Padé-approximant study of the phase transition of ortho–para mixtures in solid hydrogen

1987 ◽  
Vol 65 (11) ◽  
pp. 1552-1553
Author(s):  
Hiroshi Miyagi ◽  
Akira Mishima ◽  
Tuto Nakamura
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
High Temperature ◽  
Transition Temperature ◽  
Solid Hydrogen ◽  
Temperature Phase ◽  
Ortho Hydrogen ◽  
Temperature Expansion ◽  
High Temperature Expansion ◽  
Low Temperature Phase

The phase transition of solid hydrogen is studied in the Padé approximation, with newly calculated coefficients in the high-temperature expansion series for the free energy. For the low-temperature phase, the free energy is obtained by a previous libron study of ortho–para mixtures. The transition temperature is predicted to be 2.1Γ for pure ortho-hydrogen. The phase transition disappears at ~ 60% of ortho-hydrogen, in agreement with experiment.

35Cl NQR Studies of Hexachlorometallates(IV) with Organic Cations, A2 [MCl6] and A'[MCl6], M=Sn, Te, Pb and A+, A'2+ = Organic Cation

1990 ◽  
Vol 45 (3-4) ◽  
pp. 293-302 ◽  
Author(s):  
Dirk Borchers ◽  
Alarich Weiss
Keyword(s):  
Phase Transition ◽  
High Temperature ◽  
Low Temperature ◽  
Resonance Line ◽  
Organic Cation ◽  
Phase Changes ◽  
Organic Cations ◽  
Temperature Phase ◽  
35Cl Nqr ◽  
Low Temperature Phase

Abstract35Cl NQR spectra of eleven hexachlorometallates (IV) A1 [MCl6] and A'[MCl6], M = Sn, Te, Pb, and A+ =ethylammonium, 4-picolinium, anilinium, triethylammonium, chinoxalinium, and piperi-dinium ions, and A'2+ = 1.3-propylenediammonium ion, have been observed as a function of tem-perature. The ethylammonium hexachlorometallates(IV) (C2H5 NH3)2 [MCl6], M = Sn, Te, show a phase transition at 128.8 K and 204 K, respectively. Both compounds yield a single resonance line in their high temperature phases. In case of the stannate this single 35Cl resonance line splits up into two lines at Tc = 128.8 K, whereas for the tellurate no 35Cl NQR signals could be found in the low temperature phase. A phase transition was also found for the 1.3-propylenediammonium hexa-chlorostannate(IV) at 287 K where the six line NQR spectrum of the low temperature phase changes into a four line spectrum. In contrast, the corresponding plumbate shows no transition. All other compounds studied contain distorted [MCl6]2- octahedra, and therefore they yield more than one 35Cl resonance line. The complexes have been investigated in the temperature range temperature where the lines fade out. In case of the hexachlorostannates(IV) with the ethylammonium, the 1.3-propylenediammonium and the triethylammonium ions, the crystal structures of the compounds are known and compared with the results of the 35Cl NQR spectroscopy.

Phase transitions in solid cycloheptene

1990 ◽  
Vol 68 (4) ◽  
pp. 604-611 ◽  
Author(s):  
Julian Haines ◽  
D. F. R. Gilson
Keyword(s):  
Phase Transition ◽  
High Temperature ◽  
Low Temperature ◽  
Lattice Relaxation ◽  
Proton Spin ◽  
Spin Lattice Relaxation ◽  
Temperature Phase ◽  
Scanning Calorimetry ◽  
Spin Lattice ◽  
Low Temperature Phase

The phase transition behaviour of cycloheptene has been investigated by differential scanning calorimetry, proton spin-lattice relaxation, and vibrational spectroscopy (infrared and Raman). Two solid–solid phase transitions were observed, at 154 and 210 K, with transition enthalpies and entropies of 5.28 and 0.71 kJ mol−1 and 34.3 and 3.4 JK−1, respectively. Cycloheptene melted at 217 K with an entropy of melting of 4.5 JK−1 mol−1. The bands in the vibrational spectra of the two high temperature phases were broad and featureless, characteristic of highly disordered phases. The presence of other conformers, in addition to the chair form, was indicated from bands in the spectra. The ring inversion mode was highly phase dependent and exhibited soft mode type behaviour prior to the transition from the low temperature phase. The low frequency Raman spectra (external modes) of these phases indicated that the molecules are undergoing isotropic reorientation. In the low temperature phase, the vibrational bands were narrow; the splitting of the fundamentals into two components and the presence of nine external modes are consistent with unit cell symmetry of either C2 or Cs with two molecules per primitive unit cell. A glassy state can be produced from the intermediate phase and the vibrational spectra were very similar to those of the high temperature phases, indicating that static disorder was present. The barriers to reorientation, as obtained from proton spin-lattice relaxation measurements, are 9.0 kJ mol−1 in both the high temperature phases, and 15.4 kJ mol−1 in the low temperature, ordered phase. Keywords: cycloheptene, phase transition, differential scanning calorimetry, NMR, vibrational spectroscopy.

HIGH-TEMPERATURE SERIES FOR THERMODYNAMIC FUNCTIONS

2003 ◽  
Vol 02 (01) ◽  
pp. 1-5 ◽  
Author(s):  
FRANCISCO M. FERNÁNDEZ
Keyword(s):  
Free Energy ◽  
Perturbation Theory ◽  
High Temperature ◽  
Thermodynamic Functions ◽  
Temperature Series ◽  
Present Approach ◽  
Rigid Rotor ◽  
Temperature Expansion ◽  
High Temperature Expansion

We propose a high-temperature expansion for thermodynamic functions. As an example we calculate the free energy for a restricted plane rigid rotor and compare present approach with perturbation theory.

Single-crystal structure refinement of NaTiSi2O6 clinopyroxene at low temperatures (298 < T < 100 K)

2003 ◽  
Vol 59 (6) ◽  
pp. 730-746 ◽  
Author(s):  
Günther J. Redhammer ◽  
Haruo Ohashi ◽  
Georg Roth
Keyword(s):  
Phase Transition ◽  
High Temperature ◽  
Low Temperature ◽  
Bond Length ◽  
Octahedral Site ◽  
Tetrahedral Site ◽  
Temperature Phase ◽  
Bond Lengths ◽  
Distortion Parameters ◽  
Low Temperature Phase

The alkali-metal clinopyroxene NaTi3+Si2O6, one of the rare compounds with trivalent titanium, was synthesized at high temperature/high pressure and subsequently investigated by single-crystal X-ray diffraction methods between 298 and 100 K. One main difference between the high- and the low-temperature form is the sudden appearance of two different Ti3+—Ti3+ interatomic distances within the infinite chain of the TiO6 octahedra just below 197 K. This change can be seen as direct evidence for the formation of Ti—Ti singlet pairs in the low-temperature phase. Mean Ti—O bond lengths smoothly decrease with decreasing temperature and the phase transition is associated with a slight jump in the Ti—O bond length. The break in symmetry, however, causes distinct variations, especially with respect to the two Ti—Oapex bond lengths, but also with respect to the four Ti—O bonds in the equatorial plane of the octahedron. The TiO6 octahedron appears to be stretched in the chain direction with a slightly larger elongation in the P\bar 1 low-temperature phase compared with the C2/c high-temperature phase. Polyhedral distortion parameters such as bond-length distortion and octahedral angle variance suggest the TiO6 octahedron in P\bar 1 to be closer to the geometry of an ideal octahedron than in C2/c. Mean Na—O bond lengths decrease with decreasing temperature and the variations in individual Na—O bond lengths are the result of variations in the geometry of the octahedral site. The tetrahedral site acts as a rigid unit, which does not show pronounced changes upon cooling and through the phase transitions. There are neither large changes in bond lengths and angles nor in polyhedral distortion parameters, for the tetrahedral site, when they are plotted. In contrast with the C2/c → P21/c phase transition, found especially in LiMSi2O6 clinopyroxenes, no very large variations are found for the tetrahedral bridging angle. Thus, it is concluded that the main factor inducing the phase transition and controlling the structural variations is the M1 octahedral site.

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