Journal Articles
Permanent URI for this collectionhttps://mro.massey.ac.nz/handle/10179/7915
Browse
2 results
Search Results
Item Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions(AIP Publishing LLC, 2025-09-07) Robles-Navarro A; Cooper S; Buchheit AA; Busse JK; Burrows A; Smits O; Schwerdtfeger PThree-body interactions have long been conjectured to play a crucial role in the stability of matter. However, rigorous studies have been scarce due to the computational challenge of evaluating small energy differences in high-dimensional lattice sums. This work provides a rigorous analysis of Bain-type cuboidal lattice transformations, which connect the face-centered cubic (fcc), mean-centered cubic (mcc), body-centered cubic (bcc), and axially centered cubic (acc) lattices. Our study incorporates a general (n, m) Lennard-Jones (LJ) two-body potential and a long-range repulsive Axilrod-Teller-Muto (ATM) three-body potential. The two-body lattice sums and their meromorphic continuations are evaluated to full precision using super-exponentially convergent series expansions. Furthermore, we introduce a novel approach to computing three-body lattice sums by converting the multi-dimensional sum into an integral involving products of Epstein zeta functions. This enables us to evaluate three-body lattice sums and their meromorphic continuations to machine precision within minutes on a standard laptop. Using our computational framework, we analyze the stability of cuboidal lattice phases relative to the close-packed fcc structure along a Bain transformation path for varying ATM coupling strengths. We analytically demonstrate that the ATM cohesive energy exhibits an extremum at the bcc phase and show numerically that it corresponds to a minimum for repulsive three-body forces along the Bain path. Our results indicate that strong repulsive three-body interactions can destabilize the fcc phase and render bcc energetically favorable for soft LJ potentials. However, even in this scenario, the bcc phase remains susceptible to further cuboidal distortions. These results suggest that the stability of the bcc phase is, besides vibrational, temperature, and pressure effects, strongly influenced by higher than two-body forces. Because of the wrong short-range behavior of the triple-dipole ATM model, the LJ potential is limited to exponents n > 9 for the repulsive wall, otherwise one observes distortion into a set of linear chains collapsing to the origin.Item Tipping the Balance Between the bcc and fcc Phase Within the Alkali and Coinage Metal Groups.(Wiley-VCH GmbH on behalf of Angewandte Chemie International Edition, 2023-10-25) Robles-Navarro A; Jerabek P; Schwerdtfeger PWhy the Group 1 elements crystallize in the body-centered cubic (bcc) structure, and the iso-electronic Group 11 elements in the face-centered cubic (fcc) structure, remains a mystery. Here we show that a delicate interplay between many-body effects, vibrational contributions and dispersion interactions obtained from relativistic density functional theory offers an answer to this long-standing controversy. It also sheds light on the Periodic Table of Crystal Structures. A smooth diffusionless transition through cuboidal lattices gives a detailed insight into the bcc→fcc phase transition for the Groups 1 and 11 elements.