Rietveld analysis of LiB13 with β-rhombohedral boron structure

Journal of

ALLOYS AND C O M ~ U N D 5 ELSEVIER

Journal of Alloys and C o m p o u n d s 221 (1995) 120-124

Rietveld analysis of LIB13 with /3-rhombohedral boron structure Masayoshi Kobayashi ~'*, Iwami Higashi ~, Hirofumi Matsuda b, Kaoru Kimura b " The Institute of Physical and Chemical Research (Riken), Wako, Saitama 351-01, Japan b Department of Materials Science, The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan Received 31 August 1994

Abstract

A lithium-containing boron-rich solid was prepared from lithium and powdery /3-rhombohedral boron in a tantalum boat which was enclosed in a quartz tube heated at 1000 °C. The boron framework of the Li-B reaction product has the same structure as the framework of /3-rhombohedral boron. The lattice constants are ah¢,=10.9654(9) /~ and ch~x=24.0495(23) /~ (space group R3m, no. 166). The lithium atoms occupy the D and E holes in the boron framework with full occupancy. The occupancies of B(13) and B(16) sites are 0.64(3) and 0.10(3) respectively. The chemical composition obtained by Rietveld analysis is LiB12.9(l). Keywords: Rietveld analysis; Lithium; Boron-rich solids

1. Introduction

A large number of binary [1-5] and ternary [6,7] boron-rich solids of the /3-rhombohedral boron (/3boron) structure have been reported. The doping elements are transition metals [1-6], partially filled p-level elements [3], or aluminum [8]. Although /3-boron is the least space-filling modification of elementary boron, the interstitial holes occupied by other atoms are mainly limited to the holes designated A, D, and E [1] depending on the preparation method [4] reflecting thermal equilibrium of the system, but not always on the radii of the doped atoms [3,4,7]. Doped/3-boron structures have been studied by single-crystal X-ray diffractometry except for one study in which a Rietveld-type powder method was applied to X-ray powder-film data [5]. Despite much research, no crystal and structural data for alkali-doped /3-boron have so far been reported. Because of the structural similarity of the B84 unit to the f.c.c, potassium-doped C60 unit [9], lithium-doped /3-boron is attracting much interest and has been prepared by vapor-solid reaction in a sealed tube. Some of the physical properties of the reaction product are described elsewhere [10]. In this paper, we describe the result of the first structural analysis of lithium-

* Corresponding author.

0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925-8388(94)01438-8

doped /3-boron using the Rietveld method, that is an X-ray powder profile refinement technique.

2. Experimental details

2.1. Sample preparation Polycrystalline B-boron powder (Rare Metallic Co. 250 mg, approximately 99%) and lithium metal bits (22 mg, approximately 99.9%) settled apart at both ends of a tantalum boat were enclosed in an evacuated quartz tube. The heating temperature was raised to 1000 °C and maintained for 140 h. The reaction product was black agglomerated globules, which were crushed down and ground gently in an agate mortar for X-ray diffraction and property measurements. Chemical analysis was done by inductively coupled plasma (ICP) and atomic absorption spectroscopic methods giving the boron and lithium contents as 86.35(25) and 4.92(14) wt.%; the balance (ca. 9%) from 100% was in the main ascribed to lithium-boron-oxide impurities. The nominal boron-to-lithium atomic ratio is calculated as 11.3(3).

2.2. X-ray measurement and data reduction A powder specimen was spread on a non-reflective quartz specimen holder with a well depth of 0.2 ram.

M. Kobayashi et aL / Journal of Alloys and Compounds 221 (1995) 120-124

X-ray diffraction (XRD) intensity profiles for Rietveld refinement were obtained on an automated X-ray diffractometer (Rigaku RAD-R theta/theta goniometer system) using monochromatized Cu Ka radiation through a graphite monochromator in the diffracted beam. The XRD intensities, each of which was measured for 10 s, were registered at each data point step-scanned by 0.05 ° over the 20 range from 8° to 90°. The intensities were corrected for both the specimen area irradiated and the specimen thickness [11] successively. The corrected diffraction intensity data profiles were used for structure refinement employing the Rietveld method using the computer program RIETAN [12], supplied by Izumi.

3. Structure refinement and discussion

The collected XRD peak profiles shown in Fig. I(A) are similar to those of the pristine /3-boron shown in Fig. I(B) except for a few small extra peaks. However, the profile of the background or base line with broad undulations is different from that of /3-boron. This suggests the presence of primary fine particles and/or some amorphous phases due partly to a transition state from the reactant to the reaction product and amorphous impurities. The Rietveld refinement was carried out using these XRD peak profiles without excluding the undulations of the background line, starting from the structural data of CUBE3 [2]. Throughout the structural T

T

q

3

2

cO k~

O_L

.~

a

J

EB}

@ I0

20

30

40

50

20 ( DEO )

60

70

80

90

( CuK~ )

Fig. I. Collected X R D peak profiles (Cu g ~ ) for (A) lithium-doled fl-boron, and (B) for pristine fl-boron. Profiles of the background or base line observed in (A) show much stronger and broader undulations compared with (B).

121

refinement, constant isotropic thermal parameters of 0.5, 1.0 and 1.5 tl,2 were applied respectively for B(1-12, 14), B(13, 16) and lithium atoms, and B(15). Full occupancy was assumed for all the boron atom sites except the B(13) and B(16) sites. The preferred orientation was not considered because of the hard and brittle nature of B12 icosahedral materials giving no cleavage planes. The Rietveld refinements were performed consecutively as summarized in Table 1. They are explained as follows. (1) First a structural refinement was done for the occupational parameter (OP) of B(13) by fixing the positional parameters (PPs) of B(1)--B(15) without metal atoms; the reliability R factors [12] obtained were Rwp=0.24, Re=0.19, R~=0.27, and RF=0.16. (2) Next, putting lithium atoms at the D and E positions, a refinement was done for the PPs and OPs of the metal sites, resulting in greatly reduced R factors, Rwp = 0.17, Rp = 0.13, RI = 0.13, and Rv = 0.092. The OPs were 1.07(5) and 1.23(8) for the D and E positions respectively, indicating that both positions are practically fully occupied. Since simultaneous occupation of E and A holes is impossible owing to the short distance between the two [4], the completely filled E hole seems to indicate that the A hole is completely vacant. To examine whether the A hole is really vacant, the lithium atom was moved from the E site to the A1, A2 or A3 site [1] and a refinement was done in the same manner. As a result, the A1, A2 or A3 site was found to be vacant. Therefore, another refinement was done again fixing the OPs of the D and E sites at unity. The R factors obtained at this stage w e r e g w v --- 0.17, Rv = 0.13, RI=0.15, and RE=0.099. (3) Further refinement was done including the occupancy of the B(16) site newly added, fixing the PPs. The R factors obtained were Rwp=0.17, Rv=0.13, R I = 0.15, and Rv = 0.098 with an occupancy of 0.08(2). (4) By adjusting the PPs of B(1)-B(15), D and E, but not those of B(16), the R factors obtained were Rwp=0.11, Rv=0.088, R,=0.071 and Rv=0.052, with OPs of 0.64(3) and 0.10(3) for the B(13) and B(16) sites respectively. In this final stage, eleven small peaks which did not correspond with the calculated peaks were excluded from the diffraction data. (Some of these peaks were also observed in the X R D profile of a similarly heat-treated specimen of /3-boron without added lithium.) Since refinement of the PPs of the B(16) site gave unusual or impossible interatomic distances between this site and neighboring boron atoms 2B(1), 2B(5) and 2B(7), which constitute a hexagonal ring, the B(16) atom was fixed at the centre of the boron hexagon as is often seen in boron-rich solids with the/3-boron structure. The same PPs and OPs as determined by starting with the structural data of CUB23 were obtained from the refinement performed starting

122

M. Kobayashi et al. / Journal of Alloys and Compounds 221 (1995) 120-124

Table 1 Refinement of parameters and R factors obtained Refinement number

Structure

1

B(1-15) b.~

2

B(I-15) b,~ Li(D,E) ~

3

B(1-15) b., Li(D,E) ~ B(16) ~ B(1-15) ~ Li(D,E) o B(16) g

4f

Refined parameters"

LCs(a,b) OP(B(13)) LCs(a,b) OP(B(13)) PPs(Li(D,E)) LCs(a,b) OPs(B(13,16)) PPs(Li(D,E)) LCs(a,b) PPs(B(1-15)) Oas(B(13,16)) PPs(Li(D,E))

Reliability factors

Rwe

Re

Rt

R~

0.24(2)

0.18(8)

0.27(2)

0.16(3)

0.17(2)

0.13(4)

0.14(7)

0.099(4)

0.16(9)

0.13(3)

0.14(8)

0.097(6)

0.11(2)

0.088(4)

0,071(2)

0.052(3)

" LCs, OP(s) and PPs denote lattice constants, occupational and positional parameters respectively. b PPs for B(1-15) were fixed at those of CUB23. OPs of B(1-15) except B(13) were fixed at unity. d OPs of lithium atom positions for D and E were fixed at unity as found presently. PPs for B(16) were fixed at those of CUB23. f 11 peaks were excluded from the intensity profile data. g PPs for B(16) were fixed at the calculated values are described in the text.

with the data for CrB41 [1] or ScB=8 [13], with added PPs and occupancy of the B(16) site. The CrB4~ comprises B(1)-B(15) and two metal positions A~ and D, while the SCB28 consists of B(1)-B(15) and three metal positions D, E, and F. This shows that a reasonable convergence of the adjusted parameters has been achieved. The F position found for SCB28 was checked as the dopant position of the lithium atom which substituted for two B(4) atoms. However, the presence of the lithium atom at the F position was not confirmed. Further, occupation of the boron sites from B(17) to B(20) [14] was examined, but no boron atoms were found at these sites. Fig. 2 illustrates the profile fit and difference patterns for the specimen. The positions of the possible Bragg peaks (Cu Ka~ and Ka2) are denoted by short vertical lines. The figure shows that the calculated pattern (solid line) fits the observed pattern (crosses) well except for the range of 20 around 18° ~ 40 ° where many differences are observed owing to a great many peaks accompanied by large and wide undulations with intense fluctuations of the background. The final structure data obtained at stage (4) are shown in Table 2. The lattice constants were refined to a,¢,= 10.9654(9) /~ and ch~=24.0495(23) ,~. They shows light increments in ah~x and c,,, by 0.3% and 1.0% compared with those of ~3-boron [14]. A significant feature of the metal distribution is that the lithium atoms occupy D and E holes with full occupancy. The occupancies of the B(13) and B(16) sites are 0.64(3) and 0.10(3) respectively. Accordingly, there are 24

"o 4 ×

3

2

L III

I I Itll I IIII III IIIIIIIII I I I I I l l U l I I IIIIIII I I I l l N I l l l N I l ~ l i i

I

I

I

I

I

I

I

I

10

20

30

40

50

60

70

80

2 0 ( DEC, )

90

( CuKct )

Fig. 2. Rietveld refinement patterns for the lithium-doped /3-boron. The slender line ( - - ) shows calculated intensities and the crosses ( × x ) are observed intensities corrected for both the specimen area irradiated and the specimen thickness. Ayi is the difference between the observed and calculated intensities on the same scale as above.

lithium and 310.3(1.1) boron atoms in a hexagonal unit cell, giving a boron-to-lithium atomic ratio of 12.9(1), in good agreement with that (11.3(3)) measured by chemical analysis. Therefore, we denote this material hereafter LIB13. The B-B bond lengths in LiBla range from 1.57(3) to 2.04(4) A. A significant feature is that the intercluster B-B bonds are shorter than those of undoped/3-boron [15]. Interatomic distances from the D and E positions to neighboring B atoms are given in Table 3. As for the D position, the 15 Li-B distances cover a wide

M. Kobayashi et al. / Journal of Alloys and Compounds 221 (1995) 120-124

123

Table 2 Structural data for LiB13 (Ram, ahcx= 10.9654(9) A., Ch~= 24.0495(23) ]k) Atom

Position

x ( x 104)

y

z

Occupancy"

B(A2) b

B(1) B(2) B(3) B(4) B(5) B(6) B(7) B(8) B(9) B(10) B(I1) B(12) B(13) B(14) B(15) a(16) Li(D) Li(E)

36i 36i 36i 36i 18h 18h 18h 18h 18h 18h 18h 18h 18h 6c 3b lSh 18h 6c

1732(14) 3171(17) 2682(21) 2346(19) 548(9) 868( 11) 1110(12) 1697(11) 1267(13) 1042(13) 553(10) 901(14) 581(17) 0 0 565(25) 1935(17) 0

1711(16) 2968(16) 2269(22) 2547(16) -x -x -x -x -x -x -x -x -x 0 0 -x -x 0

1770(7) 1268(7) 4182(7) 3443(8) -594 134(12) - 1111(10) 296(12) - 2318(10) - 2984(12) 3260(9) 4006(14) -4536(14) 3919(21) 1/2 1182(18) 1880(16) 2162(25)

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 0.64(3) 1.0 1.0 0.10(3) 1.0 1.0

0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 1.0 1.0 1.5 1.0 1.0 1.0

"The Li(D) and Li(E) sites were practically fully occupied. b A fixed value is used. Table 3 Comparison of metal-boron distances (/~.) with those observed for the fl-rhombohedral boron type solids" Position

Boron

LIB13b

CuB.z3c

ScB2~a

CrB41 •

D D D D D D D D D Average

2B(1) 2B(2) 2B(2) 2B(3) 2B(3) 2B(13) 1B(12) 1B(13) 1B(15)

2.28(3) 2.51 (3) 2.27(2) 2.29(4) 2.68(4) 2.39(3) 2.10(5) 2.25(4) 2.70(2) 2.39(3)

2.24(7) 2.40(7) 2.34(7) 2.43(7) 2.43(7) 2.55(5) 2.36(7) 2.27(7) 2.67(7) 2.41 (7)

2.440(4) 2.454(3) 2.428(2) 2.388(3) 2.447(3) 2.404(5) 2.357(3) 2.097(5) 2.457(1) 2.402(3)

2.442(3) 2.431(3) 2.419(3) 2.446(4) 2.283(4) 2.398(4) 2.363(5) 2.005(5) 2.434(2) 2.376(4)

E E E E Average

6B( 1) 3B(11) 3B(9) 3B(10)

2.11 (3) 2.84(6) 2.44(2) 2.80(5) 2.46(4)

2.25(6) 2.65(1) 2.47(1) 2.67(1) 2.46(3)

2.405(2) 2.492(3) 2.467(2) 2.506(3) 2.455(2)

"The listed D-B distances for CuB2a, ScB2s and CrB41, in which the D site is split, are those of DI-B. b Present work. c Ref. [2]. a Ref. [13]. e Ref. [1]. r a n g e f r o m 2.10(5) to 2 . 7 0 ( 2 ) / ~ . T h e a v e r a g e v a l u e o f 2.39(3) A is, however, c o m p a r a b l e with t h o s e o f 2.41(7), 2.402(3), a n d 2.376(4) A r e s p e c t i v e l y o b s e r v e d for CuB23 [2], S¢B28 [13], a n d CrB4~ [1] which w e r e o b t a i n e d by single-crystal X - r a y analysis. A s i m i l a r s i t u a t i o n is f o u n d for t h e L i - B d i s t a n c e s f r o m t h e E p o s i t i o n to t h e s u r r o u n d i n g 15 B a t o m s . T h e a v e r a g e v a l u e o f 2.46(4) /~, o b s e r v e d c o r r e s p o n d s well w i t h 2.46(3) a n d 2.455(2) o b s e r v e d for CUB23 a n d ScB2s respectively.

4. Conclusions

T h e s t r u c t u r e o f a l i t h i u m - c o n t a i n i n g b o r o n - r i c h solid was a n a l y z e d by t h e R i e t v e l d m e t h o d , a n d was r e f i n e d to t h e R factors R w v = 0 . 1 1 , R F = 0 . 0 8 8 , R ~ = 0 . 0 7 1 a n d R v = 0 . 0 5 2 . T h e s t r u c t u r e o f t h e b o r o n f r a m e w o r k is t h e s a m e as that o f f l - r h o m b o h e d r a l b o r o n . T h e l a t t i c e c o n s t a n t s a r e a ~ x = 10.9654(9)/~ a n d Chex= 24.0495(23) /~. (space g r o u p R a m , no. 166). T h e l i t h i u m a t o m s

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M. Kobayashi et al. / Journal of Alloys and Compounds 221 (1995) 120-124

occupy the D and E holes in the boron framework with full occupancy. The occupancies of B(13) and B(16) sites are 0.64(3) and 0.10(3) respectively. The chemical composition obtained by Rietveld analysis is LiBmg(1).

Acknowledgements The authors would like to thank Professor H. Suematsu and Dr. Y. Murakami of Department of Physics, The University of Tokyo, for technical supports to dope Li into the /3-rhombohedral boron.

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