# Multi-Directional Displacement Threshold Energy and Crystal Irradiation Damage Model
Moreover, numerous research groups have also developed binary collision programs with distinct characteristics over the past decades, including CASWIN [15], while a Monte Carlo program has been presented for simulating ion beam analysis data as well [16]. To enhance studies on breakdown damage effects related to electric field, magnetic field, and pulsed heating effects, [PERSON] et al. designed a dual-mode cavity system [17]. [PERSON] provided a comprehensive summary of the significant effects observed in the optical absorption spectra of various oxide materials under 20 MeV proton irradiation and drew both general and detailed conclusions regarding known defect types, fluency dependencies, and sensitivity to protons [2]. In 2013, the International Atomic Energy Agency (IAEA) launched a four-year program known as the Primary Radiation Damage Cross Sections, aimed at investigating the calculation of initial defect damage caused by neutron irradiation. This program aims to calculate the cross-sections for initial defect generation and gas product generation during neutron irradiation. The project encompasses various aspects such as neutron-matter interaction cross-section, initial damage calculation, radiation damage effect characterization, and gas generation in the fission process. Currently, a benchmark scale database has been established for researchers' reference [18]. [PERSON] et al. [19] discovered in 2022 that the presence of a significant quantity of pre-existing lattice defects in carbon fiber reinforced carbon matrix composites can significantly influence the unexpectedly high level of lattice disorder across the entire ionic range. These findings reveal that PCIB graphite, which possesses fewer pre-existing crystal lattice defects, exhibits a more predictable response to accumulated irradiation damage. [PERSON] et al. [20] conducted a classical molecular dynamics simulation to investigate the response of \(\delta\)-phase Pu-Ga alloy under self-radiation. He employed the thermodynamic integration method to calculate the Helmholtz free energy of these microstructures and drew conclusions regarding their relative thermodynamic stability under ambient conditions. Additionally, equilibrium parameters were estimated for the presence of spatiotemporal bit clusters within the lattice and at the edge of misalignment. In this study, starting from the binary collision model and based on the existing well-established atomic collision dissociation model, an atomic dissociation model is proposed that takes into account the influence of bond energy. Section 2 describes the energy transfer mechanism of particles in binary collisions and explains the reasons for differences in displacement threshold energy of atoms in different directions. Section 3 compares existing models for atomic collision displacement, elucidates the fundamental principles behind various methods to determine the number of displaced atoms, and summarizes previous methodological innovations. A probability model for atomic displacement is introduced, taking into account the crystal structure. GaAs is utilized in a case study to compute the total displaced atom count under varying-energy particle impacts using the Monte Carlo expansion technique. Additionally, a comparison is conducted between this statistical method, which considers direction-dependent displacement threshold energies within crystal structures, and other conventional approaches.