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Crystal structure of Pd13Pb9.r
Journal of the Less-Common Metals, 71 (1980) P29 - P38 @ Elsevier Sequoia S.A., Lausanne - Printed in the Netherlands
CRYSTAL
STRUCTURE
H. W. MAYER, M. ELLNER
P29
OF Pd,3Pb,.r
and K. SCHUBERT
Max-Planck-Znstitut fiir Metallforschung, 7000 Stuttgart (F. R.G.)
Znstitut fiir Werkstoffwissenschaften,
Seestr. 75,
(Received August 5,1979)
Summary
The phase PdrsPb,.r has a quasi-orthorhombic N26.18 structure which is a superstructure of the NiAs type with the trigonal prismatic interstices partly filled. In the unmixed atom rows parallel to (u3)NiAs few palladium atoms are substituted by lead atoms so that on average in the NiAs subcell there are more than two lead atoms. The increase, compared with Pd,Pbs, of the number of valence electrons and incidentally of the number of peripheral core electrons per subcell is caused by a change of the commensurability of the binding to the subcell, which conserves the FF2 type of binding present in Pd,Pb,.
1. Introduction
In the mixture PdPbM (M = undetermined mole number) there is a phase bundle which is stable at a mole fraction N& of 0.40 f 0.025. The bundle consists of PdsPbs.h (partially filled NiAs type, ah = (H4.46; 5.70) 8, SR10.65) [l, 21, PdBPbs.r (NisGes.r, SR39.119) [2] and PdisPbs (superstructure of the NiAs type) [ 21. A division of PdBPba.h into the two phases Pd,Pb,.h, and PdsPbs.h, is caused by a very weak transformation [ 21 and is not considered here. As a rule displacive transformations can occur in various steps. The question immediately arises as to why such superstructures of the NiAs type are stabilized. A study of Pd,sPb, was therefore desirable in order to find the difference in binding which must cause the difference in the superstructures.
2. Results The compound PdrsPb, forms peritectically at 611 “C [ 21 whilst the strong ordering transformation of Pd,Pb, has been found at 430 “C. It is therefore probable that Pd,,Pb, also undergoes some ordering transformation.
fn Fig. I the results of five thermal analyses are given. The alloy PdGOPbM shows strongly the 430 “C transformation of PdBPbs and the peritectic decomposition of Pd13Pb9 ; the transformation in PdsPba,h [ 21 could not be found in the present experiments which, however, should be considered as less sensitive than earlier experiments. The ahoy Pdss.rSPb,,_S gave on cooling an effect at 405 “C which must be interpreted as an undercooled formation of PdPb; also the cooling effect at 425 “C may be caused by some remaining PdSPbs.h. This cannot be said of the effect at 445 “C on heating which apparently is an ordering effect of Pd13Pb9, A further distributed effect on heating before the peritectic effect at 611 “C is found at 600 “C. The effect at 445 “C was confirmed in the alloy PdS7PbM. The undercooled formation of PdPb and, in a heating run, the equilibrium peritectic temperature were corroborated in the alloy PdS1Pbh9; the transformations at 316 and 273 “C [2] were confirmed and a very distinct transformation at 180 “C was found for the first time. Therefore PdPb is a good example for stepwise transformations of displacive structures. An additional indication for transformations in PdzsPbs was a domain structure observed microscopically in the crystals of samples which were quenched from tempe~tures above 445 “C. A Guinier photograph at 599 “C showed a hexagonal NiAs-like diagram with the non-calibrated lattice constants a = 4.493( 2) a and c = 5.76213) A ; this phase may be named Pd,sPbg.h,. Photographs recorded at temperatures between 600 and 450 “C showed a diagram which is very similar to that of Pd,,Pb,.r but which seems to have a different axial ratio; therefore this phase, Pd,sPbs.h,, might be orthorhombic. The splat cooling of PdWPbdl was two phase and resulted in the attainment of powder diagrams containing the
Fig. 1. NiAs-type
phase bundle of the mixture
PdPhM,
P31
following NiAs-type cells: lait = 4.454(l) A, last = 5.726(2) A, lasl/lall = 1.286,and (all = 4.506(l) A, JaaI = 5.748(2) 8, lasl/larl = 1.276, belonging to PdsPbs.h, and PdraPbs.ha respectively. The decrease of lasl/larl at the valence-electron-rich end of the homogeneous range of an NiAs-type phase has been discussed previously [3]. The thermal treatment of the crystals described in Table 1 permitted the domain structure to be avoided so that they may be considered as true single crystals. The composition PdlaPba was confirmed by the alloys given in Fig. 1. The pseudo-o~horhombic N26.18 cell and space group CZ/c [Z] were also confirmed, together with the morphotropic commensurabili~ a = ~r~,r,,.~(2, -2, -1; 2,&l; O,O,Z). From the commensurabi~ty it follows that 16 NiAs cells are contained in the centred N cell. The number of 36 lead atoms in this cell (which is confirmed by density measurements [ 21) shows that the anomalous substitution process first found in PdrsTls [43 is also present in Pd1sPb9. It is clear that this substitution has an influence on the number of non-occupied places per place in the ideal fully occupied cell (Nkp = 0.083), compared with the value for PdsPb,.r of NE = 0.111. This decrease of the number of non-occupied places per atom place with increasing valence electron concentration N&* is an exception since in general ZVf increases with increasing N&*. Also the fact that there are more than two lead atoms in the substructure cell is an exception of an often fulfilled rule [ 51. The structure, solved by Patterson methods, is described in Table 1. Table 2 gives an evaluation of the powder diagram, which shows that monoclinic symmetry could not be derived from the pseudo-orthorhombic line positions but only from the F, values in singlecrystal photographs.
3. Discussion Pd,,Pb,.r belongs to the family of partially filled NiAs structures. Recently it has been shown that these structures belong to a greater family of structures, which has been called the tungsten family since all types are commensurable to the hexagonal tungsten cell with three atoms cwaH [6]. Substitution of the relation cNiAs= UW.H (1;1;2) into the commensurability a = cNiAs (2,-2,-1;2,2,1;0,0,2)yieldsu=uw~n (2,-2,-1;2,2,1;0,0,4).Consideration of the primitive monoclinic cell up of Pd,sPba .r results in up = uw,n (2,0,-l; 0,2,1; 0,0,4). This shows (see p. 174 of ref. 6) that the structure of Pd1,Pb9 is related to NilsGas, Pd1sT19, NisP, and NihGaGea. Since NE = 0.083, the relation to N&Gag and Ni,GaGez is especially close. The well-confirmed structure of PtrJns [7] (Fig. 2) is isotypic to N&Gas, but there are also two statistically distributed vacancies as well as the four ordered vacancies. Here the morphotropic commensurability is (I~,,~~, = (IW.n (2,-2,-l; 2,2,1; 0,0,2). The ordered vacancies are contained in the mixed atom rows parallel to (us)NiAs,since these have small distances in the (ui & ca)NiAsplane. The nei~bour~g indiUm atoms move onto the vacancies. The vacancies form chains parallel to (--ul + o2 + Ua)NiAswhich are straight in
P32
the projection on (ai & Ul)NiAs and have links which alternate in length between 5 (--q + as)NiAs and :(---a, + up)NiAs. In the unmixed atom rows parallel to (Us)niAs few indium atoms substitute platinum atoms. This substitution increases the number of valence electrons per cell. In the structure of Pd,sPbs.r (Fig. 3) strongly mixed and essentially unmixed atom rows parallel to (as)NiAs are found. Only the mixed rows bear vacancies, and the lead atoms with a neighbouring vacancy in the (ai & as)niAs plane move onto the vacancies. The vacancy chains consist, similar to those in NirsGas and P&Ins, of short and long links; however, the chains projected on (a1 & as)mAs are now not straight but broken. This property causes the element Kss of the morphotropic commensurability to be 4 compared with 2 in PtisIna. In order to understand the superstructures of the phase bundle Pd,Pb, . . .PdiaPba it is necessary to consider the binding in the mixture PdPbM; for the notation see refs. 8 and 9. From Pd(Cu, SR1.15)3.83 A = b,(l) = c,(2,-2,0; 2,2,0; 2.8) and PdsPb(CusAu, SR10.65)4.02 A = br(1) = crzci, electron distances may be calculated which make the binding Pdr,Pbs.h(NiAs, SR10.65)H4.47; 5.70 A = brn(l,l,O; -1,2,0; 2.7) = crnK’( 2) probable; this is nearly the same as that assumed earlier [ 91 and gives a place number A$+! of 12.5. The factorial commensurability brn = ~rn( 2) assumed here between valence electron correlation and core electron TABLE 1 Structure and X-ray data for PdIaPbg.r Experiment: Pd5a.5Pb41.5(Gran. 1 min 1000 OC,Wa; 9 d 590 “C, 17 d + 30 “C), crystal approximately spherical, radius 0.04 mm. Diffractometer measurement with MO Ko: radiation of 2047 reflections of the kind +h, +k, _+Iup to 28 = 55” ; w scan, scan breadth l”, number of independent reflections 1990; 810 reflections with I, Q 20(Z,) were set equal to zero only for calculating CIIFoi - lFolI/zIF,,l, (lo = net count, u = standard deviation), 5 reflections measured 36 times in $ scan. Structure: PdlaPbg(N26.18 type), C”u, C2/c, al = 15.6027(g) A, a2 = 9.0599(5) 4 a3 = 13.911(l) A, 0~~= 55.875(5)“. 4Pd(e).0.3751(11).25 6 X 8Pd(f) .1257(5).1125(7).5064(5) .3688(4).1316(7).0009(5) .1355(5).1171(7) .1405(5) .0992(5).8732(8).3701(6) .2493(5).1239(9).2517(6) .1424(5) .6345(8).1243(6) 4Pb(e).0.8735(5).25 4 x SPb(f).4689(2).6645(3).1139(2) .4647(2).0805(3).1251(2) .2340(2).3768(3).1174(2) .2614(2).8717(3) .1181(2). Calculation: X-ray 72, spherical absorption, /JR = 4.1, lOOU-temperature coefficients full, u22, u33a u12> u13, u23): (1.5(4), l-7(4), 1.4(4), 0, -0.5(3), O), (1.5(3), 1.9(3), 1.5(3),-0.1(2),-0.7(2), 0.4(2)), (1.3(2), 1.7(3), 1.3(2), 0.1(2),-0.6(2),-0.3(2)), (1.5(3), 1.4(3), 2.0(3),-0.0(2),-1.1(2), -0.1(2)),(2.0(3), 1.8(3), 3.5(4), 0.1(3),-1.7(3), 0.1(3)), (1.2(2), 2.5(3), 1.9(3), -0.3(2),-0.9(2), -0.0(2)), (1.8(3), 1.6(3), 2.6(3),-0.0(2), -1.3(3), 0.1(3)), (0.9(2), 0.9(2), 0.8(2), 0, -0.2(l), 0) (0.8(l), 1.2(l), 1.1(l),-0.2(l),-0.5(l), 0.2(l)), (1.1(l), 1.2(l), 1.4(l), 0.2(1),-0.8(l), -0.2(l)), (1.4(l), 1.0(l), 1.6(l),-0.0(l),-0.8(l),-0.0(l)), (0.9(l), 0.9(l), 1.2(l), 0.0(l), -0.4(l), -0.1(l)). ZllF,I - IF,lI/~IF,I = 0.093. Table : L, F&O, FJlO.
P33 TABLE 1 (a)
9
n.
0
P34 TABLE 1 (b)
.
n.
*
P35 TABLE
2
Evaluation
of a powder
Experiment
:
Structure: Calculation:
Column
headings:
of Pdi3Phg.r
Pd5a.4Pb41,e (regulus 3 d 590 “C, water quenched; powder 15 d 430 “C!, 6 d -+ 30 “C, air quenched), Guinier photograph Cu Ko,, calibrated with silicon. Pd1aPba.r (N26.18) type, al = 15.6027(g) 8, a2 = 9.0599(5) A, a3 = 13.911(l) 19, (112= 55.875(5)“. I, = lo@ ZZPLG IF,12 = intensity calculated, H = multiplicity, P = polarization factor, L = Lorentz factor, G = geometric factor, F, = calculated amplitude, I, = intensity observed. Designation of intensity intervals: nbb, not observable; nbt, not observed; sss, 8(7); ss, 26(10); s, 51(14); m, 96(30); st, 291(164); sst, 678(222). (Ml), 103d, (A), 103d, (A), I,, I,.
--+a3 cosct2
k-
photograph
07
t a2
Fig. 2. PtlaIna, C&, C2/m, al = 15.338 A, az = 8.802 A, aa = 9.439 A, oz = 36.11”, 4Pt(g).0.253.0 4Pt(f).25.25.5 4Pt(i).451.0.272 8 X 0.748Pt(j).802.257.735 4Pt(i).258.0 .988 2Pt(c).0.0.5 4In(i).713.0.752 4In(i).177.0.772 8In(j).961.212.766 2In(d).0.5.5.
P36
t
b a3 cosq
---a7 t a2
Fig.3.Pd13Pb9,C6,,CP/c,o= (15.603,0, 7.804;9.060;11.515)~,4Pd(e).0.375.25 6 X 8Pd(f).126.113.506 .369.132.001.136.117.141 .099.873.370 .249.124.252.142.635 .1244Pb(e).0.874.25 4 X 8Pb(f).469.665.114 .465.081.125 .234.377.117 .261.872.118.
correlation is energetically favourable and leads to the name FF2 binding. Clearly the FF2 binding is closely related to the BB2 binding [ 8, 91 which is responsible for the p-brass and y-brass phases. The phase Pd,Pb,.r must have essentially the same binding as PdsPb3.h since it differs only by an ordering transformation. In Pd13Pba the number N&s of valence electrons in the NiAslike subcell as = (H4.52; 5.76) A is 9 instead of 8 as in PdsPb3. This may be rationalized by the assumption that the binding in PdBPb3 is energetically so favourable that the system strives to conserve it by accepting a new commensurability in the basal plane of the substructure as = cFH (3,1,0; -1,4,0; 0,0,5.7/3) = bFnK”/2, which gives just full occupation for the valence electron correlation. The occupation rule [ 81 thus gives an explanation for the substitution of additional lead atoms in as. It might be that this commensurability change is connected with a curious change of axial ratio in the dependence on composition found in Ni3Ge, [3]. A similar morphotropy occurred for PdGa(FeSi) [lo] . The commensurability difference of the binding to the structure causes a difference of the induced electron dipoles at the vacancies [ 51 and therefore a difference in the geometry of the vacancy chains. The average distance in the valence electron correlation fits well into the function d ‘(A&,), whereas the distance d ” in the core electron correlation shows some decrease, which evidently is forced by the d’ decrease; therefore d”(N&,) need not be perfectly smooth (Fig. 4). To give a complete description of the binding in the mixture PdPb, we consider the pseudo-orthorhombic phase PdPb.r(Z16.16) in the description PdPb.r(S16.16) 7.15;8.52;42.36A = bFu(-2,2.5,0;2,2.5,0;0,0,12c 13)= cHT (-4,5,0; 4,5,0; 0,0,20). Here both correlations give a quadratic net in the (a1 & up)rdpb plane, and these nets yield the mutual commensurability (2); however, in the (u3)rdPb direction the nets are stacked in a manner such that
P31
mole fraction
h$b/‘%
Fig. 4. A distance diagram for the mixture PdPbM where d ’ is the distance in the valence electron correlation and d” is the distance in the core electron correlation.
b is closer than an F stacking and c is more open than an F stacking. This is what is expected when we start from the FF2 binding and increase the value of N&A. For the phase which is most rich in lead it may be assumed that PdPb, (CUA1~,SR9.84)6.85;5.83~=b~(1.5,-1.5,0;1.5,i.5,0;0,0,1.8)=ca~’ (2). This is the frequently found FB2 binding which may be derived from an FF2 binding by choosing another commensurability in the tetragonal basal plane and adjusting the stacking distance of the parallel nets. Adding to these proposals the bindings Pd(Cu)3.89 a = b,(l) = ca(2,-2,O; 2,2,0; 0,0,2.8) and Pb(Cu)4.95 A = bs (2) results in the d(N&,) diagram given in Fig. 4. It can be seen that the distances fulfil the distance rule satisfactorily [ 71. From the present discussion it becomes clear that the phase bundle with NiAs-related structures and the FF2 binding replaces in PdPbM the fl and y phases in brasses with the BB2 binding.
Acknowledgments We wish to acknowledge the Deutsche Forschungsgemeinschaft for financial support, Professor H. G. von Schnering and Dr. K. Peters for the diffractometer measurements and Frau A. Kornau and Herr-n W. Furmanski for assistance.
References 1 H. Nowotny, K. Schubert and U. Dettinger, 2. Metallkd., 37 (1946) 137 - 145. 2 M. Ellner, T. Godecke and K. Schubert, Z. Metallkd., 64 (1973) 566 - 568. 3 M. Ellner, S. Heinrich, M. K. Bhargava and K. Schubert, J. Less-Common Met., 66 (1979) 163 - 173. 4 P. K. Panday and K. Schubert, J. Less-Common Met., 18 (1969) 175 - 202.
P38 5 I(. Schubert, Kristallstrukfuren Zweikomponentiger Phasen, Springer, Berlin, 1964, p. 336. 6 K. Schubert, Struct. Bonding ~BerZin~,33 (1977) 139 - 177. 7 S. Heinrich and K. Schubert, 2. Metallkd., 69 (1978) 230 - 236. 8 K. Schubert, J. Less-Common Met., 70 (1980) 167 - 180. 9 K. Schubert, 2. Kristallogr., 148 (1978) 221 - 236. 10 M. K. Bhargava, A. A. Gadalla and K. Schubert, J. Less-Common Met., 42 (1975) 69 - 76.
CRYSTAL
STRUCTURE
H. W. MAYER, M. ELLNER
P29
OF Pd,3Pb,.r
and K. SCHUBERT
Max-Planck-Znstitut fiir Metallforschung, 7000 Stuttgart (F. R.G.)
Znstitut fiir Werkstoffwissenschaften,
Seestr. 75,
(Received August 5,1979)
Summary
The phase PdrsPb,.r has a quasi-orthorhombic N26.18 structure which is a superstructure of the NiAs type with the trigonal prismatic interstices partly filled. In the unmixed atom rows parallel to (u3)NiAs few palladium atoms are substituted by lead atoms so that on average in the NiAs subcell there are more than two lead atoms. The increase, compared with Pd,Pbs, of the number of valence electrons and incidentally of the number of peripheral core electrons per subcell is caused by a change of the commensurability of the binding to the subcell, which conserves the FF2 type of binding present in Pd,Pb,.
1. Introduction
In the mixture PdPbM (M = undetermined mole number) there is a phase bundle which is stable at a mole fraction N& of 0.40 f 0.025. The bundle consists of PdsPbs.h (partially filled NiAs type, ah = (H4.46; 5.70) 8, SR10.65) [l, 21, PdBPbs.r (NisGes.r, SR39.119) [2] and PdisPbs (superstructure of the NiAs type) [ 21. A division of PdBPba.h into the two phases Pd,Pb,.h, and PdsPbs.h, is caused by a very weak transformation [ 21 and is not considered here. As a rule displacive transformations can occur in various steps. The question immediately arises as to why such superstructures of the NiAs type are stabilized. A study of Pd,sPb, was therefore desirable in order to find the difference in binding which must cause the difference in the superstructures.
2. Results The compound PdrsPb, forms peritectically at 611 “C [ 21 whilst the strong ordering transformation of Pd,Pb, has been found at 430 “C. It is therefore probable that Pd,,Pb, also undergoes some ordering transformation.
fn Fig. I the results of five thermal analyses are given. The alloy PdGOPbM shows strongly the 430 “C transformation of PdBPbs and the peritectic decomposition of Pd13Pb9 ; the transformation in PdsPba,h [ 21 could not be found in the present experiments which, however, should be considered as less sensitive than earlier experiments. The ahoy Pdss.rSPb,,_S gave on cooling an effect at 405 “C which must be interpreted as an undercooled formation of PdPb; also the cooling effect at 425 “C may be caused by some remaining PdSPbs.h. This cannot be said of the effect at 445 “C on heating which apparently is an ordering effect of Pd13Pb9, A further distributed effect on heating before the peritectic effect at 611 “C is found at 600 “C. The effect at 445 “C was confirmed in the alloy PdS7PbM. The undercooled formation of PdPb and, in a heating run, the equilibrium peritectic temperature were corroborated in the alloy PdS1Pbh9; the transformations at 316 and 273 “C [2] were confirmed and a very distinct transformation at 180 “C was found for the first time. Therefore PdPb is a good example for stepwise transformations of displacive structures. An additional indication for transformations in PdzsPbs was a domain structure observed microscopically in the crystals of samples which were quenched from tempe~tures above 445 “C. A Guinier photograph at 599 “C showed a hexagonal NiAs-like diagram with the non-calibrated lattice constants a = 4.493( 2) a and c = 5.76213) A ; this phase may be named Pd,sPbg.h,. Photographs recorded at temperatures between 600 and 450 “C showed a diagram which is very similar to that of Pd,,Pb,.r but which seems to have a different axial ratio; therefore this phase, Pd,sPbs.h,, might be orthorhombic. The splat cooling of PdWPbdl was two phase and resulted in the attainment of powder diagrams containing the
Fig. 1. NiAs-type
phase bundle of the mixture
PdPhM,
P31
following NiAs-type cells: lait = 4.454(l) A, last = 5.726(2) A, lasl/lall = 1.286,and (all = 4.506(l) A, JaaI = 5.748(2) 8, lasl/larl = 1.276, belonging to PdsPbs.h, and PdraPbs.ha respectively. The decrease of lasl/larl at the valence-electron-rich end of the homogeneous range of an NiAs-type phase has been discussed previously [3]. The thermal treatment of the crystals described in Table 1 permitted the domain structure to be avoided so that they may be considered as true single crystals. The composition PdlaPba was confirmed by the alloys given in Fig. 1. The pseudo-o~horhombic N26.18 cell and space group CZ/c [Z] were also confirmed, together with the morphotropic commensurabili~ a = ~r~,r,,.~(2, -2, -1; 2,&l; O,O,Z). From the commensurabi~ty it follows that 16 NiAs cells are contained in the centred N cell. The number of 36 lead atoms in this cell (which is confirmed by density measurements [ 21) shows that the anomalous substitution process first found in PdrsTls [43 is also present in Pd1sPb9. It is clear that this substitution has an influence on the number of non-occupied places per place in the ideal fully occupied cell (Nkp = 0.083), compared with the value for PdsPb,.r of NE = 0.111. This decrease of the number of non-occupied places per atom place with increasing valence electron concentration N&* is an exception since in general ZVf increases with increasing N&*. Also the fact that there are more than two lead atoms in the substructure cell is an exception of an often fulfilled rule [ 51. The structure, solved by Patterson methods, is described in Table 1. Table 2 gives an evaluation of the powder diagram, which shows that monoclinic symmetry could not be derived from the pseudo-orthorhombic line positions but only from the F, values in singlecrystal photographs.
3. Discussion Pd,,Pb,.r belongs to the family of partially filled NiAs structures. Recently it has been shown that these structures belong to a greater family of structures, which has been called the tungsten family since all types are commensurable to the hexagonal tungsten cell with three atoms cwaH [6]. Substitution of the relation cNiAs= UW.H (1;1;2) into the commensurability a = cNiAs (2,-2,-1;2,2,1;0,0,2)yieldsu=uw~n (2,-2,-1;2,2,1;0,0,4).Consideration of the primitive monoclinic cell up of Pd,sPba .r results in up = uw,n (2,0,-l; 0,2,1; 0,0,4). This shows (see p. 174 of ref. 6) that the structure of Pd1,Pb9 is related to NilsGas, Pd1sT19, NisP, and NihGaGea. Since NE = 0.083, the relation to N&Gag and Ni,GaGez is especially close. The well-confirmed structure of PtrJns [7] (Fig. 2) is isotypic to N&Gas, but there are also two statistically distributed vacancies as well as the four ordered vacancies. Here the morphotropic commensurability is (I~,,~~, = (IW.n (2,-2,-l; 2,2,1; 0,0,2). The ordered vacancies are contained in the mixed atom rows parallel to (us)NiAs,since these have small distances in the (ui & ca)NiAsplane. The nei~bour~g indiUm atoms move onto the vacancies. The vacancies form chains parallel to (--ul + o2 + Ua)NiAswhich are straight in
P32
the projection on (ai & Ul)NiAs and have links which alternate in length between 5 (--q + as)NiAs and :(---a, + up)NiAs. In the unmixed atom rows parallel to (Us)niAs few indium atoms substitute platinum atoms. This substitution increases the number of valence electrons per cell. In the structure of Pd,sPbs.r (Fig. 3) strongly mixed and essentially unmixed atom rows parallel to (as)NiAs are found. Only the mixed rows bear vacancies, and the lead atoms with a neighbouring vacancy in the (ai & as)niAs plane move onto the vacancies. The vacancy chains consist, similar to those in NirsGas and P&Ins, of short and long links; however, the chains projected on (a1 & as)mAs are now not straight but broken. This property causes the element Kss of the morphotropic commensurability to be 4 compared with 2 in PtisIna. In order to understand the superstructures of the phase bundle Pd,Pb, . . .PdiaPba it is necessary to consider the binding in the mixture PdPbM; for the notation see refs. 8 and 9. From Pd(Cu, SR1.15)3.83 A = b,(l) = c,(2,-2,0; 2,2,0; 2.8) and PdsPb(CusAu, SR10.65)4.02 A = br(1) = crzci, electron distances may be calculated which make the binding Pdr,Pbs.h(NiAs, SR10.65)H4.47; 5.70 A = brn(l,l,O; -1,2,0; 2.7) = crnK’( 2) probable; this is nearly the same as that assumed earlier [ 91 and gives a place number A$+! of 12.5. The factorial commensurability brn = ~rn( 2) assumed here between valence electron correlation and core electron TABLE 1 Structure and X-ray data for PdIaPbg.r Experiment: Pd5a.5Pb41.5(Gran. 1 min 1000 OC,Wa; 9 d 590 “C, 17 d + 30 “C), crystal approximately spherical, radius 0.04 mm. Diffractometer measurement with MO Ko: radiation of 2047 reflections of the kind +h, +k, _+Iup to 28 = 55” ; w scan, scan breadth l”, number of independent reflections 1990; 810 reflections with I, Q 20(Z,) were set equal to zero only for calculating CIIFoi - lFolI/zIF,,l, (lo = net count, u = standard deviation), 5 reflections measured 36 times in $ scan. Structure: PdlaPbg(N26.18 type), C”u, C2/c, al = 15.6027(g) A, a2 = 9.0599(5) 4 a3 = 13.911(l) A, 0~~= 55.875(5)“. 4Pd(e).0.3751(11).25 6 X 8Pd(f) .1257(5).1125(7).5064(5) .3688(4).1316(7).0009(5) .1355(5).1171(7) .1405(5) .0992(5).8732(8).3701(6) .2493(5).1239(9).2517(6) .1424(5) .6345(8).1243(6) 4Pb(e).0.8735(5).25 4 x SPb(f).4689(2).6645(3).1139(2) .4647(2).0805(3).1251(2) .2340(2).3768(3).1174(2) .2614(2).8717(3) .1181(2). Calculation: X-ray 72, spherical absorption, /JR = 4.1, lOOU-temperature coefficients full, u22, u33a u12> u13, u23): (1.5(4), l-7(4), 1.4(4), 0, -0.5(3), O), (1.5(3), 1.9(3), 1.5(3),-0.1(2),-0.7(2), 0.4(2)), (1.3(2), 1.7(3), 1.3(2), 0.1(2),-0.6(2),-0.3(2)), (1.5(3), 1.4(3), 2.0(3),-0.0(2),-1.1(2), -0.1(2)),(2.0(3), 1.8(3), 3.5(4), 0.1(3),-1.7(3), 0.1(3)), (1.2(2), 2.5(3), 1.9(3), -0.3(2),-0.9(2), -0.0(2)), (1.8(3), 1.6(3), 2.6(3),-0.0(2), -1.3(3), 0.1(3)), (0.9(2), 0.9(2), 0.8(2), 0, -0.2(l), 0) (0.8(l), 1.2(l), 1.1(l),-0.2(l),-0.5(l), 0.2(l)), (1.1(l), 1.2(l), 1.4(l), 0.2(1),-0.8(l), -0.2(l)), (1.4(l), 1.0(l), 1.6(l),-0.0(l),-0.8(l),-0.0(l)), (0.9(l), 0.9(l), 1.2(l), 0.0(l), -0.4(l), -0.1(l)). ZllF,I - IF,lI/~IF,I = 0.093. Table : L, F&O, FJlO.
P33 TABLE 1 (a)
9
n.
0
P34 TABLE 1 (b)
.
n.
*
P35 TABLE
2
Evaluation
of a powder
Experiment
:
Structure: Calculation:
Column
headings:
of Pdi3Phg.r
Pd5a.4Pb41,e (regulus 3 d 590 “C, water quenched; powder 15 d 430 “C!, 6 d -+ 30 “C, air quenched), Guinier photograph Cu Ko,, calibrated with silicon. Pd1aPba.r (N26.18) type, al = 15.6027(g) 8, a2 = 9.0599(5) A, a3 = 13.911(l) 19, (112= 55.875(5)“. I, = lo@ ZZPLG IF,12 = intensity calculated, H = multiplicity, P = polarization factor, L = Lorentz factor, G = geometric factor, F, = calculated amplitude, I, = intensity observed. Designation of intensity intervals: nbb, not observable; nbt, not observed; sss, 8(7); ss, 26(10); s, 51(14); m, 96(30); st, 291(164); sst, 678(222). (Ml), 103d, (A), 103d, (A), I,, I,.
--+a3 cosct2
k-
photograph
07
t a2
Fig. 2. PtlaIna, C&, C2/m, al = 15.338 A, az = 8.802 A, aa = 9.439 A, oz = 36.11”, 4Pt(g).0.253.0 4Pt(f).25.25.5 4Pt(i).451.0.272 8 X 0.748Pt(j).802.257.735 4Pt(i).258.0 .988 2Pt(c).0.0.5 4In(i).713.0.752 4In(i).177.0.772 8In(j).961.212.766 2In(d).0.5.5.
P36
t
b a3 cosq
---a7 t a2
Fig.3.Pd13Pb9,C6,,CP/c,o= (15.603,0, 7.804;9.060;11.515)~,4Pd(e).0.375.25 6 X 8Pd(f).126.113.506 .369.132.001.136.117.141 .099.873.370 .249.124.252.142.635 .1244Pb(e).0.874.25 4 X 8Pb(f).469.665.114 .465.081.125 .234.377.117 .261.872.118.
correlation is energetically favourable and leads to the name FF2 binding. Clearly the FF2 binding is closely related to the BB2 binding [ 8, 91 which is responsible for the p-brass and y-brass phases. The phase Pd,Pb,.r must have essentially the same binding as PdsPb3.h since it differs only by an ordering transformation. In Pd13Pba the number N&s of valence electrons in the NiAslike subcell as = (H4.52; 5.76) A is 9 instead of 8 as in PdsPb3. This may be rationalized by the assumption that the binding in PdBPb3 is energetically so favourable that the system strives to conserve it by accepting a new commensurability in the basal plane of the substructure as = cFH (3,1,0; -1,4,0; 0,0,5.7/3) = bFnK”/2, which gives just full occupation for the valence electron correlation. The occupation rule [ 81 thus gives an explanation for the substitution of additional lead atoms in as. It might be that this commensurability change is connected with a curious change of axial ratio in the dependence on composition found in Ni3Ge, [3]. A similar morphotropy occurred for PdGa(FeSi) [lo] . The commensurability difference of the binding to the structure causes a difference of the induced electron dipoles at the vacancies [ 51 and therefore a difference in the geometry of the vacancy chains. The average distance in the valence electron correlation fits well into the function d ‘(A&,), whereas the distance d ” in the core electron correlation shows some decrease, which evidently is forced by the d’ decrease; therefore d”(N&,) need not be perfectly smooth (Fig. 4). To give a complete description of the binding in the mixture PdPb, we consider the pseudo-orthorhombic phase PdPb.r(Z16.16) in the description PdPb.r(S16.16) 7.15;8.52;42.36A = bFu(-2,2.5,0;2,2.5,0;0,0,12c 13)= cHT (-4,5,0; 4,5,0; 0,0,20). Here both correlations give a quadratic net in the (a1 & up)rdpb plane, and these nets yield the mutual commensurability (2); however, in the (u3)rdPb direction the nets are stacked in a manner such that
P31
mole fraction
h$b/‘%
Fig. 4. A distance diagram for the mixture PdPbM where d ’ is the distance in the valence electron correlation and d” is the distance in the core electron correlation.
b is closer than an F stacking and c is more open than an F stacking. This is what is expected when we start from the FF2 binding and increase the value of N&A. For the phase which is most rich in lead it may be assumed that PdPb, (CUA1~,SR9.84)6.85;5.83~=b~(1.5,-1.5,0;1.5,i.5,0;0,0,1.8)=ca~’ (2). This is the frequently found FB2 binding which may be derived from an FF2 binding by choosing another commensurability in the tetragonal basal plane and adjusting the stacking distance of the parallel nets. Adding to these proposals the bindings Pd(Cu)3.89 a = b,(l) = ca(2,-2,O; 2,2,0; 0,0,2.8) and Pb(Cu)4.95 A = bs (2) results in the d(N&,) diagram given in Fig. 4. It can be seen that the distances fulfil the distance rule satisfactorily [ 71. From the present discussion it becomes clear that the phase bundle with NiAs-related structures and the FF2 binding replaces in PdPbM the fl and y phases in brasses with the BB2 binding.
Acknowledgments We wish to acknowledge the Deutsche Forschungsgemeinschaft for financial support, Professor H. G. von Schnering and Dr. K. Peters for the diffractometer measurements and Frau A. Kornau and Herr-n W. Furmanski for assistance.
References 1 H. Nowotny, K. Schubert and U. Dettinger, 2. Metallkd., 37 (1946) 137 - 145. 2 M. Ellner, T. Godecke and K. Schubert, Z. Metallkd., 64 (1973) 566 - 568. 3 M. Ellner, S. Heinrich, M. K. Bhargava and K. Schubert, J. Less-Common Met., 66 (1979) 163 - 173. 4 P. K. Panday and K. Schubert, J. Less-Common Met., 18 (1969) 175 - 202.
P38 5 I(. Schubert, Kristallstrukfuren Zweikomponentiger Phasen, Springer, Berlin, 1964, p. 336. 6 K. Schubert, Struct. Bonding ~BerZin~,33 (1977) 139 - 177. 7 S. Heinrich and K. Schubert, 2. Metallkd., 69 (1978) 230 - 236. 8 K. Schubert, J. Less-Common Met., 70 (1980) 167 - 180. 9 K. Schubert, 2. Kristallogr., 148 (1978) 221 - 236. 10 M. K. Bhargava, A. A. Gadalla and K. Schubert, J. Less-Common Met., 42 (1975) 69 - 76.