Kaolinite is often a cause of deformation in soft-rock tunnel engineering, leading to safety problems. In order to gain a better predictive understanding of the governing principles associated with this phenomenon, the physical and chemical properties of kaolinite were investigated using an efficient, firstprinciples scheme for studying isomorphic substitution of Al ions in kaolinite by two kinds of other elements (namely, the dual defect). Elements that are relatively common in natural kaolinite were chosen from groups II (Be, Mg, Ca, and Sr) and III (Fe and Sc) of the Periodic Table as dual-defect ions to substitute for Al ions in kaolinite. By systematically calculating the impurity-formation energies (which characterize the difference in the total crystal energy before and after the defect arises) and transitionenergy levels, which characterize the energy cost for the transformation between two different charge states, the (Be + Sc)Al (i.e. the replacement of two specific Al ions in kaolinite by external Be and Sc ions), (Ca + Sc)Al, (Mg + Sc)Al, and (Sr + Sc)Al ion pairs were determined to have low formation energies, suggesting that these combinations of ions can easily substitute for Al ions in kaolinite. The (Be + Fe)Al, (Ca + Fe)Al, (Mg + Fe)Al, and (Sr + Fe)Al ion pairs have relatively high formation energies which make isomorphic substitution (or doping) in kaolinite difficult. Moreover, these combinations of elements from groups II and III were found to have relatively low transition-energy levels compared with other element pairs. Among them, (Sr + Sc)Al have the lowest transition-energy level at 0.06 eV above the valence band maximum. When compared with single external substitutional defects in kaolinite, remarkably, the dual defects have relatively low formation energies and transition-energy levels. The results are helpful in understanding the chemical and physical properties of natural kaolinite.

The effect of zirconium alloying on the crystal structures and mechanical properties of binary tungsten–zirconium alloys is investigated in this study using the first-principles method. Firstly, we investigate the cell volumes, lattice constants, and formation energies of binary W1−xZrx (x = 0, 0.0625, 0.125, 0.1875, 0.25, and 0.5) alloys. It is shown that binary tungsten–zirconium alloys maintain BCC structures. When the concentration of zirconium atoms is lower than 12.5%, the structures of binary tungsten–zirconium alloys can be thermodynamically stable. The elastic constants of binary tungsten–zirconium alloys are calculated based on the optimized atomic lattice. Then, the elastic modulus and other mechanical parameters are deduced according to the relevant formulas. It is shown that the mechanical strength of binary tungsten–zirconium alloy decreases with an increasing concentration of zirconium atoms, which is lower than the mechanical strength of pure tungsten metal. However, the mechanical strength of binary tungsten–zirconium alloys is higher than that of pure zirconium metal. In addition, zirconium alloying can be effective in improving the ductility of pure tungsten metal.