Displacements Produced by a Primary Knock-on

The simplest calculation of the damage function, (Nd(E) is based on the hard-sphere model of Kinchin and Pease (1955). The following assumptions are made in the Kinchin and Pease model  

The probability of transferring energy during the collision process is determined by a hard sphere cross-section, i.e.  

All collisions are elastic, only consider nuclear processes, ignoring electronic stopping  

The energy consumed in displacing an atom, Ed, is neglected in the energy balance of the binary collision that transfers kinetic energy to the struck atom  

The arrangement of the atoms in the solid is random, and effects due to the crystal structure are neglected  

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Radiation Damage. It has been known for many years that bombardment of a crystal with energetic (keV to MeV) heavy ions produces regions of lattice disorder. An implanted ion entering a soHd with an initial kinetic energy of 100 keV comes to rest in the time scale of about 10 due to both electronic and nuclear coUisions. As an ion slows down and comes to rest in a crystal, it makes a number of coUisions with the lattice atoms. In these coUisions, sufficient energy may be transferred from the ion to displace an atom from its lattice site. Lattice atoms which are displaced by an incident ion are caUed primary knock-on atoms (PKA). A PKA can in turn displace other atoms, secondary knock-ons, etc. This process creates a cascade of atomic coUisions and is coUectively referred to as the coUision, or displacement, cascade. The disorder can be directiy observed by techniques sensitive to lattice stmcture, such as electron-transmission microscopy, MeV-particle channeling, and electron diffraction. 

Molecular-dynamics calculations provide valuable insight into the evolution with time of defect structures created in the collision caiscade. Consider, for example, the molecular-dynamics simulations of low-energy displacement cascades in the Bll-ordered compound CuTi (Figure 7) by Zhu et al, (1992). Figure 8 shows the number of Frenkel pairs produced by a Cu primary knock-on atom (PKA) as a function of recoil energy at the end of the collisional phase (0.2 p ) and at the end of the cooling phase (2.5 ps). The number of Frenkd... 

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