※ 引述《Lanjaja ()》之铭言： : 最近一直被reciprocal lattice所困扰 : 尤其是Kittel从reciprocal lattice的关系导出Bragg result (24). : 我看不懂p32他说的 : The integer hkl that define G are not necessarily identical with the indices of : an actual crystal plane, because the hkl may contain a common factor n, : whereas in the definition of the indices in Chapter 1 the common factor has : been eliminated. : 最後 d is the spacing between adjacent parallel planes with indices h/n, k/n, : l/n. Considering the following simple example: cubic system with lattice constant a. Take {100} diffraction as example.. a = d(100). 2 d(100) sin(theta(100)) = lambda 2 d(200) sin(theta(200)) = lambda 2 d(300) sin(theta(300)) = lambda ............ 2 d(n00) sin(theta(n00)) = lambda => You can choose d = a = d(100) = 2 d(200) = .....= n d(n00) i.e. we can write the above equations as 2 d sin(theta) = n lambda. where d = a. For the order n, G corrsponds to d(n00), i.e. h=n, k=l=0. d = a = d(100) which has (h,k,l) = (1,0,0) = (n/n, 0, 0). If there exists extinctions for (100), (300), (500), etc., 2 d(200) sin (theta(200)) = lambda 2 d(400) sin(theta(400)) = lambda ......... 2 d(2n 00) sin(theta(2n 00)) = lambda => you can choose d = d(200) = 2 d(400) = ....... = n d(2n 00) = a/2. i.e. the equations can be written as 2 d sin(theta) = n lambda, where d = a/2. For the order n, G corresponds to d(2n 00), i.e. (hkl) = (2n,0,0). d = d(200), which has (hkl) = (2,0,0) = (2n/n, 0,0). ps: Usually, we don't write 2 d sin(theta) = n lambda... This is for high school. Solid state physicists and crystallographers usually write 2 d(hkl) sin(theta) = lambda. --

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