DIFFUSION IN SOLIDS. IE-114 Materials Science and General Chemistry Lecture-5

Transcription

1 DIFFUSION IN SOLIDS IE-114 Materials Science and General Chemistry Lecture-5

2 Diffusion The mechanism by which matter is transported through matter. It is related to internal atomic movement. Atomic movement; Gases > Liquids > Solids Gases Liquids Atomic-scale motion (diffusion) in liquids and gases is rapid and easy to visualize

3 Diffusion in solids The slower diffusion rate in the solid state than in the liquid state. Heat Treatment of Metals Case hardening of steel (carbon diffusion in steel) Oxidation of metals Thin film electronics (doping of semiconductors) Sintering (fusion of powder particles at solid state) EXAMPLE : CASE HARDENING OF STEEL Methods used: Carburizing, Nitriding Fe + 2CO Fe (c) + CO 2

4 Origin of Diffusion Thermal energy Concentration gradient (effective in diffusion of impurities) In solids, atomic movements are restricted to equilibrium positions due to bondings. If energy is provided to the solids, it can cause the thermal vibrations of atoms about their equilibrium position and at sufficient energy vibration may be strong enough to break the bonding and make the atom move Types of diffusion in Solids Self-diffusion Interdiffusion (Impurity diffusion)

5 1) Self-diffusion Diffusion in pure metals All atoms exchanging positions are of the same type Label some atoms After some time C A D B HEAT

6 2) Impurity-diffusion (Interdiffusion) The process, whereby atoms of one metal diffuse into another metal Upon heating, diffusion of atoms from high concentration to low concentration takes place Initially After some time HEATING 100% 0 Concentration Profiles

7 COPPER NICKEL

8 Diffusion Mechanisms In atomic point of view diffusion is stepwise migration of atoms from lattice site to lattice site For an atom to make such a move; a) there must be an empty adjacent site b) atom that is moving should have enough energy to break bonds with the neighboring atoms and cause some distortion. The energy is vibrational in nature. There are two types of diffusion mechanisms: 1) Vacancy diffusion 2) Interstitial Diffusion

9 Vacancy (substitutional) Diffusion a) Self-diffusion (pure metals) b) Impurity Diffusion Interstitial Diffusion a) Self-diffusion (pure metals) b) Impurity Diffusion

10 1) Vacancy (substitutional) Diffusion A host or substitutional atom exchanges places with a vacancy Activation energy = Act. Ener. (to form a vacancy) + Act. Ener. (to move the atom to the vacancy) (Both vacancies and required activation energy is provided by thermal energy which results in vibrations of atoms and impurities) Activation energy (Q) as melting temp. (Stronger bonds exist in higher-melting-temperature metals) Rate of diffusion depends on; Number of vacancies Activation energy to migrate

11 2) Interstitial Diffusion: Atoms move from an interstitial position to another one closeby. Migrating atoms should be small in size such as N, C, H and O. Interstitial diffusion occurs much more rapidly than diffusion by the vacancy mode, since interstitial atoms are smaller, and thus mobile. jumping of a smaller atom (black) from one interstitial site to another in a BCC structure. e.g. Interstitial diffusion of carbon in iron R carbon =0.071 nm R Fe = nm

12 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 (kbt)

13 Diffusion Modeling 1) Steady-State diffusion: Diffusion is a time dependent process; the quatity of an element that is transported within another is a function of time. The rate of mass transfer is explained by diffusion flux (J): the mass of (or, number of atoms) M diffusing through and perpendicular to a unit crosssectional area per unit of time mass In differential form: time crosssectional area UNIT: kg/m 2 s or atoms/m 2 s

14 Steady state condition exists when the diffusion flux does not change with time Concentrations(pressures) of two species are held constant, P A and P B and P A >P B

15 The steady-state diffusion in one (x) direction : FICK S FIRST LAW D: diffusivity or diffusion coefficient (m 2 /sec or cm 2 /sec). The negative sign indicates that the direction of diffusion is down the concentration gradient. Concentration gradient (dc/dx) is the driving force in diffusion reactions. The steeper the concentration gradient, the greater will be the diffusion or the mass transfer

16 2)Nonsteady state diffusion: The diffusion flux and concentration gradient at a selected point vary with time causing a net accumulation or depletion. For nonsteady state diffusion Fick s first law is not valid. FICK S SECOND LAW

17 Depending on the selected boundary conditions there may be different solutions for Fick s second law. Semi-finite solid in which the surface concentration is held constant. Assume: a) before diffusion, diffusing solute concentration is uniform, Co. b) the value of x is zero at the surface and increases with distance into the solid. c) the time is zero at the instant before the diffusion begins. Surface concentration is held constant Gaussian error function C x : concentration at depth x after time t. C s : concentration at surface C o : initial concentration

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19 Factors affecting diffusion: 1) Diffusing species: Different materials have different diffusion coefficient (D o ), which is also the indication of the diffusion rate. 2) Crystal structure (BCC, FCC,..) 3) Imperfection (grain boundary, dislocation, vacancy, lattice) 4) Temperature: Diffusion is thermally activated process Temperature dependence can be expressed as follows:

20 Diffusion coefficient vs 1/T 1200 C 900 C 600 C 400 C D, m 2 /s Fe in bcc Fe Fe in fcc Fe C in bcc Fe C in fcc Fe Mn in fcc Fe /T(K)

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