DIFFUSIONLuis Linde Torres

Phase Transformation

12th of December, 2013

INDEX

1. INTRODUCTION

2. STABILITY OF ATOMS

3. DIFFUSION MECHANISM

4. ACTIVATION ENERGY FOR DIFFUSION

5. RATE OF DIFFUSION (FICK’s FIRST LAW)

6. COMPOSITION PROFILE (FICK’s SECOND LAW)

7. DIFFUSION AND MATERIAL PROCESSING

INTRODUCTION

• Diffusion is the movement of atoms within a material. Atoms move in a predictable fashion to eliminate concentration differences and produce homogeneous, uniform composition. These movements are required for many of the treatments that we perform on materials.

• Diffusion is required for the heat treatment of metals, the manufacture of ceramics, the manufacture of transistor and solar cells.

Interstitial Atomic diffusion across a 4-coordinated lattice.

STABILITY OF ATOMS

• We know that imperfections could be introduced into the lattice of a crystal. These imperfections are not stable or at rest. Atoms possess some thermal energy and they will move. An atom may move from a normal lattice point to occupy a nearby vacancy. An atom may move from one interstitial site to another.

• The ability of atoms and imperfections to diffuse increases as the temperature or thermal energy. The rate of movement is related to temperature o thermal energy by the Arrhenius equation:

0_cRate

STABILITY OF ATOMS

• C0 is a constant.

• R is the gas constant (8.314 J·mol-1·K-1).

• T is the absolute temperature (K).

• Q is the activation energy (J·mol-1) required to cause the imperfection to move.

ARRHENIUS EQUATION

DIFFUSION MECHANISM

• The are four important mechanisms by which atoms diffuse:

Self Diffusion

Interchange Diffusion

Vacancy Diffusion

Interstitial Diffusion

DIFFUSION MECHANISM

• Even in absolutely pure solid materials, atoms move from one lattice position to another. This process, know as self-diffusion can be detected by using radioactive tracers. Although self-diffusion occurs continually in all materials, the effect on the material’s behaviour is not significant.

SELF-DIFFUSION (SUBSTITUTIONAL)

DIFFUSION MECHANISM

• Diffusion of unlike atoms in materials also occurs.

Diffusion of copper atoms into nickel. Eventually, the cooper atom are randomly distributed throughout the nickel.

Interchange diffusion

INTERCHANGE DIFFUSION

DIFFUSION MECHANISM

• In self-diffusion, an atom leaves its lattice sit to fill a nearby vacancy. As diffusion continues, we have a counter-current flow of atoms and vacancies, called vacancy diffusion.

• The number of vacancies, which increases as the temperature increases, helps determine the extent of both self-diffusion and diffusion of substitutional atoms.

VACANCY DIFFUSION

Vacancy diffusion animation.

DIFFUSION MECHANISM

• When an small interstitial atom is present in the crystal structure, the atom moves from one interstitial site to another. No vacancies is required for this mechanism. Partly because there are many more interstitial sites than vacancies.

• Interstitial diffusion is expected to be rapid.

INTERSTITIAL DIFFUSION

Interstitial diffusion animation.

ACTIVATION ENERGY FOR DIFFUSION

• A diffusing atom must squeeze past the surrounding atomos to reach its new site. In order for this to happen, energy must be supplied to force the atom to its new position. The atom is originally in a low-energy, relatively stable location.

• In order to move to a new location, the atom must overcome an energy barrier. The energy barrier is the activation energy Q. heat supplies the atom with the energy needed to exceed this barrier.

ACTIVATION ENERGY FOR DIFFUSION

A high energy is required to squeeze atoms past one another during diffusion. This energy is the activation energy Q.Generally more energy is required for a substitutional atom than for an interstitial atom.

RATE OF DIFFUSION (FICK’s FIRS LAW)

• The rate at which atoms diffuse in a material can be measured by the flux J, which is defined as the number of atoms passing through a plane of unit area per unit time.

• Fick’s firs law explains the net flux of atoms:

RATE OF DIFFUSION (FICK’s FIRS LAW)

• J is the flux (atoms·m-2·s-1).

• D is the diffusity or diffusion coefficient (m2·s-1).

• is the concentration gradient (atoms/m-3·m)

• Several factors affect the atoms during diffusion.

Illustration of the concentration gradient

RATE OF DIFFUSION (FICK’s FIRS LAW)

• The concentration gradient shows how the composition of the material varies with distance. c is the difference concentration over the distance x. The concentration gradient may be created when two materials of different composition are placed in contact when a gas or liquid is in contact with a solid material, when nonequilibrium structures are produced in a material due.

CONCENTRATION GRADIENT

The flux during diffusion is defined as the number of atoms passing through a plane of unit area per unit time.

COMPOSITION PROFILE (FICK’s SECOND LAW)

• Fick’s second law, which describes the dynamic, or nonsteady state, diffusion of atoms, is the differential equation dc/dt = D2 (d2 c / dx2), whose solution depends on the boundary conditions for a particular situation.

Diffusion of atoms into the surface of a material, illustrating the use of Fick’s second law.

COMPOSITION PROFILE (FICK’s SECOND LAW)

• Fick’s second law, which describes the dynamic, or nonsteady state, diffusion of atoms, is the differential equation dc/dt = D2 (d2 c / dx2), whose solution depends on the boundary conditions for a particular situation.

• One solution is:

• Cs is a constant concentration of the diffusing atoms at the surface of the material.

• C0 is the initial uniform concentration if the diffusing atoms in the material.

• Cx is the concentration of the diffusing atom at location x below the surface after time t.

COMPOSITION PROFILE (FICK’s SECOND LAW)

• Fick’s second law, which describes the dynamic, or nonsteady state, diffusion of atoms, is the differential equation dc/dt = D2 (d2 c / dx2), whose solution depends on the boundary conditions for a particular situation.

• One solution is:

• erf is error function and it is tabuled.

DIFFUSION AND MATERIALS PROCESSING

• Diffusional processes become very important when materials are used or processed at elevated temperatures.

• We are going to consider three cases in which diffusion is important.:

Grain Growth

Diffusion Bonding

Sintering

DIFFUSION AND MATERIALS PROCESSING

• A material composed of many grains contains a large number of grain boundaries, which represent a high-energy area because of the inefficient packing of the atomos.

• Grain growth involves the movement of grain boundaries, permitting some grains to grow at the expense of other. Diffusion of atoms across the grain boundary is required and, consequently, the growth of the grains is related to the activation energy needed for an atom to jump across the boundary.

• High temperatures or low activation energies increase the size of the grains.

• Many heat treatment can cause an excessive grain growth.

GRAING GROWTH

DIFFUSION AND MATERIALS PROCESSING

GRAING GROWTH

Grain growth occurs as atom diffuse across the grain boundary from one grain to another

Grain growth variation

DIFFUSION AND MATERIALS PROCESSING

• Diffusion bonding, a method used to join materials, occurs in three steps.

1. The first step forces the two surfaces together at a high temperature and pressure, flattening the surface, fragment impurities and producing a high atom-to-atom area.

2. Atoms diffuse along grain boundaries to the remaining voids. The atoms condense and reduce the size of any voids in the interface. This step occurs very quickly.

3. The final step -final elimination of the voids- volume diffusion, which is comparatively slow, must occur.

DIFFUSION BONDING

DIFFUSION AND MATERIALS PROCESSING

DIFFUSION BONDING

Diffusion bonding steps. The last image (d) represents the final result.

DIFFUSION AND MATERIALS PROCESSING

• A number of materials are manufactured into useful shapes by a process that requires consolidation of small particles into a solid mass. Sintering is the high-temperature treatment that causes particles to join together and gradually reduces the volume of pore space between them.

• Sintering is a frequent step in the manufacture of ceramic components, as well as in the production of metallic parts by powder metallurgy.

• A variety of composite materials are produced using the same techniques.

SINTERING

DIFFUSION AND MATERIALS PROCESSING

SINTERING

Diffusion processes during sintering and powder metallurgy. Atoms diffuse to points in contact, creating bridges and reducing the pore size.

BIBLIOGRAPHY

• The Science and Engineering of Materials

Askeland, Donald R., Third Edition.

• The Science and Engineering of Materials

Askeland, Donald R., Fourth Edition.

• Principles of Materials Science and Engineering

Smith, William F., Third Edition.

• Principles of Materials Science and Engineering

Smith, William F., Fourth Edition.

• Ciencia e Ingeniería de los Materiales

Sánchez Solís, Arturo.

BIBLIOGRAPHY

• www.wikipedia.org (some languages)

• www.slideshare.net

• www.ujaen.es