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Heat capacity and phase transition of some f.c.c. hexammine iodides above 1 K
Physica 51 (1971) 630-633 o North-Holland Publishing Co.
LETTER
HEAT
CAPACITY
TO THE EDITOR
AND PHASE
OF SOME F.C.C. HEXAMMINE
TRANSITION
IODIDES
ABOVE
1K
F. W. KLAAI JSEN, H. SUGA* and 2. DOKOUPIL Kamerlingh Onnes Laboratory, Leiden, Nederland Received 26 January 1971
Synopsis Heat capacity of a series of f.c.c. hexammine iodides was measured from 1.3-80 K. A method for the separation of different contributions to the heat capacity has been suggested. The transition temperatures, T c, were determined and a rough estimate of the orientational entropy was calculated on the basis of a librational behaviour of the NHs molecules in the solid.
The existence of a transition in some Ni-hexammine halides was noted by Palma-Vitorellii) in EPR measurements in 1960. The entropy anomaly below 1 K, found by van Kempens) in 1964, confirmed the librator behaviour of the NHs-groups in the hexammine molecules. In 1969 Bates and Stevenss) considered theoretically the possibility of the orientational ordering of the oscillating NHs-groups in the nickelhexammine halides and calculated the energy in the less symmetric phase below the transition temperature. In some papers23 3, one could find a remark concerning the entropy change of about R In 3 per mole for nickelhexammine iodide (Miss Voorhoeve, unpublished). In order to investigate systematically the thermal behaviour of these compounds we performed heat-capacity measurements for X(NHs)6Is, X = Ni, Co, Mn, Zn, Cd and Ca. As the molecule contains six NHs-groups, large effects could be expected. Most of our samples were prepared using the dry methodd). The calorimetric measurements were carried out in the usual manner. The results of the heat-capacity measurements between 1.3 and 80 K are graphically presented for the six samples in fig. 1. The plotted points show a well-defined phase transition at temperatures T, = 19.7, 20.9, 25.0, 25.4, 32.6, 51.8 K for the Ni, Co, Mn, Zn, Cd and Ca samples, respectively. At low temperatures (l-2 K) there is excellent agreement between our measurements and those of Van Kempens) and Sugas). In the temperature region 4-7 K all curves show nearly the same temperature dependence. For T > 70 K, howt On leave of absence from Osaka University, Toyonaka, Osaka, Japan.
HEAT CAPACITY
OF HEXAMMINE
IODIDES
631
Fig. 1. Specific heats C vewus temperature T for X(NHs)&. X = 0 Ni, 0 Co, A Mn, q Zn, A Cd, o Ca.
ever, there seems to exist a systematic increase of the heat capacity for samples having higher T,. In the temperature range close to 1.3 K we can localize the tails of the anomalies below 1 K for the Ni and Mn salt27 5). The Cd and Ca sample, however, do not show a rising heat capacity towards lower temperatures. For the Co and Zn samples data below 7 K are not yet available. We want to mention as a preliminary result that Tc for the Fe salt is 40.7 K. The shape of the transition peaks is apparently not the same for various compounds. One can evaluate the entropy contribution of the transition peak, A&, subtracting a lattice contribution by a smooth interpolation of the total heat capacity curve below and above the transition temperature. The AS, values are 8.2, 10.5, 15.6, 10.6, 21.0, and 29.8 J/mole K (Rln 3 -R In 32). In order to calculate a more realistic entropy contribution associated with the transition, ASr, we need to make a better approximation for the total heat capacity of the lattice, C,tot. This contribution can be split up into a librational, Car, and a vibrational part. The existence of a librational mode follows from a Schottky anomaly below 1 K due to the splitting of the ground rotational level of the NH3 molecule2.3). The six NH3 groups
F. W. KLAAIJSEN,
632
H. SUGA AND Z. DOKOUPIL
in one molecule thus behave like one-dimensional rotators executing torsional oscillations around some equilibrium configuration under the influence of the threefold barrier Ve/k (K = Boltzmann constant). For the Ni, Co, and Mn sample the numerical evaluation of the Schottky anomaly provides a useful order of magnitude for the heights of the potentional barrier. For these samples Va/k has approximately the same value, namely 250 K2~5). For large values of Ve/K, however, the splitting of the ground level becomes too small to be observed in the temperature range 0. l-l K. Although there are no experimental data for the Cd and Ca sample below 1 K we can conclude from the monotonic decrease of our data that Vo/k > 400 K. Because of small values of Vo/k and the relatively low temperature region, the well-known tables of Pitzer and Gwinn6) could not be used for calculation of Chr: Therefore, using the tables for the characteristic values of the Mathieu equation7) together with the proper statistical weights for threefold symmetry of a NH3 libratorg), we determined the first 33 energy levels. For a fixed set of Ire/K values we calculated the heat capacity of such a hindered rotator, Chr ,in the temperature range O-250 K. The preliminary results are shown in fig. 2 for six NH3 groups. The subtraction of Chr from the measured specific heat allows us to make an approximate adjustment of the vibrational contribution to the heat capacity in the temperature regions outside the transition peak. The lowtemperature region (2-5 K) provides one three-dimensional Debye function, 3D(Or). After subtraction of 3D(Or) the rest of the vibrational modes needs
J mole
K
40
0 0
T
_
50
100
150
200
Fig. 2. Specific heats Chr VIYSUS temperature T for 6NH3.
K
250
HEAT CAPACITY
to be approximated
OF HEXAMMINE
by additional
interval 70-80 K. The from the total measured A!$*, for those samples now in contradiction to AS, = R In 32 for most
Debye
IODIDES
and Einstein
633
functions
in the
subsequent subtraction of this third contribution heat capacity allows us to compute the entropy, where the necessary data were available. We find the AS, values nearly the same amount of entropy of the samples.
The series of investigated hexammine iodides seems to have roughly the same amount of entropy for the transition, which indicates that the transitions might have the same physical background. A detailed and extensive analysis of the possible orientational transition of the hexammine halides has been performed theoretically by Bates and Stevenss) on the basis of an electrostatic interaction model between the protons of the NH3 groups. The suggestion arises therefore that the order-disorder transition entropy AS, 2 R In 32 could be correlated with a possible number of 32 low-energy inter-cluster configurations of the NH3 octahedral clusters throughout the whole crystals). Acknowledgement. for valuable suggestions
We are much indebted to Professor and interest throughout the work.
C. J. Gorter
REFERENCES
1) Palma-Vitorelli, M. B., Palma, M. V., Drewes, G. W. J. and Koerts, W., Physica 26 (1960) 922.
4 Van Kempen, H., Duffy, W. T., Miedema, A. R. and Huiskamp, W. J., Physica 3) 4) 5) 6) 7) 8) 9)
30 (1964) 1131; 31 (1965) 678. Bates, A. R. and Stevens, K. W. H., J. Phys. C2 (1969) 1573; Bates, A. R., thesis (1965) unpublished. Ephraim, F., Ber. Deutsche Chem. Gesell. 45 (19 12) 1322. Suga, H., Blote, H. W. J., Lagendijk, E. and Huiskamp, W. J., Proc. Int. Conf. on Low Temp. Phys., LT 12, Kyoto, Japan (1970). Pitzer, K. S. and Gwinn, W. D., J. them. Phys. 10 (1942) 428. Tables Relating to Mathieu Functions, Columbia Univ. Press (New York, 1967). Kilb, R. W., Tables for Mathieu Eigenvalues and Eigenfunctions for special Boundary Conditions, Dept. of Chem., Harvard University (1956). Wilson, E. B., Jr., J. them. Phys. 3 (1935) 276.
LETTER
HEAT
CAPACITY
TO THE EDITOR
AND PHASE
OF SOME F.C.C. HEXAMMINE
TRANSITION
IODIDES
ABOVE
1K
F. W. KLAAI JSEN, H. SUGA* and 2. DOKOUPIL Kamerlingh Onnes Laboratory, Leiden, Nederland Received 26 January 1971
Synopsis Heat capacity of a series of f.c.c. hexammine iodides was measured from 1.3-80 K. A method for the separation of different contributions to the heat capacity has been suggested. The transition temperatures, T c, were determined and a rough estimate of the orientational entropy was calculated on the basis of a librational behaviour of the NHs molecules in the solid.
The existence of a transition in some Ni-hexammine halides was noted by Palma-Vitorellii) in EPR measurements in 1960. The entropy anomaly below 1 K, found by van Kempens) in 1964, confirmed the librator behaviour of the NHs-groups in the hexammine molecules. In 1969 Bates and Stevenss) considered theoretically the possibility of the orientational ordering of the oscillating NHs-groups in the nickelhexammine halides and calculated the energy in the less symmetric phase below the transition temperature. In some papers23 3, one could find a remark concerning the entropy change of about R In 3 per mole for nickelhexammine iodide (Miss Voorhoeve, unpublished). In order to investigate systematically the thermal behaviour of these compounds we performed heat-capacity measurements for X(NHs)6Is, X = Ni, Co, Mn, Zn, Cd and Ca. As the molecule contains six NHs-groups, large effects could be expected. Most of our samples were prepared using the dry methodd). The calorimetric measurements were carried out in the usual manner. The results of the heat-capacity measurements between 1.3 and 80 K are graphically presented for the six samples in fig. 1. The plotted points show a well-defined phase transition at temperatures T, = 19.7, 20.9, 25.0, 25.4, 32.6, 51.8 K for the Ni, Co, Mn, Zn, Cd and Ca samples, respectively. At low temperatures (l-2 K) there is excellent agreement between our measurements and those of Van Kempens) and Sugas). In the temperature region 4-7 K all curves show nearly the same temperature dependence. For T > 70 K, howt On leave of absence from Osaka University, Toyonaka, Osaka, Japan.
HEAT CAPACITY
OF HEXAMMINE
IODIDES
631
Fig. 1. Specific heats C vewus temperature T for X(NHs)&. X = 0 Ni, 0 Co, A Mn, q Zn, A Cd, o Ca.
ever, there seems to exist a systematic increase of the heat capacity for samples having higher T,. In the temperature range close to 1.3 K we can localize the tails of the anomalies below 1 K for the Ni and Mn salt27 5). The Cd and Ca sample, however, do not show a rising heat capacity towards lower temperatures. For the Co and Zn samples data below 7 K are not yet available. We want to mention as a preliminary result that Tc for the Fe salt is 40.7 K. The shape of the transition peaks is apparently not the same for various compounds. One can evaluate the entropy contribution of the transition peak, A&, subtracting a lattice contribution by a smooth interpolation of the total heat capacity curve below and above the transition temperature. The AS, values are 8.2, 10.5, 15.6, 10.6, 21.0, and 29.8 J/mole K (Rln 3 -R In 32). In order to calculate a more realistic entropy contribution associated with the transition, ASr, we need to make a better approximation for the total heat capacity of the lattice, C,tot. This contribution can be split up into a librational, Car, and a vibrational part. The existence of a librational mode follows from a Schottky anomaly below 1 K due to the splitting of the ground rotational level of the NH3 molecule2.3). The six NH3 groups
F. W. KLAAIJSEN,
632
H. SUGA AND Z. DOKOUPIL
in one molecule thus behave like one-dimensional rotators executing torsional oscillations around some equilibrium configuration under the influence of the threefold barrier Ve/k (K = Boltzmann constant). For the Ni, Co, and Mn sample the numerical evaluation of the Schottky anomaly provides a useful order of magnitude for the heights of the potentional barrier. For these samples Va/k has approximately the same value, namely 250 K2~5). For large values of Ve/K, however, the splitting of the ground level becomes too small to be observed in the temperature range 0. l-l K. Although there are no experimental data for the Cd and Ca sample below 1 K we can conclude from the monotonic decrease of our data that Vo/k > 400 K. Because of small values of Vo/k and the relatively low temperature region, the well-known tables of Pitzer and Gwinn6) could not be used for calculation of Chr: Therefore, using the tables for the characteristic values of the Mathieu equation7) together with the proper statistical weights for threefold symmetry of a NH3 libratorg), we determined the first 33 energy levels. For a fixed set of Ire/K values we calculated the heat capacity of such a hindered rotator, Chr ,in the temperature range O-250 K. The preliminary results are shown in fig. 2 for six NH3 groups. The subtraction of Chr from the measured specific heat allows us to make an approximate adjustment of the vibrational contribution to the heat capacity in the temperature regions outside the transition peak. The lowtemperature region (2-5 K) provides one three-dimensional Debye function, 3D(Or). After subtraction of 3D(Or) the rest of the vibrational modes needs
J mole
K
40
0 0
T
_
50
100
150
200
Fig. 2. Specific heats Chr VIYSUS temperature T for 6NH3.
K
250
HEAT CAPACITY
to be approximated
OF HEXAMMINE
by additional
interval 70-80 K. The from the total measured A!$*, for those samples now in contradiction to AS, = R In 32 for most
Debye
IODIDES
and Einstein
633
functions
in the
subsequent subtraction of this third contribution heat capacity allows us to compute the entropy, where the necessary data were available. We find the AS, values nearly the same amount of entropy of the samples.
The series of investigated hexammine iodides seems to have roughly the same amount of entropy for the transition, which indicates that the transitions might have the same physical background. A detailed and extensive analysis of the possible orientational transition of the hexammine halides has been performed theoretically by Bates and Stevenss) on the basis of an electrostatic interaction model between the protons of the NH3 groups. The suggestion arises therefore that the order-disorder transition entropy AS, 2 R In 32 could be correlated with a possible number of 32 low-energy inter-cluster configurations of the NH3 octahedral clusters throughout the whole crystals). Acknowledgement. for valuable suggestions
We are much indebted to Professor and interest throughout the work.
C. J. Gorter
REFERENCES
1) Palma-Vitorelli, M. B., Palma, M. V., Drewes, G. W. J. and Koerts, W., Physica 26 (1960) 922.
4 Van Kempen, H., Duffy, W. T., Miedema, A. R. and Huiskamp, W. J., Physica 3) 4) 5) 6) 7) 8) 9)
30 (1964) 1131; 31 (1965) 678. Bates, A. R. and Stevens, K. W. H., J. Phys. C2 (1969) 1573; Bates, A. R., thesis (1965) unpublished. Ephraim, F., Ber. Deutsche Chem. Gesell. 45 (19 12) 1322. Suga, H., Blote, H. W. J., Lagendijk, E. and Huiskamp, W. J., Proc. Int. Conf. on Low Temp. Phys., LT 12, Kyoto, Japan (1970). Pitzer, K. S. and Gwinn, W. D., J. them. Phys. 10 (1942) 428. Tables Relating to Mathieu Functions, Columbia Univ. Press (New York, 1967). Kilb, R. W., Tables for Mathieu Eigenvalues and Eigenfunctions for special Boundary Conditions, Dept. of Chem., Harvard University (1956). Wilson, E. B., Jr., J. them. Phys. 3 (1935) 276.