Mechanical stability of body-centered cubic iron at Earth’s core pressure and temperature conditions using a molecular graph kernel and Gaussian process regression

Gaussian process regression was performed on graph kernels quantifying the similarity of mathematical graphs that encode the atomic configurations of the body-centered cubic (BCC) crystal lattice of iron with thermal atomic displacements to predict the energy associated with arbitrary atomic configurations. The energies and atomic configurations used in the regression were obtained via density functional theory molecular dynamics (MD) at pressures expected to occur in the Earth's core and at temperatures ranging from several hundred to several thousand kelvin. Random MD simulation time steps were selected and each atom in the supercell was displaced in the direction of the first, second, and third nearest neighbors, calculating the force exerted on the displaced atom by numerical differentiation. The BCC structure is unstable at low temperatures, but the atoms generally experience a restoring force at high temperatures, particularly in the direction of the first and the third nearest neighbors.