题目
三维简立方结构晶格点阵的基矢a_(1)=ai,a_(2)=aj,a_(3)=ak,原胞体积为a^3,对应的倒格子基矢为____,____,____。
三维简立方结构晶格点阵的基矢$a_{1}=ai,a_{2}=aj,a_{3}=ak$,原胞体积为$a^{3}$,对应的倒格子基矢为____,____,____。
题目解答
答案
根据倒格子基矢的定义:
\[
\mathbf{b}_1 = \frac{2\pi}{a^3} (a \mathbf{j} \times a \mathbf{k}) = \frac{2\pi}{a} \mathbf{i}
\]
\[
\mathbf{b}_2 = \frac{2\pi}{a^3} (a \mathbf{k} \times a \mathbf{i}) = \frac{2\pi}{a} \mathbf{j}
\]
\[
\mathbf{b}_3 = \frac{2\pi}{a^3} (a \mathbf{i} \times a \mathbf{j}) = \frac{2\pi}{a} \mathbf{k}
\]
因此,倒格子基矢为:
\[
\mathbf{b}_1 = \frac{2\pi}{a} \mathbf{i}, \quad \mathbf{b}_2 = \frac{2\pi}{a} \mathbf{j}, \quad \mathbf{b}_3 = \frac{2\pi}{a} \mathbf{k}
\]