Use the method of Section 3.1 to estimate the surface energy of {111},.{200} and

Question

Use the method of Section 3.1 to estimate the surface energy of {111},.{200} and {220} surface planes in an fcc crystal. Express your answer in J/surface atom and in J/m2 . Differentiate Equation 3.8 to obtain the slope of the Esv - curve at = 0. If a two-dimensional rectangular crystal is bounded by sides of lengths l1 and l2 show by differentiation that the equilibrium shape is given by l1/l2 = 2/ 1 where 1 and 2 the energies of the sides l1 and l2 respectively. (The area of the crystal l1l2 is constant.) Measure for the low-angle tilt boundary in Fig. 3.11. Determine the Burgers vector of the interface dislocations by making a Burgers circuit around one of the dislocations. Does the mean spacing of the dislocations agree with that predicted by Equation 3.9? Explain why grain boundaries move towards their center of curvature during grain growth but away from their center of curvature recrystallization.

Explanation / Answer

represent only the most frequently studied surface planes of the fcc system - however, they are also the most commonly occurring surfaces on such metals and the knowledge gained from studies on this limited selection of surfaces goes a long way in propagating the development of our understanding of the surface chemistry of these metals.

For the three cubic structures the structural arrangement within a plane and between different planes may be different. Below are shown the (100) planes of simple, body centred and face centred cubic lattices. In the body centred and face centred cubic structures there are planes of atoms (marked in green) interleaving the (100) planes. These, together with the (100) planes, make up the (200) set of planes (intercepts (

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