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Miller–Bravais indices. With hexagonal and rhombohedral lattice systems, it is possible to use the Bravais–Miller system, which uses four indices (h k i ℓ) that obey the constraint h + k + i = 0. Here h, k and ℓ are identical to the corresponding Miller indices, and i is a redundant index.
nanoHUB.org is a science and engineering gateway comprising community-contributed resources and geared toward education, professional networking, and interactive simulation tools for nanotechnology. [1] Funded by the United States National Science Foundation (NSF), it is a product of the Network for Computational Nanotechnology (NCN).
Xilinx Simulator (XSIM) comes as part of the Vivado design suite. It is a compiled-language simulator that supports mixed language simulation with Verilog, SystemVerilog, VHDL and SystemC language. It supports standard debugging tool such as step through code, breakpoints, cross-probing, value probes, call stack and local variable Window.
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.
If, on the other hand, the Miller indices are not relative prime, the family of planes defined by them is not a family of lattice planes, because not every plane of the family then intersects lattice points. [2] Conversely, planes that are not lattice planes have aperiodic intersections with the lattice called quasicrystals; this is known as a ...
() defines a reciprocal lattice point at (,,) which corresponds to the real-space plane defined by the Miller indices (see Bragg's law). F h k ℓ {\displaystyle F_{hk\ell }} is the vector sum of waves from all atoms within the unit cell.
The attitude of a lattice plane is the orientation of the line normal to the plane, [12] and is described by the plane's Miller indices. In three-space a family of planes (a series of parallel planes) can be denoted by its Miller indices (hkl), [13] [14] so the family of planes has an attitude common to all its constituent planes.
where is the lattice spacing of the cubic crystal, and h, k, and ℓ are the Miller indices of the Bragg plane. Combining this relation with Bragg's law gives: Combining this relation with Bragg's law gives: