X-ray diffraction by random layers: ideal line profiles and determination of structure amplitudes from observed line profiles
X-ray diffraction by random layers: ideal line profiles and determination of structure amplitudes from observed line profiles
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随机层的 X 射线衍射：理想的线轮廓和根据观察到的线轮廓确定结构振幅
DOI：
10.1107/s0365110x49000631
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发表时间：
1949
期刊：
影响因子：
--
通讯作者：
A. Wilson
中科院分区：
文献类型：
--
作者：
A. Wilson
沃伦对随机层绕射的线形的计算依赖于近似函数的使用。这是可能的。(A)结构振幅缓慢变化的理想线形，以及(B)根据层形和观察到的线形，绕射强度随倒易空间中高强度“棒”位置的函数而变化的表达式。理想的线型是，在一个三角因子内，{i(\sigma)=FF{^*}S{{0^1\over2}}\int_{-\inty}^A(T)，\，|t|{^{1\over 2}}(\cos 2\pi\sigma+\sin2\pi\sigma\，\，|t|)，其中S0(=2 Sin θ0/λ)是从倒易点阵的原点到‘Rod’中心线的垂直距离，σ=(Sin 2 θ − Sin 2 θ0)/λ Sin θ0，F是结构幅度，A(T)是层的公共区域，并且它的‘Ghost’平行于S0移动了距离t。这个表达式对不同的层形状进行了评估，给出的绕射强度比沃伦发现的略低，并在一定程度上取决于层的形状。特别是，σ的大负体积的强度与|σ|−3/2乘以层的最大宽度成正比。如果w是从S0的脚下沿‘杆’测量的，则F(W) F*(W) + F(−w) F*(−w)可以通过利用双重傅里叶变换对观测的I(σ)进行‘展开’而得到。因此，随机层的衍射可以提供比完美晶体的衍射更多的信息，因为后者只给出折射率的积分值的Ff*。
Warren's calculation of the line profile for diffraction from random layers depends on the use of an approximation function. This can be. avoided, and expressions found for (a) the ideal line profile for slow variation of the structure amplitude, and (b) the variation of the intensity of diffraction as a function of position along the `rod' of high intensity in reciprocal space, in terms of the layer shape and the observed line profile. The ideal line profile is, within a trigonometrical factor, {I(\sigma) = FF{^*}S{_0^{1 \over 2}} \int_{-\infty}^{\infty} A(t)\,\, |t|{^{1 \over 2}} (\cos 2\pi\sigma t + \sin 2\pi\sigma\,\, |t|)\,\, dt,} where S0(= 2 sin θ0/λ) is the perpendicular distance from the origin of the reciprocal lattice to the centre line of the `rod', σ = (sin2 θ − sin2 θ0)/λ sin θ0, F is the structure amplitude, and A(t) is the area common to a layer and its `ghost' shifted a distance t parallel to S0. This expression, evaluated for various layer shapes, gives intensities of diffraction slightly lower than those found by Warren and depending somewhat on the layer shape. In particular, the intensity for large negative volumes of σ is proportional to |σ|−3/2 multiplied by the maximum breadth of the layer. If w is measured along the `rod' from the foot of S0, F(w) F*(w) + F(−w) F*(−w) can be obtained by `unfolding' the observed I(σ) by means of a double Fourier transformation. Diffraction by random layers can thus give more information than diffraction by a perfect crystal, as the latter gives FF* only for integral values of the indices.