The diffusion coefficients in metallic materials

Binary system에서는 Boltzmann-Matano method를 이용하여 상호확산계수의 계산이 일반적이다.

Ternary system의 경우, Matano-Kirkaldy method 또는 Whittle-Green method를 이용하여 계산이 가능하다. Matano-Kirkaldy method의 경우 정확한 방법이지만, Matano plane의 계산이 필요하다.

 

Intrinsic diffusion coefficient

Intrinsic diffusion coefficient refers to the diffusion coefficient of a species in a homogeneous material, where no concentration gradients or other factors can affect the diffusion process. It measures the rate at which atoms or molecules move through the material due to their thermal energy. It is determined by temperature, crystal structure, and the type of diffusion mechanism involved (e.g., vacancy diffusion, interstitial diffusion, etc.). The intrinsic diffusion coefficient is an essential parameter in materials science, as it governs many material properties, such as the rate of phase transformations, the growth of crystals, and the kinetics of chemical reactions.

 

The difference between the self-diffusion coefficient and the intrinsic diffusion coefficient

Self-diffusion coefficient refers to the diffusion of atoms within a homogeneous material, while the intrinsic diffusion coefficient refers to the distribution of atoms through a crystal lattice.

Self-diffusion coefficient measures the mobility of the atoms within a single phase of a material, which can be caused by thermal energy, mechanical stress, or other factors. This diffusion occurs without any external concentration gradient, as the atoms exchange places within the same material phase.

On the other hand, the intrinsic diffusion coefficient is the diffusion of atoms through the crystal lattice, driven by concentration gradients. The crystal lattice structure of a material can affect the inherent diffusion coefficient, and it is typically measured at high temperatures where the mobility of the atoms is increased. Crystal structure, atomic bonding, and temperature influence the intrinsic diffusion coefficient.

In summary, the self-diffusion coefficient measures the mobility of atoms within a homogeneous material, while the intrinsic diffusion coefficient measures the mobility of atoms through a crystal lattice.

 

Interdiffusion coefficient

The interdiffusion coefficient measures the diffusion rate between two different species in a material or between two different materials. It is the diffusion coefficient of one species in the presence of another species. Interdiffusion can occur in solid, liquid, or gaseous materials. Interdiffusion can be affected by temperature, pressure, concentration, crystal structure, and other factors. It plays a vital role in many processes, including alloy formation, chemical reactions, and diffusion bonding. Interdiffusion coefficient can be determined experimentally by several methods, including diffusion couple experiments, tracer diffusion, and surface diffusion measurements.

 

Here are some common classifications of diffusion coefficients in metallic materials:

1. Vacancy diffusion coefficient: This diffusion coefficient describes the rate at which atoms move through vacancies in the crystal lattice of a material. Vacancy diffusion is the most common mechanism of diffusion in metals.
2. Interstitial diffusion coefficient: This diffusion coefficient describes the rate at which atoms move through interstitial sites in the crystal lattice of a material. Interstitial diffusion occurs when smaller atoms, such as hydrogen or carbon, diffuse through the lattice.
3. Self-diffusion coefficient: This diffusion coefficient describes the rate at which atoms of a pure metal move through its own crystal lattice.
4. Impurity diffusion coefficient: This diffusion coefficient describes the rate at which foreign atoms diffuse through a metal.
5. Temperature-dependent diffusion coefficient: This diffusion coefficient is a function of temperature and describes how the diffusion rate changes as a function of temperature.
6. Concentration-dependent diffusion coefficient: This diffusion coefficient is a function of concentration and describes how the diffusion rate changes as a function of concentration.

These classifications are not mutually exclusive; different diffusion mechanisms can coexist in a single material. For example, in some cases, interstitial diffusion can occur in addition to vacancy diffusion. Similarly, the diffusion coefficient can be both temperature and concentration-dependent.

 

Whittle-Green method

The Whittle-Green method is a mathematical approach used to determine the interdiffusion coefficients of ternary systems. In a ternary system, three different components are present. The method involves analyzing the concentration profiles of each component using a set of differential equations that describe the diffusion process in the system.

The Whittle-Green method is based on Fick's first and second laws of diffusion, which describe the rate of diffusion and the concentration gradient, respectively. The equations are modified to apply to a ternary system, and a set of boundary conditions are added to reflect the constraints of the specific system being analyzed.

The resulting equations can be solved using numerical techniques like finite difference or finite element methods. Moreover, the solutions yield the interdiffusion coefficients of each component, critical parameters for understanding and predicting the behavior of ternary systems.

Overall, the Whittle-Green method is a powerful tool for analyzing the diffusion behavior of ternary systems. Materials science research has widely used it to gain insights into various complex systems, including alloys and geological materials.

 

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확산의 기초 / Diffusion in solids