The change in the vacancy concentration during the quench of noble metals such as gold, with particular reference to the sink density and the cooling rate, has been computed semi-analytically by taking into account the annihilation of divacancies to sinks, which has not been treated before. For the convenience of integrating the nonlinear differential equation for the reaction kinetics, the cooling curve is divided into a number of steps, each of which consists of the instantaneous temperature-drop
ΔT and the subsequent isothermal aging for a short time
ts=
ΔT⁄β, where β is the cooling rate. In this calculation, point sinks uniformly dispersed are assumed, which could be converted into line sinks such as dislocations. Main results obtained are as follows:
(1) The vacancy loss is dominant in the early stage of quenching above 500°C. The loss is mostly attributed to the annihilation of mono-vacancies to sinks but not to that of divacancies, since the divacancy concentration itself is very small in the high-temperature range. Thus, the total vacancy concentration retained in a specimen can be reasonably expressed by the equation
C=
C0exp(−
ACs⁄β), where
A is a constant,
C0 the total vacancy concentration at the quench temperature, and
Cs the sink concentration. The above relationship is valid for the effective density of line sinks of the order of 10
7 cm/cm
3 or less. (2) Below 350°C, for example in gold, the vacancy loss to sinks during the quench becomes negligibly small (<10
−9), thereby the total vacancy concentration being almost conserved. Even below this temperature, the concentration of divacancies continues to increase in expense of monovacancies during the quench down to the critical temperature
T*, below which the rate of reaction
V1+
V1\
ightleftharpoons
V2 extremely slows down. (3) The divacancy abundance in the total vacancy concentration, 2
C2⁄
C, is affected by the sink density, the quench temperature and the cooling rate.
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