Chapter_5 - Rate Process in Solids (1) Chapter 5 Thermal...

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1 5.1 Rate Process Chapter 5 Thermal Diffusion Chapter 3 ME 201: Materials Science, Z. Hao 1 5.2 Atomic diffusion in solids 5.3 Effect of temperature on diffusion 5.4 Industrial applications Rate Process in Solids (1) ± Reactions occur in solid state resulting in more stable atomic arrangement. ± Reacting atoms (reactants) must have sufficient energy to overcome activation energy barrier. ± At a given temperature, not all atoms have activation energy E*. It should be supplied to them. Chapter 3 ME 201: Materials Science, Z. Hao E* E r E P AE* Activation Energy Energy released Due to reaction Reaction Coordinate Reactants Products E r = Energy of reactants E* = Activation Energy Level Δ E* = Activation Energy E p = Energy of Products ± As temperature increases, more and more atoms acquire activation energy level. ± Probability of finding an atom/molecule with energy E* greater than average energy E of all atoms/ molecules is given by Rate Process in Solids (2) Chapter 3 ME 201: Materials Science, Z. Hao KT E E e / ) * ( y Probabilit K = Boltzman’s Constant = 1.38 x 10 -23 J/(atom·K). T = Temperature in Kelvin. E = Average energy of all atoms/molecules in a system ± The fraction of atoms having energies greater than E* in a system (when E* is greater than average energy E) is given by T K E tota Ce N n . * = Rate Process in Solids (3) Chapter 3 ME 201: Materials Science, Z. Hao total n = Number of molecules greater than energy E* N total = Total number of molecules K = Boltzman’s Constant C = Constant T = Temperature in Kelvin. ± The number of vacancies at equilibrium at a particular temperature in a metallic crystal lattice is given by T K E v V Ce N n . = Nb f i 3 ft Rate Process in Solids (4) Chapter 3 ME 201: Materials Science, Z. Hao n v = Number of vacancies per m of metal N = Total number of atom sites per cubic meter of metal E v = Activation Energy to form a vacancy T = Absolute Temperature K = Boltznam’s Constant C = Constant Rate Process in Solids (5) Example: Solution: Chapter 3 ME 201: Materials Science, Z. Hao
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2 Arrhenius Equation (1) ± The rate of chemical reaction is given by Arrhenius equation: Rate of reaction = Ce -Q/RT Q = Activation energy J/mol Chapter 3 ME 201: Materials Science, Z. Hao R = Molar gas constant (8.314J/mol.K) T = Temperature in Kelvin C = Rate constant ( Independent of temperature) ± Rate of reaction Æ number of reacting molecules.
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This note was uploaded on 04/14/2008 for the course ME 201 taught by Professor Hao during the Fall '07 term at Old Dominion.

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Chapter_5 - Rate Process in Solids (1) Chapter 5 Thermal...

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