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