Connecting the hexagonal closed packed structure with the cuboidal lattices: A Burgers-Bain type martensitic transformation for a Lennard-Jones solid derived from exact lattice summations

• DOI: 10.48550/arxiv.2406.09635
• Publication Date: 2024-06-13
• Authors: Peter Schwerdtfeger; S. Barry Cooper; Odile R. Smits; Andrés Robles‐Nav...
• Keywords: Lattice (music); Diffusionless transformation; Hexagonal Lattice

The diffusionless martensitic phase transition from a hexagonal close-packed (hcp) arrangement to the face-centered (fcc) and subsequently body-centered cubic (bcc) lattice is discussed for Lennard-Jones solid. associated vectors construct underlying bi-lattice Burgers-Bain-type of transformation require minimum four parameters $(a,\alpha,\beta,\gamma=c/a)$ describing, beside change in base $a$ $c$, shear force acting on plane through parameter $\alpha$, sliding middle layer original AB packing $\beta$. By optimizing $\beta$ $(n,m)$-Lennard-Jones potential, we obtain simple two-dimensional picture complete hcp$\leftrightarrow$fcc$\leftrightarrow$bcc transition. From generalized were able corresponding sums terms inverse power potentials applying fast converging Bessel function expansions using Terras decomposition Epstein zeta combined with Van der Hoff-Benson expansion sums. This allows cohesive energy be determined computer precision For six different combinations $(\alpha,\gamma)$ hypersurface was then mapped out studied more detail. We show that model path found two-step hcp$\rightarrow$fcc$\rightarrow$bcc process. lowest state each case can regarded as an upper limit hypothetical true many possibilities