“…To the best of our knowledge, we are not aware of any experimental and theoretical works reporting the values of a and c for Sc Ta B , except for ScB and TaB . We note that the reliability of our approach used to derive the properties of ScB and TaB , including the lattice parameters, has already been demonstrated and discussed in our theoretical works on Sc V B 12 and B-deficient TaB 19 , in which our calculated values of lattice parameters (both a and c ) of the two diborides were compared and found to be in excellent agreement with the existing experimental and theoretical data, available in the literature 38 , 43 – 48 . Figure 6 Formation energies ( ) of B vacancy in the dilute limit of ordered (red shaded circles) and disordered (blue shaded squares) solid solutions of Sc Ta B , where 0 x 1 and = 1/3.…”
Section: Resultssupporting
confidence: 52%
“…As demonstrated and discussed in the theoretical works on metal diborides, previously published in the literature 12 , 14 – 16 , 18 , 19 , 38 , the negative values of for both ordered and disordered Sc Ta B solid solutions, indicating their thermodynamic stability relative to ScB and TaB , can be directly explained by the changes in the number of electrons filling bonding and antibonding states of Sc Ta B . Due to the interactions between metal atoms arranging themselves in the simple hexagonal geometry 2 , as in the case of metal diborides, the electronic density of states of the diborides displays a valley-like feature, frequently separating the bonding states from the antibonding states, around the Fermi level 14 , 15 , 18 , 38 – 40 .…”
Section: Resultsmentioning
confidence: 60%
“…Given that the effects of pressure, lattice vibrations, and electronic excitations are neglected, as a function of temperature T and chemical composition x can be expressed as; To estimate for disordered Sc Ta B , the models of Sc Ta B created by the SQS technique 29 are employed, together with the DFT calculations, to obtain of the disordered solid solutions (blue shaded squares shown in Fig. 1 ), and their are analytically derived from the mean-field approach 12 . That is, Note that, since our of disordered Sc Ta B are calculated at 5 discrete compositions ( x = 0.167, 0.333, 0.5, 0.667, and 0.833), they together with of ScB ( x = 0) and TaB ( x = 1) are interpolated by the cubic spline function and then combined with the term , where = 0.01, to estimate for disordered Sc Ta B .…”
Section: Resultsmentioning
confidence: 99%
“…Due to the interactions between metal atoms arranging themselves in the simple hexagonal geometry 2 , as in the case of metal diborides, the electronic density of states of the diborides displays a valley-like feature, frequently separating the bonding states from the antibonding states, around the Fermi level 14 , 15 , 18 , 38 – 40 . For ScB , the valley is located above the Fermi level, implying that there exist still unfilled bonding states of the material 12 , 15 , 18 , 39 . This can also be confirmed by considering the corresponding chemical bondings of the compound, visualized through its crystal orbital Hamilton population (−COHP) 18 , 41 .…”
Section: Resultsmentioning
confidence: 99%
“…Another example is that introducing Cr (Al) atoms into ZrB (TiB ) films increases wear, oxidation, and corrosion resistances of the films, and the mechanical properties of the resulting off-stoichiometric films of Zr Cr B (Ti Al B ) can be improved or tuned via controlling the films’ composition 6 , 8 , 11 . The enhancement of stabilities and mechanical properties of M M B with respect to M B and M B has been suggested to be directly related to the changes in the number of valence electrons filling bonding and antibonding electronic states of the material 14 – 16 , controlled by variation of M B and M B contents, as recently demonstrated in Sc V B exhibiting superior thermodynamic stability and mechanical properties, especially hardness, as compared to ScB and VB 12 .…”
Mixtures of different metal diborides in the form of solid solutions are promising materials for hard-coating applications. Herein, we study the mixing thermodynamics and the mechanical properties of AlB$$_{2}$$
2
-structured Sc$$_{1-x}$$
1
-
x
Ta$$_{x}$$
x
B$$_{2}$$
2
solid solutions using the first-principles method, based on the density functional theory, and the cluster-expansion formalism. Our thermodynamic investigation reveals that the two diborides readily mix with one another to form a continuous series of stable solid solutions in the pseudo-binary TaB$$_{2}$$
2
$$-$$
-
ScB$$_{2}$$
2
system even at absolute zero. Interestingly, the elastic moduli as well as the hardness of the solid solutions show significant positive deviations from the linear Vegard’s rule evaluated between those of ScB$$_{2}$$
2
and TaB$$_{2}$$
2
. In case of Sc$$_{1-x}$$
1
-
x
Ta$$_{x}$$
x
B$$_{2}$$
2
, the degrees of deviation from such linear trends can be as large as 25, 20, and 40% for the shear modulus, the Young’s modulus, and the hardness, respectively. The improvement in the stability as well as the mechanical properties of Sc$$_{1-x}$$
1
-
x
Ta$$_{x}$$
x
B$$_{2}$$
2
solid solutions relative to their constituent compounds is found to be related to the effect of electronic band filling, induced upon mixing TaB$$_{2}$$
2
with ScB$$_{2}$$
2
. These findings not only demonstrate the prominent role of band filling in enhancing the stability and the mechanical properties of Sc$$_{1-x}$$
1
-
x
Ta$$_{x}$$
x
B$$_{2}$$
2
, but also it can potentially open up a possibility for designing stable/metastable metal diboride-based solid solutions with superior and widely tunable mechanical properties for hard-coating applications.
“…To the best of our knowledge, we are not aware of any experimental and theoretical works reporting the values of a and c for Sc Ta B , except for ScB and TaB . We note that the reliability of our approach used to derive the properties of ScB and TaB , including the lattice parameters, has already been demonstrated and discussed in our theoretical works on Sc V B 12 and B-deficient TaB 19 , in which our calculated values of lattice parameters (both a and c ) of the two diborides were compared and found to be in excellent agreement with the existing experimental and theoretical data, available in the literature 38 , 43 – 48 . Figure 6 Formation energies ( ) of B vacancy in the dilute limit of ordered (red shaded circles) and disordered (blue shaded squares) solid solutions of Sc Ta B , where 0 x 1 and = 1/3.…”
Section: Resultssupporting
confidence: 52%
“…As demonstrated and discussed in the theoretical works on metal diborides, previously published in the literature 12 , 14 – 16 , 18 , 19 , 38 , the negative values of for both ordered and disordered Sc Ta B solid solutions, indicating their thermodynamic stability relative to ScB and TaB , can be directly explained by the changes in the number of electrons filling bonding and antibonding states of Sc Ta B . Due to the interactions between metal atoms arranging themselves in the simple hexagonal geometry 2 , as in the case of metal diborides, the electronic density of states of the diborides displays a valley-like feature, frequently separating the bonding states from the antibonding states, around the Fermi level 14 , 15 , 18 , 38 – 40 .…”
Section: Resultsmentioning
confidence: 60%
“…Given that the effects of pressure, lattice vibrations, and electronic excitations are neglected, as a function of temperature T and chemical composition x can be expressed as; To estimate for disordered Sc Ta B , the models of Sc Ta B created by the SQS technique 29 are employed, together with the DFT calculations, to obtain of the disordered solid solutions (blue shaded squares shown in Fig. 1 ), and their are analytically derived from the mean-field approach 12 . That is, Note that, since our of disordered Sc Ta B are calculated at 5 discrete compositions ( x = 0.167, 0.333, 0.5, 0.667, and 0.833), they together with of ScB ( x = 0) and TaB ( x = 1) are interpolated by the cubic spline function and then combined with the term , where = 0.01, to estimate for disordered Sc Ta B .…”
Section: Resultsmentioning
confidence: 99%
“…Due to the interactions between metal atoms arranging themselves in the simple hexagonal geometry 2 , as in the case of metal diborides, the electronic density of states of the diborides displays a valley-like feature, frequently separating the bonding states from the antibonding states, around the Fermi level 14 , 15 , 18 , 38 – 40 . For ScB , the valley is located above the Fermi level, implying that there exist still unfilled bonding states of the material 12 , 15 , 18 , 39 . This can also be confirmed by considering the corresponding chemical bondings of the compound, visualized through its crystal orbital Hamilton population (−COHP) 18 , 41 .…”
Section: Resultsmentioning
confidence: 99%
“…Another example is that introducing Cr (Al) atoms into ZrB (TiB ) films increases wear, oxidation, and corrosion resistances of the films, and the mechanical properties of the resulting off-stoichiometric films of Zr Cr B (Ti Al B ) can be improved or tuned via controlling the films’ composition 6 , 8 , 11 . The enhancement of stabilities and mechanical properties of M M B with respect to M B and M B has been suggested to be directly related to the changes in the number of valence electrons filling bonding and antibonding electronic states of the material 14 – 16 , controlled by variation of M B and M B contents, as recently demonstrated in Sc V B exhibiting superior thermodynamic stability and mechanical properties, especially hardness, as compared to ScB and VB 12 .…”
Mixtures of different metal diborides in the form of solid solutions are promising materials for hard-coating applications. Herein, we study the mixing thermodynamics and the mechanical properties of AlB$$_{2}$$
2
-structured Sc$$_{1-x}$$
1
-
x
Ta$$_{x}$$
x
B$$_{2}$$
2
solid solutions using the first-principles method, based on the density functional theory, and the cluster-expansion formalism. Our thermodynamic investigation reveals that the two diborides readily mix with one another to form a continuous series of stable solid solutions in the pseudo-binary TaB$$_{2}$$
2
$$-$$
-
ScB$$_{2}$$
2
system even at absolute zero. Interestingly, the elastic moduli as well as the hardness of the solid solutions show significant positive deviations from the linear Vegard’s rule evaluated between those of ScB$$_{2}$$
2
and TaB$$_{2}$$
2
. In case of Sc$$_{1-x}$$
1
-
x
Ta$$_{x}$$
x
B$$_{2}$$
2
, the degrees of deviation from such linear trends can be as large as 25, 20, and 40% for the shear modulus, the Young’s modulus, and the hardness, respectively. The improvement in the stability as well as the mechanical properties of Sc$$_{1-x}$$
1
-
x
Ta$$_{x}$$
x
B$$_{2}$$
2
solid solutions relative to their constituent compounds is found to be related to the effect of electronic band filling, induced upon mixing TaB$$_{2}$$
2
with ScB$$_{2}$$
2
. These findings not only demonstrate the prominent role of band filling in enhancing the stability and the mechanical properties of Sc$$_{1-x}$$
1
-
x
Ta$$_{x}$$
x
B$$_{2}$$
2
, but also it can potentially open up a possibility for designing stable/metastable metal diboride-based solid solutions with superior and widely tunable mechanical properties for hard-coating applications.
Abstract‐type is one of the transition‐metal diborides, a class of refractory ceramics, that has increasingly received attention due particularly to their potential for hard‐coating applications. In this work, the first‐principles calculations are performed, in combination with the cluster‐expansion method, to investigate the effect of mixing with on the thermodynamic stability, structural parameters, electronic density of states, and mechanical behavior of the resulting (Ta,Al) solid solutions. It is found that the solid solutions display the chemical ordering of Ta and Al atoms both residing on the metal sublattice of the material, together with the preference for partial substitution of vacancies for Al atoms. This results in the formation of Al‐deficient (Ta,Al) with the chemical composition , predicted to be thermodynamically stable even at absolute zero in the ternary Ta−Al−B system. It is further found that such formation of Al vacancies in (Ta,Al) not only enhances the stability of the solutions but also improves their elastic properties and hardness, both of which could be attributed to the effect of electronic band filling. This investigation indeed sheds light on the interplay between the mixing of Ta and Al atoms and the presence of Al vacancies on the alloying and mechanical behaviors of (Ta,Al), and it thus offers valuable insights for further research and development of these ceramics.
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