diffusion report

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DiffusionMaterial Science Presentation

by Group 5

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Topics Covered What is Diffusion?

• Interdiffusion• Self-diffusion

Diffusion Mechanisms Vacancy Diffusion Interstitial Diffusion

Mathematics of Diffusion (Fick’s Laws)

• Steady-State Diffusion• Non Steady-State Diffusion

Factors affecting Diffusion• Diffusing Species• Host Solid• Temperature• Microstructure



What is Diffusion?o It is the motion of atoms, ions, or vacancies

through a material.

o Inhomogeneous materials can become homogeneous by diffusion.



Interdiffusion and Self-diffusion

Interdiffusion (Impurity Diffusion) occurs in response to a concentration gradient.

Concentration Gradient - concentration that exists between a two different materials.



Interdiffusion and Self-diffusion

Self-diffusion is the diffusion of an atom to a new site in a crystal when all atoms are of the same type.



Diffusion Mechanisms

1) Vacancy Diffusion

An atom from its normal lattice

position changes position with an

adjacent vacancy lattice site, so the

atoms and vacancies travel in opposite

directions.




1) Vacancy Diffusion




2) Interstitial Diffusion

Atoms move from one interstitial site to another vacant interstitial site.

Interstitial diffusion is generally faster than vacancy diffusion because bonding of 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.




2) Interstitial Diffusion



Other mechanisms which are quite rare but nonetheless important in semiconductors are:1) Indirect interstitial mechanism for self-interstitials

> The simulation shows the elementary step: A self-interstitial (shown in light blue for easier identification) pushes a lattice atom into the interstitial lattice. The net effect is the migration of an self-interstitial from one interstitial site to an different one.

2) The "kick-out" mechanism for impurity atoms

> Interstitial impurity atoms move rather fast by a direct interstitial mechanism, until they eventually displace a lattice atom. This is shown in the simulation. We now have a self-interstitial (that may or may not be very mobile) and a rather immobile substitutional impurity atom, which may now diffuse with one of the other (slow) mechanisms.



3) Frank-Turnbull mechanisms (or dissociative mechanism).

> This is the pendant to the kick-out mechanism. Except that the diffusing impurity atom does not dislodge a lattice atom, but gets trapped in a vacancy, whereupon it is almost immobile. The total effect may be quite similar to the kick-out mechanism.

4) Various direct diffusion mechanisms

> Shown is a direct exchange of places between two atoms. Variants are exchanges involving more that 2 atoms (a whole "ring" that "rotates").Direct mechanisms are every now and then suggested in the literature to account for some new diffusion phenomena, but so far do not seem to occur in crystals.

> This is a possibility not yet discussed or observed. It is mentioned just to show that there might be more atomic mechanisms than have been discovered so far.

5) “Extended interstitial" mechanism



Mathematics of DiffusionSteady-State Diffusion - Rate of diffusion independent of time. Flux proportional to concentration gradient =

dx

dC

dx

dCDJ

Fick’s First Law of Diffusion

Where: D = diffusion coefficient



Mathematics of DiffusionSteady-State Diffusion

C1

C2

x

C1

C2

x1 x2

12

12 linear ifxx

CC

x

C

dx

dC




Example: Chemical Protective Clothing (CPC)

Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn.

If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the glove?

Data: diffusion coefficient in butyl rubber: D = 110 x10-8 cm2/s

surface concentrations:

C2 = 0.02 g/cm3

C1 = 0.44 g/cm3




Example: Chemical Protective Clothing (CPC)

Solution – Assuming linear conc. Gradient

Dtb 6

2

12

12- xx

CCD

dx

dCDJ

scm

g 10 x 16.1

cm) 04.0(

)g/cm 44.0g/cm 02.0(/s)cm 10 x 110(

25-

3328-

J

C1

C2

skinpaintremover

x1 x2

D = 110 x 10-8 cm2/s

C2 = 0.02 g/cm3

C1 = 0.44 g/cm3

x2 – x1 = 0.04 cm

Data:



Mathematics of DiffusionNon Steady-State Diffusion - Concentration profile and the concentration gradient are changing with time. The solution of this equation is concentration profile asfunction of time, C(x,t)

Fick’s Second Law of Diffusion

Where: D = diffusion coefficientt = temperature

x = positionC = concentration profile



Mathematics of Diffusion

𝐶𝑥−𝐶𝑜𝐶𝑠−𝐶𝑜

=1−erf ( 𝑥2√𝐷𝑡 )

Where:x – is the distance into the solidCx – is the concentration of diffusing species

at distance xCo – is the initial bulk concentration of the

diffusing species in the solid.Cs- is the surface concentration (constant)D- is the Diffusivityt – is timeerf – is the Gaussian Error Function.

Non Steady-State Diffusion



Mathematics of DiffusionNon Steady-State Diffusion

Fick’s second law relates the rate of change of composition with time to the curvature of the concentration profile:

Concentration increases with time in those parts of the system where concentration profile has a positive curvature. And decreases where curvature is negative.




Example:




Solution:



Factors Affecting Diffusion Diffusion of interstitials is typically faster

as compared to the vacancy diffusion mechanism.

Smaller atoms cause less distortion of the lattice during migration and diffuse more readily than big atoms.

Diffusion is faster in open lattices or in open directions.



Factors Affecting Diffusion Temperature - diffusion rate increases very

rapidly with increasing temperature

Diffusion mechanism – diffusion by interstitial mechanism is usually faster than by vacancy 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.



Factors Affecting DiffusionFormula (Arrhenius dependence):

Where:


diffusion report

Engineering

diffusion coefficient

state diffusion rate

fasterthan vacancy diffusion

steadystate diffusion

somenew diffusion phenomena

interstitial lattice

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manymore interstitial