lecture 9. defects in materials - welcome to aml...
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AML 883 Properties and selection of engineering materials
LECTURE 9. Defects in materials
M P GururajanEmail: [email protected]
Room No. MS 207/A3 Phone: 1340
Defects!
Crystals are like people; only defects make them interesting!
Attributed to F C Frank Also in Barsoum's book, Introduction to
Ceramics, I think
Defects in metals and ceramics
● What are defects?
Any deviation from the crystalline state
Also, impurities!
● How to classify defects?
0,1, 2D, and, 3D defects
● Point defects: vacancies, interstitials, substitutional impurities, ...
● Line defects: dislocations, ...● Planar defects: grain boundaries, twin
boundaries, stacking faults, ...● Volume defects: voids, precipitates, ...
Presence of defects
● Vacancies – always present equilibrium● Impurities and second phases – almost always
present● Dislocations – hard not to have● Grain boundaries, voids – can be avoided
Point defects
● Vacancies: missing atoms
● Can you “see” vacancies?
● Or, for that matter, can you “see” atoms?
● Image courtesy: wiki
Yes!
How? Using what technique were atoms first seen?
Field Ion Microscopy
● First time atoms were seen!
● E W Mueller● Tip: positive potential
and low temperatures ● Imaging gas● Image courtesy: wiki
FIM
● FIM: tip schematic● Polarised gas atom –
attracted by the field● Thermalised● Ionised● Leave the tip for
screen● Image courtesy: wiki
FIM image of Tungsten tipRezeq et al J Chem Phys 2006
Vacancies – direct observation
● High resolution transmission electron microscopy (HRTEM)
● Images of carbon vacancies in irradiated graphene layer
● Hashimoto et al, Nature (2004)
One atom layer – seeing with naked eye!
● Graphene in transmitted light
● Visible because it absorbs 2.3% of light
● You cannot see atoms – but the layer Yes!
● Image courtesy: wiki
Why vacancies?
● Vacancies are equilibrium defects● Any temperature above zero, it is favourable for
the crystal to have vacancies. Why?● Bondbreaking model – Energy of creation of
vacancies is positive● Entropy contribution to the free energy due to
the distribution of a given number of vacancies on the atomic sites – increases with increasing temperature
Free energy and vacancies
● Schematic (based on Porter and Easterling) explaining the equilibrium nature of vacancies!
● Vacancies play a key role in diffusion, creep, movement of dislocations etc
Vacancy concentration
n /N=exp −H f /RT
N – Avogadro's numberR – Universal gas constantT – Absolute temperature
H f Enthalpy of formation of vacancies
Arrhenius plot
Schematic vacancy contration versus temperature plots (Courtest: H Foell
Point defects
Image courtesy: wiki
Point defects
● Vacancies● Substitutional● Interstitial● Frenkel pair – A vacant site with the atom in the
interstitial site● Schottky pair – Missing atoms● Antisites
Point defects and strength
● Strengthening mechanisms: substitutional or interstitial defects distort their surroundings (leading to strengthening of alloys as compared to their pure metallic counterparts)
● Contrary to popular belief, the alloyed pleasures are many – S Ranganathan (FIM of grain boundaries)
Dislocations● Line defects● Almost always are present● Can be seen using TEMs● Edge and Screw dislocations Easy to
understand classification● Most in materials have charactersitics of both
types – mixed● Dislocations also distort the lattice – hence can
be expected to strengthen – but that is only one part of the story, as you will see
Dislocations – TEM image
Image Courtesy: H Foell
Dislocations – TEM image
Image Courtesy: H Foell
Edge dislocation
● Courtesy: H Foell
Screw dislocation
● Courtesy: H Foell
Burgers vectors
Image courtesy: wiki
Burgers vector
● Vector that represents the magnitude and distortion lattice
● Buergers vector and dislocation lineParallel – screw dislocationPerpendicular – edge
● Mixed dislocations – angle continuously changes, of course!
Grain boundaries
● Zinc grains and boundaries
● Differently oriented crystallites in space
● Sources and sinks of defects
● Can also move● Image courtesy: wiki
Grain boundaries
● HRTEM image in strontiumtitanate
● Grain boundaries – high angle and low angle
● Image courtesy: C Carter, NANOAM, at mit website
Dislocations and plastic flow
When a large force is applied to a crystal two things may happen; the atoms in the crystal may slide past one another; and they may pull part.
The purpose of this book is to describe the theory of the first of these processes. This does not
mean that the theory of plastic flow in crystals is now complete, for it is still all too easy to confound it by asking certain questions, even some that are
apparently of a very simple kind.
Continued
Dislocations and plastic flow
Neverless, a few permanent features have now been established in the theory; even if all the
devious convolutions of the action have not yet been sorted out the main characters in the plot are
plain enough. The theory of dislocations constitutes an advance in the degree of precision
with which we can describe the structure and properties of matter in the solid state.
A H Cottrell, in his preface to his classic Dislocations and plastic flow in crystals (1953)
Dislocations and plastic flow
● Discrepancy between observed strengths and calculated ideal strengths
● Mystery – solved by G I Taylor, E Orowan and M Polanyi
● Dislocations move easily through the crystal – by a process called slip – which is compared to the movement of heavy carpet by pushing a fold across or that of a caterpillar
G I Taylor
● Image courtesy: wiki● MIT – Brenner –
Classical physics through the work of G I Taylor
E Orowan
● Image courtesy: iMechanica
M Polanyi
● Image courtesy: wiki
Dislocation movement
Image courtesy: Lecture notes of Leonid Zhiglei
Slip
Image courtesy: University of Cambridge (Go there for movies too – of bubble rafts)
What is the idea?
● Theoretical strength – calculated using the breaking point of springs
● In crystals, dislocations exist – some sort of broken springs are already in place
● It is just a question of sliding them a bit!