Based on the idea that the hardness of covalent crystal is intrinsic and equivalent to the sum of the resistance to the indenter of each bond per unit area, a semiempirical method for the evaluation of hardness of multicomponent crystals is presented. Applied to beta-BC2N crystal, the predicted value of hardness is in good agreement with the experimental value. It is found that bond density or electronic density, bond length, and degree of covalent bonding are three determinative factors for the hardness of a polar covalent crystal. Our method offers the advantage of applicability to a broad class of materials and initializes a link between macroscopic property and electronic structure from first principles calculation.

First-principles calculations are used to investigate ionicities of boron-boron bonds in B(12) icosahedra. It is observed that the geometrical symmetry breaking of B(12) icosahedra results in the spatial asymmetry of charge density on each boron-boron bond, and further in the ionicity of B(12) icosahedra. The results calculated by a new ionicity scale, a population ionicity scale, indicate that the maximum ionicity among those boron-boron bonds is larger than that of boron-nitrogen bonds in the III-V compound cubic BN. It is of great importance that such an ionicity concept can be extended to boron-rich solids and identical atom clusters.

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An interactive program, POWD, written in Fortran77, for powder diffraction data interpretation and indexing is described. Various functions such as the least‐squares refinement and the systematic absence test are also included in this versatile program. The modified de Wolff figure of merit [Wu (1988). J. Appl. Cryst.21, 530–535] is introduced in the program to decrease the execution time and estimate the reliability of the indexing. Very high success rates for indexing and tolerance of the presence of limited impurity lines are demonstrated by testing the program on several groups of powder data.

The conventional wisdom to tailor the properties of binary transition metal carbides by order-disorder phase transformation has been inapplicable for the machinable ternary carbides (MTCs) due to the absence of ordered phase in bulk sample. Here, the presence of an ordered phase with structural carbon vacancies in Nb4AlC3–x (x ≈ 0.3) ternary carbide is predicted by first-principles calculations, and experimentally identified for the first time by transmission electron microscopy and micro-Raman spectroscopy. Consistent with the first-principles prediction, the ordered phase, o-Nb4AlC3, crystalizes in P63/mcm with a = 5.423 Å, c = 24.146 Å. Coexistence of ordered (o-Nb4AlC3) and disordered (Nb4AlC3–x) phase brings about abundant domains with irregular shape in the bulk sample. Both heating and electron irradiation can induce the transformation from o-Nb4AlC3 to Nb4AlC3–x. Our findings may offer substantial insights into the roles of carbon vacancies in the structure stability and order-disorder phase transformation in MTCs.