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A neutron diffraction study of the interstitial sites of deuterium in the A-15 compound Ti3Ir
Solid State Communications,Vol. 101 No. 8 d 1997 &%~:9z%z Printedin Great Bribiu. All rights nserwd 0038-1098197 S17.OOt.MJ
Pergamon
PII:soo38-1098(96)00653-9
A NEUTRON DIFFRACTION STUDY OF THE INTERSTITIAL SITES OF DEUTERIUM IN THE A-15 COMPOUND Ti8Ir K. Comell,a H. Wipf,” U. Stub? and A.V. Skripov’ “Technische Hochschule Darmstadt, Institut ftir Festkorperphysik, D-64289 Darmstadt ‘Hahn-Meitner-Institut, BENSC, D-14109 Berlin ‘Urals Branch of the Academy of Sciences, Institute of Metal Physics, Ekaterinburg 620219, Russia (Received 27 September 1996; accepted 28 October 1996 by P.H. Dederichs) The interstitial D sites in the D-doped A-15 compound Ti31rDX with x = 0.70 and 3.63 were determined by neutron diffraction (space group Pm% (No. 223)). For x = 0.70, we confirm the D occupation of sixfold d positions (6d positions) already found for other H- and D-doped A-15 compounds. The complete and sole occupation of these positions yields the concentration x = 3. Accordingly, we found for the sample with x = 3.63 the additional occupation of 24k (or nearly 24k) positions. Our study suggests in particular a structural mechanism that successively replaces 6d positions by two adjacent and simultaneously occupied 24k positions in order to allow an increase of the D concentration above x = 3. 0 1997 Elsevier Science Ltd. All rights reserved
Keywords: A. metals, C. crystal structure and symmetry, D. order-disorder effects, E. neutron scattering.
1. INTRODUCTION Intermetallic A8B compounds with the cubic A-15 structure, such as Ti31r, are of scientific and technological interest, particularly with respect to their superconducting properties [l]. Many of these compounds can absorb considerable amounts of hydrogen (H and D) on interstitial sites where (i) the A-15 structure of the A3B host compound remains unchanged and (ii) the lattice parameter increases essentially linearly with H(D) concentration ([2-71 and references therein). Neutron diffraction studies on H-(D-)doped A-15 compounds Nb$nH, (x = 1) [2], Nb3SnDX (x = 0.69) [S] and Ti3SbDX (x = 2.6) [7] showed that the H(D) interstitials occupied sixfold d positions (6d positions) of the space group Pm% (No. 223) [9]. The left-hand side of Fig. 1 shows such a position, located in the center of a tetrahedron formed by four A atoms (Ti atoms in the case of Ti31r). Since a unit cell comprises two A3B formula units, the maximum H concentration of a H-doped AsBH, compound is x = 3 as long as the H solely occupies ti positions and the A-15 host lattice persists. However, a number of A-15 compounds reaches higher
concentrations than x = 3 after H absorption without a change of the host lattice structure. Ti31r is such a compound [5], together with, for instance, Nb3Au, Nb31r, Nb,Pt and Nb30s [4]. It is obvious that the H(D) in these compound8 cannot, or at least not exclusively, occupy 6d positions for x > 3. This paper reports on a neutron diffraction study in which we determined the interstitial sites of D in Ti31rDX for concentrations x below and above 3. We find that D occupies 6d positions for x < 3, whereas it occupies both 6d and 24k (or nearly 24k) positions for x > 3. The right-hand side of Fig. 1 shows four such 24k positions, located within tetrahedra formed by three A(Ti) atoms and one B(b) atom. For x > 3, our results suggest specifically that the D occupies successively two 24k positions which are (essentially in opposite direction) nearest neighbors to a 6d position which then is unoccupied (the full or the cross-hatched circles in Fig. 1 represent two such 24k positions each). This means a splitting of the D sites from a single 6d position into two adjacent and simultaneously occupied 24k positions taking place in order to allow the D-concentration to increase above x = 3.
570
INTERSTITIAL SITES OF DEUTERIUM IN THE A-15 COMPOUND Ti&
Vol. 101, No. 8
3. EXPERIMENTAL RESULTS AND DISCUSSION
0
l
Ti
@
or
6 d position (left)
0,.
24k positions bight)
Fig. 1. The A-15 structure of Ti& together with a 6d interstitial position (left) and four 24k interstitial positions (right)
2. EXPERIMENTAL DETAILS The experiments were carried out on two Ddoped T&IrD, powder samples with x = 0.70 f 0.01 and 3.63 * 0.04 and on a D-(H-)free Ti31r reference. The TisIr host material was prepared in an induction furnace from stoichiometric amounts of Ti (nominal purity 99.98%) and Ir (99.9%) which were repeatedly melted (at least 20 times) in a water-cooled Cu crucible (Ar atmosphere of -1 bar). For homogenization, the material was rotated between the individual melting processes and, finally, annealed for -3Omin first at 1400°C and then at 1300°C [lo]. For D doping, the TiJr material was pulverized and exposed to Dz gas in an ultra-high-vacuum system at elevated temperatures [5]. The resulting D concentrations were determined (i) from the amount of the absorbed gas and (ii) by vacuum extraction of small fractions of the doped material (accuracy -1%). X-ray powder diffraction on the D-doped samples (and the undoped reference) yielded a single-phase A-15 structure of the T&b host compounds, showing (i) the absence of any impurity phases and (ii) that the samples were outside the room-temperature miscibility gap for the isotope H between x = 0.9 and 2.3 [lo]. The neutron powder diffraction measurements were performed at room temperature with instrument E6 at the Hahn-Meitner-Institute (BENSC) in Berlin. The instrument is a two-axis diffractometer equipped with a double-focusing PG monochromator and a linear BF3 multicounter with 200 channels of 0.1” width. The samples were in a cylindrical V can (5 mm inner diameter). The $ffractograms were taken with a wavelength h = 2.387 A and different overlapping detector positions covering a total angular range of -lOO”.
Figure 2 presents neutron diffractograms from the two investigated Ti$D, samples and from the undoped TisIr reference (x = 0). We analyzed the data by Rietveld refinement with Rodriguez-Carvajal’s program FULLPROF [ll], using the space group P&z (No. 223) [9] with 2u sites for the Ir and 6c sites for the Ti and considering different possible space-group positions for the D interstitials where the variable coordinates of a given position (e.g. 2 coordinates for the 24k positions) were fitted parameters. Our analysis accounted for the measured absorption and applied Gaussian profiles for the peaks and polynomial functions for the background between the peaks. A common temperature factor B,,, was used for Ti and Ir and it was assumed that the investigated samples had an identical BI value and an identical temperature factor BD (#B,) for D. The solid lines in Fig. 1 represent the diffractograms as calculated in our optimal fits and the difference between the calculated and the measured diffractograms. The fits to the D-free Ti& reference confirmed its A-15 structure and yielded a lattice parameter a = (5.0118 + 0.0004) A in reasonable agreement with literature data (see [S] and references therein; our iattice parameter values hold for a nominal X = 2.387A and do not consider inaccuracies in the determination of X). We found BM = (0.658 +Z0.1) A2, a result subsequently used as a fixed parameter for the analysis of the D-doped
12 :
8:
1
x=0
I I:;* -1 *:.,..c.....*‘.
$8 ’
1
YT-7-3 20 I”]
Fig. 2. Neutron diffractograms of the TisIr reference sample (x = 0) and of the two T&IrD, 9amples with x = 0.7 and 3.63, respectively (h = 2.387A)
Vol. 101, No. 8
INTERSTITIAL SITES OF DEUTERIUM IN THE A-15 COMPOUND Ti&
samples. The agreement factors were Rp = 5.3%, R, = 7.04% and R, = 1.74% and the goodness of the fit was X2 = 16.4. The analysis of the Ti&D, sample with the lower D concentration x = 0.7 showed that the D interstitials occupy 6d positions, as reported for D (or II) in Nb$n [2, 8) and TisSb [7], thus contirming the occupation of these positions for D(H) conce$rations below x = 3. We found (L= (5.0541~ 0.0002) A for the lattice parameter and BD = (1.99 * 0.32)A2. The latter result was again used as a fixed parameter for the analysis of the sample with the higher concentration x = 3.63. Finally, the agreement factors were Rp = 4.48%, R, = 5.99% and R, = 1.52%, together with a goodness of the fit of X2 = 15.6. We discuss now the sample with x = 3.63. For this sample, all calculations carried out for the most simple case where the D atoms occupy solely interstitial sites of one given positional type (the multiplicity of the positions must exceed 6 to account for x > 3) yielded an unsatisfactory description of the measured diffractogram. Therefore, we considered a situation in which the D interstitials occupy both 6d positions and sites of an additional position. This introduces a new variable parameter in our fits, the concentration xl of D interstitials on 6d positions. The concentration x2 of the D atoms on the additional position is then given by the fact that x1 and x2 specify the total concentration according to x,+x2=x=3.63.
(1)
Figure 3 shows the goodness X2 of our fits as a function of x1, obtained under the assumption that the additional positions of the D interstitials are 16i, 24k or 481 positions, respectively. From a nuclear magnetic x2
0.63
1.03
(additional site@+ 1.43
1.83
2.23
2.63
571
resonance study on the H-doped A-15 compound Ti$bH,, 16i positions (located on the space diagonals of the unit cell) were proposed as (exclusive or additional) D(H) sites in A-15 compounds [12]. Our X2 results in Fig. 3 demonstrate that these positions are not occupied, at least not in the presently investigated system. Further, the figure shows that additional sites on either 24k or 481 positions provide a satisfactory description of our diffractogram, where the difference in X2 between these two additional positions is almost negligible at the o timum concentration x1 = 2.4 (or P x2 = 1.23) where X exhibits its minimum (the optimum concentration is identical for both the 24k and 481 positions). Table 1 collects, for the optimum concentration x1 = 2.4, the lattice parameter a and the other structural parameters resulting from our fits for the additional 24k and 481 positions, together with the various agreement factors and X2. The 481 positions are the most general space group positions (three variable coordinates X, Y and Z), so that they become identical to any of the other more special positions if a number of the three variable coordinates is suitably fixed (e.g., the fixed coordinate X = 0 makes the 481 positions identical to the 24k positions). Therefore, none of the more special positions will describe our data better than the 481 positions as long as all the coordinates of the 481 positions are variable (as in our fits). Figure 3 demonstrates this since X2 for the additional occupation of 481 positions is in all cases (slightly) lower than for an occupation of 24k positions. However, it is also seen from Fig. 3 and from Table 1 that, for the optimum concentration x 1 = 2.4, the differences in X2 and in the agreement factors between an occupation of 24k and 481 positions are in fact negligibly small. Table 1 shows further that our fits yielded coordinate values for the 481 and the more symmetric 24k positions which are identical (within the quoted accuracy) for Y and Z and Table 1. The structural parameters found for the additional occupation 24k and 481 positions in the case of the Ti$rD, sample with x = 3.63 (space group Pm% (No. 223) [9]). Th e meaning of the listed quantities is explained in the text Quantity
3
2.6
2.2
1.8
1.4
1
+ I(,(d sitea)
Fig. 3. The occupation of 6d positions plus either 16i, 24k or 481 positions in the case of the Ti+D, sample with x = 3.63. The goodness of the fit X2is plotted vs the concentraiton x1 of the D interstitials on 6d positions. The upper abscissa shows the D concentration x2 on the 16i, 24k or 482 positions, respectively. The total D concentration x = 3.63 is the sum of x1 and x2
; Y Z RP R,
24k positions
481 positions
(5.2410 i 0.0003) A 0 (fixed) 0.148 f 0.003 0.262 * 0.003 5.86% 7.16% 2.06% 12.1
5.2410 * 0.0003 A 0.025 f 0.010 0.145 f 0.003 0.267 * 0.003 5.83% 7.13% 2.06% 12.0
572
INTERSTITIAL SITES OF DEUTERIUM IN THE A-15 COMPOUND TisIr
differ by only -0.13 A for X. It is doubtful whether our study really substantiates the small difference in the X values if we realistically account for inaccuracies not considered in the error value of our fit routine (for instance the inaccuracies in the concentration x, in the absorption correction and in our assumptions on the temperature factors BM and BD). However, we can conclude in any case that the additional sites of the D interstitials are either true 24k positions or off-cent:r 24k positions which are slightly shifted (-0.13A) against true 24k positions. The additional occupation of the 24k (or nearly 24k) positions has interesting geometrical aspects. First, the results in Table 1 show hoat the 24k positions are considerably displaced (-0.27A) from the center of the tetrahedra formed by the four nearest-neighbour metal atoms (the center is equally distant to all four atoms). Further, the distance between a 6d position and one of its four adjacent (nearest-neighbor) 24k positions is -1.36k which is drastically smaller than the minimum distance of -2.1 A usually found between H(D) atoms in metal hydrides [13]. Therefore, we can anticipate that a 6d position becomes unoccupied as soon as one of its four adjacent 24k positions is populated. ln this case, we can calculate the average number s of D atoms populating the four adjacent 24k positions of an unoccupied 6d position according to the relation s = (x -x1)/(3 -x*),
(2)
which yields s = 2.05 for our optimum concentration Xl = 2.4. Accounting for inaccuracies in our determination of both x and the optimum x1, we can conclude that the occupation of in fact two (instead of 2.05) adjacent 24k positions replaces successively the occupation of 6d positions for D concentrations x > 3. A second geometrical aspect is most readily seen from the right-hand side of Fig. 1. The figure shows that the four adjacent 24k positions of a 6d position can be considered to form two pairs as indicated by the crosshatched and the full circles, respectively. qe distance between the two positions of a pair (-2.49A) is much larger than $e distance between positions of different pairs (-2.06 A), where the latter distance is even slightiy smaller than the usual minimum distance (-2.1 A) between D atoms in metals. Therefore, it is suggestive to assume that the D atoms occupy only the positions of one of the two pairs in order to maximize their distance, which is equivalent to a splitting of the D sites from a single 6d position into two adjacent and simultaneously occupied 24k pair positions. The possible occurrence of slightly off-center 24k positions may also reflect a tendency for a maximum D distance. Consider, for instance, the pair formed by the two 24k positions indicated by full circles in Fig. 1. The
Vol. 101, No. 8
coordinate X = 0.0249 by which the 481 positions in Table 1 differ from the true 24k positions (X = 0) means for this pair that its two 24k positions shift by -0.13 A in Z-direction (up- or down). It is seen that such shifts would indeed increase the distance between the D atoms if they occur in opposite direction. The successive replacement of H(D) positions by other positions of a higher multiplicity, as found in our present experiments, seems to be a natural way for a continuous increase of the H(D) content above the maximum concentration allowed by the positions with lower multiplicity. In spite of this, it is in fact a quite uncommon structural mechanism that is rarely observed. The system ZrsPD, is an example where a similar situation is found in a limited concentration range below x = 3 (space group P4zlnbc, No. 86,4a positions are replaced by 16k positions) [14, 151. Finally, our results show a (linear) increase of the lattice parameter a with D concentration according to the relation d&lx = (6.3 * 0.1) 10m2A. ‘Ibis value is -10% lower than that found for the isotope H (da& = (7.2 * 0.3) . 10e2 A [5]), demonstrating a sizable isotope effect. However, the fact that D expands the lattice less than H is, for instance, also reported for the A-15 compound Ti$b [7]. l
4. CONCLUSIONS We determined the interstitial sites of D in the D-doped A-15 compound Ti@D, for concentrations x below and above 3. The D occupies 6d positions for x < 3 and both 6d and 24k (or nearly 24k) positions for x > 3. For x > 3, our results indicate that the occupation of ti positions is successively replaced by an occupation of two 24k positions which are (essentially in opposite direction) adjacent to an 6d position which then becomes unoccupied. This corresponds to an effective splitting of the D sites from a single 6d position into two adjacent and simultaneously occupied 24k positions in order to allow an increase of the D concentration above x = 3. Acknowledgements-The authors thank S. Rundqvist and N. StiiSer for valuable discussions. The work was financially supported by the Bundesministerium fiir Bildung, Wissenschaft, Forschung und Technologie. REFERENCES 1. 2.
Muller, J., Rep. Prog. Phys., 43, 1980, 641. Vieland, L.J., Wicklund, A.W. and White, J.G., Phys. Rev., Bll, 1975,331l. 3. Rama Rao, K.V.S., Mrowietx, M. and Weiss, A., Ber. Bunsenges. Phys. Chem., 86, 1982, 1135. 4. Antonov, V.E., Antonova, T.E., Belash, LT., Zharikov, O.V., Latynin, A.I., Palnichenko, A.V.
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5. 6. 7. 8. 9.
INTERSTITIAL SITES OF DEUTERIUM IN THE A-15 COMPOUND TisIr
and Rashchupkin, V.I., Sov. Phys. - Solid State, 31,1989, 1659. Schlereth, M. and Wipf, H., J. Phys.: Condens. Matter, 2, 1990, 6929. Baier, M., Wordel, R., Wagner, F.E., Antonova, T.E. and Antonov, V.E., J. Less-Common Met., 172,1991,358. Skripov, A.V., Podlesnyak, A.A. and Fischer, P., J. Alloys Comp., 210,1994,27. Cornell, K., Stuhr, U., Wipf, H., StiiBer, N. and Skripov, A.V. (to be published). Int. Tables for Crystallogr., Vol. A: Space-Group Symmetry, 2nd revised Edition (Edited by T. Hahn), Kluwer Academic Publishers, Dordrecht, 1989, p. 670.
10. 11. 12. 13.
14. 15.
573
Junod, A., Flukiger, R. and Muller, J., J. Phys. Chem. Solidr, 37,1976,27. Rodriguez-Carvajal, J., Abstracts of the Satellite Meeting on Powder Diffraction, XVIII Congr. of the Int. Union of Crystall., Toulouse 1990, p. 127. Skripov, A.V., Belyaev, M.Yu. and Petrova, S.A., J. Phys.: Condens. Matter, 4, 1992, LS37. Yvon, K. and Fischer, P., in Topics in Applied Physics, Vol. 63, Hydrogen in lntermetallic Compounds Z (Edited by L. Schlapbach), Springer-Verlag, Berlin, 1988, p. 87. Ahlzen, P.-J., Andersson, Y., Rundqvist, S. and Tellgren, R., J. Less-Common Met., 161,1990,269. Ahlzen, P.-J., Andersson, Y., Rundqvist, S. and Tellgren, R., J. Less-Common Met., 170,1991,263.
Pergamon
PII:soo38-1098(96)00653-9
A NEUTRON DIFFRACTION STUDY OF THE INTERSTITIAL SITES OF DEUTERIUM IN THE A-15 COMPOUND Ti8Ir K. Comell,a H. Wipf,” U. Stub? and A.V. Skripov’ “Technische Hochschule Darmstadt, Institut ftir Festkorperphysik, D-64289 Darmstadt ‘Hahn-Meitner-Institut, BENSC, D-14109 Berlin ‘Urals Branch of the Academy of Sciences, Institute of Metal Physics, Ekaterinburg 620219, Russia (Received 27 September 1996; accepted 28 October 1996 by P.H. Dederichs) The interstitial D sites in the D-doped A-15 compound Ti31rDX with x = 0.70 and 3.63 were determined by neutron diffraction (space group Pm% (No. 223)). For x = 0.70, we confirm the D occupation of sixfold d positions (6d positions) already found for other H- and D-doped A-15 compounds. The complete and sole occupation of these positions yields the concentration x = 3. Accordingly, we found for the sample with x = 3.63 the additional occupation of 24k (or nearly 24k) positions. Our study suggests in particular a structural mechanism that successively replaces 6d positions by two adjacent and simultaneously occupied 24k positions in order to allow an increase of the D concentration above x = 3. 0 1997 Elsevier Science Ltd. All rights reserved
Keywords: A. metals, C. crystal structure and symmetry, D. order-disorder effects, E. neutron scattering.
1. INTRODUCTION Intermetallic A8B compounds with the cubic A-15 structure, such as Ti31r, are of scientific and technological interest, particularly with respect to their superconducting properties [l]. Many of these compounds can absorb considerable amounts of hydrogen (H and D) on interstitial sites where (i) the A-15 structure of the A3B host compound remains unchanged and (ii) the lattice parameter increases essentially linearly with H(D) concentration ([2-71 and references therein). Neutron diffraction studies on H-(D-)doped A-15 compounds Nb$nH, (x = 1) [2], Nb3SnDX (x = 0.69) [S] and Ti3SbDX (x = 2.6) [7] showed that the H(D) interstitials occupied sixfold d positions (6d positions) of the space group Pm% (No. 223) [9]. The left-hand side of Fig. 1 shows such a position, located in the center of a tetrahedron formed by four A atoms (Ti atoms in the case of Ti31r). Since a unit cell comprises two A3B formula units, the maximum H concentration of a H-doped AsBH, compound is x = 3 as long as the H solely occupies ti positions and the A-15 host lattice persists. However, a number of A-15 compounds reaches higher
concentrations than x = 3 after H absorption without a change of the host lattice structure. Ti31r is such a compound [5], together with, for instance, Nb3Au, Nb31r, Nb,Pt and Nb30s [4]. It is obvious that the H(D) in these compound8 cannot, or at least not exclusively, occupy 6d positions for x > 3. This paper reports on a neutron diffraction study in which we determined the interstitial sites of D in Ti31rDX for concentrations x below and above 3. We find that D occupies 6d positions for x < 3, whereas it occupies both 6d and 24k (or nearly 24k) positions for x > 3. The right-hand side of Fig. 1 shows four such 24k positions, located within tetrahedra formed by three A(Ti) atoms and one B(b) atom. For x > 3, our results suggest specifically that the D occupies successively two 24k positions which are (essentially in opposite direction) nearest neighbors to a 6d position which then is unoccupied (the full or the cross-hatched circles in Fig. 1 represent two such 24k positions each). This means a splitting of the D sites from a single 6d position into two adjacent and simultaneously occupied 24k positions taking place in order to allow the D-concentration to increase above x = 3.
570
INTERSTITIAL SITES OF DEUTERIUM IN THE A-15 COMPOUND Ti&
Vol. 101, No. 8
3. EXPERIMENTAL RESULTS AND DISCUSSION
0
l
Ti
@
or
6 d position (left)
0,.
24k positions bight)
Fig. 1. The A-15 structure of Ti& together with a 6d interstitial position (left) and four 24k interstitial positions (right)
2. EXPERIMENTAL DETAILS The experiments were carried out on two Ddoped T&IrD, powder samples with x = 0.70 f 0.01 and 3.63 * 0.04 and on a D-(H-)free Ti31r reference. The TisIr host material was prepared in an induction furnace from stoichiometric amounts of Ti (nominal purity 99.98%) and Ir (99.9%) which were repeatedly melted (at least 20 times) in a water-cooled Cu crucible (Ar atmosphere of -1 bar). For homogenization, the material was rotated between the individual melting processes and, finally, annealed for -3Omin first at 1400°C and then at 1300°C [lo]. For D doping, the TiJr material was pulverized and exposed to Dz gas in an ultra-high-vacuum system at elevated temperatures [5]. The resulting D concentrations were determined (i) from the amount of the absorbed gas and (ii) by vacuum extraction of small fractions of the doped material (accuracy -1%). X-ray powder diffraction on the D-doped samples (and the undoped reference) yielded a single-phase A-15 structure of the T&b host compounds, showing (i) the absence of any impurity phases and (ii) that the samples were outside the room-temperature miscibility gap for the isotope H between x = 0.9 and 2.3 [lo]. The neutron powder diffraction measurements were performed at room temperature with instrument E6 at the Hahn-Meitner-Institute (BENSC) in Berlin. The instrument is a two-axis diffractometer equipped with a double-focusing PG monochromator and a linear BF3 multicounter with 200 channels of 0.1” width. The samples were in a cylindrical V can (5 mm inner diameter). The $ffractograms were taken with a wavelength h = 2.387 A and different overlapping detector positions covering a total angular range of -lOO”.
Figure 2 presents neutron diffractograms from the two investigated Ti$D, samples and from the undoped TisIr reference (x = 0). We analyzed the data by Rietveld refinement with Rodriguez-Carvajal’s program FULLPROF [ll], using the space group P&z (No. 223) [9] with 2u sites for the Ir and 6c sites for the Ti and considering different possible space-group positions for the D interstitials where the variable coordinates of a given position (e.g. 2 coordinates for the 24k positions) were fitted parameters. Our analysis accounted for the measured absorption and applied Gaussian profiles for the peaks and polynomial functions for the background between the peaks. A common temperature factor B,,, was used for Ti and Ir and it was assumed that the investigated samples had an identical BI value and an identical temperature factor BD (#B,) for D. The solid lines in Fig. 1 represent the diffractograms as calculated in our optimal fits and the difference between the calculated and the measured diffractograms. The fits to the D-free Ti& reference confirmed its A-15 structure and yielded a lattice parameter a = (5.0118 + 0.0004) A in reasonable agreement with literature data (see [S] and references therein; our iattice parameter values hold for a nominal X = 2.387A and do not consider inaccuracies in the determination of X). We found BM = (0.658 +Z0.1) A2, a result subsequently used as a fixed parameter for the analysis of the D-doped
12 :
8:
1
x=0
I I:;* -1 *:.,..c.....*‘.
$8 ’
1
YT-7-3 20 I”]
Fig. 2. Neutron diffractograms of the TisIr reference sample (x = 0) and of the two T&IrD, 9amples with x = 0.7 and 3.63, respectively (h = 2.387A)
Vol. 101, No. 8
INTERSTITIAL SITES OF DEUTERIUM IN THE A-15 COMPOUND Ti&
samples. The agreement factors were Rp = 5.3%, R, = 7.04% and R, = 1.74% and the goodness of the fit was X2 = 16.4. The analysis of the Ti&D, sample with the lower D concentration x = 0.7 showed that the D interstitials occupy 6d positions, as reported for D (or II) in Nb$n [2, 8) and TisSb [7], thus contirming the occupation of these positions for D(H) conce$rations below x = 3. We found (L= (5.0541~ 0.0002) A for the lattice parameter and BD = (1.99 * 0.32)A2. The latter result was again used as a fixed parameter for the analysis of the sample with the higher concentration x = 3.63. Finally, the agreement factors were Rp = 4.48%, R, = 5.99% and R, = 1.52%, together with a goodness of the fit of X2 = 15.6. We discuss now the sample with x = 3.63. For this sample, all calculations carried out for the most simple case where the D atoms occupy solely interstitial sites of one given positional type (the multiplicity of the positions must exceed 6 to account for x > 3) yielded an unsatisfactory description of the measured diffractogram. Therefore, we considered a situation in which the D interstitials occupy both 6d positions and sites of an additional position. This introduces a new variable parameter in our fits, the concentration xl of D interstitials on 6d positions. The concentration x2 of the D atoms on the additional position is then given by the fact that x1 and x2 specify the total concentration according to x,+x2=x=3.63.
(1)
Figure 3 shows the goodness X2 of our fits as a function of x1, obtained under the assumption that the additional positions of the D interstitials are 16i, 24k or 481 positions, respectively. From a nuclear magnetic x2
0.63
1.03
(additional site@+ 1.43
1.83
2.23
2.63
571
resonance study on the H-doped A-15 compound Ti$bH,, 16i positions (located on the space diagonals of the unit cell) were proposed as (exclusive or additional) D(H) sites in A-15 compounds [12]. Our X2 results in Fig. 3 demonstrate that these positions are not occupied, at least not in the presently investigated system. Further, the figure shows that additional sites on either 24k or 481 positions provide a satisfactory description of our diffractogram, where the difference in X2 between these two additional positions is almost negligible at the o timum concentration x1 = 2.4 (or P x2 = 1.23) where X exhibits its minimum (the optimum concentration is identical for both the 24k and 481 positions). Table 1 collects, for the optimum concentration x1 = 2.4, the lattice parameter a and the other structural parameters resulting from our fits for the additional 24k and 481 positions, together with the various agreement factors and X2. The 481 positions are the most general space group positions (three variable coordinates X, Y and Z), so that they become identical to any of the other more special positions if a number of the three variable coordinates is suitably fixed (e.g., the fixed coordinate X = 0 makes the 481 positions identical to the 24k positions). Therefore, none of the more special positions will describe our data better than the 481 positions as long as all the coordinates of the 481 positions are variable (as in our fits). Figure 3 demonstrates this since X2 for the additional occupation of 481 positions is in all cases (slightly) lower than for an occupation of 24k positions. However, it is also seen from Fig. 3 and from Table 1 that, for the optimum concentration x 1 = 2.4, the differences in X2 and in the agreement factors between an occupation of 24k and 481 positions are in fact negligibly small. Table 1 shows further that our fits yielded coordinate values for the 481 and the more symmetric 24k positions which are identical (within the quoted accuracy) for Y and Z and Table 1. The structural parameters found for the additional occupation 24k and 481 positions in the case of the Ti$rD, sample with x = 3.63 (space group Pm% (No. 223) [9]). Th e meaning of the listed quantities is explained in the text Quantity
3
2.6
2.2
1.8
1.4
1
+ I(,(d sitea)
Fig. 3. The occupation of 6d positions plus either 16i, 24k or 481 positions in the case of the Ti+D, sample with x = 3.63. The goodness of the fit X2is plotted vs the concentraiton x1 of the D interstitials on 6d positions. The upper abscissa shows the D concentration x2 on the 16i, 24k or 482 positions, respectively. The total D concentration x = 3.63 is the sum of x1 and x2
; Y Z RP R,
24k positions
481 positions
(5.2410 i 0.0003) A 0 (fixed) 0.148 f 0.003 0.262 * 0.003 5.86% 7.16% 2.06% 12.1
5.2410 * 0.0003 A 0.025 f 0.010 0.145 f 0.003 0.267 * 0.003 5.83% 7.13% 2.06% 12.0
572
INTERSTITIAL SITES OF DEUTERIUM IN THE A-15 COMPOUND TisIr
differ by only -0.13 A for X. It is doubtful whether our study really substantiates the small difference in the X values if we realistically account for inaccuracies not considered in the error value of our fit routine (for instance the inaccuracies in the concentration x, in the absorption correction and in our assumptions on the temperature factors BM and BD). However, we can conclude in any case that the additional sites of the D interstitials are either true 24k positions or off-cent:r 24k positions which are slightly shifted (-0.13A) against true 24k positions. The additional occupation of the 24k (or nearly 24k) positions has interesting geometrical aspects. First, the results in Table 1 show hoat the 24k positions are considerably displaced (-0.27A) from the center of the tetrahedra formed by the four nearest-neighbour metal atoms (the center is equally distant to all four atoms). Further, the distance between a 6d position and one of its four adjacent (nearest-neighbor) 24k positions is -1.36k which is drastically smaller than the minimum distance of -2.1 A usually found between H(D) atoms in metal hydrides [13]. Therefore, we can anticipate that a 6d position becomes unoccupied as soon as one of its four adjacent 24k positions is populated. ln this case, we can calculate the average number s of D atoms populating the four adjacent 24k positions of an unoccupied 6d position according to the relation s = (x -x1)/(3 -x*),
(2)
which yields s = 2.05 for our optimum concentration Xl = 2.4. Accounting for inaccuracies in our determination of both x and the optimum x1, we can conclude that the occupation of in fact two (instead of 2.05) adjacent 24k positions replaces successively the occupation of 6d positions for D concentrations x > 3. A second geometrical aspect is most readily seen from the right-hand side of Fig. 1. The figure shows that the four adjacent 24k positions of a 6d position can be considered to form two pairs as indicated by the crosshatched and the full circles, respectively. qe distance between the two positions of a pair (-2.49A) is much larger than $e distance between positions of different pairs (-2.06 A), where the latter distance is even slightiy smaller than the usual minimum distance (-2.1 A) between D atoms in metals. Therefore, it is suggestive to assume that the D atoms occupy only the positions of one of the two pairs in order to maximize their distance, which is equivalent to a splitting of the D sites from a single 6d position into two adjacent and simultaneously occupied 24k pair positions. The possible occurrence of slightly off-center 24k positions may also reflect a tendency for a maximum D distance. Consider, for instance, the pair formed by the two 24k positions indicated by full circles in Fig. 1. The
Vol. 101, No. 8
coordinate X = 0.0249 by which the 481 positions in Table 1 differ from the true 24k positions (X = 0) means for this pair that its two 24k positions shift by -0.13 A in Z-direction (up- or down). It is seen that such shifts would indeed increase the distance between the D atoms if they occur in opposite direction. The successive replacement of H(D) positions by other positions of a higher multiplicity, as found in our present experiments, seems to be a natural way for a continuous increase of the H(D) content above the maximum concentration allowed by the positions with lower multiplicity. In spite of this, it is in fact a quite uncommon structural mechanism that is rarely observed. The system ZrsPD, is an example where a similar situation is found in a limited concentration range below x = 3 (space group P4zlnbc, No. 86,4a positions are replaced by 16k positions) [14, 151. Finally, our results show a (linear) increase of the lattice parameter a with D concentration according to the relation d&lx = (6.3 * 0.1) 10m2A. ‘Ibis value is -10% lower than that found for the isotope H (da& = (7.2 * 0.3) . 10e2 A [5]), demonstrating a sizable isotope effect. However, the fact that D expands the lattice less than H is, for instance, also reported for the A-15 compound Ti$b [7]. l
4. CONCLUSIONS We determined the interstitial sites of D in the D-doped A-15 compound Ti@D, for concentrations x below and above 3. The D occupies 6d positions for x < 3 and both 6d and 24k (or nearly 24k) positions for x > 3. For x > 3, our results indicate that the occupation of ti positions is successively replaced by an occupation of two 24k positions which are (essentially in opposite direction) adjacent to an 6d position which then becomes unoccupied. This corresponds to an effective splitting of the D sites from a single 6d position into two adjacent and simultaneously occupied 24k positions in order to allow an increase of the D concentration above x = 3. Acknowledgements-The authors thank S. Rundqvist and N. StiiSer for valuable discussions. The work was financially supported by the Bundesministerium fiir Bildung, Wissenschaft, Forschung und Technologie. REFERENCES 1. 2.
Muller, J., Rep. Prog. Phys., 43, 1980, 641. Vieland, L.J., Wicklund, A.W. and White, J.G., Phys. Rev., Bll, 1975,331l. 3. Rama Rao, K.V.S., Mrowietx, M. and Weiss, A., Ber. Bunsenges. Phys. Chem., 86, 1982, 1135. 4. Antonov, V.E., Antonova, T.E., Belash, LT., Zharikov, O.V., Latynin, A.I., Palnichenko, A.V.
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5. 6. 7. 8. 9.
INTERSTITIAL SITES OF DEUTERIUM IN THE A-15 COMPOUND TisIr
and Rashchupkin, V.I., Sov. Phys. - Solid State, 31,1989, 1659. Schlereth, M. and Wipf, H., J. Phys.: Condens. Matter, 2, 1990, 6929. Baier, M., Wordel, R., Wagner, F.E., Antonova, T.E. and Antonov, V.E., J. Less-Common Met., 172,1991,358. Skripov, A.V., Podlesnyak, A.A. and Fischer, P., J. Alloys Comp., 210,1994,27. Cornell, K., Stuhr, U., Wipf, H., StiiBer, N. and Skripov, A.V. (to be published). Int. Tables for Crystallogr., Vol. A: Space-Group Symmetry, 2nd revised Edition (Edited by T. Hahn), Kluwer Academic Publishers, Dordrecht, 1989, p. 670.
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Junod, A., Flukiger, R. and Muller, J., J. Phys. Chem. Solidr, 37,1976,27. Rodriguez-Carvajal, J., Abstracts of the Satellite Meeting on Powder Diffraction, XVIII Congr. of the Int. Union of Crystall., Toulouse 1990, p. 127. Skripov, A.V., Belyaev, M.Yu. and Petrova, S.A., J. Phys.: Condens. Matter, 4, 1992, LS37. Yvon, K. and Fischer, P., in Topics in Applied Physics, Vol. 63, Hydrogen in lntermetallic Compounds Z (Edited by L. Schlapbach), Springer-Verlag, Berlin, 1988, p. 87. Ahlzen, P.-J., Andersson, Y., Rundqvist, S. and Tellgren, R., J. Less-Common Met., 161,1990,269. Ahlzen, P.-J., Andersson, Y., Rundqvist, S. and Tellgren, R., J. Less-Common Met., 170,1991,263.