= Diffraction indexing under a cell change
{title2=$\mathbf h_{\rm new}=P^T\mathbf h_{\rm old}$}
If new direct-cell vectors are columns of $P$ in old fractional coordinates, an unchanged reciprocal vector has the displayed new coordinates. Noninteger coordinates must not be rescaled when tracking the same diffraction order. Under the <Bain path> cell change, $P=\begin{pmatrix}1/2&-1/2&0\\1/2&1/2&0\\0&0&1\end{pmatrix}$. The old FCC $(100)$ reflection becomes $(1/2,-1/2,0)$ and remains absent; doubling that triple gives the different, allowed reflection that originated as FCC $(200)$. Orientation indices and order-resolved reciprocal vectors carry different information.
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