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.

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Physics

Rigoberto Christensen

16 November, 06:41

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.

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Griffin Larson · Answer 1

for this problem, 2.5 = (5+2/2) - (5-2/2) erf (50*10-6m/2Dt)

It now becomes necessary to compute the diffusion coefficient at 750°C (1023 K) given that D0 = 8.5 * 10-5m2/s and Qd = 202,100 J/mol.

we have D = D0exp (-Qd/RT)

= (8.5*105m2/s) exp (-202,100/8.31*1023)

= 4.03 * 10-15m2/s