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.
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
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.
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
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…
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)
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?
