October 1995
| Lattice Position | ||
| $\frac{1}{2}$$\frac{1}{4}$0 | Position in a unit cell: coordinates measured along axes in units of corresponding cell dimensions. Each coordinate is thus 0 or a proper fraction, except that in NaCl-type crystals the unit-cell dimension is often taken as 2. | |
| Symbols based on Miller Indices (These are integers, not all 0, with no common factor; −h is represented by $\overline{h}$) |
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| [hkl] | Direction; set of parallel axes; an axis in such a set. This is not the name of a vector; one may write k||[110] but not k=[110]. In noncubic crystals the direction [hkl] is not in general orthogonal to the plane (hkl), and it is sometimes convenient to specify directions in terms of the perpendicular planes. In that case, “(100) direction” and “{100} directions” are legitimate. Be sure to warn the reader explicitly if you use this notation, and write “direction” each time. | |
| ⟨hkl⟩ | Set of directions or axes equivalent to [hkl] under the symmetry group of the crystal; a direction or axis in the set. For example, in a cubic crystal the⟨100⟩ directions are [100], [010], [001], [100], [010], and [001]. | |
| (hkl) | Plane; set of parallel planes. N.B. Use commas for a vector, but not for a plane: (kx , ky , kz) represents the vector k in terms of Cartesian coordinates and is a point with that radius vector. | |
| {hkl} | Set of planes equivalent to (hkl) under the symmetry group; a plane in that set. | |
Hexagonal Notation
In a hexagonal lattice, the forms [hkk'l], etc., are often used, the redundant index k'= −h−k corresponding to the third equivalent axis. [hk.l] and [hk l] are also used. Similarly, points can be labeled h, k, k , l or hk.l, for example, $\frac{1}{3},\frac{1}{3},-\frac{2}{3}$, 0 or $\frac{1}{3}\frac{1}{3}$.0. The latter form is not widely known or used in the United States, and so the preferred style of Physical Review is to use the forms h, k, k', l, [hkk', l], and (hkk'l) for points, directions, and planes, respectively.
Examples of Usage
H is in the [001] direction or in a ⟨001⟩ direction
The six {100} faces of a cube
The two opposite (100) faces of a cube