Question

A diffusion couple composed of two silver– gold alloys is formed; these alloys have compositions of 98 wt% Ag–2 wt% Au and 95 wt% Ag– 5 wt% Au. Determine the time this diffusion couple must be heated at 750°C (1023 K) in order for the composition to be 2.5 wt% Au at the 50 μm position into the 2 wt% Au side of the diffusion couple. Preexponential and activation energy values for Au diffusion in Ag are 8.5 × 10−5 m2/s and 202,100 J/mol, respectively.

Consider a diffusion couple composed of two semi-infinite solids of the same metal, and that each side of the diffusion couple has a different concentration of the same elemental impurity; assume each impurity level is constant throughout its side of the diffusion couple. For this situation, the solution to Fick's second law (assuming that the diffusion coefficient for the impurity is independent of concentration), is as follows: / C-C2 2 The schematic diffusion profile in the figure shows these concentration parameters as well as concentration profiles at times t=0 and t > 0. Please note that at t = 0, the x = 0 position is taken as the initial diffusion couple interface, whereas C1 is the impurity concentration for x < 0, and C2 is the impurity content for x > 0. Leri C= C2 + ili * 2+ t> C1-C2 Concentration C--- < x<0 x>0 → Position Schematic concentration profiles in the vicinity of the interface (located at x = 0) between two semi-infinite metal alloys before (i.e., 1 = 0) and after a heat treatment (i.e., 1 > 0). The base metal for each alloy is the same: concentrations of some elemental impurity are different-C and C denote these concentration values at t = 0. A diffusion couple composed of two silver-gold alloys is formed; these alloys have compositions of 98 wt% Ag-2 wt% Au and 95 wt% Ag-5 wt% Au. Determine the time this diffusion couple must be heated at 750°C (1023 K) in order for the composition to be 2.5 wt% Au at the 50 um position into the 2 wt% Au side of the diffusion couple. Preexponential and activation energy values for Au diffusion in Ag are 8.5 x 10-5m2/s and 202,100 J/mol, respectively. hours

Answer 1

solution. The platinum gold diffusion couple which c, = 5 wt%. Au and c = 2 wt%. Au. We are asked t o determine the diffusion time at 75o c that will que a composition of 2.5 wt% Al at the so um position. G = 2.5

We will use the equation quien in the question (x+(9tce) -695-63) enf () substituting the values of a , la and C we get 2.5 = Derf/sox10 om e 7 (zoots Now we have to calculate diffusion coefficient at 750 C (1023k) gwen Do = 8.5 x 10 mils and 8 200, 6005/ u know D = Do exp(- 8d) .: D=18.5x16%m apl 202, 100 Ilmo!! L 15:317011) (10237)] D = 4.03 x 1015 m²ls ...-5 substitution of D in t we get 2.5=1542) -48.3.) est souvent LV4:03XD.

-.0.6667 = exf/3.93.8 v5) - ut We will use the linear as follows interpolation Z 0.650 elf (2) 0.6420 0.6667 0.6778 @ZS Y-0.650 = 0.26667-0c6420 .ö. Foo-0.650 0.6778- 0.6420 & y = 0.6844= 393.85 solving for t gues t = 3.31 103 t-92 hours