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Miller indices form a notation system in crystallography for lattice planes in crystal (Bravais) lattices. In particular, a family of lattice planes of a given (direct) Bravais lattice is determined by three integers h , k , and ℓ , the Miller indices .
Miller indices of a plane (hkl) and a direction [hkl].The intercepts on the axes are at a/ h, b/ k and c/ l. The International Union of Crystallography (IUCr) gives the following definition: "The law of rational indices states that the intercepts, OP, OQ, OR, of the natural faces of a crystal form with the unit-cell axes a, b, c are inversely proportional to prime integers, h, k, l.
Planes with different Miller indices in cubic crystals Vectors and planes in a crystal lattice are described by the three-value Miller index notation. This syntax uses the indices h , k , and ℓ as directional parameters.
Miller indices in parentheses such as (100) denote a plane of the crystal structure, and regular repetitions of that plane with a particular spacing. In the cubic system, the normal to the (hkl) plane is the direction [hkl], but in lower-symmetry cases, the normal to (hkl) is not parallel to [hkl].
Miller–Bravais index for HCP lattice. Crystallographic features of HCP systems, such as vectors and atomic plane families, can be described using a four-value Miller index notation ( hkil) in which the third index i denotes a degenerate but convenient component which is equal to −h − k.
Wood's notation takes the form (| | | | | | | |)where M is the chemical symbol of the substrate, A is the chemical symbol of the overlayer, () are the Miller indices of the surface plane, R and correspond to the rotational difference between the substrate and overlayer vectors, and the vector magnitudes shown are those of the substrate (subscripts) and of the overlayer (subscripts).
Barkla created the x-ray notation for sharp spectral lines, noting in 1909 two separate energies, at first naming them "A" and "B" and then supposing that there may be lines prior to "A", he started an alphabet numbering beginning with "K." [9] [10] Single-slit experiments in the laboratory of Arnold Sommerfeld suggested that X-rays had a ...
With miller indices You would write a=[100], b=[010] and a+b=[110]. If You look carefully a+b is just the same as a or b, only rotated by 60°. So it is convenient to have a notation where this similarity is apparent. in the hkil notation a is 2,-1,-1, 0 while a+b is 1,1,-2,0. They look similar, that is why we use this notation.