Imperfections in Solids: Understanding Point Defects, Dislocations, and Grain Boundaries, Lecture notes of Material Engineering

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Imperfections in Solids

Imperfections in Solids

The properties of some materials are

profoundly influenced by the presence

of imperfections.

It is important to have knowledge about

the types of imperfections that exist and

the roles they play in affecting the

behavior of materials.

• Vacancy atoms
• Interstitial atoms
• Substitutional atoms

Point defects

1-2 atoms

Types of Imperfections

• Dislocations

Line defects

1-dimensional

• Grain Boundaries

Area defects

2-dimensional

• Vacancies:

-vacant atomic sites in a structure.

• Self-Interstitials:

-"extra" atoms positioned between atomic sites.

Point Defects in Metals

Vacancy

distortion

of planes

self-interstitial

distortion

of planes

• Vacancies

-- vacancies exist in ceramics for both cations and anions

• Interstitials

-- interstitials exist for cations

-- interstitials are not normally observed for anions because anions

are large relative to the interstitial sites

Adapted from Fig. 5.2, Callister & Rethwisch 3e.

(Fig. 5.2 is from W.G. Moffatt, G.W. Pearsall, and

J. Wulff, The Structure and Properties of

Materials , Vol. 1, Structure , John Wiley and Sons,

Inc., p. 78.)

Point Defects in Ceramics

Cation Interstitial

Cation Vacancy

Anion Vacancy

• Frenkel Defect

To maintain the charge neutrality, a cation vacancy-cation interstitial

pair occur together. The cation leaves its normal position and moves to the

interstitial site.

• Schottky Defect

To maintain the charge neutrality, remove 1 cation and 1 anion;

this creates 2 vacancies.

Adapted from Fig. 5.3, Callister & Rethwisch 3e.

(Fig. 5.3 is from W.G. Moffatt, G.W. Pearsall, and

J. Wulff, The Structure and Properties of

Materials , Vol. 1, Structure , John Wiley and Sons,

Inc., p. 78.)

Point Defects: Frenkel and Schottky

Schottky

Defect

Frenkel

Defect

• We can get Q

v

from

an experiment.

N

v

N

= exp^

Q

v

kT

Measuring Activation Energy

• Measure this...

N

v

N

T

exponential

dependence!

defect concentration

• Replot it...

1/ T

N

N

v

ln

• Q

v

/ k

slope

• Find the equil. # of vacancies in 1 m

3

of Cu at 1000C.

• Ex 5.1 - Given:

A

Cu

= 63.5 g/mol

 (^) = 8.4 g/cm

3

Q

v

= 0.9 eV/atom N

A

= 6.02 x 10

23

atoms/mol

Estimating Vacancy Concentration

For 1 m

3

, N =

N

A

A

Cu

 (^) x x 1 m

3

= 8.0 x 10

28

sites

8.62 x 10

eV/atom-K

0.9 eV/atom

1273 K

N

v

N

exp

Q

v

kT

= 2.7 x 10

• Answer:

N

v

= (2.7 x 10

)(8.0 x 10

28

) sites = 2.2 x 10

25

vacancies

Alloying

• (^) Given a metal (with only 1 type of atom) refined to

99.9999% purity, there would still exist 10

22

to 10

23

impurity atoms in 1 cubic meter of material.

• (^) Most metals are alloys. Alloying is done to

improve strength, corrosion resistance, ductility,

lower melting T.

For example, sterling silver is an alloy of 92.5%

silver, 7.5% copper. At room temperature, “pure”

silver is highly corrosion resistant, but also very

soft. The addition of copper improves the strength

and maintains good corrosion behavior.

Solid Solution

• (^) The addition of impurity atoms to a metal

results in the formation of a solid solution.

The solvent represents the element that is

present in the greatest amount (the host

atoms). For example, in Lab 8 (MSE 227) Precipitation Hardening of

Aluminum, aluminum is the solvent and copper is

the solute (present in minor concentration ).

Solid solutions form when the solute atoms

(Cu) are added to the solvent (Al), assuming

the crystal structure is maintained and no new

structures are formed.

What are the outcomes if impurity (B) is added to host (A)?

• Solid solution of B in A (random distribution of point defects)
• Solid solution of B in A plus particles of a new

phase (usually for a larger amount of B)

OR

Substitutional solid solution.

(e.g., Cu in Ni)

Interstitial solid solution.

(e.g., C in Fe)

Second phase particle

-- different composition

-- often different structure.

Imperfections in Metals

Hume - Rothery Rules

The Hume-Rothery rules are basic conditions for

an element to dissolve in a metal, forming a

substitutional solid solution.

1. The atomic radius of the solute and solvent atoms must

differ by no more than 15% ( r < 15%).

2. The solute and solvent should have similar

electronegativities.

3. Same crystal structure for “pure” metals.
4. Maximum solubility occurs when the solvent and solute

have the same valence. Metals with lower valence will

tend to dissolve metals with higher valence.

Carbon forms an interstitial solid solution when

added to iron; the maximum concentration of

carbon that can be added is roughly 2%.

The atomic radius of the carbon atom is much

less than that of iron (0.071nm vs 0.124 nm).

• (^) For interstitial solid solutions, the Hume-Rothery

rules are:

• 1. Solute atoms must be smaller than the pores in the

solvent lattice.

• (^) 2. The solute and solvent should have similar

electronegativity.

Interstitial Solid Solution

• Since there are both anions and cations in ceramics, a substitutional

impurity will replace the host ion most similar in terms of charge.

• Charge balance must be maintained when impurities are present.
  • Ex: NaCl

Imperfections in Ceramics

Na

Cl

• Substitutional cation impurity

without impurity Ca

2+

impurity with impurity

Ca

2+

Na

Na

Ca

2+

cation

vacancy

• Substitutional anion impurity

without impurity O

2-

impurity

O

2-

Cl

anion vacancy

Cl

with impurity