Application Of Cluster Expansion Method In Predicting Structures And Properties Of Alloys

The cluster expansion method developed from Ising model is a relatively accurate and efficient method for Ising energy calculation of substitutional alloys.A compact representation of the energy of an alloy constructed from the formation energy of various atomic arrangements calculated by first-principles is called cluster expansion.In this paper,the electronic-structure and thermodynamic properties of ternary alloy semiconductor ZnO_1-xTe_x（0≤x≤1）,Cd_1-xSe_x（0≤x≤1）and ZnS_1-xSe_x（0≤x≤1）are studied by cluster expansion method combined with the first-principles calculations,and then it is extended to study the magnetic order and phase diagram of anti-ferromagnetic alloy Mg_xNi_1-xO（0≤x≤1）and its application in the study of metal hydride PdH_x（x=1–3）.The main research contents and conclusions of this thesis are as follows:In ZnO_1-xTe_xalloy,high formation enthalpy indicates that it is difficult for ZnO and ZnTe to form an alloy,and ZnO_1-xTe_xcan only exist in the form of metastable state.The considerable difference in atomic radius,electronegativity and lattice constants determines that ZnOTe is a highly mismatched alloy.Since Te is difficult to be dissolved into ZnO in solid solution,there is no stable structure in ZnOTe alloy and only metastable phase structure can be formed.In the metastable phase of wurtzite ZnO_1-xTe_x,the solid solubility of Te is 0≤x≤0.039,while the solid solubility of O is 0.907≤x≤1.With the vibration free energy included,the solid solubility of O in ZnTe increased from 0.093 to 0.129 at the temperature of2025 K,while the solid solubility of Te in ZnO barely changed.If both the vibration free energy and vibration entropy are taken into account,the solid solubility of O in ZnTe will further increase from 0.129 to 0.155,but the solid solubility of Te in ZnO is still almost uninfluenced.In Cd S_1-xSe_xalloy,lattice parameters increases with the increment of Se concentration,and volume modulus decreases linearly with the increase of Se concentration.CdS_1-xSe_xalloy has a direct band gap,which ranges from 1.82 to 2.59 e V in wurtzite（WZ）phase,and 1.90 to 2.56 e V in zincblende（ZB）phase.The calculated formation enthalpy indicates that the solid solution CdS_1-xSe_xis prone to phase separation at low temperature,and the phase transition from WZ to ZB structure will occur when the Se content is 32%.When the lattice vibration effect is taken into account,the critical temperatures of WZ and ZB phases are 255 K and 233 K respectively.Because the critical temperature of both phases is very low,the lattice vibration effects on the phase diagram of CdS_1-xSe_xalloy is limited.The binary phase diagram clearly reflects the phase change process of the alloy with the content and temperature,on this basis,we can better control the phase growth and synthesis of CdS_1-xSe_xalloy.In ZnS_1-xSe_xalloy system,the band gap in both WZ and ZB structures is direct,and it decreases with the increase of the Se content.The valence band maxima are contributed by S-2p,Se-3p and Zn-3d electronics,and the conduction band minima are occupied by S-2s,Se-3s and a small amount of p electronics.The calculated formation enthalpies show that the ZB structure is more stable than WZ structure and the ZnS_1-xSe_xsolid solutions tend to phase separate at low temperatures.When the contribution of lattice vibration is taken into account,the critical phase transition temperature of WZ and ZB phases is 529 K and 415 K,respectively.Because the critical phase transition temperature of the alloy is very low,the effect of lattice vibration on the phase diagram is limited.With the increase of temperature,within the range of T=2000 K and Se content less than 7%（S-rich side）,ZnS_1-xSe_xalloy will present a phase transition from ZB to WZ structure.In the study of anti-ferromagnetic alloy Mg_xNi_1-xO,the magnetic Ni atom was divided into two states,spin up and spin down,to optimize the structure through the calculation of spin polarization density functional theory（DFT）.Compared with other methods,the calculation time is greatly shortened.Three intermediate ground states Mg₂Ni₆O₈,Mg₂Ni₂O₄and Mg₆Ni₂O₈as well as magnetic phase diagrams are obtained,and the anti-ferromagnetic mixed phase is determined.When Mg content is lower than 0.75,the anti-ferromagnetic phase is mainly composed of three ground states.With increasing temperature,it transforms from anti-ferromagnetic to paramagnetic through a mixing state of anti-ferromagnetic and paramagnetic.For Mg content less than 30%,the linear variation trend of T_Nis consistent with the experiment.However,at high Mg content,there is a big difference in T_Ndecreasing trend between theoretical and experimental results,and this can be attributed to the misinterpretation of experimental data caused by the low neutron diffraction intensity of the intermediate two ground state structures(x _Mg=0.25 and 0.75).The combination of multi-element cluster expansion method and Monte Carlo method can further promote the study of complex magnetic phase diagrams in the future.In PdH_x,three intermediate ground state structures:PdH,PdH_2.67,and PdH_2.75were predicted by the cluster expansion method.The electronic structure calculation shows that the metallic nature of palladium is unchanged by H atoms entering the interstices.PdH₂is an unstable structure,and there are three possible decomposition paths to decompose it into a more stable structure ZB-PdH.Differential charge density indicates that Pdloses electrons,H gains electrons,and electron transfers between Pdand H.Compared with rocksalt（RS）PdH,ZB-PdH has lower formation enthalpy and stronger binding energy,which means that ZB-PdH has stronger thermodynamic stability than RS-PdH.Phonon dispersion curve verified the dynamic stability of RS-and ZB-PdH.However,regarding the dynamic stability,the lower zero-point energy and vibration free energy of RS-PdH compared to ZB-PdH favor H occupying the O sites.