Chapter 6


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Chapter 6

  2. 2. Introduction This chapter will discuss the atomic mechanismsby which diffusion occurs, the mathematics ofdiffusion, and the influence of temperature anddiffusing species on the rate of diffusion. Diffusion isdemonstrated with the use of diffusion couple which isformed by joining bars of two faces of specific solids.Interdiffusion or impurity diffusion is a process whereatoms of one metal diffuse into another. The diffusionthat occurs for pure metals is called self-diffusion. Self-diffusion is the transport of atoms from high to lowconcentration regions but the exchanging positions areof the same type.
  3. 3. Interdiffusion and Self-diffusion BEFORE AFTER
  4. 4. Diffusion Mechanisms The conditions needed for diffusion are(1) there must be an empty and adjacent site and(2) the atoms must have sufficient energy to break bonds with itsneighbor atoms and then cause some lattice distortion during thedisplacement. The two models for atomic motion for metals are vacancydiffusion and interstitial diffusion. Vacancy diffusion involves theinterchange of an atom from a normal position to an adjacentvacant site or vacancy while Interstitial diffusion is involvesatoms to migrate from a position to a neighboring one that isempty.
  5. 5. Vaccancy Diffusion Mechanism BEFORE AFTER
  6. 6. Interstitial Diffusion Mechanism BEFORE AFTER
  7. 7. Steady-State diffusion The rate of mass transfer in diffusion isfrequently express as a diffusion flux (J).Diffusion flux is equal to mass over area ofthe solid per unit of time.J=M/AtDiffusion flux has the unit kg/m2*s oratom/m2*s. Steady-state diffusion occurswhen the diffusion flux does not changewith time.
  8. 8. The concentration gradient is often called the drivingforce in diffusion. The minus sign in the equationmeans that diffusion is down the concentrationgradient.
  9. 9. Nonsteady-State Diffusion Most of the diffusion situations are nonsteady-state. The diffusion flux and concentration gradient areat some particular point in a solid and vary with time. Itresults to a net accumulation or depletion of diffusingspecies. In many real situations the concentrationprofile and the concentration gradient are changingwith time. The changes of the concentration profile canbe described in this case by a differential equation.
  10. 10. Factors that influence DiffusionTemperature - diffusion rate increases very rapidly withincreasing temperature.Diffusion mechanism – diffusion by interstitial mechanismis usually faster than by vacancy mechanism.Diffusing and host species - Do, Qd are different for everysolute, solvent pairMicrostructure - diffusion is faster in polycrystallinematerials compared to single crystals because of theaccelerated diffusion along grain boundaries
  11. 11. Example Problem 6.1A plate of iron is exposed to a carburizing (carbon-rich)atmosphere on oneside and a decarburizing (carbon-deficient)atmosphere on the other side at 700C (1300F). If a condition ofsteady state is achieved, calculate the diffusion flux of carbonthrough the plate if the concentrations of carbon at positions of 5and 10 mm (5 x10-3 and 10-2 m) beneath the carburizing surfaceare 1.2 and 0.8 kg/m3, respectively. Assume adiffusion coefficient of 3 x10-11 m2/s at this temperature.
  12. 12. SOLUTIONJ = -D(CA - CB / XA _XB ) =(3 x10-11 m2/s)[(1.2 - 0.8) kg/m3 / (5 x 10-3 – 10-2) m =2.4 x 10-9 kg/m2-s Submitted by: Jason A. Rempillo