Effect of the zero-point rotational motions on the quadrupolar glass order parameter in solid hydrogen

1994 ◽  
Vol 50 (17) ◽  
pp. 12437-12440 ◽  
Author(s):  
K. Lukierska-Walasek ◽  
K. Walasek
Keyword(s):  
Order Parameter ◽  
Zero Point ◽  
Solid Hydrogen ◽  
Rotational Motions ◽  
Quadrupolar Glass

Calculation of the order parameter of solid hydrogen in the quadrupolar-glass phase

1994 ◽  
Vol 49 (14) ◽  
pp. 9460-9468 ◽  
Author(s):  
K. Walasek ◽  
K. Lukierska-Walasek
Keyword(s):  
Order Parameter ◽  
Glass Phase ◽  
Solid Hydrogen ◽  
Quadrupolar Glass

THEORY OF THE INTERACTION BETWEEN THE LATTICE VIBRATIONS AND THE ROTATIONAL MOTION IN SOLID HYDROGEN

1966 ◽  
Vol 44 (2) ◽  
pp. 313-335 ◽  
Author(s):  
J. Van Kranendonk ◽  
V. F. Sears
Keyword(s):  
Rotational Motion ◽  
Zero Point ◽  
Solid Hydrogen ◽  
The Self ◽  
Intermolecular Potential ◽  
Lattice Vibrations ◽  
Energy Effect ◽  
Self Energy ◽  
Blowing Up ◽  
Point Lattice

The effects of the interaction between the rotational motion of the molecules in solid hydrogen and the lattice vibrations, resulting from the anisotropic van der Waals forces, have been investigated theoretically. For the radial part of the anisotropic intermolecular potential an exp–6 model has been adopted. First, the effect of the lattice vibrations, and of the anistropic blowing up of the crystal by the zero-point lattice vibrations, is discussed. The effective anisotropic interaction resulting from averaging the instantaneous interaction over the lattice vibrations is calculated by assuming a Gaussian distribution for the modulation of the relative intermolecular separations by the lattice vibrations. Secondly, the displacement of the rotational levels due to the self-energy of the molecules in the lattice is calculated both classically and quantum mechanically, and the resulting shifts in the frequencies of the rotational transitions in solid hydrogen are given. Finally, the splitting of the rotational levels due to the anisotropy of the self-energy effect is calculated. The theory is applied to the calculation of the asymmetry of the S0(0) triplet in the rotational Raman spectrum of solid parahydrogen, and of the specific heat anomaly in solid hydrogen at low ortho-concentrations.

Elastic anomalies of Hg2X2 compounds

1992 ◽  
Vol 70 (9) ◽  
pp. 745-751
Author(s):  
K. S. Viswanathan ◽  
J. C. Jeeja Ramani
Keyword(s):  
Elastic Constants ◽  
Fourth Order ◽  
Order Parameter ◽  
Zero Point ◽  
Stability Conditions ◽  
Point Energy ◽  
The Third ◽  
Limit Formula ◽  
The Stability ◽  
Elastic Anomalies

The anomalies of the second-, third-, and fourth-order elastic constants are considered for the phase transition of Hg2X2 type of compounds. Expressions are obtained for the equilibrium values of the order parameters in the ferroelastic phase from the stability conditions. The fluctuation in the order parameter is evaluated from the Landau–Khalatnikov equation. An expression is derived for the shift in the zero-point energy in the low-temperature ferroelastic phase and the specific heat anomaly. It is shown that these are proportional to (T − T)2 and (T − Tc), respectively. All the anomalies of the second-order elastic (SOE) constants are obtained from a single general formula, and relations among them are established. The temperature variation of the SOE constants in the limit [Formula: see text] is discussed. Similarly, expressions are derived for the anomalies of the third- and fourth-order elastic constants. In the limit [Formula: see text] it is shown that these constants diverge as [Formula: see text] and [Formula: see text], respectively.

CALCULATION OF THE STRUCTURE OF THE S1(0) AND S1(0)+S1(0) LINES IN THE INFRARED SPECTRUM OF SOLID HYDROGEN

1962 ◽  
Vol 40 (10) ◽  
pp. 1461-1479 ◽  
Author(s):  
H. P. Gush ◽  
J. Van Kranendonk
Keyword(s):  
Lattice Structure ◽  
Hexagonal Lattice ◽  
Solid Hydrogen ◽  
Absorption Feature ◽  
Lattice Vibrations ◽  
Doublet Structure ◽  
Rotational Motions ◽  
Experimental Values ◽  
Best Fit ◽  
Para Molecule

At low ortho concentrations, the satellites appearing in the S1(0) infrared absorption feature of solid hydrogen arise from transitions in para molecules possessing one nearest-neighboring ortho molecule. The 15-fold degeneracy of the combination of the v = 1, J = 2 excited state of the para molecule and the v = 0, J = 1 ground state of the ortho molecule is partially lifted by the quadrupole–quadrupole interaction between the two molecules. The calculated structure of the S1(0) line is in good over-all agreement with the observed profile. The agreement is improved by taking into account the quadrupole–hexadecapole interaction. The best fit is obtained for a positive value of the hexadecapole moment of about 1.2 atomic units. The fine structure of the S1(0)+S1(0) line in the overtone region of pure parahydrogen, resulting from the splitting of the 25-fold degeneracy of the upper state by the combined quadrupole–quadrupole and quadrupole–hexadecapole interaction, is also calculated. The splitting and relative intensity of the two components of the resulting doublet structure are in close agreement with the experimental values. All the calculations are performed assuming a rigid close-packed hexagonal lattice structure. The discrepancy of about 20% between the theoretical values of the quadrupole moment of a hydrogen molecule in the v = 0 and v = 1 states and the empirical values deduced from the analysis of the S1(0) and S1(0)+S1(0) lines may be due to the neglect of the splittings arising from the coupling between the rotational motions of the molecules and the lattice vibrations.

Evidence for quadrupolar glass phases in solid hydrogen at reduced ortho concentrations

1978 ◽  
Vol 17 (12) ◽  
pp. 5016-5024 ◽  
Author(s):  
N. S. Sullivan ◽  
M. Devoret ◽  
B. P. Cowan ◽  
C. Urbina
Keyword(s):  
Solid Hydrogen ◽  
Quadrupolar Glass

Correlation functions in the quadrupolar glass phase of solid hydrogen

1984 ◽  
Vol 30 (9) ◽  
pp. 4935-4945 ◽  
Author(s):  
N. S. Sullivan ◽  
M. Devoret ◽  
D. Estève
Keyword(s):  
Correlation Functions ◽  
Glass Phase ◽  
Solid Hydrogen ◽  
Quadrupolar Glass
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