Elastic and Dynamical Properties of YB ₄ : First-Principles Study

Abstract

We present the elastic and dynamical properties of YB4 from first-principles calculations. It is found that the optimized lattice constants and bulk modulus (182 GPa) agree well with the experimental data. The structural stability of tetragonal YB4 is confirmed by the calculated elastic constants and phonon spectra. YB4 holds a Debye temperature of 874 K and has small elastic anisotropy. The estimated hardness of YB4 is about 17 GPa, indicating that YB4 is a hard solid while not a superhard one.

Necessary and sufficient elastic stability conditions in various crystal systems

“…We noticed however, through a review of the recent literature on the experimental measurements and first principles calculations of elastic constants of solids, that there is a large amount of confusion about the form that these conditions should take for other crystal classes, including hexagonal, tetragonal, rhombohedral and orthorhombic classes. In more than a few cases, incorrect generalizations of the cubic criteria have been published; [6][7][8][9][10] this is particularly frequent for orthorhombic crystals. [11][12][13][14][15][16][17] In other papers, the authors rely on conditions that are necessary but not sufficient.…”

Crystal Structure and Physical Properties of HfB4 via First-Principles Calculations

“…Thus the Debye temperature can be derived from the elastic constants at low temperature [74][75][76]. At 0 GPa and 0 K, our calculated Debye temperature is 845 K for the Cmcm-HfB4, which is lower than those of HfB12, ZrB12 [63][64][65], YB4 [66], and FeB4 [67,68], but much larger than the values of the known ultra-incompressible material ReB2 (755.5 K) [77], OsB2 (601.09 K, 591 K) [78,79], RuB2 (780 K) [79], ReN2 (735 K) [80], and HfB2 [44,46]. All these results suggest that the Cmcm-HfB4 is a potential candidate as superhard materials.…”

“…The calculated bulk modulus, shear modulus, Young's modulus, and Poisson's ratio of the Cmcm phase together with the reference materials mentioned above are tabulated in Table 2. As shown in Table 2, the calculated bulk modulus of the Cmcm-HfB4 (243 GPa) is larger than those of HfB [39,40], ZrB12 [63][64][65], and YB4 [8,66] but is comparable to those of HfB2 [43][44][45], HfB12 [48], and other TMB4 (TM= Fe [12,13,67,68], Cr [13,14,69], Mn [11,70], Zr [23], and Ta [27]), indicating its strong ability to resist the volume deformation. Moreover, the bulk modulus (B=243 GPa) for the Cmcm-HfB4 is in consistent with that directly obtained from the fitting results (B0=244 GPa) of the third-order Birch-Murnaghan equation of states, which further demonstrates the good accuracy of our elastic calculations.…”

Structural, elastic, mechanical and thermodynamic properties of HfB 4 under high pressure

“…The larger the Young's modulus a material has, the harder it is to deform. From table 3, the Young's modulus (535 GPa for GGA and 577 GPa for LDA) of HfB 4 is larger than the other compounds [31,[49][50][51][52], indicating that HfB 4 has a higher hardness than the other TM compounds. All of these excellent mechanical properties strongly suggest that m-HfB 4 is a potential candidate for a superhard material.…”

“…, it is found that Cmcm-HfB 4 has a much larger shear modulus (237 and 255 GPa for GGA and LDA, respectively) than TMB 4 (TM = Y, Fe, Mn, Ta, Zr, Mo, Re, Os, and V)[31,[49][50][51][52][53][54].…”