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Proposal of Simplified Modified Williamson-Hall Equation

机译：简化的改进的Williamson-Hall方程的建议

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摘要

Williamson-Hall (WH) plots are characterized by irregular arrangement of data due to the elastic anisotropy in each {hkl} plane. In order to correct the effect of elastic anisotropy, Ungar developed a unique methodology using the contrast factor C, so called the modified Williamson-Hall (mWH) method. When X-ray with the wave length λ was used for diffraction analysis and diffraction angle 6 and integral breadth βt was obtained in each diffraction peak, the following mWH equation is constructed as functions of the parameter K (=2sinθ/λ) and ∆K (=βcosθ/λ). ∆K =α+φk√C+OK~2C Here, the parameter α is dependent on the crystallite size. The parameter φ and O are constants but the O-value is much smaller than the φ-value. In the mWH plots in 60% cold rolled ferrite (Fe-0.0056%C), ultra low carbon martensite (Fe-18%Ni) and 20% cold rolled austenite (SUS316L), it was confirmed that the value of OK~2C is negligibly small. As a result, the following simplified equation is applicable for the analysis by mWH method. ∆K =α+φk√C
机译：由于每个{hkl}平面中的弹性各向异性，Williamson-Hall（WH）图的特征在于数据的不规则排列。为了校正弹性各向异性的影响，Ungar开发了一种使用对比度因子C的独特方法，即所谓的改进的Williamson-Hall（mWH）方法。当使用波长为λ的X射线进行衍射分析并在每个衍射峰中获得衍射角6和积分宽度βt时，以下mWH方程将作为参数K（=2sinθ/λ）和∆K的函数构建（＝βcosθ/λ）。 ΔK＝α+φk√C+ OK〜2C在此，参数α取决于微晶尺寸。参数φ和O是常数，但是O值比φ值小得多。在60％冷轧铁素体（Fe-0.0056％C），超低碳马氏体（Fe-18％Ni）和20％冷轧奥氏体（SUS316L）的mWH图中，确定OK〜2C的值为小到可以忽略不计。结果，以下简化方程适用于通过mWH方法进行的分析。 ΔK=α+φk√C

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