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MSE 110 Introduction to Materials
Characterization: Crystal Structure and X-ray
Diffraction of Materials
Lecture 1
Fall 2015
Today:
Syllabus
Office Hours / Recitation Sections
Textbook(s): Pecharsky, Wasada, Cullity&
Origin of phemomenonBackground
Syllabus On-line:
CCLE
Textbooks
On-line On-line Paperback or hardcover
Lecture Topics and Reading List : (Cullity chapters)
Introduction, Electromagnetic radiation - Ch. 1 Properties of x-rays: x-ray spectrum - Ch. 1 Properties of x-rays: Absorption and Filters - Ch. 1 Crystallography: Unit Cell, Cell Geometry - Ch. 2 Crystallography: Crystal Systems - Ch. 2 Crystallography: Crystal Structures, Defects - Ch. 2 Reciprocal space - Ch. 2 and Appendix 1/ Review for Quiz QUIZ / Stereographic Projection - Ch. 2 Stereographic Projection cont. - Ch. 2 Elements of diffraction physics: Geometry - Ch. 3, 4 and 5 Elements of diffraction physics: Scattering - Ch. 4 Structure Factor Calculations - Ch. 4 Determination of Crystal Structure: Powder Method - Ch. 7, 10 and 13/ Review for Midterm MIDTERM Determination of Crystal Structure: Order-Disorder Transformations - Ch. 10 Analysis of Epitaxial Layers - Ch. 17, 19, handout Orientation of Single Crystals: Laue Method - Ch. 8 and 16 Qualitative Chemical Analysis by XRD: Phase Identifications Ch. 9 Quantitative Chemical Analysis by XRD: Determination of Phase Diagrams and Phase Analysis Ch. 11 and 12 Special Topics: Internal Stresses, Crystallographic Texture - Ch.14, 15 / Review for the Final
Syllabus
Grade Distribution:
Final Exam: 35%
Mid-term Exam: 30% (2 hr)
Quiz: 15% (1 hr)
Homework 20%
Background MSE 104
Length scales: nm, , lattice, polycrystal, amorphous, single crystal
e-m waves, constructive / destructive interference
MSG
Why 110? Understand basic properties of crystals
Points, directions, PLANES
XRD is used among all MSE specialties Responsible for advances in may scientific fields
Non-destructive
Evolving field
Properties of new classes of materials
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?
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Examples
Metals:
Strain hardening
Defects
Alloys vs compounds
Order-disorder transitions
Polymers
Structure
Degree of crystallinity
Examples
Semiconductors Structural perfection Alloy Composition (Bandgap Engineering)
Ceramics Quantitative multi-phase analysis Glasses: non-crystalline, s.r.o.
Bio-materials W&C Double Helix deduced from XRD measurement
Name of crystallographer?
Quasicrystals
Historical background: X -ray diffraction
Mid 1850s Cathode rays (electrons) were a hot topic
Electrons could be extracted (freed) from a cathode placed in an evacuated container (~ 1854)
By 1895, properties of electrons fairly well understood Charged (negative)
could be extracted from a window in the tube
Decayed exponentially in air Experiments worked best in a vacuum
William Crookes and the "Crookes Tube.
In a "Crookes" tube, a negatively biased electrode, called the cathode, emits cathode rays (electrons) which accelerate toward the anode. Many cathode rays miss the anode and instead strike the glass end of tube, causing it to fluoresce.
(2008 Copyright James H. Wittke, Northern Arizona University)
Historical Background
Discovery of x-rays Wilhelm Conrad Rntgen (Roentgen)
November 8, 1895:
Studied e- interactions with matter
Observed a fluorescent screen illuminate when electrons were generated in a Crookes tube
Roentgen
Observation: Screen was too far away for these to be electrons
Some unknown ray: X-ray
Other observations Exposed photographic film
Could see brass key in wooden box
Mrs. Roentgens contribution
Nobel Prize in Physics (1901)
A different era would it be any different today?
Lack of understanding: pathological science - (N-rays)
Uncritical analysis: OPERA experiment reports anomaly in flight time of neutrinos from CERN to Gran Sasso (Italy)
Radiography medical applications
First applications were not so scientific
History lesson continues
Wien showed that ~ and confirmed e-m nature
Not everyone agreed
Visible light could be diffracted
Scattering sites interspaced ~ wavelength
Could x-rays be diffracted?
Roentgen couldnt do it on his own
History Lesson
1912 Roentgen visits Munich Labs of Debye, Laue, Summerfeld
P.P. Ewald was Summerfeld Ph.D. student Modeled crystal as small oscillators (to
represent atoms) with ~ 1 spacing Laue: since x-rays have 1 , atoms may be a 3-
dimensional diffraction grating for x-rays
Summerfeld (senior guy) thought atomic movement was too great (> 0.3 )
Rubber balls and springs
And more history
Laue has some help
Knipping and Friendrich
Knipping: just finished Ph.D. thesis fun to help
Friedrich: good with setting up apparatus, did experiments on the sly
X-rays CuSO4 || (film)
X-rays (film) || CuSO4 (Worked both ways)
Nobel Prize 1914
Rest of world notices
W.H. Bragg (Leeds U.) (Father)
W.L. Bragg (Cambridge) (Son)
Nobel Prize 1915
Extended ideas about phenomenon
Constructive interference
Braggs Law
= radiation wavelength
d = distance between planes
B = angle between source and plane
Bdn sin2
B
Properties of X-rays
X-rays are electromagnetic radiation
Much shorter wavelength than visible light
1 = 10-10m, 1 nm = 10 = 10-9m
X-ray wavelengths are in the range 0.5 2.5 .
Wavelength of visible light ~ 3900-7500
Properties of Electromagnetic Waves
t
xAE
2sin
A = wave amplitude = wavelength = frequency c = velocity of light = 3x108 m/s Photon energy: h= 6.636x10-34 Js
c
hE
X-ray Spectrum How x-rays are produced
[Roentgen] X-rays are produced when electrically charged particles (electrons) decelerate
The kinetic energy of the electrons is equal to the product of the accelerating voltage (V) and charge on the electron (e)
Most of the kinetic energy of the electrons striking the target is converted into heat, less than 1% transformed into x-rays.
2
2
1mveVEK
e = electron charge (1.610-19C) EK = kinetic energy V = applied voltage m = mass of the electron (9.1110-31kg) v = electron velocity (m/sec)
Continuous X-ray Spectrum
Results from the deceleration of electrons at the target
Each electron loses energy differently (all at once or in differing increments)
)(
102.1)(
4
voltsVSWL
White radiation
Continuous radiation
Bremsstrahlung
Continuous radiation spectrum
The total x-ray energy emitted per second depends on the atomic number Z of the target material and on the x-ray tube current. This total x-ray intensity is given by
Aproportionality constant
itube current (measure of the number of electrons per second striking the target)
mconstant 2
mAiZVI
Characteristic Radiation
In addition to the continuous radiation spectrum, there are sharp intensity peaks that occur. The wavelength (or energy) of these peaks corresponds to the target material
Referred to as characteristic (of the target) radiation
Physics of characteristic radiation
Incident electron with sufficient energy knocks K (or L or) electron out of shell
Cascade of other electrons to fill shell releases energy
CANNOT gain energy: Energy (Kedge) > Energy (K,, etc)
Kedge
The shell model of the atom, is useful for understanding the origin of the characteristic lines
Atomic Energy Transitions
Atomic Energy Transitions
Atomic Energy Transitions
Transitions
Characteristic Radiation
K lines are usually most useful for x-ray applications of materials
I(k1) 2I(k2) Twice as many states
I(k) 5I(k)
Intensity of Characteristic Spectrum
nkVVBiI
I = Intensity
i = Electron current applied to target
V = Voltage between electron source and target
Vk = Voltage that corresponds to Kedge energy
n 1.5, B is target-dependent constant
Importance of characteristic radiation
K lines provide monochromatic source to make diffraction measurements feasible and relatively easy to interpret
Line widths are on the order of 0.001
width usually means
FWHM: Full width at half maximum (intensity)
Other aspects of characteristic radiation
Moseleys Law
http://chimie.scola.ac-paris.fr/sitedechimie/hist_chi/text_origin/moseley/Moseley-article.htm
Shorter wavelength (higher frequency []) for higher Z target
= 1 for K = 7.4 for L
ZC
K
L
Source of characteristic radiation
Roentgen experiment
Electrons decelerate and produce photons (-x-rays)
His discovery: serendipitous
Components to make a commercial x-ray tube are based on the principles established with Roentgens experiment
X-ray source (tube)
Basics:
Source of electrons: Filament
Acceleration of electrons to target: High Voltage
Produce characteristic radiation: Target
X-ray Tube Details
X-Ray Tube Components
Filament Low work function, high melting point metal
Tungsten (W)
Target Elemental metal
High thermal conductivity
More than one element more than one characteristic spectrum
High Voltage Electrical isolation is important
Body of x-ray tube is an insulator Glass or ceramic
Other tube details
Vacuum
Electrons absorb in air, vacuum maximizes electron current to the target
Water cooling
X-ray production is very inefficient (99% heat)
Target melts w/o cooling
Windows
X-rays need to exit tube without excessive absorption (next section on absorption)
Lightest solid, non-porous, relatively stable element
Beryllium