Odile Smits | Searcharxiv

arXiv2025

Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions

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 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.

cond-mat.mtrl-sci↗

arXiv2024

Lattice Instabilities Along the Transformation from Hexagonal to Cuboidal Structures in Hard- and Soft-Sphere Models

The diffusionless Burgers-Bain phase transition from a hcp arrangement to a cuboidal lattice (fcc and bcc) is analysed in great detail for Lennard-Jones solids. From the lattice vectors of an underlying bi-lattice smoothly connecting these phases, we are able to express the corresponding lattice sums for inverse power potentials in terms of fast converging Bessel function expansions resulting in an efficient evaluation to computer accuracy for cohesive energies. From the kissing hard-sphere limit we derive exact analytical expressions for the lattice parameters varying along the minimum energy path of the phase transition. This simple model suggests that for the Burgers-Bain transformation of a LJ solid requires a minimum of four lattice parameters, $(a,\alpha,\beta,\gamma=c/a)$, describing the change in the base lattice lengths $a$ and $c$, the shear force acting on the hexagonal base plane ($\alpha$), the sliding force of the middle layer of the original hexagonal packing arrangement($\beta$), and the cuboidal transformation ($\gamma=c/a$). This choice results in a two-step process: hcp$\to$fcc$\to$bcc. However, a further extension of the parameter space including an additional slide parameter for the middle layer, one suddenly observes a distinct symmetry-breaking effect along the hcp$\rightarrow$fcc transition path with a bifurcation point appearing joining the original Burgers with the Bain path of the bcc$\rightarrow$fcc cuboidal transition. Furthermore, for soft LJ potentials the bcc phase appears as a local minimum along the Burgers hcp$\rightarrow$fcc path with two transition states to either the hcp or fcc phase. The underlying topology of the Burgers-Bain phase transition also incorporates the rhombohedral distortion of the bcc phase, which is analyzed in detail.

cond-mat.mtrl-sci↗