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Crystal growth and structural investigation of the new quaternary compound Mo1−xCrxAlB with x = 0.39
Journal of
,~.~YS AND COM~)UNDS ELSEVIER
Journal of Alloys and Compounds 226 ( 1995 ) 5-9
Crystal growth and structural investigation of the new quaternary compound MOl _xCrxA1B with x = 0.39 Yang Yu, Torsten Lundstrt~m Institute of Chemistry, Uppsala University, Box 531, S-751 21 Uppsala, Sweden Received 26 January 1995
Abstract Single, crystals of Mo~ _xCrxAIB (quaternary representative of UBC) were synthesized by the high-temperature metal-solution method using aluminium flux, chromium, molybdenum metals and boron powder as starting materials. The mixture, with atomic ratio [Cr] / [Mo] = 3, [B] / [C;+Mo] = 1.5 and [A1] / [Cr+ Mo] =28, was heated to 1650 °C, soaked at this temperature for 5 h and then cooled to 1000 °C at a cooling rate of 50 °C h- ~.Under these conditions, Mo: _xCrxAIBsingle crystals were obtained with maximum dimensions of about 0.1 × 0.1 × 1 mm3 together with CrB2 and (Crn-~Mox)3B4 crystals. MOl_xCrxAIB crystallizes in the orthorhombic space group Cmcm (No. 63) with a = 3.1702(6) A, b ffi 13.948(2) A, c = 3.0743 (4)/k and Z--4. The structural parameters of MO 1_~CrxA1Bwere refined with a full-matrix least-squares program using single-crystal X-ray diffraction data. The molybdenum and chromium atoms occupy the same position with x-0.39. The refinement converged at a conventional R(F 2) value of 0.029 for 856 reflections. The homogeneity range and the structural characteristics of MOl _ xCrxAIBare discussed. There is evidence that the early reported phase MOTA16B7crystallizes in the UBC-type structure. Keywords: Crystal growth; Structural investigations
1. Introduction The ternary MoA1B phase was first reported by Rieger et al. [ 1] in 1965 and then the crystal structure was determined by Jeitschko in 1966 using a single-crystal film technique [ 2 ]. At that time the single-crystal film method did not permit direct determination of the boron position, which could only be found from space consideration. Prior to these two publications, another ternary phase, Mo7AI6B7, in the M o AI-B system had been reported [3]. The formula was obtaine6 by chemical analysis and the unit cell parameters were characterized with a = 7.03/~,, b = 6.34/~ and c = 5.76 /~ in the orthorhombic system. This phase has a composition very close to that of MoAIB but completely different unit cell dimensions. In 1987, Zhang et al. [4] reported the synthesis of the new compound WA1B which was characterized as an isotype of UBC. Up to now, no other ternary or quaternary isotype of UBC has been reported to occur in the TM-AI-B (TM stands for transition metal) systems. During investigation of the single-crystal growth of (Cr] -~Mox)aB4 in the Cr-Mo-AI-B system using the hightemperature metal-solution method, a new phase was found together with the desired phases. According to indexing and EDS measurement, this phase was characterized as an isotype of MoA1B, containing chromium and with a decrease in the 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved
SSDI0925-8388(95)01598-1
unit cell volume compared with MoAIB. In the present work, details of the crystal structure of the quaternary Cr~ _~Mo,~AIB were determined by single-crystal X-ray diffractometry.
2. Experimental details
2.1. Crystal growth Single-crystal growth of the quaternary Mo] _xCr~AIB was performed by the high-temperature metal-solution method using aluminium flux [5,6]. The claimed purities of the starting materials were 99.6%, 99.998%, 99.6% and 99.997% for molybdenum and chromium metals, crystalline boron and aluminium metal respectively. The initial atomic ratios [ Cr] / [Mo], [ B ] / [ C r + M o ] and [ A l l / [ C r + M o ] were3, 1.5 and 28 respectively. A vertical graphite furnace (Thermal Technology Inc. 1000-3560-FP-20) was used equipped with an inner alumina tube separating the sample space from the furnace muffle tube to prevent it from being contaminated by the vaporized aluminium. The mixture of the starting materials was placed in an alumina crucible and was initially heated to 1650 °(2, soaked at this temperature for 5 h, then cooled to 1000 °C at a cooling rate of 50 °C h - i and finally cooled to room tem-
6
Y. Yu, T. Lundstrrm/Journal of Alloys and Compounds226 (1995) 5-9
Table 1 Results of phase analysisof the as-growncrystals;the estimatedstandarddeviationsare givenin parentheses Phase
Space group
a (A)
b (/~)
c (A)
Moi - xCr:~.lB (Crl -xMox)3Ba CrB2
Cmcm Immm P6/mmm
3.1702(6 ) 3.0628(4) 2.9763(2)
13.948( 2 ) 13.140( 1)
3.0743(4 ) 2.9783(3) 3.0132(3)
perature. The synthesis was performed under a flow of pure argon gas (AGA, Sundbyberg, Sweden, claimed purity 99.998%). The as-grown crystals were separated from the solidified excess aluminium in diluted hydrochloric acid (6 M). 2.2. X-ray and element analysis
X-ray powder diffraction studies were performed using a Guinier-H~igg camera with strictly monochromatic Cu Kal radiation (A= 1.540 598/~) and semiconductor-grade silicon (a = 5.431 065 ~t) as internal calibration standard [7]. The powder samples were obtained by crushing selected crystals of different morphology. Three different phases were
identified from the as-grown crystals, namely those crystallizing in the MoAIB type (MOl _xCr~eMB), Ta3B4 type and AIB2 type structures. The unit-cell parameters were determined by least-squares refinement using the local program UNITCELL [8]. The results of the phase analysis and the cell dimensions are listed in Table 1. An optical microscope and a Weissenberg X-ray camera were used to examine the asgrown crystals. The morphology of the Mol _~CrxA1B single crystals is shown in Fig. 1. Several well formed candidate single crystals of Mol _xCr~A1B were selected for element analysis. Electron microprobe analysis of the selected crystals was performed on a SEM (JEOL JSM-840) equipped with an energy dispersive detector. Chromium was found in the analysed crystals together with molybdenum, aluminium and boron. A semi-quantitative element analysis was done on the surface of the Mol _~Cr~AIB single crystals. Since boron is a light element, its concentration could only be obtained by difference. A single crystal with the highest chromium concentration was selected for X-ray intensity data collection. 2.3. Intensity measurement
{a)
The X-ray intensities were measured with a Rigaku AFC6R automatic four-circle single-crystal diffractometer using graphite monochromated Mo Kot radiation (A -- 0.7107 A) and to-20 scan technique. Six standard reflections were measured at each of 150 reflections to check the stability of the primary X-ray beam and the equipment. A long-term systematic decrease in intensity within the time period of measurement was observed (approximately 1%). The collected intensity data were first corrected for Lorentz-polarization effects. A linear decay correction was then applied on the measured intensities. Absorption corrections were applied using the Gaussian grid technique. All these pre-refinement corrections on the original reflection data were carded out using the TEXSANsoftware system [9].
3. Refinement of Mo~_xCrxAIB
(b) Fig. 1. An SEMimageof (a) MoAIBand (b) Mol _~CrxA1Bsinglecrystals.
The structure refinement of Mot _xCrxAIB was carried out using the full-matrix least-squares program OUPALS [ 10]. The initial structural parameters were taken from study of the ternary MoAIB [2]. Considering the similarities of the chromium atoms with the molybdenum atoms, the chromium atoms were placed at the molybdenum atomic position. The atomic parameters, isotropic displacement parameters and the
Y. Yu, T. LundstrOm / Journal of Alloys and Compounds 226 (1995) 5-9 Table 2 Crystal data and refinement parameters of Moo.~Cro.39A1B
Cmcm, 4
Space group, Z Crystal dimensions (mm) Cell parameters (/~)
Refined formula Formula weight Density (calculated) (g cm -3) Absorption coefficient ( c m - ~) Number of boundary planes Transmission factor 20 limit (deg) Reflections measured observed ( > 3~) independent
0.1 x 0.08 × 0.08 a =3.1702(6) b = 13.948(2) c = 3.0743(4) Moo.61Cro.39AIB 116.59 5.70 88.54 6 0.550-0.850 124.6 856 784 598
type I isotropic extinction was found to give the best result in the refinement, which decreased the R value form 15% to 10%. The occupancy parameters for aluminium and boron positions were also refined, but no significant deviation from full occupancy was obtained. The anisotropic displacement parameters were then refined for molybdenum, aluminium and boron atoms and constrained for the chromium atom. In order to compare the differences in the positional and anisotropic displacement parameters of the chromium atoms with those of the molybdenum atoms, the constraint conditions were removed. Since the parameters for chromium and molybdenum atoms are strongly correlated, the parameters for the molybdenum atom were fixed and only the parameters for the chromium atom were refined. In order to obtain a correct weighting scheme, the standard deviation of the structure factor of each reflection is modified [ 10] as o-2(mod) = (Cltr(F))2 + ( C 2 F ) 2
occupancy factor of the chromium atom were constrained to the corresponding parameters of the molybdenum atom. After a few cycles, the refinement converged at about 15%. When the chromium atom was put at the atomic position of aluminium and the structural parameters of chromium were constrained to those of aluminium, the refinement diverged. This indicated that chromium atoms occupy only the molybdenum positions and not the aluminium positions. It was found that for the strongest reflections the observed intensities were systematically lower than the calculated intensities, which means that they suffer from extinction effects. Consequently, an extinction correction was applied in the refinement. Different types of extinction correction were tried and finally the
The final refinement was based on F 2, with a total of 15 refined parameters (one scale factor, three positional, one occupancy, nine anisotropic displacement and one isotropic extinction parameter), and five constrained parameters (one positional, one occupancy and three anisotropic displacement parameters). For the final refinement, the C~ and C2 values defined above were 1.6 and 0.016 respectively. The S value (standard deviation of an observation of unit weight) [ 11 ] was 1.086, which indicated that the weights in the refinement are reasonable. Similarly, analysis of the normal probability plot [ 11 ] of the ranked weighted differences gave a least-squares line slope of 0.96 and ay intercept of - 0.08, which indicates that a correct weighting scheme was used. Crystal data and refinement parameters are listed in Table 2. The final structure data are presented in Table 3 and the interatomic distances in Table 4.
)' B
©e
J
.o ¢o[ ,,o Oe~ O~ O O
•
4. Results and discussion
Cr 0 4. I. Description of the crystal structure of Mol _ xCrxAIB MO
A1
•
©
),
I Fig. 2. The crystal structure of Mo~ _xCr~A1B. The boron bonding and one of the trigonal prisms are indicated. The molybdenum and chromium atoms are distributed randomly at the same atomic positions.
The crystal structure of Mo~ _xCr~A1B is illustrated in Fig. 2. The structure is conveniently described in terms of the trigonal prismatic arrangement of six transition metal atoms (Cr, Mo) surrounding each boron atom (indicated in Fig. 2). There are two boron and one aluminium atom situated outside the rectangular faces of the trigonal prism. The prisms are packed in such a manner that all prism axes are parallel to the x direction, while the boron atoms from zig-zag chains in the z direction. This is indicated in the lower part of Fig. 2. The arrangement consists of a TM double layer extending in the x-z plane and accommodating zig-zag boron chains. A double layer of this type, although displaced by the vector ½,0, 0, is also repeated at y = 1/2. The aluminium atoms form strongly puckered metal layers interleaved between the TM double layers. Thus the structure can be described as a stack-
8
Y. Yu, T. Lundstrbm/Journal of Alloys and Compounds 226 (1995) 5-9
Table 3 Final structure data for Moo.61CrOo.39A1B,where the estimated standard deviations are given in parentheses Atom
Position
x
y
z
Occupancy
B(eq)
U11
U22
U33
Mo Cr a AI B
4c
0
0.08829(2)
0.25
0.324(5)
41.6(5)
46.0(7)
35.3(8)
4c 4c
0 0
0.30359(6) 0.4670(2)
0.25 0.25
0.608(8) 0.392(8) 1 1
0.63(2) 0.52(6)
87(2) 75(6)
66(3) 69(8)
88(4) 60(10)
The displacement factor is described as exp{ - 2"tr2( U1 lh2a .2 + U22k2b.2 + U3312c.2 + 2Ui2hka*b* + 2 UI 3hla*c* + 2U23klb*c* ) }, where U12= U13 = U23= 0 (R = 0.0388, Rw = 0.0514, for all measured reflections). a The differences of all the structural parameters except the occupancy parameter between chromium and molybdenum atoms are within 3o" (estimated standard deviations). Table 4 Interatomic distances in Moo.61Cro.agA1B Atoms
Distance (/~)
Atoms
Distance (/~)
TM-2TM -2TM -2TM -4AI -AI -2B -4B
2.9032(3) 3.1702(6) 3.1743(4) 2.6739(9) 3.0030(9) 2.318(2) 2.339(1)
AlgAl -2AI -2AI -B -2B B-2B -2B -2B
2.667(1) 3.0743(7) 3.1702(5) 2.279(3) 3.550(3) 1.792(3) 3.0743(4) 3.1702(6)
Since molybdenum and chromium atoms are at the same atomic position, both of them are expressed as TM. Distances listed are all TM-TM < 3.6 A, TM-AI < 3.5 ,~ and B-B < 3.2 ,~. The estimated standard deviations are given in parentheses.
ing in the y direction of TM double layers containing boron zig-zag chains, and strongly puckered aluminium layers.
4.2. Characteristics of the homogeneity range From the crystal structure refinement of Mol _ ~CrxA1B,the chromium atoms were found to occupy the molybdenum atomic positions, and the chromium concentration was refined to x = 0.39. From the powder X-ray diffraction film, it was found that the main reflection peaks of Mo~_ xCr~AIB were broadened, which indicates that a homogeneity range exists for the compound Mo~ _xCrxAIB. Electron microprobe analysis of different Mol_xCrxA1B single crystals grown from the same batch also indicated differences in chromium concentration. This is due to the fact that the local concentrations of chromium and molybdenum varied in the aluminium flux during crystal growth. The single crystal used for data collection was selected by EDS analysis, and contains the
largest chromium concentration out of all the examined MO 1 _xCrxAIB crystals. Accordingly, it is suggested that the upper limit for chromium solid solubility in MOl _xCr~AIB is very close to x=0.4 for [Cr]/[Mo] = 3 in the starting materials. According to Okada et al. [ 12], single-crystal growth of Cr2B3, Cr3B4 and CrB can be performed in an aluminium flux with the starting atomic ratios [B]/[Cr] = 1.55 and [All/ [Cr] = 28.9, which is very close to the initial atomic ratios and the cooling conditions for crystal growth of the present work. No ternary CrAIB was reported in their publication. In the present work, the atomic ratio [Cr] / [Mo] in the starting materials was 3, but this ratio is evaluated to be about 2/3 for the most chromium-rich Mo~_~CrxAIB single crystals obtained. These facts support the suggestion that for the quaternary MOI_xCr~A1B, the x values corresponding to the homogeneity range are about 0 ~
Table 5 Representatives of the UBC-type structure, the estimated standard deviations are given in parentheses Phase
a (/k)
b (/~)
c (/k)
V (,~3)
~o(%)
Reference
UBC MoAIB MoAIB Moo.61Cro.39AlB WAIB
3.591 3.212 3.2085 ( 3 ) 3.1702 ( 6 ) 3.205( 1 )
11.95 13.985 13.980 ( 1) 13.948 ( 2 ) 13.947(1)
3.372 3.102 3.1002 ( 3 ) 3.0743 (4) 3.108(1)
144.7 139.3 139.06 135.94 138.93
57.5 76.6 76.5 75.0 77.3
[ 14] [2 ] This work This work [4]
Y. Yu, T. LundstrSm / Journal of Alloys and Compounds 226 (1995) 5-9
phase, as shown in Fig. 1. Like the other ternary compound WAIB [4], MoA1B crystallizes in the shape of plate-like needles extending along the (001) direction, with maximum crystal dimensions 0 . 0 4 × 0 . 2 × 1 0 nlm 3. The quaternary phase M(h -xCrxA1B crystallizes in the shape of squared needles extending along the same direction and they always crystallize in the form of aggregates. This is mainly due to the contribution of chromium atoms in the formation of the quaternary phase Mo~_ xCrxA1B. 4.3. Discussion o f the phases MoAIB and Mo7AI6B 7
It was noted by Jeitschko [2] that the Mo7AI6B7 (MoAlo.86B) phase reported by Halla and Thury [3] has a composition very close to MoAIB. The unit cells reported, however, differed completely, which indicates that there are indeed two different phases with nearly the same composition in the system. It has also been reported [ 1 ] that MoA1B has a range of homogeneity. Since MoAIB was studied by singlecrystal methods [2], it was suspected that the diffraction pattern of Mo7AI6B 7 might have been indexed incorrectly. To study this question in more detail the diffraction data published by Halla and Thury [ 3 ] were utilized for an indexation with a least-squares refinement program UNITCELL [ 8 ]. The refined parameters (all lines indexed) for the originally reported unit cell were a = 7.036(4)/k, b = 6.340(4)/~ and c = 5 . 7 5 7 ( 4 ) ~k. The refined parameters (also all lines indexed) for a cell isotypical with MoAIB were a = 3.237 ( 2 ) /~, b = 14.007(6) ~ and c = 3 . 1 1 1 ( 2 ) /~. An "agreement index", defined as 5'. I Qcalc,i - Qobs,i[ and with summation over all diffraction lines i, was calculated. The value of this index was found to be 0.0578 for the first-mentioned phase and 0.0466 for the latter. From the lower standard deviations and the lower agreement index it is concluded that the latter indexation a = 3 . 2 3 7 (2) /~, b = 14.077 (6) /~ and c=3.111 (2) A is correct, although the experimental data for MOTAi6B 7 are relatively poor. This indicates that the phase Mo7A16B7 reported by Halla and Thury [ 3 ] is in fact the same phase as MoAIB. This conclusion is also in agreement with the ternary phase diagram of the Mo-A1-B system, presented by Rieger et al. [ 1 ], which displays only one MoA1B phase, although a small homogeneity range is also shown. 4.4. The crystal chemistry o f phases crystallizing in the UBC-type structure
The presently known phases crystallizing in the UBC-type structure are collected in Table 5 together with the unit cell dimensions, cell volumes and the space filling ratios ~p. This ratio is defined as E( Vatom ' i/Vunit_cell), with summation taken over all atoms in the unit cell. Atomic radii were taken from Ref. [ 15]. It is noted that the prototype structure UBC deviates from the other structures in several respects, which to
9
some extent arises from the large atomic radius of uranium. The degree of space filling is much lower for UBC than for the other compounds, which is a consequence of the fact that the cell volumes are relatively equal while the large aluminium atoms are replaced by small carbon atoms in the uranium compound. The values of the a and c axes are determined by the large atomic radius of the uranium atom and therefore are considerably larger than those of the other representatives. The b axis of UBC, however, is considerably shorter than those of the other phases. This is a consequence of the fact that the bonding between the uranium double layers (containing the boron zig-zag chains) is mainly due to the small carbon atoms, which occupy the positions of the relatively large aluminium atoms in the other representatives. The degree of space filling is lower for Moo.61Cro,39A1B than for MoA1B, as shown in Table 5. This is mainly due to the fact that about two-fifths of the molybdenum atoms are replaced by the smaller chromium atoms in Moo.61Cro.39A1B, while the decrease in unit cell volume is not so large.
Acknowledgements Financial support provided by the Swedish Nature Science Research Council is gratefully acknowledged. The authors are also indebted to Res. Eng. Lars-Erik Tergenius for his assistance in X-ray data collection and crystal structure refinement.
References [ 1] W. Rieger, H. Nowotnyand F. Benesovsky,Monatsch. Chem., 96 (1965) 844. [2] W. Jeitschko,Monatsch. Chem., 97 (1966) 1472. 13] F. Hallaand W. Thury,Z. Anorg. Allg. Chem., 249 (1942). [4] Y. Zhang, S. Okada, T. Atoda, T. Yamabe and I. Yasumori, YogyoKyokai-Shi, 95 (1987) 374. [5] D. Elwell and H.J. Scheel, Crystal Growth from High-Temperature Solutions, AcademicPress,London, 1975. [6] T. Lundstr6m,J. Less-Common Met., 100 (1984) 215. [7l R.D. Deslattesand A. Henins,Phys. Rev. Lett., 31 (1973) 972. [8] B.I. Nolang, Institute of Chemistry, Box 531, S-751 21 Uppsala, personalcommunication,1989. [9] Texsan, Single Crystal Structure Analysis Software, Version 5.0, MolecularStructureCorporation,The Woodlands,TX, 1989. [10] J.-O. Lundgren (ed.), Crystallographiccomputerprograms, UUIC Publ. B18-4-5, 1982(Instituteof Chemistry,Uppsala University). [ 11] J.A. Ibers and W.C. Hamilton (eds.), International Tablesfor X-ray Crystallography, Vol. IV, KynochPress, Birmingham, 1974. [12] S. Okada, T. Atoda and I. Higashi,J. Solid State Chem., 68 (1987) 61. [ 13] S. Okadaand T. Lundstr6m,J. Cryst. Growth, 129 (1993) 543. [ 14] L. Toth, H. Nowotny,F. Benesovskyand E. Rudy, Mh. Chem., 92 (1961) 794. [ 15l F. Laves,in The Theory of Alloy Phases, AmericanSocietyfor Metals, Cleveland,OH, 1956,p. 124.
,~.~YS AND COM~)UNDS ELSEVIER
Journal of Alloys and Compounds 226 ( 1995 ) 5-9
Crystal growth and structural investigation of the new quaternary compound MOl _xCrxA1B with x = 0.39 Yang Yu, Torsten Lundstrt~m Institute of Chemistry, Uppsala University, Box 531, S-751 21 Uppsala, Sweden Received 26 January 1995
Abstract Single, crystals of Mo~ _xCrxAIB (quaternary representative of UBC) were synthesized by the high-temperature metal-solution method using aluminium flux, chromium, molybdenum metals and boron powder as starting materials. The mixture, with atomic ratio [Cr] / [Mo] = 3, [B] / [C;+Mo] = 1.5 and [A1] / [Cr+ Mo] =28, was heated to 1650 °C, soaked at this temperature for 5 h and then cooled to 1000 °C at a cooling rate of 50 °C h- ~.Under these conditions, Mo: _xCrxAIBsingle crystals were obtained with maximum dimensions of about 0.1 × 0.1 × 1 mm3 together with CrB2 and (Crn-~Mox)3B4 crystals. MOl_xCrxAIB crystallizes in the orthorhombic space group Cmcm (No. 63) with a = 3.1702(6) A, b ffi 13.948(2) A, c = 3.0743 (4)/k and Z--4. The structural parameters of MO 1_~CrxA1Bwere refined with a full-matrix least-squares program using single-crystal X-ray diffraction data. The molybdenum and chromium atoms occupy the same position with x-0.39. The refinement converged at a conventional R(F 2) value of 0.029 for 856 reflections. The homogeneity range and the structural characteristics of MOl _ xCrxAIBare discussed. There is evidence that the early reported phase MOTA16B7crystallizes in the UBC-type structure. Keywords: Crystal growth; Structural investigations
1. Introduction The ternary MoA1B phase was first reported by Rieger et al. [ 1] in 1965 and then the crystal structure was determined by Jeitschko in 1966 using a single-crystal film technique [ 2 ]. At that time the single-crystal film method did not permit direct determination of the boron position, which could only be found from space consideration. Prior to these two publications, another ternary phase, Mo7AI6B7, in the M o AI-B system had been reported [3]. The formula was obtaine6 by chemical analysis and the unit cell parameters were characterized with a = 7.03/~,, b = 6.34/~ and c = 5.76 /~ in the orthorhombic system. This phase has a composition very close to that of MoAIB but completely different unit cell dimensions. In 1987, Zhang et al. [4] reported the synthesis of the new compound WA1B which was characterized as an isotype of UBC. Up to now, no other ternary or quaternary isotype of UBC has been reported to occur in the TM-AI-B (TM stands for transition metal) systems. During investigation of the single-crystal growth of (Cr] -~Mox)aB4 in the Cr-Mo-AI-B system using the hightemperature metal-solution method, a new phase was found together with the desired phases. According to indexing and EDS measurement, this phase was characterized as an isotype of MoA1B, containing chromium and with a decrease in the 0925-8388/95/$09.50 © 1995 Elsevier Science S.A. All rights reserved
SSDI0925-8388(95)01598-1
unit cell volume compared with MoAIB. In the present work, details of the crystal structure of the quaternary Cr~ _~Mo,~AIB were determined by single-crystal X-ray diffractometry.
2. Experimental details
2.1. Crystal growth Single-crystal growth of the quaternary Mo] _xCr~AIB was performed by the high-temperature metal-solution method using aluminium flux [5,6]. The claimed purities of the starting materials were 99.6%, 99.998%, 99.6% and 99.997% for molybdenum and chromium metals, crystalline boron and aluminium metal respectively. The initial atomic ratios [ Cr] / [Mo], [ B ] / [ C r + M o ] and [ A l l / [ C r + M o ] were3, 1.5 and 28 respectively. A vertical graphite furnace (Thermal Technology Inc. 1000-3560-FP-20) was used equipped with an inner alumina tube separating the sample space from the furnace muffle tube to prevent it from being contaminated by the vaporized aluminium. The mixture of the starting materials was placed in an alumina crucible and was initially heated to 1650 °(2, soaked at this temperature for 5 h, then cooled to 1000 °C at a cooling rate of 50 °C h - i and finally cooled to room tem-
6
Y. Yu, T. Lundstrrm/Journal of Alloys and Compounds226 (1995) 5-9
Table 1 Results of phase analysisof the as-growncrystals;the estimatedstandarddeviationsare givenin parentheses Phase
Space group
a (A)
b (/~)
c (A)
Moi - xCr:~.lB (Crl -xMox)3Ba CrB2
Cmcm Immm P6/mmm
3.1702(6 ) 3.0628(4) 2.9763(2)
13.948( 2 ) 13.140( 1)
3.0743(4 ) 2.9783(3) 3.0132(3)
perature. The synthesis was performed under a flow of pure argon gas (AGA, Sundbyberg, Sweden, claimed purity 99.998%). The as-grown crystals were separated from the solidified excess aluminium in diluted hydrochloric acid (6 M). 2.2. X-ray and element analysis
X-ray powder diffraction studies were performed using a Guinier-H~igg camera with strictly monochromatic Cu Kal radiation (A= 1.540 598/~) and semiconductor-grade silicon (a = 5.431 065 ~t) as internal calibration standard [7]. The powder samples were obtained by crushing selected crystals of different morphology. Three different phases were
identified from the as-grown crystals, namely those crystallizing in the MoAIB type (MOl _xCr~eMB), Ta3B4 type and AIB2 type structures. The unit-cell parameters were determined by least-squares refinement using the local program UNITCELL [8]. The results of the phase analysis and the cell dimensions are listed in Table 1. An optical microscope and a Weissenberg X-ray camera were used to examine the asgrown crystals. The morphology of the Mol _~CrxA1B single crystals is shown in Fig. 1. Several well formed candidate single crystals of Mol _xCr~A1B were selected for element analysis. Electron microprobe analysis of the selected crystals was performed on a SEM (JEOL JSM-840) equipped with an energy dispersive detector. Chromium was found in the analysed crystals together with molybdenum, aluminium and boron. A semi-quantitative element analysis was done on the surface of the Mol _~Cr~AIB single crystals. Since boron is a light element, its concentration could only be obtained by difference. A single crystal with the highest chromium concentration was selected for X-ray intensity data collection. 2.3. Intensity measurement
{a)
The X-ray intensities were measured with a Rigaku AFC6R automatic four-circle single-crystal diffractometer using graphite monochromated Mo Kot radiation (A -- 0.7107 A) and to-20 scan technique. Six standard reflections were measured at each of 150 reflections to check the stability of the primary X-ray beam and the equipment. A long-term systematic decrease in intensity within the time period of measurement was observed (approximately 1%). The collected intensity data were first corrected for Lorentz-polarization effects. A linear decay correction was then applied on the measured intensities. Absorption corrections were applied using the Gaussian grid technique. All these pre-refinement corrections on the original reflection data were carded out using the TEXSANsoftware system [9].
3. Refinement of Mo~_xCrxAIB
(b) Fig. 1. An SEMimageof (a) MoAIBand (b) Mol _~CrxA1Bsinglecrystals.
The structure refinement of Mot _xCrxAIB was carried out using the full-matrix least-squares program OUPALS [ 10]. The initial structural parameters were taken from study of the ternary MoAIB [2]. Considering the similarities of the chromium atoms with the molybdenum atoms, the chromium atoms were placed at the molybdenum atomic position. The atomic parameters, isotropic displacement parameters and the
Y. Yu, T. LundstrOm / Journal of Alloys and Compounds 226 (1995) 5-9 Table 2 Crystal data and refinement parameters of Moo.~Cro.39A1B
Cmcm, 4
Space group, Z Crystal dimensions (mm) Cell parameters (/~)
Refined formula Formula weight Density (calculated) (g cm -3) Absorption coefficient ( c m - ~) Number of boundary planes Transmission factor 20 limit (deg) Reflections measured observed ( > 3~) independent
0.1 x 0.08 × 0.08 a =3.1702(6) b = 13.948(2) c = 3.0743(4) Moo.61Cro.39AIB 116.59 5.70 88.54 6 0.550-0.850 124.6 856 784 598
type I isotropic extinction was found to give the best result in the refinement, which decreased the R value form 15% to 10%. The occupancy parameters for aluminium and boron positions were also refined, but no significant deviation from full occupancy was obtained. The anisotropic displacement parameters were then refined for molybdenum, aluminium and boron atoms and constrained for the chromium atom. In order to compare the differences in the positional and anisotropic displacement parameters of the chromium atoms with those of the molybdenum atoms, the constraint conditions were removed. Since the parameters for chromium and molybdenum atoms are strongly correlated, the parameters for the molybdenum atom were fixed and only the parameters for the chromium atom were refined. In order to obtain a correct weighting scheme, the standard deviation of the structure factor of each reflection is modified [ 10] as o-2(mod) = (Cltr(F))2 + ( C 2 F ) 2
occupancy factor of the chromium atom were constrained to the corresponding parameters of the molybdenum atom. After a few cycles, the refinement converged at about 15%. When the chromium atom was put at the atomic position of aluminium and the structural parameters of chromium were constrained to those of aluminium, the refinement diverged. This indicated that chromium atoms occupy only the molybdenum positions and not the aluminium positions. It was found that for the strongest reflections the observed intensities were systematically lower than the calculated intensities, which means that they suffer from extinction effects. Consequently, an extinction correction was applied in the refinement. Different types of extinction correction were tried and finally the
The final refinement was based on F 2, with a total of 15 refined parameters (one scale factor, three positional, one occupancy, nine anisotropic displacement and one isotropic extinction parameter), and five constrained parameters (one positional, one occupancy and three anisotropic displacement parameters). For the final refinement, the C~ and C2 values defined above were 1.6 and 0.016 respectively. The S value (standard deviation of an observation of unit weight) [ 11 ] was 1.086, which indicated that the weights in the refinement are reasonable. Similarly, analysis of the normal probability plot [ 11 ] of the ranked weighted differences gave a least-squares line slope of 0.96 and ay intercept of - 0.08, which indicates that a correct weighting scheme was used. Crystal data and refinement parameters are listed in Table 2. The final structure data are presented in Table 3 and the interatomic distances in Table 4.
)' B
©e
J
.o ¢o[ ,,o Oe~ O~ O O
•
4. Results and discussion
Cr 0 4. I. Description of the crystal structure of Mol _ xCrxAIB MO
A1
•
©
),
I Fig. 2. The crystal structure of Mo~ _xCr~A1B. The boron bonding and one of the trigonal prisms are indicated. The molybdenum and chromium atoms are distributed randomly at the same atomic positions.
The crystal structure of Mo~ _xCr~A1B is illustrated in Fig. 2. The structure is conveniently described in terms of the trigonal prismatic arrangement of six transition metal atoms (Cr, Mo) surrounding each boron atom (indicated in Fig. 2). There are two boron and one aluminium atom situated outside the rectangular faces of the trigonal prism. The prisms are packed in such a manner that all prism axes are parallel to the x direction, while the boron atoms from zig-zag chains in the z direction. This is indicated in the lower part of Fig. 2. The arrangement consists of a TM double layer extending in the x-z plane and accommodating zig-zag boron chains. A double layer of this type, although displaced by the vector ½,0, 0, is also repeated at y = 1/2. The aluminium atoms form strongly puckered metal layers interleaved between the TM double layers. Thus the structure can be described as a stack-
8
Y. Yu, T. Lundstrbm/Journal of Alloys and Compounds 226 (1995) 5-9
Table 3 Final structure data for Moo.61CrOo.39A1B,where the estimated standard deviations are given in parentheses Atom
Position
x
y
z
Occupancy
B(eq)
U11
U22
U33
Mo Cr a AI B
4c
0
0.08829(2)
0.25
0.324(5)
41.6(5)
46.0(7)
35.3(8)
4c 4c
0 0
0.30359(6) 0.4670(2)
0.25 0.25
0.608(8) 0.392(8) 1 1
0.63(2) 0.52(6)
87(2) 75(6)
66(3) 69(8)
88(4) 60(10)
The displacement factor is described as exp{ - 2"tr2( U1 lh2a .2 + U22k2b.2 + U3312c.2 + 2Ui2hka*b* + 2 UI 3hla*c* + 2U23klb*c* ) }, where U12= U13 = U23= 0 (R = 0.0388, Rw = 0.0514, for all measured reflections). a The differences of all the structural parameters except the occupancy parameter between chromium and molybdenum atoms are within 3o" (estimated standard deviations). Table 4 Interatomic distances in Moo.61Cro.agA1B Atoms
Distance (/~)
Atoms
Distance (/~)
TM-2TM -2TM -2TM -4AI -AI -2B -4B
2.9032(3) 3.1702(6) 3.1743(4) 2.6739(9) 3.0030(9) 2.318(2) 2.339(1)
AlgAl -2AI -2AI -B -2B B-2B -2B -2B
2.667(1) 3.0743(7) 3.1702(5) 2.279(3) 3.550(3) 1.792(3) 3.0743(4) 3.1702(6)
Since molybdenum and chromium atoms are at the same atomic position, both of them are expressed as TM. Distances listed are all TM-TM < 3.6 A, TM-AI < 3.5 ,~ and B-B < 3.2 ,~. The estimated standard deviations are given in parentheses.
ing in the y direction of TM double layers containing boron zig-zag chains, and strongly puckered aluminium layers.
4.2. Characteristics of the homogeneity range From the crystal structure refinement of Mol _ ~CrxA1B,the chromium atoms were found to occupy the molybdenum atomic positions, and the chromium concentration was refined to x = 0.39. From the powder X-ray diffraction film, it was found that the main reflection peaks of Mo~_ xCr~AIB were broadened, which indicates that a homogeneity range exists for the compound Mo~ _xCrxAIB. Electron microprobe analysis of different Mol_xCrxA1B single crystals grown from the same batch also indicated differences in chromium concentration. This is due to the fact that the local concentrations of chromium and molybdenum varied in the aluminium flux during crystal growth. The single crystal used for data collection was selected by EDS analysis, and contains the
largest chromium concentration out of all the examined MO 1 _xCrxAIB crystals. Accordingly, it is suggested that the upper limit for chromium solid solubility in MOl _xCr~AIB is very close to x=0.4 for [Cr]/[Mo] = 3 in the starting materials. According to Okada et al. [ 12], single-crystal growth of Cr2B3, Cr3B4 and CrB can be performed in an aluminium flux with the starting atomic ratios [B]/[Cr] = 1.55 and [All/ [Cr] = 28.9, which is very close to the initial atomic ratios and the cooling conditions for crystal growth of the present work. No ternary CrAIB was reported in their publication. In the present work, the atomic ratio [Cr] / [Mo] in the starting materials was 3, but this ratio is evaluated to be about 2/3 for the most chromium-rich Mo~_~CrxAIB single crystals obtained. These facts support the suggestion that for the quaternary MOI_xCr~A1B, the x values corresponding to the homogeneity range are about 0 ~
Table 5 Representatives of the UBC-type structure, the estimated standard deviations are given in parentheses Phase
a (/k)
b (/~)
c (/k)
V (,~3)
~o(%)
Reference
UBC MoAIB MoAIB Moo.61Cro.39AlB WAIB
3.591 3.212 3.2085 ( 3 ) 3.1702 ( 6 ) 3.205( 1 )
11.95 13.985 13.980 ( 1) 13.948 ( 2 ) 13.947(1)
3.372 3.102 3.1002 ( 3 ) 3.0743 (4) 3.108(1)
144.7 139.3 139.06 135.94 138.93
57.5 76.6 76.5 75.0 77.3
[ 14] [2 ] This work This work [4]
Y. Yu, T. LundstrSm / Journal of Alloys and Compounds 226 (1995) 5-9
phase, as shown in Fig. 1. Like the other ternary compound WAIB [4], MoA1B crystallizes in the shape of plate-like needles extending along the (001) direction, with maximum crystal dimensions 0 . 0 4 × 0 . 2 × 1 0 nlm 3. The quaternary phase M(h -xCrxA1B crystallizes in the shape of squared needles extending along the same direction and they always crystallize in the form of aggregates. This is mainly due to the contribution of chromium atoms in the formation of the quaternary phase Mo~_ xCrxA1B. 4.3. Discussion o f the phases MoAIB and Mo7AI6B 7
It was noted by Jeitschko [2] that the Mo7AI6B7 (MoAlo.86B) phase reported by Halla and Thury [3] has a composition very close to MoAIB. The unit cells reported, however, differed completely, which indicates that there are indeed two different phases with nearly the same composition in the system. It has also been reported [ 1 ] that MoA1B has a range of homogeneity. Since MoAIB was studied by singlecrystal methods [2], it was suspected that the diffraction pattern of Mo7AI6B 7 might have been indexed incorrectly. To study this question in more detail the diffraction data published by Halla and Thury [ 3 ] were utilized for an indexation with a least-squares refinement program UNITCELL [ 8 ]. The refined parameters (all lines indexed) for the originally reported unit cell were a = 7.036(4)/k, b = 6.340(4)/~ and c = 5 . 7 5 7 ( 4 ) ~k. The refined parameters (also all lines indexed) for a cell isotypical with MoAIB were a = 3.237 ( 2 ) /~, b = 14.007(6) ~ and c = 3 . 1 1 1 ( 2 ) /~. An "agreement index", defined as 5'. I Qcalc,i - Qobs,i[ and with summation over all diffraction lines i, was calculated. The value of this index was found to be 0.0578 for the first-mentioned phase and 0.0466 for the latter. From the lower standard deviations and the lower agreement index it is concluded that the latter indexation a = 3 . 2 3 7 (2) /~, b = 14.077 (6) /~ and c=3.111 (2) A is correct, although the experimental data for MOTAi6B 7 are relatively poor. This indicates that the phase Mo7A16B7 reported by Halla and Thury [ 3 ] is in fact the same phase as MoAIB. This conclusion is also in agreement with the ternary phase diagram of the Mo-A1-B system, presented by Rieger et al. [ 1 ], which displays only one MoA1B phase, although a small homogeneity range is also shown. 4.4. The crystal chemistry o f phases crystallizing in the UBC-type structure
The presently known phases crystallizing in the UBC-type structure are collected in Table 5 together with the unit cell dimensions, cell volumes and the space filling ratios ~p. This ratio is defined as E( Vatom ' i/Vunit_cell), with summation taken over all atoms in the unit cell. Atomic radii were taken from Ref. [ 15]. It is noted that the prototype structure UBC deviates from the other structures in several respects, which to
9
some extent arises from the large atomic radius of uranium. The degree of space filling is much lower for UBC than for the other compounds, which is a consequence of the fact that the cell volumes are relatively equal while the large aluminium atoms are replaced by small carbon atoms in the uranium compound. The values of the a and c axes are determined by the large atomic radius of the uranium atom and therefore are considerably larger than those of the other representatives. The b axis of UBC, however, is considerably shorter than those of the other phases. This is a consequence of the fact that the bonding between the uranium double layers (containing the boron zig-zag chains) is mainly due to the small carbon atoms, which occupy the positions of the relatively large aluminium atoms in the other representatives. The degree of space filling is lower for Moo.61Cro,39A1B than for MoA1B, as shown in Table 5. This is mainly due to the fact that about two-fifths of the molybdenum atoms are replaced by the smaller chromium atoms in Moo.61Cro.39A1B, while the decrease in unit cell volume is not so large.
Acknowledgements Financial support provided by the Swedish Nature Science Research Council is gratefully acknowledged. The authors are also indebted to Res. Eng. Lars-Erik Tergenius for his assistance in X-ray data collection and crystal structure refinement.
References [ 1] W. Rieger, H. Nowotnyand F. Benesovsky,Monatsch. Chem., 96 (1965) 844. [2] W. Jeitschko,Monatsch. Chem., 97 (1966) 1472. 13] F. Hallaand W. Thury,Z. Anorg. Allg. Chem., 249 (1942). [4] Y. Zhang, S. Okada, T. Atoda, T. Yamabe and I. Yasumori, YogyoKyokai-Shi, 95 (1987) 374. [5] D. Elwell and H.J. Scheel, Crystal Growth from High-Temperature Solutions, AcademicPress,London, 1975. [6] T. Lundstr6m,J. Less-Common Met., 100 (1984) 215. [7l R.D. Deslattesand A. Henins,Phys. Rev. Lett., 31 (1973) 972. [8] B.I. Nolang, Institute of Chemistry, Box 531, S-751 21 Uppsala, personalcommunication,1989. [9] Texsan, Single Crystal Structure Analysis Software, Version 5.0, MolecularStructureCorporation,The Woodlands,TX, 1989. [10] J.-O. Lundgren (ed.), Crystallographiccomputerprograms, UUIC Publ. B18-4-5, 1982(Instituteof Chemistry,Uppsala University). [ 11] J.A. Ibers and W.C. Hamilton (eds.), International Tablesfor X-ray Crystallography, Vol. IV, KynochPress, Birmingham, 1974. [12] S. Okada, T. Atoda and I. Higashi,J. Solid State Chem., 68 (1987) 61. [ 13] S. Okadaand T. Lundstr6m,J. Cryst. Growth, 129 (1993) 543. [ 14] L. Toth, H. Nowotny,F. Benesovskyand E. Rudy, Mh. Chem., 92 (1961) 794. [ 15l F. Laves,in The Theory of Alloy Phases, AmericanSocietyfor Metals, Cleveland,OH, 1956,p. 124.