The Miller Indices are also enclosed within standard brackets (….) when one is specifying a unique surface such as that being considered here. The reciprocals of 1 and ∞ are 1 and 0 respectively, thus yielding. Miller Indices: (100) So the surface/plane illustrated is the (100) plane of the cubic crystal. Other Examples. 1. The (110) surface Miller indices are represented by a set of 3 integer numbers. Example of the (111) plane: If you want to describe the orientation of a crystal face or a plane of atoms within a crystal lattice, then there are series of steps that will lead you to its notation using Miller indices. 1. Miller Indices – Directions and Planes. Example: –(234) –[234] 22.14 -Intro to Nuclear Materials. Symmetry and Structure, Slide 33. Origin c b. a Miller_Indices of Planes, Directions - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. Miller indices, definition and examples. Derivation of Miller indices for crystal planes and directions. Examples and drawings.
Calculation of Miller indices from Miller-Bravais indices. Direction
Miller Indices for Directions •A vector r passing from the origin to a lattice point can be written as: r = r 1 a + r 2 b + r 3 c where, a, b, c → basic vectors and miller indices → (r 1 r 2 r 3) •Fractions in (r 1 r 2 r 3) are eliminated by multiplying all components by their common denominator. •[e.g. (1, ¾ ,½ ) will be expressed as (432)] Example: Let the intercepts are x = 2a, y = 3/2b, z – c. We first form the set , , 2,3 2,1 c z b y a x, Then invert it , 2 3,1 2 1 y and finally multiply by a common (factor) denomenator. Which is 6, to obtain the miller indices (3 4 6). Exercise: x = 2a, y = 3b, z = 6c (321). The indices of some important planes in a cubic crystal
Miller indices are represented by a set of 3 integer numbers. Example of the (111) plane: If you want to describe the orientation of a crystal face or a plane of atoms within a crystal lattice, then there are series of steps that will lead you to its notation using Miller indices. 1. Miller Indices – Directions and Planes. Example: –(234) –[234] 22.14 -Intro to Nuclear Materials. Symmetry and Structure, Slide 33. Origin c b. a Miller_Indices of Planes, Directions - Free download as Powerpoint Presentation (.ppt), PDF File (.pdf), Text File (.txt) or view presentation slides online. Miller indices, definition and examples. Derivation of Miller indices for crystal planes and directions. Examples and drawings. MATERIALS SCIENCE & ENGINEERING MILLER INDICES Part of A Learner s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani Materials Science and – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 4cb946-NjM0O • Miller Indices: Reciprocals of the (three) axial intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller indices. • Algorithm 1. Read off intercepts of plane with axes in terms of a, b, c 2. Take reciprocals of intercepts 3. Reduce to smallest integer values 4. Enclose in parentheses, no • To find the Miller indices of a plane, take the following steps: 1. Determine the intercepts of the plane along each of the three crystallographic directions. 2. Take the reciprocals of the intercepts. 3. If fractions result, multiply each by the denominator of the smallest fraction. 18 19. 19 Crystallographic Planesz x y a b c 4. Miller Indices (110) example a b c z x y a b c 4. 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).
MATERIALS SCIENCE & ENGINEERING MILLER INDICES Part of A Learner s Guide AN INTRODUCTORY E-BOOK Anandh Subramaniam & Kantesh Balani Materials Science and – A free PowerPoint PPT presentation (displayed as a Flash slide show) on PowerShow.com - id: 4cb946-NjM0O • Miller Indices: Reciprocals of the (three) axial intercepts for a plane, cleared of fractions & common multiples. All parallel planes have same Miller indices. • Algorithm 1. Read off intercepts of plane with axes in terms of a, b, c 2. Take reciprocals of intercepts 3. Reduce to smallest integer values 4. Enclose in parentheses, no • To find the Miller indices of a plane, take the following steps: 1. Determine the intercepts of the plane along each of the three crystallographic directions. 2. Take the reciprocals of the intercepts. 3. If fractions result, multiply each by the denominator of the smallest fraction. 18 19. 19 Crystallographic Planesz x y a b c 4. Miller Indices (110) example a b c z x y a b c 4. 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).