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The thermodynamic properties of MgCaSi and its mother phase Ca2Si are comparatively investigated from ab initio calculations and quasi-harmonic Debye-Gruneisen model. At 0 K, MgCaSi is more thermodynamically stable. Under high temperature, the advantage of higher thermodynamically stability of MgCaSi is reduced, originating from the less negative entropy contribution because the thermodynamic entropy of MgCaSi increases more slowly with temperature and the entropy values are slightly smaller. With increasing temperature, the anti-softening ability for MgCaSi is slightly smaller due to the slightly faster decrease trend of bulk modulus than that of Ca2Si, although the bulk modulus of MgCaSi is higher in the whole temperature range considered. The thermal expansion behaviors of both MgCaSi and Ca2Si exhibit similar increase trend, although thermal expansion coefficient of MgCaSi is slightly lower and the increases is slightly slower at lower temperature. The isochoric heat capacity CV and isobaric heat capacity CP of MgCaSi and Ca2Si rise nonlinearly with temperature, and both CV are close to the Dulong–Petit limit at high temperature due to the negligibly small electronic contribution. The Debye temperature of both phases decrease with increasing temperature, and the downtrend for MgCaSi is slightly faster. However, MgCaSi possess slightly higher Debye temperature, implying the stronger chemical bonds and higher thermal conductivity than the mother phase Ca2Si. The Gruneisen parameter of MgCaSi and Ca2Si increase slightly with temperature, the values of MgCaSi are slightly larger. The investigation of electronic structures shows that with substitution of partial Ca by Mg in Ca2Si, the stronger Mg Si, Mg Ca and Si Si covalent bonds are formed, and plays a very significant role for the structural stability and mechanical properties.

The elastic and thermodynamic properties of novel high entropy carbide (HfTaZrTi)C and (HfTaZrNb)C are studied within density functional theory framework, adopting special quasi-random structure to model the chemical disorder of high entropy compounds. The optimized lattice parameters are in good agreement with the available experimental data. Both high entropy carbides are thermodynamically stable due to the negative formation enthalpies. Then mechanical properties in small elastic range are studied, results show that (HfTaZrTi)C and (HfTaZrNb)C are mechanical stable, and (HfTaZrNb)C has greater strength and stiffness in spite of larger brittleness due to stronger covalent bonds. The derived higher Debye temperature of (HfTaZrNb)C indicates stronger covalent interactions. The calculated electronic structures show covalent characteristics accompanied by ionicity for both (HfTaZrTi)C and (HfTaZrNb)C. The thermodynamic properties are further investigated by further combination with Debye-Gruneisen model. As temperature increases, thermodynamic properties of two materials exhibit essentially similar trend, and (HfTaZrTi)C may be more beneficial for reducing the thermal stress mismatch as a tool coating due to larger thermal expansion coefficient whilst (HfTaZrNb)C has strength advantage of greater bulk modulus in engineering applications. The present research will be valuable for understanding and designing of high entropy carbides.

The structural, elastic, and electronic properties of multi-performance ternary phase MgCaSi have been investigated by density functional theory. The present results show that MgCaSi is thermodynamically and mechanically stable. The derived elastic constants indicate that the c axis is the easiest to compress, followed by the a and b axes. The bulk, shear, and Young’s moduli of MgCaSi are higher than these of the mother phase Ca2Si, demonstrating that the hardness of MgCaSi has been favorably improved. The higher Debye temperature of MgCaSi also indicates stronger interatomic interactions and better thermal conductivity. Although MgCaSi exhibits less brittleness based on Pugh’s empirical formula, Poisson’s ratio, and the Cauchy pressure, orthorhombic MgCaSi possesses lower anisotropy than Ca2Si based on several criteria. To reveal the bonding nature of MgCaSi, the electronic structures are further investigated. It is found that the strong Si−Si bond plays a significant role for structural stability and elastic properties.

Ternary alloy ZrHfTi is a novel hexagonal close-packed medium entropy material. As a fundamental parameter for understanding the deformation behavior and mechanical property especially ductility, the stacking fault energy (SFE) of basal plane for ZrHfTi alloy has been studied. Unlike the case of CrCoNi-based alloys, the derived SFEs for intrinsic and twin-like stacking faults of alloy ZrHfTi are relatively high. From the evolution features of stacking fault energies from unitary to binary and ternary materials, the SFEs of studied alloys are intermediate between component materials due to merely mixing effect. Because the SFEs of the constituent elements are relatively large, the SFEs of multicomponent alloys are not necessarily small. The SFE of ZrHfTi is obviously affected by alloying of constituent elements with strong structural propensity. Based on the generalized stacking fault energy, mechanical properties and deformation characteristics are further studied. Our results demonstrate that ZrHfTi has good ductility and high yield strength, and deformation twin in ZrHfTi is also very possible based on the twinning criteria. The research of this paper is beneficial for the design and development of more valuable high-performance multicomponent alloys.

Based on density functional theory calculation in conjunction with quasi-harmonic Debye-Gruneisen model, thermodynamic properties of (TaNbHfTiZr)C and (TaNbHfTiZr)N are studied, in which the chemical disorder is modeled with the special quasi-random structure. Thermodynamic entropies for both materials rise significantly due predominantly to vibrational contribution, and (TaNbHfTiZr)N is more stable at high temperatures because its entropy increment is more dramatic with increasing temperature. Although the high temperature softening effect is very similar, (TaNbHfTiZr)N is more beneficial for higher temperature applications because of the much larger bulk modulus. Thermal expansion coefficients for both materials increase first rapidly then slowly, and (TaNbHfTiZr)N is more slightly susceptible to temperature. For (TaNbHfTiZr)C and (TaNbHfTiZr)N, the heat capacities at constant volume and pressure demonstrate similar behaviors, being larger than metal high entropy HfNbTaTiZr. The present investigations provide helpful insights into the thermodynamic behaviors for both materials.

The structural, mechanical and electronic properties of (TaNbHfTiZr)C high entropy carbide are studied by using density functional theory in conjunction with special quasi-random structures. The proposed lattice constant difference as an empirical criterion for high entropy compounds and mixing enthalpy show the formation of (TaNbHfTiZr)C solid solution. The derived elastic stiffness constants also indicate the mechanical stability of (TaNbHfTiZr)C high entropy carbide. At zero pressure, the calculated elastic mechanics obeys the rule of mixture, whereas Vickers hardness is slightly larger than the average value of constituent binary carbides. The computed elastic parameters show that (TaNbHfTiZr)C is brittle, similar to constituent binary carbides. Under high pressure, the lattice constants decrease slightly, and mechanical properties are improved, even the brittleness-ductility transition takes place. The calculated electronic structures show that covalence in (TaNbHfTiZr)C is relatively weaker than ionic bonding. With increasing pressure, covalence in (TaNbHfTiZr)C decreases while ionicity increases. The present research will be valuable for understanding and designing of high-entropy carbides.

Mechanical and electronic properties of high entropy (-like) alloys Wx(TaTiVCr)1-x (x = 0.30-0.67) with body centered cubic structure are investigated employing density function theory in combination with special quasi-random structure (SQS) model. With simultaneous addition of multi-principle alloying elements with smaller average of atomic radii, the lattice constants drop slightly, and structural stability is lowered due to the higher formation enthalpies. The calculated elastic stiffness constants and elastic moduli derived within the Voigt-Reuss-Hill approximation suggest the noticeable decrease of hardness and strength of the Wx(TaTiVCr)1-x (x = 0.30-0.67) alloys. Interestingly, ductility of Wx(TaTiVCr)1-x (x = 0.30-0.67) alloys is apparently increased, whereas elastic anisotropy is somewhat larger from several criterions. The further studied electronic structures show that bonding of Wx(TaTiVCr)1-x (x = 0.30-0.67) dominantly originates from the contributions of d electrons of constituent elements, W W bonding is stronger than W M (M = Ta, Ti, V, Cr) and M M interactions (M = Ta, Ti, V, Cr). With simultaneous addition of multi-principle alloying elements, values of DOSs at Fermi level are higher and the interplay between atoms is decreased, showing the lower stability. These results provide a guideline for further optimizing the composition and mechanical properties of tungsten alloy.

On basis of systematical ab initio study of mechanical properties of body-centered cubic NbTiZrM (M = Hf, Ta, W) refractory high entropy alloys, the correlation between mechanical properties and valence electron concentration (VEC) is appreciably revealed. The present investigation demonstrates that both the single-crystal elastic parameters and the elastic moduli of NbTiZrM alloys increase for M from Hf to W, similar to the variation trend of VEC. Hence, the strength and hardness of NbTiZrM alloys exhibit apparent correlation with the VEC. Because the Poisson's ratio and the Pugh’s ratio suggest the alloys are more ductile for M from W to Hf, the lower VEC obviously correlates with the better ductility of NbTiZrM alloys. Moreover, with increasing VEC, the elastic anisotropies of NbTiZrM alloys are predicted to decrease, whereas the Debye temperatures of these alloys show increasing tendency. Noticeably, the VEC is an effective adjusting parameter to obtain excellent mechanical properties.

The crystal structure, elastic and magnetic properties of important ternary Mg-based alloys NdMgT4 (T = Co, Ni, Cu) have been studied using reliable ab initio calculations. Both cohesive energy and charge density difference suggest that three alloys have good structural stability with the order: NdMgCo4 > NdMgNi4 > NdMgCu4. It shows that NdMgCo4 alloy has magnetic moments with the Co atoms being the main contribution, which is also in agreement with the calculated electronic structures. We find that NdMgT4 (T = Co, Ni, Cu) alloys are all ductile materials with bulk-to-shear modulus (B/G) values higher than 1.75. The trends of calculated values for the shear moduli Cs and C44 are consistent with that of shear modulus G and young's modulus E, proving that NdMgT4 (T = Co, Ni, Cu) alloys exhibit good plasticity with the trend: NdMgNi4 > NdMgCu4 > NdMgCo4. These calculated results give the basis guidance for the design of rare earth-magnesium-transition metal (R-Mg-T) alloys with improved mechanical properties.

The intrinsic mechanical properties of novel hexagonal high entropy alloys (HEAs) Hf0.25Ti0.25Zr0.25Sc0.25−xAlx (x ≤ 15%) have been studied using first-principles theory based on special quasi-random structure, and influence of Al content is stressed. The derived formation enthalpy and elastic constants indicate the thermodynamical and mechanical stability of the studied alloys. With substitution of Al for Sc, bulk modulus, shear modulus and Young's modulus tend to decrease, while HEAs become more ductile. The estimated elastic anisotropies of alloys show an ascending trend with increasing Al content, and the shear and tensile Young's moduli along several typical directions have been obtained for the studied HCP crystal. Furthermore, the studied ideal strength of HCP HEAs suggest that the ideal tensile strength (ITS) of HEAs occurs in [11 2 0] direction, and decreases from 5.34 GPa to 3.80 GPa with increasing Al content for x goes from 0.00 to 0.15, whereas corresponding critical tensile strain increases from 0.07 to 0.08. The ideal shear strength (ISS) of HEAs takes place in (10 1 0) 2 0 > shear system. With increasing Al content for x goes from 0.00 to 0.15, the ISS decrease from 3.71 GPa to 2.46 GPa, the corresponding critical shear strains increase also from 0.10 to 0.11. So HEAs are more ductile as increasing Al concentration at expense of both ITS and ISS. It is worth noting that the initial slopes of tensile and shear stress–strain are in good agreement with the tensile and shear modulus from elastic parameter, also exhibiting descending trend with Al content. The critical resolved shear stresses (CRSS) estimated from the ITS for HEAs is smaller than the corresponding ISS, suggesting that slip is preference to cleavage. The shearability and half-width of the dislocation are also evaluated and discussed. Furthermore, the detailed electronic structure in bond length evolution is further studied, from feature of the Al-M atom pairs due to addition of Al element, the mechanism for enhancement of ductility for HfTiZrSc1−xAlx is uncovered, all of these provide more details for more adequate understanding deeply the intrinsic mechanism of mechanical properties of alloys HfTiZrSc1−xAlx.

The stacking fault energy (SFE) is fundamental to understand the mechanical behavior of materials, and is also closely related to the structural phase transition. In present work, the generalized stacking fault energies of basal plane for novel hexagonal close-packed high-entropy alloys Hf0.25Ti0.25Zr0.25Sc0.25−xAlx (x

High-entropy ceramics have been increasingly attracting great attention due to their novel properties and widespread applications. In this paper, the local lattice distortion (LLD) of hexagonal closed-packed high-entropy (MoNbTaV) (AlSi)2 and the influence on thermodynamic properties are studied using density functional theory and special quasi-random structure for modelling the chemical disorder. The comparative study between pristine and distorted structures shows that LLD improves the stability and ductility of (MoNbTaV) (AlSi)2, in spite of the little effect on lattice constants. Then LLD is quantified in terms of the standard deviation of statistical distribution of bond lengths. The results show that in (MoNbTaV) (AlSi)2, the LLD in the intra-layer is obviously stronger. Moreover, the influence of LLD on electronic structure is further studied, showing that the larger DOS at EF may be correlated with the larger LLD. The Fermi level of distorted structure is closer to the bottom of pseudogap, and the TDOS at Fermi level decreases significantly, so the LLD stabilizes the structure. Especially, the effect of LLD on thermodynamic properties is deeply investigated. Stemming from the normal high-temperature softening of vibration of LLD, thermodynamic entropy is larger, the thermal expansion is stronger, and the heat capacity is enhanced particularly at low temperature. The present study shows that the stability, ductility and thermodynamic properties can be adjusted by LLD, so is valuable for the understanding and designing of the multi-anionic high-entropy ceramics.

The mechanical properties of novel hexagonal close-packed medium entropy alloy TiZrHf have been studied using first-principles method based on special quasi-random structure. The elastic properties and stress-strain relations of unitary Ti, Zr, Hf, binary alloys TiZr, TiHf and ZrHf have also been studied to benchmark the calculation accuracy. The derived elastic constants suggest the mechanical stability of TiZrHf alloy and all three binary alloys. The elastic constants of TiZrHf indicate a weak strengthening effect. Relatively, TiZrHf has larger strength and stiffness, and also exhibits small elastic anisotropy from several criteria. Especially, ideal strength is further studied. The ideal tensile strength (ITS) of TiZrHf along with all unitary and binary materials takes place in the [11 2 ¯ 0] direction. The ITS of TiZrHf is 3.87 GPa and the corresponding critical tensile strain is 0.08. The ideal shear strength (ISS) for all studied materials occurs in the (10 1 ¯ 0) 2 ¯ 0> shear system. The obtained ISS τ{10-10}[11-20] for TiZrHf is 2.11 GPa at critical strain of ~0.09. The initial slopes of tensile and shear stress - strain curves correspond well to the tensile Young's modulus and shear modulus computed from elastic constants. Moreover, the resolved shear stress estimated from the ITS is smaller than the ISS τ{10-10}[11-20] for each calculated alloy, indicating that the studied alloys are preference to shear slip before tensile failure. From shear stress-stain relation, the intrinsic shearability and half-width of the dislocation core are also studied for all calculated alloys. Then the inherent mechanism of mechanical properties of TiZrHf is further studied by examination of the detailed bond length distribution and the charge density distribution evolution. At critical point under tensile loading, the simultaneous breakdown of bonds results in a steep drop in tensile stress due to homogeneity. Whereas gradual breakdown of chemical bonds under shear deformation is predicted.

High-entropy ceramics have recently attracted considerable attentions because of excellent combination of exceptional properties. In this work, the temperature dependent elastic properties of (ZrTaNbTi)C have been systematically studied from the density functional perturbation theory combined with self-consistent quasi-harmonic approximation. High entropy ceramic (ZrTaNbTi)C is thermodynamically stable due to the negative formation enthalpy, and is also mechanically stable from the obtained elastic properties. The phonon dispersion relation computed at equilibrium volume contains no imaginary-frequency, implying the dynamical stability. At 0 K, (ZrTaNbTi)C possesses evidently high elastic moduli and hardness. The calculated electronic density of state and Bader charge at 0 K and 2000 K show that (ZrTaNbTi)C have covalent characteristics accompanied by ionic feature while the covalency decreases and the ionicity increases as temperature increases. The temperature-dependent elastic properties show that (ZrTaNbTi)C is mechanically stable in temperature range studied, and remains high strength and hardness at high temperature due to the slight softening of strong covalent bonding. Poisson's ratio, Pugh's ratio and Cauchy pressure suggest the higher brittle-ductile transformation trend as the temperature increases. Moreover, (ZrTaNbTi)C shows less anisotropy at higher temperature from the Zener index AZ and three-dimensional projections, being beneficial to reduce cracking and improve durability. The present study provides more insight into the high temperature behavior of mechanical properties, would be valuable for understanding and design of high-temperature properties of high entropy carbide ceramics.

Nine possible native point defects in ternary C14 Laves phase Mg2Cu3Si are investigated from ab initio calculation based on density function theory. The two-dimensional phase diagram of chemical potentials is determined, and then defect formation energy is calculated. The energetic results show that CuSi and CuMg are more favorable over a broad range of chemical potentials. The formation enthalpies for defective Mg2Cu3Si also demonstrate the same stability. Local distortions around point defects increase from SiCu to SiMg, showing that the polyhedral symmetry and coordination number for constituent atoms will affect the structure of defects. The electronic structure shows the strong (Cu, Si)–Si covalent bonding, also indicates that the CuMg is favorable because the weak Mg-Cu bonding is replaced by the strong Cu–Cu bonding, whereas MgCu and MgSi are unfavorable because the strong Cu–Si bonding is replaced by the weak Mg–(Cu, Si) bonding.

To predict and compare the main reinforcement effects of the key precipitation phases Mg2Cu3Si, Mg2Si and MgCu2 in Mg-Cu-Si alloy, the structural, mechanical and electronic properties of these phases have been studied by ab initio calculations. The lowest formation enthalpy and cohesive energy indicate that Mg2Cu3Si has the strongest alloying ability and structural stability. The mechanical modulus indicates that Mg2Cu3Si has the strongest resistance to reversible shear/volume distortion and has maximum hardness. The characterization of brittle (ductile) behavior manifests that MgCu2 has favorable ductility. Meanwhile the evaluation of elastic anisotropy indicates that Mg2Si possesses elastic isotropy. Debye temperature prediction shows that Mg2Si and Mg2Cu3Si have better thermal stability. To achieve an unbiased interpretation on the phase stability and mechanical behavior of these precipitation phases, the density of states and differential charge densities are also analyzed. The current study deepens the comprehensive understanding of main reinforcement effects of these precipitation phases on Mg-Cu-Si alloys, and also benefits to optimize the overall performances of Mg-Cu-Si alloy from the hardness, ductility and thermal stability by controlling these second precipitation phases during the heat treatment process.

Nine possible native point defects in MgCaSi have been studied by employing density functional theory based ab initio calculations. The complex chemical potential limits are first determined using a two-dimension (ΔμMg, ΔμCa) diagram, then the defect formation energies as a function of the atomic chemical potential are gained. The energetic results show that under Mg-rich conditions, the most favorable defect is MgCa rather than MgSi, while CaMg is predominant compared to CaSi under Ca-rich conditions. The bonding energy is first introduced to uncover the intrinsic feature of defect formation energy. The local geometric distortion around CaMg, MgSi, and CaSi antisite defects gradually increases due to the smaller atomic radii from Ca to Mg and Si, showing the important role of the geometrical mismatch. The density of states indicates that the higher stability of CaMg and MgCa originates from the smaller deviation of the Fermi level from the pseudo-gap.

Ti-doping and Li-vacancy (VLi) crucially affect the dehydrogenation properties of LiBH4 surface. However, theoretical investigations on individual Ti or VLi could not completely explain experimental observations. In this article, we investigated the synergistic effects of co-existing Ti and VLi on the dehydrogenation properties of LiBH4 (010) surface. Our result shows mutual stabilization between Ti-dopant and Li-vacancy, implying expectable co-existence of Ti and VLi. Thermodynamic destabilization from composite Ti + VLi defect agrees with experiments better than that from single Ti or VLi. The kinetic barrier on Ti + VLi decorated surface also becomes closer to experimental result. Therefore, the co-existing Ti and VLi synergistically and crucially affect the dehydrogenation thermodynamics and kinetics on LiBH4 surface. The electronic structure further reveals strong H H, B B, and Ti B bonds as well as weakened B H bond in transition states on Ti + VLi co-existed surface, which is the main factor of low kinetic barrier.

Point defects and atomic diffusion in Al2Ca have been studied from first-principles calculations within density functional framework. After formation energy and relative stability of point defects are investigated, several predominant diffusion processes in Al2Ca are studied, including sublattice one-step mechanism, 3-jump vacancy cycles and antistructure sublattice mechanism. The associated energy profiles are calculated with climbing image nudged elastic band (CI-NEB) method, then the saddle points and activation barriers during atomic diffusion are further determined. The resulted activation barriers show that both Al and Ca can diffuse mainly mediated by neighbor vacancy on their own sublattice. 3-jump cycle mechanism mediated by VCa may make some contribution to the overall Al diffusion. And antistructure (AS) sublattice mechanism can also play an important role in Ca atomic diffusion owing to the moderate activation barrier.

First principle calculation, based on density functional theory, is applied to study the electronic and magnetic properties of Co-doped ZnO ∑7 (12 3 0) twin grain boundary. Co atoms substituting Zn at the threefold-coordination sites have the lowest formation energy, compared with other sites. More importantly, the configuration can result in the stable formation of ferromagnetic state (FM). Meanwhile, the strong Co-Co interaction is found to be responsible for the ferromagnetic state. Due to the structural character of the twin grain boundary, periodical defects can be offered, which favors the macroscopic FM ordering. The result also gives us a new thinking to understand the origin of FM in transition metal doped ZnO.

Temperature dependence of mechanical and thermodynamic properties of refractory high entropy alloys Ti(25+x)Zr25Nb25Ta(25-x) (x ≤ 20) are studied from ab initio quasi-harmonic Debye-Gruneisen model, and the influences of substitution of Ti for Ta are emphasized. The substitution of Ti for Ta results in the significantly reduced densities and the apparently enhanced specific elastic properties of Ti(25+x)Zr25Nb25Ta(25-x) alloys. Moreover, the increases of Ti content obviously improves ductility. At high temperature, the alloys with higher Ti content demonstrate the stronger thermal expansion behavior and thermal conductivity. Importantly, the alloys with higher Ti content possess the greater specific elastic properties at high temperature. Especially, in the studied temperature range, the present alloys exhibit good anti-softening ability based on temperature-dependent mechanical properties. Therefore, the replacement of Ta by Ti in refractory Ti(25+x)Zr25Nb25Ta(25-x) alloys is beneficial for formation of novel high temperature light-weight structural materials with lower density, better ductility and higher specific mechanical properties.

The finite temperature elastic properties of non-equiatomic refractory high-entropy alloys (RHEAs) HfNbZrTa1−xTix are investigated using the exact muffin‑tin orbitals method in combination with coherent potential approximation and Debye-Gruneisen model, especially the effect of Ta and Ti addition is emphasized. Taking HfNbZr as a reference, the lattice constants decrease when alloying with Ta, and continue to decline slightly with replacement of Ta by Ti. Estimating from calculated elastic parameters, mere Ta addition leads to the high strength and stiffness accompanying evident lowering of ductility, while sole Ti addition brings about the high ductility at the expense of reducing strength and hardness. With substitution of Ti for Ta, HfNbZrTa1−xTix alloys achieve a relatively high ductility accompanied a gentle decline in high strength and hardness. As temperature increases, although the obtained single-elastic and polycrystalline elastic parameters exhibit decreasing trend, the anti-softening ability is enhanced with substitution of Ti for Ta, and HfNbZrTa1−xTix alloys remain an overall good combination of strength and ductility at high temperature. The proper strength-ductility trade-off can be gained by tuning Ti/Ta ratio, which is beneficial for designing the high temperature mechanical properties of alloy.

Atomic diffusion in pure and transition element (TM = Ti, Y, Zr or Hf)-doped Al3Sc has been studied mainly along vacancy-mediated diffusion paths. After the point defect formation energies are determined, the energy profiles for dominant diffusion paths are obtained using climbing image nudged elastic band method. The energetic results show that Al atom diffusion through nearest-neighbor jump mediated by Al vacancy is most favorable due to the lowest activation barrier, the other diffusion processes would make very small contribution due to the high activation barrier or unstable final state. The dominant Sc atom diffusion mechanisms are the Al-vacancy mediated nearest-neighbor jump under Al-rich condition and antistructure sublattice mechanism under Sc-rich condition. The 6-jump cycle and next nearest-neighbor jump are greatly restricted with high activation barriers. Moreover, effect of typical transition element (Ti, Y, Zr or Hf) doping on atomic diffusion is further studied. The activation barriers for dominant diffusion mechanisms increase with increasing atom size mismatch in sequence of Zr

Employing first-principles calculations, the point defect in C15 Laves phase MgCu2 is studied. The formation enthalpies of point defects and defective C15 MgCu2 compound show that the dominating defect structure is MgCu and CuMg antisite defect on Mg-rich and Cu-rich side of off-stoichiometry, respectively. The concentration of various point defects as a function of composition of MgCu2 is analyzed from grand canonical statistics. The calculated local geometrical variation around defect demonstrates an apparent size effect, and the electronic densities of states and charge density difference distributions indicate the gradually weaker bonding from MgCu to VCu and from CuMg to VMg systems. Furthermore, doping of Zn atom in defective MgCu2 has been investigated. It is found that Zn has a stronger preference for occupying the Cu sublattice than for Mg sublattice because of the relative lower formation enthalpy. The electronic structure further reveals that the stability of Zn-doped system is associated with the stronger covalent bonds between Cu–Cu and Zn–Cu atoms.

Thermal properties and thermoelasticity of L12 Al3RE (RE = Er, Tm, Yb, Lu) phases have been studied by first principles calculations combined with density functional perturbation theory and quasi-harmonic approximation. In the temperature range considered, the calculated thermal properties including equilibrium volume, isothermal bulk modulus, Grüneisen parameters for different Al3RE phases exhibit analogous variation tendency and the numerical values are associated with the atomic radius of RE. The calculated thermal expansion and heat capacity for different Al3RE are almost indistinguishable from each other. The obtained elastic constants and polycrystalline elastic moduli exhibit gentle softening trends with temperature, and the variation tendency is also very similar. In the temperature range considered, Al3RE phases are nearly isotropic. The present study would be valuable for future investigation and design of high temperature Al alloys. Keywords: First principles calculations, Thermal properties, Thermoelasticity, Density functional perturbation theory, Quasi-harmonic approximation

The newly synthesized novel double-Ga layer nanolaminated carbide Mo2Ga2C is stimulating tremendous research interests. In the present exploration of Mo2Ga2C structure, another plausible metastable structure with close-packed Ga layers is predicted from density functional calculations. This new structure (denoted as m-structure) is slightly less stable by only 52 meV/atom than the experimentally determined structure (e-structure) with on-top stacked Ga layers. Importantly, this m-structure is dynamically stable from the calculated phonon dispersion. Moreover, the stability behavior of this m-structure under compression shows that possible phase transition from e-phase to m-phase could occur under a pressure above 24.3 GPa, which requires further experimental confirmation. Phase transition model is proposed, and the energy barrier for phase transition is further derived. The electronic structures show that Mo–C bonds and Ga–Ga bonds are weaker in metastable m-phase than in e-phase. During compression, more strengthening of Ga–Ga and Mo–Ga bonds and less weakening of Mo–Mo bonds in m-phase explain the stabilization of m-phase under pressure.

The elastic properties of L1 2 -type Al 3 Sc at high temperature have been studied using the first-principles calculations combined with the quasi-harmonic approximation. The obtained elastic constants and polycrystalline elastic moduli exhibit a very gentle descent trend with increasing temperature. Elastic anisotropy of Al 3 Sc is slightly enhanced with increasing temperature, while the brittle nature is insensitive to temperature. The relevant important thermodynamic properties including thermal expansion coefficient and heat capacity are further derived and discussed. The moderate variation of elastic properties and the thermal properties may be attributed to the slightly weakened Al–Sc covalent bonding with temperature increasing. Our results would be valuable for further experimental study of high temperature mechanical properties of the relevant Al-based alloys.

Eight possible native point defects in Mg24Y5 are studied from the density functional theory (DFT) calculations within GGA approximation. The energetic results show that anti-site defects with lower formation energies are energetically favored over vacancies. Under both Mg-rich and Y-rich conditions, MgY1 defect is dominant due to the lowest defect formation energy, followed by YMg2, MgY2 and YMg1, which reasonably explains the Mg-rich off-stoichiometry of Mg24Y5 alloys. For vacancy defects, the formation energies on the two Mg sub-lattices are smaller than ones on two Y sub-lattices, and VMg1 has the lowest formation energy, while VY2 is most unlikely due to the highest formation energy originating from the large mismatch in atomic size and the strong interaction of Y with surrounding atoms. The defect concentration distribution as a function of temperature and stoichiometry is further obtained from grand canonical statistics. The size factor and electronic structure are further discussed, demonstrating that Mg24Y5 alloy is typical system in which the point defects are affected by strong size effect due to the large atomic size radius and strong electronic factor caused by the intensive interaction of Y with the surrounding atoms.

First-principles calculations have been performed to study the structural, mechanical and magnetic properties of the MgYCo4 and MgYNi4 phases in AuBe5-type structure. The obtained values of cohesive energy as well as formation energy prove that the MgYCo4 and MgYNi4 phases have a good combination of structural stability and alloying ability, which is also supported by electronic structure. It is found that the magnetic moment of the MgYCo4 phase is 19.06 µB per unit cell mainly owed to the 3d state of Co atom, and the MgYNi4 phase exhibits no magnetism. Both the trigonal shear constant C 44 and the shear modulus G of the MgYNi4 phase are larger than those of the MgYCo4 phase. Plasticity of alloys has been estimated by the C 11–C 12 and Young’s modulus E, and C 12–C 44, shear to bulk modulus ratio G/B and Poisson’s ratio ν have been studied to predict the ductility of alloys. According to the calculated results, the MgYCo4 phase has better plasticity as well as ductility, compared with the MgYNi4 phase.

HfTiZrSc is a novel hexagonal close-packed refractory high entropy alloys, addition of Al as typical additives significantly enhances the strength and ductility. To reveal the effect of Al addition on thermal properties, we combine the EMTO-CPA ab initio calculations with quasi-harmonic Debye-Gruneisen model to studied the thermodynamic properties of the Hf0.25Ti0.25Zr0.25Sc0.25-xAlx (x ≤ 15 at.%) HEAs. With Al substitution for Sc, the strength of Hf0.25Ti0.25Zr0.25Sc0.25-xAlx (x ≤ 15 at.%) is enhanced significantly, despite essentially similar thermal softening trend. Thermal expansion coefficient of Hf0.25Ti0.25Zr0.25Sc0.25-xAlx increase with increasing Al content. Thermodynamic entropy of Hf0.25Ti0.25Zr0.25Sc0.25-xAlx (x ≤ 15 at.%) increases dramatically with temperature, the trend is to some degree suppressed with increase of Al content, which is discussed from vibrational, electronic and configuration entropy contribution. The influences of Al content on Debye-temperature and Gruneisen parameter are also further studied. The present investigation is valuable for optimal designing of overall performance of Hf0.25Ti0.25Zr0.25Sc0.25-xAlx alloys.

The pressure dependence of elastic properties of Mo2Ga2C is studied via first-principles calculation. The present investigation shows that differing from other MAX phases, in Mo2Ga2C the [Formula: see text] is larger than [Formula: see text], because of the strong Ga–Ga interlayer bonds along [Formula: see text]-axis. Moreover, under pressure, the [Formula: see text] increases more rapidly, originating from the faster strengthening of Ga–Ga bonds. Interestingly, elastic constants [Formula: see text] soften under high pressure (more than 20 GPa). Especially, the calculated phonon structure demonstrates that transverse acoustic (TA) phonon mode also softens under pressure, implying possible phase transition. The reduction of [Formula: see text] and softening of phonon mode are attributed to significantly weakened Mo–Mo interaction in contrast to the strengthening of Ga–Ga bonds under high pressure. Our present results further indicate that Mo2Ga2C is more ductile under pressure.

The native point defects in C14 Mg 2 Ca Laves phase are studied from the first-principles density functional theory calculations within GGA approximation. The defect formation energies indicate that anti-site defects are energetically favored over vacancies. Under Mg-rich and even general Ca-rich condition, defect Mg Ca of Mg anti-site on Ca sublattice is favorable owing to the lowest formation energy. The Ca Mg2 defect of Ca anti-site on Mg2 sublattice is also likely dominant only under extreme Ca-rich environment. The present results could explain reasonably the asymmetric off-stoichiometry of Mg 2 Ca. The effective point defect concentrations of Mg 2 Ca as a function of composition and temperature at experimental range are also calculated from a canonical statistical model, and the derived results show a linear relationship between the logarithm of defect concentration and T −1 . Geometrical factor is further studied, and it is found that atomic size possesses an obvious influence on the structure of point defect in Mg 2 Ca. The electronic feature is further studied to reveal underlying mechanism for formation of point defects.

A comparative study of single- and co-substitution of Ti on dehydrogenation of Mg2NiH4 has been carried out from first-principles calculations based on density functional theory. In comparison with Ti single-substitution, the formation enthalpy in co-substituted Mg2NiH4 is higher, showing the lower thermodynamic stability. In Ti co-doped Mg2NiH4, the average Ni H bond length of entire unit cell is larger, implying weaker Ni H bonds and lower stability of complexes NiH44−. Ti co-substitution further shows a more favorable dehydrogenation effect on Mg2NiH4 due to lower hydrogen dehydrogenation energy, and significantly reduces the dehydrogenation reaction enthalpy of Mg2NiH4 by about 30% compared to the pure state. Further calculated electronic structure demonstrates that the co-substituted Mg2NiH4 displays a metallic behavior with the Fermi level locating at the doping band, and the underlying mechanism for improving dehydrogenation properties of co-substituted Mg2NiH4 can be attributed to the weakened Ni H interactions together with the narrowed energy gap.

The structural evolution and electronic mechanism for KBH 4 phase transition have been systematically investigated using first-principles calculations. The present results demonstrate experimentally observed stability order of α-KBH 4 > β-KBH 4 > γ-KBH 4 , and the predicted transition pressure at 0 K for cubic → tetragonal → orthorhombic phase transformation agrees reasonably with experimental measure. The atomic process indicates that KBH 4 structural evolution is closely related to rotation and deformation of [BH 4 ] − clusters as well as shift of [BH 4 ] − clusters and K atoms. Along with phase transformation, the band gap of KBH 4 narrows, the B H covalent bond weakens while K H interaction enhances, the K K anti-bonding and coulomb repulsion are also stronger.

It’s important to get accurate carrier phase and frequency information when using a standalone GPS receiver. In weak signal applications, to keep a stable tracking is hard to achieve because measuring error will be huge when the SNR is low. Different methods are used to improve the SNR before the detector in a tracking process, such as coherence integration. And this paper keeps eyes on a different viewpoint, on how to refine estimation results. A cascade structure is introduced for weak signal tracking. This structure is divided into two levels. In the first level, raw phase estimation and accurate frequency estimation is provided to achieve stable work in low CNR environment. In the second level, the raw phase estimation is refined to achieve accurate tracking requirement. This cascade structure can also work jointly with any other SNR-improving technology to get a better performance.

The crystal structure of LiCa(AlH4)3 was investigated via first principle calculations, especially the positions of hydrogen atoms undetected in XRD experiments were predicted, then the thermodynamic favourability of the experimentally reported structure with respect to several candidates from the inorganic crystal structure database (ICSD) was confirmed. It is found that hexagonal packing of AlH4 layers along the c axis is present in LiCa(AlH4)3, and the detailed geometrical feature is further revealed. The electronic structures show that in LiCa(AlH4)3 the Li–AlH4 interaction is more covalent than in LiAlH4, while the Ca–AlH4 covalence is less than in Ca(AlH4)2. The overall stronger covalence in LiCa(AlH4)3 leads to weakened Al–H bonds. The Li–H interaction in LiCa(AlH4)3 dramatically turns out to be strong bonding, opposite to the Li–H anti-bonding in LiAlH4. The Ca–H bonds are more anti-bonding in LiCa(AlH4)3.

Structure and bonding features of hydride Ae 6 Mg 7 H 26 (Ae = Sr, Ba) were investigated by first principles calculations. The Ba–H distance in Ba 6 Mg 7 H 26 is longer relative to the Sr–H in Sr 6 Mg 7 H 26 , while the Ba-containing polyhedron with higher symmetry and high coordination numbers possesses high stability reflected by the more negative formation enthalpy obtained for Ba 6 Mg 7 H 26 . Hydrogen release from Sr 6 Mg 7 H 26 would be easier. The electronic structures indicate that the Ae 6 Mg 7 H 26 (Ae = Sr, Ba) exhibits non-metallic properties and the valence band is primarily dominated by H–s electrons. The chemical bonds in Ae 6 Mg 7 H 26 (Ae = Sr, Ba) exhibit primary covalent feature with definite ionic component, the covalent feature of Ba–H is more obvious than that of Sr–H. These electronic structures reveal the underlying mechanism for structure and bonding features of the hydride Ae 6 Mg 7 H 26 (Ae = Sr, Ba).

Full a-dislocations on the (0001) basal plane, $$(10\bar 10)$$ prismatic plane, and $$(10\bar 11)$$ and $$(10\bar 12)$$ pyramidal planes in pure magnesium are investigated by using the Peierls-Nabarro model combined with generalized stacking fault (GSF) energies from first-principles calculations. The results show that the $$\left( {10\bar 11} \right)\left\langle {11\bar 20} \right\rangle$$ and $$\left( {10\bar 12} \right)\left\langle {11\bar 20} \right\rangle$$ slip modes have nearly the same GSF energy barriers, which are obviously larger than the GSF energy barriers of the $$\left( {0001} \right)\left\langle {11\bar 20} \right\rangle$$ and $$\left( {10\bar 10} \right)\left\langle {11\bar 20} \right\rangle$$ slip modes. For both edge and screw full dislocations, the maximum dislocation densities, Peierls energies, and stresses of dislocations on the $$(10\bar 10)$$ , (0001), $$(10\bar 11)$$ , and $$(10\bar 12)$$ planes eventually increase. Moreover, the Peierls energies and the stresses of screw full dislocations are always lower than those of edge full dislocations for all slip systems. Dislocations on the $$(10\bar 11)$$ and $$(10\bar 12)$$ pyramidal planes possess smaller core energies, while the $$(10\bar 10)$$ prismatic plane has the largest ones, implying that the formation of full dislocations on the $$(10\bar 10)$$ plane is more difficult.

The Cu-doping effects on dehydrogenation of MgH2 (001) and (110) surfaces were investigated by using first-principles calculations. On the basis of the calculation results of total energy, the Cu dopant prefers to occupy the interstitial site on both surfaces rather than substitute a Mg atom, and the Cu dopant bonds with four adjacent H ions to form a CuH4 cluster. The electronic structures show that Cu–Mg and Cu–H interactions strongly weaken Mg–H interactions, which leads to a reasonable expectation of decreased dehydrogenation temperature. The kinetic barriers for Cu-doped (001) and (110) surfaces are, respectively, reduced to 1.83 and 1.48 eV, showing that improved kinetics can be expected due to the much lower desorption barriers on both Cu-doped surfaces. The present results are beneficial to resolve the disputes between previous reports on the catalytic effects of Cu-doping in the MgH2 system.

With the substitution of part Mg in LaMg3 by Cu, the elastic constants C 11 and C 12 increase while C 44 decreases, implying an enhanced Poisson effect and smaller resistance to 〈001〉(100) shear. Furthermore, the bulk modulus B increases, while the shear modulus G, elastic modulus E and anisotropic ratio A are reduced. The calculated Debye temperature of LaCuMg2 is lower, implying the weaker interaction between atoms in LaCuMg2. Then, the stress-strain curves in entire range and the ideal strength at critical strain are studied. The present results show that the lowest ideal tensile strength for LaMg3 and LaCuMg2 is in the 〈100〉 direction. The ideal shear strength on the $$\left\langle {1 \bar 1 0} \right\rangle \left( {110} \right)$$ slip system of LaMg3 is greater than LaCuMg2. The density of states and charge density distribution are further studied to understand the inherent mechanism of the mechanical properties.