Weiss indices and miller indices
Weiss indices are, therefore, rather awkward in use and have consequently been replaced by miller indices. Taking the reciprocals of Weiss indices and multiplying throughout by the smallest number in order to make all reciprocals as integers obtain the Miller indices of a plane. The Miller indices for a particular family of planes are usually written (h, k, l) where h, k and l are positive or negative integers or zero. Crystal faces or Weiss indices can be defined by their intercepts on the crystallographic axes. and for the non-hexagonal crystals there are three cases. 1.A crystal face intersects only one of the crystallographic axes. As an example the top crystal face shown here intersects the c axis but does not intersect Bravais-Miller indices (hexagonal axes) In the case of a hexagonal lattice, one uses four axes, a 1 , a 2 , a 3 , c and four indices, (hkil), called Bravais-Miller indices, where h, k, i, l are again inversely proportional to the intercepts of a plane of the family with the four axes. Thus, the Miller indices are 3,6,2. If a plane is parallel to an axis, its intercept is at infinity and its Miller index is zero. A generic Miller index is denoted by (hkl). If a plane has negative intercept, the negative number is denoted by a bar above the number. Never alter negative numbers. For example, do not divide -1, -1, -1 by -1 to get 1,1,1. Miller Indices. The Miller Index for a crystal face is found by first determining the parameters; second inverting the parameters, and; third clearing the fractions. For example, if the face has the parameters 1 a, 1 b, ¥ c. inverting the parameters would be 1/1, 1/1, 1/ ¥ this would become 1, 1, 0
The miller indices are obtained by taking the reciprocal of the Weiss indices and multiplying them by LCM of the Weiss indices ,finally expressing the miller indices in the form of simple ratio eg a,b,care called miller indices
Bravais class. 30. Bravais flock. 31. Bravais lattice. 32. Bravais–Miller indices. 33 The first to introduce indices to denote a crystal plane was C. S.. Weiss. hu + kv + lw = 0 (Weiss Zone Law – true in all crystal systems). In hexagonal Between Miller-Bravais indices and Miller indices are simple relations: 2.1. Okay, I haven't really given a materials science answers for sometime now. Let us understand why do we need anything like Miller Indices. When we talk about In the following four questions you are asked to identify a given plane in a lattice. The diagram shows unit cells for a cubic lattice. Question 1. Click on the
Thus, the Miller indices are 3,6,2. If a plane is parallel to an axis, its intercept is at infinity and its Miller index is zero. A generic Miller index is denoted by (hkl). If a plane has negative intercept, the negative number is denoted by a bar above the number. Never alter negative numbers. For example, do not divide -1, -1, -1 by -1 to get 1,1,1.
Miller Bravais Indices. Since the hexagonal system has three "a" axes perpendicular to the "c" axis, both the parameters of a face and the Miller Index notation must be modified. The modified parameters and Miller Indices must reflect the presence of an additional axis. Related Discussions:- Weiss indices and miller indices. Structure and bonding in solids-crystals and glasses, Crystals and glasses Crystals and glasses Unlike a complex ion or molecule, which is a finite (often small) assembly of atoms, a solid has no fixed shape and size but can add atoms indefinit. Concept of Miller Indices or Law of Rational Indices: This law states that the intercepts of any phase of crystals along the crystallographic axis are either equal to the unit intercepts a,b,c or same simple whole number multiples of them i.e la , ma ,nc. However, the Weiss zone law is more general, and can be shown to work for all crystal systems, to determine if a direction lies in a plane. From the Weiss zone law the following rule can be derived: The direction, [UVW], of the intersection of (h 1 k 1 l 1) and (h 2 k 2 l 2) is given by: U = k 1 l 2 − k 2 l 1. V = l 1 h 2 − l 2 h 1. W = h 1
Weiss indices are, therefore, rather awkward in use and have consequently been replaced by miller indices. Taking the reciprocals of Weiss indices and multiplying throughout by the smallest number in order to make all reciprocals as integers obtain the Miller indices of a plane. The Miller indices for a particular family of planes are usually written (h, k, l) where h, k and l are positive or negative integers or zero.
Weiss indices are, therefore, rather awkward in use and have consequently been replaced by miller indices. Taking the reciprocals of Weiss indices and multiplying throughout by the smallest number in order to make all reciprocals as integers obtain the Miller indices of a plane. c. Miller Indices Early in the 19th century W.H. Miller developed a system of crystal face notation which has many advantages over Weiss symbols. These symbols, called Miller indices, are simply the reciprocals of Weiss parameters, cleared of fractions, with the letters denoting the axes omitted. A face that has the Weiss symbol 3a:3b:1c. Miller Bravais Indices. Since the hexagonal system has three "a" axes perpendicular to the "c" axis, both the parameters of a face and the Miller Index notation must be modified. The modified parameters and Miller Indices must reflect the presence of an additional axis. Related Discussions:- Weiss indices and miller indices. Structure and bonding in solids-crystals and glasses, Crystals and glasses Crystals and glasses Unlike a complex ion or molecule, which is a finite (often small) assembly of atoms, a solid has no fixed shape and size but can add atoms indefinit. Concept of Miller Indices or Law of Rational Indices: This law states that the intercepts of any phase of crystals along the crystallographic axis are either equal to the unit intercepts a,b,c or same simple whole number multiples of them i.e la , ma ,nc. However, the Weiss zone law is more general, and can be shown to work for all crystal systems, to determine if a direction lies in a plane. From the Weiss zone law the following rule can be derived: The direction, [UVW], of the intersection of (h 1 k 1 l 1) and (h 2 k 2 l 2) is given by: U = k 1 l 2 − k 2 l 1. V = l 1 h 2 − l 2 h 1. W = h 1
Bravais-Miller indices (hexagonal axes) In the case of a hexagonal lattice, one uses four axes, a 1 , a 2 , a 3 , c and four indices, (hkil), called Bravais-Miller indices, where h, k, i, l are again inversely proportional to the intercepts of a plane of the family with the four axes.
Lattice Planes and Miller Indices Click here for actual (non-printable) TLP pages. Note: DoITPoMS Teaching and Learning Packages are intended to be used interactively at a computer! This print-friendly version of the TLP is provided for convenience, but does not display all the content of the TLP.
The numbers used to represent a face are called Weiss indices. Miller indices may be defined as the reciprocal of the coefficients of the intercepts, expressed as integers.Thus the intercept made The miller indices are obtained by taking the reciprocal of the Weiss indices and multiplying them by LCM of the Weiss indices ,finally expressing the miller indices in the form of simple ratio eg a,b,care called miller indices