STRUCTURE OF MATERIALS The Key to its Properties A ...
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STRUCTURE OF MATERIALSSTRUCTURE OF MATERIALS
The Key to its Properties
A A MultiscaleMultiscale PerspectivePerspective
Anandh SubramaniamMaterials and Metallurgical Engineering
INDIAN INSTITUTE OF TECHNOLOGY KANPURINDIAN INSTITUTE OF TECHNOLOGY KANPURKanpur-
208016Email: [email protected]
http://home.iitk.ac.in/~anandh
Jan 2009
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Properties of Materials
The Scale of “Microstructures”
Crystal Structures
+ Defects
Microstructure
With Examples from the Materials World
OUTLINEOUTLINE
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PROPERTIES
Structure sensitive Structure Insensitive
E.g. Yield stress, Fracture toughness E.g. Density, Elastic Modulus
Structure Microstructure
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What determines the properties?
Cannot just be the composition!
Few 10s of ppm
of Oxygen in Cu can degrade its conductivity
Cannot just be the amount of phases present!
A small amount of cementite
along grain boundaries can cause the material to have poor impact toughness
Cannot just be the distribution of phases!
Dislocations can severely weaken a crystal
Cannot just be the defect structure in the phases present!
The presence of surface compressive stress toughens glass
Composition
Phases & Their
Distribution
Defect Structure
Residual Stress
[1]
[1] Metals Handbook, Vol.8, 8th Edition, ASM, 1973
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Nucleus Atom Crystal Microstructure Component
Defects
Length Scales Involved
Unit Cell* Crystalline Defects Microstructure Component
*Simple Unit Cells
AngstromsDislocation Stress fields
→ Nanometers Microns Centimeters
Grain Size
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Atom Structure
Crystal
Electro-magnetic
Microstructure Component
Thermo-mechanical Treatments
Phases Defects+
• Casting• Metal Forming• Welding• Powder Processing• Machining
• Vacancies• Dislocations• Twins• Stacking Faults• Grain Boundaries• Voids• Cracks
+Residual
Stress
Processing determines shape and microstructure of a component
• Crystalline• Quasicrystalline• Amorphous
• Ferromagnetic• Ferroelectric• Superconducting
Property based
Structure based
• Avoid Stress Concentrators• Good Surface Finish
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Atom Structure
Crystal
Electro-magnetic
Microstructure Component
Thermo-mechanical Treatments
Phases Defects+
• Casting• Metal Forming• Welding• Powder Processing• Machining
• Vacancies• Dislocations• Twins• Stacking Faults• Grain Boundaries• Voids• Cracks
+Residual
Stress
Processing determines shape and microstructure of a component
• Crystalline• Quasicrystalline• Amorphous
• Ferromagnetic• Ferroelectric• Superconducting
Property based
Structure based
• Avoid Stress Concentrators• Good Surface Finish
& their distribution
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METALSEMI-METAL
SEMI-CONDUCTORINSULATOR
GAS
BAND STRUCTURE
AMORPHOUS
ATOMIC
STATE / VISCOSITY
SOLID LIQUIDLIQUID
CRYSTALS
QUASICRYSTALS CRYSTALSRATIONAL APPROXIMANTS
STRUCTURE
NANO-QUASICRYSTALS NANOCRYSTALS
SIZE
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Atom Structure
Crystal
Electro-magnetic
Microstructure Component
Why is BCC Iron the stable form of Iron at room temperature and not the FCC form of Iron?
1 Atm
G vs
T showing regions of stability of FCC and BCC Iron
(Computed using thermo-calc software and database developed at the Royal Institute of Technology, Stockholm)The Structure of Materials, S.M. Allen & E.L. Thomas, John Wiley & Sons, Inc. New York, 1999.
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Microstructure
Phases Defects+
• Vacancies• Dislocations• Twins• Stacking Faults• Grain Boundaries• Voids• Cracks
+Residual
Stress
This functional definition of “microstructure”
includes all lengthscales
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Microstructure
Phases Defects+
• Vacancies• Dislocations• Twins• Stacking Faults• Grain Boundaries• Voids• Cracks
+Residual
Stress
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Microstructure
Phases Defects+
• Vacancies• Dislocations• Twins• Stacking Faults• Grain Boundaries• Voids• Cracks
+Residual
Stress
Microstructural
Defects (Crystalline)
Component
• Vacancies• Dislocations
• Phase Transformation• Voids• Cracks
•
Stress corrosion cracking•
+ Residual Surface Compressive Stress
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CRYSTAL STRUCTURESCRYSTAL STRUCTURES
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Crystal = Lattice (Where to repeat)
+ Motif (What to repeat)
Crystal = Space group
(how to repeat)
+ Asymmetric unit
(Motif’: what to repeat)
+ =
Unit cell of BCC lattice
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Cubic
Tetragonal
Triclinic
Monoclinic
Orthorhombic
Progressive lowering of symmetry amongst the 7 crystal systems
Hexagonal
Trigonal
Incr
easi
ng sy
mm
etry
Arrow marks lead from supergroups to subgroups
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1.
Cubic Crystalsa = b= c
=
=
= 90º
• Simple Cubic (P)
• Body Centred
Cubic (I) –
BCC
• Face Centred
Cubic (F) -
FCC
FluoriteOctahedron
Pyrite Cube
m23
m4 432, ,3m 3m,4 23, groupsPoint
[1] http://www.yourgemologist.com/crystalsystems.html[2] L.E. Muir, Interfacial Phenomenon in Metals, Addison-Wesley Publ. co.
[1] [1]Garnet
Dodecahedron
[1]
Vapor grown NiO crystal
[2]
Tetrakaidecahedron(Truncated Octahedron)
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(The symmetry of) Any physical property of a crystal has at least the symmetry of the crystal
Crystals are anisotropic with respect to most properties
The growth shape of a (well grown) crystal has the internal symmetry of the crystal
Polycrystalline materials or aggregates of crystals may have isotropic properties (due to averaging of may randomly oriented grains)
The properties of a crystal can be drastically altered in the presence of defects (starting with crystal defects)
Crystals and Properties
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0D (Point defects)
CLASSIFICATION OF DEFECTS BASED ON DIMENSIONALITY
1D (Line defects)
2D (Surface / Interface)
3D (Volume defects)
Vacancy
Impurity
Frenkel
defect
Schottky
defect
Dislocation Surface
Interphase
boundary
Grain
boundary
Twin
boundary
Twins
Precipitate
Faulted
region
Voids / Cracks
Stacking
faults
Disclination
Dispiration
Thermal vibration
Anti-phase
boundaries
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0D (Point defects)
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0D (Point defects)
Vacancy
Impurity
Frenkel
defect
Schottky
defect
Non-ionic crystals
Ionic crystals
Imperfect point-like regions in the crystal about the size of 1-2 atomic
diameters
Interstitial
Substitutional
Other ~
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Vacancy
Missing atom from an atomic site Atoms around the vacancy displaced Tensile stress field produced in the vicinity
Tensile Stress Fields
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Impurity
Interstitial
Substitutional
SUBSTITUTIONAL IMPURITY
Foreign atom replacing the parent atom in the crystal
E.g. Cu sitting in the lattice site of FCC-Ni
INTERSTITIAL IMPURITY
Foreign atom sitting in the void of a crystal
E.g. C sitting in the octahedral void in HT FCC-Fe
Compressive stress fields
Tensile Stress Fields
Compressive Stress Fields
Relative size
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Interstitial C sitting in the octahedral void in HT FCC-Fe
rOctahedral
void
/ rFCC
atom
= 0.414
rFe-FCC
= 1.29 Å
rOctahedral
void
= 0.414 x 1.29 = 0.53 Å
rC
= 0.71 Å
Compressive strains around the C atom
Solubility limited to 2
wt% (9.3 at%)
Interstitial C sitting in the octahedral void in LT BCC-Fe
rTetrahedral
void
/ rBCC
atom
= 0.29
rC
= 0.71 Å
rFe-BCC
= 1.258 Å
rTetrahedral
void
= 0.29 x 1.258 = 0.364 Å
► But C sits in smaller octahedral void-
displaces fewer atoms
Severe
compressive strains around the C atom
Solubility limited to 0.008
wt% (0.037 at%)
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Equilibrium Concentration of Vacancies
Formation of a vacancy leads to missing bonds and distortion of
the lattice
The potential energy (Enthalpy) of the system increasesWork required for the formaion
of a point defect →
Enthalpy of formation (Hf
)
[kJ/mol or eV/defect] Though it costs energy to form a vacancy its formation leads to
increase in configurational entropy above zero Kelvin there is an equilibrium number of vacancies
Crystal Kr Cd Pb Zn Mg Al Ag Cu NikJ / mol 7.7 38 48 49 56 68 106 120 168
eV / vacancy 0.08 0.39 0.5 0.51 0.58 0.70 1.1 1.24 1.74
G = H
T S ln( )ConfigS k
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T (ºC) n/N
500 1 x 1010
1000 1 x 105
1500 5 x 104
2000 3 x 103
Hf
= 1 eV/vacancy= 0.16 x 1018
J/vacancyG (G
ibbs
free
ene
rgy)
n (number of vacancies)
Gmin
Equilibriumconcentration
G (perfect crystal)
Certain equilibrium number of vacancies are preferred at T > 0K
Vacancies play a role in:
Diffusion
Climb
Electrical conductivity
Creep etc.
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1D (Line defects)
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2G
m
The shear modulus of metals is in the range 20 –
150 GPa
DISLOCATIONS
Actual shear stress is 0.5 –
10 MPa
I.e. (Shear stress)theoretical
> 100 * (Shear stress)experimental
!!!!
The theoretical shear stress will be in the range 3 –
30 GPa
Dislocations weaken the crystal
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EDGE
DISLOCATIONS
MIXED SCREW
Usually dislocations have a mixed character and Edge and Screw dislocations are the ideal extremes
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Motion of Edge
dislocation
Conservative (Glide)
Non-conservative (Climb)
For edge dislocation: as b
t → they define a plane → the slip plane Climb involves addition or subtraction of a row of atoms below the
half plane► +ve
climb = climb
up → removal of a plane of atoms
► ve
climb = climb
down → addition of a plane of atoms
Motion of dislocationsOn the slip plane
Motion of dislocation
to the slip plane
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Mixed dislocations
b
tb
Pure EdgePure screw
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Slip
Role of Dislocations
FractureFatigue
Creep Diffusion (Pipe)
Structural
Grain boundary
(low angle)
Incoherent Twin
Semicoherent
Interfaces
Disc of vacancies ~ edge dislocationCreep
mechanisms in crystalline materials
Dislocation climb
Vacancy diffusion
Cross-slip
Grain boundary sliding
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2D (Surface / Interface)
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Grain Boundary
The grain boundary region may be distorted with atoms belonging to
neither crystal The thickness may be of the order of few atomic diameters The crystal orientation changes abruptly at the grain boundary In an low angle boundary the orientation difference is < 10º In the low angle boundary the distortion is not so drastic as the
high-angle boundary → can be described as an array of dislocations
Grain boundary energy is responsible for grain growth on heating ~ (>0.5Tm
) Large grains grow at the expense of smaller ones The average no. of nearest neighbours
for an atom in the grain
boundary of a close packed crystal is 11
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Type of boundary Energy (J/m2)Grain boundary between BCC crystals 0.89Grain boundary between FCC crystals 0.85Interface between BCC and FCC crystals 0.63
Grain boundaries in SrTiO3
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Twin Boundary
The atomic arrangement on one side of the twin boundary is related to the other side by a symmetry operation (usually a mirror)
Mirror twin boundaries usually occur in pairs such that the orientation difference introduced by one is restored by the other
The region between the regions is called the twinned region
Annealing twins (formed during recrystallization)
Deformation twins (formed during plastic deformation)
Twin
[1] Transformations in Metals, Paul G. Shewmon,McGraw-Hill Book Company, New York, 1969.
Annealing twins in Austenitic Stainless Steel
[1]
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Twin boundary in Fe doped SrTiO3
bicrystals
(artificially prepared)
[1] S. Hutt, O. Kienzle, F. Ernst and M. Rühle, Z Metallkd, 92 (2001) 2
Twin plane
Mirror relatedvariants
High-resolution micrograph
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Grain size and strength
dk
iy y
→ Yield stress i
→ Stress to move a dislocation in single crystal
k → Locking parameter (measure of the relative
hardening contribution of grain boundaries)
d → Grain diameterHall-Petch
Relation
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Defects:Defects:
Further EnquiryFurther Enquiry
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Random
DEFECTS
Structural
Based onorigin
• Vacancies• Dislocations• Ledges
The role played by a random defect is very different from the role played by a structural defect in various phenomenon
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b
2h2
Low Angle Grain Boundaries
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No visible Grain Boundary
2.761 Å
Fourier filtered image
Dislocation structures at the Grain boundary
~8º
TILT BOUNDARY IN SrTiO3
POLYCRYSTAL
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Random
DEFECTS
Ordered
Based onposition
Ordered defects become part of the structure and hence affect the basic symmetry of the structure
• Vacancies• Stacking Faults
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Crystal with vacancies
Vacancy ordering
E.g. V6
C5
, V8
C7
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Effect of Atomic Level Residual Stress
→
→
→
→
Yield Point Phenomenon
(GPa)
x (Å) →
y (Å
) →
Interaction of the stress fields of dislocations’
with Interstitial atoms’
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3D (Volume defects)
&
MICROSTRUCTURES
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T.J. Konno, K. Hiraga and M. Kawasaki, Scripta mater. 44 (2001) 2303–2307
HAADF
micrographs of the GP zones: (a) Intercalated monatomic Cu layers several nm in width are clearly resolved, (b) a GP-zone two Cu layers thick can ‘chemically’
be identified.
Bright field TEM micrograph of an Al-
3.3% Cu alloy, aged at room temperature for 100 days, showing the GP-I zones.
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Precipitate particleb
b
Hardening effect Part of the dislocation line segment (inside the precipitate) could face a higher PN stress
Increase in surface area due to particle shearing
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Pinning effect of the precipitate
Can act like a Frank-Reed source
rGb2
~
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Controlling microstructures:Controlling microstructures:
Examples
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%C →
T →
Fe Fe3
C6.74.30.80.16
2.06
PeritecticL +
→
Eutectic L →
+ Fe3
C
Eutectoid
→
+ Fe3
C
L
L +
+ Fe3 C
1493ºC
1147ºC
723ºC
Fe-Cementite
diagram
Austenite () → FCC
Ferrite () → BCC
Cementite
(Fe3
C) → Orthorhombic
Fe3 C
[1] rruff.geo.arizona.edu/doclib/zk/vol74/ZK74_534.pdf
[1]
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Austenite
Austenite
Pearlite
Pearlite + Bainite
Bainite
Martensite100
200
300
400
600
500
800
723
0.1 1 10 102 103 104 105
Eutectoid temperature
Ms
Mf
Coarse
Fine
t (s) →
T →
Time-
Temperature-Transformation (TTT) Curves –
Isothermal Transformation
Eutectoid steel (0.8%C)
[1] Physical Metallurgy for Engineers, D S Clark and W R Varney,
Affiliated EastWest
Press Pvt. Ltd., New Delhi, 1962
[1]348C
[1]278C
Metals Handbook, Vol.8, 8th
edition, ASM, Metals Park, Ohio
[2] Introduction to Physical Metallurgy, S.H. Avner, McGraw-Hill Book Company, 1974
[2]
[2]
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AustenitePearlite
Pearlite + Bainite
Bainite
Martensite100
200
300
400
600
500
800
723
0.1 1 10 102 103 104 105
Eutectoid temperature
Ms
Mf
t (s) →
T →
Time-
Temperature-Transformation (TTT) Curves –
Isothermal Transformation
Eutectoid steel (0.8%C)
+ Fe3 C
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Eutectoid steel (0.8%C)
100
200
300
400
600
500
800
723
0.1 1 10 102 103 104 105
t (s) →
T →
Water quench Oil quench
Normalizing
Full anneal
Different cooling treatments
M = Martensite
P = Pearlite
Coarse P
P M M + Fine P
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% Carbon →
Har
dnes
s (R
c) →
20
40
60
0.2 0.4 0.6
Harness of Martensite
as a function of Carbon content
Properties of 0.8% C steelConstituent Hardness (Rc
) Tensile strength (MN / m2)Coarse pearlite 16 710Fine pearlite 30 990Bainite 45 1470Martensite 65 -Martensite
tempered at 250 oC 55 1990
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Cooling
C1 C2
%C →
T →
0.80.02
Eutectoid
→
+ Fe3
C
+ Fe3 C
+
+ Fe3 C
Fe
C3
[1] Materials Science and Engineering, W.D.Callister, Wiley India (P) Ltd., 2007.
Pro-eutectoidCementite
Pearlite
1.4%C [1]
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White CI
3.4%C, 0.7% Si, 0.6% Mn
Grey CI
Fully Malleabilized10 m
Ferrite (White)
Graphite (black)
Malleable CI
10 m Ferritic
MatrixFerrite
Graphite nodules
Nodular CI Ductile
3Fe C Graphite NodulesHeat Treatment
3.4% C,1.8% Si, 0.5% Mn
3.4% C, 0.1% P, 0.4% Mn,1.0% Ni, 0.06% Mg
2.5% C, 1.0% Si, 0.55% Mn
3 3 3L ( ) ( )Ledeburite Pearlite
Fe C Fe C Fe C
Change
Composition
0%
0.5%
12%
18%
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Texture can reintroduce anisotropy in material properties
Anisotropy in Material Properties: an example
11E
12E
111 12244 E EE
Cubic Crystal
(3 Elastic Moduli)
PolycrystalAnisotropic Isotropic Anisotropic
TextureRolling/
Extrusion
Cold Worked
Moly Permalloy: 4% Mo, 79% Ni, 17% Fe
Annealed
Textured samples
EquiaxedElongated
[1] Metals Handbook, Vol.8, 8th Edition, ASM, 1973
[1]
[1]
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CONCLUSIONCONCLUSION
To understand the properties of materials the To understand the properties of materials the structurestructure at many different at many different lengthscaleslengthscales must must
be viewedbe viewed
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Ionic Crystals
Overall electrical neutrality has to be maintained
Frenkel
defect
Cation
(being smaller get displaced to interstitial voids E.g. AgI, CaF2
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Schottky
defect
Pair of anion and cation
vacancies E.g. Alkali halides
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Other defects due to charge balance
If Cd2+
replaces Na+
→ one cation
vacancy is created
Defects due to off stiochiometry
ZnO
heated in Zn vapour
→ Zny
O
(y >1) The excess cations
occupy interstitial voids
The electrons (2e) released stay associated to the interstitial cation
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FeO
heated in oxygen atmosphere → Fex
O
(x <1) Vacant cation
sites are present
Charge is compensated by conversion of ferrous to ferric ion:Fe2+
→ Fe3+
+ e
For every vacancy (of Fe cation) two ferrous ions are converted to
ferric ions → provides the 2 electrons required by excess oxygen
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Cubic48
Tetragonal16
Triclinic2
Monoclinic4
Orthorhombic8
Progressive lowering of symmetry amongst the 7 crystal systems
Hexagonal24
Trigonal12
Incr
easi
ng sy
mm
etry
Superscript to the crystal system is the order of the lattice point group
Arrow marks lead from supergroups to subgroups
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A semimetal is a material with a small overlap in the energy of the conduction band and valence bands.However, the bottom of the conduction band is typically situated
in a different part of momentum space (at a different k-
vector) than the top of the valence band. One could say that a semimetal is a semiconductor with a negative indirect bandgap, although they are seldom described in those terms.
Schematically, the figure showsA) a semiconductor with a direct gap (like e.g. CuInSe2
), B) a semiconductor with an indirect gap (like Si) and C) a semimetal (like Sn
or graphite). The figure is schematic, showing only the lowest-energy conduction band and the highest-energy valence band in one
dimension of momentum space (or k-space). In typical solids, k-space is three dimensional, and there are an infinite number of bands.
Unlike a regular metal, semimetals have charge carriers of both types (holes and electrons), so that one could also argue that they should be called 'double-metals' rather than semimetals. However, the charge carriers typically occur in much smaller numbers than in a real metal. In this respect they resemble degenerate semiconductors more closely. This explains why the electrical properties of semimetals are partway between those of metals and semiconductors.
As semimetals have fewer charge carriers than metals, they typically have lower electrical and thermal conductivities. They also have small effective masses for both holes and electrons because the overlap in energy is usually the result of the fact that both energy bands are broad. In addition they typically show high diamagnetic susceptibilities and high lattice dielectric constants.
The classic semimetallic
elements are arsenic, antimony, and bismuth. These are also considered metalloids but the concepts are not synonymous. Semimetals, in contrast to metalloids, can also be compounds, such as HgTe, and tin and graphite are typically not considered metalloids.
Graphite and hexagonal boronnitride
(BN) are an interesting comparison. The materials have essentially the same layered structure and are isoelectronic, which means that their band structure should be rather similar. However, BN
is a white semiconductor and graphite a black semimetal, because the relative position of the bands in the energy direction is somewhat different. In one case the bandgap
is positive (like case B in the figure), explaining why BN
is a semiconductor. In the other case the conduction band lies sufficiently lower to overlap with the valence band in energy, rendering the value for the bandgap
negative (see C).
http://en.wikipedia.org/wiki/File:Semimetal.PNG
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