Let us consider a kinetic Monte Carlo model of a core-shell binary spherical nanoparticle on a rigid f.c.c. lattice with lattice parameter ##a##, where ##N_A = 45995## atoms of the faster diffuse species A are located in the core with radius ##r_c \sim 14a## whilst ##N_B = 30434## atoms of the slower diffuse species B form the shell with external radius ##r_s \sim 16.58a##. We assume that the three nearest neighbour pair-interaction energies are equal ##\phi_{AA}=\phi_{BB}=\phi_{AB}## but the effective attempt frequencies ##\nu_{A0}## and ##\nu_{B0}## of A and B atoms for exchange with a vacancy are strongly different ##\nu_{A0} / \nu_{B0} =10^3## and do not depend on the local arrangement of a vacancy. This model has a zero enthalpy of mixing. Furthermore, it has been shown [12,14-16] that with an appropriate choice of reduced pair-interaction energy ##\phi/kT## and using the equation:
$$-6\phi/kt \sim \frac{1}{(1-2c_v^{eq})} \ln{\left(\frac{1-c_v^{eq}}{c_v^{eq}}\right)} \quad (1)$$
for a pure element f.c.c. system it is possible to fulfil two requirements necessary for our numerical simulation. These are a reasonable calculation speed and a value of the equilibrium vacancy composition ##c_v^{eq}## sufficiently close to the vacancy composition at the melting temperature ##T_m## of a typical crystalline solid. For the case of very small ##c_v^{eq}## Eq. (1) will correctly describe an equilibrium vacancy composition in a model of a binary alloy with equal pair-interaction energies.
In this case, the vacancy formation energy will not depend on the atomic distributions and the additional configurational entropy term for vacancies appearing in a binary alloy will be negligible (for details see [18]). Following these reasons, the reduced pair-interaction energy ##\phi/kT = -1.5## was chosen using Eq. (1) to provide an equilibrium vacancy composition of ##c_v \sim 1.24×10^{-4}## in pure A and B as well as in a binary A-B alloy of f.c.c. systems.
The Kirkendall effect is a phenomenon in materials science where there is a difference in diffusion rates between two different components in a solid material. This results in the formation of voids or pores in the material, leading to changes in its microstructure and properties.
The Kirkendall effect occurs due to a difference in the diffusion rates of two different components in a solid material. This can be caused by differences in atomic size, chemical bonding, or temperature gradients within the material.
Vacancy concentration refers to the number of vacant lattice sites in a solid material. These vacancies can be caused by defects or imperfections in the material, and can affect its properties and behavior.
Pair interaction energy refers to the energy associated with the interaction between two atoms or ions in a solid material. This energy can be influenced by factors such as atomic size, chemical bonding, and temperature, and can play a significant role in the Kirkendall effect.
The Kirkendall effect can have significant impacts on the microstructure and properties of materials. It can lead to changes in porosity, grain boundaries, and diffusion pathways, which can affect mechanical, electrical, and chemical properties of the material. Understanding and controlling the Kirkendall effect is important in materials design and engineering.