Yang Ze-Jin(杨则金) a) † , Gao Qing-He(高清河) b) , Li Jin(李 劲) c) , Linghu Rong-Feng(令狐荣锋) d) , Guo Yun-Dong(郭云东) e) , Cheng Xin-Lu(程新路) f) , Zhu Zheng-He(朱正和) f) , and Yang Xiang-Dong(杨向东) f)

First-principles calculations of the crystal structures, phase transition, and elastic properties of B1-B2 phase calcium sulfide (CaS) have been carried out with the plane-wave pseudopotential density functional theory method. The calculated values (for crystal structures and the phase transition) are in very good agreement with experimental data as well as with some of the existing model calculations. The dependence of the elastic constants c(ij), the aggregate elastic modulus, the deviation from the Cauchy relation, and the elastic anisotropy on pressure have been investigated. The normalized elastic constants c(ij)' have been introduced to investigate the elasticity of CaS in detail. Moreover, the variation of the Poisson ratio, Debye temperature, and longitudinal and transverse elastic wave velocity with pressure P up to 70 GPa at 0 K have been investigated for the first time.

The structural properties of Mo2Ga2C are simulated by first-principles under pressure. At 40 GPa, the axial compressibilities of [Formula: see text]- and [Formula: see text]-axes are 0.9763 and 0.9264, respectively, which are the known largest and smallest values in the [Formula: see text] compounds. A phase transition at 48 GPa is observed with an abrupt increase of [Formula: see text]-axis and a rapid decrease of [Formula: see text]-axis. The elastic properties and phonon imaginary frequencies confirmed the structural transition at 48 GPa, which probably should be the lowest-pressure transition in the [Formula: see text] ([Formula: see text], etc.) phases. The anti-expansion of Mo–Mo bond length is responsible for the [Formula: see text]-axis ultra-incompressibility as well as the structural transition at 48 GPa.

No abstract

The elastic, thermodynamic, and optical properties of Mo 2 TiAlC 2 are investigated by first-principles calculations. Our results indicate that the a axis is stiffer than c axis within 0~100 GPa. Elastic constants calculations predict the large stability range of Mo 2 TiAlC 2 under pressure. Several important thermodynamic properties are discussed detailedly, including the Debye temperature, thermal expansion coefficient, and heat capacity etc. The bonding properties are studied from the elastic quantities and electronic properties. The electronic properties are investigated, including the energy band structure, density of states, and so on. The evidence of the instability of Mo 3 AlC 2 and stability of Mo 2 TiAlC 2 are successfully obtained.

The magnetism of Fe2MnAl and Mn2FeAl compounds are studied by first principles. Evolutions of magnetic moment of Fe2MnAl display distinct variation trends under pressure, showing three different slopes at different pressure intervals, 0~100 GPa, 100~250 GPa, 250–400 GPa, respectively, and the moment collapses finally at 450 GPa. The magnetic moment of Mn2FeAl shows an increasing tendency below 40 GPa and decreases subsequently with pressure, and collapses ultimately at about 175 GPa. Such non-continuing decrease of Fe2MnAl originates from the unusual charge transfer of Fe and Mn and bond populations rearrangement of Fe-Fe and Mn-Fe, whereas the distinct moment evolution of Mn2FeAl is attributed to the complicated distributions of bond populations. The half-metallicity of the compounds can be maintained at low pressure, below about 100 GPa in Fe2MnAl and 50 GPa in Mn2FeAl. The magnetic moment collapse process didn’t induce volume and bond length anomalies in the two compounds, the unique anomaly is the elastic softening behaviour in elastic constant c 44 and shear (G) and Young’s (E) moduli of Fe2MnAl at 270 GPa, where the second moment collapse occurs.

The electronic structure and thermodynamical properties of Cr2TiAlC2 are studied by first principles under pressure. The obtained results observed that the ferromagnetic order is the most stable ground state and the magnetic moment will collapse at about 50 GPa. As a result, the lattice a axis becomes stiffer above about 420 GPa, ultimately presenting the same axial compressibility trends with those of nonmagnetic compounds Mo2TiAlC2 and hypothetical Cr2TiAlC2. The elastic constants and phonon dispersion curves demonstrate the structural stability during the disappearance of magnetic moment and occurrence of axial alternative compressibility. The density of states and energy band calculations confirmed the existence of magnetic moment of Cr2TiAlC2 at 0 GPa and disappearance at high pressures above 50 GPa. Evolutions of magnetic moment collapse with pressure are confirmed by a variety of properties. The obtained grüneisen parameter and thermal expansion coefficients show the maximum value among the known MAX phases, to date and to the author’s knowledge.

The structural inheritance and difference between Ti2AlC, Ti3AlC2 and Ti5Al2C3 under pressure from first principles are studied. The results indicate that the lattice parameter a are almost the same within Ti2AlC, Ti3AlC2 and Ti5Al2C3, and the value of c in Ti5Al2C3 is the sum of Ti2AlC and Ti3AlC2 which is revealed by the covalently bonded chain in the electron density difference: Al–Ti–C–Ti–Al for Ti2AlC, Al–Ti2–C–Ti1–C–Ti2–Al for Ti3AlC2 and Al–Ti3–C2–Ti3–Al–Ti2–C1–Ti1–C1–Ti2–Al for Ti5Al2C3. The calculated axial compressibilities, volumetric shrinkage, elastic constant [Formula: see text], [Formula: see text] ratio, bulk modulus, shear modulus, and Young’s modulus of Ti5Al2C3 are within the range of the end members (Ti2AlC and Ti3AlC2) in a wide pressure range of 0–100 GPa. Only Ti2AlC is isotropic crystal at about 50 GPa within the Ti–Al–C compounds. All of the Ti 3d density of states curves of the three compounds move from lower energy to higher energy level with pressure increasing. The similarities of respective bond length, bond overlap population (Ti–C, Ti–Al and Ti–Ti), atom Mulliken charges under pressure as well as the electron density difference for the three compounds are discovered. Among the Ti–Al–C ternary compounds, Ti–Ti bond behaves least compressibility, whereas the Ti–Al bond is softer than that of Ti–C bonds, which can also been confirmed by the density of states and electron density difference. Bond overlap populations of Ti–Ti, Ti–C and Ti–Al indicate that the ionicity interaction becomes more and more stronger in the three structures as the pressure increasing. Mulliken charges of Ti1, Ti2, Ti3, C and Al are 0.65, 0.42, 0.39, −0.73, −0.04 at 0 GPa, respectively, which are consistent with the Pauling scale.