Miller indices

Download Miller indices and structure and more Schemes and Mind Maps Crystallography in PDF only on Docsity!Miller indices, group of three numbers that indicates the orientation of a plane or set of parallel planes of atoms in a crystal. If each atom in the crystal is represented by a point and these points are connected by lines, the resulting lattice may be divided into a number of identical blocks, or unit cells; the intersecting edges of one of the unit cells defines a set of crystallographic axes, and the Miller indices are determined by the intersection of the plane with these axes. The reciprocals of these intercepts are computed, and fractions are cleared to give the three Miller indices (hkl). For example, a plane parallel to two axes but cutting the third axis at a length equal to one edge of a unit cell has Miller indices of (100), (010), or (001), depending upon the axis cut; and a plane cutting all three axes at lengths equal to the edges of a unit cell has Miller indices of (111). Miller indices Why are crystallographic planes important? Uses of Miller indices X- Important features of Miller indices Crystal Planes Crystal Planes Determined Miller Indices from Lattice Planes Determined Miller Indices from Lattice Planes Plane can not touch origin Choose cloases corner Determined Miller Indices from Lattice Planes Determined Miller Indices from Lattice Planes Crystal Planes Crystal Planes Crystal Planes Directions Crystal Planes Directions Crystal Planes Directions Relation Between Interplaner spacing and Miller indices

Miller indices and crystal directions - PowerPoint PPT Presentation Description: Miller indices and crystal directions? How to describe a particular crystallographic plane and direction not necessarily of equal length Primitive translation vectors ... – PowerPoint PPT presentation Number of Views:170Avg rating:3.0/5.0 lessTranscript and Presenter's NotesTitle: Miller indices and crystal directions 1 Miller indices and crystal directions?How to describe a particular crystallographic plane and directionnot necessarily of equal lengthPrimitive translation vectors a1, a2, a3 not necessarily right anglesDetermine the intercepts of the face along the crystallographic axes, in terms of unit cell dimensions n1,n2,n3here 1,3,1Miller indices (h,k,l) specify set of equivalent planesTake the reciprocals 1/n1,1/n2,1/n3here 1,1/3,1here 3,1,3Clear fractions with the smallest possible integer 2Simplified example for cubic system 3negative intercept is denoted by a bar the symbol denotes all planes equivalent to (h,k,l) 4(No Transcript) 5Set of four Miller indices for hexagonal crystals first three Miller indices add up to zero 6Crystal directions n1 n2 n3 direction defined by E.g., 111 instead of 222Note hkl is in general not normal to the (hkl) plane > -->

Integers are usually written in lowest terms, i.e. their greatest common divisor should be 1. Miller indices are also used to designate reflections in X-ray crystallography. In this case the integers are not necessarily in lowest terms, and can be thought of as corresponding to planes spaced such that the reflections from adjacent planes would have a phase difference of exactly one wavelength (2π), regardless of whether there are atoms on all these planes or not.There are also several related notations:[1]In the context of crystal directions (not planes), the corresponding notations are:Note, for Laue–Bragg interferences lacks any bracketing when designating a reflectionMiller indices were introduced in 1839 by the British mineralogist William Hallowes Miller, although an almost identical system (Weiss parameters) had already been used by German mineralogist Christian Samuel Weiss since 1817.[2] The method was also historically known as the Millerian system, and the indices as Millerian,[3] although this is now rare.The Miller indices are defined with respect to any choice of unit cell and not only with respect to primitive basis vectors, as is sometimes stated.Examples of determining indices for a plane using intercepts with axes; left (111), right (221)There are two equivalent ways to define the meaning of the Miller indices:[1] via a point in the reciprocal lattice, or as the inverse intercepts along the lattice vectors. Both definitions are given below. In either case, one needs to choose the three lattice vectors a1, a2, and a3 that define the unit cell (note that the conventional unit