Crystal structure of Tl3AsSe3

M a t . R e s . B u l l . Vol. 9, pp. 3 6 5 - 3 7 0 , in the U n i t e d S t a t e s .

1974.

Pergamon

Press,

Inc.

Printed

CRYSTAL STRUCTURE OF TI3AsSe3*

H. Y-P. Hong and J. C. Mikkelsen, Jr. Lincoln Laboratory, Massachusetts Institute of Technology Lexington, M a s s a c h u s e t t s 02173 and G. W. Roland R e s e a r c h and Development Center, Westinghouse E l e c t r i c Corp. Pittsburgh, Pennsylvania 15235 ( R e c e i v e d J a n u a r y 31, 1974; C o m m u n i c a t e d b y J. B. G o o d e n o u g h )

ABSTRACT The s t r u c t u r e of T13AsSe^, which has been solved by the s i n g l e - c r y s t a l x - r a y method, is rliombo~edral, with space group R3m and cell p a r a m e t e r s a = 9. 870(2)~, c = 7 . 0 9 4 ( 3 ) L z = 3. A f u l l - m a t r i x l e a s t - s q u a r e s refinement gives weighted R = 0.058. The Se a t o m s form equilateral t r i angles around T1 at 3.178A and around As at 2.207~. The s t r u c t u r e may be d e s c r i b e d in t e r m s of units f o r m e d from three T1Se 3 triangles by c o r n e r - s h a r i n g . These units share c o r n e r s to produce a helical a r r a n g e ment along the c axis. The triangles of AsSe 3 a r e isolated f r o m each other.

Introduction Single c r y s t a l s of T13AsSe 3 a r e of interest f o r the nonlinear optical p r o c e s s e s of second harmonic generation and p a r a m e t r i c oscillation (1), and for opto-acoustic applications such a s modulation and filtering.

The nonlinear optical susceptibilities

a r e about t h r e e t i m e s those of Ag3AsS 3 (proustite), a s i m i l a r sulfosalt material.

The

interpretation of the optical p r o p e r t i e s has so far r e l i e d on s y m m e t r y information

*The l.incoln Laboratory portion of this work was s p o n s o r e d by the Department of the Air Force. 365

366

CRYSTAL

STRUCTURE

O~-" TI3AsSe 3

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obtained f r o m s i n g l e - c r y s t a l p r e c e s s i o n photographs and the Laue photographs used f o r c r y s t a l orientation. T13AsSe 3.

In this paper we r e p o r t on the s t r u c t u r a l determination of

The s t r u c t u r a l data confirm our e a r l i e r s y m m e t r y assignment (1) (Laue

space group R3m) and provide information needed f o r theoretical calculations of nonlinear optical p r o p e r t i e s using models such as the bond charge model of Levine (2) or the m o l e c u l a r orbital theory of Tang (3). In addition, knowledge of the s t r u c t u r e of T13AsSe 3 is r e q u i r e d f o r the interpretation of Raman s p e c t r a and piezoelectric and e l e c t r i c a l p r o p e r t i e s , and f o r the g e n e r a l understanding of the c r y s t a l c h e m i s t r y of sulfosalt compounds. Sample Preparation Growth of T13AsSe 3 single c r y s t a l s by the Bridgman-Stockharger technique has been r e p o r t e d previously (1).

Laue hack-reflection and oscillation photographs of

s a m p l e s cleaved f r o m these c r y s t a l s w e r e v e r y diffuse, indicating a high degree of mechanical damage and the unsuitability of such s a m p l e s for a s i n g l e - c r y s t a l s t r u c ture determination.

In o r d e r to r e m o v e s u r f a c e damage, cleaved pieces s e v e r a l mm

on a side w e r e etched to 0 . 1 mm dimensions in a solution of 10°7oBr 2 in methanol. Although the etched c r y s t a l s produced much s h a r p e r oscillation photographs, x - r a y intensity data f o r one of them yielded an u n s a t i s f a c t o r y s t r u c t u r e determination, with a weighted d i s c r e p a n c y

(Rw) value of 0.10.

This poor r e s u l t was probably due in

p a r t to a s t r a i n e d c r y s t a l m o s a i c produced during c r y s t a l growth o r in subsequent handling, including cleaving. In o r d e r to obtain improved c r y s t a l s , the t e m p e r a t u r e profile f o r BridgmanS t o c k ~ r g e r growth was changed by providing n e a r l y i s o t h e r m a l upper and lower furnace zones of 345 ° C and 275 ° C (± 10 ° C over the length of the boule) r e s p e c t i v e l y , with a furnace gradient of 30 ° C / c m at the melting point of 310 ° C.

The lowering rate

w a s r e d u c e d to 8 m m / d a y , and the sample was cooled to room t e m p e r a t u r e at less than 40 ° C/day.

The cleaving n e c e s s a r y to provide s a m p l e s f o r etching was minimized

by growing the boule as a 2 mm o.d. rod.

X - r a y intensity m e a s u r e m e n t s w e r e made

on a sample that had been etched to 0 . 2 x 0 . 1 x 0 . 1 ram.

The s t r u c t u r e determination

gave an R value of 0.058, a s r e p o r t e d below, a significant i m p r o v e m e n t o v e r the e a r w l i e r determination; since the shapes of the two m e a s u r e d c r y s t a l s w e r e quite similar, this improvement m a y have been due to a l e s s - s t r a i n e d c r y s t a l mosaic.

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CRYSTAL

STRUCTURE

O F TI3AsSe 3

367

Structure Determination The T13AsSe 3 c r y s t a l was mounted on a g o n i o m e t e r head along the c axis f o r x - r a y investigation.

Oscillation and Weissenberg photographs showed a rhombohedral

lattice with diffraction s y m m e t r y 3rn.

T h e r e was no s y s t e m a t i c absence, which is

consistent with space groups R32, R3rn and R3m.

The 2e m e a s u r e m e n t s and intensity

data w e r e taken with a General E l e c t r i c XRD s i n g l e - c r y s t a l d i f f r a c t o m e t e r .

Twenty

high-angle reflections w e r e carefully centered on Kc~1 of s i l v e r radiation ()~ = 0.55936) using a 1° take-off angle and a 0.02 slit. e t e r s a = 9.870(2)A, c = 7.094(3)~.

A l e a s t - s q n a ~ s refinement gave cell p a r a m -

T h r e e - d i m e n s i o n a l intensity data to 20 = 50 ° , a

total of 293 independent reflections, were collected by the s t a t i o n a r y - c r y s t a l , s t a t i o n a r y - c o u n t e r method, using Pd-filtered AgKC~ radiation and a 5 ° take-off angle. Each peak was counted for l0 sec, and the background was also counted for I0 sec. Lorentz, polarization and C-angle absorption c o r r e c t i o n s were applied.

The l a t t e r

c o r r e c t i o n n e v e r exceeded 20~o. The variance f o r the s t r u c t u r e f a c t o r s was calculated 1 + IB/Ip]1/2 F f r o m the eqnation cT(F) -- 1/2|K._ 1 - i ~ J- , where I B i s t h e background, I p i s the

B"P peak count, and K is the product of the Lorentz, polarization and absorption c o r r e c tions. The intensity data were used to generate a t h r e e - d i m e n s i o n a l Patterson map, which showed strong interactions on the z = 0 plane at (0. 60, 0, 0), (0, 0.60, 0) and (0.60,0.60,0).

Of the three possible space groups, R3m should give interactions at

( 1 / 2 , 0 , 0) and (0, 1/2, 0), while R32 cannot produce interactions at (x, 0, 0), hence R3m was chosen.

This confirms the assignment of R3m by F e i c h m e r and Roland (1) based

on the p r e s e n c e of p i e z o e l e c t r i c i t y and absence of optical activity. Since the m e a s u r e d density is 7.83 g / c c (1), the unit cell must contain three (T13AsSe3) molecules, yielding D calc = 7.82 g / c c .

The nine T1 and Se atoms in the

unit cell should occupy the special position (x,x, z), (x, 2x, z), (2x, x, z) of R3m.

The x

coordinate of T1 can be computed f r o m the Patterson map interaction (0, 3x, 0), which gives x = 0.20.

The z coordinate of the T1 atoms was a r b i t r a r i l y chosen as zero,

while the z coordinate of the Se atoms was calculated f r o m the peak at (0, 0, 0.45) appearing on the Patterson map.

The (0, 0, z) interaction indicates that T1 and Se atoms

have the same x, y coordinates.

The As atoms at special position (0, 0, z) also can be

located f r o m the Patterson map.

The atomic positions, scale f a c t o r and anisotropic

368

C R Y S T A L S T R U C T U R E O F T13AsSe 3

Vol. 9, No. 4

t e m p e r a t u r e f a c t o r s w e r e then refined, using a full-matrix, l e a s t - s q u a r e s p r o g r a m , to give R w = 0.058 and R = 0. 105 for all reflections, w h e r e Rw = [Zw (F ° - Fc)2/ 5:wF2]l/2withw

=x/g 2andR =r [ F

0

- F o

a large n u m b e r of weak reflections.

I/Z I F C

I.

The high R value is due to

0

The final atomic positions and anisotropic t e m p e r -

a t u r e factors a r e listed in Table 1, and the bond distances and angles a r e listed in Table 2. TABLE 1 Final Atomic Positions f o r T13AsSe3* Space Group: R3m; cell p a r a m e t e r s : a = 9.870(2)~, c = 7.094(3)~ Atoms T1 As Se

x

y

z

0.2052(1) 0.4103(2) 0

0

$11

0 0.745(1)

$22

~33

S12

$23 $31

0.0074(2) 0.0074(2) 0.0121(4) 0.0037(1)

0

0

0.0052(7) 0.0052(7) 0.006(2)

0

0

0

0.0034(9)

0

0

0.2052(4) 0.4103(8) 0.4480(9) 0.0069(5) 0.0069(5) 0.024(3)

*Standard deviations a r e given in parentheses. The t e m p e r a t u r e f a c t o r is exp [- (•11 h2 + 822 k2 + ~33 ~2 + S12hk + B23k6+ ~31h~)].

TABLE 2 Bond Distances and Angles for T13AsSe 3 Triangle around As Distance As - Se

Angle

3 x 2.207(7)~

Se - As - Se

118.7(2) deg

Pentagon around T1 Distances T1 - Se

3 x 3. 176(6)~

T1 - Se

2 x 3.438(5)~

Description of the Structure Although the T13AsSe 3 s t r u c t u r e and proustite (Ag3AsS 3) a r e both rhombohedral and have comparable lattice p a r a m e t e r s , the R3m cell of T13AsSe 3 contains Z = 3 molecules w h e r e a s the R3c cell of proustite has Z = 6. Both s t r u c t u r e s contain equilateral trianglss of cb.alcogenitte with As atoms displaced from the c e n t e r

Vol. 9, No. 4

CRYSTAL

STRUCTURE

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FIG. 2

FIG. 1

An a - b projection of Ag3AsS 3, showhug the AsS 3 triangles a r e c l o s e - p a c k e d by the Ag-S covalent bonding.

An a - b projection of T13AsSe3, showing the AsSe 3 triangles a r e connected by T1 atoms to form a helical spiral about the c - a x i s .

perpendicular to the plane, as shown in the a - b projection of T13AsSe 3, Fig. 1, and the basal-plane projection of proustite, Fig. 2. cal spiral about the c - a x i s .

In both, these triangles form a heli-

However, in proustite there is a double spiral with a zig-

zag chain of s i l v e r atoms along the s p i r a l axis, w h e r e a s in T13AsSe 3 the second spiral is f o r m e d from equilateral T l - a t o m triangles located 0.45c beneath the Se triangles and there is no m e t a l - a t o m chain along the spiral axis.

This configuration gives each

T1 atom a fivefold Se coordination: t h r e e at 3. 178A form an equilateral triangle with o

T1 displaced perpendicular to its center, and two at 3.438A, as shown in the upper right of Fig. 1. The A s - A s separation is 7.09A, w h e r e a s formation of the double helix makes this separation 4.35 ~ in proustite.

The Ag-S (2.40A) bond in proustite is

m o r e covalent than the T1-Se (3.178A) bond in T13AsSe3, which is consistent with a s m a l l e r c h a r g e on the Ag atoms, which have s h o r t e r (3.14~) Ag-Ag separations within the zig-zag c - a x i s chains. References 1. J. D. F e i c h m e r and G. W. Roland, Appl. Optics 11, 993 (1972). 2.

B. F. Levine, Phys. Rev. Lett. 22, 787 (1969).

3.

C. L. Tang, IEEE J. Quantum Electron. QE-9, 755 (1969).

4.

R. W. G. Wyckoff, C r y s t a l Structures, Vol. 2, p. 511. New York (1960).

Interscience Publishers,