A Reflection on the Theory of Solid Hydrogens

Nakamura, Tuto

doi:10.1143/ptps.46.343

Cited by 15 publications

(2 citation statements)

References 14 publications

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“…5 To describe the lattice vibrations, the Debye model is employed in this paper, with 0t) = 122 K. 9 Using the data on the Raman rotational spectrum of pure para-hydrogen, 5' ~o one can obtain from Eqs. (2), (11), and (18)…”

Section: Ortho-hydrogen Singlesmentioning

confidence: 99%

Thermal conductivity of solid hydrogen at low ortho-hydrogen concentrations

Kokshenev

1975

J Low Temp Phys

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The interaction Hamiltonian of lattice vibrations and "impurity" orthohydrogen molecules of solid para-hydrogen has been derived from the potential of the anisotropic valence and dispersion forces. Below the thermal conductivity peak, along with boundary scattering, inelastic scattering of phonons by isolated ortho-hydrogen molecules has been shown to provide the principal contribution to the thermal resistivity at ortho concentrations c < 0.01. For c > 0.01 the heat flux in the lattice varies mainly through the resonant absorption and emission of phonons between rotational states of ortho-hydrogen molecular pairs. The thermal conductivity is calculated in the relaxation-time approximation for the equilibrium distribution of ortho-hydrogen molecules. The calculated dependences of the thermal conductivity on temperature and concentration are compared with those measured at temperatures up to 3.2 K and with c < 0.05. The derived values are of the right order of magnitude and show good qualitative agreement with experiment.

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Section: Ortho-hydrogen Singlesmentioning

confidence: 99%

Thermal conductivity of solid hydrogen at low ortho-hydrogen concentrations

Kokshenev

1975

J Low Temp Phys

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“…We have solved these equations for solid hydrogen using the intermolecular potential as given by Nakamura. 1 We have used the modern value Q= 0.1368xlO" 16 cm 2 for the quadrupole moment of a hydrogen molecule. 18 Because of the cubic symmetry, one has a x = a 2 and cr 3 = o^ = c 5 , and the same relations hold for the r's.…”

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confidence: 99%

Effect of Correlations on the Transition Temperature in Solid Orthohydrogen

Englman

Friedman

1973

Phys. Rev. Lett.

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The transition temperature and the nature of the ordered state below it are calculated for solid orthohydrogen subject to quad rupole-type interactions. We introduce correlations similar to those in Lines*s method, and obtain a transition temperature of 2.56°K, very near the observed 2.83°K.The phase transition in solid hydrogen has been studied thoroughly, both experimentally and theoretically, in the past few years. The main effort has been directed towards an understanding of the cooperative ordering of orthohydrogen molecules on rigid fee and hep lattices. The molecular ordering in solid hydrogen is due to the anisotropic orientational interactions. It has already been shown that these interactions can be represented to a good approximation as a quasiquadrupolar interaction. 1 * 2 Several calculations, based on molecular field theories, 3 " 6 Green'sfunction methods, 7 * 8 and cluster expansions 9 " 11 have been made in order to calculate the transition temperature in solid orthohydrogen. All these theories consistently overestimate the transition temperature by about a factor ranging from 1.3 to 2. Moreover, for all these theories one had to know the structure of the ordered state. In this paper we present a quantum-mechanical where H {° is the rotational kinetic-energy operator; v u represents the interaction of the ith and jth molecules, which depends on the direction of the intermolecular axis and is zero for i = j> Q\i is the \ith quadrupole component of the ith molecule 17 (/i= 1,. . . , 5); and hj is some general external field. The intermolecular interaction will be written as ^iA)=£^VV^'-(2)In the conventional molecular field approximation an effective Hamiltonian is written for each particle i as H^H^Yj^^vJKq^q^T.^^q;,theory which is an extension of a theory originally developed by Lines 12 ' 13 for ferroelectrics, and which introduces correlations in the framework of the molecular field approximation, while still retaining the single-particle picture. As in two previous papers 14 * 15 the transition temperature and the ordered state below it are given by the largest eigenvalue and the corresponding eigenvector of a simple Hermitian matrix. Unlike the previous calculations, this approach yields a transition temperature very near the observed 2.83°K. 16 We consider a system of molecules interacting via orientational quasiquadrupolar forces. The molecules are represented by a system of rigid rotators with centers of gravity fixed at the points of a rigid fee lattice. The orientation of the molecule on the site i is described by the polar angles (0 i ,(Pi) = &i of the internuclear axis. The Hamiltonian is a)where every operator on j±i has been replaced by its thermal average. We shall allow for correlations by writing

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Nuclear magnetic resonance of ortho-H2 impurities in solid para-H2 at high pressures

et al. 1975

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We have observed an anomalous broadening of the NMR absorption line of diluted ortho-H z (with rotational angular momentum J :-1) in solid para-H 2 (J = O) as pressure is applied. Samples with 0.015 < x < 0.06, where x is the ortho mole fraction, were studied over the temperature range 1.2 < T < 4.2 K. The density range covered was Po < P < 1.7po, Po being the density at zero pressure. The observed broadening was much larger than that estimated from intermolecular and intramolecular nuclear dipolar interaction, the latter resulting from short-range orientational molecular ordering caused by electric quadrupole-quadrupole (EQQ) interactions. Furthermore, the "average" longitudinal relaxation time T~ measured from the initial nuclear magnetization recovery after saturation is found to decrease with increasing density, contrary to what is predicted from the relaxation mechanism based on EQQ interaction. Arguments based on NMR measurements taken in solid Dz show that any orientational ordering of the J = 0 molecules caused by an admixture of J = 2 states is too small to lead to polarization of the J = 1 molecules large enough to account for the anomalous line shape. Another possible explanation of the anomaly--rapid clustering of the J = 1 impurities--is also Jound to be unlikely. The anomalously broadened line, with a width proportional to T-1 gt a given density, is discussed in terms of local molecular alignment of the 'J = 1 impurities as produced by a crystalline field V c and that causes an increase In the intramolecular dipolar feld. From the NMR line shape, we can get information on the distribution of such fields throughout the lattice. A crude analysis indicates that the distribution is approximately Gaussian around a characteristic value V,/k e where the width of this distribution is of the order of Vc/k B. At p = 1.7po, [V,l/k n is found to have a value of ~0.6 K, which is about 30 times larger than previous determinations at p = Po. The origins of the anomalously large crystalline field are discussed.

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A Reflection on the Theory of Solid Hydrogens

Cited by 15 publications

References 14 publications

Thermal conductivity of solid hydrogen at low ortho-hydrogen concentrations

Thermal conductivity of solid hydrogen at low ortho-hydrogen concentrations

Effect of Correlations on the Transition Temperature in Solid Orthohydrogen

Nuclear magnetic resonance of ortho-H2 impurities in solid para-H2 at high pressures

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