First-principle Analyzes Thermodynamic Properties Of Ti₂ALC And Ti₃AlC₂by Combustion Synthesis

In recent decades, ternary layered compounds Ti₂AlC and Ti₃AlC₂attract extensiveattention for their perfect combination of metal-and ceramic-properties. In this paper,we employed first-principle method CASTEP（Cambridge Sequential Total EnergyPackage） code of Materials studios based on DFT （density functional theory） to obtainphonon spectrum of Ti₂AlC and Ti₃AlC₂, systematically investigated thethermodynamic properties of Ti₂AlC and Ti₃AlC₂, obtained heat capacity at constantvolume, heat capacity at constant pressure, thermal expansion coefficient, Debyetemperature, bulk modulus, standard molar Gibbs free energy of formation, standardmolar enthalpy of formation, standard entropy et al. thermal data as functions oftemperature.Our investigated results indicate that the cell volumes of Ti₂AlC and Ti₃AlC₂increase with increasing temperature, which induced volume expansion coefficients andthermal expansion coefficients increase with increase with temperature. The therrmalexpansion coefficient sharply increases with temperature, then slowly.The heat capacities of Ti₂AlC and Ti₃AlC₂show that the heat capacity at constantpressure CPis equivalent to the heat capacity at constant volume CV, and they increaserapidly with temperature, then slowly. The heat capacities at constant pressure CPofTi₂AlC and Ti₃AlC₂are higher than the heat capacities at constant volume CVrespectively. The difference between CVand CPis larger and larger with increasingtemperature. At high temperature, CVreaches the Dulong-Petit constant, however, CPstill keeps positive slope. The heat capacity of Ti₂AlC and Ti₃AlC₂is twice and3timesof that of TiC, respectively.The bulk modulus of Ti₂AlC and Ti₃AlC₂approach to the constant at lowtemperature, then decrease linearly. Consequently the compression resistance of Ti₂AlCand Ti₃AlC₂decrease with increasing temperature.The standard entropy of Ti₂AlC and Ti₃AlC₂increase with temperature, which isdue to microcosmic states increase. Because the more the molecular weight, the morethe entropy, it is understandable that the standard entropy of Ti₃AlC₂is greater thanTi₂AlC. Simultaneously the standard molar Gibbs energy of formation and standard molar enthalpy of formation show inverse condition.The phonon dispersion curves and phonon density of states curves reveal that thecrystal structures of Ti₂AlC and Ti₃AlC₂are both very stable. Due to the mass of Ti andAl atom are relatively larger than C atom, the vibrational frequency of them is lower,therefore they are mainly consist of acoustic branch; C atom is relatively lighter, hashigh vibrational frequency, mainly consist of optic branch.