Etching pit nucleation

A very accurate measurement of Ccrjt would allow back-calculation of the surface energy for a given crystal. Because Ccrjt is dependent on the square of Y, such a measurement could be a very sensitive method of measuring interfacial energy at dislocation outcrops. The calculated interfacial energy from our experiments is 280+ 90 mJm- for the rhombohedral face of quartz at 300°C. Parks (10) estimated 25°C value of 360 + 30 mJm is well within the experimental error of our measurement. The best way to determine the value of Ccrjt would be to measure etch pit nucleation rate on... 

Thus for < 1, there is an energy barrier for etch-pit nucleation at a dislocation site but the value of this barrier is less than that at the perfect surface. For = 1, there is a double root ... 

Values of r satisfying Equation 3 (corresponding to the minimum and maximum points in Ag) will yield steady state solutions where a pit radius should remain constant, while the rest of the crystal grows or dissolves depending on the chemical affinity (Equation 2). If the term t b2g /2Tt2Y2 > 1, there are no real solutions to Equation 3 and there is no steady state value of r, which indicates that a small pit nucleated at a dislocation core should spontaneously open up to form a macroscopic etch pit. The critical concentration at which this occurs (setting the above term equal to one) is ... 

For C crit t 161"6 ls a double root to the maximization equation, and there is an inflection point in the AG function (curve D on Figure 1). Since there is no activation barrier to opening up the etch pit, any pit nucleated at a dislocation should open up into a macroscopic etch pit. Similarly, for C < Ccr t, there are no real solutions and no maxima and minima in the A G function, and nucleated pits open up into etch pits. At 300°C, the calculated Ccr t for quartz equals 0.6CQ. 

Above Ccrlt (i.e. E or F in Figure 1), there are two real roots to the equation, so there is a minimum and a maximum in the A G function. If a pit is nucleated at the core, the pit should spontaneously open until its radius fulfills the condition that A G is at a minimum ("10 A). There is then an activation barrier Ag (=AGmax m -A Gm. jmul) toward further opening of the pit into a macroscopic etch pit. Monte Carlo simulations of etch pit formation have shown that such hollow tubes should be stable for some materials, including guartz (27). Above Ccr t, the height of the activation barrier (Ag ) will determine the rate of formation of etch pits. If metastable equilibrium is assumed for the pit nuclei size distribution, the rate of formation of pits per unit area, J, for concentrations above critical should have the form ... 

Several refinements of our experiments could test these theories further. By measuring etch pit densities as well as pit dimensions on sequentially-etched crystals, nucleation rate data and pit growth data could be collected, yielding information about the rate-limiting steps and mechanisms of dissolution. In addition, since the critical concentration is extremely dependent on surface energy of the crystal-water interface (Equation 4), careful measurement of Ccrit yields a precise measurement of Y. Our data indicates an interfacial energy of 280 + 90 mjm- for Arkansas quartz at 300°C, which compares well with Parks value of 360 mJm for 25°C (10). Similar experiments on other minerals could provide essential surface energy data. 

THE FORMATION OF dislocation etch pits and in particular the nucleation of steps at dislocations and the motion of steps are briefly discussed. The role of dislocations in oxidation processes is summarized. 

There is ample evidence that the initiation of an etch pit is a nucleation process. Indeed pitting occurs only under sufficiently high undersaturations and is very sensitive to small changes of this variable. This behavior would be difficult to understand if a nucleation process were not involved. 

The effect of inhibitor ions on etch pit formation in LiF is shown in Fig. 5. As the concentration of inhibitor in the solvent is increased, the sides of the etch pits become increasingly steep. It has also been found that the rate of deepening of the etch pits is almost independent of the inhibitor concentration. Therefore the rate at which steps move away from the place where they are nucleated must be strongly influenced by inhibitor ions. Since the rate of nucleation is unaffected by... 

Here, the parameters A" and B are determined from dissolution far from and near equilibrium, respectively, and AGcut is the critical value for the driving force for dissolution (AG) such that when lAGl > lAGcntl etch pits spontaneously nucleate at dislocations. Fits of Equation (64) to several mineral dissolution datasets are shown in Figure 10. 

The theoretical model developed to take account of these factors, Eqs. (31)—(35), is consistent with the experimental data presented in Figure 21. This model indicates that —20 lattice layers of the crystal surface are removed in each current surge [given the deduced value of N = 12.5 X 10 9 mol cm-2, and the density of Cu2+ in the (100) surface of —5.3 X 10 10 mol cm-2 (51)]. The value of Ccrit = 1.25 X 10 6, is some five orders of magnitude smaller than the value typically required for the nucleation of observable dissolution etch pits at dislocation sites (3,52,53). Intuitively, this indicates that the measured value of Ccrit is consistent with dissolution from a dislocation-free area. 

Figure 2.7(a) shows the SEM image of a low-doped 6H-SiC sample anodized for 5 min. A characteristic etch pit pattern appears in the anodized sample, since in this case the pore nucleation occurs mostly at dislocations and dislocation walls. Similar to the other two types of substrates, the pore openings on the surface could not be observed neither under the optical microscope nor under the SEM without the skin layer removal. The SEM image of the cross-section of the cleaved sample demonstrates that pores increase in diameter with depth and might reach a size of several micrometers [Figure 2.7(b)]. Moreover, the pore density for the low-doped samples is relatively low compared with those in the high and... 

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