Presentation is loading. Please wait.

Presentation is loading. Please wait.

Materials Science and Metallurgy Mathematical Crystallography

Published byMarilyn Nicholson Modified over 6 years ago

Similar presentations

Presentation on theme: "Materials Science and Metallurgy Mathematical Crystallography"— Presentation transcript:

1 Materials Science and Metallurgy Mathematical Crystallography
Professor Harry Bhadeshia Lecture 1: vectors, coordinate transformations, reciprocal lattice

2

3

4

5

6

7

8

9

10

11 coordinate transformation matrix J

12 each column of (B J A) represents the components of a basis vector of A with respect to B

13

14

15

16

17

18

19

20 The reciprocal basis A*

21

22

23

24 directions: refer to real space
plane normals: refer to reciprocal space

25 to take a dot product between two vectors in any coordinate system, express one in the reciprocal basis and the other in real basis.

Download ppt "Materials Science and Metallurgy Mathematical Crystallography"

Similar presentations

Reciprocal lattice and the metric tensor

Reciprocal lattice and the metric tensor
1 3D Vector & Matrix Chapter 2. 2 Vector Definition: Vector is a line segment that has the direction. The length of the line segment is called the magnitude.

1 3D Vector & Matrix Chapter 2. 2 Vector Definition: Vector is a line segment that has the direction. The length of the line segment is called the magnitude.
Reciprocal lattice How to construct reciprocal lattice

Reciprocal lattice How to construct reciprocal lattice
2-D Geometry. The Image Formation Pipeline Outline Vector, matrix basics 2-D point transformations Translation, scaling, rotation, shear Homogeneous.

2-D Geometry. The Image Formation Pipeline Outline Vector, matrix basics 2-D point transformations Translation, scaling, rotation, shear Homogeneous.
3-D Geometry.

3-D Geometry.
Basic Math Vectors and Scalars Addition/Subtraction of Vectors Unit Vectors Dot Product.

Basic Math Vectors and Scalars Addition/Subtraction of Vectors Unit Vectors Dot Product.
CPSC 452: Lecture 1 Introduction, Homogeneous transformations and Coordinate frames.

CPSC 452: Lecture 1 Introduction, Homogeneous transformations and Coordinate frames.
Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships.

Introduction and point groups Stereographic projections Low symmetry systems Space groups Deformation and texture Interfaces, orientation relationships.
Lecture 2: Geometry vs Linear Algebra Points-Vectors and Distance-Norm Shang-Hua Teng.

Lecture 2: Geometry vs Linear Algebra Points-Vectors and Distance-Norm Shang-Hua Teng.
Part IB Materials Science and Metallurgy Course A: Metals & Alloys Professor Harry Bhadeshia Lecture 6: The Solid-State.

Part IB Materials Science and Metallurgy Course A: Metals & Alloys Professor Harry Bhadeshia Lecture 6: The Solid-State.
Lesson 4 Review of Vectors and Matrices. Vectors A vector is normally expressed as or in terms of unit vectors likewise.

Lesson 4 Review of Vectors and Matrices. Vectors A vector is normally expressed as or in terms of unit vectors likewise.
11.3 The Dot Product of Two Vectors. The dot product of u and v in the plane is The dot product of u and v in space is Two vectors u and v are orthogonal.

11.3 The Dot Product of Two Vectors. The dot product of u and v in the plane is The dot product of u and v in space is Two vectors u and v are orthogonal.
5.1 Orthogonality.

5.1 Orthogonality.
5-1 5.1 Length and Dot Product in R n Notes: is called a unit vector. Notes: The length of a vector is also called its norm. Chapter 5 Inner Product Spaces.

Length and Dot Product in R n Notes: is called a unit vector. Notes: The length of a vector is also called its norm. Chapter 5 Inner Product Spaces.
Kansas State University Department of Computing and Information Sciences CIS 736: Computer Graphics Monday, 26 January 2004 William H. Hsu Department of.

Kansas State University Department of Computing and Information Sciences CIS 736: Computer Graphics Monday, 26 January 2004 William H. Hsu Department of.
6.837 Linear Algebra Review Patrick Nichols Thursday, September 18, 2003.

6.837 Linear Algebra Review Patrick Nichols Thursday, September 18, 2003.
©College of Computer and Information Science, Northeastern University CS 4300 Computer Graphics Prof. Harriet Fell Fall 2012 Lecture 12 – October 1, 2012.

©College of Computer and Information Science, Northeastern University CS 4300 Computer Graphics Prof. Harriet Fell Fall 2012 Lecture 12 – October 1, 2012.
Chapter 2 Section 2.4 Lines and Planes in Space. x y z.

Chapter 2 Section 2.4 Lines and Planes in Space. x y z.
Chapter 3 Vectors in n-space Norm, Dot Product, and Distance in n-space Orthogonality.

Chapter 3 Vectors in n-space Norm, Dot Product, and Distance in n-space Orthogonality.
General Introduction to Symmetry in Crystallography A. Daoud-Aladine (ISIS)

General Introduction to Symmetry in Crystallography A. Daoud-Aladine (ISIS)

Similar presentations

Ads by Google