Quantum-Mechanical Theory of Orientational Ordering in Solid Methanes

1972 ◽  
Vol 50 (13) ◽  
pp. 1568-1578 ◽  
Author(s):  
S. Alexander ◽  
M. Lerner-Naor
Keyword(s):  
Low Temperature ◽  
Field Approximation ◽  
Quantum Mechanical ◽  
Temperature Phase ◽  
Mechanical Theory ◽  
Crystal Fields ◽  
Quantum Mechanical Theory ◽  
Full Symmetry ◽  
Orientational Ordering ◽  
Low Temperature Phase

The quantum-mechanical theory of the low temperature phase transitions of the solid methanes is discussed. It is shown how the standard techniques for treating the molecular field approximation can be applied to these problems. It is shown how internal and external symmetries should be combined so as to utilize the full symmetry of the problem. This analysis is quite general and applicable to all problems of orientational ordering. Results of detailed calculations for the James–Keenan model of CH4 and CD4 are presented and compared with experimental results. The calculations assume octupole interactions, include no crystal fields, and include all states up to J = 6. It is suggested that the inclusion of crystal field and possibly states of higher J is essential for describing the low temperature behavior.

Static and dynamic crystal-field effects in ferrous fluosilicate

1987 ◽  
Vol 65 (10) ◽  
pp. 1280-1293 ◽  
Author(s):  
D. C. Price
Keyword(s):  
Low Temperature ◽  
Crystal Field ◽  
Metal Ion ◽  
Vibronic Coupling ◽  
Spin Lattice Relaxation ◽  
Temperature Phase ◽  
Relaxation Rates ◽  
Zinc Compounds ◽  
Crystal Fields ◽  
Low Temperature Phase

This paper examines the crystal fields acting on Fe2+ ions in ferrous fluosilicate, and the way that they influence the magnetic and spectroscopic properties of the compound. The crystal structures of ferrous fluosilicate and of the structurally similar magnesium, manganese, cobalt, nickel, and zinc compounds are described to establish the point symmetries of the metal-ion sites. In the low-temperature monoclinic (P21/c) phase of the Fe2+, Mg2+, Co2+, and Mn2+ compounds, although the metal-ion site is required crystallographically to have only inversion symmetry, all of the available low-temperature data are consistent with a crystal field of C2h symmetry. In the high-temperature phases of these salts, and for nickel and zinc fluosilicates at all temperatures, the site symmetries are either exactly or approximately C3i. The dominant effect of the phase transition on the Fe2+ crystal field in FeSiF6∙6H2O is to remove the nonaxial terms [Formula: see text] and [Formula: see text] that are present in the low-temperature phase. The other terms appear to be relatively unaffected.Both the time-dependent (spin-lattice relaxation) and time-independent (vibronic coupling) manifestations of the dynamic crystal field at the Fe2+ ions are qualitatively examined. A new interpretation of the 57Fe Mössbauer spectra of FeSiF6∙6H2O in the low-temperature phase is described, from which relaxation rates comparable to those deduced from other measurements are obtained. Evidence that the measured 57Fe Mössbauer quadrupole splittings of Fe2+ ions in FeSiF6∙6H2O and in ZnSiF6∙6H2O show significant effects of vibronic coupling is examined.

Low‐temperature phase formation in the SrF 2 ‐ LaF 3 system

2020 ◽  
Author(s):  
Pavel P. Fedorov ◽  
Alexander A. Alexandrov ◽  
Valery V. Voronov ◽  
Maria N. Mayakova ◽  
Alexander E. Baranchikov ◽  
...  
Keyword(s):  
Low Temperature ◽  
Phase Formation ◽  
Temperature Phase ◽  
Low Temperature Phase
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