Six vertex model with domain-wall boundary conditions in the Bethe-Peierls approximation

We use the Bethe-Peierls method combined with the belief propagation algorithm to study the arctic curves in the six vertex model on a square lattice with domain-wall boundary conditions, and the six vertex model on a rectangular lattice with partial domain-wall boundary conditions. We show that this rather simple approximation yields results that are remarkably close to the exact ones when these are known, and allows one to estimate the location of the phase boundaries with relative little effort in cases in which exact results are not available.Comment: 19 pages, 14 figure

The role of aggregates in the thermal stability of Mg-PSZ refractories for vacuum induction melting

Mg-PSZ refractories used as vacuum induction melting crucibles are particle-reinforced composites with aggregate and matrix phases comprising fused zirconia. Three commercial varieties were cycled eight times to service temperatures and their microstructural and thermomechanical evolution investigated, with focus placed on the aggregate populations. Two refractories, with large aggregates of similar size, were found to retain stiffness after cycling but in the refractory containing aggregates with high stabiliser levels, reaction between the stabiliser and Al and Si impurities produced secondary phases. Volume changes accompanying formation of these phases, and subsequent thermal expansion mismatches, led to aggregate break-up with consequent reductions in refractory toughness and strength. Secondary phases developed only rarely in the aggregates (with lower levels of stabiliser) of the second refractory. These aggregates remained intact and the refractory retained its toughness and strength. A third refractory contained small, unstabilised aggregates in a stabilised matrix and the strain mismatches that ensued during polymorphic transformation damaged microstructural interfaces. Refractory stiffness halved within eight cycles and toughness and strength were lost. All three refractories displayed R-curve behaviour and quasi-stable fracture curves were observed during bend tests. The study shows that when using fused zirconia aggregates to design refractories, engineers need to i) limit stabiliser concentrations - a difference of just ±1 wt% Mg (in the presence of impurity elements) may determine whether secondary phase formation occurs and ii) eliminate alumina and silica impurities when possible through substitution of zircon sand with baddeleyite as the source for fused zirconia.Open Acces