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Low temperature heat capacity of some rare earth aluminum Laves phase compounds: YAl2, LaAl2 and LuAl2
LOW TEMPERATURE EARTH ALUMINUM YAl,, R. institute
for
HEAT CAPACITY OF SOME RARE LAVES PHASE COMPOUNDS: LaAl, AND LuAl,*
E. HUNGSBERCt
Atomic
Research
and
K.
A.
and Department Ames. lowa50010.
Abstract-The heat capacity of three rare earth Laves were measured in the temperature range of 2.5”-20°K. in LaAI, at 3.29”K. The C/T vs. 7’ data yielded
GSCHNEIDNER. of Metallurgy. U.S.A.
Jr. Iowa
State
phase compounds A superconducting
y = I.81 ml/g at.-OK’ and 0 = 473°K for YAI,. y = 3.65 ml/g at.-OK’ and H = 352°K for LaAI?. y = 1.9 ml/g at-OK’ and 0 = 384°K for LuAI,. The Debye temperatures indicate that the low temperature B element (aluminum). The Debye temperature of LaAI, is YAI, and LuAI,. and the electronic specific constant. y. of YAI, and LuAI,. The high y value is thought to account for sence of superconductivity in the other two Laves phases. It superconductor.
University.
YAI,. LaAI, and LuAI, transition was observed
and
lattice dynamics are controlled by the anomalously low compared to those of LaAI, is anomalously high compared to superconductivity in LaAI, and the abis found that LaAI, behaves as a B.C.S.
Several years ago Joseph and Gschneidner [6] noted a correlation between the measured Debye temperature of a number of Laves phase compounds and the radius ratio of the component atoms of the compound. They found that when the radius ratio indicated A-A metal contacts the Debye temperature of the Laves phase compound was found to be closer to the Debye temperature of pure A than pure B. The converse was also found when the radius ratio indicated B-B contacts. Upon examination of radius ratios of the RAI, Laves phase compounds, one would expect A-A contacts for the larger rare earth atoms (La, etc.) and B-B contacts for the smaller rare earth atoms (Lu, SC, etc.). This is interesting because if the JosephGschneidner correlation holds, the Debye temperature for the RAI, compounds should change from values in the 150-200°K range
1. INTRODUCTION
A LAVES phase compound generally has the AB, stoichiometry and the A atom is always larger than the B atom. From the geometrical arrangement of atoms it can be shown that if these atoms behave as hard spheres the ideal packing of atoms occurs when the radius ratio is I .225. At the ideal ratio there are both A-A and B-B contacts; when the radius ratio is I .225. At the ideal ratio there are contacts. and when the ratio is greater than the ideal value there are only A-A contacts. However. there are no A-B contacts at any value of the radius ratio. assuming hard spheres. Although it is known that atoms do not behave as hard spheres, this model of Laves phase compounds has proven to be a useful concept in the understanding of these materials [ l-51. “Work was performed in the Ames Laboratory of the U.S. Atomic Energy Commission. Contribution No. 2887. ipresent Address: GTE Automatic Electric Laboratories, Inc., Tube Station B-3. Dept. 490. P.O. Box 17. Northlake. Illinois 60164. U.S.A.
for
the
light
]anthanides
to
va]ues
in the
JO&
450°K range for the heavy lanthanides, scandium and yttrium. This suggests a significant 401
401
R.
E. HUNGSBERG
and
change in the nature of the bonding for this series of closely-related compounds. However, examination of the known physical properties, such as the lanthanide contraction and melting points. of these RAI, compounds shows that nothing unusual occurs that would indicate a change in bond nature in the RAI, compounds. Because of this dilemma it was felt that determination of the low temperature heat capacity of a number of RAI, Laves phase compounds could help to resolve the problem. Furthermore. the determination of the electronic specific heat constant. y. and the Debye temperature. 0. for Laves phases will aid in our understanding of the nature of this large family of intermetallic compounds. especially since such information is scarce. The Laves phase compounds YAI,. LaAI,, and LuAI, were chosen since the A metal (Y. La. Lu) has no 4felectrons or a completely filled 4f level, and thus there will be no magnetic contribution to the heat capacities of Furthermore. LaAI, these compounds. should be representative of the first lanthanide RAI, phases. YAI, of the mid lanthanide RAI, phases* and LuAI, of the last of the lanthanide RAI, compounds. 2. EXPERIMENTAL
Sample
preparation
The impurity contents of the materials used in this investigation are given in Table I. All three compounds were prepared by arc melting weighed amount of the components on a water cooled copper hearth under a zirconium gettered argon atmosphere. To obtain homogeneity. each sample was turned over and remelted one or more times. Shattering or cracking of the brittle samples would occur upon restriking of the arc if the samples were permitted to cool below a red heat, but restriking the arc while still red hot prevented *Since yttrium in many of its compounds and alloys behaves much like dysprosium or holmium. we believe that the y and H values for DyAI, and HoAI, will be similar to those measured for Y Al,.
K.
A. GSCHNEIDNER.
JR.
Table 1. Cllemical analysis of cow pottents (itnprrrity levels are given it1 pptn by \t,eight) Starting Y
Impurity
Al
H C N 0 F M.kt Al Si l-a SC Cr Mn Fe Ni cu Zn Y La Ce Pr Nd Gd Tb Dy Ho El Ta
___
10 M 10 ___ ___ ___ i IO IO ___ 10 i IO ___ ___ --___ ----___ ----___ ___
materials La
5 __. 12 175 ___ ___ ___ __. ___ ___ ___ _.. ___ ___ ___ M ___ ___ ___ _.. _.. ___ ___ ___ ___ ___
Lu
29 36 78 79 19 5 10 5 IO s ,o s 10 ___ s IO _.. 5 40 100 20 ___ ___
6 IO 9 107 <3 ----___ --I 0.3 ___ ‘.J I IO --_ 7.5
M s 3.50 c I50 s loo _.. _.. _-. _-_ _-. s 500
I6 ’ II 4 -l ; 7 9 3 loo
< less than. < less than or equal to ___ not analyzed for. M major component.
this. To prevent cracking. power to the arc was reduced as much as possible after the last melting to allow the sample to cool down as slowly as possible. Metallographic examination? and X-ray analysis showed that the YAI., and LaAl, samples were single phase and homogeneous. The LuAI, was found to have a small amount of a second phase. Point count analysis revealed the two-phase area to be 8- 16 per cent of the total area. Higher power magnification showed the second phase occupying 25 per cent of the two-phase area and thus, +Keller’s 95 ml H,O)
solution t I ml HF. lfml was used to etch the RAI,
HCI. 2tml compounds.
HNO,.
RARE
EARTH
ALUMINUM
about 2-4 per cent of the second phase was present. A conventional spark cutter was used to cut two parallel faces on the samples to allow mounting in the calorimeter. Because the compounds were very brittle. small portions broke off even with careful handling. Sample surfaces left unprotected for several weeks remained bright and shiny, indicating very little or no oxidation. The lattice parameters for the compounds are as follows and were found to agree well with other values reported in literature[7,8]: YAI., LaAI, LuAI,
7.864-e-0.001 A. 8.148 ?O.OOl A. 7.743 & 0.001 A.
Calorimetry Specific heat measurements were made in an adiabatic calorimeter. The accuracy of the calorimeter was checked by measuring the heat capacity of a Calorimetry Conference Copper Standard [9]. Measured values agreed with published copper data[9. IO] to within I per cent in the temperature range of 2.5-20°K. 3. RESULTS
Experimental values of the heat capacity and temperature for the three Laves phases are shown in Figs. l-4’k. Figure I is a plot of C/T vs. T’ for YAI., over the entire temperature range covered. The linear portion of the curve is shown expanded in Fig. 2. A least squares fitting of the points to the equation C/T = y+PT’ yielded y = I.81 kO.02 ml/g at.-OK’. p = 0.01835 +0.00045 mJ/g at-OK4 and 8 = 473 2 4°K. Only the lower. linear portion of the C/T *The experimental heat capacity vs. temperature data may be obtained by ordering NAPS Document No. 01525 from ASlS National Auxiliary Publications Service. c/o CCM Information Sciences. inc.. 22 West 34th Street. New York. New York 1000 I : remitting $2.00 for microfiche or $S.OO for photocopies: or from K. A. Gschneidner. Jr. Ames Laboratory. Iowa State University. Ames. Iowa50010. U.S.A. (free).
LAVES
PHASE
COMPOUNDS
403
vs. T’ data for LaAI, is shown in Fig. 3. Because the higher temperature portion (T > 9°K) is similar to that of YAI, there is no need to show a plot of the data. A similar fitting of the data in the linear region shown in Fig. 3 yielded y = 3.65 20.04 ml/g at.-“K’, /3 = 0.04441 & 0.00110 ml/g at.-“K”. and 0 = 352 & 3°K. The peak at 3~29”%0~03”K has a shape typical of a superconducting transition and is in good agreement with a reported[ 1 I] superconducting transition temperature of 3~2°K obtained from resistivity measurements. Other specific heat data [ 121 on LaA& in the temperature range of IO-280°K are lower than the present values by IO-15 per cent in the overlapping range of 14-20°K. The LuAI, data (Fig. 4) were handled in a similar manner. giving 1.92 2 0.02 ml/g at.-OK2 for y. O-03421 I+ 0.00050 mJ/g at.-“K4 for /3. and 384 -C2°K for 0. The y and 0 values may be in error due to the presence of a second phase in this sample. Assuming linear combination of the LuAI, and second phase quantities ty and 8) we estimate that the above measured y value lies within -+3 per cent of the true value for LuAl, on the assumption that the second phase y value lies between 0.2 and 4.0 rnJ/g at.-“K”. However. if the second phase y value were an unusually high value such as IO mJ/g at.-“K’ then the observed y might be in error by as much as I5 per cent. Similarly. we estimate that the measured 0 value lies within ?2 per cent of the true value for LuAI, on the assumption that the second phase 0 value lies between 150” and 575°K. It is very unlikely that the second phase 0 value lies outside this range, and thus the measured 0 value is probably reliably known, 384”& 7°K. Unlike 0. y is a very difficult quantity to estimate, and accordingly, we have less confidence in the y value for LuAI,, 1.9:::; ml/g at.-“K’. 4. DISCUSSION
Debye temperatures A close examination of Figs. 2-4 indicates that the low temperature T” approximation
404
R. E. HUNGSBERG
and
K. A.
GSCHNEIDNER.
JR.
0 0
40
80
Fig.
IM
1. Heat
160
capacity
200
240
of YAI,
280
from
l
2
320
360
400
2.4” to 21°K.
RUN
2”d
r’ I. 5 0
IO
20
30
40
50
60
70
60
T2 ii&
Fig.
2. Heat
capacity
of YAI,
from
2.5” to9”K.
IO 0
I 10
I
I
20
30
Fig. 3. Heat
capacity
40 50 T21K21
60
of LaAI,
from
70
80
2.8” to 9.5”K.
90
440
RARE
EARTH
Fig.
ALUMINUM
4. Heat
capacity
LAVES
of LuAI,
of Debye theory is no longer valid for temperatures greater than = 7.5”K. (T’ = 60”KZ), which is much lower than one might expect for these materials.* The T” approximation begins to differ from the rigorous treatment of the Debye theory at T/O = 10, and thus departures would be expected to occur at about 35°K for LaAI,, 38°K for LuAI, and 47°K for YAl*. A reasonable explanation for this behavior may be forthcoming from the JosephGschneidner model[6] of the Laves phase compounds. At temperatures below 7°K the vibrational contribution to the specific heat is due to the B metal (i.e., Al) contacts only, but as the temperature is increased above 7°K the higher vibrational modes which are due to the A metal (i.e., rare earth) contacts begin to contribute. Since the A metal modes are much
PHASE
from
COMPOUNDS
3.4” to 9.0%
‘softer’ (see Table 2) the overall Debye temperature of the compound is lowered and an increase in the heat capacity (C/T in the case of Figs. 2-4) occurs. A comparison of the Debye temperatures of the three RAl, Laves phases with those of their component metals is shown in Table 2 along with the radius ratios. It is seen that for each of the compounds eRAlzis closer to or, implying that near absolute zero lattice dynamics are controlled more by B-B contacts than by A-A contacts. For LaAl, this is in disagreement with the rAcalc/rg valuet which suggests, because it is greater than the ideal 1.225 value, that there are A-A contacts rather than B-B contacts. But the rAcalC/rg values for YAI, and LuAI, are in agreement Table 2. Comparison
*Because of these deviations. the data were fitted to an expression which included a higher order term (T”) in addition to the T and T” terms. Although the resultant y and 0 values increased from those given herein by 2-7 per cent and 6- 19 per cent. respectively, the standard deviations of the three parameter fits were 2-3 times larger than those of the two parameter fits. For this reason the two parameter equation was thought to adequately represent the electronic and vibrational contributions to the heat capacity. Elastic constant measurements near 0°K. however. would give an independent measure of 0 and would indicate whether the two parameter or three parameter equation is the better way to treat these data.
405
Compound LaAI, YAIZ LuAI,
of Debye temperatures
~.~/r,,
r.,ca’c/rg
bf131
&[I31
1.311 I .238 1.211
I.232 1.188 I.170
142 268 210
423 423 423
hl. 352 473 384
tThe r.rci”C/rR ratio is determined from the radius of the A atom as calculated from the lattice constant of the Laves phase and the pure B metal radius. The rA/rB ratio is determined from the pure A metal and pure B metal radii.
t
406
R.
E. HUNGSBERG
and
with the measured 0 values. The failure of the Joseph-Gschneidner correlation for LaAI, suggests that the method (based on radius ratios) which has been used previously to determine whether a Laves phase has one type of contact or another type may not be universally applied. It is believed that Debye temperature measurements based on low temperature heat capacity or elastic constant data are necessary to determine the type of contacts in the compound.’ As these data become available further understanding of the nature of Laves phases should result. It is, however, satisfying to find that the three RAl, compounds have B-B contacts. indicating that bonding in this series of closely related compounds is similar. At first glance the Debye temperatures appear to be reasonable with OTAls> OLuAi2> eLa.Alz,however, a more careful examination shows this order of 0 values is anomalous. An extension of the usual textbook treatment, for example Kittel[ 141, for a polyatomic lattice, shows that the Debye temperature is inversely proportional to the square root of the mass of the atoms per formula unit. The results for the three RAI., compounds were examined to determine if that relationship was followed. The Debye temperatures, I9RAlz’ relative to OyAl, were calculated from the equation
(1) where MRAiz is the mass of the atoms per formula unit of RAI,, and the results are given in Table 3. The close agreement (2.6 per cent) for the calculated and observed B values for LuAl, indicates that the interatomic forces in LuAI, and YAl? are similar. The lack of agreement ( 16 per cent) between the calculated and observed 8 values for LaAl, suggests that there are significant differences in the interatomic forces in LaAI, compared to those in YA12 and LuAI,. It is noted that the electronic density of states in LaAI,. which is about
K. A.
GSCHNEIDNER.
JR.
Table 3. Comptrrison of Debye temprrrrtlrres trtld.forrnulti mt~ssc.7 Compound
(M,,.,,,)
YAI, LaAI, LuAI,
I I .9s 13.89 15.13
’2
Calculated (“K)
H Observed (“K)
473 407 374
473
H
352 384
twice those of YAI, and LuAI, (discussed below). may be associated with an anomaly found in the Debye temperature comparison for these RAI, phases. Unfortunately. without knowledge of the Fermi surfaces of these three compounds one cannot tell whether the two anomalies in LaAI, are associated. Electronic speci$c herrt constant
An examination of the electronic specific constants. y. for these three compounds shows that the y values for YA12 and LuAI, are essentially identical (even if allowances are made for the uncertainty for the LuAI, value) and about half of the LaAI, value. Since y is proportional to the density of states at the Fermi surface. these results suggest that the Fermi surface of LaAI, is different from those of YAI, or LuAI,. which are probably quite similar. This difference may arise from the 4f band in lanthanum lying close to the Fermi level in LaAI,. while the 4f‘band is energetically too high to be a factor in YAI, and it is completely filled in LuAI,. The high density of states for LaAI, may account for superconductivity in this compound. while the lower density of states may account for the absence of superconductivity in YAI? and LuAI,. This observation is consistent with the theories proposed by Hamilton and Jensen [ 151 and Havinga and von Maaren [lb]. oJ‘LaA1, The increase in the heat capacity superconducting transition according B.C.S. theory [ 171 is given by Superconductivity
at the to the
RARE
EARTH
ALUMINUM
LAVES
AL,,, . YTS where T,Y is the superconducting transition temperatures. Analysis of the data for LaAI, reveals that the left-hand side of equation (3) is I .5 20.1 which is in very good agreement with theory and apparently somewhat unusual for rare-earth intermetallic compounds. For example. Satoh and Ohtsuka[ 181 found AC/YT,~ to be 0.80 for YGe,.,;?, 0.90 for LaSi,, and 0.76 for Lace, and Joseph and Gschneidner[ I91 found it to be I .48 for LaRu, and I.29 for CeRu,. The first three compounds are not Laves phases. but the last two are cubic Laves phases. isotypic with LaAI,. The difference between the ideal behavior of LaAI, and the non-ideal behavior of most of the other compounds may be due to a complicated Fermi surface for the four non-ideal compounds as compared to the Fermi surface of LaAI,. Further experimental and theoretical studies are needed to see if this would account for the difference.
5 6: 7. 8. 9. IO.
I I.
12.
13. 14. 15. 16.
rl[.~,~~,~~,/r~i~r,,~rrrrs - We wish to thank N. T. Panousis. J. Croat. J. T. Demel. D. C. Koskimaki and H. H. Baker for their assistance in carrying out some of the various aspects of this experimental investigation. and 0. D. McMasters for his helpful comments and discussions. Acknowledgement is also due to the Ames Laboratory analytical chemistry groups for their analyses of the starting materials.
17. 18. 19.
PHASE
COMPOUNDS
407
REFERENCES BERRY R. L. and RAYNOR G. V.. Acta. crysrollogr. 6. I78 (1953). LAVES F.. Thwr.v oj’Al/o~ Phases. p. 124. American Society for Metals. Metals Park. Ohio (1956). SCHULZE G. E. R., 2. Krislallogr. 111.249 (1959). NEVITT M. V.. Elecrronic S/rucfure und AIlov Chemisfry of fire Transifion Elemenrs (Edited by P. A. Beck). p. 101. Interscience. New York (1963). PEARSON W. B.. Acfcr crysrallogr. B24. 7 (1968). JOSEPH R. R. and GSCHNEIDNER K. A.. JR.. Scripfa Meftrll. 2. 63 1 t 1968). GSCHNEIDNER K. A.. JR., Row Earth AIloys. van Nostrand. Princeton. New Jersey (1961). MCMASTERS 0. D. and GSCHNEIDNER K. A. JR.. Nfccl. Meccrll. X. 93 t 1964). OSBORNE D. W.. FLOTOW H. E. and SCHREINER F.. Rec. Scienr. fnsrrrrrn. 38. I59 (1967). FURUKAWA G. T.. SABA W. G. and REILLY M. L.. Nntioncrl Standard Reference Dutcr SeriesNarional Bureurr of Standards No. I8 (1968). HAMILTON D. C.. RAUB C. J.. MATTHIAS B. T.. CORENZWIT E. and HULL G. W.. JR.. J. P/I.vs. Chern. Solids 26. 655 (1965). AOYAGI M.. LOI{, Trrnperorure Thermcrl Choracferisrics of Some Itl~ern~ercrllic Comporrnds Contclininp Lanfhtrnides. unpublished Ph.D. thesis. University of Pittsburgh. Pittsburgh. Pa.. 1967. GSCHNEIDNER K. A.. JR., So/id Slafe Phys. 16. ‘75 t 1964). KlTTEL C.. Inrroducrion 10 Solid Store Physics. 3rd edition. John Wiley. New York t 1966). HAMILTON D. C. andJENSON M. A.. Pl7ys. Rec. Lerr. 11. 205 (1963). HAVINGA E. E. and van MAAREN M. H.. P11.w. Left. 31A. 167 (1970). BARDEEN J.. COOPER L. N. and SCHRIEFFER J. R.. Pips. Rec. 108. I 175 (1957). SATOH T. and OHTSUKA T.. Phys. Left. 20, 565 ( 1966). JOSEPH R. R. and GSCHNEIDNER K. A.. JR.. Lm Temperrrrwe Hetlr Ctrpucity of LoRu,. CeRu, crnd CeRumIPt,. to be published in Phys. Rev.
for
HEAT CAPACITY OF SOME RARE LAVES PHASE COMPOUNDS: LaAl, AND LuAl,*
E. HUNGSBERCt
Atomic
Research
and
K.
A.
and Department Ames. lowa50010.
Abstract-The heat capacity of three rare earth Laves were measured in the temperature range of 2.5”-20°K. in LaAI, at 3.29”K. The C/T vs. 7’ data yielded
GSCHNEIDNER. of Metallurgy. U.S.A.
Jr. Iowa
State
phase compounds A superconducting
y = I.81 ml/g at.-OK’ and 0 = 473°K for YAI,. y = 3.65 ml/g at.-OK’ and H = 352°K for LaAI?. y = 1.9 ml/g at-OK’ and 0 = 384°K for LuAI,. The Debye temperatures indicate that the low temperature B element (aluminum). The Debye temperature of LaAI, is YAI, and LuAI,. and the electronic specific constant. y. of YAI, and LuAI,. The high y value is thought to account for sence of superconductivity in the other two Laves phases. It superconductor.
University.
YAI,. LaAI, and LuAI, transition was observed
and
lattice dynamics are controlled by the anomalously low compared to those of LaAI, is anomalously high compared to superconductivity in LaAI, and the abis found that LaAI, behaves as a B.C.S.
Several years ago Joseph and Gschneidner [6] noted a correlation between the measured Debye temperature of a number of Laves phase compounds and the radius ratio of the component atoms of the compound. They found that when the radius ratio indicated A-A metal contacts the Debye temperature of the Laves phase compound was found to be closer to the Debye temperature of pure A than pure B. The converse was also found when the radius ratio indicated B-B contacts. Upon examination of radius ratios of the RAI, Laves phase compounds, one would expect A-A contacts for the larger rare earth atoms (La, etc.) and B-B contacts for the smaller rare earth atoms (Lu, SC, etc.). This is interesting because if the JosephGschneidner correlation holds, the Debye temperature for the RAI, compounds should change from values in the 150-200°K range
1. INTRODUCTION
A LAVES phase compound generally has the AB, stoichiometry and the A atom is always larger than the B atom. From the geometrical arrangement of atoms it can be shown that if these atoms behave as hard spheres the ideal packing of atoms occurs when the radius ratio is I .225. At the ideal ratio there are both A-A and B-B contacts; when the radius ratio is I .225. At the ideal ratio there are contacts. and when the ratio is greater than the ideal value there are only A-A contacts. However. there are no A-B contacts at any value of the radius ratio. assuming hard spheres. Although it is known that atoms do not behave as hard spheres, this model of Laves phase compounds has proven to be a useful concept in the understanding of these materials [ l-51. “Work was performed in the Ames Laboratory of the U.S. Atomic Energy Commission. Contribution No. 2887. ipresent Address: GTE Automatic Electric Laboratories, Inc., Tube Station B-3. Dept. 490. P.O. Box 17. Northlake. Illinois 60164. U.S.A.
for
the
light
]anthanides
to
va]ues
in the
JO&
450°K range for the heavy lanthanides, scandium and yttrium. This suggests a significant 401
401
R.
E. HUNGSBERG
and
change in the nature of the bonding for this series of closely-related compounds. However, examination of the known physical properties, such as the lanthanide contraction and melting points. of these RAI, compounds shows that nothing unusual occurs that would indicate a change in bond nature in the RAI, compounds. Because of this dilemma it was felt that determination of the low temperature heat capacity of a number of RAI, Laves phase compounds could help to resolve the problem. Furthermore. the determination of the electronic specific heat constant. y. and the Debye temperature. 0. for Laves phases will aid in our understanding of the nature of this large family of intermetallic compounds. especially since such information is scarce. The Laves phase compounds YAI,. LaAI,, and LuAI, were chosen since the A metal (Y. La. Lu) has no 4felectrons or a completely filled 4f level, and thus there will be no magnetic contribution to the heat capacities of Furthermore. LaAI, these compounds. should be representative of the first lanthanide RAI, phases. YAI, of the mid lanthanide RAI, phases* and LuAI, of the last of the lanthanide RAI, compounds. 2. EXPERIMENTAL
Sample
preparation
The impurity contents of the materials used in this investigation are given in Table I. All three compounds were prepared by arc melting weighed amount of the components on a water cooled copper hearth under a zirconium gettered argon atmosphere. To obtain homogeneity. each sample was turned over and remelted one or more times. Shattering or cracking of the brittle samples would occur upon restriking of the arc if the samples were permitted to cool below a red heat, but restriking the arc while still red hot prevented *Since yttrium in many of its compounds and alloys behaves much like dysprosium or holmium. we believe that the y and H values for DyAI, and HoAI, will be similar to those measured for Y Al,.
K.
A. GSCHNEIDNER.
JR.
Table 1. Cllemical analysis of cow pottents (itnprrrity levels are given it1 pptn by \t,eight) Starting Y
Impurity
Al
H C N 0 F M.kt Al Si l-a SC Cr Mn Fe Ni cu Zn Y La Ce Pr Nd Gd Tb Dy Ho El Ta
___
10 M 10 ___ ___ ___ i IO IO ___ 10 i IO ___ ___ --___ ----___ ----___ ___
materials La
5 __. 12 175 ___ ___ ___ __. ___ ___ ___ _.. ___ ___ ___ M ___ ___ ___ _.. _.. ___ ___ ___ ___ ___
Lu
29 36 78 79 19 5 10 5 IO s ,o s 10 ___ s IO _.. 5 40 100 20 ___ ___
6 IO 9 107 <3 ----___ --I 0.3 ___ ‘.J I IO --_ 7.5
M s 3.50 c I50 s loo _.. _.. _-. _-_ _-. s 500
I6 ’ II 4 -l ; 7 9 3 loo
< less than. < less than or equal to ___ not analyzed for. M major component.
this. To prevent cracking. power to the arc was reduced as much as possible after the last melting to allow the sample to cool down as slowly as possible. Metallographic examination? and X-ray analysis showed that the YAI., and LaAl, samples were single phase and homogeneous. The LuAI, was found to have a small amount of a second phase. Point count analysis revealed the two-phase area to be 8- 16 per cent of the total area. Higher power magnification showed the second phase occupying 25 per cent of the two-phase area and thus, +Keller’s 95 ml H,O)
solution t I ml HF. lfml was used to etch the RAI,
HCI. 2tml compounds.
HNO,.
RARE
EARTH
ALUMINUM
about 2-4 per cent of the second phase was present. A conventional spark cutter was used to cut two parallel faces on the samples to allow mounting in the calorimeter. Because the compounds were very brittle. small portions broke off even with careful handling. Sample surfaces left unprotected for several weeks remained bright and shiny, indicating very little or no oxidation. The lattice parameters for the compounds are as follows and were found to agree well with other values reported in literature[7,8]: YAI., LaAI, LuAI,
7.864-e-0.001 A. 8.148 ?O.OOl A. 7.743 & 0.001 A.
Calorimetry Specific heat measurements were made in an adiabatic calorimeter. The accuracy of the calorimeter was checked by measuring the heat capacity of a Calorimetry Conference Copper Standard [9]. Measured values agreed with published copper data[9. IO] to within I per cent in the temperature range of 2.5-20°K. 3. RESULTS
Experimental values of the heat capacity and temperature for the three Laves phases are shown in Figs. l-4’k. Figure I is a plot of C/T vs. T’ for YAI., over the entire temperature range covered. The linear portion of the curve is shown expanded in Fig. 2. A least squares fitting of the points to the equation C/T = y+PT’ yielded y = I.81 kO.02 ml/g at.-OK’. p = 0.01835 +0.00045 mJ/g at-OK4 and 8 = 473 2 4°K. Only the lower. linear portion of the C/T *The experimental heat capacity vs. temperature data may be obtained by ordering NAPS Document No. 01525 from ASlS National Auxiliary Publications Service. c/o CCM Information Sciences. inc.. 22 West 34th Street. New York. New York 1000 I : remitting $2.00 for microfiche or $S.OO for photocopies: or from K. A. Gschneidner. Jr. Ames Laboratory. Iowa State University. Ames. Iowa50010. U.S.A. (free).
LAVES
PHASE
COMPOUNDS
403
vs. T’ data for LaAI, is shown in Fig. 3. Because the higher temperature portion (T > 9°K) is similar to that of YAI, there is no need to show a plot of the data. A similar fitting of the data in the linear region shown in Fig. 3 yielded y = 3.65 20.04 ml/g at.-“K’, /3 = 0.04441 & 0.00110 ml/g at.-“K”. and 0 = 352 & 3°K. The peak at 3~29”%0~03”K has a shape typical of a superconducting transition and is in good agreement with a reported[ 1 I] superconducting transition temperature of 3~2°K obtained from resistivity measurements. Other specific heat data [ 121 on LaA& in the temperature range of IO-280°K are lower than the present values by IO-15 per cent in the overlapping range of 14-20°K. The LuAI, data (Fig. 4) were handled in a similar manner. giving 1.92 2 0.02 ml/g at.-OK2 for y. O-03421 I+ 0.00050 mJ/g at.-“K4 for /3. and 384 -C2°K for 0. The y and 0 values may be in error due to the presence of a second phase in this sample. Assuming linear combination of the LuAI, and second phase quantities ty and 8) we estimate that the above measured y value lies within -+3 per cent of the true value for LuAl, on the assumption that the second phase y value lies between 0.2 and 4.0 rnJ/g at.-“K”. However. if the second phase y value were an unusually high value such as IO mJ/g at.-“K’ then the observed y might be in error by as much as I5 per cent. Similarly. we estimate that the measured 0 value lies within ?2 per cent of the true value for LuAI, on the assumption that the second phase 0 value lies between 150” and 575°K. It is very unlikely that the second phase 0 value lies outside this range, and thus the measured 0 value is probably reliably known, 384”& 7°K. Unlike 0. y is a very difficult quantity to estimate, and accordingly, we have less confidence in the y value for LuAI,, 1.9:::; ml/g at.-“K’. 4. DISCUSSION
Debye temperatures A close examination of Figs. 2-4 indicates that the low temperature T” approximation
404
R. E. HUNGSBERG
and
K. A.
GSCHNEIDNER.
JR.
0 0
40
80
Fig.
IM
1. Heat
160
capacity
200
240
of YAI,
280
from
l
2
320
360
400
2.4” to 21°K.
RUN
2”d
r’ I. 5 0
IO
20
30
40
50
60
70
60
T2 ii&
Fig.
2. Heat
capacity
of YAI,
from
2.5” to9”K.
IO 0
I 10
I
I
20
30
Fig. 3. Heat
capacity
40 50 T21K21
60
of LaAI,
from
70
80
2.8” to 9.5”K.
90
440
RARE
EARTH
Fig.
ALUMINUM
4. Heat
capacity
LAVES
of LuAI,
of Debye theory is no longer valid for temperatures greater than = 7.5”K. (T’ = 60”KZ), which is much lower than one might expect for these materials.* The T” approximation begins to differ from the rigorous treatment of the Debye theory at T/O = 10, and thus departures would be expected to occur at about 35°K for LaAI,, 38°K for LuAI, and 47°K for YAl*. A reasonable explanation for this behavior may be forthcoming from the JosephGschneidner model[6] of the Laves phase compounds. At temperatures below 7°K the vibrational contribution to the specific heat is due to the B metal (i.e., Al) contacts only, but as the temperature is increased above 7°K the higher vibrational modes which are due to the A metal (i.e., rare earth) contacts begin to contribute. Since the A metal modes are much
PHASE
from
COMPOUNDS
3.4” to 9.0%
‘softer’ (see Table 2) the overall Debye temperature of the compound is lowered and an increase in the heat capacity (C/T in the case of Figs. 2-4) occurs. A comparison of the Debye temperatures of the three RAl, Laves phases with those of their component metals is shown in Table 2 along with the radius ratios. It is seen that for each of the compounds eRAlzis closer to or, implying that near absolute zero lattice dynamics are controlled more by B-B contacts than by A-A contacts. For LaAl, this is in disagreement with the rAcalc/rg valuet which suggests, because it is greater than the ideal 1.225 value, that there are A-A contacts rather than B-B contacts. But the rAcalC/rg values for YAI, and LuAI, are in agreement Table 2. Comparison
*Because of these deviations. the data were fitted to an expression which included a higher order term (T”) in addition to the T and T” terms. Although the resultant y and 0 values increased from those given herein by 2-7 per cent and 6- 19 per cent. respectively, the standard deviations of the three parameter fits were 2-3 times larger than those of the two parameter fits. For this reason the two parameter equation was thought to adequately represent the electronic and vibrational contributions to the heat capacity. Elastic constant measurements near 0°K. however. would give an independent measure of 0 and would indicate whether the two parameter or three parameter equation is the better way to treat these data.
405
Compound LaAI, YAIZ LuAI,
of Debye temperatures
~.~/r,,
r.,ca’c/rg
bf131
&[I31
1.311 I .238 1.211
I.232 1.188 I.170
142 268 210
423 423 423
hl. 352 473 384
tThe r.rci”C/rR ratio is determined from the radius of the A atom as calculated from the lattice constant of the Laves phase and the pure B metal radius. The rA/rB ratio is determined from the pure A metal and pure B metal radii.
t
406
R.
E. HUNGSBERG
and
with the measured 0 values. The failure of the Joseph-Gschneidner correlation for LaAI, suggests that the method (based on radius ratios) which has been used previously to determine whether a Laves phase has one type of contact or another type may not be universally applied. It is believed that Debye temperature measurements based on low temperature heat capacity or elastic constant data are necessary to determine the type of contacts in the compound.’ As these data become available further understanding of the nature of Laves phases should result. It is, however, satisfying to find that the three RAl, compounds have B-B contacts. indicating that bonding in this series of closely related compounds is similar. At first glance the Debye temperatures appear to be reasonable with OTAls> OLuAi2> eLa.Alz,however, a more careful examination shows this order of 0 values is anomalous. An extension of the usual textbook treatment, for example Kittel[ 141, for a polyatomic lattice, shows that the Debye temperature is inversely proportional to the square root of the mass of the atoms per formula unit. The results for the three RAI., compounds were examined to determine if that relationship was followed. The Debye temperatures, I9RAlz’ relative to OyAl, were calculated from the equation
(1) where MRAiz is the mass of the atoms per formula unit of RAI,, and the results are given in Table 3. The close agreement (2.6 per cent) for the calculated and observed B values for LuAl, indicates that the interatomic forces in LuAI, and YAl? are similar. The lack of agreement ( 16 per cent) between the calculated and observed 8 values for LaAl, suggests that there are significant differences in the interatomic forces in LaAI, compared to those in YA12 and LuAI,. It is noted that the electronic density of states in LaAI,. which is about
K. A.
GSCHNEIDNER.
JR.
Table 3. Comptrrison of Debye temprrrrtlrres trtld.forrnulti mt~ssc.7 Compound
(M,,.,,,)
YAI, LaAI, LuAI,
I I .9s 13.89 15.13
’2
Calculated (“K)
H Observed (“K)
473 407 374
473
H
352 384
twice those of YAI, and LuAI, (discussed below). may be associated with an anomaly found in the Debye temperature comparison for these RAI, phases. Unfortunately. without knowledge of the Fermi surfaces of these three compounds one cannot tell whether the two anomalies in LaAI, are associated. Electronic speci$c herrt constant
An examination of the electronic specific constants. y. for these three compounds shows that the y values for YA12 and LuAI, are essentially identical (even if allowances are made for the uncertainty for the LuAI, value) and about half of the LaAI, value. Since y is proportional to the density of states at the Fermi surface. these results suggest that the Fermi surface of LaAI, is different from those of YAI, or LuAI,. which are probably quite similar. This difference may arise from the 4f band in lanthanum lying close to the Fermi level in LaAI,. while the 4f‘band is energetically too high to be a factor in YAI, and it is completely filled in LuAI,. The high density of states for LaAI, may account for superconductivity in this compound. while the lower density of states may account for the absence of superconductivity in YAI? and LuAI,. This observation is consistent with the theories proposed by Hamilton and Jensen [ 151 and Havinga and von Maaren [lb]. oJ‘LaA1, The increase in the heat capacity superconducting transition according B.C.S. theory [ 171 is given by Superconductivity
at the to the
RARE
EARTH
ALUMINUM
LAVES
AL,,, . YTS where T,Y is the superconducting transition temperatures. Analysis of the data for LaAI, reveals that the left-hand side of equation (3) is I .5 20.1 which is in very good agreement with theory and apparently somewhat unusual for rare-earth intermetallic compounds. For example. Satoh and Ohtsuka[ 181 found AC/YT,~ to be 0.80 for YGe,.,;?, 0.90 for LaSi,, and 0.76 for Lace, and Joseph and Gschneidner[ I91 found it to be I .48 for LaRu, and I.29 for CeRu,. The first three compounds are not Laves phases. but the last two are cubic Laves phases. isotypic with LaAI,. The difference between the ideal behavior of LaAI, and the non-ideal behavior of most of the other compounds may be due to a complicated Fermi surface for the four non-ideal compounds as compared to the Fermi surface of LaAI,. Further experimental and theoretical studies are needed to see if this would account for the difference.
5 6: 7. 8. 9. IO.
I I.
12.
13. 14. 15. 16.
rl[.~,~~,~~,/r~i~r,,~rrrrs - We wish to thank N. T. Panousis. J. Croat. J. T. Demel. D. C. Koskimaki and H. H. Baker for their assistance in carrying out some of the various aspects of this experimental investigation. and 0. D. McMasters for his helpful comments and discussions. Acknowledgement is also due to the Ames Laboratory analytical chemistry groups for their analyses of the starting materials.
17. 18. 19.
PHASE
COMPOUNDS
407
REFERENCES BERRY R. L. and RAYNOR G. V.. Acta. crysrollogr. 6. I78 (1953). LAVES F.. Thwr.v oj’Al/o~ Phases. p. 124. American Society for Metals. Metals Park. Ohio (1956). SCHULZE G. E. R., 2. Krislallogr. 111.249 (1959). NEVITT M. V.. Elecrronic S/rucfure und AIlov Chemisfry of fire Transifion Elemenrs (Edited by P. A. Beck). p. 101. Interscience. New York (1963). PEARSON W. B.. Acfcr crysrallogr. B24. 7 (1968). JOSEPH R. R. and GSCHNEIDNER K. A.. JR.. Scripfa Meftrll. 2. 63 1 t 1968). GSCHNEIDNER K. A.. JR., Row Earth AIloys. van Nostrand. Princeton. New Jersey (1961). MCMASTERS 0. D. and GSCHNEIDNER K. A. JR.. Nfccl. Meccrll. X. 93 t 1964). OSBORNE D. W.. FLOTOW H. E. and SCHREINER F.. Rec. Scienr. fnsrrrrrn. 38. I59 (1967). FURUKAWA G. T.. SABA W. G. and REILLY M. L.. Nntioncrl Standard Reference Dutcr SeriesNarional Bureurr of Standards No. I8 (1968). HAMILTON D. C.. RAUB C. J.. MATTHIAS B. T.. CORENZWIT E. and HULL G. W.. JR.. J. P/I.vs. Chern. Solids 26. 655 (1965). AOYAGI M.. LOI{, Trrnperorure Thermcrl Choracferisrics of Some Itl~ern~ercrllic Comporrnds Contclininp Lanfhtrnides. unpublished Ph.D. thesis. University of Pittsburgh. Pittsburgh. Pa.. 1967. GSCHNEIDNER K. A.. JR., So/id Slafe Phys. 16. ‘75 t 1964). KlTTEL C.. Inrroducrion 10 Solid Store Physics. 3rd edition. John Wiley. New York t 1966). HAMILTON D. C. andJENSON M. A.. Pl7ys. Rec. Lerr. 11. 205 (1963). HAVINGA E. E. and van MAAREN M. H.. P11.w. Left. 31A. 167 (1970). BARDEEN J.. COOPER L. N. and SCHRIEFFER J. R.. Pips. Rec. 108. I 175 (1957). SATOH T. and OHTSUKA T.. Phys. Left. 20, 565 ( 1966). JOSEPH R. R. and GSCHNEIDNER K. A.. JR.. Lm Temperrrrwe Hetlr Ctrpucity of LoRu,. CeRu, crnd CeRumIPt,. to be published in Phys. Rev.