X-rays and Crystal Spacing

Crystal Lattice Spacing

a repeated distance

A simplified crystal diagram uses repeated planes to represent a measured spacing. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.

highlighted = computed this step

A crystal model repeats a spacing

Parallel planes mark a repeating distance in this simplified crystal model.

parallel planes set the repeat distance\text{parallel planes set the repeat distance}
Crystal planesParallel planes are the only geometry claim.planeplaneplaneplaneincomingreflectedrepeating planes

The repeat distance is exact

The spacing from one drawn plane to the next is 4 meters. Real protein crystals are three-dimensional and need phase retrieval; this lesson only checks spacing geometry.

d=4 md=4\ \text{m}
Crystal planesThe plane coordinates use one exact repeat.planeplaneplaneplaneincomingreflectedrepeating planes

Repeated plane coordinates keep the same spacing

The coordinate differences are checked between adjacent drawn planes. Each repeated step is the same spacing.

fromtod1545949134\begin{array}{c|c|c}\text{from}&\text{to}&d\\1&5&4\\5&9&4\\9&13&4\end{array}
Crystal planesThe third row extends the same repeat distance.planeplaneplaneplaneincomingreflectedrepeating planes