The complete set of independent second- and third-order elastic constants of rare-earth hexaborides LaB ${}_6$ and CeB ${}_6$ are determined by the combination method of first-principles calculations and homogeneous deformation theory. The ground-state lattice parameters, second-order elastic constants, and bulk modulus are in reasonable agreement with the available experimental data. The third-order elastic constant of longitudinal mode $C_{111}$ has a larger absolute value than other shear modes, showing the contribution to lattice vibrations from longitudinal modes to be greater. The pressure derivatives of the second-order elastic constants related to the third-order elastic constants are calculated to be positive for the two hexaborides, which are consistent with those of their polycrystalline bulk modulus and shear modulus. Furthermore, the effect of pressure on the structural stability, mechanical property, and elastic anisotropy of the two hexaborides are investigated, showing a reduction in mechanical stability and an increase in ductility and anisotropy with increasing pressure.

We reveal for the first time an ordering phenomenon of a type of carbonitrides in a Super304H austenitic steel via the techniques of transmission electron microscopy and atom probe tomography. Solution-treated Super304H austenitic steel samples containing a few primary carbonitrides were aged at 923 K for 5000 h. The results show that the primary carbonitrides in the Super304H steel are non-stoichiometric compounds enriched in Nb and with a NaCl-type structure. The crystal structure of the Nb-rich carbonitrides is in a disordered state in the solution-treated steel, while in an ordered state in the aged steel. This observation suggests the occurrence of a disorder–order structural transition in the primary carbonitrides during long-term aging. We found that such a disorder–order structural transition is accompanied by carbon diffusion from the primary carbonitrides into the austenitic matrix. The ordering phenomenon is discussed based on the long-range ordering of structure vacancies in the non-metal lattice of the superstructure, providing new insights for the understanding of ordering in non-stoichiometric compounds.

The effects of yttrium (Y) addition on the formation of inclusions in 0.5C-1Cr-0.2Mo-0.1V spring steel were studied via thermodynamic calculations and scanning electron microscope (SEM) coupled with energy dispersive spectrum (EDS). According to thermodynamic calculations of Gibbs free energy, [Y] reacts with [O] and [S] but not with [C] in molten steel, with Y ₂ O ₂ S and Y ₂ O ₃ being more easily formed inclusions in steel at 1873 K than YS and Y ₂ S ₃ when the Y content is less than 0.06%. The experimental results show that the inclusions in spring steel without Y addition are mainly large irregular aluminum silicate, Al ₂ O ₃ -SiO ₂ -TiO ₂ and MnS inclusions. The addition of 0.011% Y can eliminate large inclusions and form square Y ₂ O ₃ and complex Y ₂ O ₃ -Y ₂ O ₂ S inclusions with Y ₂ O ₂ S in the core and surrounding Y ₂ O ₃ . When the Y content increased to 0.019%, the size of Y ₂ O ₃ decreased, and isolated spherical Y ₂ O ₂ S formed. The addition of 0.031% Y can further decrease the size of Y ₂ O ₂ S, and Y ₂ O ₃ is replaced by YS. A good consistency was observed between the calculated result of the Gibbs free energy and the experimental result. Moreover, a three-dimensional stability diagram of precipitation under equilibrium conditions at 1873 K is established to predict the formation sequence of Y-containing inclusions with different Y contents. The formation sequences are Y ₂ O ₂ S → Y ₂ O ₃ with Y contents in the range of 0.01−0.02%, YS → Y ₂ O ₂ S → Y ₂ O ₃ with Y contents in the range of 0.02−0.06% and Y ₂ S ₃ → YS → Y ₂ O ₂ S → Y ₂ O ₃ with Y contents in the range of 0.06−0.08%.