Calculation Of Crystal Cohesive Energy Of (ZrTi)B_ 2 Solid Solution

ZrB₂, TiB₂ and its solid solution are one kind of Ultra-high-temperature ceramics (UHTCs),with an excellent and unique set of bulk properties including unusually high melting points, high thermal conductivity, high elastic modulus, retained strength at high temperatures, relatively good thermal shock resistance and modest thermal expansion, is being widely used in carbide, composites and Ultra-high-temperature ceramics. Crystal cohesive energy is not only an important parameter of materials, but also of great important significance in revealing the micro-structure of solids and molecules.In this paper , based on the EET (The Empirical Electron Theory of Solid sand Molecules) ,we calculate the hybrid level of the two compound ZrB₂ and TiB₂, with the BLD (bond length different) method, the result leads to A15,5 and A14,4 respectively. Their melting points are calculated to be 3345K and 3119K the relative error are only 0.9% and 1.8% respectively.According to the EET, the cohesive energy contents three parties the cohesive energy similar to elements while all the bonds are considered as covalent bonds, ionization-like energy and affinity-like energy, to reach the second and the third parties we have to calculate the electron offset number and at last the cohesive energy are calculated to be -1539.56KJ/mol and TiB₂-1469.71KJ/molWhen we calculate the solid solution, three models are used they are AAM (average atom model), RAM (real atom model), ACR (average cell model), the last two models are based on the first model.The covalence structure, melting point, and the electron offset number are gotten using the three models. After analyze the three different models we thing that AAM is the most reasonable. The energy is calculated to be Zr_0.8Ti_0.2B₂ -1498.12KJ/mol, and Ti_0.8Zr_0.2B₂ -1479.54KJ/mol. This result is accord with the melting point tendency. We believe that the EET method is simpler and more precise reporting to first principle.