| The materials with particular properties are demanded on special occasions. Such as,the lower elastic modulus,excellent over-all mechanical properties and biological compatibility for the biomedical Ti alloys are demanded in the biomedical metallic material research areas.Confined by the experiment conditions,some quantities can't be obtained only through the experiment.Based on the micro-structure,theory studies of the relationship between metal materials' bulk modulus and components' structure,components' elastic properties,et al are required.It will help instructing the research and design of new materials.The factors affecting the bulk modulus of metal materials are analyzed from the atomic level.The temperature and pressure dependence of bulk modulus for BCC Fe metal are studied.The physical picture of relationship between solid solution's bulk modulus and components' structure,components' elastic properties,et al are clearly obtained.Three semi-empirical models are presented to study the composition dependence of bulk modulus for binary and ternary solid solution.In the paper,the innovative results are obtained:1 Considering the MAEAM model and anharmonic effect,the relationships between the bulk modulus and temperature and between the bulk modulus and pressure are obtained for BCC Fe metal.That is,the bulk modulus for Fe metal can be described by the quadratic function of temperature,the results reveal that the main reason for the variation of bulk modulus with temperature is interatomic anharmonic vibration.And the bulk modulus will increase with the enlargement of pressure,there is great agreement between the calculated results and the experiment data when the pressure is less than 400GPa,and the bulk modulus is not affected by both the harmonic coefficient and the second anharmonic coefficient.2 The effect of solute atoms to the bulk modulus for binary solid solution is considered.Three semi-empirical models are presented based on the Vegard law, Hooke law and harmonic theory.These are linear model,harmonic model and force constant model,respectively.The three models are used to calculate the bulk modulus for 11 isomorphic binary solid solutions Al-Ni,Al-Cu,Ni-Au,Au-Ag, Au-Cu,Fe-Cr,Mo-Nb,Nb-Cr,Hf-Ti,Hf-Zr,Zr-Ti and 19 isomerous binary solid solutions Ag-Zn,Cu-Zn,Cu-Be,Ni-Co,Ni-Ti,Al-Li,Cr-Al,Fe-Ni,Fe-Ir,Fe-Rh, Fe-Pd,Fe-Pt,Cr-Ti,Li-Mg,Ti-Ta,Fe-Co,Mo-Re,Fe-Re,Fe-Ru.The calculated results indicate that,the bulk modulus for the isomerous binary solid solutions and the FCC-FCC,BCC-BCC isomorphic solid solutions can well be described with the models presented,but the bulk modulus for the HCP-HPC isomorphic solid solutions can't well be calculated with the three models.Concretely,for the FCC-FCC solid solution Au-Ag,Au-Ni,Al-Cu and Al-Ni, the maximum relative errors of the calculated results compared with the available experiment data are less than 13%,5%,5%and 13%,respectively,and the maximum relative error is less than 4%for Au-Cu system;the maximum relative errors are 16%,21%and 6%for the BCC-BCC solid solution Cr-Fe,Nb-Cr and Mo-Nb.However,there is great deviation for the HCP-HPC solid solution from the experiment results.The relative errors ranges are 58～61%,58～65%and 60～64%for solid solution Hf-Ti,Hf-Zr and Zr-Ti.The results reveal that the three models can well be used to investigate the bulk modulus for the FCC-FCC and BCC-BCC solid solution,but they aren't good models for HCP-HCP solid solution.Linear model,harmonic model and force constant model are applied to investigate the bulk modulus of binary isomerous solid solutions.Great agreements are obtained for FCC-HCP solid solutions,for Cu-Be,Ni-Co,Cu-Zn and Ni-Ti,the maximum relative errors are less than 19%,13%,17%and 24%, respectively.For the FCC-BCC solid solution Al-Li,Cr-Al,Fe-Ni,Fe-Ir,Fe-Pd and Fe-Pt,the bulk modulus can well be described with three models,however, for Fe-Rh system,the maximum relative error approximates to 100%with the models presented.The main reason for the great deviation from experiment data is that,the bulk modulus of the materials will be affected by the ferromagnetism of Fe atoms.For HCP-BCC solid solution Cr-Ti,Ti-Ta,Fe-Co,the maximum relative errors are less than15%,8%,7%,respectively,the goodness of fit between the calculated results and the experiment data is:linear model＞harmonic model＞force constant model.For Li-Mg,Fe-Re and Fe-Ru,the maximum relative errors are less than 18%,18%and 19%,respectively,the goodness of fit:force constant model＞harmonic model＞linear model.In the Mo-Re system,the maximum relative error is less than 36%,and the relative error will be less than 9%with the Mo composition range is 60～90at%.3 With the help of semi-empirical models presented for the binary solid solution,we expand the linear model,harmonic model and force constant model to study the bulk modulus of ternary solid solution.Neglecting the structure difference of component atoms,the expanding models are used to study the isomorphic ternary solid solution Nb-Cr-V,the isomerous solid solution Nb-Al-Cr, Ti-Ni-Cu,and the laves phase Nb-Cr-Ti system.For Nb-Cr-V system,the bulk modulus can well be studied with three expanding models,and the force constant model is the best,the relative error of which is less than 9%.For Ti-Ni-Cu system, the maximum relative error is less than 30%.For laves phase Nb-Cr-Ti system, the linear model is the best when the composition of Cr is fixed to 67at%,and if the composition of Cr fluctuates from 67at%,there is the best result when use the force constant model. |
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