Crystallography & Symmetry
patterns derived from their groups
Concept

Blind region — where it appears

The blind region is the set of reciprocal lattice points that a rotation about one fixed axis can never bring onto the Ewald sphere. It is a cusp about the axis, and no amount of rotation reaches it, though a different axis would.

Named by 2 essays across one field — each of them below, with the objects they name alongside it.

Also named here as completeness, ewald sphere — the same set of essays touches all of them, so they are one junction rather than several.

66 reflections that no rotation reaches. Every reflection inside the limiting sphere of an orthorhombic cell, 7 × 11 × 13 Å at 1.4 ångström, plotted by its distance from the rotation axis against its height along it. The ones marked are those a rotation about that axis can never bring into diffracting position: turning the crystal moves a point on a circle at fixed height, so a point too close to the axis can never acquire the component along the beam that the Ewald condition demands. The blind region is a cusp about the axis, it is 4.3 per cent of the sphere here, and nothing but remounting the crystal removes it.

What one turn of the crystal reaches

Every reflection inside the limiting sphere is measurable by some orientation. A crystal on a spindle has one axis, and a region around it never reaches the Ewald sphere at all — however patiently the crystal is turned.

diffraction · Resolution Completeness against sweep, for four spindles. Completeness against rotation range for one tetragonal crystal, class 4/mmm, on four different spindles. The four-fold spindle rises fastest at first, then stops at 88.9 per cent at forty degrees and never improves. The two-fold spindles reach completion near 87 degrees. The general spindle is highest at forty-five degrees and reaches completion at the same 87.

The same measurements, and a hole that stays

How much of the sphere must be swept for a given redundancy? The question has two answers, because it has two parts. The mean number of observations depends only on the sweep, to within two per cent whichever axis the crystal turns on. Completeness depends entirely on the axis, and on one kind of axis no sweep ever finishes: when the Laue group keeps the spindle's line, every copy of a blind reflection is blind too, and fifteen of a tetragonal crystal's 135 reflections are never measured.

diffraction · Resolution

Named alongside it

The objects these essays reach for when they reach for this one.

CompletenessEwald sphereLaue classReciprocal latticeResolutionLimiting sphere

All concepts