The Muppet’s Guide to: The Structure and Dynamics of Solids 7. Defects and Solutions

The Muppet’s Guide to:The Structure and Dynamics of Solids

7. Defects and Solutions

• Vacancy atoms• Interstitial atoms• Substitutional atoms

Point defects

Types of Imperfections

• Dislocations Line defects

• Grain Boundaries Area defects

Grain boundaries

D = b/

b

Internal surfaces of a single crystal where ideal domains (mosaic) meet with some misalignment: high-angle and small(low)-angle.

NB – in polycrystalline materials, grain boundaries are more extensive and may even separate different phases

Small-angle grain boundary equivalent to linear array of edge dislocations

bonding not fully satisfied region of higher energy, more reactive, impurities present.

(Callister: Materials Science and Engineering)

Point Defects

small substitutional atom

All of these defects disrupt the perfect arrangement of the surrounding atoms –relaxation effects

Schottky and Frenkel normally v low conc. since formation energy high

vacancy interstitial

large substitutional atom

Frenkel defect Schottky defect

Frenkel Defect• Tend to be found in ionic solids

with large size difference between the anion and cation

• The defect forms when an atom or cation leaves its place in the lattice, creating a vacancy, and becomes an interstitial.

• occur due to thermal vibrations

• occurrence depends on– size of ion– charge on ion– electronegativity– temperature

Ag

Ag

• Found in ionic crystals

• Oppositely charged ions leave their lattice sites, creating vacancies

• anion and cation vacancies balance such that charge neutrality is preserved

Schottky Defects

• Vacancies:

-vacant atomic sites in a structure.

• Self-Interstitials:

-"extra" atoms positioned between atomic sites.

Point Defects

Vacancydistortion of planes

self-interstitial

distortion of planes

(Callister: Materials Science and Engineering)

Material PropertiesDislocations & plastic deformation• Cubic & hexagonal metals - plastic deformation by

plastic shear or slip where one plane of atoms slides over adjacent plane by defect motion (dislocations).

• If dislocations don't move, deformation doesn't occur!

Adapted from Fig. 7.1, Callister 7e.

Edge Defect Motion

Dislocation Motion• Dislocation moves along slip plane in slip direction

perpendicular to dislocation line• Slip direction same direction as Burgers vector

Edge dislocation

Screw dislocation

Adapted from Fig. 7.2, Callister 7e.

(Callister: Materials Science and Engineering)

Dislocations & Materials Classes

• Covalent Ceramics

(Si, diamond): Motion hard. -directional (angular) bonding

• Ionic Ceramics (NaCl):

Motion hard. -need to avoid ++ and - - neighbours.

+ + + +

+++

+ + + +

- - -

----

- - -

• Metals: Disl. motion easier.

-non-directional bonding -close-packed directions for slip.

electron cloud ion cores

++

++

++++++++ + + + + +

+++++++

(Callister: Materials Science and Engineering)

Pinning dislocations

• dislocations make metals easier to deform• to improve strength of metals, need to stop dislocation motion

trap with:- impurity atoms;- other dislocations (work hardening;

- grain boundaries.

atom trap

(Callister: Materials Science and Engineering)

• Impurity atoms distort the lattice & generates stress.• Stress can produce a barrier to dislocation motion.

Modify Material Properties

• Smaller substitutional impurity

Impurity generates local stress at A and B that opposes dislocation motion to the right.

A

B

• Larger substitutional impurity

Impurity generates local stress at C and D that opposes dislocation motion to the right.

C

D

Increase material strength through substitution

(Callister: Materials Science and Engineering)

Modify Material Properties

• Grain boundaries are barriers to slip.• Barrier "strength" increases with Increasing angle of miss-orientation.• Smaller grain size: more barriers to slip.

Increase material strength through reducing Grain size

(Callister: Materials Science and Engineering)

Solid Solutions

Solid state mixture of one or more solutes in a solvent

Crystal structure remains unchanged on addition of the solute to the solvent

Mixture remains in a homogenous phase

Generally composed on metals close in the periodic tableNi/Cu, Pb/Sn etc.

Otherwise compounds tend to formNaCl, Fe2O3 etc.

Two outcomes if impurity (B) added to host (A):

• Solid solution of B in A (i.e., random dist. of point defects)

ORSubstitutional solid soln.

(e.g., Cu in Ni)Interstitial solid soln.

(e.g., C in Fe)

Point Defects in Alloys

(Callister: Materials Science and Engineering)

Hume-Rothery Rules – Substitutional Solutions

1. The solute and solvent should be of a similar size. (<15% difference)

2. The crystal structures must match.

3. Both solute and solvent should have similar electronegativity

4. The valence of the solvent and solute metals should be similar.

Rules to describe how an element might dissolve in a metal. Stable composition in equilibrium (thermodynamics)

Metals – Ni/Cu, Pd/Sn, Ag/Au, Mo/W

Phase Equilibria – Example

CrystalStructure

electroneg r (nm)

K BCC 0.93 0.235

Na BCC 1.00 0.191

• Both have the same crystal structure (BCC) and have similar electronegativities but different atomic radii.

• Rules suggest that NO solid solution will form.

K-Na

• K and Na sodium are not miscible.

Phase Equilibria – Example

CrystalStructure

electroneg r (nm)

Ni FCC 1.9 0.1246

Cu FCC 1.8 0.1278

• Both have the same crystal structure (FCC) and have similar electronegativities and atomic radii (W. Hume – Rothery rules) suggesting high mutual solubility.

Simple solution system (e.g., Ni-Cu solution)

• Ni and Cu are totally miscible in all proportions.

Hume-Rothery Rules – Interstitial Solution

1. The solute must be smaller than the interstitial sites in the solvent lattice

2. Solute and Solvent should have similar electro-negativities

Rules to describe how an element might dissolve in a metal. Stable composition in equilibrium (thermodynamics)

Light elements – H,C, N and O.

Phase Diagrams

• A phase diagram is a graphical representation of the different phases present in a material.

• Commonly presented as a function of composition and temperature or pressure and temperature

Applies to elements, molecules etc. and can also be used to show magnetic, and ferroelectric behaviour (field vs. temperature) as well as structural information.

• Components: The elements or compounds which are present in the mixture (e.g., Al and Cu)

• Phases: The physically and chemically distinct material regions that result (e.g., a and b).

Aluminum-CopperAlloy

Components and Phases

a (darker phase)

b (lighter phase)

Figure adapted from Callister, Materials science and engineering, 7 th Ed.

Unary Phase DiagramsA pressure-temperature plot showing the different phases present in H2O.

Phase Boundaries

Upon crossing one of these boundaries the phase abruptly changes from one state to another. Latent heat not shown

Crossing any line

results in a structural

phase transition

Reading Unary Phase Diagrams

Melting Point (solid → liquid)

Boiling Point(liquid→ gas)

Sublimation (solid → gas)

As the pressure falls, the boiling point reduces, but the melting/freezing point remains reasonably constant.

Triple Point (solid + liquid + gas)

Reading Unary Phase Diagrams

Melting Point: 0°C Boiling Point: 100°C

Melting Point: 2°C Boiling Point: 68°C

P=1atm

P=0.1atm

Water Ice

http://images.jupiterimages.com/common/detail/13/41/23044113.jpg, http://www.homepages.ucl.ac.uk/~ucfbanf/ice_phase_diagram.jpg

• When we combine two elements... what equilibrium state do we get?• In particular, if we specify... --a composition (e.g., wt.% Cu – wt.% Ni), and --a temperature (T )

then... How many phases do we get? What is the composition of each phase? How much of each phase do we get?

Binary Phase DiagramsPhase BPhase A

Nickel atomCopper atom

Phase Equilibria: Solubility Limit– Solutions – solid solutions, single phase– Mixtures – more than one phase

• Solubility Limit: Max concentration for which only a single phase solution occurs.

Question: What is the solubility limit at 20°C?

Answer: 65 wt% sugar.

If Co < 65 wt% sugar: syrup

If Co > 65 wt% sugar: syrup + sugar.65

Sucrose/Water Phase Diagram

Pu

re

Su

gar

Tem

per

atu

re (

°C)

0 20 40 60 80 100Co =Composition (wt% sugar)

L (liquid solution

i.e., syrup)

Solubility Limit L

(liquid)

+ S

(solid sugar)20

40

60

80

100

Pu

re

Wat

er

Salt-Water(ice)

http://webserver.dmt.upm.es/~isidoro/bk3/c07sol/Solution%20properties_archivos/image001.gif