diffusion in solids’’ - 5- diffusion - mass transport by atomic motion mechanisms

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  • DIFFUSION IN SOLIDS

    MSE-225 Introduction to Materials Science Lecture-5

  • Diffusion Diffusion - Mass transport by atomic motion

    Mechanisms Gases & Liquids Brownian motion Solids vacancy diffusion or interstitial

    diffusion.

  • Interdiffusion (impurity diffusion): In an alloy, atoms tend to migrate from regions of high concentration to regions of low concentration.

    Initially

    Interdiffusion

    After some time

  • Self-diffusion: In an elemental solid, atoms also migrate.

    Label some atoms After some time

    A

    B

    C

    D

    Self-diffusion

  • Diffusion Mechanisms Atoms in solid materials are in constant motion, rapidly

    changing positions. For an atom to move, 2 conditions must be met:

    1. There must be an empty adjacent site, and 2. The atom must have sufficient (vibrational) energy to

    break bonds with its neighboring atoms and then cause lattice distortion during the displacement. At a specific temperature, only a small fraction of the atoms is capable of motion by diffusion. This fraction increases with rising temperature.

    There are 2 dominant models for metallic diffusion: 1. Vacancy Diffusion 2. Interstitial Diffusion

  • Vacancy Diffusion Vacancy Diffusion:

    atoms exchange with vacancies

    both self diffusion and interdiffusion occur by this mechanism rate depends on: -- number of vacancies -- activation energy to exchange.

    increasing elapsed time

  • Atom needs enough thermal energy to break bonds and squeeze through its neighbors. Energy needed energy barrier Called the activation energy Q or Qd

    Diffusion Thermally Activated Process

    Atom

    Vacancy

    Qd

    Distance

    Ener

    gy

  • Qsurface < Qgrain boundary < Qlattice

    Experimentally determined activation energies for diffusion

    Lower activation energy automatically implies higher diffusivity

    Diffusion Paths with less Resistance

  • Simulation of interdiffusion across an interface:

    Rate of vacancy diffusion depends on: --vacancy concentration --frequency of jumping.

    (Courtesy P.M. Anderson)

    DIFFUSION SIMULATION

  • Interstitial Diffusion

    Interstitial diffusion smaller atoms (H, C, O, N) can diffuse between atoms.

    More rapid than vacancy diffusion due to more mobile small atoms and more empty interstitial sites.

  • (Courtesy P.M. Anderson)

    Applies to interstitial impurities. More rapid than vacancy diffusion. Simulation: --shows the jumping of a smaller atom (gray) from one interstitial site to another in a BCC structure. The interstitial sites considered here are at midpoints along the unit cell edges.

    INTERSTITIAL SIMULATION

  • Case Hardening: --Diffuse carbon atoms into the host iron atoms at the surface. --Example of interstitial diffusion is a case hardened gear.

    Result: The "Case" is --hard to deform: C atoms "lock" planes from shearing. --hard to crack: C atoms put the surface in compression.

    Fig. 5.0, Callister 6e. (Fig. 5.0 is courtesy of Surface Division, Midland-Ross.)

    PROCESSING USING DIFFUSION

  • Diffusion How do we quantify the rate of diffusion?

    J Flux moles (or mass) diffusingsurface area( ) time( )

    =molm2s

    or kgm2s

    Measured empirically Make thin film (membrane) of known surface area Impose concentration gradient Measure how fast atoms or molecules diffuse through the

    membrane

  • Rate of diffusion is independent of time; the diffusion flux does not change with time.

    The concentration profile shows the concentration (C) vs the position within the solid (x); the slope at a particular point is the concentration gradient.

    Steady-state diffusion across a thin plate

  • Steady-State Diffusion

    dxdC

    DJ =

    Ficks first law of diffusion C1

    C2

    x

    C1

    C2

    x1 x2 D diffusion coefficient

    12

    12 linear ifxxCC

    xC

    dxdC

    =

  • Cross-sectional area dndt= DA dC

    dxNo. of atoms

    crossing area A per unit time Concentration gradient

    Matter transport is down the concentration gradient

    Diffusion coefficient/ diffusivity

    A Flow direction

    J = D dCdx

  • Diffusion and Temperature

    Diffusion coefficient increases with increasing T.

    D =

    Do exp

    -

    Qd R T

    = pre-exponential [m2/s] = diffusion coefficient [m2/s]

    = activation energy [J/mol or eV/atom] = gas constant [8.314 J/mol-K] = absolute temperature [K]

    D Do Qd R T

  • The diffusing species, host material and temperature influence the diffusion coefficient.

    For example, there is a significant difference in magnitude between self-diffusion and carbon interdiffusion in iron at 500 C.

    Factors that influence diffusion

  • Nonsteady State Diffusion The concentration of diffusing species is a

    function of both time and position C = C(x,t). In this case, Ficks Second Law is used.

    2

    2

    xC

    DtC

    =

    Ficks Second Law

  • Non-steady State Diffusion Copper diffuses into a bar of aluminum.

    pre-existing conc., Co of copper atoms Surface conc., C of Cu atoms bar s

    General solution:

    "error function

    Co

    Cs

    position, x

    C(x,t)

    tot1

    t2t3 Adapted from Fig. 5.5,

    Callister 6e.

  • Factors that Influence Diffusion

    Temperature - diffusion rate increases very rapidly with increasing temperature

    Diffusion mechanism - interstitial is usually faster than vacancy

    Diffusing and host species - Do, Qd is different for every solute, solvent pair

    Microstructure - diffusion faster in polycrystalline vs. single crystal materials because of the rapid diffusion along grain boundaries and dislocation cores.

  • Diffusion FASTER for... open crystal structures lower melting T materials materials w/secondary bonding smaller diffusing atoms cations lower density materials

    Diffusion SLOWER for... close-packed structures higher melting T materials materials w/covalent bonding larger diffusing atoms anions higher density materials

    SUMMARY: STRUCTURE & DIFFUSION

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