Example Stress implied by measured d—spacing

The residual strains in an aluminum film, 1 pan in thickness, on a Si substrate, 550 //m thick and 200 mm in diameter, were studied by x-ray diffraction. It was found that the d-spacing of crystallographic planes in the film, which were oriented parallel to the plane of the film, decreased by 0.054%, compared to the situation when the film was stress-free. 

From (3.56) 1, the mismatch strain in the film with the (100) texture is written as 

Noting from Table 3.1 that cn = 107.3 GPa and ci2 = 60.9 GPa for aluminum, it follows that Cm = 0.00047. Substituting the values of Cn and Ci2 into (3.45), the biaxial modulus of the aluminum film with the (001) texture is found to be 99.1 GPa. This result, in conjunction with (3.56)2, provides the mismatch stress in the film as (Tm = 47.2 MPa. 

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