Origin of the low compressibility in hard nitride spinels

Abstract

A microscopic investigation of first-principles electron densities of ␥-A 3 N 4 ͑A:C,Si,Ge͒ spinels reveals a clear relationship between the compressibility and the chemical bonding of these materials. Three striking findings emanate from this analysis: ͑i͒ the chemical graph is governed by a network of highly directional strong bonds with covalent character in ␥-C 3 N 4 and different degrees of ionic polarization in ␥-Si 3 N 4 and ␥-Ge 3 N 4 , ͑ii͒ nitrogen is the lowest compressible atom controlling the trend in the bulk modulus of the solids, and ͑iii͒ the group-IV counterions show strong site dependent compressibilities enhancing the difficulty in the synthesis of the spinel phases of these nitrides.

Electronegativity‐related bulk moduli of crystal materials

“…From Table 3, we can see that all calculated results agree well with the available experimental data 35, 37–41 except for γ ‐Ge 3 N 4 . For nitride spinels, the obvious increase of the volume of unit cell from silicon spinel to tin spinel leads to the large change of bond modulus, which is the reason for the large difference between their bulk moduli.…”

Elastic and structural instability of cubicSn3N4andC3N4<

“…3͒, variation in B 0 with 1 / a is almost linear and has been found to fit the linear equation, B 0 = ͑5857/ a͒ − 475. ͑In studying the variation in B 0 with 1 / a, the B 0 and a values for ␥-Ge 3 N 4 have been taken from the calculation done by Mori-Sánchez et al 30 ͒ This means that the bond-stiffness in the nitrides studied here is quite similar and it is the volume of the unit cell that is responsible largely for the monotonous decrease in the Bulk modulus from carbon to tin nitride. As the spinel structure contains cations with tetrahedral and octahedral coordination, it is not straightforward to describe it with a single type of a bond.…”

Recent Advances in New Hard High‐Pressure Nitrides

“…A more systematic study is necessary in order to fully understand the underlying mechanism that leads to the superb mechanical properties of this class of compounds. [105] The other recent properties measured include the thermal expansion coefficient in c-Si 3 N 4 . [68,110,112] The measurements show that the thermal expansion behaviors at low and high temperatures are very different.…”

“…The long-term thermal stability of c-Si 3 N 4 has also been examined. After annealing in air for 24 h at 1233 K in a steel container, the Raman spectrum of a powder sample is still dominated by the most in- [100,101] 290, 302 [39] 262 [114] 259 [117] 311 (LDA), 273 (GGA) [111] 317, 309 [110] 305 (LDA) [49] 286 (LDA) [113] 335 (LDA) [105] C 11 [GPa] 551 (LDA), 500 (GGA) [111] 413 (LDA) [115] 397 [65] 533 (LDA) [49] 406 (GGA) [115] 343 [116] 504 (LDA) [113] 433 [117] C 33 [GPa] 538 (LDA) [115] 600 [116] 517 (GGA) [115] 574 [117] C 12 [GPa] 191 (LDA), 159 (GGA) [111] 196 (LDA) [115] 151 [65] 191 (LDA) [49] 160 (GGA) [115] 136 [116] 177 (LDA) [113] 195 [117] C 13 [GPa] 97 (LDA) [115] 120 [116] 165 (GGA) [115] 127 [117] C 44 [GPa] 349 (LDA), 334 (GGA) [111] 104 (LDA) [115] 123 [65] 341 (LDA) [49] 107 (GGA) [115] 124 [116] 327 (LDA) [113] 108 …”