Diffusion in Ordered and Disordered Copper-Zinc

The diffusivities of ${\mathrm{Cu}}^{64}$, ${\mathrm{Zn}}^{65}$, and ${\mathrm{Sb}}^{124}$ in single crystals of 47-48 atomic percent zinc copper-zinc (beta brass) have been measured over the temperature range 265-817°C, by using sectioning techniques. The diffusion coefficients show a striking dependence on the degree of long-range order at temperatures below the critical temperature (468°C). A slight dependence of the diffusion coefficient on short-range order is noted above the critical temperature. The diffusion coefficients obey an Arrhenius equation only in the fully disordered phase, with temperature dependences given by $D_{\mathrm{Cu}}=0.011\mathrm{}\exp (-\frac{22000}{\mathrm{RT}})$ ${\mathrm{cm}}^2$/sec, $D_{\mathrm{Zn}}=0.0035\mathrm{}\exp (-\frac{18800}{\mathrm{RT}})$ ${\mathrm{cm}}^2$/sec; $D_{\mathrm{Sb}}=0.08\mathrm{}\exp (-\frac{23500}{\mathrm{RT}})$ ${\mathrm{cm}}^2$/sec. The variation of the diffusion coefficients with temperature in the ordered phase is considered in terms of a simple elastic model. Excellent agreement is obtained by using the measured elastic constants and assuming that the energy for motion of the imperfection is simply related to the smallest (110) shear modulus. In the disordered phase Sb diffuses faster than Zn or Cu, while in the ordered phase Sb diffuses at the same rate as Zn, which is faster than Cu. This result is shown to be inconsistent with an interchange, interstitial, or nearest-neighbor vacancy mechanism for diffusion. The result is consistent with an interstitialy mechanism.