. |9] J. Redriguez-Carvajal, Physica B, 192 (1993) 55. [10] S.R. Hall, G.S.D. King and J.M. Stewart (Eds.), Xtal3.4 User's Manual, Univ. Western Australia, Lamb, Perth, 1995.