1. Atom and Ion Movements in Materials
Chapter 5: Atom and Ion Movements in Materials
Chapter 5:
Atom and Ion Movements
in Materials
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Chapter 5: Atom and Ion Movements in Materials
Learning Objectives
Applications of diffusion
Stability of atoms and ions
Mechanisms for diffusion
Activation energy for diffusion
Rate of diffusion [Fick’s first law]
Factors affecting diffusion
Permeability of polymers
Composition profile [Fick’s second law]
Diffusion and materials processing
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3. Applications of Diffusion
Chapter 5: Atom and Ion Movements in Materials
Applications of Diffusion
Diffusion
Net flux of any species, such as ions, atoms, electrons, holes, and molecules.
Carburization for surface hardening of steels - A source of carbon is diffused into steel components.
In nitriding, nitrogen is introduced into the surface of a metallic material.
Dopant diffusion for semiconductor devices
A p-n junction is a region of the semiconductor, one side of which is doped with n-type dopants and the other side is doped with p-type dopants.
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4. Applications of Diffusion
Chapter 5: Atom and Ion Movements in Materials
Applications of Diffusion
Conductive ceramics
Used in products such as oxygen sensors in cars, touch- screen displays, fuel cells, and batteries.
Creation of plastic beverage bottles - limit the occurrence of diffusion for certain species
For instance, the diffusion of CO2 must be minimized.
Oxidation of aluminum
Al2O3 forms a thin oxide coating. The coating does not have a color (making it invisible) and hinders further oxidation of the metal.
Coatings and thin films
Used to limit the diffusion of water vapor, oxygen, or other chemicals.
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5. Applications of Diffusion
Chapter 5: Atom and Ion Movements in Materials
Applications of Diffusion
Thermal barrier coatings for turbine blades
Ceramic coatings that protect the underlying alloy from high temperatures.
Optical fibers and microelectronic components
Optical fibers are coated with polymeric materials to prevent diffusion of water molecules.
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6. Stability of Atoms and Ions
Chapter 5: Atom and Ion Movements in Materials
Stability of Atoms and Ions
Arrhenius equation
where
c constant
R gas constant, cal/(mol*K)
T absolute temperature (K)
Q activation energy required to cause Avogadro’s number of atoms or ions to move
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Chapter 5: Atom and Ion Movements in Materials
Figure Diffusion
Diffusion of copper atoms into nickel. Eventually, the copper atoms are randomly distributed throughout the nickel.
Materials containing vacancies, atoms move or “jump” from one lattice position to another. This process is known as self-diffusion.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.6
Diffusion mechanisms in materials
(a) Vacancy or substitutional atom diffusion
(b) Interstitial diffusion
Interdiffusion - Diffusion of different atoms in different directions.
Vacancy diffusion: Counter flows of atoms and vacancies.
Interstitial diffusion: The atom or ion moves from one interstitial site to another.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.7
The activation energy Q is required to squeeze atoms past one another during diffusion. Generally, more energy is required for a substitutional atom than for an interstitial atom.
Diffusion couple is used to indicate a combination of an atom of a given element (e.g., carbon) diffusing in a host material (e.g., BCC Fe).
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10. Rate of Diffusion [Fick’s First Law]
Chapter 5: Atom and Ion Movements in Materials
Rate of Diffusion [Fick’s First Law]
Fick’s first law explains the net flux of atoms:
J = -D dc dx
where
J flux
D diffusivity or diffusion coefficient (cm2/s) dc
dx concentration gradient (atoms/(cm3∙cm))
The negative sign in the equation indicates that the flux of diffusing species is from higher to lower concentrations.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.8
The flux during diffusion is defined as the number of atoms passing through a plane of unit area per unit time.
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12. Figure 5.9 - Illustration of the Concentration Gradient
Chapter 5: Atom and Ion Movements in Materials
Figure Illustration of the Concentration Gradient
Δc is the difference in concentration over the distance Δx.
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13. Factors Affecting Diffusion
Chapter 5: Atom and Ion Movements in Materials
Factors Affecting Diffusion
Temperature and the diffusion coefficient
where
Q activation energy, in units of (cal/mol)
R gas constant, cal/(mol*K)
T absolute temperature (K)
D pre-exponential term
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.12
The diffusion coefficient D as a function of reciprocal temperature for some metals and ceramics. In this Arrhenius plot, D represents the rate of the diffusion process. A steep slope denotes a high activation energy.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.13
Diffusion coefficients for different dopants in silicon.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.14
Diffusion in ionic compounds. Anions can only enter other anion sites. Smaller cations tend to diffuse faster.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.15
Diffusion coefficients of ions in different oxides.
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18. Factors Affecting Diffusion
Chapter 5: Atom and Ion Movements in Materials
Factors Affecting Diffusion
Types of diffusion
Volume diffusion: Diffusion of atoms through the interior of grains.
Grain boundary diffusion: Atoms can also diffuse along boundaries, interfaces, and surfaces in the material. In this type of diffusion, atoms can diffuse easily.
Surface diffusion: Diffusion of atoms along surfaces, such as cracks or particle surfaces.
Time
Times for heat treatments may be reduced by using higher temperatures or by making the diffusion distances (related to Δx) as small as possible.
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19. Factors Affecting Diffusion
Chapter 5: Atom and Ion Movements in Materials
Factors Affecting Diffusion
Dependence on bonding and crystal structure
Interstitial diffusion, with a low-activation energy, usually occurs much faster than vacancy, or substitutional, diffusion.
Activation energy, which depends on the strength of atomic bonds, is higher for diffusion of atoms in materials with a high melting temperature (Figure 5.17).
Dependence on concentration of diffusing species and composition of matrix
The diffusion coefficient (D) depends on the concentration of diffusing species and composition of the matrix.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.17
The activation energy for self-diffusion increases as the melting point of the metal increases.
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21. Permeability of Polymers
Chapter 5: Atom and Ion Movements in Materials
Permeability of Polymers
Permeability is expressed in terms of the volume of gas or vapor that can permeate per unit area per unit time, or per unit thickness, at a specified temperature and relative humidity.
Polymers that have a polar group (e.g., ethylene vinyl alcohol) have higher permeability for water vapor than for oxygen gas.
Diffusion of some molecules into a polymer can cause swelling problems.
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22. Composition Profile [Fick’s Second Law]
Chapter 5: Atom and Ion Movements in Materials
Composition Profile [Fick’s Second Law]
Fick’s second law
If D is not a function of location x and the concentration (c) of diffusing species
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23. Composition Profile [Fick’s Second Law]
Chapter 5: Atom and Ion Movements in Materials
Composition Profile [Fick’s Second Law]
Solution to the Fick’s second law equation depends on the boundary condition.
where
cs concentration of the diffusing atoms at the surface of the material.
c initial uniform concentration of the diffusing atoms in the material.
cx concentration of the diffusing atom at location x below the surface after time t.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.18
Diffusion of atoms into the surface of a material illustrating the use of Fick’s second law.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.19
Graph showing the argument and value of the error function encountered in Fick’s second law.
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26. Composition Profile [Fick’s Second Law]
Chapter 5: Atom and Ion Movements in Materials
Composition Profile [Fick’s Second Law]
The mathematical definition of the error function
Fick’s second law is the technique behind carburization
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27. Composition Profile [Fick’s Second Law]
Chapter 5: Atom and Ion Movements in Materials
Composition Profile [Fick’s Second Law]
Limitations to applying the error-function solution
It is assumed that D is independent of the concentration of the diffusing species.
The surface concentration of the diffusing species (cs) is always constant.
There are situations under which these conditions may not be met and hence the concentration profile evolution will not be predicted by the error-function solution.
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28. Diffusion and Materials Processing
Chapter 5: Atom and Ion Movements in Materials
Diffusion and Materials Processing
Melting and casting
Diffusion plays a particularly important role in solidification of metals and alloys.
Sintering
High temperature treatment that causes particles to join, gradually reducing the volume of pore space between them.
Powder metallurgy - a processing route by which metal powders are pressed and sintered into dense, monolithic components.
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29. Diffusion and Materials Processing
Chapter 5: Atom and Ion Movements in Materials
Diffusion and Materials Processing
Liquid phase sintering: Process in which a small amount of liquid forms and assists densification.
Hot pressing – unidirectional pressure is applied while the material is being sintered.
Hot isostatic pressing – the pressure is applied in all directions while the material is being sintered.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.20
Diffusion processes during sintering and powder metallurgy. Atoms diffuse to points of contact, creating bridges and reducing the pore size.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.23
Grain growth in alumina ceramics can be seen from the scanning electron micrographs of alumina ceramics.
(a) The left micrograph shows the microstructure of an alumina ceramic sintered at 1350°C for 15 hours.
(b) The right micrograph shows a sample sintered at 1350°C for 30 hours.
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32. Diffusion and Materials Processing
Chapter 5: Atom and Ion Movements in Materials
Diffusion and Materials Processing
Grain growth: Movement of grain boundaries, permitting larger grains to grow at the expense of smaller grains (Figure 5.23).
Driving force for grain growth is the reduction in grain boundary area.
In normal grain growth, the average grain size increases steadily and the width of the grain size distribution is not affected severely.
In abnormal grain growth, the grain size distribution tends to become bi-modal.
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Chapter 5: Atom and Ion Movements in Materials
Figure 5.24
The steps in diffusion bonding:
Initially the contact area is small;
application of pressure deforms the surface, increasing the bonded area;
grain boundary diffusion permits voids to shrink;
final elimination of the voids requires volume diffusion.
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Chapter 5: Atom and Ion Movements in Materials
Key Terms
Diffusion
Nitriding
Conductive ceramics
Thermal barrier coatings
Activation energy
Self-diffusion
Interdiffusion
Vacancy diffusion
Interstitial diffusion
Diffusion couple
Flux
Fick’s first law
Diffusivity or diffusion coefficient
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Chapter 5: Atom and Ion Movements in Materials
Key Terms
Concentration gradient
Volume diffusion
Grain boundary diffusion
Diffusion distances
Permeability
Fick’s second law
Sintering
Powder metallurgy
Liquid phase sintering
Hot pressing
Hot isostatic pressing
Grain growth
Driving force
Normal grain growth
Abnormal grain growth
Diffusion bonding
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