Question

Problem 3: A large block of high purity aluminum is placed in contact with magnesium. The materials are heated to 500°C and held at that temperature for 24 hours. What is the concentration of magnesium at a depth of 500 um into the aluminum at the end of this heat treatment? The density of magnesium is 1.74 gm/cm, respectively. At 500°C the Arrhenius parameters for the diffusion of Mg into Al are: D.= 1.2x10° (mº/s) Q = 131 kJ/mol

Answer 1

The concentration of Mg at a depth of 500 micro meter into the aluminium is 0.00696 gm/cm³ .

The detail calculation is shown below.

The diffusion coefficient of my into AL is expressed as Da Do exp(-9%) Do = 1. 2x109 mis. a = 131 kJ/mole = 131x10 3 5/mole. R = 8.31 J/mol/k. T = 500°c = (500+ 273) = 7736 Do Do exp(-9%+) = 1.2x10-1 mys empl- 1310103 8.31x773 - 1.67 X1013 mms The concentration of ing at can be deteromined According to this Louw. depth x Rick's into Al second law. - eroff DE) where Depth, x = 500 um 500 410 m. se concentration of my at the surface . : 14 2 cro 3 D = 1.67 103 m/s. it = time a 29 lip = (24m 360o).

This enf (2 t) - ex- NOW, 500155 2 DE 211.67X1073 x 240 3600 enf ( t) = exf (2.08). - 0.996

es lo = 0.996 end 0.004 - vero = 0.004 ex = 6.96910-3 - 0.00696 the concentration of mg at a depth of 500 um into al at the end of heal- treatment is a. 00696 gen/em3