5_diffusion in solids

7/29/2019 5_Diffusion in Solids

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Chapter 5-

Chapter 5: Diffusion in Solids


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Chapter 5-

What is diffusion?

is material transport by atomic motion.

Phenomenon of material transport by atomicmotion.


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Chapter 5-

results of an atomistic simulation of atomic mixing

Inhomogeneous materials can become homogeneous bydiffusion. For an active diffusion to occur, the temperature

should be high enough to overcome energy barriers to atomic

motion.


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Chapter 5-

Applicable/Dominate in Metallic Diffusion


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Chapter 5-

Interdiffusion and Self-diffusion Interdiffusion or impurity diffusion:

In an alloy, atoms tend to migrate from regions of large

concentration

the process where atoms of one metal diffuse into

another.

occurs in response to a concentration gradient.

Self-diffusion:

Atomic migration in pure metals.

is diffusion in one-component material, when all atomsthat exchange positions are of the same type.


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Chapter 5- 3

Initially After some time

100%

Concentration Profiles0

Interdiffusion or Impurity Diffussion

Heat

Inhomogeneous materials can become homogeneous by diffusion. For an active diffusion to

occur, the temperature should be high enough to overcome energy barriers to atomic motion.


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Chapter 5- 4

Self-diffusion: In an elemental solid, atoms

also migrate.

Label some atoms After some time

A

B

C

D

Self Diffusion

Heat

Self-diffusion:

Atomic migration in pure metals.

is diffusion in one-component material, when all atoms

that exchange positions are of the same type.


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Chapter 5-

Chapter 5:

Diffusion Mechanisms


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Chapter 5-

Diffusion Mechanisms

Vacancy diffusion:The diffusion mechanism wherein net atomic

migration is from lattice site to an adjacent

vacancy.

Interstitial diffusion:

A diffusion mechanism where atomic motion is

from interstitial site to interstitial site.


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Chapter 5-

Vacancy diffusion mechanism

To jump from lattice site to lattice site, atoms need energy to break bonds with

neighbors, and to cause the necessary lattice distortions during jump. This energy

comes from the thermal energy of atomic vibrations (Eav ~ kBT)

The direction of flow of atoms is opposite the vacancy flow direction.


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Chapter 5-

Interstitials diffusion mechanism

Interstitial diffusion is generally faster than vacancy diffusion because bondingof interstitials to the surrounding atoms is normally weaker and there are many

more interstitial sites than vacancy sites to jump to.

Requires small impurity atoms (e.g. C, H, O) to fit into interstices in host.


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Chapter 5-

Steady and Unsteady State Diffusion


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Chapter 5-

Diffusion Flux The flux of diffusing atoms, J,

is used to quantify how fast diffusion occurs.

The flux is defined as either the number of atoms

diffusing through unit area per unit time (atoms/m2-

second) or the mass of atoms diffusing through unit

area per unit time, (kg/m2- second).


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Chapter 5-

whereA denotes the area across whichdiffusion is occurring and

tis the elapsed diffusion time.

In differential form, this expression

becomes


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Chapter 5-

Steady and Non- Steady State Diffusion

Steady-state diffusion:

1. The diffusion condition for which there is no net

accumulation or depletion of diffusing species.

2. The diffusion flux is independent of time.

Non steady-State Diffusion1. This is the case when the diffusion flux depends on

time, which means that a type of atoms accumulates in

a region or that it is depleted from a region (which

may cause them to accumulate in another region).2. The diffusion condition for which there is some net

accumulation or depletion of diffusing species. The

diffusion flux is dependent on time.


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Chapter 5-

Steady-State Diffusion

Steady state diffusion: the diffusion flux does not change with time.

Concentration profile: concentration of

atoms/molecules of interest as function ofposition in the sample.

Concentration gradient: dC/dx (Kg m-4):

the slope at a particular point on concentration

profile.


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Chapter 5-


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Chapter 5-

Steady-State Diffusion: Ficks first law Ficks first law: the diffusion flux along

direction x is proportional to theconcentration gradient


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Chapter 5-

The concentration gradient is often called the driving force in

diffusion (but it is not a force in the mechanistic sense).

The minus sign in the equation means that diffusion is down

the concentration gradient.


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Chapter 5-

Sample Problem 5.1.

A plate of iron is exposed to a carburizing(carbon-rich) atmosphere on one side and a

decarburizing (carbon-deficient) atmosphere on

the other side at 700C (1300F). If a condition of

steady state is achieved, calculate the diffusion

flux of carbon through the plate if the

concentrations of carbon at positions of 5 and 10

mm (5x10^-3 and 10^-2 m) beneath thecarburizing surface are 1.2 and 0.8 kg/m3,

respectively. Assume a diffusion coefficient of

3x10^-11 m2/s at this temperature.


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Chapter 5-

Solution:


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Chapter 5-

Nonsteady-State Diffusion: Fickssecond law

In many real situations the concentration profileand the concentration gradient are changing with

time.

The changes of the concentration profile can be

described in this case by a differential equation,Ficks second law.


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Chapter 5-

Factors affecting Diffusion


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Chapter 5-

As stated above, there is a barrier to diffusion created

by neighboring atoms that need to move to let the

diffusing atom pass.

Thus, atomic vibrations created by temperature assist

diffusion. Also, smaller atoms diffuse more readily than big ones,

and diffusion is faster in open lattices or in open

directions.

Similar to the case of vacancy formation, the effect of

temperature in diffusion is given by a Boltzmann

factor: D = D0 exp(Qd/kT).


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Chapter 5-

Diffusing Species

magnitude of the diffusion coefficientD isindicative of the rate at which atoms

diffuse.

The diffusing species as well as the hostmaterial influence the diffusion coefficient


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Chapter 5-

there is a significant difference in magnitude between self-diffusion and carbon

interdiffusion in iron at 500C, the D value being greater for the carbon interdiffusion

(3.0 x10^-21 vs. 2.4x10 -12 m2/s).This comparison also provides a contrast between

rates of diffusion via vacancy and interstitial modes as discussed earlier


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Chapter 5-

Temperature

has a most profound influence on thecoefficients and diffusion rates.

temperature dependence of diffusion

coefficients.


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Chapter 5-

Sample Problem 5.4

compute the diffusion coefficient formagnesium in aluminum at 550C.


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Chapter 5-


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Chapter 5-

Solution:


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Chapter 5-

Factors that influence diffusion

Temperature

diffusion rate increases very rapidly with increasing

temperature

Diffusion mechanism

diffusion by interstitial mechanism is usually faster than byvacancy mechanism

Diffusing and host species

Do, Qd are different for every solute, solvent pair

Microstructure

diffusion is faster in polycrystalline materials compared to

single crystals because of the accelerated diffusion along

grain boundaries.


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Chapter 5-

Diffusion in material processingCase Hardening:

Hardening the surface of ametal by exposing it to

impurities that diffuse into

the surface region

and increase surfacehardness.

Common example of case

hardening is carburization

of steel.

Diffusion of carbon atoms

(interstitial mechanism)

increases concentration of

C atoms and makes iron

(steel) harder.


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Chapter 5-

Quiz on

Chapter 5:Diffusion in solids

thisJanuary 5, 2012 (Saturday)


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Chapter 5-

Advanced Reading Stress and Strain

Tension Compression

Shear

Torsion

Elastic deformation

Plastic Deformation

Yield Strength

Tensile Strength Ductility

Resilience

Toughness

Hardness


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Chapter 5-

Assignment (for Chapter 6)

1. Define engineering stress and engineeringstrain.

2. Draw and label of its parts of a stress-strain

curve of metals.3. State Hookes law and note the conditions

under which it is valid.

4. Define Poissons ratio.5. What is meant by 0.002 strain offset?

6. Determine on how to compute the working

stress for a ductile material.


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Chapter 5-

Assignment (Continuation)

7. Given an engineering stressstrain diagram, determine

a. the modulus of elasticity,

b. the yield strength (0.002 strain offset), and

c. the tensile strength, and

d. Estimate the percent elongation.8. For the tensile deformation of a ductile cylindrical

specimen, describe changes in specimen profile to the

point of fracture.

9. Show theoretically on hoe to compute ductility in terms

of both percent elongation and percent reduction of area

for a material that is loaded in tension to fracture.


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Chapter 5-

Assignment (Continuation)

10. Give brief definitions of and the units formodulus of resilience and toughness (static).

11. For a specimen being loaded in tension,

given the applied load, the instantaneous crosssectional dimensions, and original and

instantaneous lengths, be able to compute true

stress and true strain values.


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Chapter 5

Quiz onChapter 6: Mechanical Properties of

Materials

thisJanuary 5, 2012 (Saturday)

(Parallel with the Chapter 5 Quiz)

5_diffusion in solids

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