- Email: [email protected]
Low temperature specific heat of praseodymium magnesium nitrate
TECHNICAL
2231
NOTES
In conclusion, we note that the above simple model predicts the saturation macroscopic magnetisation to be & (8 + 8 - 12)gS = 0.57 Bohr magnetons per Fe ion, taking S arbitrarily as 2 and the g factor as 2 [ 181. Measured values are somewhat lower than this; better quantitative agreement probably requires the development of a more sophisticated theory.
14. The hype&e coupling constant for Fe is negative, See e.g. WERTHEIM G. Miissbauer Eflect, Chan. VII. Academic Press. New York (1964). 1.5. BESNUS M. J., MUNSCHY G. and MEYER A. J. P., J. appl. Phys. 39,903 (I 968). J. B., In Magnetism and the 16. GOODENOUGH Chemical Bond, p. 278. Interscience, New York (1963). E. and MURAKAMI M., J. Phys. 17. HIRAHARA Chem. Solids 7,281 (1958). 18. SCOlT G. G. and MEYER A. J. P., Phys. Rev. 23.1269 (1961).
Acknowledgements- We thank Professor S. Shtrikman for suggesting this problem and for the helpful guidance and advice during the course of the investigation. Thanks are also due to E. Hermon for preparing the material and for the X-ray analysis. LIONEL M. LEVINSON
J. Phys. Chem. Solids
D. TREVES Department of Electronics, Weizmann Institute of Science, Rehovot, Israel REFERENCES 1. Earlier references may be found in LandoZt-Bornstein, Vol. 9, Sect. 3-35. Springer-Verlag. Berlin (1962). 2. BESNUS M. J. and MEYER A. P. J., Proc. Znt. Conf. on Magnetism, Nottingham, 1964, p. 507. The Institute of Physics and the Physical Society. 3. SAT0 K., J. phys. Sot. Japan 21, 733 (1966). F. K., Phil. Res. Rep. 11, 190 4. LOTGERING (1956). E., J. phys. 5. ON0 K., IT0 A. and HIRAHARA Soc.Japan 17,1615(1962). 6. HAFNER S. and KALVIUS M., Z. Kristallogr. 123,443 (1966). 7. Relevant references are given by HAFNER S. and KALVIUS M. Z. Kristallogr. 123, 443 (1966). 8. BERTAUT E. F., Acta Crystallogr. 6, 557 (1953). 9. See for example references [2] and [3], and LUCAS C. and SOUTIF-GUICHERD J.. C. r. hebd s6anc Acad. Sci. Paris 263, 811 (1966); HIRONE T., SAT0 K. and YAMADA M., Proc. Znt. Conf. on Magnetism, Nottingham, 1964, p. 505. The Institute of Physics and the Physical-Society; and ADACHI K..J. Phvs. 24.725 (1963). ‘Effect Spectrometer,’ produced by 10. MGssbauer “Elron” Electronics Industries, Haifa, Isreal. 11. The coordination is well depicted by GOODENOUGH J. B. In Magnetism and the Chemical Bond, p. 276. Interscience Publishers, New York (1963). 12. See for example reference121 and BIN M. and PAUTHENET R., J. appl. Phys. 34, 1161 (1963). 13. WALKER L. R., WERTHEIM G. K. and JACCARINO V., Phys. Rev. Lett. 6, 98 (1961); de BENEDETTI S., LANG G. and INGALLIS R., Phys. Rev. Lett. 6,60 (1961).
Vol. 29, pp. 2231-2233.
Low temperature specific heat of praseodymium magnesium nitrate* (Received 15 April 1968) EXCEPT FOR
the specific heat measurements on cerium and lanthanum double nitrates by Bailey [ 11, no other calorimetric studies on the rare-earth double nitrates have been reported. The praseodymium magnesium nitrate result presented here is part of a program to measure the specific heat of the homologous series of salts with the general formula X,Mg, NO,),, - 24H20, (to be denoted in this letter as XMN) where X is a trivalent rare-earth ion. These crystals are grown by slow evaporation of the saturated solution of the double nitrate and have the shape of an hexagonal prism with two parallel horizontal surfaces. The average crystal weighs 15 g. The heat capacity measurements were performed in the temperature range 2-19°K in an adiabatic calorimeter employing a mechanical heat switch. In our initial work we measured the specific heat of the salts of La, Ce, and Pr. The La and Ce results agree to within 2 per cent with the work of Bailey. The Pr results are presented in Table 1 in the form of smoothed data, and in Fig. 1. Lanthanum has no 4f electrons so *Work partially supported by National Aeronautic and Space Administration Grant No. NGR 36-004-014.
2232
TECHNICAL
Tuble
1. Specific
heat of PrMN
(“K)
(J/mole-“K)
T (“K)
Cl. (J/mole-“K)
2 3 4 5 6 7 8 9 10
0.289 0.381 0.719 1.30 2.26 3.78 5.90 8.40 11.51
11 12 13 14 15 16 17 18 19
15.23 19.51 2460 30.21 36.72 43.68 50.01 56.94 63.48
CP
I
I
TEMPERATURE
( OK )
Fig. 1. Specific heat of PrMN vs. temperature. The points refer to experimental data of two different runs. The curve labeled C,,, is the estimated magnetic contribution to the total specific heat.
that LaMN is diamagnetic. It is therefore expected that the total specific heat of this salt is due only to the lattice vibrations. Furthermore, the differences in the dynamical properties of neighboring salts in the rareearth series are small, and one may assume that the lattice specific heat of the other salts is equal to the total specific heat of LaMN.
NOTES
The magnetic specific heat (C,) reported here was obtained by subtracting the smoothed LaMN data from the total specific heat of PrMN. The free PI?+ ion has an even number of 4felectrons and thus does not show a Kramers degeneracy. Assuming C,, symmetry for the crystal field, the ground state, 3H,. is split by the double nitrate crystal field into three singlets and three doublets. The energy level scheme was worked out by Judd[2] and is also given by Scott and Jeffries [3]. The ground state is a doublet and the first excited state is a singlet. Recently Culvahouse et a/.[41 showed that electric field induced transitions are the dominant absorption mechanism for the non-Kramers doublets for the resonance of PI3+ in the double nitrate crystal PrZnN. One would expect a similar effect in PrMN. The crystal lattice distortion resolves the lowest doublet by a splitting Ed. Our low temperature results do indeed indicate that this is the case. Analysis of the data below 2.5”K for a Schottky type anomaly (see the insert in the figure) suggests a splitting of l0 = O-45-+ 0.0.5”K. Clearly it would be worthwhile to map out the detailed structure of this Schottky anomaly. Work is now in progress to extend our measurements to lower temperatures. Above 6°K a second Schottky peak is visible, verifying that the singlet becomes populated at the higher temperatures. The separation of the singlet from the doublet was found to be E = 52.2 -+ 2.5”K with a ratio of the degeneracies of 0.54 which compares well with the expected value of fr. The result for the splitting is in good agreement with the value of 54.6”K obtained from the optical absorption data of Hellwege and Hellwege [51. This value was also verified by the spin-lattice relaxation measurements of Scott and Jeffries. Acknowled~ernents-We wish to thank Drs. J. W. Culvahouse and R. C. Sapp of the University of Kansas for suggesting this research and for their interest in the project. We are also grateful to Mr. J. Hoffman for growing the Pr crystal used in this work.
TECHNICAL W. H. RAUCKHORST*
University . of_ Cincinnati, Cincinnati, Ohio 45221, U.S.A.
H. FENICHEL
REFERENCES 1. BAILEY C. A., Proc.phys. Sot. 83,369 (1964). 2. JUDD B. R., Proc. R. Sot. A232,458 (1955). 3. SCOTT P. L. and JEFFRIES C. D., Phys. Rev. 127, 32 (1962). 4. CULVAHOUSE J. W., SCHINKE D. F. and FOSTER D. L., Phys. Rev. Lett. 18,117 (1967). 5. HELLWEGE A. M. and HELLWEGE K. H., Z. Phys. 135,92 (1953).
*Present Kentucky.
address:
J. Phys. Chem. pp. 2233-2236.
Bellarmine
Solids.
Pergamon
College,
Press
Louisville,
1968, Vol. 29.
Comments on the relation between band-gap energy in semiconductors and heats of formation (Received
1OApril 1968)
OBJECT of this brief paper is to explore further the proposal of Ruppel, Rose and Gerritsen[l] that the value of forbidden gap for a wide variety of semiconductors may be taken as lying approximately between one and two times the heats of formation per mole of the corresponding compounds. Theoretically, it is obvious that the values of heat of formation used must be taken as per equivalent (i.e. neither as per mole nor as per atom but as per atom equivalent)[2]. Heats of formation per mole may be divided by the number of total valencies (either cationic or anionic) participating in a compound, to obtain heat of formation per equivalent; e.g. heat of formation per equivalent for A&O, is Q of the heat of formation per mole for the same compound[2]. The probable reason for the original selection of values of heats of formation per mole was, it THE
NOTES
2233
believed, the fact that for Sb,S,, heat of formation per mole is quite close to the value of the forbidden gap[3]. This particular case, it will be shown, is rather fortuitous. Here an attempt has been made to explore the relation of the forbidden gap, Eg, of 73 semiconducting compounds to the corresponding heats of formation per equivalent (Fig. l), -AHfleq. and heats of formation per mole, -AHflmole. The main conclusions are listed below: (1) Only for three compounds out of 73. -AH,/mole = EQ+-20%. The compounds are Sb,S, (!), AlSb and ZnTe. (2) For 11 compounds out of 73, the relation, -AH,lmole = 2 X (-AHJeq.) = Eg k 20%, is obeyed. (3) For 2 1 compounds out of 73, the relation, 2 x (-AH,leq.) = Egk 20% # -AH,lmole, is valid. of 73, -AHJeq. = (4) For 4 compounds E, k 20%. (5) For 34 compounds out of 73, E,&20% is not related to heats of formation either per mole or per equivalent in any simple manner. The significance of these conclusions may be summarized as: (1) The relationship between E, and 2 x (--AHJeq.) is probably more significant than the relationship between heats of formation per mole and E,g (See Fig. I .). (2) Such relations are very approximate and not universally applicable. (3) For a great number of compounds in Ruppel et al. ‘s plot. E, is approximately equal to -AHflmole because for a majority of the compounds used in constructing that relationship, -AHflmole = 2 x (-AHf/eq.). The examples are ZnI,, CoCl,, PbCl,, PbBr,, Cd12, ZnO, ZnS, ZnSe, CdS, PbI*, PbO, Se,, Cu,O, PbS, SB,Tl$, CdTe, PbTe, ZnTe. From the foregoing discussion and from Fig. 1, it may be noted that the approximate relationship (ignoring for a moment the scatter in this plot), is
2231
NOTES
In conclusion, we note that the above simple model predicts the saturation macroscopic magnetisation to be & (8 + 8 - 12)gS = 0.57 Bohr magnetons per Fe ion, taking S arbitrarily as 2 and the g factor as 2 [ 181. Measured values are somewhat lower than this; better quantitative agreement probably requires the development of a more sophisticated theory.
14. The hype&e coupling constant for Fe is negative, See e.g. WERTHEIM G. Miissbauer Eflect, Chan. VII. Academic Press. New York (1964). 1.5. BESNUS M. J., MUNSCHY G. and MEYER A. J. P., J. appl. Phys. 39,903 (I 968). J. B., In Magnetism and the 16. GOODENOUGH Chemical Bond, p. 278. Interscience, New York (1963). E. and MURAKAMI M., J. Phys. 17. HIRAHARA Chem. Solids 7,281 (1958). 18. SCOlT G. G. and MEYER A. J. P., Phys. Rev. 23.1269 (1961).
Acknowledgements- We thank Professor S. Shtrikman for suggesting this problem and for the helpful guidance and advice during the course of the investigation. Thanks are also due to E. Hermon for preparing the material and for the X-ray analysis. LIONEL M. LEVINSON
J. Phys. Chem. Solids
D. TREVES Department of Electronics, Weizmann Institute of Science, Rehovot, Israel REFERENCES 1. Earlier references may be found in LandoZt-Bornstein, Vol. 9, Sect. 3-35. Springer-Verlag. Berlin (1962). 2. BESNUS M. J. and MEYER A. P. J., Proc. Znt. Conf. on Magnetism, Nottingham, 1964, p. 507. The Institute of Physics and the Physical Society. 3. SAT0 K., J. phys. Sot. Japan 21, 733 (1966). F. K., Phil. Res. Rep. 11, 190 4. LOTGERING (1956). E., J. phys. 5. ON0 K., IT0 A. and HIRAHARA Soc.Japan 17,1615(1962). 6. HAFNER S. and KALVIUS M., Z. Kristallogr. 123,443 (1966). 7. Relevant references are given by HAFNER S. and KALVIUS M. Z. Kristallogr. 123, 443 (1966). 8. BERTAUT E. F., Acta Crystallogr. 6, 557 (1953). 9. See for example references [2] and [3], and LUCAS C. and SOUTIF-GUICHERD J.. C. r. hebd s6anc Acad. Sci. Paris 263, 811 (1966); HIRONE T., SAT0 K. and YAMADA M., Proc. Znt. Conf. on Magnetism, Nottingham, 1964, p. 505. The Institute of Physics and the Physical-Society; and ADACHI K..J. Phvs. 24.725 (1963). ‘Effect Spectrometer,’ produced by 10. MGssbauer “Elron” Electronics Industries, Haifa, Isreal. 11. The coordination is well depicted by GOODENOUGH J. B. In Magnetism and the Chemical Bond, p. 276. Interscience Publishers, New York (1963). 12. See for example reference121 and BIN M. and PAUTHENET R., J. appl. Phys. 34, 1161 (1963). 13. WALKER L. R., WERTHEIM G. K. and JACCARINO V., Phys. Rev. Lett. 6, 98 (1961); de BENEDETTI S., LANG G. and INGALLIS R., Phys. Rev. Lett. 6,60 (1961).
Vol. 29, pp. 2231-2233.
Low temperature specific heat of praseodymium magnesium nitrate* (Received 15 April 1968) EXCEPT FOR
the specific heat measurements on cerium and lanthanum double nitrates by Bailey [ 11, no other calorimetric studies on the rare-earth double nitrates have been reported. The praseodymium magnesium nitrate result presented here is part of a program to measure the specific heat of the homologous series of salts with the general formula X,Mg, NO,),, - 24H20, (to be denoted in this letter as XMN) where X is a trivalent rare-earth ion. These crystals are grown by slow evaporation of the saturated solution of the double nitrate and have the shape of an hexagonal prism with two parallel horizontal surfaces. The average crystal weighs 15 g. The heat capacity measurements were performed in the temperature range 2-19°K in an adiabatic calorimeter employing a mechanical heat switch. In our initial work we measured the specific heat of the salts of La, Ce, and Pr. The La and Ce results agree to within 2 per cent with the work of Bailey. The Pr results are presented in Table 1 in the form of smoothed data, and in Fig. 1. Lanthanum has no 4f electrons so *Work partially supported by National Aeronautic and Space Administration Grant No. NGR 36-004-014.
2232
TECHNICAL
Tuble
1. Specific
heat of PrMN
(“K)
(J/mole-“K)
T (“K)
Cl. (J/mole-“K)
2 3 4 5 6 7 8 9 10
0.289 0.381 0.719 1.30 2.26 3.78 5.90 8.40 11.51
11 12 13 14 15 16 17 18 19
15.23 19.51 2460 30.21 36.72 43.68 50.01 56.94 63.48
CP
I
I
TEMPERATURE
( OK )
Fig. 1. Specific heat of PrMN vs. temperature. The points refer to experimental data of two different runs. The curve labeled C,,, is the estimated magnetic contribution to the total specific heat.
that LaMN is diamagnetic. It is therefore expected that the total specific heat of this salt is due only to the lattice vibrations. Furthermore, the differences in the dynamical properties of neighboring salts in the rareearth series are small, and one may assume that the lattice specific heat of the other salts is equal to the total specific heat of LaMN.
NOTES
The magnetic specific heat (C,) reported here was obtained by subtracting the smoothed LaMN data from the total specific heat of PrMN. The free PI?+ ion has an even number of 4felectrons and thus does not show a Kramers degeneracy. Assuming C,, symmetry for the crystal field, the ground state, 3H,. is split by the double nitrate crystal field into three singlets and three doublets. The energy level scheme was worked out by Judd[2] and is also given by Scott and Jeffries [3]. The ground state is a doublet and the first excited state is a singlet. Recently Culvahouse et a/.[41 showed that electric field induced transitions are the dominant absorption mechanism for the non-Kramers doublets for the resonance of PI3+ in the double nitrate crystal PrZnN. One would expect a similar effect in PrMN. The crystal lattice distortion resolves the lowest doublet by a splitting Ed. Our low temperature results do indeed indicate that this is the case. Analysis of the data below 2.5”K for a Schottky type anomaly (see the insert in the figure) suggests a splitting of l0 = O-45-+ 0.0.5”K. Clearly it would be worthwhile to map out the detailed structure of this Schottky anomaly. Work is now in progress to extend our measurements to lower temperatures. Above 6°K a second Schottky peak is visible, verifying that the singlet becomes populated at the higher temperatures. The separation of the singlet from the doublet was found to be E = 52.2 -+ 2.5”K with a ratio of the degeneracies of 0.54 which compares well with the expected value of fr. The result for the splitting is in good agreement with the value of 54.6”K obtained from the optical absorption data of Hellwege and Hellwege [51. This value was also verified by the spin-lattice relaxation measurements of Scott and Jeffries. Acknowled~ernents-We wish to thank Drs. J. W. Culvahouse and R. C. Sapp of the University of Kansas for suggesting this research and for their interest in the project. We are also grateful to Mr. J. Hoffman for growing the Pr crystal used in this work.
TECHNICAL W. H. RAUCKHORST*
University . of_ Cincinnati, Cincinnati, Ohio 45221, U.S.A.
H. FENICHEL
REFERENCES 1. BAILEY C. A., Proc.phys. Sot. 83,369 (1964). 2. JUDD B. R., Proc. R. Sot. A232,458 (1955). 3. SCOTT P. L. and JEFFRIES C. D., Phys. Rev. 127, 32 (1962). 4. CULVAHOUSE J. W., SCHINKE D. F. and FOSTER D. L., Phys. Rev. Lett. 18,117 (1967). 5. HELLWEGE A. M. and HELLWEGE K. H., Z. Phys. 135,92 (1953).
*Present Kentucky.
address:
J. Phys. Chem. pp. 2233-2236.
Bellarmine
Solids.
Pergamon
College,
Press
Louisville,
1968, Vol. 29.
Comments on the relation between band-gap energy in semiconductors and heats of formation (Received
1OApril 1968)
OBJECT of this brief paper is to explore further the proposal of Ruppel, Rose and Gerritsen[l] that the value of forbidden gap for a wide variety of semiconductors may be taken as lying approximately between one and two times the heats of formation per mole of the corresponding compounds. Theoretically, it is obvious that the values of heat of formation used must be taken as per equivalent (i.e. neither as per mole nor as per atom but as per atom equivalent)[2]. Heats of formation per mole may be divided by the number of total valencies (either cationic or anionic) participating in a compound, to obtain heat of formation per equivalent; e.g. heat of formation per equivalent for A&O, is Q of the heat of formation per mole for the same compound[2]. The probable reason for the original selection of values of heats of formation per mole was, it THE
NOTES
2233
believed, the fact that for Sb,S,, heat of formation per mole is quite close to the value of the forbidden gap[3]. This particular case, it will be shown, is rather fortuitous. Here an attempt has been made to explore the relation of the forbidden gap, Eg, of 73 semiconducting compounds to the corresponding heats of formation per equivalent (Fig. l), -AHfleq. and heats of formation per mole, -AHflmole. The main conclusions are listed below: (1) Only for three compounds out of 73. -AH,/mole = EQ+-20%. The compounds are Sb,S, (!), AlSb and ZnTe. (2) For 11 compounds out of 73, the relation, -AH,lmole = 2 X (-AHJeq.) = Eg k 20%, is obeyed. (3) For 2 1 compounds out of 73, the relation, 2 x (-AH,leq.) = Egk 20% # -AH,lmole, is valid. of 73, -AHJeq. = (4) For 4 compounds E, k 20%. (5) For 34 compounds out of 73, E,&20% is not related to heats of formation either per mole or per equivalent in any simple manner. The significance of these conclusions may be summarized as: (1) The relationship between E, and 2 x (--AHJeq.) is probably more significant than the relationship between heats of formation per mole and E,g (See Fig. I .). (2) Such relations are very approximate and not universally applicable. (3) For a great number of compounds in Ruppel et al. ‘s plot. E, is approximately equal to -AHflmole because for a majority of the compounds used in constructing that relationship, -AHflmole = 2 x (-AHf/eq.). The examples are ZnI,, CoCl,, PbCl,, PbBr,, Cd12, ZnO, ZnS, ZnSe, CdS, PbI*, PbO, Se,, Cu,O, PbS, SB,Tl$, CdTe, PbTe, ZnTe. From the foregoing discussion and from Fig. 1, it may be noted that the approximate relationship (ignoring for a moment the scatter in this plot), is