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11 The lattice parameter for sample B is the same as that calculated for pure copper. Therefore sample B is high-purity copper. 75 per cent greater than that for pure copper. Sample A is not pure and the presence of impurity atoms (in solid solution) has imposed strain in the crystal lattice of the copper. 13 Assume a unit cell contains x carbon atoms and 2x hydrogen atoms. Find mass of x carbon and 2x hydrogen atoms. Calculate volume of unit cell from data given. Knowing density x can be evaluated.

2 (b) Miller-Bravais system. (a) reference axes, (b) unit cell, showing equivalence to three Miller cells It should be observed that it is only necessary to quote two parameters, the axis lengths a and c, to define a specific tetragonal or hexagonal crystal as b is equal to a and, in tetragonal, all angles are right angles, while in hexagonal it is known that ex and pare right angles andy= 60°. Similarly, only one parameter, axis length a, is needed to fully define a cubic crystal. (b) Miller Indexing System Planes and directions within crystals can be identified using the Miller notation.

The variation of u with (} for a constant value of r is shown in the accompanying diagram. Magnesium crystallises as HCP and has one set of parallel slip planes, the basal planes. If these planes are aligned at oo or 90° to the line of direct stress there will be no shear stress on the slip planes, hence no slip, and the crystal will fracture in a brittle manner when the fracture stress is exceeded. For crystals with the basal planes aligned at some other angle a shear stress will be developed and when this exceeds the critical value, slip will occur.

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