Crystal structure of magnesium heptaboride Mg2B14

Journal of the Less-Common

CRYSTAL

A. GUETTE,

Metals, 82 (1981) 325

STRUCTURE

M. BARRET,

325

- 334

OF MAGNESIUM

R. NASLAIN

HEPTABORIDE

and P. HAGENMULLER

Laboratoire de Chimie du Solide du CNRS, UniversitC de Bordeaux 33405 Talence Ct!dex (France) L.-E. TERGENIUS

Mg2B,,

I, 351 cows de la Lib&ration,

and T. LUNDSTR6M

Institute of Chemistry,

University of Uppsala, Box 531, S-751 21 Vppsala (Sweden)

Summary The crystal structure of a magnesium heptaboride, whose structural formula is Mg2Bi4, was determined from X-ray powder patterns according to a profile refinement technique and on the basis of isotypism with MgAlB,,. The symmetry is orthorhombic and the lattice parameters are a = 5.970 A, b = 8.125 A and c = 10.480 A. The refinement is based on the space group Imam. The unit cell contains five non-equivalent boron and two nonequivalent magnesium atoms. The structure consists of chains of B,, icosahedra extending in the direction of the c axis. The chains are linked laterally via inter-icosahedral bonds or B-B bonds involving nonicosahedral atoms, thus forming a three-dimensional boron network. The magnesium atoms occupy two types of holes in this network, corresponding to coordination numbers 12 and 16.

1. Introduction Several investigators have reported the occurrence of a phase in the Mg-B system, which contains more boron than MgB, [l - 31. However, the powder patterns as well as the compositions of the phases studied displayed discrepancies, as shown in Table 1. During investigations in the Mg-B system, which led us to the preparation of pure MgB, and its structure determination, a new more boron-rich phase with a composition close to MgB, was identified [4 - 61. Magnesium heptaboride was prepared according to different procedures which have been described elsewhere. In both cases the reaction was * Paper presented at the 7th International Symposium Compounds, Uppsala, Sweden, June 9 - 12, 1981. 0022.5088/81/0000-0000/$02.50

on Boron, Borides and Related

(F Elsevier Sequoia/Printed

in The Netherlands

326

TABLE 1 Chemical

analyses of some boron-rich

magnesium

borides

B (wt.%)

M&?(wt.%)

B+ Mg (wt.%)

B/Mg (at.)

MgB, (theoretical) “MgB,” according to Duhart

72.74 73.8

27.26 25

100 98.8

6 6.64

“Phase B” according to Markovskii et al. MgB, (theoretical)

76.7

19.8

96.5

8.71

75.69

24.31

100

Reference

[31

7

accomplished in an evacuated and sealed molybdenum crucible to avoid magnesium losses at high temperatures [5, 71. In one synthesis a B-Mg mixture containing an excess of magnesium (B/Mg = 6) was heated at 1400 ‘C and subsequently cooled slowly. The reaction products consisted of two phases clearly separated in the crucible. One phase was black and it was identified as MgB, while the other, which was the major phase, was brick red and was analysed as 74.52 wt.% B, 24.96 wt.% Mg, 99.48 wt.% (B+Mg) and B/Mg (at.) = 6.7. In the other synthesis a stoichiometric mixture of elemental boron (a rhombohedral modification) and finely divided magnesium tetraboride was heated in an evacuated and sealed molybdenum crucible at 1400 “C. After the product had been slowly cooled to room temperature, the powder pattern obtained from it indicated that the reaction was complete. The heptaboride was found to be nearly pure (traces of MgO were present, however), a finding which was also supported by chemical analysis: 75.06 wt.% B; 24.20 wt.% Mg; 99.26 wt.% (B+Mg); B/Mg (at.) = 6.97. Thus the new phase was obtained with a B/Mg ratio close to 7 (rather than 6) irrespective of the procedure used for its synthesis.

2. Determination

of the crystal structure

2.1. Isotypism with MgAlB,, Single crystals suitable for X-ray intensity measurements were not obtained and, consequently, powder specimens had to be used. In view of the limitations of the powder method, isotypic compounds were sought. Since the structure determination of MgB, previously showed that this compound contains icosahedral fragments, it seemed more likely that we should find isostructural compounds among the icosahedral boride phase structures than among the cubic hexaborides [5 - 71. It soon became evident that the powder pattern of magnesium heptaboride displayed close similarities to that of MgAlB,,, whose structure was determined by Matkovich and Economy using single-crystal diffractometer techniques [8]. The structure mentioned is closely related to that of NaBB,,,

327

determined by Naslain and Kasper who also used single-crystal diffractometer techniques 191. From this isotypism the ideal formula of magnesium heptaboride appeared to be Mg2B14, in excellent agreement with the experimental data mentioned above. Powder patterns of Mg,B,, were recorded with a Guinier-Hagg focusing camera using Co Kcl radiation and germanium or silicon as internal calibration standards. After the powder patterns had been indexed by comparison with the powder pattern of MgAlB,,, the cell dimensions were refined using the least-squares method. The following lattice parameters were obtained (orthorhombic) : a = 5.970 f 0.003 A ; b = 8.125 f 0.003 A ; c = 10.480~0.005 A. These values are not far from those given for MgAlB,, by Matkovich and Economy: a = 5.848 A; b = 8.115 A; c = 10.313 A. The small number of powder reflections available did not permit a reliable determination of the space group from systematic extinctions. Therefore the space group adopted in the refinements was that of MgAlB,,, namely Imam. The isotypism leads to a cell content of four Mg,B,, formula units. The density calculated on this assumption is 2.61 g cmm3, which is in close agreement with the experimental density 2.59 g cmV3 measured according to a hydrostatic pressure technique [lo]. 2.2. Re~nement of the structure from Lfebye-Scherrer intensities Under the assumption of isotypism between Mg,B,, and MgAlB~~, a first refinement was accomplished using Debye-Scherrer intensities recorded with a diffractometer (monochromated Co KCYradiation). We used 20 nonoverlapping diffraction lines and in total 39 lines. The intensities were correcte&for Lorentz and polarization effects. Atomic coordinates as well as temperature factors were refined using a method of least-squares fitting [ll]. The magnesium atoms of Mg,B,, were initially located in the positions occupied by the magnesium and aluminium atoms respectively in MgAlB,,. After a few refinement cycles the conventional R value falls to 0.05 for the 39 reflections (the observed overlapped intensities were partitioned in proportion to the Fc2 values of the overlapping lines, as discussed in ref. 11). The refinement described above gave the main features of the structure and rendered a first crystal chemical comparison possible between Mg,B,,, MgAIB,, and NaBB,, [6]. 2.3. Refinement by profile analysis of Cuinier-Hkigg powder film data In order to improve the structure refinement of Mg2B,,, a second X-ray investigation was carried out using the technique of profile refinement originally developed in the field of neutron diffraction by Rietveld [12] and later adapted for Guinier-Hagg X-ray powder films by Malmros and coworkers [13, 141. According to this method, the intensities of the X-ray diffraction lines (a small number in a powder pattern) are replaced by the line profiles measured point by point, thereby increasing the number of experimental observations. In addition, the method takes full account of overlap

328

and renders possible the refinement of the structures in a multiphase specimen. The profile refinement technique was successfully applied to boron-rich phases by Callmer and coworkers [15, 161 in the refinement of the solid solution of zirconium in p rhombohedral boron. The powder film intensity data were obtained from measurements made with an automatic microdensitometer on powder films exposed on a GuinierHagg focusing camera (strictly monochromatic Cu Kcr, radiation) [17]. The microdensitometer is directly connected to a computer for data processing. After correction for Lorentz and polarization effects, the structure was refined according to the procedure described by Malmros and coworkers

[13,181. Since the specimens contained traces of magnesia, the refinements of the Mg*B,, and MgO structures were carried out simultaneously. Occurrence of a preferred orientation in the samples was observed and, to study this effect in more detail, several films were exposed using specimens prepared in different manners. The Guinier-Hagg powder pattern contained 121 reflections (116 belonging to Mg2B,, and five to MgO). A total of 1700 measured intensities (on the average 14 per line profile) were used in the refinement of 31 parameters (including the line profile parameters). We refined 20 parameters for Mg,B,,, namely (Table 2) (1) atomic coordinates for boron and magnesium (13), (2) isotropic temperature factors (six) and (3) the occupation coefficient for Mg(1) (one). The refinement was carried out under the assumption that Mg,B,, and MgAlB,, are isotypic. Although there were indications of a preferred orientation, the R values obtained were below 0.14. As an example, the structure data from one refinement are given in Table 2. The refinement was, as already mentioned, based on 1700measured intensities and 116 contributing reflections. It converged to the reliability indices R(1) = 0.124and R(F) = 0.115, the R values being defined as

R(F) = 1 (Ik, ohsli 2- Ik,ca,c” ‘>/c Ik. ohs” 2 k

k

TABLE 2 Structure

data for Mg,B,,

Position

Occupation

1Sj 16j 8h 8h 8h 4e 4d

100 100 100 100 100 93(1.5) 100

(%)

Atom

.x

B(1) B(2) B(3) B(4) B(5) Mg(1)

0.250(l) 0.160(l) 0 0 0 0

Mg(2)

l/4

Standard deviations are in parentheses. b = 8.125(3) li; c = 10.480(5) A.

Y 0.0407(9) -0.166(l) 0.181(l) -0.028(l) 0.382(l) 0.3664(5)

Space group, Imam;

l/4

*

B 6’)

0.0830(7) 0.0671(6) 0.081(l) 0.1644(8) 0.142(l) 314

2.48(U) 2.54(11) 2.65(11) 2.57(11) 2.61(11) 3.01(10) 3.01(10)

l/4

2 = 4; a = 5.970(3) A;

l

Intensity A(arbitrary

units)

+

501!+

+

~~ +

25

+

0 . 24.830

25

Fig. 1. Profile of the (112) reflection in the Guinier-Hagg experimental values; --. theoretical profile.

:r Intensity

hl

(orbitrory

powder pattern of MgzBi4:

+.

units)

I

t

2W’)

a 339

L

I-

Fig. 2. Profile of a Guinier-Hagg powder pattern of Mg,B,,: +, experimental values: -theoretical profile. The lower curve gives the difference between the two series of values on the same scale. -

.

330

The R(F) value can thus roughly be compared with the conventional R, value for single-crystal data. The satisfactory agreement between experimental and calculated line profiles is demonstrated in Figs. 1 and 2. The differences between observed and calculated intensities are shown in Fig. 2. The occurrence of significant differences, for a few diffraction lines, may be attributed to the observed slight preferred orientation in the sample and/or to faint lines from a nonidentified impurity other than MgO. A comparison of the calculated standard deviations of the present structure refinement of Mg,B,, (Table 2) and those obtained in the structure refinement of MgAlB,, shows that the precision is nearly the same in the two refinements although the latter was based on single-crystal diffractometer data [8]. However, the standard deviations do not allow for systematic errors (e.g. the preferred orientation in the present investigation and absorption effects in the single-crystal study). The absolute accuracy is estimated to be better in the single-crystal refinement although no quantitative measure can be given. Finally a difference Fourier synthesis was calculated. The “noise” peaks were all below 20% of the boron peak in the Fobs synthesis. In conclusion, the isotypism between Mg2B,, and MgAlB,, was established and the interatomic distances were determined with relatively good accuracy.

3. Description

of the crystal structure

of Mg,B,,

The crystal structure of Mg2B,, contains five independent boron and two independent magnesium atoms. Four of the boron atoms (B(1) - B(4)) form icosahedra while the other atoms occupy interstitial holes between the icosahedra. Projections of the structure on the planes xy0 and Oyz respectively are shown in Figs. 3 and 4. Mg,B,, is characterized by a covalent boron network, consisting of chains of B,, icosahedra extending in the c axis direction. Within one chain the icosahedra are connected via direct B-B bonds (of type 4,-4,) parallel to the c axis. The boron icosahedra possess a mirror plane parallel to Oyz, and one of their pseudofivefold axes is inclined f4’ to the c axis. The three-dimensional boron network is formed through lateral bonds between the chains as in MgAlB,, and NaBB,,. The lateral bonds are of two types : one type consists of direct inter-icosahedral bonds (e.g. 2,-2, J, the other of bridges via isolated (non-icosahedral) boron atoms (B(5)) or metal atoms. The nature of these bridges constitutes the main difference between the three compounds, as has already been recognized by Naslain et al. [6]. In both MgAlB,, and Mg,B,, the bridges involve one single type of isolated atom (B(5)) while, in NaBB,,, two types of isolated atoms (B(5) and B(6)) are involved. Furthermore, while the occupation number is 100% for B(5), it is not more than 80% for B(6) in NaBB,,.

331

Fig. 3. Schematic projection of the structure - l/4 < z < + l/4 are indicated).

of Mg,B,,

on the plane Ony (atoms in the slab

3

Fig. 4. Schematic projection of the structure -l/4 < x < + l/4 are indicated).

of Mg,B,,

on the plane Oyz (atoms in the slab

332

Magnesium atoms are accommodated in two types of interstitial holes. Site I (position 4e), surrounded by 16 neighbouring boron atoms, is larger than site II (position 4d), surrounded by only 12 boron neighbours (Figs. 5 and 6). Indeed, the size difference accounts for the fact that site I is occupied solely in NaBB,,, the sodium atoms being too large to occupy site II. As could be anticipated from the chemical formula, the refinement of the structure of Mg,B,, results in almost full occupation of both sites by magnesium (Table 2). It has already been shown by Naslain et al. that the preparation of magnesium heptaboride in a sealed crucible leads to a maximum magnesium content, since in such a case no magnesium is lost during the high temperature synthesis (in MgAlB,, which had been prepared in an open system sites I and II were found to be occupied only to approximately 75%) [6, 81.

0

Mg

08 Fig. 5. The environment

of a magnesium

atom in site I.

Fig. 6. The environment

of a magnesium

atom in site II.

The interatomic distances in Mg,B,, are listed in Tables 3 and 4. The average intra-icosahedral distance is 1.853 A while the average of distances toward an extra-icosahedral boron atom (belonging either to a neighbouring icosahedron or an isolated boron atom) is not more than 1.746 A. This result is in agreement with the general rule that, in a three-dimensional boron network formed by boron units B, (with n = 6 or n = 12), the average B-B distance within the unit is invariably longer than that of the interunit boron distances. In the comparative study of MgAlB,,, Mg2B,, and NaBB,, by Naslain et al., it was found that the rule seemed to be violated by Mg2B,,. However, Naslain et al. were aware of the fact that the structure was incompletely known at that time [6]. The present study has thus removed this ambiguity and shown that Mg,B,, adheres to the rule. The interatomic distances given for Mg,B,, in ref. 6, Tables 3 - 8, should be replaced by those of Tables 3 and 4 in the present study. Finally, it is interesting to compare the M-B distances in MgAlB,,, Mg,B,, and NaBB,,. They are presented in Table 5. The 16-coordinated hole is slightly expanded when occupied by sodium compared with occupation by aluminium or magnesium. The smaller 12coordinated hole is expanded from

333

TABLE 3 B-B distances

in Mg,B,,

Boron atom A

Boron atom B

Number

Distance A-B

22

2 IS

4” 10 3” 10 2” 3” 10 10 20 20 10 1,

4, 5, 5” 4” 4” 40 1, 22 2, 32 3,) 2,

4 2 4 2 4 4 2 2 4 2 4 4 4

1.730” 1.794a 1.734” l.iFi3” 1.811b 1.795h 1.913b 1.864h 1.953b 1.917h 1.83Bb 1.884h 1.775h

a Bonds directed towards another icosahedron h Intra-icosahedral bonds.

(A)

o (4 0.016 0.018 0.009

0.015 0.009 0.011 0.015 0.015 0.010 0.015 0.011 0.010 0.011

(B(2), B(4)) or an isolated boron atom (B(5)).

TABLE 4 Mg-Mg

and Mg-B distances in MgZB,4

Atom A

Atom B

Number

Ml) M&4 MU,) MU,) W&l,) Mg(l,) Wl,) M&J M&J M&4,)

M&9 MgW

2 2 2 4 2 4 4 4 4 4

B(4,) B(2,) B(5,) B(2,,) B(l,,) B(1,) B(3,) B(5,,)

-

Distance A-B

(A)

CT(A) 0.004 0.000 0.011 0.008 0.011 0.007 0.008 0.008 0.008 0.007

3.456 2.987 2.892 2.690 2.328 2.805 2.702 2.441 2.376 2.158

TABLE 5 Average

M-B distances

in MgAlB,,

MgAlBi4 Occupation

[a], MgZB,4 (present investigation)

Occupation

(4 M(l)-16B M(2)-12B

25% Al + 50% Mg 75% Al

[9]

NuBB,~

M&J?/, Average distance

and NaBB,,

Average distance

Occupation

(4

2.69

93% Mg

2.70

2.27

1OO’y”Mg

2.33

Average distance (4

looq,, Na

2.74

334

an average of 2.27 A to 2.33 A when aluminium is replaced by magnesium. This hole can be occupied neither by the large sodium atom nor by the small boron atom. In NaBB,, the boron atom was actually found to occupy a fourcoordinated position situated at a distance of 1.46 i% from the M(1) position.

Acknowledgments Part of this investigation was supported through an exchange fellowship for A.G. from Centre National de la Recherche Scientifique and the Swedish Natural Science Research Council.

References 1 2

V. Russel, R. Hirst, F. A. Kanda and A. J. King, Acta Crystallogr., 6 (1953) 870. P. Duhart, Thesis 4699, University of Paris, 1962; Ann. Chim. (Paris), 7 (13)

(1962) 339. L. Ya. Markovskii, Ya. Kondrashev and G. Kaputovskaya, Zh. Obshch. Khim., 25 (1955) 433. 4 A. Guette, R. Naslain and J. Galy, CR. Acud. Sci., S&r. C, 275 (1972) 41. 5 R. Naslain, A. Guette and M. Barret, J. Solid State Chem., 8 (1973) 68. 6 R. Naslain, A. Guette and P. Hagenmuller, J. mess-~ornrno~ Met., 47 (1976) 1. 7 A. Guette, Thesis 462, University of Bordeaux I, 1974. 8 V. I. Matkovich and J. Economy, Acta Crystallogr., Sect. B, 26 (1970) 616. 9 R. Naslain and J. S. Kasper, J. Solid State Chem., -1 (1970) 150. 10 L. Rabardel, M. Pouchard and P. Hagenmuller, Mater. Res. BuEE.,6 (1971) 1325; Brevet CNRS 72118, 1966. 11 G. Perez and M. Saux, Bull. Sot. Chim. Fr., 10 (1970) 3478. 12 H. M. Rietveld, J. Appl. CrystaZZogr., 2 (1969) 65. 13 G. Malmros and J. 0. Thomas, J. Appl. Crystallogr., 10 (1977) 7. 14 P. E. Werner, S. SalomB, G. M_almros and J. 0. Thomas, J. Appl. Crystullogr., 12 (1979) 107. 15 B. Callmer, Thesis, University of Uppsala, 1977. 16 B. Callmer, L.-E. Tergenius and J. 0. Thomas, J. Solid State Chem., 26 (3) (1978) 275. 17 S. Abrahamsson, J. Sci. I~stram., 43 (1966) 931. 18 G. Malmros and P. E. Werner, Actu Chem. Stand., 27 (1973) 493. 3