Quartz dislocations

Dislocation lines do not move concertedly, that is, all at once. They move, by forming kinks along their lengths, and when the kinks move, the lines move. The open crystal structure of quartz (crystobalite) results in a relatively large amount of volume being associated with a kink on a dislocation line. This relatively large volume lowers the value of quartz s bond modulus, making its hardness consistent with those of other covalently bonded substances. 

The distance that the small segment of a dislocation line moves when a kink moves is called the Burgers displacement, b. Figure 11.2 illustrates it for the case of quartz. It determines the amount of work that is done by the advance of a kink (per unit width of the kink) which is acted upon by the virtual force generated by the applied shear stress, x. This force is xb per unit length of the dislocation line. Letting the kink width be b since the displacement is b, the work done is xb3. This is resisted by the strength, U (eV) of a Si-O bond which... 

Figure 1. Calculated values of AG, free energy of formation of a pit at a dislocation on a quartz surface at 300°C, plotted vs. pit radius, r. Labels defined in text. Adapted with permission from Ref. 16. Copyright 1986 Pergamon Press.

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. 

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... 

In general, the shape and character of etch pits may reveal information about the impurity content of the crystal. "Beaked pits (pits with curved apexes, see 12) can indicate impurity haloes. Some forms of the arcuate etching we observed in quartz (16) may be examples of beaking. Very shallow pits can form at aged dislocations while very deep pits form at new dislocations. "Aging" may be related to impurity diffusion in the crystal lattice. 

Wintsch ana Dunning (8) calculated that the solubility of plasticly deformed quartz in water should not be significantly higher than the ideal equilibrium value. However, enhanced dissolution at dislocations could significantly increase the dissolution... 

Anomalously high extended defect concentrations may be achieved in crystals by submitting them to directional stress. For example, Willaime and Gaudais (1977) induced dislocation densities of 10 cm in sanidine crystals (KAlSi30g triclinic), and Ardell et al. (1973) reached a dislocation density of 10 cm in quartz with the same method. 

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