# 布拉格定律

X射線與一晶體內原子的交互作用。

${\displaystyle n\lambda =2d\sin \theta \!}$

## 布拉格條件

${\displaystyle 2d\sin \theta =n\lambda \!}$

## 倒空間

${\displaystyle {\vec {G}}\ =\ {\vec {k_{f}}}\ -\ {\vec {k_{i}}}}$

${\displaystyle Q={\frac {4\pi \sin \left(\theta \right)}{\lambda }}}$

## 另一種推導

${\displaystyle (AB+BC)-(AC')}$

${\displaystyle (AB+BC)-(AC')=n\lambda }$， （需要為C'下定義）

${\displaystyle AB=BC={\frac {d}{\sin \theta }}\,}$${\displaystyle AC={\frac {2d}{\tan \theta }}}$

${\displaystyle AC'=AC\cdot \cos \theta ={\frac {2d}{\tan \theta }}\cos \theta =\left({\frac {2d}{\sin \theta }}\cos \theta \right)\cos \theta ={\frac {2d}{\sin \theta }}\cos ^{2}\theta }$

${\displaystyle n\lambda ={\frac {2d}{\sin \theta }}(1-\cos ^{2}\theta )={\frac {2d}{\sin \theta }}\sin ^{2}\theta }$

${\displaystyle n\lambda =2d\sin \theta }$

## 選擇定則與實驗晶體學

${\displaystyle d={\frac {a}{\sqrt {h^{2}+k^{2}+l^{2}}}}}$

${\displaystyle \left({\frac {\lambda \ }{2a}}\right)^{2}={\frac {\sin ^{2}\theta \ }{h^{2}+k^{2}+l^{2}}}}$

l為偶數或h + 2k ≠ 3n l為奇數且h + 2k = 3n

## 參考資料

1. ^ John M. Cowley (1975) Diffraction physics (North-Holland, Amsterdam) ISBN 0-444-10791-6.
2. ^ 例如，見使用布拉格定律計算原子間距離的例子 網際網路檔案館存檔，存檔日期2011-07-10.。
3. ^ 有一些資料來源，例如《美國學術百科》，把這項發現歸功於威廉·勞倫斯·布拉格及其父威廉·亨利·布拉格，然而 諾貝爾獎官方網站及關於他的傳記 ("Light Is a Messenger: The Life and Science of William Lawrence Bragg", Graeme K. Hunter, 2004 and "Great Solid State Physicists of the 20th Century", Julio Antonio Gonzalo, Carmen Aragó López) 都有明確指出，威廉·勞倫斯·布拉格是獨立地推導出這條定律的。
4. ^ H. P. Myers. Introductory Solid State Physics. Taylor & Francis. 2002. ISBN 0-7484-0660-3.
5. ^ Carl. R. Nave. Bragg's Law. HyperPhysics, Georgia State University. [2008-07-19].
6. ^ Pieranski, P. Colloidal Crystals. Contemporary Physics. 1983, 24: 25. Bibcode:1983ConPh..24...25P. doi:10.1080/00107518308227471.
7. ^ Hiltner, PA; IM Krieger. Diffraction of Light by Ordered Suspensions. Journal of Physical Chemistry. 1969, 73: 2306.
8. ^ Aksay, IA. Microstructural Control through Colloidal Consolidation. Proceedings of the American Ceramic Society. 1984, 9: 94.
9. ^ Luck, W. et al., Ber. Busenges Phys. Chem. , Vol. 67, p.84 (1963)

## 延伸閱讀

• Neil W. Ashcroft and N. David Mermin, Solid State Physics (Harcourt: Orlando, 1976).
• Bragg, W.L. The Diffraction of Short Electromagnetic Waves by a Crystal. Proceedings of the Cambridge Philosophical Society. 1913, 17: 43–57. 已忽略未知參數|author-separator= (幫助)