The diffusionless Burgers-Bain phase transition from a hexagonal close-packed (hcp) arrangement to a cuboidal lattice (face-centered cubic, fcc, and body-centered cubic, bcc) is analyzed in great detail for Lennard-Jones (LJ) solids. From the lattice vectors of an underlying bilattice 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 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 through a parameter $\alpha$, the sliding force of the middle layer in the original hexagonal packing arrangement through a single parameter $\beta$, and the cuboidal transformation through a parameter $\gamma =c/a$. This choice results in a smooth transformation through a two-step process: $\mathrm{hcp}\to \mathrm{fcc}\to \mathrm{bcc}$. 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 $\mathrm{hcp}\to \mathrm{fcc}$ transition path with a bifurcation point appearing joining the original Burgers with the Bain path of the $\mathrm{bcc}\to \mathrm{fcc}$ cuboidal transition. Furthermore, for soft LJ potentials the bcc phase appears as a local minimum along the Burgers $\mathrm{hcp}\to \mathrm{fcc}$ 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. As a first application of our formalism, we discuss solid argon and compare the LJ results with variable-cell nudge elastic band optimizations using density functional theory. We find that the activation energy for the $\mathrm{hcp}\to \mathrm{fcc}$ transformation is highly sensitive to the density functional applied, and that dispersion corrections are important as expected for weakly interacting systems.

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• Crystal phenomena
• Packing & jamming problems
• Specific phase transitions
• Structural phase transition
• Crystalline systems
• Lattice types
• Lattices
• Density functional theory
• Exact solutions for many-body systems
• Quantum chemistry methods