Introduction to Materials Science and Engineering Chapter 5: Diffusion Textbook: chapter 7

Content Introduction Diffusion Mechanisms Steady-state Diffusion Nonsteady-state Diffusion Factors that Influence Diffusion Diffusion in Semiconducting Materials Diffusion in Ionic and Polymer Materials

ISSUES TO ADDRESS... some simple cases? and temperature? • How does diffusion occur? • Why is it an important part of processing? • How can the rate of diffusion be predicted for some simple cases? • How does diffusion depend on structure and temperature?

Introduction atoms and molecules can be quite mobile at Tset in both liquids and solids: Drop of ink in a beaker of water spread water evenly colored. Intermixing at molecular level diffusion continuous motion of H2O molecules in water at R.T. exemplifies self-diffusion. atomic-scale motion (diffusion) in liquids is relatively rapid and easy to visualize. more difficult to visualize diffusion in rigid solids, but it does occur.

Introduction Difference between liquid-state and solid-state diffusion is the slower diffusion rate in the solid. Tight atomic structure of atoms has an impact on the diffusion of atoms or ions within the solid. The energy requirements to squeeze most atoms or ions through a perfect crystal structure are so high that diffusion is nearly impossible.

Diffusion-Phenomenon (1) Inter-diffusion in diffusion couple atoms migrate from high- to low- concentration regions Initially after some time

Diffusion-Phenomenon (2) Self diffusion in pure materials all atoms exchanging positions are of the same type label some atoms after some time C C A D A D B B * Labeling by isotope (tracer diffusion)

Content Introduction Diffusion Mechanisms Steady-state Diffusion Nonsteady-state Diffusion Factors that Influence Diffusion Diffusion in Semiconducting Materials Diffusion in Ionic and Polymer Materials

Diffusion Mechanism Vacancy diffusion - atom interchange from a normal lattice position to an adjacent vacant lattice site. - the extent of vacancy diffusion is controlled by the concentration of these defects. - the direction of vacancy motion is opposite to direction of diffusing atoms. - both self-diffusion and interdiffusion occur by this mechanism.

Diffusion Mechanism Interstitial diffusion typical interstitial atoms: hydrogen, carbon. - in most metals, interstitial diffusion occurs much more rapidly than vacancy diffusion.

Activation Energy for Diffusion Conditions for atom migration: - empty adjacent site. - atom must have enough energy to break bonds and cause lattice distortion during displacement. diffusive motion influenced by atom vibrational energies  f(T)

Content Introduction Diffusion Mechanisms Steady-state Diffusion Nonsteady-state Diffusion Factors that Influence Diffusion Diffusion in Semiconducting Materials Diffusion in Ionic and Polymer Materials

Steady-state Diffusion Flux:

Steady-state Diffusion Fick's First Law: dC = - J D x dx the steeper the concentration profile, the greater the flux!

Steady-state Diffusion Steady state: the concentration profile doesn't change with time. Concentration, C, in the box doesn’t change w/time. J x (right) (left) - apply Fick's First Law: - if Jx)left = Jx)right , then Result: the slope, dC/dx, must be constant (i.e., slope doesn't vary with position)!

Steady-state Diffusion Example - steel plate at 700oCwith geometry shown: - Q: how much carbon transfers from the rich to the deficient side?

Content Introduction Diffusion Mechanisms Steady-state Diffusion Nonsteady-state Diffusion Factors that Influence Diffusion Diffusion in Semiconducting Materials Diffusion in Ionic and Polymer Materials

Nonsteady-state Diffusion steady-state diffusion not commonly encountered in engineering materials. in most cases the concentration of solute atoms at any point in the material changes with time  non-steady state diffusion. t2 t1 t0

Nonsteady-state Diffusion Concentration profile,C(x), changes with time. to conserve matter: Fick's First Law: Governing Equation: Fick’d Second Law

Nonsteady-state Diffusion Example: copper diffuses into a bar of aluminum. semi-infinite solid General solution: "error function"

Nonsteady-state Diffusion

Nonsteady-state Diffusion Copper diffuses into a bar of aluminum. 10 hours at 600oC gives desired C(x). How many hours would it take to get the same C(x) if we processed at 500oC? key point 1: C(x,t500oC) = C(x,t600oC). key point 2: both cases have the same Co and Cs. Result: Dt should be held constant. (Dt) 500oC =(Dt) 600oC Answer: Note: values of D are provided here.

Content Introduction Diffusion Mechanisms Steady-state Diffusion Nonsteady-state Diffusion Factors that Influence Diffusion Diffusion in Semiconducting Materials Diffusion in Ionic and Polymer Materials

Factors That Influence Diffusion Diffusing Species - Magnitude of diffusion coefficient : indicative of the rate at which atoms diffuse : depends on diffusing species and host materials - example : Diffusing species in a-Fe Fe (self diffusion) << C (interdiffusin) 3.0x10-21 m2/s 2.4x10-12 m2/s at 500oC vacancy interstitial mechanism : Host material (crystal structure) a-Fe (BCC) > g-Fe (FCC) 1.8x10-15 m2/s 1.1x10-17 m2/s at 900oC ( lower packing factor- open structure low coordination number- fewer bonds broken)

Factors That Influence Diffusion Diffusing Species

Factors That Influence Diffusion Temperature - diffusion- thermally activated process

Factors That Influence Diffusion Temperature lnDo ln D -Qd/R

Factors That Influence Diffusion Determination of activation energy

Factors That Influence Diffusion 참고자료 Factors That Influence Diffusion Diffusion paths - short circuit diffusion path- dislocation, grain boundary, external surface (open structure) - diffusing area should be considered for the comparison of relative contribution of each path

Factors That Influence Diffusion 참고자료 Factors That Influence Diffusion Miscellaneous - melting temperature - concentration dependence The activation energy for self-diffusion increases as the melting point of the metal increases The dependence of diffusion Coefficient of Au on concentration

Factors That Influence Diffusion Summary 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

Content Introduction Diffusion Mechanisms Steady-state Diffusion Nonsteady-state Diffusion Factors that Influence Diffusion Diffusion in Semiconducting Materials Diffusion in Ionic and Polymer Materials

Diffusion in Semiconducting Materials 1. Electrical properties of semiconducting materials can be tuned by incorporating substitutional impurities into the semiconductor – which we call doping. N-type doping with P and As P-type doping with B For instance,

Diffusion in Semiconducting Materials How you incorporate doping elements into Si? Using two-step process: Pre-deposition (Furnace Diffusion or Ion Implantation) – surface concentration fixed Drive-in Diffusion – total amount of impurity is fixed

Content Introduction Diffusion Mechanisms Steady-state Diffusion Nonsteady-state Diffusion Factors that Influence Diffusion Diffusion in Semiconducting Materials Diffusion in Ionic and Polymer Materials

Diffusion in Ionic and Polymeric Materials Ionic Materials: Diffusion mechanism is much more complicated than for metals – should consider the charge nature: Ion vacancies occur in pairs They form in non-stoichiometric compounds They are created by substitutional impurity ions having different charge states Ions can move with electric field applied to materials – field driven transport 2. Polymer Materials: Steady-state diffusion through a polymer membrane is, where, PM=DS (D: diffusivity, S: solubility) where, S=C/P