arXiv subjects

J. K. Christie

Publications and source records attributed to J. K. Christie.

5 recordsLinked to original sources

arXiv2010

A polarizable interatomic force field for TiO$_2$ parameterized using density functional theory

We report a classical interatomic force field for TiO$_2$, which has been parameterized using density functional theory forces, energies, and stresses in the rutile crystal structure. The reliability of this new classical potential is tested by evaluating the structural properties, equation of state, phonon properties, thermal expansion, and some thermodynamic quantities such as entropy, free energy, and specific heat under constant volume. The good agreement of our results with {\em ab initio} calculations and with experimental data, indicates that our force-field describes the atomic interactions of TiO$_2$ in the rutile structure very well. The force field can also describe the structures of the brookite and anatase crystals with good accuracy.

cond-mat.mtrl-sci↗

arXiv2007

Vibrational behaviour of a realistic amorphous-silicon model

The vibrational properties of a high-quality realistic model of amorphous silicon are examined. The longitudinal and transverse dynamical structure factors are calculated, and fitted to a damped harmonic oscillator (DHO) function. The width $Γ$ of the best-fit DHO to the longitudinal dynamical structure factor scales approximately as $k^{2}$ for wavevectors $k\lesssim0.55\textrmÅ^{-1}$, which is above the Ioffe-Regel crossover frequency separating the propagating and diffusing regimes, occurring at $k=0.38\pm0.03\textrmÅ^{-1}$. Using the DHO function as a fitting function for the transverse dynamical structure factor (without theoretical justification), gives a dependence of $Γ\propto k^α$ with $α\sim2.5$ for wavevectors $k\lesssim0.7\textrmÅ^{-1}$. There was no evidence for $Γ\propto k^{4}$ behaviour for either polarization.

cond-mat.mtrl-sci↗

arXiv2005

Modelling the atomic structure of very high-density amorphous ice

The structure of very high-density amorphous (VHDA) ice has been modelled by positionally disordering three crystalline phases, namely ice IV, VI and XII. These phases were chosen because only they are stable or metastable in the region of the ice phase diagram where VHDA ice is formed, and their densities are comparable to that of VHDA ice. An excellent fit to the medium range of the experimentally observed pair-correlation function g(r) of VHDA ice was obtained by introducing disorder into the positions of the H2O molecules, as well as small amounts of molecular rotational disorder, disorder in the O--H bond lengths and disorder in the H--O--H bond angles. The low-k behaviour of the experimental structure factor, S(k), is also very well reproduced by this disordered-crystal model. The fraction of each phase present in the best-fit disordered model is very close to that observed in the probable crystallization products of VHDA ice. In particular, only negligible amounts of ice IV are predicted, in accordance with experimental observation.

cond-mat.mtrl-sci↗

arXiv2004

Atomic vibrations in disordered systems: Comparison of disordered diamond lattices and a realistic amorphous silicon model

Force-constant and positional disorder have been introduced into diamond lattice models in an attempt to mimic the vibrational properties of a realistic amorphous silicon model. Neither type of disorder is sufficient on its own to mimic the realistic model. By comparing the spectral densities of these models, it is shown that a combination of both disorders is a better representation, but still not completely satisfactory. Topological disorder in these models was investigated by renumbering the atoms and examining the dynamical matrix graphically. The dynamical matrix of the realistic model is similar to that of a positionally-disordered lattice model, implying that the short-range order in both systems is similar.

cond-mat.dis-nn↗

arXiv2004

Structural characteristics of positionally-disordered lattices: relation to the first sharp diffraction peak in glasses

Positional disorder has been introduced into the atomic structure of certain crystalline lattices, and the orientationally-averaged structure factor S(k) and pair-correlation function g(r) of these disordered lattices have been studied. Analytical expressions for S(k) and g(r) for Gaussian positional disorder in 2D and 3D are confirmed with precise numerical simulations. These analytic results also have a bearing on the unsolved Gauss circle problem in mathematics. As the positional disorder increases, high-k peaks in S(k) are destroyed first, eventually leaving a single peak, that with the lowest-k value. The pair-correlation function for lattices with such high levels of positional disorder exhibits damped oscillations, with a period equal to the separation between the furthest-separated (lowest-k) lattice planes. The last surviving peak in S(k) is, for example for silicon and silica, at a wavevector nearly identical to that of the experimentally-observed first sharp diffraction peak (FSDP) in the amorphous phases of those materials. Thus, for these amorphous materials at least, the FSDP can be regarded as arising from scattering from atomic configurations equivalent to the single family of positionally-disordered local Bragg planes having the furthest separation.

cond-mat.mtrl-sci↗