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Heat capacity of α-cerium between 2.5 and 20°K
Solid State Communications,Vol. 8, pp. 1779—1782, 1970. Pergamon Press.
Printed in Great Britain
HEAT CAPACITY OF a-CERIUM BETWEEN 2.5 AND 20°K* N.T. Panousis and K.A. Gschneidner, Jr. Institute for Atomic Research and Department of Metallurgy Iowa State University, Ames, Iowa 50010 U.S.A. (Received 25 June 1970 by M.F. Collins)
The low temperature heat capacity of a-cerium free from other allotropic modifications has been determined for the first time at standard pressures. The low-tempprature dat~is represented by the equation: C = 9.79 T + (12/5) ii R(T/117) where C is in mJ mole’ deg
METALLIC cerium has been the topic of numerous theoretical1 ~ and experimental9• 15studies origmating mainly from its variable electronic and allotropic natures. At the present time, there is considerable controversy concerning the electronic configuration of a-Ce. Some evidence indicates it has no 4f electrons, other information suggests a-Ce has a partially-filled 41 band, and other results suggest that it has one 41 electron. In part, this is because there are essentially no reliable experimental data available on the pure a-Ce phase. The purpose of this study is to provide some reliable experimental values which can be used to support or refute current models.
We report here the first determination of the low temperature heat capacity of pure a-cerium at normal pressure. Other low temperature heat capacity measurements on cerium have either been on samples containing mixtures of the a and ~ allotropes9”°or done at high pressure.’1 The values heretofore for the electronic specific heat constant and the Debye temperature of a-cerium, which result&d from the normal pressure runs, were obtained by assuming values for the $-phase and an estimate of the amounts of a. and ~ present. Values so derived for a-cerium are open to serious criticism.
y-cerium. Upon cooling the sample at normal pressure, the Vallotrope begins to transform to a second allotrope, .$-cerium (d.h. c.p., a = 3.68 A, c = 11.92A) at 250°K. Further cooling results in the remaining y transforming to a third allotrope, a-cerium (f.c.c., a 4.85A) at 116°K.Unless special precautions are taken, a sample of y-cerium cooled to cryogenic temperatures at normal pressure will invariably contain a mixture of the a. and f~ phases.
The three-step technique used to prepare pure a-cerium is based on the pressure-temperature diagram pro 1osed by Gschneidner, Elliott and McDonald.’ First, a well annealed sample of y-cerium was compressed at room temperature to 10,000 atmospheres pressure to transform it to the a-allotrope. Second, while maintaining this pressure the sample was quenched with liquid nitrogen. The third step was to release the pressure after reaching Uquid nitrogen temperature. The sample was maintained at 77°Kwhile loading it into the calorimeter after which it was cooled to 4.2°K.
Work performed in the Ames Laboratory of the
The heat capacity of a-cerium from 2.5 to
At room temperature and one atmosphere pressure, the stable allotrope is f.c.c. (a = 5. 16 A),
*
Atomic Energy Commission. Contribution No. 2744.
1779
20°Kis shown in Fig. 1. The smooth data
1780
HEAT CAPACITY OF a-CERIUM BETWEEN 2.5 AND 20°K 9000 I
I
I
I
I
I
I
8000
I
I
Vol. 8, No. 21
I
ALPHA CERIUM
7000
~
T6000~-
L~5oo0~•~40o0F
~0
E30o0 .— 2000k-
0
00
00
—
0
.1
I000I-~
1
0000000
0
0
2
~
4
6
8
I
‘0 I (deg)
I
I
2
I
I
4
I
I
6
8
20
FIG. 1. Heat capacity of a-cerium at normal pressure.
ALPHA CERIUM
~
C.979To~..r’RI~j~)’
_-~
lot-
-
o~ 0
0
20
2) 40
~ (deq
I ~0
60
70
FIG. 2. CIT vs. T2plot for a-cerium to determine Debye temperature and electronic specific heat constant.
indicates that the sample was free of the other cerium allotropes. Since $-cerium is known to magnetically order at about 13°K,’3”4the presence of any $ would be indicated by a peak at about 13°K.’6 We estimate we can detect the presence of about 0.25 per cent $-cerium because of the large heat capacity associated with the magnetic ordering of this phase. Figure 2 shows the standard CIT vs. T2 plot of the low temperature data. The points between T2=27 and 75 were least-squares fitted by computer to. give
V 9.79 mJ mole’ deg’ and a Debye temperature of 117°K.Below T2 27 the experimental points show a systematic positive deviation from linearity and so they were not used in the fit to determine 7 and 0. Our yand 0 values agree reasonably well with the high pressure (11 kbar) heat capacity results of Phillips, Ho, and Smith” who found V = 11.3 mJ mole1 deg’ and 9 = 200°K.The larger difference between our 0 value and that of
Vol. 8, No. 21
HEAT CAPACITY OF a-CERIUM BETWEEN 2.5 AND 20°K
Phillips and co-workers is consistent with the observed increase in the a-cerium Debye temperature with increasing pressure as re~orted by Vornov, Vereshchagin and Goncharova.’ In fact, our value of 117°Kfor the Debye temperature compares very well with the value of 118°K,as obtained by extrapolation of the high pressure room temperature data of Vomov and co-workers to atmospheric pressure. The electronic specific heat constants, as determined from Mukhopadhyay’s and Majumdar’s destiny of states values for a-Ce,8 are 3.7 inj mole~ deg~for three S d electrons and 2.9 mJ mole1 deg 2for the four S d electrons. These values, respectively, are 2 1/2 and 3 1/2 times smaller than the observed value. Probably this is due to electron—phonon and electron—electron interactions which cause an enhancement of the observed electronic specific heat constant. This enhancement is somewhat larger than the factor of two observed for Sc,’7 Y, 8 and the heavy lanthanides. for which density of states values
1781
were calculated by using an APW method, the same method as used for a-Ce. The origin of the positive curvature in the CIT vs. T2 plots at the lowest temperatures is not known. Impurity ordering is a possibility although analysis of our samples before and after the measurements indicated high purity cerium was used in this study. Expresses in parts per million by weight, the major impurities were: H, 3; 0, 63; Fe, 12; Ni, 6; La, 7; Pr, 15; Nd, 36; Gd, 31; Tb, 5; Dy, 9; Ho, 4; Er, 9; Ta, 13. Mn, Co, Sm, Eu, Tm, Yb and Lu were not detected. The above results will be discussed in more detail in another paper which will also include our results on $-stabilized cerium—yttrium alloys as well as a description of the apparatus.’9
A cknowledgements We would like to acknowledge the assistance of Mr. R.E. Hungsberg in performing the experiments. —
REFERENCES 1. 2.
MURRAO T. and MATSUBARA T., Prog. theor. Phys. (Kyoto) 18, 215 (1957). GSCHNEIDNER Jr., K.A. and SMOLUCHOWSKI R., J. Less-Common Metals 5, 374 (1963).
3.
BLEANEY B., Rare Earth Research II p.417 (edited by VORRES K.S.) Gordon & Breach, New York, (1964).
4.
6.
GSCHNEIDNER Jr., K.A., Rare Earth Research III p. 153 (edited by EYRING L.) Gordon & Breach, New York, (1965). WABER J.T. and SWITENDICK A.C., paper presented at the Fifth Rare Earth Research Conf, Ames, Iowa, August 30 September 1, 1965; Book two of Conference Preprints, AD—627, 222 (1965), p.75. COQBLIN B. and BLANDIN A., Adv. Phys. 17, 281 (1968).
7. 8.
EDELSTEIN A.S., Phys. Rev. Len. 20, 1348 (1968). MUKHOPADHYAY G. and MAJUMDAR C.K., J. Phys. C. (Solid State Phys.) 2, 924 (1969).
9.
PARKINSON D.H. and ROBERTS L.M., Proc. Phys. Soc. (London) B70, 471 (1957).
5.
—
10.
LOUNASMAA O.V., Phys. Rev. 133, A502 (1964).
11. 12. 13.
PHILIPS N.E., HO J.C. and SMITH T.F., Phys. Lett. 27A, 49 (1968). GSCHNEIDNER Jr., K.A., ELLIOTT R.O. and McDONALD R.R., J. Phys. Chem. Solids 23, 555 (1962). LOCK J.M., Proc. Phys. Soc. (London) B70, 566 (1967).
14.
WILKINSON M.K., CHILD H.R., McHARGUE C.J., KOEHLER W.C. and WOLLAN E.O., Phys. Rev. 122, 1409 (1961). VORNOV F.F., VERESHCHAGIN L.F. and GONCHAROVA V.A, Dokl. Akad, Nauk, SSSR 135, 1104 (1960); Eng, Transl., Soviet Phys. Doklady 135, 1280 (1960).
15.
1782
HEAT CAPACITY OF a-CERIUM BETWEEN 2.5 AND 20°K
Vol. 8, No. 21
16.
Another cerium sample containing a few per cent fi was run through the same cycle as described above and the presence of $ was immediately obvious in the heat capacity curve.
17.
FLEMING G.S. and LOUCKS T.S., Phys. Rev. 173, 685 (1968).
18.
LOUCKS T.S., Phys. Rev. 144, 504 (1966).
19.
PANOUSIS N.T. and GSCHNEIDNER Jr., K.A., Low temperature specific heat of cerium and cerium—yttrium alloys. To be published.
Es wurde zum ersten Mal bei normallem Druck die spezifische W~irme von a-Cerium, von anderen allotropischen Abwandlungen gereinigt, bei tiefen Temperatures gemessen. Die Tieftemperaturdaten lassen sich durch die Gleichung, C = 9.79 T + (12/5) rT4R( T/117)3 repr~sentiertwerden (C in Einheiten von mJ mole~deg~).
Printed in Great Britain
HEAT CAPACITY OF a-CERIUM BETWEEN 2.5 AND 20°K* N.T. Panousis and K.A. Gschneidner, Jr. Institute for Atomic Research and Department of Metallurgy Iowa State University, Ames, Iowa 50010 U.S.A. (Received 25 June 1970 by M.F. Collins)
The low temperature heat capacity of a-cerium free from other allotropic modifications has been determined for the first time at standard pressures. The low-tempprature dat~is represented by the equation: C = 9.79 T + (12/5) ii R(T/117) where C is in mJ mole’ deg
METALLIC cerium has been the topic of numerous theoretical1 ~ and experimental9• 15studies origmating mainly from its variable electronic and allotropic natures. At the present time, there is considerable controversy concerning the electronic configuration of a-Ce. Some evidence indicates it has no 4f electrons, other information suggests a-Ce has a partially-filled 41 band, and other results suggest that it has one 41 electron. In part, this is because there are essentially no reliable experimental data available on the pure a-Ce phase. The purpose of this study is to provide some reliable experimental values which can be used to support or refute current models.
We report here the first determination of the low temperature heat capacity of pure a-cerium at normal pressure. Other low temperature heat capacity measurements on cerium have either been on samples containing mixtures of the a and ~ allotropes9”°or done at high pressure.’1 The values heretofore for the electronic specific heat constant and the Debye temperature of a-cerium, which result&d from the normal pressure runs, were obtained by assuming values for the $-phase and an estimate of the amounts of a. and ~ present. Values so derived for a-cerium are open to serious criticism.
y-cerium. Upon cooling the sample at normal pressure, the Vallotrope begins to transform to a second allotrope, .$-cerium (d.h. c.p., a = 3.68 A, c = 11.92A) at 250°K. Further cooling results in the remaining y transforming to a third allotrope, a-cerium (f.c.c., a 4.85A) at 116°K.Unless special precautions are taken, a sample of y-cerium cooled to cryogenic temperatures at normal pressure will invariably contain a mixture of the a. and f~ phases.
The three-step technique used to prepare pure a-cerium is based on the pressure-temperature diagram pro 1osed by Gschneidner, Elliott and McDonald.’ First, a well annealed sample of y-cerium was compressed at room temperature to 10,000 atmospheres pressure to transform it to the a-allotrope. Second, while maintaining this pressure the sample was quenched with liquid nitrogen. The third step was to release the pressure after reaching Uquid nitrogen temperature. The sample was maintained at 77°Kwhile loading it into the calorimeter after which it was cooled to 4.2°K.
Work performed in the Ames Laboratory of the
The heat capacity of a-cerium from 2.5 to
At room temperature and one atmosphere pressure, the stable allotrope is f.c.c. (a = 5. 16 A),
*
Atomic Energy Commission. Contribution No. 2744.
1779
20°Kis shown in Fig. 1. The smooth data
1780
HEAT CAPACITY OF a-CERIUM BETWEEN 2.5 AND 20°K 9000 I
I
I
I
I
I
I
8000
I
I
Vol. 8, No. 21
I
ALPHA CERIUM
7000
~
T6000~-
L~5oo0~•~40o0F
~0
E30o0 .— 2000k-
0
00
00
—
0
.1
I000I-~
1
0000000
0
0
2
~
4
6
8
I
‘0 I (deg)
I
I
2
I
I
4
I
I
6
8
20
FIG. 1. Heat capacity of a-cerium at normal pressure.
ALPHA CERIUM
~
C.979To~..r’RI~j~)’
_-~
lot-
-
o~ 0
0
20
2) 40
~ (deq
I ~0
60
70
FIG. 2. CIT vs. T2plot for a-cerium to determine Debye temperature and electronic specific heat constant.
indicates that the sample was free of the other cerium allotropes. Since $-cerium is known to magnetically order at about 13°K,’3”4the presence of any $ would be indicated by a peak at about 13°K.’6 We estimate we can detect the presence of about 0.25 per cent $-cerium because of the large heat capacity associated with the magnetic ordering of this phase. Figure 2 shows the standard CIT vs. T2 plot of the low temperature data. The points between T2=27 and 75 were least-squares fitted by computer to. give
V 9.79 mJ mole’ deg’ and a Debye temperature of 117°K.Below T2 27 the experimental points show a systematic positive deviation from linearity and so they were not used in the fit to determine 7 and 0. Our yand 0 values agree reasonably well with the high pressure (11 kbar) heat capacity results of Phillips, Ho, and Smith” who found V = 11.3 mJ mole1 deg’ and 9 = 200°K.The larger difference between our 0 value and that of
Vol. 8, No. 21
HEAT CAPACITY OF a-CERIUM BETWEEN 2.5 AND 20°K
Phillips and co-workers is consistent with the observed increase in the a-cerium Debye temperature with increasing pressure as re~orted by Vornov, Vereshchagin and Goncharova.’ In fact, our value of 117°Kfor the Debye temperature compares very well with the value of 118°K,as obtained by extrapolation of the high pressure room temperature data of Vomov and co-workers to atmospheric pressure. The electronic specific heat constants, as determined from Mukhopadhyay’s and Majumdar’s destiny of states values for a-Ce,8 are 3.7 inj mole~ deg~for three S d electrons and 2.9 mJ mole1 deg 2for the four S d electrons. These values, respectively, are 2 1/2 and 3 1/2 times smaller than the observed value. Probably this is due to electron—phonon and electron—electron interactions which cause an enhancement of the observed electronic specific heat constant. This enhancement is somewhat larger than the factor of two observed for Sc,’7 Y, 8 and the heavy lanthanides. for which density of states values
1781
were calculated by using an APW method, the same method as used for a-Ce. The origin of the positive curvature in the CIT vs. T2 plots at the lowest temperatures is not known. Impurity ordering is a possibility although analysis of our samples before and after the measurements indicated high purity cerium was used in this study. Expresses in parts per million by weight, the major impurities were: H, 3; 0, 63; Fe, 12; Ni, 6; La, 7; Pr, 15; Nd, 36; Gd, 31; Tb, 5; Dy, 9; Ho, 4; Er, 9; Ta, 13. Mn, Co, Sm, Eu, Tm, Yb and Lu were not detected. The above results will be discussed in more detail in another paper which will also include our results on $-stabilized cerium—yttrium alloys as well as a description of the apparatus.’9
A cknowledgements We would like to acknowledge the assistance of Mr. R.E. Hungsberg in performing the experiments. —
REFERENCES 1. 2.
MURRAO T. and MATSUBARA T., Prog. theor. Phys. (Kyoto) 18, 215 (1957). GSCHNEIDNER Jr., K.A. and SMOLUCHOWSKI R., J. Less-Common Metals 5, 374 (1963).
3.
BLEANEY B., Rare Earth Research II p.417 (edited by VORRES K.S.) Gordon & Breach, New York, (1964).
4.
6.
GSCHNEIDNER Jr., K.A., Rare Earth Research III p. 153 (edited by EYRING L.) Gordon & Breach, New York, (1965). WABER J.T. and SWITENDICK A.C., paper presented at the Fifth Rare Earth Research Conf, Ames, Iowa, August 30 September 1, 1965; Book two of Conference Preprints, AD—627, 222 (1965), p.75. COQBLIN B. and BLANDIN A., Adv. Phys. 17, 281 (1968).
7. 8.
EDELSTEIN A.S., Phys. Rev. Len. 20, 1348 (1968). MUKHOPADHYAY G. and MAJUMDAR C.K., J. Phys. C. (Solid State Phys.) 2, 924 (1969).
9.
PARKINSON D.H. and ROBERTS L.M., Proc. Phys. Soc. (London) B70, 471 (1957).
5.
—
10.
LOUNASMAA O.V., Phys. Rev. 133, A502 (1964).
11. 12. 13.
PHILIPS N.E., HO J.C. and SMITH T.F., Phys. Lett. 27A, 49 (1968). GSCHNEIDNER Jr., K.A., ELLIOTT R.O. and McDONALD R.R., J. Phys. Chem. Solids 23, 555 (1962). LOCK J.M., Proc. Phys. Soc. (London) B70, 566 (1967).
14.
WILKINSON M.K., CHILD H.R., McHARGUE C.J., KOEHLER W.C. and WOLLAN E.O., Phys. Rev. 122, 1409 (1961). VORNOV F.F., VERESHCHAGIN L.F. and GONCHAROVA V.A, Dokl. Akad, Nauk, SSSR 135, 1104 (1960); Eng, Transl., Soviet Phys. Doklady 135, 1280 (1960).
15.
1782
HEAT CAPACITY OF a-CERIUM BETWEEN 2.5 AND 20°K
Vol. 8, No. 21
16.
Another cerium sample containing a few per cent fi was run through the same cycle as described above and the presence of $ was immediately obvious in the heat capacity curve.
17.
FLEMING G.S. and LOUCKS T.S., Phys. Rev. 173, 685 (1968).
18.
LOUCKS T.S., Phys. Rev. 144, 504 (1966).
19.
PANOUSIS N.T. and GSCHNEIDNER Jr., K.A., Low temperature specific heat of cerium and cerium—yttrium alloys. To be published.
Es wurde zum ersten Mal bei normallem Druck die spezifische W~irme von a-Cerium, von anderen allotropischen Abwandlungen gereinigt, bei tiefen Temperatures gemessen. Die Tieftemperaturdaten lassen sich durch die Gleichung, C = 9.79 T + (12/5) rT4R( T/117)3 repr~sentiertwerden (C in Einheiten von mJ mole~deg~).