The Effects of Al and Ti Additions on the Structural Stability, Mechanical and Electronic Properties of D8 m -Structured Ta 5 Si 3

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Introduction
In order to meet the ever-increasing demand for high performing and durable structural components to be used in harsh environments, much attention has been focused upon transition metal silicides [1,2].As the largest family of intermetallic compounds, transition metal silicides are of great interest to a wide variety of applications due to their unique properties, such as ultra-high melting temperatures, excellent electrical properties, superior thermal stability, high oxidation resistance, good creep tolerance, and excellent mechanical strength at elevated temperature [3][4][5].Compared with other transition metal silicides, such as Mo and Ti silicides, that have been extensively investigated over the past few decades, Ta-Si compounds with higher melting point than the former two silicides systems have received limited attention.As the most refractory compound in the Ta-Si binary system [6], Ta 5 Si 3 has a melting point of 2550 ˝C, and thus has a great potential for structural applications at ultra-high temperatures.Moreover, although the high cost and density of Ta make its direct clinical application in a bulk form difficult, tantalum-based compounds are particularly suitable for use as implant coatings to improve the performance of metal substrates, due to their good corrosion resistance, exceptional biocompatibility, osseointegration properties, hemocompatibility, and high radiopacity [7].The Ta 5 Si 3 was reported to have three different polymorphs: Mn 5 Si 3 , W 5 Si 3 and Cr 5 B 3 type [8].A D8 8 -structured Ta 5 Si 3 (Mn 5 Si 3 prototype) with the P6 3 /mcm symmetry is a metastable phase, a D8 1 -structured Ta 5 Si 3 (Cr 5 B 3 prototype) with the I4/mcm symmetry is the low-temperature phase and a D8 m -structured Ta 5 Si 3 (W 5 Si 3 prototype) with the I4/mcm symmetry is the high-temperature phase.Tao et al. [9] predicted the ductile behavior of the three prototype structures for Ta 5 Si 3 and they found that the Cr 5 B 3 -prototype phase is slightly prone to brittleness, and the W 5 Si 3 -prototype phase is more prone to ductility.Therefore, in comparison to the other two prototype structures, D8 m -structured Ta 5 Si 3 exhibits more potential as a candidate material for structural applications under an aggressive environment and has been chosen as the subject of our present work.However, as with many other intermetallic materials, owing to its strong covalent-dominated atomic bonds and intrinsic difficulties of dislocation movement, its low toughness poses a serious obstacle to its commercial application.To address this problem, several effective strategies have been developed, including densification [10,11], grain refinement [12], substitutional alloying [13], and the incorporation of a second reinforcing phase to form a composite [14].In contrast to the ionic or covalent bonding that is prevalent in ceramics, the partial metallic character of bonding endows metal silicides with a degree of alloying ability, making it possible to improve toughness through an alloying approach.An alloying approach is achieved either by doping the metal silicides with interstitial atoms [15], or by the incorporation of substitutional atoms into the lattice of metal silicides crystal [13].
Compared with additions of interstitial atoms, incorporation of substitutional atoms into Ta 5 Si 3 is more complex, and the site substitution of the added alloying elements in Ta 5 Si 3 plays an important role in influencing the electronic structure and hence the mechanical properties of the material.Unfortunately, to our knowledge, no first-principles calculations have been employed to elucidate the effects of substitutional elements on the electronic structure and mechanical properties of D8 m -structured Ta 5 Si 3 .In this paper, Ti and Al were selected to investigate the site occupancy behavior of the two elements in D8 m -structured Ta 5 Si 3 and, based upon that, the elastic moduli including bulk modulus, shear modulus, and Young's modulus were calculated for the binary and ternary Ta 5 Si 3 with D8 m -structure.This, in turn, was used to gain insight into the effect of the two substitutional elements on the electronic structure and mechanical properties of D8 m -structured Ta 5 Si 3 .

Calculation Details
The first-principal calculations in this work were performed based on density functional theory (DFT) by using the Cambridge Sequential Total Energy Package code (CASTEP) [16].The electron exchange and correlations were treated within the generalized gradient approximation using the Perdew, Burke and Ernzerhof function (GGA-PBE) [17].The interactions between the electron and ionic cores were described by the projector augmented wave (PAW) [18] method.The ultrasoft pseudo-potentials set 5p 6 5d 3 6s 2 for Ta, 3s 2 3p 2 for Si, 3s 2 3p 1 for Al and 3p 6 3d 2 4s 2 for Ti as valence electrons, respectively, for each element.A 350 eV cutoff energy determined by the converged test for the total-energy remained constant for both the binary and ternary Ta 5 Si 3 compounds.The special points sampling integration over the Brillouin zone were carried out using the Monkhorst-Pack k-points (the reciprocal space) mesh grid [19].Confirming convergence to a precision of 1 meV/atom, a 4 ˆ4 ˆ4 Monkhorst-Pack grid of k-points was adopted.Geometry optimization was processed to create a steady bulk structure with the lowest energy close to the natural structure by adjusting the lattice parameters of the models.In the optimization process, the energy change, maximum force, maximum stress, and maximum displacement tolerances were set as 5.0 ˆ10 ´6 eV/atom, 0.01 eV/Å, 0.02 GPa and 5.0 ˆ10 4 Å, respectively.All calculations were performed under non-spin-polarized condition.
A stoichiometric D8 m -structured Ta 5 Si 3 unit cell consisting of 20 Ta atoms and 12 Si atoms is used for the computations.The atomic configuration of D8 m -structured Ta 5 Si 3 is shown in Figure 1.The stacking sequence of layers along the c-axis for this structure is the same as that for D8 m -structured Mo 5 Si 3 and can be viewed as repeated ABAC ... stacking (see Figure 1b).The A-layer has a more open atomic environment (i.e., lower atomic packing density), which links together with the more close-packed B-and C-layers through the transition metal-silicon bonds [20].Both Ta and Si have two symmetrically non-equivalent positions in the lattice.The elements that are localized on the more close-packed planes are termed Ta 16k and Si 8h , and those on the less close-packed planes are termed Ta 4b and Si 4a .For the determination of which of the doped sites is the preferential site for the alloying elements under consideration (Ti and Al).Ta 20 Si 12 is substituted by either one Ti or one Al atom (that is, the additions concentration is 3.125 at.% (atomic concentration)), resulting in four possible substitution structures: Ta 19 M 16k Si 12 , Ta 19 M 4b Si 12 , Ta 20 Si 11 M 8h and Ta 20 Si 11 M 4a (M = Ti or Al).The enthalpies of formation of the four substitutional structures were calculated according to the following equation: where M denotes the alloying element Ti or Al, N represents the total atom number of Ta α Si β M (M is Ti or Al), and α, β means the atom number of Ta, Si.E(Ta α Si β M) is the value for the enthalpy of formation of Ta α Si β M. E(Ta), E(Si) and E(M) are the ground states enthalpy of per atom for Ta, Si, Al and Ti, respectively.
A stoichiometric D8m-structured Ta5Si3 unit cell consisting of 20 Ta atoms and 12 Si atoms is used for the computations.The atomic configuration of D8m-structured Ta5Si3 is shown in Figure 1.The stacking sequence of layers along the c-axis for this structure is the same as that for D8m-structured Mo5Si3 and can be viewed as repeated ABAC ... stacking (see Figure 1b).The A-layer has a more open atomic environment (i.e., lower atomic packing density), which links together with the more closepacked B-and C-layers through the transition metal-silicon bonds [20].Both Ta and Si have two symmetrically non-equivalent positions in the lattice.The elements that are localized on the more close-packed planes are termed Ta 16k and Si 8h , and those on the less close-packed planes are termed Ta 4b and Si 4a .For the determination of which of the doped sites is the preferential site for the alloying elements under consideration (Ti and Al).Ta20Si12 is substituted by either one Ti or one Al atom (that is, the additions concentration is 3.125 at.% (atomic concentration)), resulting in four possible substitution structures: Ta19M 16k Si12, Ta19M 4b Si12, Ta20Si11M 8h and Ta20Si11M 4a (M = Ti or Al).The enthalpies of formation of the four substitutional structures were calculated according to the following equation: where M denotes the alloying element Ti or Al, N represents the total atom number of TaαSiβM (M is Ti or Al), and α, β means the atom number of Ta, Si.E(TaαSiβM) is the value for the enthalpy of formation of TaαSiβM.E(Ta), E(Si) and E(M) are the ground states enthalpy of per atom for Ta, Si, Al and Ti, respectively.The elastic constants can gauge the mechanical stress required to produce a given deformation.Both stress [σαβ] and strain [εαβ] are symmetric tensors of rank two, which can be described by matrix σi (i = 1, 2, …, 6) and Ɛj (j = 1, 2, …, 6).As a result, the elastic constants can be represented by a 6 × 6 symmetric matrix [Cij] under the conditions of small stresses and small strains: The elastic constants can gauge the mechanical stress required to produce a given deformation.Both stress [σ αβ ] and strain [ε αβ ] are symmetric tensors of rank two, which can be described by matrix σ i (i = 1, 2, . . ., 6) and ε j (j = 1, 2, . . ., 6).As a result, the elastic constants can be represented by a 6 ˆ6 symmetric matrix [C ij ] under the conditions of small stresses and small strains: Meanwhile, under the conditions of small stresses and small strains on a crystal, Hooke's law is applicable and the elastic energy ∆E is a quadratic function of the strains: where V is the total volume of the unit cell, e i are the components of the strain matrix [21] For the symmetry of a tetragonal crystal (a = b ‰ c, α = β = γ = 90 ˝), there are six independent elastic constants: C 11 , C 12 , C 33 , C 13 , C 44 , and C 66 .In order to determine these independent elastic constants, a set of six independent total-energy calculations are performed [22].The lattice is deformed uniformly in six different ways, and for each of them we calculated the total energy as a function of strain (up to 2%-3%).The new lattice axes a' i are related to the original ones a' j by a' i = (I + ε') ˆaj , where I is the identity matrix and Thus, if the elastic energy of a crystal is known, the elastic constants at equilibrium volumes can be calculated using Equations ( 2) and (3).
For the cubic symmetry (a = b = c, α = β = γ = 90 ˝), its geometry renders some elastic constant components equal, resulting in the remaining three independent elastic constants; namely, C 11 , C 12 and C 44 .The details of the calculations can be found elsewhere [9] and are not detailed here.
The effective elastic moduli of polycrystalline aggregates are usually calculated by two approximations according to Voigt [23] and Reuss [24], where uniform strain and stress are assumed throughout the polycrystal.Hill [25] has shown that the Voigt and Reuss averages are limited and suggested that the actual effective modulus can be approximated by the arithmetic mean of the two bounds, referred to as the Voigt-Reuss-Hill (VRH) value.
The Voigt bounds for the cubic system are: The Voigt bounds for tetragonal systems are: B V " 1{9r2pC 11 `2C 12 q `C33 `4C 14 qs (10) and the Reuss bounds are: G R " 15tp18B V {C 2 q `r6{pC 11 ´C12 q `p6{C 44 q `p3{C 66 qsu -1 (13) For both cubic and tetragonal crystals, the VRH mean values are finally computed by: The Young's modulus and the Poisson's ratio can be calculated based on the values of both bulk and shear modulus by the relations: υ " p3B ´2Gq{2p3B `Gq

Lattice Parameter
The structures of both pure elements and compounds are optimized by relaxing the simulation cell and the corresponding calculated lattice constants are obtained at a minimum energy.The phases of b.c.c tantalum, diamond-structured silicon, h.c.p titanium and f.c.c Al are used as the reference ground states.The calculated lattice constants, together with available experimental data and theoretical values, are listed in Table 1.The lattice constants of the pure elements are in good agreement with the values reported in the literature [26][27][28][29][30], giving confidence to the reliability of the data for this investigation.Figure 2 shows the change of unit cell volume versus the substitution sites occupied by one Ti or one Al atom.As shown in Figure 2, it can be seen that the change of unit cell volume is only over a range from ´0.75% to 1.75%, indicating that the lattice distortion is very small when one of the four possible substitution sites is replaced by either Ti or Al.The substitution of Ti for Si in D8 m -structured Ta 5 Si 3 slightly increases unit cell volume because the Ti atom has a larger atomic radius than the Si.After the substitution of Ti for Ta, the unit cell volume of D8 m -structured Ta 5 Si 3 hardly changes due to a small difference of the atomic radius between Ti and Ta.The lattice expansion for Ti atom occupying the Ta 4b site is significantly smaller than that for Ti atom occupying the other three sites (i.e., Ta 16k , Si 4a and Si 8h ), implying a lower lattice distortion.Meanwhile, from Table 1, it is clear that only the Ti substitution for Ta 4b site, the lattice constants a and b are of equal value, which can maintain the tetragonal structure of D8 m Ta 5 Si 3 .For Al substitutional alloying, it can be observed that Al substitution for Ta and Si cause lattice contraction and lattice expansion, respectively.As can be seen from Figure 2, Al atom occupying the Ta 16k site yields the lowest lattice distortion.However, from Table 1, only Al substitution for Si 8h site can retain the tetragonal structure of D8 m Ta 5 Si 3 .

Site Occupancy of Ternary Elements
It is generally assumed that the preference sites of the solute atoms are decided by their atomic radius and electronegativity.In this regard, Ti shows a preference for occupying the Ta sublattice and Al prefers to occupy the Si sublattice to maintain the minimum energy state.To confirm this assumption, the energetics of the preferential sites of M(Ti or Al) in the D8m Ta20Si12 structure can be studied based on the substitutional sites energy difference, which is defined as the difference between two different formation enthalpies [31]:

Site Occupancy of Ternary Elements
It is generally assumed that the preference sites of the solute atoms are decided by their atomic radius and electronegativity.In this regard, Ti shows a preference for occupying the Ta sublattice and Al prefers to occupy the Si sublattice to maintain the minimum energy state.To confirm this assumption, the energetics of the preferential sites of M(Ti or Al) in the D8 m Ta 20 Si 12 structure can be studied based on the substitutional sites energy difference, which is defined as the difference between two different formation enthalpies [31]: where E site´Ta represents the formation enthalpies of Ta  1 shows the enthalpy of formation for D8 m Ta 20 Si 12 which shows good agreement between experimental data [28] and theoretical results [9].The calculations show that all of the binary and ternary D8 m Ta 20 Si 12 compounds have negative values of enthalpy of formation, meaning that all these compounds are energetically stable.Furthermore, it is clear that the E site is less than zero for the Ti substitution and the enthalpy of formation of Ta 19 Ti 4b Si 12 is smaller than that for Ta 19 Ti 16k Si 12 , implying that Ti exhibits the tendency to occupy Ta 4b site.In the case of one Al atom substitution, the E site is larger than zero and Ta 20 Si 11 Al 8h has a relatively low enthalpy of formation, suggesting that Al has a strong site preference for the Si 8h site.

Elastic and Mechanical Properties
The elastic properties of a solid are essential for understanding the macroscopic mechanical properties of the solid and for its potential technological applications.In order to shed some light on the influence of these two alloying elements on the mechanical properties of D8 m -structured Ta 5 Si 3 , when only one atom in D8 m -structured Ta 5 Si 3 is substituted by ternary elements, the elastic constants of the pure elements and binary and ternary D8 m Ta 5 Si 3 have been calculated and are listed in Table 2.The calculated results for b.c.c Ta and diamond-structured Si are in good consistence with the experimental data [32,33] and the elastic properties for the alloying element Al are comparable to the values reported by Kang et al. [34], which is indicative of the reliability and accuracy of the theoretically predicted results.As is well known, the elastic stability is a necessary condition for a stable crystal.For the tetragonal system, the mechanical stability criteria are decided by the following restrictions of its elastic constants, C 11 > 0, C 33 > 0, C 44 > 0, C 66 > 0, C 11 ´C12 > 0, (C 11 + C 33 ´2C 13 ) > 0, and 2(C 11 + C 12 ) + C 33 + 4C 13 > 0. The calculated elastic constants of all the binary and ternary D8 m -structured Ta 5 Si 3 compounds satisfy the above criteria, indicating that these compounds are mechanically stable.The elastic constants provide valuable information about the bonding character between adjacent atomic planes and the anisotropic character of the bonding.It can be seen from Table 2 that the values of C 11 are larger than that of C 33 , which indicates that their a-axis direction ([100] direction) and b-axis direction ([010] direction) are stiffer than c-axis direction ([001] direction).The values of (C 11 + C 12 ) are greater than that of C 33 , suggesting that the elastic modulus is higher in the (001) plane than along [001] direction.Regardless of the binary and ternary D8 m -structured Ta 5 Si 3 compounds, the values of C 66 is larger than C 44 , indicating that the [100](001) shear is easier than the [100](010) shear.The elastic anisotropy of the transition metal silicides has an important impact on the mechanical properties of the systems, especially on dislocation structures and mechanisms [35].The anisotropy factors for tetragonal phases can be estimated as A = 2C 66 /(C 11 ´C12 ).A is equal to one for an isotropic crystal.The values of A are 1.03, 1.09 and 1.13 for the Ta 20 Si 12 , Ta 20 Si 11 Al 8h and Ta 19 Ti 4b Si 12 , indicating that the shear elastic properties of the (001) plane are nearly independent of the shear direction for all the binary and ternary D8 m -structured Ta 5 Si 3 compounds.Similar properties have been found for the D8 m -structured phase of V 5 Si 3 [36] and Mo 5 Si 3 [37].
Based on the calculated elastic constants, the bulk modulus (B), shear modulus (G) and Young's modulus (E) for binary and ternary D8 m -structured Ta 5 Si 3 are calculated based on the Voigt-Reuss-Hill approximation, and are shown in Figure 3.The calculated values for the bulk modulus (B), shear modulus (G) and Young's modulus (E) for D8 m -structured Ta 5 Si 3 are also in good agreement with the previous calculations [9].Therefore, with respect to the available data, the present calculations yield comparable values.The substitution of Ta by Ti simultaneously lowers the values of B, G, and E, while the substitution of Si by Al also lowers the values of G and E, but slightly enhances the value of B. Since bulk moduli are generally believed to be related to the cohesive energy of materials, the variation of bulk modulus is related to changes in cohesive strength between atoms [38].The binary Ta 5 Si 3 Metals 2016, 6, 127 8 of 18 has the largest values of shear modulus and Young's modulus, confirming that it has a higher shear deformation resistance and elastic stiffness as compares to ternary Ta 5 Si 3 compounds.The ductility or brittleness of a solid is very important, because ductile materials are more resistant to catastrophic failure under critical mechanical stress conditions.There is no universally accepted criterion to gauge ductility or brittleness of a given material purely based on elastic data derived from linear elastic theory, but a reasonable representation of it can be realized by ratio of bulk/shear modulus B/G proposed by Pugh [39].According to Pugh's empirical rule, the critical number of this parameter separating the ductile and brittle nature of a material is 1.75.If B/G > 1.75, the material behaves in a ductile manner; otherwise, the material deforms in a brittle mode.As shown in Figure 4, the B/G ratios for all of binary and ternary Ta 5 Si 3 compounds are slightly larger than this critical value, implying that all of binary and ternary Ta 5 Si 3 compounds exhibit ductile behavior.Meanwhile, the additions of Ti and Al further increase in the calculated B/G ratios, suggesting that both Ti and Al are beneficial to the improvement of ductility of the Ta 5 Si 3 compound.Based on the values of B/G, the addition of Al is more efficient than Ti addition to improve the ductility of Ta 5 Si 3 .Poisson's ratio (υ) is associated with the volume change during uniaxial deformation and has been used to quantify the stability of the crystal against shear.In addition, Poisson's ratio provides more information about the degree of directionality of the covalent bonding than any of the other elastic coefficients and its value can also be employed to evaluate the ductility or brittleness of materials [40].It is generally assumed that when υ is less than 0.26, the material is brittle, and at higher values it is ductile.The variation of the values of Poisson's ratios for the binary and ternary Ta 5 Si 3 compounds is the same as those for B/G ratios.The results indicate that the additions of Ti and Al reduce the directionality of atomic bonding of Ta 5 Si 3 and the directionality in atomic bonding in Ta 5 Si 3 alloyed with Al is weaker than that in Ta 5 Si 3 alloyed with Ti.Cauchy pressure (C 12 ´C44 ) describes the angular characteristics of interatomic bonds in metals and compounds, thus serving as an indication of ductility.According to Pettifor [41], if the value of Cauchy pressure is positive, the material is expected to be ductile in nature; otherwise, it is brittle in nature.It can be seen from Figure 5 that the values of Cauchy pressure for the binary and ternary Ta 5 Si 3 compounds is positive, further confirming that they are expected to be ductile in nature.As one of the most basic mechanical properties of a material, hardness of a given material is characterized by the ability to resist to both elastic and irreversible plastic deformations, when a force is applied [42].Some researchers have tried to create a correlation between hardness and elasticity [43,44].For the partially covalent transition metal-based materials, since the shear modulus scales with the stresses required to nucleate or move isolated dislocations and hence is proportional to the hardness, it is regarded as a good indicator of hardness [45].Thus, in the term of the values of shear modulus, the hardness increases in the following sequence: Ta 20 Si 11 Al 8h < Ta 19 Ti 4b Si 12 < Ta 20 Si 12 .Chen et al. [46] assumed that unlike the moduli of G and B, which only measured the elastic response, the Pugh's modulus ratio (B/G) seemed to correlate much more reliably with hardness because it responded to Metals 2016, 6, 127 9 of 18 both elasticity and plasticity, which were the most intrinsic features of hardness.They proposed a semiempirical formula to calculate Vickers hardness of polycrystalline materials: where k denotes the Pugh's modulus ratio, B/G.

Electronic Structure and Population Analysis
Mechanical properties of a material reflect its resistance to elastic and plastic deformation, which are controlled, in part, by the chemical bonding that is, in turn, determined by electronic structures.Hence, in order to gain insight into the mechanisms governing the mechanical properties of the binary and ternary D8m-structured Ta5Si3, the electronic structures of these materials were investigated and compared.Figures 6 and 7 present the calculated total and partial density of states (DOS) for the binary and ternary D8m-structured Ta5Si3, where the black vertical dashed of DOS represents the Fermi level.The pseudogap (the low valley near the Fermi level) is likely to split the bonding and anti-bonding states.As shown in Figure 6, the introduction of either an Al atom or a Ti atom pushes the Fermi level towards a lower energy side of the pseudogap, denoting that some bonding states may be occupied by electrons from anti-bonding states.Compared with the binary Ta5Si3, the total DOS for ternary Ta5Si3 have two new peaks of bonding states near −6 and −2 eV and a new peak of bonding states near −2 eV, respectively.As can be seen from Figure 7a, the partial densities of states (PDOS) profile of binary Ta5Si3 mainly divides into three parts.The first part is from −12 to −6.7 eV, consisting mainly of Ta-5d states, Si-3s states, and part of Si-3p states.For the second part, the main bonding states located between −6.7 and −1.0 eV are dominated by Ta-5d states, Si-3p states and part of Ta-5p.The third part ranging from −1.0 to 2 eV is contributed mainly by Ta-5d states and part of Si-3p states.For the first part, the hybridization focuses on Ta-5d states and Si-3s states, forming Ta-Si bond.It is to be noted here that Si-3s states plays an important role in charge transfer.The second and third parts are different from the first part.In the second and third parts, the charge of Si atom transfers from 3s to 3p states and the Ta-5d states play an important role in electronic contribution.The hybridization between Ta-5d states and Si-3p states forms Ta-Si bond.In the last part, the anti-bonding states dominated by Ta-5d states forms Ta-Ta anti-bonding.For the PDOS profile of Ta20Si11Al 8h (Figure 7b), the bonding states from −6 to −7 eV originate mainly from Ta-5s states and Al-3s sates, indicating strong electronic interactions for Ta-Al bonding.The Ta5s-Al3s bonding contribute to the new peak of bonding states near −6 eV in total DOS of Ta20Si11Al 8h compound (Figure 7b).States from −6.2 to 2eV are dominated by Ta-5d, Si-3p and Al-3p states.Furthermore, the hybridized Al-3p and Ta-5d states occur in an energy range that is higher than that of the hybridized Si-3p and Ta-5d states, suggesting that the Al3p-Ta5d bonds are weaker than that of the Si3p-Ta5d bonds, reducing the covalent property of bonding in D8m-structured Ta5Si3.The formation of the weaker Al-Ta covalent bonds explains why the ductility of the Ta5Si3 alloyed with Al is better than that of binary Ta5Si3.In the partial DOS profile of Ta19Ti 4b Si12 (Figure 7c), the Ti-3d states near −2 eV hybridize with Si-3p states, contributing to formation of the peak of bonding states

Electronic Structure and Population Analysis
Mechanical properties of a material reflect its resistance to elastic and plastic deformation, which are controlled, in part, by the chemical bonding that is, in turn, determined by electronic structures.Hence, in order to gain insight into the mechanisms governing the mechanical properties of the binary and ternary D8 m -structured Ta 5 Si 3 , the electronic structures of these materials were investigated and compared.Figures 6 and 7 present the calculated total and partial density of states (DOS) for the binary and ternary D8 m -structured Ta 5 Si 3 , where the black vertical dashed of DOS represents the Fermi level.The pseudogap (the low valley near the Fermi level) is likely to split the bonding and anti-bonding states.As shown in Figure 6, the introduction of either an Al atom or a Ti atom pushes the Fermi level towards a lower energy side of the pseudogap, denoting that some bonding states may be occupied by electrons from anti-bonding states.Compared with the binary Ta 5 Si 3 , the total DOS for ternary Ta 5 Si 3 have two new peaks of bonding states near ´6 and ´2 eV and a new peak of bonding states near ´2 eV, respectively.As can be seen from Figure 7a, the partial densities of states (PDOS) profile of binary Ta 5 Si 3 mainly divides into three parts.The first part is from ´12 to ´6.7 eV, consisting mainly of Ta-5d states, Si-3s states, and part of Si-3p states.For the second part, the main bonding states located between ´6.7 and ´1.0 eV are dominated by Ta-5d states, Si-3p states and part of Ta-5p.The third part ranging from ´1.0 to 2 eV is contributed mainly by Ta-5d states and part of Si-3p states.For the first part, the hybridization focuses on Ta-5d states and Si-3s states, forming Ta-Si bond.It is to be noted here that Si-3s states plays an important role in charge transfer.The second and third parts are different from the first part.In the second and third parts, the charge of Si atom transfers from 3s to 3p states and the Ta-5d states play an important role in electronic contribution.The hybridization between Ta-5d states and Si-3p states forms Ta-Si bond.In the last part, the anti-bonding states dominated by Ta-5d states forms Ta-Ta anti-bonding.For the PDOS profile of Ta 20 Si 11 Al 8h (Figure 7b), the bonding states from ´6 to ´7 eV originate mainly from Ta-5s states and Al-3s sates, indicating strong electronic interactions for Ta-Al bonding.The Ta5s-Al3s bonding contribute to the new peak of bonding states near ´6 eV in total DOS of Ta 20 Si 11 Al 8h compound (Figure 7b).States from ´6.2 to 2eV are dominated by Ta-5d, Si-3p and Al-3p states.Furthermore, the hybridized Al-3p and Ta-5d states occur in an energy range that is higher than that of the hybridized Si-3p and Ta-5d states, suggesting that the Al3p-Ta5d bonds are weaker than that of the Si3p-Ta5d bonds, reducing the covalent property of bonding in D8 m -structured Ta 5 Si 3 .The formation of the weaker Al-Ta covalent bonds explains why the ductility of the Ta 5 Si 3 alloyed with Al is better than that of binary Ta 5 Si 3 .In the partial DOS profile of Ta 19 Ti 4b Si 12 (Figure 7c), the Ti-3d states near ´2 eV hybridize with Si-3p states, contributing to formation of the peak of bonding states in the total DOS of Ta 19 Ti 4b Si 12 (Figure 7b).The anti-bonding states are dominated by Ti-3d and Ta-5d states, showing evidence for the formation of strong Ti-Ta anti-bonding.Moreover, these Ti-Ta anti-bonding states occupy some bonding states between Ta and Si in the total DOS profile of Ta 19 Ti 4b Si 12 as compares to binary D8 m Ta 20 Si 12 , weakening the covalent property of bonding in D8 m Ta 20 Si 12 .The strong Ti-Ta anti-bonding and the reduction of covalent property should be responsible for the improvement of ductility.in the total DOS of Ta19Ti 4b Si12(Figure 7b).The anti-bonding states are dominated by Ti-3d and Ta-5d states, showing evidence for the formation of strong Ti-Ta anti-bonding.Moreover, these Ti-Ta antibonding states occupy some bonding states between Ta and Si in the total DOS profile of Ta19Ti 4b Si12 as compares to binary D8m Ta20Si12, weakening the covalent property of bonding in D8m Ta20Si12.The strong Ti-Ta anti-bonding and the reduction of covalent property should be responsible for the improvement of ductility.To further reveal the charge transfer and the chemical bonding properties of both non-doped and doped Ta 5 Si 3 , the difference in bonding charge density for the three compounds was investigated.The bonding charge density, also called the deformation charge density, is defined as the difference between the self-consistent charge density of the interacting atoms in the crystal and a reference charge density constructed from the superposition of the non-interacting atomic charge density at the lattice sites [47].The distribution of the bonding charge densities in the (001) plane along the a-and b-axis for non-doped and doped Ta 5 Si 3 is given in Figures 8 and 9 where the red region denotes a high charge density and the blue region denotes a relatively low charge density.It is noted in Figure 8 that the bonding charge density shows a depletion of the electronic density at the lattice sites together with an increase of the electronic density in the interstitial region.It is also noted that the bonding charge build-up in the Ta 16k -Si 8h -Ta 16k planar triangular bonding area is strong.This feature is consistent with the PDOS plots in Figure 7a, showing the importance of the hybridization between Ta 16k -5d states and Si 8h -3p states, forming the Ta 16k -Si 8h bonds.To further reveal the charge transfer and the chemical bonding properties of both non-doped and doped Ta5Si3, the difference in bonding charge density for the three compounds was investigated.The bonding charge density, also called the deformation charge density, is defined as the difference between the self-consistent charge density of the interacting atoms in the crystal and a reference charge density constructed from the superposition of the non-interacting atomic charge density at the lattice sites [47].The distribution of the bonding charge densities in the (001) plane along the aand b-axis for non-doped and doped Ta5Si3 is given in Figures 8 and 9, where the red region denotes a high charge density and the blue region denotes a relatively low charge density.It is noted in Figure 8 that the bonding charge density shows a depletion of the electronic density at the lattice sites together with an increase of the electronic density in the interstitial region.It is also noted that the bonding charge build-up in the Ta 16k -Si 8h -Ta 16k planar triangular bonding area is strong.This feature is consistent with the PDOS plots in Figure 7a, showing the importance of the hybridization between Ta 16k -5d states and Si 8h -3p states, forming the Ta 16k -Si 8h bonds.To further reveal the charge transfer and the chemical bonding properties of both non-doped and doped Ta5Si3, the difference in bonding charge density for the three compounds was investigated.The bonding charge density, also called the deformation charge density, is defined as the difference between the self-consistent charge density of the interacting atoms in the crystal and a reference charge density constructed from the superposition of the non-interacting atomic charge density at the lattice sites [47].The distribution of the bonding charge densities in the (001) plane along the aand b-axis for non-doped and doped Ta5Si3 is given in Figures 8 and 9, where the red region denotes a high charge density and the blue region denotes a relatively low charge density.It is noted in Figure 8 that the bonding charge density shows a depletion of the electronic density at the lattice sites together with an increase of the electronic density in the interstitial region.It is also noted that the bonding charge build-up in the Ta 16k -Si 8h -Ta 16k planar triangular bonding area is strong.This feature is consistent with the PDOS plots in Figure 7a, showing the importance of the hybridization between Ta 16k -5d states and Si 8h -3p states, forming the Ta 16k -Si 8h bonds.than the Ta 16k -Si 8h -Ta 16k planar triangular bonding area.This result is consistent with the view derived from the DOS plots that the strength of Al-Ta bonds is weaker than that of the Si-Ta bonds.When one Ta 4a site is occupied by a Ti atom, see Figure 9b, the region between substitution site and Si 8h site is almost near-white, showing the decline of the interacting atomic charge density for the Ti 4b -Si 8h planar bonding area as compares with Ta 4b -Si 8h planar bonding area.Mulliken [48] analyzed correlations of overlap population with the degree of covalency of bonding and bond strength.The bonding (anti-bonding) states related to positive (negative) values of bond population, and the low (high) values imply that the chemical bond exhibits strong ionic (covalent) bonding [49].
As seen in Table 3, the covalent character for the binary and ternary Ta5Si3 are mainly attributed to the Ta 16k -Si 8h covalent bond with high overlap population and the highest bond number.The above discussion about DOS for Ta19Ti 4b Si12 indicates that the Ti substitution changes the anti-bonding states between the Ta atoms.This observation is confirmed by the following changes in the populations of bonds: (a) the number of metallic bonds Ta 16k -Ta 16k increases by four and its overlap population exhibits a significant decease; (b) a new strong anti-bonding Ti 4b -Ta 4b appears in the network of metallic bonds with the disappearance of weak Ta 4b -Ta 4b anti-bonding.The change (a) weakens the covalent character of Ta19Ti 4b Si and improves its metallic properties and (b) improves the metallic After replacing a Si atom in the 8h site with an Al atom, a significant redistribution of the bonding charge in the interstitial region is seen in Figure 9a.The region around the substitution lattice site changes from red to blue, meaning that the charge density around the Al atom is much sparser than that around the Si atom.In addition, Ta 16k -Al 8h -Ta 16k planar triangular bonding area is weaker than the Ta 16k -Si 8h -Ta 16k planar triangular bonding area.This result is consistent with the view derived from the DOS plots that the strength of Al-Ta bonds is weaker than that of the Si-Ta bonds.When one Ta 4a site is occupied by a Ti atom, see Figure 9b, the region between substitution site and Si 8h site is almost near-white, showing the decline of the interacting atomic charge density for the Ti 4b -Si 8h planar bonding area as compares with Ta 4b -Si 8h planar bonding area.
Mulliken [48] analyzed correlations of overlap population with the degree of covalency of bonding and bond strength.The bonding (anti-bonding) states related to positive (negative) values of bond population, and the low (high) values imply that the chemical bond exhibits strong ionic (covalent) bonding [49].
As seen in Table 3, the covalent character for the binary and ternary Ta 5 Si 3 are mainly attributed to the Ta 16k -Si 8h covalent bond with high overlap population and the highest bond number.The above discussion about DOS for Ta 19 Ti 4b Si 12 indicates that the Ti substitution changes the anti-bonding states between the Ta atoms.This observation is confirmed by the following changes in the populations of bonds: (a) the number of metallic bonds Ta 16k -Ta 16k increases by four and its overlap population exhibits a significant decease; (b) a new strong anti-bonding Ti 4b -Ta 4b appears in the network of metallic bonds with the disappearance of weak Ta 4b -Ta 4b anti-bonding.The change (a) weakens the covalent character of Ta 19 Ti 4b Si and improves its metallic properties and (b) improves the metallic property of the 4b-4b bonds.Clearly, those Ta-Ta metallic bonds including Ta 16k -Ta 16k and Ta 4b -Ta 4b anti-bonding lower the deformation resistance, thereby reducing the elastic properties.Consequently, the change seen in both (a) and (b) intensifies the metallic property of bonds for the Ta 19 Ti 4b Si 12 compound, resulting in a decrease of the elastic properties and an increase in ductility for Ta 19 Ti 4b Si 12 .In addition, the hybridization between Ti-3d and Si-3p forms four new Ti 4b -Si 8h bonds of which the overlap population are close to zero.This also means a decrease in covelency for Ta 19 Ti 4b Si 12 compared with Ta 20 Si 12 .In the case of Si site substitution, the bonding length and the overlap populations of Si 8h -Ta 16k bonds becomes longer and smaller and the bonding length of the Ta 16k -Ta 16k metallic bonds becomes shorter, indicating that the Si 8h -Ta 16k bonds get weaker leading to charge transfer towards the Ta 16k -Ta 16k bonds.As such, the covalent character of 8h-16k bonds becomes weaker and Ta 16k -Ta 16k bonds become stronger, resulting in the improvement of ductility for Ta 20 Si 11 Al 8h .

Debye Temperature
As a fundamental parameter, the Debye characteristic temperature correlates with many physical properties of solids, such as specific heat, elastic constants and melting temperature [50].Elastic and thermal properties are inseparable because they both originate in the lattice vibrational spectrum of a solid.Therefore, the Debye temperature can be determined from the elastic constants.Theoretically, the Debye temperature (Θ D ), at T = 0 K, can be calculated by using the average sound velocity (ν m ) from the following relationship: here, h and k B represent the Planck and Boltzmann constants; n is the number of atoms in per formula unit, N A is Avogadro's number, M is the mass of per formula unit.The density, ρ, can be obtained based on a knowledge of the unit cell lattice parameters.The parameter ν m represents the average sound velocity which is defined as: where v l and v s are the longitudinal and transverse sound velocities respectively, which can be obtained by bulk modulus (B) and shear modulus (G) The calculated longitudinal, transverse and average sound velocities and Debye temperature of both non-alloyed and alloyed D8 m -structured Ta 5 Si 3 and their constituent elements were calculated and are listed in Table 4.The results obtained agree well with previous studies [8,51,52].The Debye temperatures of the three compounds are larger than that of tantalum.This is because the mass-density of Ta (16.58 g/cm 3 ) is larger than that of these compounds (around 12.5 g/cm 3 ), so that sound velocity in Ta is lower, that is, this leads to a lower Debye temperature.In contrast, Si and Al have relatively much lower densities (2.286 and 2.66 g/cm 3 , respectively), resulting in larger Debye temperatures.Compared to the D8 m -structured Ta 5 Si 3 , the ternary Ta 5 Si 3 compounds have lower Debye temperatures.Different Θ D -values indicate different lattice dynamics or degrees of lattice stiffness [53].Thus, the reasons for the observed decrease of Θ D can be mainly attributed to structural softening and the relative low shear modulus (shown in Table 4), which results in a lower cut-off for the atomic vibrational frequency [54].

Conclusions
In summary, the influence of substitutional alloying elements (Ti and Al) on the structural stability, mechanical properties, electronic properties and Debye temperature of Ta 5 Si 3 , exhibiting a D8 m structure, were systematically investigated by first principle calculations.All of the binary and ternary Ta 5 Si 3 compounds show negative enthalpy of formation values, indicating that these compounds are energetically stable.Based on the values of formation enthalpies, Ti exhibits a preferential occupying the Ta 4b site and Al has a strong site preference for the Si 8h site.The calculated results for the elastic constants show that doping with Ti simultaneously lowers the B, G, and E values of D8 m -structuted Ta 5 Si 3 .The variation of the shear modulus and the Young's modulus of this compound with an Al addition has a similar tendency to that of a Ti addition, although an Al addition slightly enhances the bulk modulus.The change of the ductility of the D8 m -structured Ta 5 Si 3 is explained according to the shear modulus/bulk modulus ratio (G/B), the Poisson's ratio and the Cauchy's pressure.The results show that ductility was improved by doping with Ti and Al.Moreover, the hardness of the Ta 5 Si 3 is reduced by both Ti and Al additions, resulting in solid solution softening.Electronic structure analysis indicates that alloying with Ti and Al introduces a more metallic nature to the bonding, resulting in the enhancement in ductility of D8 m Ta 5 Si 3 .Moreover, the Debye temperatures, Θ D , of D8 m -structured Ta 5 Si 3 alloying with Ti and Al are decreased as compared to the binary Ta 5 Si 3 .

Figure 1 .
Figure 1.The crystal structure of D8m Ta5Si3: (a) 3D model; (b) side view; (c) top view.Ta atoms (blue balls) and Si atoms (yellow balls) have two symmetrically non-equivalent positions.The elements on the close-packed planes (represented by the B-layer and C-layer) are termed Ta 16k and Si 8h , and those on the less close-packed planes (represented by the A-layer) are termed Ta 4a and Si 4b .

Figure 1 .
Figure 1.The crystal structure of D8 m Ta 5 Si 3 : (a) 3D model; (b) side view; (c) top view.Ta atoms (blue balls) and Si atoms (yellow balls) have two symmetrically non-equivalent positions.The elements on the close-packed planes (represented by the B-layer and C-layer) are termed Ta 16k and Si 8h , and those on the less close-packed planes (represented by the A-layer) are termed Ta 4a and Si 4b .

Figure 2 .
Figure 2. The change of unit cell volume for Ti and Al additions occupying the four possible substitution sites for D8m-structured Ta20Si12.

Figure 2 .
Figure 2. The change of unit cell volume for Ti and Al additions occupying the four possible substitution sites for D8 m -structured Ta 20 Si 12 .

Figure 4 .
Figure 4.The Poisson's ratio, ν, and the Pugh modulus ratio, B/G, for Ta20Si12, Ta20Si11Al 8h and Ta19Si12Ti 4b .Theoretical values reported in the literature [8] are shown in the figure for comparison.

Figure 4 .
Figure 4.The Poisson's ratio, ν, and the Pugh modulus ratio, B/G, for Ta20Si12, Ta20Si11Al 8h and Ta19Si12Ti 4b .Theoretical values reported in the literature [8] are shown in the figure for comparison.

Figure 4 .Figure 5 .
Figure 4.The Poisson's ratio, ν, and the Pugh modulus ratio, B/G, for Ta 20 Si 12 , Ta 20 Si 11 Al 8h and Ta 19 Si 12 Ti 4b .Theoretical values reported in the literature [8] are shown in the figure for comparison.

Figure 8 .
Figure8.The difference density of contour plots for Ta20Si12 unit cell in the (001) plane.• denotes the direction perpendicular paper from inside to outside.The Ta 4b , Ta 16k , Si 4a and Si 8h symbols designate the positions of, respectively, Ta in the 4b site, Ta in the 16k site, Si in the 4a, and Si in the 8h site.

Figure 8 .
Figure8.The difference density of contour plots for Ta 20 Si 12 unit cell in the (001) plane.denotes the direction perpendicular paper from inside to outside.The Ta 4b , Ta 16k , Si 4a and Si 8h symbols designate the positions of, respectively, Ta in the 4b site, Ta in the 16k site, Si in the 4a, and Si in the 8h site.

Figure 9 .
Figure 9.The difference density of contour plots for (a) Ta20Si11Al 8h and (b) Ta19Ti 4b Si12 unit cell in (001) plane.•denotes the direction perpendicular paper from inside to outside.The Ta 4b , Ta 16k , Si 4a , Si 8h , Al 8h and Ti 4b symbols designate the positions of, respectively, Ta in the 4b site, Ta in the 16k site, Si in the 4a, Si in the 8h site, Al in the 8h site and Ti in the 4b site.

Figure 9 .
Figure 9.The difference density of contour plots for (a) Ta 20 Si 11 Al 8h and (b) Ta 19 Ti 4b Si 12 unit cell in (001) plane.denotes the direction perpendicular paper from inside to outside.The Ta 4b , Ta 16k , Si 4a , Si 8h , Al 8h and Ti 4b symbols designate the positions of, respectively, Ta in the 4b site, Ta in the 16k site, Si in the 4a, Si in the 8h site, Al in the 8h site and Ti in the 4b site.

Table 1 .
Calculated lattice constants and enthalpies of formation for D8 m -structured Ta 20 Si 12 and alloyed D8 m Ta 20 Si 12 .
19 MSi 12 including Ta 19 M 16k Si 12 and Ta 19 M 4b Si 12 ; E site´Si denotes the formation enthalpies of Ta 20 Si 11 M including Ta 19 Si 11 M 4a and Ta 19 Si 11 M 8h structures.If E site < 0, occupying the Ta sublattice is energetically more favorable, and if E site > 0, M is prone to occupying the Si sites.Table

Table 2 .
Calculated elastic constants for the binary, ternary D8 m -structured Ta 20 Si 12 and their constituent elements compared to the data obtained experimentally and theoretically.
The Vickers hardness values calculated from Equation (21) are presented in Figure 5.The values of Vickers hardness for Ta 20 Si 11 Al 8h , Ta 19 Ti 4b Si 12 and Ta 20 Si 12 are estimated to 11.40, 11.48 and 12.27 GPa.Again, the calculated results predict that Ti and Al substitutions result in solid solution softening.

Table 3 .
Mulliken overlap populations, bond lengths and numbers of bonds calculated for Ta 20 Si 12 , Ta 20 Si 11 Al 8h and Ta 19 Ti 4b Si 12 compounds.

Table 4 .
Calculated density ρ (in g/cm3), longitudinal, transverse, average sound velocities (in m/s) and Debye temperature Θ D (in K) for the binary, ternary D8 m -structured Ta 20 Si 12 and its constituent elements.