Temperature Dependence of Intrinsic Disorder in LaHX and YHX
Intrinsic disorder in fcc metal hydrides MHX, defined as xO (2), the fraction of octahedral (0) sites occupied at stoichiometry x=2, has been measured by both spectroscopic1 and thermodynamic2 techniques for M=La and Y. The spectroscopic (NMR, ESR and neutrons) data are all for temperature t < 300K while the thermodynamic (pressure vs. x isotherms) results have t > 850K. A most surprising feature is that xO(2) at 300K is greater than or equal to its value at high temperature. This is in gross disagreement with any theory which attributes xO(2) solely to the finite difference between 0-site and tetrahedral (T) site energies, including vibrational states.
My proposed explanation is based on a model in which large amplitude hydrogen vibrations combined with repulsive interactions prevent occupation of both a T and neighbor 0-site at high temperature. Thus xO(2) goes through a maximum vs. temperature as disorder is established more via vibrational entropy than by 0-site occupation.
A quantitative calculation is performed by assuming an energy level structure of bound (ε < 0) harmonic oscillator states and extended (ε > 0) particle-in-a-box states. Because of repulsion, a T(0) site ε > 0 state is possible only if the neighbor 0(T) sites are vacant. The vibrational energy is known from neutron data, and the box size for ε > 0 states is taken to agree with the available volume per site assuming cubic close packing of the metal ion spheres. The difference in well depths U0-UT is given by the low temperature data1; so the only really fre prameter is the depth of the T-site well-UT. The value-UT=0.02eV gives good agreement and corresponds to the low temperature activation energy3 for NMR in YH2. Sensitivity of the model to UT and implications for NMR relaxation are discussed.