Role of polycrystalline titanium grain size in the formation of the concentration profiles of implanted aluminum ions

Physical Base of the Metallic Gradient Surface Layers of Titanium Alloys Formed under Ion Implantation

“…The regularities of the mass transfer are found to depend upon the grain size (the average values of which are 0.3, 1.5, 17, and 38 µm) of initial samples of titanium targets under implantation of aluminum ions (Fig. 2) [8]. An increase in the modified layer thickness with decreasing grain size of the materials under study is revealed.…”

The influence of vacancy generation on the impurity distribution in the target under the conditions of surface treatment by a particle beam

“…In the works of other authors we can find slightly different formulations of the expression for determining the vacancy source [48,[57][58][59]. The expression for the vacancy chemical potential takes into account three processes at once: the diffusion of vacancies, the movement of vacancies under the action of inhomogeneous stresses and temperature [60].…”

“…The gradient of chemical potential for vacancy is the force that leads to the appearance of the vacancy flux. However, in the simplest approximation, let us assume that the presence of vacancies changes the diffusion coefficient of the introduced particle, for example, according to the law [58] $$$$\begin{equation*}D = {D}_0{f}_0\left( C \right)\left( {1 + {f}_V\left( {{C}_V} \right)} \right),\end{equation*}$$$$where D 0 is self‐diffusion coefficient; $$f( C )$$ is function of the dependence of the diffusion coefficient on the composition, its form depends on the structure of the “solution” formed in the process of treatment; $${f}_V( {{C}_V} )$$ is function of the dependence of the diffusion coefficient on the vacancy concentration.…”

Analysis of concentration field formation in titanium under aluminum ion implantation via a gas-and-metal film deposited on a target surface

“…(1) are obtained by the time integration of function (3). The contribution of the statistical dis tribution is described using the Pearson type IV distri bution [6], and details of the computational algorithm are described in [7]. Moments of the spatial distribu tions for each aluminum ion energy component in the…”