Compound A3B (like Cu3Au) has cubic lattice. In one cubic unit cell, A atoms are at
the face centers of the cubic, and B atoms are the corners of the cubic. The
radius of A is 0.13 nm and the radius of B is 0.16 nm. A and B atoms are in close
contact with
II Crystalline State
Crystallography
The theory of spatially periodic, perfectly long-range ordered
patterns. It provides a framework for categorizing and specifying
the structure of crystalline matters.
1
Crystallography
Crystallography provides a stand
MSE350: Structure of Materials
What is Structure of Materials ?
Structure: the way that something is built, arranged, or
organized (by parts or elements)
Something: Materials Crystalline State
Noncrystalline state
Liquid-crystalline state
Parts or eleme
II. 2: 3D Crystallography
Learning Objectives
A: Unique 3D Symmetry Elements/Operations
B: 32 Point Groups
C: 14 Bravais Lattice, Lattice Plane/Directions
D: 230 Space Group
E: International Tables for 3D Crystallography
1
II.2.A: Unique 3D Symmetry Eleme
1. List concrete admixtures. What can be done in hot weather to help retard concrete rapid setting
times? Explain. What are the commonly used concrete admixtures? Explain the purpose any
three of them.
a. Air-entraining agents
b. Retarders
c. Water reduce
VI- Microstructures
Generation of microstructures
3) Composite Microstructures
Composite: It is an integral object consisting of distinct parts (materials)
The main reason for making a composite material is to achieve simultaneously
various combinations o
IV- Imperfections in Ordered Media
Surface and Interface
Learning Objectives
Surfaces
The external boundaries between a material and a gaseous phase or a vacuum
-Surface Unit Cell
-Surface Defects
Interfaces
The Internal boundaries between condensed phase
V- Non-Crystalline State
Learning Objectives
Fabrication of non-crystalline (amorphous) phase of
a crystalline material.
Glass transition temperature
Characterization of short range atomic ordering in
non-crystalline state using Pair correlation function,
VI- Microstructures
Generation of microstructures
2) Transformation Microstructures
Phase transformation: Occurs when a system is moved far from thermodynamic equilibrium
i) Solidification (liquid to solid)
Microstructures
ii) Solid to solid transformatio
II. 2 The Crystallography of three dimensions
How to use Point Group?
Point group:422
International Table of Crystallography
Stereographic Projection
What do these two-fold axes mean?
If the rotation symbol is on the edge of
this circle, it means there is
III X-ray Diffraction
Learning Objectives
Determination of Unit cell dimension (lattice
parameter) of cubic substances
Indexing X-ray powder patterns using Braggs Law
Determination of Interplanar distance (dhkl) from
reciprocal space
Identification of cry
II.1.D: Plane Groups
Plane point groups: the set of all possible self-consistent point symmetries (group) found in
2D crystals (periodic patterns)
No translation symmetry involved, but under the constrain of
translation symmetry (no 5-fold rotation, no g
Problem 1:
1a): All the possible elements are the rota4ons of 0o, 120o, 240o, 90o, 180o, 270o.
Because the rota4on of 120o the rota4on of 90o = the rota4on of 210o , which is not one of
the elements men4oned
Problem 1: There is a screw symmetry 31 along z axis [0 0 1] and intercep>ng with the
origin (x=0, y = 0, z=0); and along z axis there is a transla>on symmetry with a
periodicity of 9.0 . For a posi>on with
Problem 1 (50 points):
2D boron nitride (BN) has honeycomb structure with boron and nitride atoms at different
locations as shown in the following figures (red: N, blue: B)
1) Plot the conventional unit cell in the enlarged figure at bottom.
2) Indicate t
Problem 1:
Hint: You need to write down the descriptions of all elements. Then you can check whether all these
elements with the operation satisfy all of the group axioms: closure, associativity, identity and
invertibility.
For example, for 1 b):
In 2D
p4mm
Quiz 2 (Open book, 10 Minutes, 10 Points)
A 2D crystal with plane group p4mm (No. 11) with lattice
constant of 6 . It has two types of atoms, A and B
A in site 2c,
B in site 4f with x = 1/3
(1) To plot one unit cell with A and B atoms inside one unit
Review on Crystallography Structures
Some Important Concepts
What is symmetry?
Individual(simple) symmetry operation: translation, rotation,
reflection, inversion(only in 3D)
Each operation has its symmetry elements: translation vector, rotation axis(cent
II. 3: Hard Sphere Packing and Crystal Structure
Crystal Structure Description
Learning Objectives
Structure description by close packing
Cubic close packing
Hexagonal close packing
Octahedral and tetrahedral sites
Structure description by space filling p
II.2.D: 230 Space Group
The 230 Space Groups
The combination of 14 Bravais lattices with 32 point groups, when translational
symmetry elements are included (glide planes and screw axes), gives rise to 230
possible 3-D patterns or space groups
Evgraf Stepa
IV- Imperfections in Ordered Media
Classification of crystalline imperfections
Classification can be made on the basis of their geometry or dimensionality
Point defects
0 Dimension
Line defects
1 Dimension
Surface/ Interface defects
2 Dimension
Volume
II. 2 The Crystallography of three dimensions
How to use Point Group?
Point group:422
International Table of Crystallography
Stereographic Projection
What do these two-fold axes mean?
If the rotation symbol is on the edge of
this circle, it means there is