The Role of Chemistry and Strain on Grain Boundary Structure, Energy and Composition in Two Transition Metal High Entropy Carbides

Segregation to grain boundaries is a well-established process in conventional materials that can affect stability, structure and mechanical properties. Solute atoms at grain boundaries, for example, can inhibit grain growth by establishing a local equilibrium that eliminates grain growth driving force, and through solute drag that produces kinetic stabilization. While well understood in metals and in many conventional ceramics, our current understanding of grain boundary segregation in high entropy ceramics is very limited. We have been using energies from Density Functional Theory in a Monte Carlo simulation to predict the structure and bonding of a Sigma=5 symmetric tilt grain boundary in the high entropy transition metal carbides (Hf, Mo, Nb, Ta, Zr)C and (Hf, Nb, Ta, Ti, Zr)C as well as their respective binaries. For the binaries the calculations predict a zig-zag structure formed by a lateral translation along the grain boundary interface that relieves lattice strain and forms undercoordinated cations. These grain boundary energies increase with increasing bulk carbon vacancy formation energy and with increasing bulk modulus, reflecting two major contributions to the interface energy. For the high-entropy composition containing Mo, the calculations predict that Mo energetically prefers undercoordinated sites, consistent with its small vacancy formation energy in a rocksalt structure. They also predict that Zr energetically prefers sites near the grain boundary with large Voronoi volumes. This is consistent with a relatively large lattice constant and small bulk modulus for ZrC. The second composition replaces Mo with Ti, which has a similar small size but much higher vacancy formation energy. In this case, Nb energetically prefers undercoordinated sites, again consistent with it having the lowest carbon vacancy formation energy of the bulk materials within this composition, while Zr again prefers the lattice sites with larger volumes. These results illustrate the competing roles of lattice strain and chemistry in determining grain boundary structures, energies and composition in these materials.