The study of material properties show that there is a large space and time span from the electronic level, atomic level, to molecules, clusters, mesoscopic to macroscopic continuous medium. Different levels are dealt with by using different research methods. The interatomic potential function method is an important intermediary bridging from atomic level to cluster and mesoscopic physics research. Therefore, it is not only for a research field of condensed matter physics, but also for an interdisciplinary research. The interatomic potential, as the basis of all computer simulations at an atomic level, directly affects the accuracy of simulation results. That is to say, it is a greatly significant to study the interatomic potential at the atomic level. This article is based on the inversion algorithm and microscopic phase field, and the influence of medium Al concentration and temperature on the precipitation process of Ni₇₅Al_xV_25-x alloy are studied. At the same concentration, the first nearest neighbor interatomic potential of L1₂ and DO₂₂ phase increase linearly with increasing temperature, which is proportional to each other. However, the first nearest neighbor interatomic potential for L1₂ (DO₂₂) phase increases (decreases) with the increase of Al atom concentration at a constant temperature. When the temperature is 1046.5 K and the concentration of Al is 0.06, the interatomic potential of L1₂ phase is consistent with the first principles calculation by Chen, indicating the reliability of the inversion algorithm. At the same time, the inverse interatomic potentials are taken into consideration in the microscopic phase field simulation to investigate the relationship between the precipitation sequence of the medium Al alloy and the interaction potential between atoms. That is to say, when the first neighbor interatomic potential of L1₂ is greater than (less than DO₂₂) L1₂ (DO₂₂) precipitated preferentially. The first nearest neighbor interatomic potential for L1₂ and DO₂₂ are equal, both of which are precipitated at the same time. In particular, when the concentration of Al atoms is equal to 0.0589, it is found that L1₂ and DO₂₂ are simultaneously precipitated. The precipitation mechanism of the alloy with medium Al concentration is a hybrid mechanism with both non-classical nucleation and instability decomposition characteristics. Since the precipitation mechanism of the medium-concentrated alloy is a hybrid mechanism with both non-classical nucleation and spinodal decomposition, the microscopic phase field method is used to invert the interatomic potential, which increases the reliability of the precipitation sequence of medium the Al alloy.