This document provides an introduction to crystal structure, including key discoveries and scientists in the field. It describes common crystal structures like body centered cubic (BCC), face centered cubic (FCC), and hexagonal close packed (HCP). It also discusses properties of unit cells, lattice points, primitive vectors, and Miller indices for crystal planes.

1. Introduction to Crystal structure

2. The Nobel Prize in Physics 1901
in recognition of the extraordinary services he has
rendered by the discovery of the remarkable rays
subsequently named after him
Munich University
Munich, Germany
b. 1845
d. 1923
Wilhelm Conrad Röntgen
http://nobelprize.org/nobel_prizes/physics/laureates/index.html

3. The Nobel Prize in Physics 1914
for his discovery of the diffraction of
X-rays by crystals
Max von Laue
Frankfurt-on-the-Main University
Frankfurt-on-the-Main, Germany
b. 1879
d. 1960

4. The Nobel Prize in Physics 1915
for their services in the analysis of
crystal structure by means of X-rays
Sir William Henry Bragg William Lawrence Bragg
University College
London, United Kingdom
Victoria University
Manchester, United Kingdom
b. 1862
d. 1942
b. 1890
(in Adelaide, Australia)
d. 1971

5. Basis
Lattice
Primitive
Primitive translation
vectors
Crystal axis
Translation vectors in 3D
a1∙a2xa3
is smallest
ai

6. (a) Lattice points of a space lattice in 2D
(b) Primitive cell of a space
lattice in 3D
(c) Identical atoms, sketch in on the
figure a set of lattice points, a
choice of primitive axes, a primitive
cell, and the basis of atoms d with a
lattice point.

7. Wigner-Seitz primitive cell

8. 14 Bravis lattices in three dimension

9. 14 Bravis lattices in three dimension

10. BCC metal

11. Primitive translation vector of BCC.
a1=a(x+y-z)/2
a2=a(-x+y+z)/2 a3=a(x-y+z)/2
a1+a2=? a1+a3=? a2+a3=?
a1xa2。a3=?
Primitive translation vector of FCC.
a1=a(x+y)/2
a2=a(y+z)/2
a3=a(x+z)/2
x
y
z
a1xa2。a3=?

12. FCC metal
金屬鍵沒方向性
4R=√(2) a Volume of one atom=4πR3/3
Packing fraction=[8x(1/8)+6x(1/2)] x4πR3/3/(volume of one unit cell)=0.74

13. BCC metal alloy
BCC compound

14. FCC compound (NaCl)
Sodium Chloride Structure
4 units of NaCl in each unit cube
Cl: 000; ½ ½ 0; ½ 0 ½ 0 ½ ½ Na: ½ ½ ½ ; 00 ½; 0 ½ 0; ½ 0 0
Crystals of rock salt structures:
LiH, MgO, MnO, AgBr, KCl…

15. FCC molecule crystal (CH4) 90K melting point

16. hcp
fcc
Hexagonal close packed structure (hcp)
參考Fig.21, c/a?

17. Zinc Sulfide ZnS has two major crystalline forms
zinc blende structure
Wurtzite structure
ZnSe, GaAs…..
ZnO, GaN, CdS…

18. Diamond cubic
比較zinc blende structure與diamond cubic

19. 比較(110)與(1,1,0)
dhkl=?
Index system for crystal planes
1. Find the intercepts on the axes
2. Take the reciprocal of these numbers
having the same ratio, usually the
smallest three intergers. (hkl)
Miller index
(233)

21. Coordinates and direction of axis

22. Bragg law 2d sinθ=nλ 103 to 105 planes

25. X-rays of an unknown wavelength are diffracted 43.4o by
copper (fcc), whose lattice constant a is 0.3615 nm.
Separate determinations indicate that this diffraction line
for copper is the first-order (n=1) line for d111.
(a) What is the wavelength of the x-rays?
(b) The same x-rays are used to analyze tungsten (bcc).
What is the angle, 2θ, for the second-order diffraction lines
of the d010 spacing?