Available experimental and theoretical studies demonstrate that Ti3AlC2 and Ti3SnC2 compounds exhibit excellent mechanical properties at high temperatures,and thus are rendered a promising candidate of high-temperature structural materials.However,these compounds each have a relatively low hardness,Young's modulus,and poor oxidation resistance compared with other MAX phases.In order to overcome these limits,solid solutions on the M,A and/or X sites of the MAX phase compound are considered as a promising strategy to further improve the mechanical properties. Very recently,the solid solutions of Ti3(SnxAl1-x) C2 have been synthesized.However,no theoretical work has focused on the Ti3(SnxAl1-x) C2 solid solutions so far.Therefore,in this work,we perform first-principles calculation to study the microstructures,phase stabilities,electronic,mechanical and thermal properties of Ti3(SnxAl1-x) C2 solid solutions. Particularly,the effects of Sn concentration (x) on the properties are discussed for the Ti3(SnxAl1-x) C2 solid solutions by varying x from 0 to 1.0 in steps of 0.25.All the present ab initio calculations are carried out based on density-functional theory method as implemented in the Cambridge Serial Total Energy Package (CASTEP) code.The electron-ion interaction is described by Vanderbilt-type ultrasoft pseudo-potential with an exchange-correlation function in the generalized gradient approximation (GGA-PW91).The equilibrium crystal structure is fully optimized by independently modifying lattice parameters and internal atomic coordinates,and we employ the Broyden-Fletcher-Goldfarb-Shanno minimization scheme to minimize the total energy and inter-atomic forces.For the reciprocal-space integration,a Monkhorst-Pack grid of 16164 is used to sample the Brillouin-zones for Ti3AlC2 and Ti3SnC2 compound,and 882 for 221 supercell Ti3(SnxAl1-x) C2(x=0.25-0.75) compounds.The present calculated results of the enthalpy formation energy and mechanical stability criteria indicate that all the Ti3(SnxAl1-x) C2(x=0-1.0) solid solutions are thermodynamic and elastically stable.Moreover,mechanical properties (including bulk modulus B and shear modulus G),the ductile and brittle behavior and the anisotropic factors of Ti3(SnxAl1-x) C2 solid solutions are investigated,and the results indicate that all these compounds are identified as brittle materials and isotropic in nature.On the other hand,the MAX phases are good thermal materials due to their high thermal conductivities varying from 12 to 60 W/(mK) at room temperature.As for the thermal conductivity,it has become one of the most fundamental and important physical properties of the MAX phase material,especially for applications at elevated temperatures.Therefore,the lattice thermal conductivities,the minimum thermal conductivities and temperature dependences of the lattice thermal conductivity of Ti3(SnxAl1-x) C2 solid solutions are studied.Furthermore,Debye temperatures and melting points of the Ti3(SnxAl1-x) C2 compounds are also reported.Present results predict that each of all Ti3(SnxAl1-x) C2 compounds has a relative high Debye temperature and melting point,indicating that each of all Ti3(SnxAl1-x) C2 compounds possesses a rather stiff lattice and good thermal conductivity.