推 pleasetoyou:I understand it for basis and n. Thank you. 07/25 10:06
※ 編輯: chungweitw 來自: 128.227.48.184 (10/09 03:08)
※ 引述《Lanjaja ()》之銘言：
: 最近一直被reciprocal lattice所困擾
: 尤其是Kittel從reciprocal lattice的關係導出Bragg result (24).
: 我看不懂p32他說的
: 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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◆ From: 128.227.2.223
※ 編輯: chungweitw 來自: 128.227.2.223 (07/25 07:23)