Stress-free d—spacing from asymmetric diffraction

3 Stress-free d-spacing from asymmetric diffraction 

Consider once again a thin film with equi-biaxial mismatch strain 

Alternatively, this same strain can be expressed in terms of the d—spacing values of the diffracting planes as 

Suppose that the film material is an isotropic elastic material, so that the relationships between mismatch strain and mismatch stress noted in (3.53) apply. In this case, (3.62) takes the form 

If do and the elastic constants of the film material would be known, it follows that the mismatch stress Jm could be inferred from a measurement of d by means of this expression. Note that there is some direction in the material, say -00 defined by 

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