Voronoi tessellation has been used widely to approximate and model various cellular structures and stochastic patterns appearing in nature. In this work, we present an extended version of the Voronoi tessellation method that partitions the space with certain constraints commonly encountered in either experimental measurements or theoretical models, such as cell volume or size distribution. The new Voronoi method is implemented using an inverse Monte Carlo method. We calculate the topological and statistical properties of tessellated Voronoi cells in several model systems with cell volumes obeying lognormal and bimodal distributions. We also compare the results with those obtained using the conventional Poisson–Voronoi method. We observed systematic changes in the topological properties as well as deviations from some established topological relations as the parameters in the constraint were varied. The application of this constrained Voronoi method in microstructure modelling and characterization in poly- and nano-crystalline materials is briefly discussed.

The corrosion properties of two Zr-based bulk metallic glass, ${\text{Zr}}_{41}{\text{Ti}}_{14}{\text{Cu}}_{12}{\text{Ni}}_{10}{\text{Be}}_{23}$ (LM1) and ${\text{Zr}}_{44}{\text{Ti}}_{11}{\text{Cu}}_{10}{\text{Ni}}_{10}{\text{Be}}_{25}$ (LM1b) were investigated by electrochemical measurements in simulated body fluid with pH value 7.4. With much lower current density and higher impedance values, as well as higher pitting potential, LM1b showed superior corrosion resistance to LM1. Under identical sample preparation and testing conditions, the difference in corrosion performance is found to relate closely to their surface wettability difference, as contact angle tests showed that LM1b is more hydrophobic than LM1. The excess free volume was measured and found having a close correlation with the wettability or the surface energy.

Shear bands in metallic glasses subject to uniaxial loading such as tension and compression exhibit the inclination angle different from $45°$ on the maximum resolved shear stress plane with respect to the loading axis. The cause is often attributed to the effective normal stress acting on the shear plane, which also suggests Coulomb–Mohr yield criterion for metallic glasses. We show here that this argument is conceptually ill justified. Instead, shear band inclination angle can be described by a simple model taking into consideration the volume dilatation and the pressure effects.