
Rietveld refinement is a technique devised by Hugo Rietveld for use in the characterisation of crystalline materials. The neutron and xray diffraction of powder samples results in a pattern characterised by reflections (peaks in intensity) at certain positions. The height, width and position of these reflections can be used to determine many aspects of the material's structure. The Rietveld method uses a least squares approach to refine a theoretical line profile until it matches the measured profile. The introduction of this technique was a significant step forward in the diffraction analysis of powder samples as, unlike other techniques at that time, it was able to deal reliably with strongly overlapping reflections. The method was first reported for the diffraction of monochromatic neutrons where the reflectionposition is reported in terms of the Bragg angle 2''θ''. This terminology will be used here although the technique is equally applicable to alternative scales such as xray energy or neutron timeofflight. The only wavelength and technique independent scale is in reciprocal space units or momentum transfer ''Q'', which is historically rarely used in powder diffraction but very common in all other diffraction and optics techniques. The relation is :$Q\; =\; \backslash frac\; .$ ==Peak shape== The shape of a powder diffraction reflection is influenced by the characteristics of the beam, the experimental arrangement, and the sample size and shape. In the case of monochromatic neutron sources the convolution of the various effects has been found to result in a reflex almost exactly Gaussian in shape. If this distribution is assumed then the contribution of a given reflection to the profile y_{i} at position 2''θ''_{i} is: $$ y_i = I_k \exp \left ( \frac \left (2\theta_i  2\theta_k \right )^2 \right ) where ''H''_{k} is the full width at half peak height (fullwidth halfmaximum), 2''θ''_{k} is the centre of the reflex, and I_{k} is the calculated intensity of the reflex (determined from the structure factor, the Lorentz factor, and multiplicity of the reflection) At very low diffraction angles the reflections may acquire an asymmetry due to the vertical divergence of the beam. Rietveld used a semiempirical correction factor, A_{s} to account for this asymmetry $A\_s\; =\; 1\; \; \backslash left\; (\backslash frac\; \backslash right)$ where P is the asymmetry factor and s is +1,0,1 depending on the difference 2θ_{i}2θ_{k} being positive, zero or negative respectively. At a given position more than one diffraction peak may contribute to the profile. The intensity is simply the sum of all reflections contributing at the point 2θ_{i}. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Rietveld refinement」の詳細全文を読む スポンサード リンク
