Orientational ordering in solid hydrogen

Abstract

2014 L'établissement des états d'ordre orientationnel dans l'hydrogène solide est étudié en fonction de la concentration X des espèces J = 1 (ortho-hydrogène, paradeutérium) par la méthode des traces restreintes. Les calculs des températures critiques montrent qu'en dessous d'une certaine concentration critique Xc ~ 0,5 il n'est plus possible de maintenir un état d'ordre orientationnel à longue portée. Ce résultat est en accord qualitatif avec les résultats expérimentaux. Abstract. 2014 The phenomen of orientational ordering in solid hydrogen is studied as a function of the concentration X of the J = 1 species using Kirkwood's technique of restricted traces. Calculations of the critical temperatures as a function of X demonstrate a behaviour in qualitative agreement with the experimental observation that a long range orientation order cannot be maintained in samples for which X ~ Xc ~ 0.5.

Orientational phase transition of solid ortho -hydrogen

“…15 Sullivan derived the value of T C ϭ2.99 K by using the Bethe approximation, restricted to the nearest-neighbor interactions. 16 The value of T C obtained by him ought to be slightly high, with up to the second-nearest-neighbor interactions.…”

Orientational Ordering for System of Ellipsoidal Molecules Dispersed in Cubic Lattice

“…Following [7,30,18], the electric quadupole Hamiltonian can be written as where Om are the operator equivalents of the spherical harmonics Ym2 in the manifold . | = 1, i.e., Ο° = (3J2zi -2)/3 with Jzi the z-axis component of the orbital angular momentum J on the site i, while á' are interaction constants.…”

“…In the internal-field approximation, the fluctuation terms are discarded to retain the tuncated form where for nearest neighbours X00 = -19Γ12/8 (Γ12 = 6e 2Q2u/25R512,, Qu is the molecular quadupole moment, e -the electron charge and R12 designates the intermolecular separation) [7,30].…”

“…Therefore, related to the orientational space ordering, the system of quadrupoles is equivalent to the system of ellipsoidal (or cylindrical) molecules. Following the main lines of the way given in [30][31][32][33], for the low concentration C0, below a critical temperature Teg Π 0.53c01/2, we find a state, similar to a glassy structure (an orientational glass state, i.e., a "higher rank" glass state), in which all possible orientations of ellipsoids are equally likely, but the orientation at a given site is frozen [18]. These results seem to be useful for the description of the experimental facts related to the orientational ordering in such systems as solid hydrogen, by applying a model of ellipsoidal molecules.…”

Orientational Glasses: NMR and Electric Susceptibility Studies

“…The critical concentration depends on the concentration dependence of the anisotropic interactions. A detailed restricted trace calculation [36] showed that the orientational fluctuations for ortho-para hydrogen mixtures varied as (2x − 1) where x is the ortho concentration leading to a predicted critical concentration of 50%. No detailed calculation has been made for solid N 2 -Ar mixtures.…”