Example Determination of reference lattice spacing

A thin film of a polycrystalline fee metal with 111 fiber texture was deposited onto a relatively thick Si substrate. Nonsymmetric x-ray diffraction measurements showed that the (242) and (242) planes had d—spacing values of 0.8268 and 0.8274 A, respectively. The thin film material is known to be nearly isotropic. The elastic modulus and Poisson ratio of the film material are 70 GPa and 0.33, respectively. 

Let ipi denote the angle between the normal to the (242) plane, or equivalently, the normal to (121) plane and the normal to the plane of the film, which is along the [111] direction. From the geometry of the fee crystal. 

Because the film material can be considered elastically isotropic with Poisson ratio j/f = 0.33, the orientation of zero extensional strain can be determined from (3.64) to be 

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