- Email: [email protected]
Superconductivity in the pseudoternary system YRh4B4LuRh4B4ThRh4B4
201
Journal of the Less-Common Metals, 82 (1981) 201 - 209
SUPERCONDUCTIVITY YRh,B,-LuRh,B,-ThRh,B,*
IN THE PSEUDOTERNARY
SYSTEM
KURT HIEBL lnstitut
fiir Physikalische
Chemie, Universitiit Wien, A-1090, Wiihringerstrasse
42 (Austria)
PETER ROGL? and M. J. SIENKO Department of Chemistry, Baker Laboratory,
Cornell University, Ithaca, NY 14853 (U.S.A.)
Summary Superconducting behavior was studied in the pseudoternary system YRh,B,-LuRh,B,-ThRh,B,, and isocritical temperatures and isochores were established. A minimum critical temperature was found for the pseudobinary system Y,Lu, _,Rh,B, at 10.1 K and x = 0.5. The various mixtures of the nonmagnetic elements yttrium, lutetium and thorium represent pseudoternary analogs of the lanthanide compounds RERh,B, (RE = rare earth). Thus the influence on the superconducting transition temperature of the missing magnetic ordering was studied with respect to a changing unit cell volume at constant electron density as well as a changing electron density at constant unit cell volume. A comparison was made with the results obtained from the Abrikosov-Gorkov theory.
1. Introduction The compound ErRh,B, is known from the literature to become superconducting at a critical temperature of 8.7 K ; it then returns to the normal state at a second critical temperature of 0.9 K. The return to the normal state coincides with long-range ordering of the magnetic moments of the Er3+ ions [l, 21. In this investigation, pseudoternary analogs of the lanthanide members of the LuRh,B, series of compounds were synthesized in which the magnetic-moment-bearing lanthanide atom was replaced by various combinations of the non-magnetic elements yttrium, lutetium and thorium. The
* Paper presented at the 7th International Symposium on Boron, Borides and Related Compounds, Uppsala, Sweden, June 9 - 12, 1981. tpermanent address: Institut fGr Physikalische Chemie. Universitat Wien. A-1090. Wahringerstrasse 42, Austria. 00225088/81/0000-0000/$02.50
c~ Elsevier Sequoia/Printed
in The Netherlands
202
superconducting behavior in the pseudoternary system YRh,B,-LuRh,B,ThRh,B, was observed so as to trace out the influence on the superconducting critical temperature of the missing magnetic ordering especially with respect to the dependence of the critical temperature on (1) a changing unit cell volume at constant electron density and (2) a changing electron density at constant unit cell volume.
2. Experimental
details
Alloys (about 0.5 g) were made from commercially available high purity elements: yttrium, thorium and lutetium (m3N; metal ingots; Ventron G.m.b.H., Karlsruhe); rhodium (99.9%; powder; Degussa, Hanau); boron (99.999% ; crystalline; Eagle-Picher Industries Inc.). Filings of the rare earth metals and boron powder were compacted in steel dies without the use of binders or lubricants. The pellets were then arc melted on a water-cooled copper hearth, using a non-consumable tungsten electrode in a Ti-Zrgettered high purity argon atmosphere. The buttons obtained were heat treated in vacuum on a molybdenum substrate (10m4 Pa ; 12 h ; about 1250 “C! ; radiation quench). For comparison a second set of specimens was prepared starting from YRh,B,, LuRh,B, and ThRh,B, powders (the (Y, Lu, Th)B, powders had been prepared from 99.99% pure Cerac (Y, Lu),O, and ThO, as well as boron powder heated in a tungsten mesh vacuum furnace for 2 h at 1600 “C). Samples were obtained by sintering cold-compacted powder mixtures of various compositions (Y, Lu, Th)Rh,B, in a high vacuum furnace (about 1250 “C; 48 h; radiation quench). X-ray powder diagrams were obtained for all samples and, in combination with a metallographic analysis of the arc-melted specimens, proved the described preparation techniques to be sufficient to obtain homogeneous products that were almost single phase. In some cases, however, small amounts of impurity boride phases (mainly RhB) were present. Precise lattice parameters and standard deviations were evaluated by a least-squares refinement procedure [3] on Guinier powder photographs using 99.9999% Ge as an internal standard with monochromated Cu Ku, radiation. No significant difference was found in the powder patterns of as-cast and sintered samples except for a higher level of secondary phases contained in the sintered specimens. An a.c. induction method [4] was used for the determination of superconducting critical temperatures as low as 1.5 K. The superconductivity was measured for samples in both the as-cast and the sintered condition and almost identical results were obtained except for the different level of impurity involved. This is particularly true for the lutetium-rich region where, in specimens annealed at lower temperatures, a solid state transformation is indicated.
203
3. Results and discussion 3.1. Structural chemistry Metallography and X-ray analysis of about 30 pseudobinary and pseudoternary samples in both the as-cast and the sintered condition revealed congruent melting behavior as well as complete solid solubility throughout the entire pseudoternary system for T > 1250 “C. All powder patterns could be indexed completely on the basis of a primitive tetragonal unit cell, and the intensities observed and the extinctions (space group, P4,/nmc) in all cases proved that the samples had a structure analogous with the CeCo,B,-type structure [5]. Using the atomic parameters Rh = 0.248; zah = 0.137) derived previously for RERh,B, compounds [6], the (X observed and calculated powder intensities are in excellent agreement for a statistical distribution of yttrium, lutetium and thorium atoms on the rare earth site. The lattice parameters and the volumes are represented in Fig. 1 for the pseudobinary sections YRh,B,-LuRh,B,, LuRh,B,-ThRh,B, and ThRh,B,-Y,,,LuO,,Rh,B,. Perfect agreement was found with the lattice
MATTHIAS.
1977
760 750 C 0
lL0
5540 Z” 3 530 $ ii
0
02
04x06
ThRh‘B‘
08
IO
VRh,B,
0
02
04106
YRh‘B‘
08
IO LuRh,&
z 2’ 215 V 210 750
0 02 ThRh,B‘
04x06
06
10 LuRh,&
0 02 ThRh‘B‘
06x06
06 10 (Vo,Lu,&RhcB4
Fig. I. Variations in the lattice parameters and volume for the pseudobinary YRh,B,-LuRh,B,, LuRh,B,-ThRh,B, and the section ThRh,B,-Y,,,Lu,.,Rh,B,. parison the section YRh,B,-ThRh,B, [7] is included.
sections For corn,
204
YRh,B,.
208.9
ThRh4B4 216.3
LURhaB, 206.2 -
MOLE
PERCENT
--
Fig. 2. Isochores of the ternary system: -, isochore line (constant volume) in the YRh,B,-LuRh,B,-ThRh,B, system; ---, concentrations isoelectronic with lanthanide indicated; 0, intersections of isochores and isoelectronic curves.
atoms as
parameter values derived previously by Vandenberg and Matthias [6] for YRh,B,, LuRh,B, and ThRh,B, and by Vining and Shelton [7] for the section YRh,B,-ThRh,B,. Figure 2 shows isochore lines as mapped throughout the entire pseudoternary system. If we consider the volumes of the lanthanide members of the RERh,B, borides, isochores with their volume values can be traced out within the pseudoternary (Y, Th, Lu)Rh,B, combinations (Fig. 2). Because of the slightly larger unit cell volume of LuRh,B, with respect to the thulium and ytterbium compounds, the isochores of these compounds range outside the pseudoternary considered. The structural chemistry [5, 61 of CeCo,B,-type rhodium compounds reflects a strong metal-metal bonding within the tetrahedral rhodium clusters (Rh-Rh distances, 2.64 - 2.75 8) but a weak intercluster bonding (Rh-Rh intercluster distances, about 3.14 A); thus with rather long RE-RE distances this provides the physical basis for the unusual combinations of magnetic and electrical properties of some of the RERh,B, compounds [8]. 3.2. Superconductivity and magnetism Superconducting behavior (the critical temperatures in kelvins) for the pseudobinary boundary systems is shown in Fig. 3. For the ternary constituents YRh,B,, LuRh,B, and ThRh,B, the critical temperatures observed are in fair agreement (50.5 K) with the earlier findings of Matthias et al. [2].
205
V RhlBI
LuRh,E$
0 0.2 ThRh4BL
04x06
08 10 LuRh,t&
0 02 ThRhlBI
04x06
08
IO
Luoj/osR”Si
MOLE PERCENT Fig. 3. Superconductivity (the critical temperatures in kelvins) in the pseudobinary systems YRh,B,-LuRh,B, and LuRh,B,-ThRh,B, as well as in the section ThRh,B,-Y, sLu, SRh,B,. For comparison the superconducting behavior in YRh,B,-ThRh,B, [7] is shown.
For the section LuRh,B,-ThRh,B, a similar fall-off in critical temperatures to that described for the system YRh,B,-ThRh,B, by Vining and Shelton [7] was found. The critical temperatures for YRh,B, and LuRh,B, are almost identical, but a shallow minimum (AT, z 0.5 K) was found for mixed compositions Y,Lu, _,Rh,B, at x z 0.5 (Fig. 3). The behavior of the binary boundary sections is generally reflected by the critical temperatures in the pseudoternary system as seen from Fig. 4. Isotherms with respect to critical superconducting temperatures are mapped in Fig. 4, revealing a “saddle mountain” surface which is even more obvious from the three-dimensional graph of critical temperature uersus concentration shown in Fig. 5. With respect to atomic volume as well as the electronic state of the constituent atoms yttrium, lutetium and thorium the pseudoternary mixtures Y,Lu,Th, _-x_,Rh,B, at certain values X, y constitute hypothetical rare earth members from neodymium to holmium. Thus “isoelectronic lines” (representing a lanthanide RERh,B, member synthesized by a suitable mixture of the non-magnetic yttrium, lutetium and thorium constituents) can be established as indicated by the broken lines in Fig. 2. Similarly, isochore lines were
206
207
drawn (Fig. 2, full lines) corresponding to each lanthanide member except for thulium (see Section 3.1) and lanthanum, praseodymium, europium and ytterbium (for which no compound formation was reported by Matthias and coworkers [2, 61). The lattice parameters and volume can be derived, nevertheless, for a hypothetical compound “EuRh4B4” (corresponding to Eu3+) from the almost linear dependence of the lattice parameters [2, 61 on the radius R,,,+ . (The values derived for Eu3+ are a x 5.13 A, c z 7.42 A and V z 209A3.)Most interest, however, is concerned with the intersection points (Fig. 2, full circles) of the isoelectronic lines and the isochore lines. These correspond to a synthetic lanthanide member with the same electronic number and volume as the true compound. As none of the constituent atoms yttrium, lutetium and thorium bears a magnetic moment, the pair-breaking influence of the RE-ion-localized magnetic moment on the superconducting transition temperature should mainly account for the difference AT, (K)
I
P
0 n
$ I
LO
ce
PI
Nd
q
Pln
sm
E”
Gd
Tb
0”
no
Er
Tin
Ib
L”
Th
FiEFtheE,-COMPOUNDS
Fig. 6. A comparison of critical data for RERh,B, compounds: H, superconducting Z’, values of non-magnetic equivalents Y,LuyTh, _,_,Rh,B,; q, interpolated values using Figs. 2 and 6; q, magnetic ordering temperatures Z’,,, observed for RERh,B, [2, 6, 91; 0, superconducting 5”, values observed for RERh,B, [2, 61; V, depression of Z’, values (-AT,) calculated [9] using the Abrikosov-Gorkov theory for substitution of lutetium by RE; W’, -AT, values observed for the difference between hypothetical non-magnetic and true compounds.
208
found from Fig. 6 for the data for synthetic lanthanide compounds compared with the superconductivity data of the true compounds given by Matthias and coworkers [2, 61. Rather fair agreement is found for the experimentally observed differences AT, (Fig. 6) and the values calculated for the heavier rare earths [9, lo] from the Abrikosov-Gorkov theory for isotropic elastic exchange scattering of conduction electrons by randomly distributed and non-interacting localized magnetic moments. Calculation of the (isotropic) (conduction electron)-(rare earth ion) exchange coupling parameter from the observed depression of T, (i.e. the difference between the true (magnetic rare earth ion) and the hypothetical (non-magnetic) RERh,B,) revealed, for example, for ErRh,B, a l&11va 1ue of about 1.75 x 10e2 eV per atom spin direction, even less than the values derived earlier for substitution of lutetium by RE [9]. Recent measurements [9] of the initial rate of depression of superconductivity in LuRh,B, on substitution of lutetium by RE proved the validity of the Abrikosov-Gorkov theory, even for complete substitution of lutetium in LuRh,B, [9]. In contrast, a strong influence of crystal field effects on the ground state seems [9] to account for the deviation in the measured magnetic ordering temperature T, (shift from gadolinium to dysprosium) from the values predicted by a Ruderman-Kittel-KasuyaYosida type of interaction. On the assumption that europium behaves magnetically as a tripositive ion in the hypothetical “EuRh4B4”, a rather high T, is derived from Figs. 2 and 6 corresponding to a rather low magnetic ordering temperature. The sharp fall-off in the hypothetical T, of the “NdRh,B,” compound is probably due to the high thorium concentration in the hypothetical compound; thus, values for neodymium were extrapolated from Fig. 6. The slight changes in T, with respect to different volume values at a constant ratio of electrons to atoms (Fig. 2) and the small changes in the T, of the hypothetical (heavier) rare earth series of compounds (the almost linear decrease in TchYPoth should be compared with the increasing unit cell volume of lighter rare earth members (Fig. 6)) indicate that the volume has a rather small influence on the changes in the conduction electron density of states N(E,) and confirm the earlier assumption that the term ZV(E,)f2 is almost invariant with respect to individual rare earth elements.
Acknowledgments This research was sponsored by the U.S. Air Force Office of Scientific Research (under Grant 80-0009) and was supported in part by the National Science Foundation and the Materials Science Center, Cornell University. Thanks are also due to the Austrian Science Foundation (Fonds zur Forderung der Wissenschaftlichen Forschung in Osterreich) for Grant 3620. P.R. wishes to express his gratitude to DEGUSSA (Deutsche Gold und Silber Scheideanstalt) G.m.b.H., CoKG, Hanau, for kindly supplying the noble metal.
209
References
2 3
5 6 7
8
9
10
W. A. Fertig, D. C. Johnston, L. E. DeLong, R. W. McCallum, M. B. Maple and B. T. Matthias, Phys. Rev. Lett., 38 (1977) 987. B. T. Matthias, E. Corenzwitt, J. M. Vandenberg and H. E. Barz, Proc. Nutl. Acad. Sci. U.S.A., 74 (1977) 1334. M. Holocher-Ertl, Program GITTER (adapted version by H. Boller, University of Vienna, 1976). W. G. Fisher, Ph.D. Thesis, Cornell University, 1978. Yu. B. Kuz’ma and N. S. Bilonishko, Sow. Phys.-Crystallogr., 16 (1972) 897. J. M. Vandenberg and B. T. Matthias. Proc. Natl. Acad. Sci. U.S.A., 74 (1977) 1336. C. B. Vining and R. N. Shelton, Pressure dependence of the superconducting transition temperature of (Th, _,Y,)Rh,B,, in Proc. Int. Conf. on Ternary Superconductors, Lake Geneva, WI, September 24 - 26, 1980. M. B. Maple, Superconductivity and magnetism of rare earth rhodium boride compounds and related systems, in Proc. Int. Conf. on Ternary Superconductors, Lake Geneva, WI, September 24 - 26, 1980. H. B. MacKay, L. D. Woolf, M. B. Maple and D. C. Johnston, J. Low Temp. Phys., 41 (1980) 639. A. Abrikosov and L. P. Gorkov, Sov. Phys.-JETP, 12 (1961) 1243.
Journal of the Less-Common Metals, 82 (1981) 201 - 209
SUPERCONDUCTIVITY YRh,B,-LuRh,B,-ThRh,B,*
IN THE PSEUDOTERNARY
SYSTEM
KURT HIEBL lnstitut
fiir Physikalische
Chemie, Universitiit Wien, A-1090, Wiihringerstrasse
42 (Austria)
PETER ROGL? and M. J. SIENKO Department of Chemistry, Baker Laboratory,
Cornell University, Ithaca, NY 14853 (U.S.A.)
Summary Superconducting behavior was studied in the pseudoternary system YRh,B,-LuRh,B,-ThRh,B,, and isocritical temperatures and isochores were established. A minimum critical temperature was found for the pseudobinary system Y,Lu, _,Rh,B, at 10.1 K and x = 0.5. The various mixtures of the nonmagnetic elements yttrium, lutetium and thorium represent pseudoternary analogs of the lanthanide compounds RERh,B, (RE = rare earth). Thus the influence on the superconducting transition temperature of the missing magnetic ordering was studied with respect to a changing unit cell volume at constant electron density as well as a changing electron density at constant unit cell volume. A comparison was made with the results obtained from the Abrikosov-Gorkov theory.
1. Introduction The compound ErRh,B, is known from the literature to become superconducting at a critical temperature of 8.7 K ; it then returns to the normal state at a second critical temperature of 0.9 K. The return to the normal state coincides with long-range ordering of the magnetic moments of the Er3+ ions [l, 21. In this investigation, pseudoternary analogs of the lanthanide members of the LuRh,B, series of compounds were synthesized in which the magnetic-moment-bearing lanthanide atom was replaced by various combinations of the non-magnetic elements yttrium, lutetium and thorium. The
* Paper presented at the 7th International Symposium on Boron, Borides and Related Compounds, Uppsala, Sweden, June 9 - 12, 1981. tpermanent address: Institut fGr Physikalische Chemie. Universitat Wien. A-1090. Wahringerstrasse 42, Austria. 00225088/81/0000-0000/$02.50
c~ Elsevier Sequoia/Printed
in The Netherlands
202
superconducting behavior in the pseudoternary system YRh,B,-LuRh,B,ThRh,B, was observed so as to trace out the influence on the superconducting critical temperature of the missing magnetic ordering especially with respect to the dependence of the critical temperature on (1) a changing unit cell volume at constant electron density and (2) a changing electron density at constant unit cell volume.
2. Experimental
details
Alloys (about 0.5 g) were made from commercially available high purity elements: yttrium, thorium and lutetium (m3N; metal ingots; Ventron G.m.b.H., Karlsruhe); rhodium (99.9%; powder; Degussa, Hanau); boron (99.999% ; crystalline; Eagle-Picher Industries Inc.). Filings of the rare earth metals and boron powder were compacted in steel dies without the use of binders or lubricants. The pellets were then arc melted on a water-cooled copper hearth, using a non-consumable tungsten electrode in a Ti-Zrgettered high purity argon atmosphere. The buttons obtained were heat treated in vacuum on a molybdenum substrate (10m4 Pa ; 12 h ; about 1250 “C! ; radiation quench). For comparison a second set of specimens was prepared starting from YRh,B,, LuRh,B, and ThRh,B, powders (the (Y, Lu, Th)B, powders had been prepared from 99.99% pure Cerac (Y, Lu),O, and ThO, as well as boron powder heated in a tungsten mesh vacuum furnace for 2 h at 1600 “C). Samples were obtained by sintering cold-compacted powder mixtures of various compositions (Y, Lu, Th)Rh,B, in a high vacuum furnace (about 1250 “C; 48 h; radiation quench). X-ray powder diagrams were obtained for all samples and, in combination with a metallographic analysis of the arc-melted specimens, proved the described preparation techniques to be sufficient to obtain homogeneous products that were almost single phase. In some cases, however, small amounts of impurity boride phases (mainly RhB) were present. Precise lattice parameters and standard deviations were evaluated by a least-squares refinement procedure [3] on Guinier powder photographs using 99.9999% Ge as an internal standard with monochromated Cu Ku, radiation. No significant difference was found in the powder patterns of as-cast and sintered samples except for a higher level of secondary phases contained in the sintered specimens. An a.c. induction method [4] was used for the determination of superconducting critical temperatures as low as 1.5 K. The superconductivity was measured for samples in both the as-cast and the sintered condition and almost identical results were obtained except for the different level of impurity involved. This is particularly true for the lutetium-rich region where, in specimens annealed at lower temperatures, a solid state transformation is indicated.
203
3. Results and discussion 3.1. Structural chemistry Metallography and X-ray analysis of about 30 pseudobinary and pseudoternary samples in both the as-cast and the sintered condition revealed congruent melting behavior as well as complete solid solubility throughout the entire pseudoternary system for T > 1250 “C. All powder patterns could be indexed completely on the basis of a primitive tetragonal unit cell, and the intensities observed and the extinctions (space group, P4,/nmc) in all cases proved that the samples had a structure analogous with the CeCo,B,-type structure [5]. Using the atomic parameters Rh = 0.248; zah = 0.137) derived previously for RERh,B, compounds [6], the (X observed and calculated powder intensities are in excellent agreement for a statistical distribution of yttrium, lutetium and thorium atoms on the rare earth site. The lattice parameters and the volumes are represented in Fig. 1 for the pseudobinary sections YRh,B,-LuRh,B,, LuRh,B,-ThRh,B, and ThRh,B,-Y,,,LuO,,Rh,B,. Perfect agreement was found with the lattice
MATTHIAS.
1977
760 750 C 0
lL0
5540 Z” 3 530 $ ii
0
02
04x06
ThRh‘B‘
08
IO
VRh,B,
0
02
04106
YRh‘B‘
08
IO LuRh,&
z 2’ 215 V 210 750
0 02 ThRh,B‘
04x06
06
10 LuRh,&
0 02 ThRh‘B‘
06x06
06 10 (Vo,Lu,&RhcB4
Fig. I. Variations in the lattice parameters and volume for the pseudobinary YRh,B,-LuRh,B,, LuRh,B,-ThRh,B, and the section ThRh,B,-Y,,,Lu,.,Rh,B,. parison the section YRh,B,-ThRh,B, [7] is included.
sections For corn,
204
YRh,B,.
208.9
ThRh4B4 216.3
LURhaB, 206.2 -
MOLE
PERCENT
--
Fig. 2. Isochores of the ternary system: -, isochore line (constant volume) in the YRh,B,-LuRh,B,-ThRh,B, system; ---, concentrations isoelectronic with lanthanide indicated; 0, intersections of isochores and isoelectronic curves.
atoms as
parameter values derived previously by Vandenberg and Matthias [6] for YRh,B,, LuRh,B, and ThRh,B, and by Vining and Shelton [7] for the section YRh,B,-ThRh,B,. Figure 2 shows isochore lines as mapped throughout the entire pseudoternary system. If we consider the volumes of the lanthanide members of the RERh,B, borides, isochores with their volume values can be traced out within the pseudoternary (Y, Th, Lu)Rh,B, combinations (Fig. 2). Because of the slightly larger unit cell volume of LuRh,B, with respect to the thulium and ytterbium compounds, the isochores of these compounds range outside the pseudoternary considered. The structural chemistry [5, 61 of CeCo,B,-type rhodium compounds reflects a strong metal-metal bonding within the tetrahedral rhodium clusters (Rh-Rh distances, 2.64 - 2.75 8) but a weak intercluster bonding (Rh-Rh intercluster distances, about 3.14 A); thus with rather long RE-RE distances this provides the physical basis for the unusual combinations of magnetic and electrical properties of some of the RERh,B, compounds [8]. 3.2. Superconductivity and magnetism Superconducting behavior (the critical temperatures in kelvins) for the pseudobinary boundary systems is shown in Fig. 3. For the ternary constituents YRh,B,, LuRh,B, and ThRh,B, the critical temperatures observed are in fair agreement (50.5 K) with the earlier findings of Matthias et al. [2].
205
V RhlBI
LuRh,E$
0 0.2 ThRh4BL
04x06
08 10 LuRh,t&
0 02 ThRhlBI
04x06
08
IO
Luoj/osR”Si
MOLE PERCENT Fig. 3. Superconductivity (the critical temperatures in kelvins) in the pseudobinary systems YRh,B,-LuRh,B, and LuRh,B,-ThRh,B, as well as in the section ThRh,B,-Y, sLu, SRh,B,. For comparison the superconducting behavior in YRh,B,-ThRh,B, [7] is shown.
For the section LuRh,B,-ThRh,B, a similar fall-off in critical temperatures to that described for the system YRh,B,-ThRh,B, by Vining and Shelton [7] was found. The critical temperatures for YRh,B, and LuRh,B, are almost identical, but a shallow minimum (AT, z 0.5 K) was found for mixed compositions Y,Lu, _,Rh,B, at x z 0.5 (Fig. 3). The behavior of the binary boundary sections is generally reflected by the critical temperatures in the pseudoternary system as seen from Fig. 4. Isotherms with respect to critical superconducting temperatures are mapped in Fig. 4, revealing a “saddle mountain” surface which is even more obvious from the three-dimensional graph of critical temperature uersus concentration shown in Fig. 5. With respect to atomic volume as well as the electronic state of the constituent atoms yttrium, lutetium and thorium the pseudoternary mixtures Y,Lu,Th, _-x_,Rh,B, at certain values X, y constitute hypothetical rare earth members from neodymium to holmium. Thus “isoelectronic lines” (representing a lanthanide RERh,B, member synthesized by a suitable mixture of the non-magnetic yttrium, lutetium and thorium constituents) can be established as indicated by the broken lines in Fig. 2. Similarly, isochore lines were
206
207
drawn (Fig. 2, full lines) corresponding to each lanthanide member except for thulium (see Section 3.1) and lanthanum, praseodymium, europium and ytterbium (for which no compound formation was reported by Matthias and coworkers [2, 61). The lattice parameters and volume can be derived, nevertheless, for a hypothetical compound “EuRh4B4” (corresponding to Eu3+) from the almost linear dependence of the lattice parameters [2, 61 on the radius R,,,+ . (The values derived for Eu3+ are a x 5.13 A, c z 7.42 A and V z 209A3.)Most interest, however, is concerned with the intersection points (Fig. 2, full circles) of the isoelectronic lines and the isochore lines. These correspond to a synthetic lanthanide member with the same electronic number and volume as the true compound. As none of the constituent atoms yttrium, lutetium and thorium bears a magnetic moment, the pair-breaking influence of the RE-ion-localized magnetic moment on the superconducting transition temperature should mainly account for the difference AT, (K)
I
P
0 n
$ I
LO
ce
PI
Nd
q
Pln
sm
E”
Gd
Tb
0”
no
Er
Tin
Ib
L”
Th
FiEFtheE,-COMPOUNDS
Fig. 6. A comparison of critical data for RERh,B, compounds: H, superconducting Z’, values of non-magnetic equivalents Y,LuyTh, _,_,Rh,B,; q, interpolated values using Figs. 2 and 6; q, magnetic ordering temperatures Z’,,, observed for RERh,B, [2, 6, 91; 0, superconducting 5”, values observed for RERh,B, [2, 61; V, depression of Z’, values (-AT,) calculated [9] using the Abrikosov-Gorkov theory for substitution of lutetium by RE; W’, -AT, values observed for the difference between hypothetical non-magnetic and true compounds.
208
found from Fig. 6 for the data for synthetic lanthanide compounds compared with the superconductivity data of the true compounds given by Matthias and coworkers [2, 61. Rather fair agreement is found for the experimentally observed differences AT, (Fig. 6) and the values calculated for the heavier rare earths [9, lo] from the Abrikosov-Gorkov theory for isotropic elastic exchange scattering of conduction electrons by randomly distributed and non-interacting localized magnetic moments. Calculation of the (isotropic) (conduction electron)-(rare earth ion) exchange coupling parameter from the observed depression of T, (i.e. the difference between the true (magnetic rare earth ion) and the hypothetical (non-magnetic) RERh,B,) revealed, for example, for ErRh,B, a l&11va 1ue of about 1.75 x 10e2 eV per atom spin direction, even less than the values derived earlier for substitution of lutetium by RE [9]. Recent measurements [9] of the initial rate of depression of superconductivity in LuRh,B, on substitution of lutetium by RE proved the validity of the Abrikosov-Gorkov theory, even for complete substitution of lutetium in LuRh,B, [9]. In contrast, a strong influence of crystal field effects on the ground state seems [9] to account for the deviation in the measured magnetic ordering temperature T, (shift from gadolinium to dysprosium) from the values predicted by a Ruderman-Kittel-KasuyaYosida type of interaction. On the assumption that europium behaves magnetically as a tripositive ion in the hypothetical “EuRh4B4”, a rather high T, is derived from Figs. 2 and 6 corresponding to a rather low magnetic ordering temperature. The sharp fall-off in the hypothetical T, of the “NdRh,B,” compound is probably due to the high thorium concentration in the hypothetical compound; thus, values for neodymium were extrapolated from Fig. 6. The slight changes in T, with respect to different volume values at a constant ratio of electrons to atoms (Fig. 2) and the small changes in the T, of the hypothetical (heavier) rare earth series of compounds (the almost linear decrease in TchYPoth should be compared with the increasing unit cell volume of lighter rare earth members (Fig. 6)) indicate that the volume has a rather small influence on the changes in the conduction electron density of states N(E,) and confirm the earlier assumption that the term ZV(E,)f2 is almost invariant with respect to individual rare earth elements.
Acknowledgments This research was sponsored by the U.S. Air Force Office of Scientific Research (under Grant 80-0009) and was supported in part by the National Science Foundation and the Materials Science Center, Cornell University. Thanks are also due to the Austrian Science Foundation (Fonds zur Forderung der Wissenschaftlichen Forschung in Osterreich) for Grant 3620. P.R. wishes to express his gratitude to DEGUSSA (Deutsche Gold und Silber Scheideanstalt) G.m.b.H., CoKG, Hanau, for kindly supplying the noble metal.
209
References
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