First-principles study of elastic and stability properties of ZrC–ZrN and ZrC–TiC alloys

Abstract

Ab initio calculations of the elastic constants for several cubic ordered structures of zirconium carbonitride (ZrC(x)N(1-x)) and zirconium-titanium carbide (Zr(x)Ti(1-x)C) alloys were carried out. The calculations of total and formation energies, bulk modulus and elastic constants as functions of composition were performed with an ab initio pseudo-potential method. The predicted equilibrium lattice parameters are slightly higher than those found experimentally (on average by 0.2-0.4%). The predicted formation energies indicate that the ZrC(x)N(1-x) alloys are stable even at 0 K in the whole concentration range, while the homogeneous Zr(x)Ti(1-x)C alloys can be stabilized only at high temperatures. Spinodal decomposition of the latter alloys into cubic domains takes place over a wide range of compositions and temperatures. For the carbonitrides, the shear modulus G, the Young's modulus E and the Poisson ratio σ reach an extremum for carbon-rich alloys, and this is attributed to a maximum value of the shear modulus C(44) that corresponds to a valence-electron concentration in the range of 8.2-8.3. This extremal behavior finds its origin in the response of the band structure of ZrC(x)N(1-x) alloys for 0≤x≤1, caused by the monoclinic strain that determines this shear modulus. In contrast, the other shear modulus [Formula: see text] does not exhibit any extremum over the whole composition range. These results are in contrast with those for Zr-Ti carbides for which the elastic properties gradually increase from ZrC to TiC.

First principles investigation of temperature and pressure dependent elastic properties of ZrC and ZrN using Debye–Gruneisen theory

“…The lattice parameter trends were similar to those observed for ZrC and ZrN. These results agreed well with results from other experimental and calculated results [7,8,29].…”

“…In contrast, the shear and Young's moduli were influenced by whether the electrons were present in covalent bonds (metal d orbital-nonmetal p orbital bonds) or metallic bonds (metal d orbital-metal d orbital bonds). Our results regarding the elastic modulus of ZrC and ZrN are supported by previous calculation results [8,34].…”

“…In their calculation, they used strain-stress relations to obtain elastic constants at a temperature of absolute zero. Ivashchenko et al investigated not only the elastic properties at absolute zero but also the electronic structure and mixing free energy of ZrC-ZrN and ZrC-TiC alloys [8]. In addition, Hao et al calculated several properties of ZrC and ZrN under high pressures by using first principles calculations [9].…”

Phase decomposition of TiC−ZrC solid solution prepared by spark plasma sintering

“…1 shows the phase diagram of the TiCÀ ZrC system [12][13][14][15][16][17]. This system is a complete solid solution and has an immiscibility dome below 2400 K. The 90TiCÀ 10ZrC solid solution sintered at 2373 K had a uniform microstructure, and decomposed into two phases at the heat treatment temperature of 1573 K. This behavior was in good agreement with the phase diagram.…”

“…The TiC À ZrC system is a complete solid solution system, and we have demonstrated that 10 mol% ZrC can significantly enhance the sinterability of TiC À ZrC composites by forming homogeneous solid solutions [10,11]. On the other hand, it is known that the TiC À ZrC system is immiscible at temperatures lower than 2400 K. By heat treating the TiC À ZrC solid solution at a temperature lower than the consolute temperature, the solution decomposes into two phases and forms self-assembled nanoscale composites yielding high mechanical properties [12][13][14][15].…”