Phase Equilibrium Determination And Thermodynamic Optimizations Of The Ce-Co-Sb/Fe Ternary Systems Constituting The CoSb₃-based Thermoelectric Materials

Thermoelectric materials are functional materials,which can convert heat energy to electricity or reversely.With the merit of low-pollution,easy-maintenance and reliability,thermoelectric power generators and refrigerating devices made of thermoelectric materials have been extensively applied in the fields of waste heat generation,space flights,microelectronic elements and cooling systems.The properties of thermoelectric materials can be evaluated by a dimensionless thermoelectric figure of merit ZT,which is determined by the electrical conductivity,the Seebeck coefficient and the thermal conductivity.Thermoelectric materials with excellent properties need a high electrical conductivity,a high Seebeck coefficient and a low thermal conductivity simultaneously.The CoSb3 skutterudites are the semiconductor materials of narrow band gap and with open or cage-like structure.These materials exhibit the high Seebeck coefficient and high electrical conductivity,and are considered to be the promising novel thermoelectric materials in middle temperature range.However,the high thermal conductivity of CoSb3 skutterudites results in the low thermoelectric figure of merit ZT and restrains their further application.Doping with rare-earth elements and substitution with metal elements are the main methods to reduce the thermal conductivity of the CoSb3compounds.In general,the metal atoms(such as Fe,Ni,etc.)are used to replace the Co atoms in the CoSb3 compound,and the rare-earth atoms(such as Ce,Yb,etc.)are used to occupy the cage-like interstitial positions(lattice holes)in the lattice of the CoSb3 structure,in order to enhance the mobilities of electrons or vacancies for increasing the electronic conductivity,to promote the effect scattering of phonons for decreasing the lattice thermal conductivity,and finally to increase the conversion ratio of the related thermoelectric materials.The present work mainly studies the(Ce,Va)(Co,Fe)4Sbi2 thermoelectric system,which possesses the dual effects of both the filling in the lattice intersitices and the replacement of the substitution atoms,and can be regarded as the mixture of the compounds VaCo4Sb12 and CeFe4Sb12.By means of the combinatorial optimization of the doping and the substituting effects,the coupling of electron-phonon interactions will significantly reduce the thermal conductivities,increase the electronic conductivity,and enhance the corresponding thermoelectric properties.The present work is focused on the thermodynamic study of the Ce-Co-Sb and the Ce-Co-Fe systems which are the fundamental constituents of the Ce-Co-Fe-Sb quaternary system.The phase equilibrium relations and the phase transformation temperatures of the Ce-Co-Sb and Ce-Co-Fe ternary systems are experimentally investigated via X-ray diffraction(XRD),scanning electron microscopy(SEM),electron probe micro-analyzer(EPMA)and differential scanning calorimeter(DSC)methods.On the basis of all the available experimental data,the Ce-Co-Sb/Fe ternary systems are thermodynamically optimized using the CALPHAD method,and the related thermodynamic databases are finally constructed.The main results of the present study are as follows:Firstly,since the main constituting element Sb and the substitutional element Ge of the CoSb3 based thermoelectric material systems are easy to volatilize and possess relatively high saturated vapor pressure,the phase relationships of both Sb and Ge unary systems are closely linked with temperature and pressure.In the present study,the Murnaghan equation involving the pressure correction factors of the condensed phases,and the fugacity model relating to the pressure correction factors of the real gases,are taken into fully account.With the consideration of the phase relationships(the pressure-temperature relationships at normal and high temperature pressure),thermochemical properties(the heat capacity-temperature relationships at normal and high pressure),thermophysical properties(the pressure-molar volume relationships at certain temperature)and other reasonable data,the Sb/Ge unary systems are thermodynamically optimized,and the Sb/Ge unary databases with pressure correction factors at high temperature and high pressure are established.Referring to the molar volume,thermal expansivity and compressibility of the Sb/Ge unary systems,the pressure(P)-temperature(T)phase diagram,the molar volume(Vm)-pressure(P)relationship and the heat capacity(Cp)-temperature(T)curves are calculated,and the reasonable agreements are obtained between the previously reported experimental data and the calculated ones.The Sb and Ge unary databases provide the basic thermodynamic data concerning the gas pressure related phenomenon in the sintering process of the CoSb3-based skutterudite,and the optimization method in the present study can be widely used when other unary systems associated with the pressure dependent condensed phases are concerned.Secondly,the phase equilibria and liquidus projections of the Ce-Co-Sb and the Ce-Co-Fe ternary systems are experimentally determined by means of XRD,SEM,EPMA and DSC methods.For the Ce-Co-Sb ternary system,the phase equilibrium relations at 823 and 673 K are experimentally measured,and the solidification processes of the as-cast alloy samples are analyzed.The liquidus projection and the isothermal sections at 823 and 673 K of the Ce-Co-Sb ternary system are initially constructed.For the Ce-Co-Fe ternary system,the isothermal section at 823K and the entire liquidus projection are experimentally determined.The phase equilibrium determinations of the Ce-Co-Sb and the Ce-Co-Fe ternary systems can provide the basic data for the further thermodynamic optimizations of the systems.Thirdly,considering the crystal structure information of the equilibrated phases in the Ce-Co-Sb and the Ce-Co-Fe ternary systems,the reasonable thermodynamic models are proposed.Based on the phase equilibria information(including the solubility range of the solutions,the temperature of invariant reactions,the temperature and composition of phase transformations,the primary regions of the precipitated phases,etc.),together with the related thermochemical data such as the enthalpy of mixing of liquid,the Ce-Co-Sb and the Ce-Co-Fe ternary systems are thermodynamically optimized.A set of self-consistent thermodynamic parameters are obtained for each of the Ce-Co-Sb/Fe ternary systems.On this basis,the phase equilibrium calculations and the solidification process analyses are carried out,and all the thermodynamic calculated results are in good agreement with the experimental data.Finally,according to the thermodynamically assessed databases of the Ce-Co-Sb and the Ce-Co-Fe ternary systems,combined with the literature reported ones of the Co-Fe-Sb and the Ce-Fe-Sb ternary systems,the integrated database of Ce-Co-Fe-Sb quaternary system is constructed.Using the obtained quaternary database,the VaCo4Sb12-CeFe4Sb12 vertical section is theoretically calculated,and the influences of the alloying elements Ce and Fe on the phase equilibria of the Ce-Co-Fe-Sb system are analyzed.Then,the Scheil model is used to simulate the solidification processes of the typical as-cast Ce-Co-Sb,Ce-Fe-Sb and Ce-Co-Fe-Sb alloy samples.The simulated result is compared with the solidification microstructure of the same composition alloy,showing the good reproduction of the miscrostructure evolution in the experimental measurements.The present obtained thermodynamic parameters of the Ce-Co-Fe-Sb quarternary system can provide the basic information for the further development of the doping CoSb3 based multi-component thermoelectric materials.