Evaluation of Kossel Microdiffraction Procedures: The Cubic Case

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Abstract
A complete theory of the lens‐shaped intersection of Kossel lines in the transmission pseudo‐Kossel method is developed. The general expression gives the lattice parameter with respect to the characteristics of the interaction of two arbitrary conics, i.e., conics corresponding to arbitrary diffracting planes and arbitrary wavelengths. Geometrical considerations involving the conics are developed and from these, the errors involved in lattice parameter measurement are evaluated. Lattice parameter variations of 10−5 can be easily measured with suitably chosen conic intersections. The precision to be expected as a function of measurement errors is expressed as a sensitivity ratio and tabulated for an Fe‐3wt.%Si alloy. Several methods of reducing measured lengths to lattice parameter data are evaluated. The IBM 7090 computer has been used to find suitable intersections for precise lattice parameter measurement. The computer supplies the wavelengths and conics to be used in the transmission pseudo‐Kossel method. Consequently, a long and tedious experimental investigation is avoided. Examples using Fe‐3wt.% Si are given; the lattice parameter for this alloy is found to be 2.86268±0.00003 Å. Proper radiations for investigation of Ge and diamond are indicated.

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