Diffusion in Solids PDF

CHAPTER 7 DIFFUSION IN SOLIDS  Diffusion Diffusion can be defined as the mass flow process in which atoms change their positions relative to neighbors in a given phase under the influence of thermal and a gradient.  Diffusion is the material transport by atomic migrat...

CHAPTER 7 DIFFUSION IN SOLIDS  Diffusion Diffusion can be defined as the mass flow process in which atoms change their positions relative to neighbors in a given phase under the influence of thermal and a gradient.  Diffusion is the material transport by atomic migration.  Atoms move from an area of higher concentration to one of lower concentration.  This is easy to imagine for gasses and liquids.  It is harder to imagine in solids, but diffusion does occur in solids, just very slowly.  For solids, diffusion requires the presence of point defects.  Diffusion Mechanisms in solids There are only two mechanisms by which diffusion may occur in solids 1. Vacancy Migration Atoms move from a normal lattice position to a vacancy in the crystal lattice 2. Random Walk This involves an atom moving from one interstitial position to another in the crystal lattice  Not a common mechanism for self-diffusion  Usually faster than vacancy migration because atoms are smaller.  Basic concepts Diffusion is a process which is NOT due to the action of a force, but a result of the random movements of atoms. 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 is defined as net number of atoms crossing a unit area perpendicular to a given direction per unit time. Solvent – the majority atom type (or host atoms) Solute – the element with lower concentration Interstitial – solute atoms are located in gaps between host atoms.  Factors Affecting Diffusion Diffusion is a complicated thing to quantify and describe because it is a function of many variables:  temperature  time  position in the solid  diffusion mechanisms (vacancy, interstitially, interdiffusion, self-diffusion)  crystal structure of the solvent  path of diffusion (surface, grain boundary, volume, dislocation)  concentration of the solute (usually negligible)  Fick's 1st Law  Fick's first law relates the diffusive flux to the concentration field, by postulating that the flux goes from regions of high concentration to regions of low concentration, with a magnitude that is proportional to the concentration gradient.  Stuff moves from where you have lots to where you have little.  Diffusion coefficient: A factor of proportionality representing the amount of substance diffusing across a unit area through a unit concentration gradient in unit time.  Modeling Diffusion: FLUX (J) Flux: the rate of transfer of fluid, particles, or energy across a given surface Directional Quantity x-direction Unit area A through Flux can be measured for: which atoms move --vacancies --host (A) atoms --impurity (B) atoms  Fick’s 1st Law is for steady state processes Steady state means that the diffusion flux (Jx) does not change with time. flux in x-dir. Diffusion coefficient [m2/s] [kg/m2-s] dC J x =- D concentration dx gradient [kg/m4] The negative sign in this relationship indicates that particle flow occurs in a “down” gradient direction, i.e. from regions of higher to regions of lower concentration. The flux J can be given in units of atoms/cm2s, moles/cm2s, or equivalents. Correspondingly, the diffusivity (D) will assume the dimensions cm2/s, as can be seen from a dimensional analysis.  Concentration Profiles & Flux Concentration Profile, C(x): [kg/m3] Cu flux Ni flux Concentration Concentration of Cu [kg/m3] of Ni [kg/m3] Position, x Fick's First Law: The steeper the concentration profile, the greater the flux!  STEADY STATE DIFFUSION Steady State: the concentration profile doesn't change with time. Steady State: Jx(left) Jx(right) J x(left) = J x(right) x Concentration, C, in the box doesn’t change w/time. dC Apply Fick's First Law: J x = −D dx  dC   dC If Jx)left = Jx)right , then   =   dx  left  dx  right Result: the slope, dC/dx, must be constant (i.e., slope doesn't vary with position)!  PROCESSING USING DIFFUSION 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. PBL-1:STEADY STATE DIFFUSION A plate of iron is exposed to a carburizing (carbon-rich) atmosphere on one side and a decarburizing (carbon-deficient) atmosphere on the other side at 700°C (973 K). If a condition of steady state is achieved, calculate the diffusion flux of carbon through the plate if the concentrations of carbon at positions of 5mm and 10mm (5×10-3 m and 10×10-3 m) beneath the carburizing surface are 1.2 and 0.8 kg/m3, respectively. Assume a diffusion coefficient of 3×10-11 m2 /s at this temperature. dC J x = −D dx  SUMMARY Diffusion FASTER for... Diffusion SLOWER for... open crystal structures close-packed structures lower melting T materials higher melting T materials materials w/secondary bonding materials w/covalent bonding smaller diffusing atoms larger diffusing atoms Cations anions lower density materials higher density materials