Theory of angular momentum waves in solid ortho-hydrogen

Mertens, Franz G.; Biem, W.; Hahn, H.

doi:10.1007/bf01380025

Cited by 46 publications

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“…: : o the libron theory seems to be in full agreement wi th the experiment. As to 4 tO it has been proposed [16,18,19] that the dispersion curves and the spectrum be measured by scattering of slow neutrons. Such •«>rk is in progress [25] •…”

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“…This coupling occurs for small k between the acoustical phonons and all libron modes. See the rough estimate in [18,19] • Furthermore the existing phonon theories [26,21] neglect the q-q-forces and the orientational order of the molecules. They use the division into four simple cubic sublattices only formally and probably cannot explain the number of optical phonon lines which have been observed by Raman scattering [26] • Therefore the purpose of this work is to develop within the frame of the RPA for T=O a theory which describes all low-lying collective excitations (phonons, librons, and "mixed" excitations, which arise because of the coupling) in pure o-H 2 and p-o 2 • Because these solids are quantum crystals, the problem is rather canplicated compared with normal crystals: The short range correlations (SRC) between the molecules must be taken into account.…”

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Phonons and librons in solid hydrogen and deuterium

Mertens

Biem

1972

Z. Physik

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Phonons and librons in solid hydrogen and deuterium

Mertens

Biem

1972

Z. Physik

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“…Using standard polarizability theory 9 we have calculated the relative intensities of the modes from the linear theory of Mertens, Biem, and Hahn. 5 The results are.presented for a randomly oriented polycrystalline sample. The intensities were also calculated for a sample in which the [ill] directions of the crystallites were oriented along the incident light beam, with results that do not differ significantly from the previous ones.…”

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Observation of Librational Waves in the Ordered State of Solid Hydrogen and Deuterium by Raman Scattering

1969

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conduction band. Each time this happens, as the temperature is raised for example, a magnetic ion is formed in the lattice. At higher temperature the extra entropy associated with the magnetic ion degeneracy favors its formation and the Sm becomes predominantly trivalent. While such a model is conceptually quite clear, its quantitative application to magnetic behavior is complicated by the uncertainty of the crystalfield splittings of the low-lying levels of the trivalent Sm ion. It may be surprising that the two configurations are so close in energy but actually we were more surprised that it was possible to form polycrystalline SmB 6 so well by simply reacting the elements that its intrinsic properties were not masked.We are grateful to R. C. Sherwood and G. W. Hull, Jr., for help with the magnetic measurements and W. A. Reed for the use of his laboratory. We have profited from useful conversation with J. H. Wernick, H. J. Levinstein, and R. M. White.tThe research at Stanford was sponsored by the U. S, We have observed 1 by laser Raman scattering the theoretically predicted 2 " 5 librational excitations of the ordered state of solid orthohydrogen and paradeuterium. The observations agree only qualitatively with existing theories and two possible explanations for the discrepancies are proposed. The first implies that the rigid-lattice, nearest-neighbor quadrupole-interaction model is inadequate in the present case. The second alternative explanation requires a crystal structure with symmetry lower than the previously assumed 2 " 5 PaZ space group.The ordered state of hydrogen is one in which the molecular axes assume preferential orientations with respect to the crystalline axes, analogous to the ordering of spins in an antiferromagnet. Because the anisotropic interactions are Air Force November 1968 (unpublished).small compared with the separation of the J levels and because the temperature is low, only the J=l manifold need be considered in solid o-H 2 and />-D 2 and therefore it is the axes of the J=l molecular rotational wave functions that are ordered.X-ray and neutron data 6 have shown that the molecular centers form an fee lattice. Theories 7 based on such a rigid fee lattice and electric quadrupole-quadrupole inter molecular coupling predict the structure of the ground state to be Pa3; the neutron-diffraction data are also consistent with this space group. In this structure the axes of the dumbbell-shaped raj = 0 wave functions are aligned along the four fee body diagonals. The crystal is divided into four sublattices with the oriented molecules on a given sublattice The Raman spectra of high purity o-H 2 and £-D 2 at liquid-helium temperatures have been obtained. Features which appear below the ordering temperature are attributed to librational waves within the J~ 1 manifold of states. On the basis of a comparison with recent theories of the ordered state, a new structure is proposed.297

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“…It is easily seen that in the limit of very small c, as defined by Eq. (18), the libron theory of Mertens et al 23 is recovered.…”

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confidence: 76%

k=0 Librational Spectrum for Solid α-N2

Raich

1972

The Journal of Chemical Physics

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Articles you may be interested inComment on ''Vibron and lattice frequency shifts in the Raman spectra of solid αN2 and γN2 and librational force constants of diatomic molecular crystals'' Vibron and lattice frequency shifts in the Raman spectra of solid αN2 and γN2 and librational force constants of diatomic molecular crystals 17 For sake of simplicity, no degeneracy of eigenvalues is assumed. However, provided the largest eigenvalue is not degenerate, the splitting of '\1 into '\11 and '\12, as well as Eqs. (26), are valid anyhow. In the case of Orientation A the two largest eigen-THE JOURNAL OF CHEMICAL PHYSICS values are identical except for the sign. This makes Eq. (26c) unture, and the interpretation of Eqs. (30)-(33) less obvious; however, it might be shown that the meaning of the results is unchanged. From the formal point of view, replacement of the N bond vectors l(i) with NI2 "virtual" bonds consisting of (1(i)+ 1(i+l») would avoid trouble.An alternative description of the k=O librational spectrum of solid a-N2 is given. A variational method where the wavefunctions of the hindered rotator are expanded in terms of spherical harmonics is used. The present calculations are limited to electrostatic quadrupole-quadrupole interactions. The k=O librational frequencies are compared with the results obtained by classical lattice dynamics and another variational method as well as experiment.

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Theory of angular momentum waves in solid ortho-hydrogen

Cited by 46 publications

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Phonons and librons in solid hydrogen and deuterium

Phonons and librons in solid hydrogen and deuterium

Observation of Librational Waves in the Ordered State of Solid Hydrogen and Deuterium by Raman Scattering

k=0 Librational Spectrum for Solid α-N2

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