Miller Indices David Holub Ahmad Asi.

Slides:

Advertisements

Similar presentations

INTRODUCTION TO CERAMIC MINERALS

Advertisements

Presentation on Semiconductor Fundamental Submitted by : MD. Jubayer Ahmed MD. Mehedi Hasan Tanvir Anjum A.S. Shakur Submitted to: Mohiuddin Munna Lecture.

Fundamental Concepts Crystalline: Repeating/periodic array of atoms; each atom bonds to nearest neighbor atoms. Crystalline structure: Results in a lattice.

Semiconductor Fundamentals OUTLINE General material properties Crystal structure Crystallographic notation Read: Chapter 1.

Lecture 2.1 Crystalline Solids. Poly-crystalline solids - Grains Mono-crystalline solids- Whiskers, Wafers.

II. Crystal Structure Lattice, Basis, and the Unit Cell

Lecture 2: Crystal Symmetry

PH0101 UNIT 4 LECTURE 2 MILLER INDICES

When dealing with crsytalline materials, it is often necessary to specify a particular point within a unit cell, a particular direction or a particular.

Intercepts  Intercepts measure where a crystal face hits a crystal axis. The location on the axes corresponding to unit lengths is arbitrary and chosen.

Crystal Structure Continued! NOTE!! Again, much discussion & many figures in what follows was constructed from lectures posted on the web by Prof. Beşire.

Wigner-Seitz Cell The Wigner–Seitz cell around a lattice point is defined as the locus of points in space that are closer to that lattice point than to.

Announcements 1)Revised Lab timings: 1-3 PM (all groups) 2) Quiz 1, 28 th Jan 2014, Tuesday 7:30 PM, WS 209, WS 213.

Lec. (4,5) Miller Indices Z X Y (100).

Solid Crystallography

Miller indices and crystal directions

ENE 311 Lecture 3. Bohr’s model Niels Bohr came out with a model for hydrogen atom from emission spectra experiments. The simplest Bohr’s model is that.

© Oxford Instruments Analytical Limited 2001 MODULE 2 - Introduction to Basic Crystallography Bravais Lattices Crystal system Miller Indices Crystallographic.

CONDENSED MATTER PHYSICS PHYSICS PAPER A BSc. (III) (NM and CSc.) Harvinder Kaur Associate Professor in Physics PG.Govt College for Girls Sector -11, Chandigarh.

Crystal Systems Unit cell: smallest repetitive volume which contains the complete lattice pattern of a crystal. Fig. 3.4, Callister & Rethwisch 8e. a,

Introduction to Solids. 3 Classes of Solids Amorphous – No long range order Polycrystalline – Order within grains Single Crystal – Regular, repeated pattern.

The indeterminate situation arises because the plane passes through the origin. After translation, we obtain intercepts. By inverting them, we get.

THE STRUCTURE OF CRYSTALLINE SOLIDS

Recall Engineering properties are a direct result of the structure of that material. Microstructure: –size, shape and arrangement of multiple crystals.

Lecture 10 (10/16/2006) Crystallography Part 3: Crystallographic Axes Numerical Notation of Crystal Faces and Atomic Planes – Miller Indices.

Cubic crystals: (a) simple cubic; (b) face-centered cubic, an atom in the center of every face, and (c) body-centered cubic. Figure

Crystallographic Axes are imaginary reference lines which often coincide with symmetry axes or normals to symmetry planes as in symmetry axes these aid.

CHE (Structural Inorganic Chemistry) X-ray Diffraction & Crystallography lecture 2 Dr Rob Jackson LJ1.16,

Types of Solids Three general types 1. Amorphous ― with order only within a few atomonic and molecular dimensions (Fig. (a)) 2. Polycrystalline ― with.

Miller Indices And X-ray diffraction

Introduction to Crystallography

Basic Crystallography 26 January 2015 Three general types of solids 1. Amorphous ― with order only within a few atomic and molecular dimensions (Fig. (a))

Solid State Physics Yuanxu Wang School of Physics and Electronics Henan University 双语教学示范课程.

Solid State Physics (1) Phys3710

EEE539 Solid State Electronics 1. Crystal Structure Issues that are addressed in this chapter include:  Periodic array of atoms  Fundamental types of.

Crystal Structure A “unit cell” is a subdivision of the lattice that has all the geometric characteristics of the total crystal. The simplest choice of.

MATERIALS SCIENCE Week 2 STRUCTURE OF MATERIALS. Why Study Crystal Structure of Materials? The properties of some materials are directly related to their.

MSE 630 Introduction to Solid State Physics Topics: Structure of Crystals classification of lattices reciprocal lattices bonding.

W.D. Callister, Materials science and engineering an introduction, 5 th Edition, Chapter 3 MM409: Advanced engineering materials Crystallography.

Crystallographic Points, Directions, and Planes. ISSUES TO ADDRESS... How to define points, directions, planes, as well as linear, planar, and volume densities.

ENGR-45_Lec-04_Crystallography.ppt 1 Bruce Mayer, PE Engineering-45: Materials of Engineering Bruce Mayer, PE Licensed Electrical.

PHY1039 Properties of Matter Crystallography, Lattice Planes, Miller Indices, and X-ray Diffraction (See on-line resource: )

Crystalline Solids :-In Crystalline Solids the atoms are arranged in some regular periodic geometrical pattern in three dimensions- long range order Eg.

CRYSTAL STRUCTURE.

Last lecture Introduction to materials science and engineering Atoms / electron configuration.

ESO 214: Nature and Properties of Materials

Properties of engineering materials

DESCRIBING CRYSTALS MATHEMATICALLY Three directional vectors Three distances: a, b, c Three angles:   ll points can be described using coordinate.

Crystal Structure NaCl Well defined surfaces

Properties of engineering materials

Crystallographic Points, Directions, and Planes.

Semiconductor Fundamentals

CHAPTER 3: STRUCTURE OF CRYSTALLINE SOLIDS

Groups: Fill in this Table for Cubic Structures

Concepts of Crystal Geometry

Crystal Structure of Solids

Semiconductor Processing Single Crystal Silicon

Crystal Structure Continued!

Lecture 2.1 Crystalline Solids.

Crystallographic Points, Directions, and Planes.

X-ray Neutron Electron

Lecture 2.1 Crystalline Solids.

Chapter 1 Crystallography

CRYSTAL STRUCTURE ANALYSIS

MSE420/514: Session 1 Crystallography & Crystal Structure

Basic Crystallography

MILLER PLANES Atoms form periodically arranged planes Any set of planes is characterized by: (1) their orientation in the crystal (hkl) – Miller indices.

MODULE 2 - Introduction to Basic Crystallography

William Hallowes Miller

Presentation transcript:

Miller Indices David Holub Ahmad Asi

Introduction Developed by William Miller – 1839 Primarily to describe crystalline structures Indices used to reference orientation of planes Consist of positive & negative integers Help determine material properties

Examples of Crystal Structures

Definitions Lattice Parameters Isotropic Anisotropic Lengths of the edges of a lattice, defined by distance Isotropic Uniform in all orientations, regardless of reference point Anisotropic Interactive properties are dependent on incident orientation Face-Centered Cubic Cubic lattice with atoms on each face Body-Centered Cubic Cubic lattice with atom in center

Nomenclature Indices expressed as integers x, y, z axis correspond to lengths a, b, c a, b, c, are inverted to find h, k, l Negatives expressed with ‘bar’: 1, 2, 3, etc. ( ) Brackets represent single planes { } Brackets represent family of planes

Determine Ratios Evaluate axis intercepts Invert to find: h = 1/3 Equal to 1/h, 1/k, 1/l Invert to find: h, k, l h = 1/3 k = 1/2 l = 1/2

Realization of Indices Find smallest integers with same ratio h = 1/3, k = 1/2, l = 1/2 h → 2, k → 3, l → 3 Record index (hkl) = (233)

Planes by Symmetry Planes by symmetry are a ‘family’ Therefore, {100} consists of (100), (010), (001) For an isotropic material, (100) is only defined by reference axis

Negative Indices Leave sign of negative intercept Find ratio as normal Denote negative with ‘bar’

Example of Indices

Applications Determine material properties Semi-conductor properties depend on structure Structure affects energy band-gap Band-gap determines wavelengths absorbed/emitted Manipulate lattice structure (doping)

References CRYSTAL STRUCTURE PART II. (n.d.).http://www.ocf.berkeley.edu/. Retrieved September 13, 2011, from www.ocf.berkeley.edu/~mwg/lab/Miller.pdf DoITPoMS - TLP Library Lattice Planes and Miller Indices. (n.d.). Dissemination of IT for the Promotion of Materials Science (DoITPoMS). Retrieved September 13, 2011, from http://www.doitpoms.ac.uk/tlplib/miller_indices/index.php Ferry, D., Vasieska, D., & Klimeck, G. (n.d.). Crystal Directions, Wave Propagation and Miller Indices. nanohub. Retrieved September 13, 2011, from nanohub.org/resources/9137/download Solids / Crystal Structure and Solution. (n.d.).Chemconnections.org. Retrieved September 13, 2011, from chemconnections.org/crystals/pdf/crys-solids.pdf Streetman, B. G., & Banerjee, S. K. (2006). Solid State Electronic Devices (6a. ed.). Upper Saddle River, New Jersey: Prentice-Hall.