Sinusoidal variation with distance,

The first term describes the sinusoidal variation of the particle displacement with distance, the second term the variation with time, and the final term describes the attenuation of the wave. In most text books equation 1 is written in the following form ... 

Therefore, the sinusoidal variation of /q and /g with z can be considered as the beating of the two waves whose wavevectors originate on different branches of the dispersion surface. From Figure 4.4, we see that a = BA, which is the distance between the two active tie points (A on the a branch and B on the 0 branch) that are selected by the incident wave conditions. For the symmetrical Laue case with = 0 (i.e., PL = 0), A and B lie on the line QL BA now has its minimum value and thus the period of oscillation (1/ff) has its maximum value. As we move away from the exact Bragg angle, BA increases, and thus the period of oscillation of /q and 7g with z decreases. When 5 = 0, a = 1/tg and... 

In the consideration of the resistance of materials to plastic flow it is useful to estimate theoretically the stress that may be required to shear the structure. It is necessary to do this before a sensible comparison can be made of the relative strengths of different types of materials such as metals and polymers. The general situation to be considered is shown in Fig. 5.4 where one sheet of atoms or molecules is allowed to slip over another under the action of a shear stress a. The separation of the sheets is h and the repeat distance in the direction of shear is fo. It is envisaged that the shear stress will vary periodically with the shear displacement x in an approximately sinusoidal manner and that the maximum resistance to shear will be when x = b/A. The variation of a with the displacement x can then be written as... 

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