31/10/2019 Diffusion General Note. Atomic diffusion is a process whereby the random thermally-activated hopping of Diffusion is a flux of matter in which the atoms or molecules of a certain atoms in a solid results in the net transport of atoms. For example, helium atoms type move differently (rate, amount etc) with respect to the inside a balloon can diffuse through the wall of the balloon and escape, resulting in the balloon slowly deflating. Other air molecules (e.g. oxygen, nitrogen) have lower atoms/molecules of other type. mobilities and thus diffuse more slowly through the balloon wall. There is a Please note the difference from gas or liquid flow, in this case ALL concentration gradient in the balloon wall, because the balloon was initially filled components move in the same way. with helium, and thus there is plenty of helium on the inside, but there is relatively little helium on the outside (helium is not a major component of air). The definition: “Diffusion is the movement of molecules from a high concentration to a low concentration” is wrong because there are cases when diffusion process does just opposite. Factors that Influence Diffusion Flux of matter can be caused not only by the difference in Temperature - diffusion rate increases very rapidly with increasing temperature concentration of the atom that diffuses, but also the difference in Diffusion mechanism - interstitial is usually faster than vacancy concentration of other atoms and or gradient of physical parameters Diffusing and host species - D o , Q d is different for every solute, solvent pair ( temperature, pressure, electric or magnetic field). Microstructure - diffusion faster in polycrystalline vs. single crystal materials because of the rapid diffusion along grain boundaries and dislocation cores. 1 2 1 2 Diffusion Diffusion is relative flow of one material into another Mass flow process by which species change their position relative to their neighbours. Types of diffusion Diffusion of a species occurs from a region of high concentration to low concentration (usually). More accurately, diffusion occurs down the chemical potential (µ) gradient. Diffusion paths: Diffusion - Mass transport by atomic motion Diffusion To comprehend many materials related phenomenon (as in the figure below) one must understand through the Diffusion. gas phase Mechanisms Surface diffusion • Gases & Liquids – random (Brownian) motion The focus of the current chapter is solid state diffusion in crystalline materials. • Solids – self, vacancy, interstitial, or inter In the current context, diffusion should be differentiated with flow (of usually fluids and Bulk diffusion diffusion sometime solids) . Self diffusion: Motion of host lattice atoms. The diffusion Roles of Diffusion coefficient for self diffusion depends on the Grain diffusion mechanism: baoundary diffusion Oxidation Creep Vacancy mechanism: D self = [C vac ] D vac Metals Many mechanisms Interstitial mechanism: D self = [C int ] D int Sintering Aging Inter diffusion, multicomponent diffusion: Precipitates Motion of host and foreign species. The HRTEM image of an interface fluxes and diffusion coefficient are between an aluminum (left) and a correlated germanium grain. The black dots Doping Carburizing correspond to atom columns. Semiconductors Steels In general: D gp >D sd >D gb >>D b for high 3 4 temperatures and short diffusion times Material Joining Diffusion bonding Many more… 3 4 1
31/10/2019 Processing Using Diffusion When a perfume bottle is opened at one end of a room, its smell reaches the other end via • Doping silicon with phosphorus for n -type Case Hardening: the diffusion of the molecules of the perfume. semiconductors: Diffuse carbon atoms into If we consider an experimental setup as below (with Ar and H 2 on different sides of a the host iron atoms at the chamber separated by a movable piston), H 2 will diffuse faster towards the left (as • Process: surface. compared to Ar). As obvious, this will lead to the motion of movable piston in the direction Example of interstitial of the slower moving species. 1. Deposit P rich diffusion is a case hardened layers on surface. gear. H 2 diffusion direction silicon 0.5 mm 2. Heat it. Ar H 2 3. Result: Doped magnified image of a computer chip semiconductor regions. Piston motion Movable piston with an orifice Piston moves in the light regions: Si atoms direction of the slower silicon moving species Result: The presence of C atoms makes iron ( steel ) 5 6 light regions: Al atoms Ar diffusion direction harder. 5 6 Kirkendall effect Diffusion Let us consider two materials A and B welded together with Inert marker and given Mass flow process by which species change their position relative to their neighbours. Diffusion is driven by thermal energy and a ‘ gradient’ (usually in chemical potential). a diffusion anneal (i.e. heated for diffusion to take place). Gradients in other physical quantities can also lead to diffusion (as in the figure below). In Usually the lower melting component diffuses faster (say B). This will lead to the this chapter we will essentially restrict ourselves to concentration gradients. shift in the marker position to the right. Usually, concentration gradients imply chemical potential gradients ; but there are exceptions to this rule. Hence, sometimes diffusion occurs ‘uphill’ in concentration gradients, but downhill in chemical potential gradients. Thermal energy leads to thermal vibrations of atoms, leading to atomic jumps. In the absence of a gradient, atoms will still randomly ‘jump about’, without any net flow of matter. A B Direction of marker motion First we will consider a continuum picture of diffusion Chemical potential and later consider the atomic basis for the same in Electric crystalline solids. The continuum picture is applicable Gradient to heat transfer (i.e., is closely related to mathematical Magnetic equations of heat transfer). 7 8 Inert Marker is basically a thin rod of a high melting material, which is insoluble in A & B Stress 7 8 2
31/10/2019 Diffusion – How atoms move in solids What is diffusion? Diffusion mechanisms Diffusion transport by atomic motion. Vacancy diffusion Interstitial diffusion Impurities Conditions necessary for diffusion An empty adjacent site Enough energy to break bonds and cause lattice distortions during displacement Mathematics of diffusion Steady-state diffusion (Fick’s first law) Nonsteady-State Diffusion (Fick’s second law) Factors that influence diffusion Diffusing species Host solid Temperature Microstructure Inhomogeneous material can become homogeneous by diffusion. 9 10 Temperature should be high enough to overcome energy barrier. 9 10 Diffusion Diffusion Mechanisms Vacancy diffusion Part1. Constitutional effects Atom migration Vacancy migration Diffusion is the phenomenon of spontaneous material transport by atomic motion. Diffusion is classified according to a) conditions: self-diffusion, diffusion from surface, interdiffusion, fast Before After path diffusion etc. To jump from lattice site to lattice site, atoms need energy to break bonds with b) mechanism: interstitial, substitutional; neighbors, and to cause the necessary lattice distortions during jump. Therefore, there is an energy barrier. (E av ~ kT) Energy comes from thermal energy of atomic vibrations Part 2. Atom flow is opposite to vacancy flow direction. Non-constitutional effects. Kirkendall effect, Einstein equation, etc. 11 12 11 12 3
31/10/2019 Self-diffusion: In an elemental solid, atoms also migrate. Diffusion Mechanisms After some time Interstitial diffusion C C Interstitial atom Interstitial atom before diffusion after diffusion A D A D B B Vacancy Diffusion: • atoms exchange with vacancies Probability of an atom jumping over the • applies to substitutional impurities atoms energy barrier: • rate depends on: 𝑄 = 𝑓𝑦𝑞 − 𝑅 -- number of vacancies 𝑙𝑈 -- activation energy to exchange. Generally faster than vacancy diffusion because bonding of interstitials to surrounding atoms is normally weaker and there are more interstitial sites than vacancy sites to jump to. Smaller energy barrier Only small impurity atoms (e.g. C, H, O) fit into interstitial sites. The rate of interstitial diffusion is controlled only by the easiness with which a diffusing atom can move into an interstice. 13 14 increasing elapsed time 13 14 Mechanisms of interdiffusion: Interstitial diffusion – smaller atoms can diffuse between atoms . There is an energy barrier which must be overcome when an atom changes site. More rapid than vacancy diffusion Interdiffusion: : In an alloy, atoms tend to migrate from regions of high conc. to regions of low conc. Initially After some time 15 16 15 16 4
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