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material Science 7.pptx

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This document discusses diffusion and Fick's laws of diffusion. It defines diffusion as the net flux of particles down a concentration gradient, with flux depending on concentration gradient and temperature. Diffusion processes like carburization can increase surface hardness by introducing carbon atoms. Diffusing atoms require activation energy to move into new sites. The Arrhenius equation relates diffusion rate to temperature and activation energy. The document also defines Fick's first law of diffusion, relating flux to the diffusion coefficient and concentration gradient. It provides examples calculating diffusion rates, activation energies, and concentration gradients.

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APPLICATION OF DIFFUSION ENG. KAREEM. H. MOKHTAR
DIFFUSION Diffusion refers to the net flux of any species The magnitude of this flux depends upon the concentration gradient and temperature.
APPLICATION The carburization process can be used to increase surface hardness. In carburization, a source of carbon, such as a graphite powder or gaseous phase containing carbon, is diffused into steel components
ACTIVATION ENERGY A diffusing atom must squeeze past the surrounding atoms to reach its new site. In order for this to happen, energy must be supplied to allow the atom to move to its new position
ARRHENIUS EQUATION Rate = c e-E/RT Rate: rate of diffusion (m2/s or jump per second) E: activation energy R: gas constant T: temperature ln(rate) = ln(c) E/RT Straight line equation Y= m x + c Ln (rate) 1/T Slope= -E/R
SHEET 4 Q1) Suppose that atoms are found to move from one site to another at a rate of 109 jumps per second at 400 oC and the C0 is equal to 3.8 x 1016, calculate the activation energy (Calory) needed. Answer Rate = c e-E/RT 109 = 3.8 x 1016 x e-E/1.98*673 E= 23257 cal/mol
SHEET 4 Q2) Suppose that atoms are found to move from one site to another at a rate of 5x108 jumps/ second at 500 oC and 8x 1010 jumps/s at 800 oC, calculate the activation energy needed for the process Answer Q= 27,800 cal/mol
SHEET 4 Q3) At 300尊C the diffusion and activation energy for Cu in Si are D(300尊C) = 7.8 x 10-11 m2/s E = 41.5 kJ/mol What is the diffusion at 350尊C? Answer Rate1 = c e-E/RT 7.8 x 10-11 = C e-41500/8.314* 573 Rate2 = c e-E/RT D= C e-41500/8.314* 623 Get D = 15.7 x 10-11 m2/s
DIFFUSION
FICKS FIRST LAW The rate at which atoms, ions, particles or other species diffuse in a material can be measured by the flux J. Here we are mainly concerned with diffusion of ions or atoms. The flux J is defined as the number of atoms passing through a plane of unit area per unit time
FICKS FIRST LAW J: flux D: diffusivity , cm2/s dc/dx : concentration gradient atoms / (cm3. cm) OR atomic % / cm
SHEET 4 Q4) Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn. If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the glove? diffusion coefficient in butyl rubber: D = 110 x10-8 cm2/s surface concentrations: C1 = 0.44 g/cm3 C2 = 0.02 g/cm3
ANSWER
SHEET4 Q5) One step in manufacturing transistors, which function as electronic switches in integrated circuits, involves diffusing impurity atoms into a semiconductor material such as silicon (Si). Suppose a silicon wafer 0.1 cm thick, which originally contains one phosphorus atom for every 10 million Si atom, is treated so that there are 400 phosphorus atoms for every 10 million Si atoms at the surface. calculate the concentration gradient (at % / cm)
ANSWER Initial concentration in atom % Ci= 1 ＄ 107 ＄ x 100 = 0.00001 at %P Cs= 400 ＄ 107 ＄ x 100 = 0.004 at%P ＄ 倹＄ = 0.000010.004 0.1 = - 0.04 at% P /cm
material Science 7.pptx

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material Science 7.pptx

  • 1. APPLICATION OF DIFFUSION ENG. KAREEM. H. MOKHTAR
  • 2. DIFFUSION Diffusion refers to the net flux of any species The magnitude of this flux depends upon the concentration gradient and temperature.
  • 3. APPLICATION The carburization process can be used to increase surface hardness. In carburization, a source of carbon, such as a graphite powder or gaseous phase containing carbon, is diffused into steel components
  • 4. ACTIVATION ENERGY A diffusing atom must squeeze past the surrounding atoms to reach its new site. In order for this to happen, energy must be supplied to allow the atom to move to its new position
  • 5. ARRHENIUS EQUATION Rate = c e-E/RT Rate: rate of diffusion (m2/s or jump per second) E: activation energy R: gas constant T: temperature ln(rate) = ln(c) E/RT Straight line equation Y= m x + c Ln (rate) 1/T Slope= -E/R
  • 6. SHEET 4 Q1) Suppose that atoms are found to move from one site to another at a rate of 109 jumps per second at 400 oC and the C0 is equal to 3.8 x 1016, calculate the activation energy (Calory) needed. Answer Rate = c e-E/RT 109 = 3.8 x 1016 x e-E/1.98*673 E= 23257 cal/mol
  • 7. SHEET 4 Q2) Suppose that atoms are found to move from one site to another at a rate of 5x108 jumps/ second at 500 oC and 8x 1010 jumps/s at 800 oC, calculate the activation energy needed for the process Answer Q= 27,800 cal/mol
  • 8. SHEET 4 Q3) At 300尊C the diffusion and activation energy for Cu in Si are D(300尊C) = 7.8 x 10-11 m2/s E = 41.5 kJ/mol What is the diffusion at 350尊C? Answer Rate1 = c e-E/RT 7.8 x 10-11 = C e-41500/8.314* 573 Rate2 = c e-E/RT D= C e-41500/8.314* 623 Get D = 15.7 x 10-11 m2/s
  • 10. FICKS FIRST LAW The rate at which atoms, ions, particles or other species diffuse in a material can be measured by the flux J. Here we are mainly concerned with diffusion of ions or atoms. The flux J is defined as the number of atoms passing through a plane of unit area per unit time
  • 11. FICKS FIRST LAW J: flux D: diffusivity , cm2/s dc/dx : concentration gradient atoms / (cm3. cm) OR atomic % / cm
  • 12. SHEET 4 Q4) Methylene chloride is a common ingredient of paint removers. Besides being an irritant, it also may be absorbed through skin. When using this paint remover, protective gloves should be worn. If butyl rubber gloves (0.04 cm thick) are used, what is the diffusive flux of methylene chloride through the glove? diffusion coefficient in butyl rubber: D = 110 x10-8 cm2/s surface concentrations: C1 = 0.44 g/cm3 C2 = 0.02 g/cm3
  • 14. SHEET4 Q5) One step in manufacturing transistors, which function as electronic switches in integrated circuits, involves diffusing impurity atoms into a semiconductor material such as silicon (Si). Suppose a silicon wafer 0.1 cm thick, which originally contains one phosphorus atom for every 10 million Si atom, is treated so that there are 400 phosphorus atoms for every 10 million Si atoms at the surface. calculate the concentration gradient (at % / cm)
  • 15. ANSWER Initial concentration in atom % Ci= 1 ＄ 107 ＄ x 100 = 0.00001 at %P Cs= 400 ＄ 107 ＄ x 100 = 0.004 at%P ＄ 倹＄ = 0.000010.004 0.1 = - 0.04 at% P /cm