Diffusion in Solids PDF

Diffusion in Solids (This information is taken from Callister and Raghavan’s textbook. As well as some information I got from the internet to help you understand) 1  D...

Diffusion in Solids (This information is taken from Callister and Raghavan’s textbook. As well as some information I got from the internet to help you understand) 1  Diffusion Diffusion is defined as a process of mass transfer of individual molecules of a substance , brought about by random molecular motion and associated with a driving force such as a concentration gradient. Ex: Something similar to movement of particles in sprayed perfume… dissolution of ink in water and smoke in air. Diffusion always occurs from high to low concentration. 2  Why study Diffusion Diffusion: The phenomenon of material transport by atomic motion. Heat-treated to improve their properties. Heat-treatment almost always involve atomic diffusion; desired results depends on diffusion rate. Heat-treatment temperature and time can be predicted by the mathematics of diffusion. Steel Gear Case hardened to improve hardness and resistance to fatigue diffusing excess carbon or nitrogen into outer surface layer. Result: The presence of C atoms makes the steel surface harder….. 3 Phenomenon of diffusion: Explained using diffusion couple, formed by joining bars of two different materials having intimate contact Copper and Nickel diffusion couple. Heated for an extended period at an elevated temperature ( but below melting temperature of both ) and cooled to room temperature. Inter diffusion / Impure diffusion: In an alloy, atoms tend to migrate from regions of large concentrations. Cu Tm = 1,085 °C Ni Tm = 1,455 °C Observation : Cu atoms have diffused into the Ni, and that Ni has diffused into Cu Inter diffusion Note: Diffusion also occurs for pure metals, but all atoms exchanging positions are of the same type; this is 4 termed self-diffusion.  Kirkendall effect If the diffusion rates of two metals A and B into each other are different, the boundary between them shifts and moves towards the faster diffusing metal. This is known as Kirkendall effect. Note: Materials A and B welded together with inert marker and given a diffusion anneal Usually the lower melting component diffuses Inert marker: which is a thin rod of a high melting faster (say B) material which is basically insoluble in A & B 5  Kirkendall effect: Example Zn (Tm = 419 °C) diffuses faster into Cu (Tm = 1085 °C) than Cu in Zn. A diffusion couple of Cu and Zn will lead to formation of a growing layer of Cu-Zn alloy (Brass). Same will happen in a Cu-Ni couple as Cu diffuses faster in Ni than Ni in Cu. Since this takes place by vacancy mechanism, pores will form in cu. 6  Diffusion Mechanisms From an atomic perspective, diffusion is just the stepwise migration of atoms from lattice site to lattice site. For an atom to make such a move, two conditions must be met: 1. There must be an empty adjacent site 2. The atom must have sufficient energy to break bonds with its neighbor atoms and then cause some lattice distortion during the displacement/diffusion @ specific temperature. This energy is vibrational in nature. Two dominate for metallic diffusion mechanisms: Vacancy diffusion Interstitial Diffusion 7  Interchange of an atom from a normal lattice position to an adjacent vacant lattice site ==== Vacancy diffusion Necessitates the presence of vacancies, and the extent to which vacancy diffusion can occur is a function of the number of these defects that are present at elevated temperatures. Because diffusing atoms and vacancies exchange positions, the diffusion of atoms in one direction Solute atom corresponds to the motion of vacancies in the opposite direction. Solvent atom Both self-diffusion and inter-diffusion occur by this mechanism; for the latter, the impurity atoms must substitute for host atoms. Size: Solvent atom > Solute atom Ex: Steel is an alloy of Fe (Solvent) and C (Solute) Here, atoms that migrate from an interstitial position to a neighboring one that is empty. This mechanism is found for inter-diffusion of impurities such as hydrogen, carbon, nitrogen, and oxygen, which have atoms that are small enough to fit into the interstitial positions === interstitial diffusion In most metal alloys, interstitial diffusion occurs much more rapidly than diffusion by the vacancy mode, because the interstitial atoms are smaller and thus more mobile. Note: In most metal alloys, there are more empty interstitial positions than vacancies; hence, the probability of interstitial atomic 8 movement is greater than for vacancy diffusion.  Fick’s 1st law: Steady state diffusion Diffusion is a time-dependent process: It means that the quantity of an element that is transported within another is a function of time. We need to understand how fast diffusion occurs, or the rate of mass transfer, using the diffusion flux concept. Diffusional processes can be either steady-state or non-steady-state. These two types of diffusion processes are distinguished by use of a parameter called Flux. Flux: Net number of atoms crossing a unit area perpendicular to a given direction per unit time. In mathematical form, 9  Steady state diffusion  Concentration profile not changing with time.  In steady state diffusion, there is neither accumulation nor depletion of the diffusing species anywhere in the medium at any time Flux is constant throughout the line; linear nature 10  Steady-state diffusion is described by Fick’s first law which states that flux, J, is proportional to the concentration gradient. The constant of proportionality is called diffusion coefficient (diffusivity), D (cm2/sec). Diffusivity is characteristic of the system and depends on the nature of the diffusing species, the matrix in which it is diffusing, and the temperature at which diffusion occurs. Thus under steady-state flow, the flux is independent of time and remains the same at any cross-sectional plane along the diffusion direction. For the one- dimensional case, Fick’s dimensional first law is given by: (-) (+) The negative sign in this expression indicates that the direction of diffusion is down the concentration gradient, from a high to a 11 low concentration.  Fick’s 2nd law: Non-Steady state diffusion  Most practical diffusion situations are non-steady-state ones. That is, the diffusion flux and the concentration gradient at some particular point in a solid vary with time, with a net accumulation or depletion of the diffusing species resulting. 12 13 14 15 16 17 18 Read the Callister and Raghavan’s textbooks for 19 further info…………………………