Analytic Equation of State and Thermodynamic Properties for α-, β-, and γ-Si₃N₄Based on Analytic Mean Field Approach

Abstract

The analytic mean field potential approach is applied to α-, β-, and γ-Si 3 N 4 . The analytic expressions for the Helmholtz free energy, internal energy, and equation of state were derived. The formalism for the case of the Morse potential is used in this work. Its six potential parameters are determined through fitting the compression experimental data of α-, β-, and γ-Si 3 N 4 . The calculated compression curves of α-, β-, and γ-Si 3 N 4 are in good agreement with the available experimental data. This suggests that the analytic mean field potential approach is a very useful approach to study the thermodynamic properties of Si 3 N 4 . Furthermore, we predict the variation of the free energy and internal energy with the molar volume at several higher temperatures and calculate the temperature dependence of the molar volume, bulk modulus, thermal expansion coefficient and isochoric heat capacity at zero pressure.

Equilibrium and metastable phase transitions in silicon nitride at high pressure: A first-principles and experimental study

“…Our zero-pressure results are compared with available experimental data [33][34][35][36][37][38][39][40] and previous calculations. 21,22,41,42 Conclusions are drawn in Sec. IV.…”

Pressure-induced phase transition in silicon nitride material

“…We do not plot the heat capacities of β -Si 3 N 4 at pressures higher than 10 GPa because the β phase starts to show signs of structural instability. [2,12] The calculated heat capacity of γ-Si 3 N 4 are 92.79 J/mol•K and 166.95 J/mol•K at 300 K and 1000 K, [55] respectively. The calculated C P for β -Si 3 N 4 is 111.54 J/mol•K.…”

“…Upon compression and simultaneous in situ heating, both β -Si 3 N 4 and α-Si 3 N 4 transform into the γ phase, which has been confirmed by experiments. [2,[9][10][11] Wang et al [12] have investigated the bulk modulus and some thermodynamic properties of α-, β -, and γ-Si 3 N 4 using the analytic mean field method. Chen et al [13] have calculated the phonon density of states and heat capacities for β -Si 3 N 4 through lattice dynamics.…”

Investigations of high-pressure and high-temperature behaviors of the newly-discovered willemite-II and post-phenacite silicon nitrides

“…[7,8] A third form of Si 3 N 4 with a spinel lattice (γ phase) has been synthesized by the diamond anvil cell technique, [9] which has a hardness comparable to the hardest oxide (stishovite). [10] The willemite-II structure was first reported as a low-compressible modification of C 3 N 4 . Recently, the willemite-II Si 3 N 4 (wII phase) was discovered by scientists.…”

“…The calculated transition pressure P t is about 11 GPa∼13 GPa between 0 and 3000 K. Kuwabara et al [8] found that the transition pressure of the β → γ transition is 5 GPa∼7 GPa (0∼2300 K) through first-principles calculations. More importantly, Xu et al [7] found that δ -Si 3 N 4 crystallizes into the "post-phenacite" structure and the β → δ transition would occur at 35 GPa∼36 GPa and 300 K. There is a great deal of research work on the crystal structures and thermal properties of α-Si 3 N 4 (lattice parameter, [3,10] specific heat, [8,10,14] thermal expansion, [7,8,10] entropy, [14] bulk modulus, [3,8,10,15] ) β -Si 3 N 4 (lattice parameter, [10,13] specific heat, [8,10,14] thermal expansion, [7,8,10] entropy, [14] bulk modulus, [8,10,13,15] Grüneisen parameter [7] ) and γ-Si 3 N 4 (lattice parameter, [10,13,16,17] specific heat, [8,10,18] thermal expansion, [7,8,10,17,18] entropy, [18] bulk modulus [8,10,…”