Lifetime of the top terrace

To test the validity of Eqs. (25) and (31), we have performed simulations of groove relaxation under evaporation-condensation dynamics and numerical integration of (31). Below we describe briefly the model simulated and present data for the averaged surface profile and the lifetime of the top terrace during relaxation. Details of this study will be reported elsewhere. 

Figure 8 Amplitude of the groove profile against t for Z, = 90a. The lifetime of the top terrace t can be determined from the local slope of the curve through interpolation.

Figure 8 shows the amplitude A (half the distance between top and bottom terrace, in units of layer spacing) of the surface profile as a function of t for a groove of wavelength L = 90a. The decay is slower than a simple exponential as in Mullins theory. From the function A t) one can estimate the lifetime of the top terrace t(t) using the formula,... 

Figure 9 Lifetime of the top terrace versus terrace width for grooves of different width and initial amplitude. The dashed line indicates a power law with an exponent 3. The solid line is a fit to Eq. (2.5). 

The monolayer strip with straight edges ax depicted in Fig. 1 can be taken as an idealised initial configuration of the top terrace. We are intesrested in calculating the typical time for. the top terrace to disappear (or most, part, of it, to be precise). This is actually a problem which I have not, been able to find an exact, answer. Qualitatively, however, an estimate for the lifetime of the strip can he made as follows. 

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