X‐ray diffraction from d spacing gradients along ion‐implanted zones

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American Institute of Physics


Three kinematic diffraction models are described for interpreting diffraction profiles from ion-implanted samples. Each deals with relatively large d spacing gradients. The first treats the full zone as coherent which requires a direct summation of the Fourier series. The Bragg intensity band from the full zone is applied to implanted zones that are subjected to elastic constraints without incoherent interfaces. For high-fluence samples, and foreign interstitials, a static attenuation term becomes important and is included in all models. This term was not included in previous publications by the authors. The last two models deal with finite subgrain elements that may be connected in a continuous way with interfaces. With a linear element model, slope discontinuities give a sawtooth appearance of the d spacing curve. These discontinuities are eliminated by employing a sinusoidal variation in d spacing in a third model. The additional smoothing does not provide significant changes in the fine structure of the measured intensity. The parameters that determine line shape are: DELTA-M, the total change in the attenuation factor M within a subgrain, and s = N3l(DELTA-d/) which contains three additional independent parameters. These are the subgrain size, the order of the Bragg peak l, and the fractional changes in d spacing. The static lattice displacements can be large enough to introduce an asymmetry of the diffraction profiles from individual elements. This occurs when DELTA-M is greater than 0.15. Although this factor has been introduced only in the linear element model, a similar asymmetry should be observed with a sinusoidal variation in d spacing.



Elasticity, Fourier analysis, Interstitial defects, Kinematics, Light diffraction


Rao, S. I., Houska, C. R. (1991). X‐ray diffraction from d spacing gradients along ion‐implanted zones. Journal of Applied Physics, 69(12), 8096-8103. doi: 10.1063/1.347459