Crystalline Arrangement of atomsCrystalline Arrangement of atoms

Chapter 4Chapter 4IMPERFECTIONS IN SOLIDSIMPERFECTIONS IN SOLIDS

The atomic arrangements in a The atomic arrangements in a crystalline lattice is almost always crystalline lattice is almost always not perfectnot perfect. .

There are defects in the way atoms There are defects in the way atoms are arranged in the crystalline solids.are arranged in the crystalline solids.

So we can say that in crystalline So we can say that in crystalline solids some solids some Lattice IrregularitiesLattice Irregularities are are always present.always present.

These crystalline defects are not bad. These crystalline defects are not bad. Some are intentionally introduced to Some are intentionally introduced to improve the material.improve the material.

Types of Crystalline DefectsTypes of Crystalline Defects POINT DEFECTS are classified on the POINT DEFECTS are classified on the

basis of their geometry and basis of their geometry and dimensionallity.dimensionallity.

POINT DEFECTSPOINT DEFECTS (Vacancies, self interstitials, impurity atoms)(Vacancies, self interstitials, impurity atoms)

LINE DEFECTS (LINE DEFECTS (one dimensionalone dimensional)) (Dislocations)(Dislocations)

INTERFACIAL DEFECTS (INTERFACIAL DEFECTS (two dimensionaltwo dimensional)) (Grain Boundaries)(Grain Boundaries)

VACANCYVACANCYi.e. an atom missing from lattice i.e. an atom missing from lattice

positionposition

IMPURITY ATOMSIMPURITY ATOMS

POINT DEFECTSPOINT DEFECTS

InterstitialsInterstitials

Crystalline DefectsCrystalline Defects

VacanciesVacancies Vacancies are always present in the Vacancies are always present in the

crystalline solids.crystalline solids.

Vacancies are created during process Vacancies are created during process of solidification or due to thermal of solidification or due to thermal agitations of lattice atoms.agitations of lattice atoms.

At a given temperature there is At a given temperature there is always present an EQUILIBRIUM always present an EQUILIBRIUM CONCENTRATION of VACANCIES.CONCENTRATION of VACANCIES.

EQUILIBRIUM CONCENTRATION OFEQUILIBRIUM CONCENTRATION OFVACANCIESVACANCIES

• Equilibrium concentration of vacancies increase with temperature!

Boltzmann's constant

(1.38 x 10-23 J/atom K)

(8.62 x 10-5 eV/atom K)

NvN

expQvkT

Equilibrium No. of vacancies

No. of atomic sites.

Activation energy

Temperature

Each lattice site is a potential vacancy site

5

• We can get Q from an experiment.

• Measure this... • Replot it...

MEASURING ACTIVATION ENERGYMEASURING ACTIVATION ENERGY

NvN

expQvkT

Nv

N

T

exponential dependence!

defect concentration1/T

N

Nvln 1

-Qv/k

slope

6

• Find the equil. # of vacancies in 1 m of Cu at 1000 oC.• Given:

3

ACu = 63.5g/mol = 8.4 g/cm3

QV = 0.9eV/atomNA = 6.02 x 1023 atoms/mole

• Answer:

ESTIMATING VACANCY CONC.ESTIMATING VACANCY CONC.

8.62 x 10-5 eV/atom-K

0.9eV/atom

1273K

NvN

expQvkT

For 1m3, N =NAACu

x x 1m3 = 8.0 x 1028 sites

= 2.7 · 10-4

Nv = (2.7 · 10-4) (8.0 x 1028) = 2.2x 1025 vacancies

Impurities in SolidsImpurities in Solids Pure metal containing only one type of Pure metal containing only one type of

atoms Not Possibleatoms Not Possible Impurity atoms are always present.Impurity atoms are always present. These atoms exists as point defects.These atoms exists as point defects. In alloys, impurity atoms (alloying element In alloys, impurity atoms (alloying element

atoms) are intentionally added. atoms) are intentionally added. An alloy is usually a solid solution of two or An alloy is usually a solid solution of two or

more types of atoms.more types of atoms. e.g. Fe + C e.g. Fe + C Steel Steel

SOLVENTSOLUTE

SOLID SOLUTION

TYPES OF SOLID SOLUTIONSTYPES OF SOLID SOLUTIONS

SOLID SOLUTIONSOLID SOLUTION

SUBSTITUTIONAL SOLID SOLUTION

Solute atoms replace (substitute) the solvent atoms in the solvent lattice

INTERSTITIAL SOLID SOLUTION

Solute atoms occupy the interstitial sites of the solvent lattice

Solid SolutionsSolid Solutions

Conditions For Substitutionl Solid Conditions For Substitutionl Solid SolubilitySolubility Four ConditionsFour Conditions must be satisfied for must be satisfied for

obtaining appreciable (large) solubility of the obtaining appreciable (large) solubility of the substitutional solute in a given solvent lattice.substitutional solute in a given solvent lattice.

1.1. Atomic Size Factor:Atomic Size Factor: The atomic size The atomic size difference between the solute and solvent difference between the solute and solvent atoms must be less than atoms must be less than 15%. 15%.

2.2. Crystal Structure:Crystal Structure: Crystal structure of Crystal structure of both solute and solvent must be same.both solute and solvent must be same.

3.3. Electronegative:Electronegative: The electro negativity The electro negativity difference must be small. If this difference is difference must be small. If this difference is large ionic compound will form instead of solid large ionic compound will form instead of solid solution.solution.

4.4. Valence:Valence: Higher valance metals will dissolve Higher valance metals will dissolve easily than low valance metals.easily than low valance metals.

Ni + Cu

Will they have large Solid Solubility?

Check! 4 conditions

Ni Cu

Atomic Size 0.125 nm 0.128 nm

Crystal structure FCC FCC

Electronegativity 1.8 1.9

Valence +2 +1

Answer: Yes they will

HOW about CU + Zn

Zn CuAtomic Size 0.133 nm 0.128 nmCrystal structure HCP FCCElectronegativity 1.6 1.9Valence +2 +1

Answer: No they won’t

Two most common ways to specify the composition or Two most common ways to specify the composition or concentration areconcentration are Weight or mass percentWeight or mass percent: weight of a particular : weight of a particular

element relative to the total alloy weight.element relative to the total alloy weight. Atom percentAtom percent: number of moles of an element in : number of moles of an element in

relation to the total moles of the elements in the alloy.relation to the total moles of the elements in the alloy.

Weight %:Weight %:

where mwhere m11 and m and m22 represent the weight or mass of elements. represent the weight or mass of elements.

Atom %:Atom %:

where No. of moles (nwhere No. of moles (nmm) = {(mass in grams) / Atomic ) = {(mass in grams) / Atomic weightweight

11

1 2100

mC

m m

' 11

1 2100m

m m

nC

n n

SPECIFICATION OF COMPOSITIONSPECIFICATION OF COMPOSITION

SPECIFICATION OF COMPOSITION SPECIFICATION OF COMPOSITION (Contd.)(Contd.) COMPOSITION COMPOSITION

CONVERSIONSCONVERSIONS

Weight% to Weight% to Atom%Atom%

Atom% to Atom% to Weight%Weight%

SPECIFICATION OF COMPOSITION SPECIFICATION OF COMPOSITION (Contd.)(Contd.)

Weight% to Kg/m3Weight% to Kg/m3 ( mass of one ( mass of one component per unit volume of material)component per unit volume of material)

Example 4.2Example 4.2 Derive Equation 4.6aDerive Equation 4.6a Solution:Solution: Total alloy mass, Total alloy mass, '

2'1

' mmM

Atom % of element 1, 100100

2

'2

1

'1

1

'1

21

1'1

A

m

A

m

A

m

nn

nC

mm

m

100

'1'

1

MCm

100

100100

100

2

'2

1

'1

1

'1

'1

AMC

AMC

AMC

C 1001221

21'1

ACAC

ACCSimplifies to

DISLOCATIONSDISLOCATIONS

Dislocations are LINEAR DEFECT and Dislocations are LINEAR DEFECT and represent a line around which atoms in the represent a line around which atoms in the crystalline lattice are misaligned.crystalline lattice are misaligned.

Two Types of DislocationsTwo Types of Dislocations

EDGE DISLOCATIONEDGE DISLOCATION SCREW DISLOCATIONSCREW DISLOCATION

Also MIXED DISLOCATIONAlso MIXED DISLOCATION

EDGE DISLOCATIONEDGE DISLOCATIONRepresented by a half atomic plane Represented by a half atomic plane the edge of which ends within the the edge of which ends within the

crystalcrystal

2222

Figure 4.5 The perfect crystal in (a) is cut and an extra plane of atoms is inserted (b). The bottom edge of the extra plane is an edge dislocation (c). A Burgers vector b is required to close a loop of equal atom spacings around the edge dislocation. (Adapted fromJ .D. Verhoeven, Fundamentals of Physical Metallurgy, Wiley, 1975.)

EDGE DISLOCATIONEDGE DISLOCATION

EDGE DISLOCATIONEDGE DISLOCATION

SCREW DISLOCATIONSCREW DISLOCATION

2121

(c) 2003 Brooks/Cole Publishing / Thomson Learning

Figure 4.4 the perfect crystal (a) is cut and sheared one atom spacing, (b) and (c). The line along which shearing occurs is ascrew dislocation. A Burgers vector b is required to close a loop of equal atom spacings around the screw dislocation.

SCREW DISLOCATIONSCREW DISLOCATION

MIXED DISLOCATIONMIXED DISLOCATION

MIXED DISLOCATIONMIXED DISLOCATION

2323

Figure 4.6 A mixed dislocation. The screw dislocation at the front face of the crystal gradually changes to an edge dislocation at the side of the crystal. (Adapted from W.T. Read, Dislocations in Crystals. McGraw-Hill, 1953.)

BURGERS VECTORBURGERS VECTOR

Burgers Vector Burgers Vector bb represents the represents the magnitude and direction of lattice magnitude and direction of lattice distortion created by the dislocation.distortion created by the dislocation.

FOR EDGE DISLOCATION FOR EDGE DISLOCATION bb is is perpendicular perpendicular to dislocation line. to dislocation line.

FOR SCREW DISLOCATIONFOR SCREW DISLOCATION bb is parallel to is parallel to dislocation line.dislocation line.

BURGERS VECTORBURGERS VECTOR

FOR METALLIC MATERIALSFOR METALLIC MATERIALS

The BURGERS VECTOR for a The BURGERS VECTOR for a dislocation lies along a closed dislocation lies along a closed packed direction.packed direction.

The Magnitude of the BURGERS The Magnitude of the BURGERS VECTOR is equal to the interatomic VECTOR is equal to the interatomic or interpalnar spacing.or interpalnar spacing.

BURGERS VECTORBURGERS VECTOR

DISLOCATIONSDISLOCATIONS

4.5 Interfacial Defects4.5 Interfacial Defects

Interfacial defects are boundaries that have Interfacial defects are boundaries that have two dimensionstwo dimensions and normally separate regions of the materials that have and normally separate regions of the materials that have different crystal structures and/or crystallographic orientations.different crystal structures and/or crystallographic orientations.

These imperfections These imperfections includeinclude external surfaces, grain external surfaces, grain boundaries, twin boundaries, stacking faults, and phase boundaries, twin boundaries, stacking faults, and phase boundaries.boundaries.

EXTERNAL SURFACESEXTERNAL SURFACES

One of the most obvious imperfection boundaries is the external One of the most obvious imperfection boundaries is the external surfacesurface The crystal structure The crystal structure terminatesterminates Surface atoms are not bonded to the maximum number of Surface atoms are not bonded to the maximum number of

nearest neighbors nearest neighbors higher energy statehigher energy state than interior than interior atoms.atoms.

To reduce this energy, if possible materials tend to minimize To reduce this energy, if possible materials tend to minimize surface area surface area not possible for solids. not possible for solids.

INTERFACIAL DEFECTSINTERFACIAL DEFECTS(GRAIN BOUNDARIES)(GRAIN BOUNDARIES)

Boundary separating two small Boundary separating two small grains or crystals having grains or crystals having different crystallographic different crystallographic orientations in polycrystalline orientations in polycrystalline materials.materials.

Within the boundary region, Within the boundary region, which is probably just several which is probably just several atom distances wide, there is atom distances wide, there is some some atomic mismatchatomic mismatch in a in a transition from the crystalline transition from the crystalline orientation of one grain to that orientation of one grain to that of an adjacent one.of an adjacent one.

Various degreesVarious degrees of of crystallographic misalignment crystallographic misalignment between adjacent grains are between adjacent grains are possible ( Figure 4.7).possible ( Figure 4.7).

4.5 Interfacial Defects (Contd.)4.5 Interfacial Defects (Contd.) Tilt boundaryTilt boundary

One simple small-angle grain boundaryOne simple small-angle grain boundary

Figure demonstrates how a tilt Figure demonstrates how a tilt boundary having an angle of boundary having an angle of misorientation misorientation results from an results from an alignment of edge dislocations.alignment of edge dislocations.

Twist boundaryTwist boundary

When the angle of misorientation is When the angle of misorientation is parallel to the boundaryparallel to the boundary

Due to an array of screw dislocationsDue to an array of screw dislocations

The atoms are bonded less regularly along a grain boundary The atoms are bonded less regularly along a grain boundary interfacial or grain boundary energy similar to surface interfacial or grain boundary energy similar to surface energy.energy.

Grain boundaries are more chemically reactive than the Grain boundaries are more chemically reactive than the grains themselves as a consequence of this boundary grains themselves as a consequence of this boundary energy.energy.

Impurity atoms often preferentially segregate along these Impurity atoms often preferentially segregate along these boundaries because of their higher energy state.boundaries because of their higher energy state.

Because of less total boundary area, the total interfacial Because of less total boundary area, the total interfacial energy is lower in large or coarse-grained materials than in energy is lower in large or coarse-grained materials than in fine-grained ones. fine-grained ones.

Grains grow at elevated energy to reduce the total Grains grow at elevated energy to reduce the total boundary energyboundary energy