Question

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 µm into the aluminum at the end of this heat treatment?

The density of magnesium is 1.74 gm/cm³, respectively. At 500°C the Arrhenius parameters for the diffusion of Mg into Al are:

D_o= l.2xl0^-4 (m²/s)

Q = 131 kJ/mol

Answer 1

1. Cs - . Crit - Co KX-> If the material A is difturing into B as shown above then Cs-Co whene, (s = surface concentration to diffusing species Co = concentration of difbazing species inside the target material Cxst - concentration to difturing species at a depth - from surface after time ť D = Diffusion coefficient at the given temperature 'ert' denotes (erron function' (page-

131000 J'mon! Given, Cs= 1.74 glee Co z oglec (: High purity Al contains no Mg) x = 500 um = 500X106 m t = 24 hours = 24X60x60 sec = 86400 see Do = 1.2x104 ms T=500°C = 773K Q = 131 kJ/mol Now, D = Do exp (RT) = 1.2 x16C expl-5.314 J.mohl X x 773K) = 1.685x1613 mays . Gut- o w er 500x106 ) 174-0 a Gorice =-ert (2,078) → Get = 1.74(1-0.9966) [:ent (2,0718) = 0,9966) = 5.916 x103 : The concentration will be 5.916x16° gm/em3. (page-2 1.74