A structural investigation of V2B3 by single-crystal diffractometry

Journal of

AND C O M ~ D S ELSEVIER

Journal of Alloys and Compounds 221 (1995) 86-90

A structural investigation of V2B3 by single-crystal diffractometry Y. Yu a, L.-E. Tergenius a, T. L u n d s t r 6 m a,,, S. O k a d a b Institute of Chemistry, Box 531, S-751 21 Uppsala, Sweden bDepartment of Applied Chemistry, Kanagawa University, Rokkakakubashi, Kanagawa-ku, Yokohama 221, Japan Received 5 August 1994

Abstract

The crystal structure of V2B3 was reinvestigated using single-crystal X-ray diffractometry. V2B3 crystallizes in the orthorhombic space group Cmcm with a =3.0599(4) ~ , b = 18.429(2) ~, c =2.9839(4) ~ , Z = 4 . The crystal was grown from a high temperature aluminium melt with vanadium metal chips and boron powder as starting materials. The structural parameters of V2B3 were refined with a full-matrix least-squares program to a final R(F 2) value of 0.024 for 984 unique reflections. The influence of atomic radii of transition metal elements on the unit cell parameters is discussed.

Keywords: Single crystals; Crystal structure

1. Introduction

2. Experimental details

In the late 1960s Spear and Gilles discovered V2B3 [1]. They characterized the phase by X-ray powder diffraction and proposed a crystal structure which has been proved to be correct. The crystal structure of V2B 3 has so far not been studied by single-crystal methods, although it is the prototype structure of several binary and ternary borides. In 1972 Chepiga et al. reported a ternary phase Cr3NiB6 with the V2B3 structure type [2] and the structural parameters were refined by powder X-ray diffractometry on the basis of Spear and Gilles's work. In 1973 Kuz'ma and Starodub reported the existence of CoVB3 [3]. From a single-crystal diffraction study they found an ordering of the metal atoms, which occupy two different atomic positions. In some literature these two ternary phases are incorrectly referred to as the prototype of the VzB3-type structure [4]. In 1987 Okada et al. [5] reported an accurate single-crystal study of a binary boride, Cr2B3, belonging to the V z B 3 family. Recently the preparation of single-crystal V2B3 by the high temperature metal solution method was reported [6]. In the present paper we describe the results of a refinement of the prototype structure V2B 3 by single-crystal X-ray diffractometry.

Details on the growth process and the optimum growth conditions for single-crystal V2B 3 w e r e reported elsewhere [6]. The unit cell parameters were examined by X-ray powder diffraction using a Guinier-Hagg camera with Cu Kal radiation (A--1.540598 ,~,) and semiconductor grade silicon (a=5.431065 ~) as internal calibration standard [7]. The unit cell parameters were determined by least-squares refinement using a local programme [8]. An optical microscope and a Weissenberg X-ray camera were used to examine the asgrown crystals and to select a well-formed V2B3 single crystal for the structure refinement. The X-ray intensity data collection was performed with a Rigaku AFC6R automatic four-circle singlecrystal diffractometer using graphite-monochromated Mo Ka radiation (A=0.7107 ~ ) and the w--20 scan technique. Six standard reflections were measured at every 150th reflection to check the stability of the primary X-ray beam of the equipment. Most of the pre-refinement corrections on the original intensity data were carried out using the program TEXSAN [9]. The intensity data were first corrected for Lorentz polarization effects. A linear decay correction of about 1% was then applied on the measured intensities. Absorption corrections were applied using the gaussian grid technique. Crystal and diffraction data are given in Table 1.

* Corresponding author.

0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved SSDI 0925 -8388 (94)01387-X

87

Y. Yu et al. / Journal of Alloys and Compounds 221 (1995) 86-90

Table 1 Crystal and diffraction data for V2B3 Space group Z Cell dimensions (/~) Crystal size (/.~m3) Absorption coefficient (cm -1) Number of boundary planes Transmission factors 20 limit (deg) Number of reflections collected Number of non-equivalent reflections X-Ray density (g cm -3)

Cmcm (No. 63) 4 a=3.0599(4), b=18.429(2), c=2.9839(4) 170× 170×90 111.4 12 0.22-0.51 157.307 2447 984 5.302

3. Refinement of V2B3 structure

Structure refinement was carried out using the fullmatrix least-squares program DUPALS [10]. The atomic positions and temperature factors of the isostructural Cr2B3 [5] were used as initial parameters for the refinement of V2B3. After a few cycles the refinement converged to about 18%, which included variation in all positional parameters and isotropic temperature factors. Comparison of calculated and observed structure factors showed that the strongest observed structure factors were systematically smaller than the calculated structure factors, indicating the occurrence of extinction effects. Large extinction effects have also been observed previously in single-crystal structure refinements using high temperature solution-grown crystals of e.g. LaB6 [11] and TasB6 [12]. Corrections for the extinction effect were then applied in the refinement. It was found that the model of type II (crystal-size-dominated extinction) gives a better fit than other types of correction. The R value decreased from 18% to 12% after the type II extinction correction was applied. The extinction correction for the strongest reflections was, however, very large, exceeding 20% for the 51 strongest reflections. Such large corrections are certainly outside the limit of validity of the correction theory used in the programme. Therefore the 51 reflections were excluded and the refinement then converged at about 6%. By carefully checking the raw data intensity file, it was noticed that reflections in a specific angle region (X close to 90°; 148° < 20< 154°) have a very uneven background. For every reflection in this region, background 2 (high angle side) is more than 100 times larger than background 1 (low angle side). It is likely that in this region the primary X-ray beam is not in a good setting condition for the ditfractometer. Therefore all 105 reflections in this region were also excluded. Prior to the final refinement the equivalent reflections were averaged. The final refinement was based on F 2 and a total of 16 parameters were refined, including one scale factor, five positional parameters, three isotropic tern-

Table 2 Final structure data for V2B3, where the estimated standard deviations are given in parentheses (space group Cmcm (No. 63)). All the atomic positions are full occupied Atom

Position

x

y

z

Bi~o

(As) V(1) V(2) B(1) B(2) B(3)

4c 4c 4c 4c 4c

0 0 0 0 0

0.42935(1) -0.29502(1) 0.02351(4) 0.11779(4) -0.16862(4)

0.25 0.25 0.25 0.25 0.25

Anisotropic Anisotropic 0.31(1) 0.31(1) 0.34(1)

Table 3 Anisotropic displacement parameters for V2B3 (displacement factor exp[ - 2~r2(Ulth2a .2 + U22k2b*2 + U~fl2c*2 + 2Ut2hka*b * + 2Ut~hla*c* + 2Uz~k/b*c*)], where UI2 = U13= U23= 0). The estimated standard deviations are given in parentheses Atom

V(1) V(2)

Ull

U22

U33

(A2)

(A2)

(A2)

0.00276(3) 0.00274(3)

0.00313(4) 0.00284(4)

0.00318(3) 0.00311(3)

perature factors, six anisotropic temperature factors and one isotropic extinction parameter. Refinement of occupancy parameters was performed for vanadium as well as for boron positions separately. No significant deviation from full occupancy was obtained. Refinement of anisotropic temperature factors for boron positions was also performed, resulting in a small increase in R values. Therefore the final refinement was based on full occupancy of all atomic positions, anisotropic temperature factors for vanadium atoms and isotropic temperature factors for boron atoms. The factors C1 and C2, which modify the standard deviations based on counting statistics, were given the values 2.51 and 0.005 respectively. The S value (standard deviation of an observation of unit weight [13]) was 1.296, which indicates that the weights used are reasonable. Similarly, analysis of the normal probability plot of ranked weighted differences gave a least-squares line slope of 0.92 and a y intercept of -0.04, which indicates a

88

Y. Yu et al. / Journal of Alloys and Compounds 221 (1995) 86-90

Table 4 lnteratomic distances for V2B3, where the distances listed are all V - V < 4.00/~, V - B < 3.85/~ and B - B < 3.06/~. T h e estimated standard deviations are given in parentheses Atoms

Distance

(A) V(1)-2V(2) 2V(1) 2V(1) 2V(1) V(2)~V(2) 2V(1) 2V(2) 2V(2) V(1)-4B(2) 4B(1) 2B(1) 2B(3) 4B(I) 2B(2) 4B(3) V(2)-2B(2) 4B(3) 1B(3) 2B(2) 2B(1) 4B(2) 2B(3) 2B(3) B(1)-2B(1) 1B(2) 2B(1) 2B(2) 2B(1) 2B(3) B(2)-2B(3) 2B(2) 2B(2) B(3)-ZB(3) 2B(3)

2.890(2) 2.984(0) ' 3.003(3) 3.060(0) ~ 2.705(1) 2.890(2) 2.984(2) 3.060(0) ~ 2.307(1) 2.307(1) 2.314(2) 2.365(2) 3.776(1) 3.796(2) 3.808(1) 2.219(0)" 2.240(2) 2.329(2) 3.590(2) 2.678(2) 3.718(1) 3.785(2) 3.846(2) 1.725(2) 1.738(3) 2,984(0) " 3.001(2) 3.060(0) " 3,062(2) 1,761(1) 2.984(0) " 3.060(0) " 2.984(0) " 3.060(0) ~

as shown in Fig. 1. Each slab is composed of three layers of close-packed BV 6 trigonal prisms. The prism axis is parallel to the x axis. In each slab there is a triple chain formed by boron atoms extending in the direction of the z axis on the y - z plane. These boron atoms are situated at the centre of each BV6 trigonal prism. Within the slab there are three kinds of bonding, namely B-B, B-V and V-V. Two slabs are connected by the rectangular pyramids formed by vanadium atoms. Therefore only V-V bonding exits between the slabs. Those vanadium atoms that form the rectangular pyramids are situated in V(2) positions, as shown in Fig. 2. The vanadium atoms forming BV 6 trigonal prisms below or above the boron triple chains are situated in V(1) positions. From Table 4 it can be seen that the shortest V-V interatomic distance is 2.705 /~, which is exactly twice the vanadium atomic radius (1.35 A). This indicates that vanadium atoms in V(2) positions have direct contacts forming the rectangular pyramids. It should be noted that both the B V 6 trigonal prism units and the boron triple chains are in fact distorted. For the trigonal prism units the interatomic distance V(2)-V(2) (2.984 /k) is larger than that between V(1) and V(2) (2.890/~). The boron atom in the trigonal prism is not situated exactly at the centre of the unit. This boron atom, B(3)*, is significantly closer to V(2) (2.230 /~) than to V(1) (2.365 ]k). Similarly, for the boron triple chains the interatomic distances V(1)-B(1), V(1)-B(2),

t

•

•

®

• Tog. prism

4. Discussion

As the V 2 B 3 - t y p e structure has been well described from previous studies of its binary and ternary representatives, only a general structural description is presented here. The crystal structure of V 2 B 3 c a n be described as a kind of slab packing along the y axis,

t

•

Indicates that o-<0.0005 A.

correct weighting. The final refinement converged at R(F2)=0.024, Rw(F2)=0.039 and R .... =0.016 for 984 non-equivalent reflections. A final Fourier difference map was calculated and displayed no sign of any further interstitial atom. The final structure data are presented in Tables 2 and 3 and the interatomic distances in Table 4.

slab

zI Y

Rect. pyramid

V @ O

B o .x=0 • "x= 1/2

Fig. 1. T h e crystal structure of V2B3 viewed along the x axis. The projections of the unit cell, the slab, the trigonal prism and the rectangular pyramid along the x axis are indicated.

89

Y. Y u et al. / Journal o f Alloys a n d C o m p o u n d s 221 (1995) 8 6 - 9 0

(I)

"'.'1#'

vo)

V

zI

B

@ i ~

)

:x=0 •

' x = 1/2

Y Fig. 2. Part of the structure of V2B3 viewed along the x axis. Some of the interatomic distances are indicated.

V(1)-B(1) and V(1)-B(3) are 2.307, 2.307, 2.314 and 2.365/~, respectively. This indicates that the boron triple chains are elongated along the y axis, perpendicular to the chain direction (z), as shown in Fig. 2. This can be explained by the fact that the B(3)* atom has a stronger bonding to the five V(2) neighbours situated to its left side than to the four neighbours (2V(1) +2B(2)) situated to its right side, as shown in Fig. 2. This difference in bonding strength for B(3) atoms with their neighbouring atoms makes them shift from the centre of the trigonal prisms towards the V(2) atoms. As a consequence the boron triple chain is also distorted. The outer B(3) atoms are displaced away from the chain (B(3)-B(2) distance 1.761 A), while the inner B-B distances (B(2)-B(1) 1.738/~ and B(1)-B(1) 1.725 .~) are nearly the same. It is interesting to compare the refined anisotropic displacements. It can be seen from Table 3 that for both V(1) and V(2) atoms U,1 is less than U2~ and U33. This indicates that the thermal vibration of the metal atoms is smaller in the x direction than in the y and z directions, assuming negligible static displacements. Another interesting point is that the difference between U22 for the V(1) and V(2) sites is significantly larger than the differences between U,1 and U33 for the V(1) and V(2) sites respectively. This indicates that the V(1) atoms vibrate more easily in the y direction than do the V(2) atoms in the same direction, which can be reasonably explained by the local atomic arrangement around the two metal sites. For V(2) atoms, as mentioned above, the two V(2) sheets parallel to the x - z plane have direct contacts, forming rectangular pyramids between them. This may restrict the thermal

vibrations of V(2) atoms in the y direction. On the other hand, the space to accommodate V(1) atoms above and below the boron triple chains is larger than the vanadium atomic size and the triple chains are distorted, expanding in the y direction. Therefore the thermal vibration of V(1) atoms in the y direction is larger than that of V(2) atoms. The unit cell parameters of the binary and ternary representatives of the V2B3-type structure discovered so far are listed in Table 5. The unit cell parameters of these phases vs. the atomic radii of the transition metal elements are shown in Fig. 3. It can be seen from Fig. 3 that with increasing atomic radii of the transition metal elements b increases much more than a and c. The increase in b is mainly due to the expansion Table 5 Unit cell parameters of binary and ternary representatives of the VzB3-type structure. The estimated standard deviations are given in parentheses Phase

V~B3 V2B 3 Cr2B3 Nb2B3 CraNiB6 VCoB3

a

b

c

V

(A)

(A)

(A)

(A3)

Ref.

3.061(1) 3.0599(4) 3.027(1) 3.3058(6) 3.034(3) 3.04(1)

18.40(1) 18.429(2) 18.119(1) 19.481(4) 18.11(2) 17.55(3)

2.984(1) 2.9839(4) 2.954(1) 3.1293(8) 2.956(3) 2.98(1)

168.066 168.265 162.016 201.528 162.420 158.990

Ill This work [5] [141 [2] [31

25

vco

20

...

v

. . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . .

~tx--

~ ....

~

m

~

o

,

"~" . . . . . . .

.< v

E ca. i 0 o

~..~_ . . . . ~^ . . . . . . .

0

1.25

,

I

1.3

a

,,.,-. .-. -. . . . . . . . . . . . . . .

~

I

~

1.35

I

1.4

,

0

I

1.45

c . . . . . . .

,

1.5

Atomic radii of TM elements (A) a

b c .~...@.

Fig. 3. Plot of the unit cell parameters of the known binary and ternary V2B3-type representatives vs. the atomic radii of the corresponding metal elements. The unit cell data are taken from Table 5.

90

Y. Yu et aL / Journal of Alloys and Compounds 221 (1995) 86-90

of the V(2) positions as the metallic radii increase, because these metal atoms form direct bonds. The sizes of the V(1) positions, however, are restricted by the rigidity of the boron triple chains on the y-z planes. In addition, since a is always larger than the sum of the atomic radii of the two corresponding metal atoms, there is no close contact between the metal atoms along the x direction. Therefore the influence of atomic radii of the metal atoms on a and c of the unit cell parameters is very small. It is worth mentioning that the space available to accommodate the metal atoms is different for V(1) as compared with V(2) sites. If some of the vanadium atoms in the V 2 B 3 structure are replaced by other metal atoms larger than the vanadium atoms, e.g. niobium, the niobium atoms will be accommodated preferably at the V(2) positions. This is because the size of the V(2) positions expands more in the y direction readily owing to the direct contact of the V(2) atoms, as discussed above. The size of the V(1) positions, however, is more or less restricted by the rigid boron triple chain. Therefore only those metal atoms of suitable atomic size can be accommodated at the V(1) positions.

Acknowledgements The authors are indebted to Mr. Hilding Karlsson for his kind help during the data collection. Financial

support from the Swedish Natural Science Research Council and the Research Council for Engineering Sciences is gratefully acknowledged.

References [1] K.E. Spear and P.W. Gilles, High Temp. ScL, 1 (1969) 86. [21 M.V. Chepiga, V.P. Krivutskii and Yu.B. Kuz'ma, Izv. Akad. Nauk SSSR, Neorg. Mater., 8 (1972) 1059. [31 Yu.B. Kuz'ma and P.K. Starodub, lzv. Akad. Nauk SSSI~ Neorg. Mater., 9 (1973) 376. [4] P. Villars and L.D. Calvert, Pearson's Handbook of Crystallographic Data for Intermetallic Phases, ASM, Metals Park, OH, 1985, p. 1278. [5] S. Okada, T. Atoda and I. Higashi, J. Solid State Chem., 68 (1987) 61. [6] S. Okada and T. Lundstr6m, J. Cryst. Growth, 129 (1993) 543. [7] R.D. Deslattes and A. Henins, Phys. Rev. Lett., 31 (1973) 972. [8] B.I. NoiSing, Institute of Chemistry, Uppsala, personal communication, 1990. [9] TEXSAN:Single Crystal Structure Analysis Software, Version 5.0, Molecular Structure Corporation, The Woodlands, TX, 1989. [10] J.-O. Lundgren (ed.), Crystallographic computer programs, UUIC Publ. B18-4-5, 1982 (Institute of Chemistry, University of Uppsala). [1l] M.M. Korsukova, T. Lundstr0m, V.N. Gurin and L.-E. Tergenius, Z. Kristallogr., 168 (1984) 299. [12] H. Bolmgren, T. Lundstr6m, L.-E. Tergenius, S. Okada and I. Higashi, 3'. Less-Common Met., 161 (1990) 341. [13] J.A. Ibers and W.C. Hamilton (eds.), Intemational Tables for X-Ray Crystallography, Vol. IV, Kynoch, Birmingham, 1974. [141 S. Okada, K. Hamano, T. Lundstr6m and I. Higashi, in D. Emin et al. (eds.), Boron-rich solids, AlP Conf. Proc. No. 231, American Institute of Physics, NY, 1991, p. 456.