Crystal Defect: Definition of Defects, Stoichiometric, Non-stoichiometric and Impurity Defect, Practice Problems and FAQs

Have you ever seen or better participated in march past during republic day or independence day?

Well, we all love participating in that, wearing uniforms and going forward with unity.

You must have observed that in order to maintain the coordination of a group participating in the march, all members should align their shoulders and leg with everyone.

If that doesn’t happen then the rhythm will fall out. Sometimes it occurs due to one individual or sometimes due to a group of individuals, which becomes quite obvious for onlookers.

Crystal is solids that exhibit a long-range order in their arrangements. But, in crystals, due to several factors defects occurs. Let’s understand the different types of defects observed in crystals and their impact.

Table of Content

• Definition of Defects
• Line Defect
• Point defect
• Stoichiometric Defects
• Non-Stoichiometric Defects
• Impurity Defect
• Practice Problems
• Frequently Asked Questions (FAQs)

Definition of Defects

Imperfection or defect refers to any variation from the perfectly ordered arrangement of a crystal's component particles.

There are two types of defects

1. Point defect
2. Line defect

Line Defect

When the divergence from the ideal arrangement affects the entire row (or in one direction/axis) of lattice points, the defect is referred to as a Line defect.

In the final three rows of the crystal in the illustration, a different group (vertical line) of particles may be seen.

Point defect

A point defect occurs when there are differences or inconsistencies from the ideal arrangement around a point or an atom in a crystalline solid.

Point defects in a crystal may be classified into the following three categories

1. Stoichiometric defects
2. Impurity defects
3. Non-stoichiometric defects

Stoichiometric Defects

Stoichiometric defects are those present in crystals that do not change the solid's stoichiometry, meaning that the ratio of cations to anions remains the same as indicated by the molecular formula.

These are also called intrinsic defects or thermodynamic defects and it is further classified into the following types:

1. Defects shown by non-ionic solids
2. Defects shown by ionic solids

Defects shown by Non-Ionic Solids

Defects shown by Ionic Solids

AgBr shows both Frenkel and Schottky defect.

Consequences of Schottky and Frenkel Defects

• As an ion moves from its lattice site to occupy a hole, it creates a new hole. A hole is created in the crystal, which causes the charge to move in the opposite direction. As a result, solids with these defects conduct electricity.
• Due to the presence of holes, lattice energy or stability of the crystal decreases.
• Dielectric constant of the crystal increases in case of Frenkel defects because in this defect similar charges come closer.

Non-Stoichiometric Defects

These are the imperfections in the crystal leading to a difference in, the ratio of the cations to the anions than expected from an ideal pure crystal lattice. The stochiometry of these crystals are hence different from the pure crystals and so are allied non-stoichiometric defects.

Nonstoichiometric defects may arise by

1. Metal excess
2. Metal deficiency

1. Metal Excess Defect:

Metal-nonmetal ratio may become larger under two circumstances, One is due to the preferential loss of anions or by the excess addition of cations.

2. Metal Deficiency Defect

This defect occurs when the metal shows variable valency. This defect usually occurs due to the missing of a cation having a higher charge in the adjacent lattice site.

Examples: FeO, FeS and NiO. Due to metal deficiency defects, the compounds are non-stoichiometric.

• FeO is found, mostly, with a composition of Fe0.₉₅O, loss of some Fe²⁺ions is compensated by presence of a required number of Fe³⁺ions

Impurity Defect

An impurity defect is a crystal lattice distortion caused by an impurity (foreign atom/ion) occupying an interstitial site in the lattice or replacing the parent atom/ion in the regular sites.

Impurity defects can be classified into the following type is:

• Substitutional impurity
• Interstitial impurity

Substitutional Impurity

Defects in ionic crystals, can be introduced by adding impurities. Similar-sized cation substitute the existing cation of an ionic crystal.

Example:

When molten NaCl is crystallized having a small amount of SrCl₂, some Na+ ion’lattice points are replaced with Sr²⁺ ions. Each divalent Sr²⁺ ion empties two Na⁺ sites. One such empty site will be occupied by strontium ion leaving the other site vacant.

The number of cationic vacancies generated = Number of Sr²⁺in the crystal

Other examples: solid solution of CdCl₂ and AgCl.

Interstitial Impurity Defect

Here, some small foreign atoms (like B, C, N, H) are trapped in interstitial voids of the lattice without any chemical reaction.

Doping is the addition of impurities to a crystalline substance in order to alter its properties.

1. Introducing impurity defect in ionic solids

• Presence of ions other than that of the crystal ions will create impurity defect in ionic solids. If the other ions are of different valency from the crystal ions, then they will create vacancies related to the difference in valency in the crystal
• If a molten NaCl, containing a little SrCl₂ as impurity is allowed to cool, in the crystals of NaCl formed, at some lattice sites, Na⁺ ions are substituted by Sr²⁺ ion. For every Sr²⁺ion thus introduced, two Na⁺ions are removed to maintain electrical neutrality. One of these lattice sites is occupied by Sr²⁺ and remains vacant. These vacancies will increase the electrical conductivity of the solid. Similar defects and behaviour are observed when CdCl₂ is added to AgCl.

2. Introducing impurity defect in covalent solids

In the case of covalent solids such as silicon germanium (group 14 elements) which have 4 valence electrons in their outermost shell, the impurities added may be of the elements which may have more than 4 valence electrons (for example Group 15 elements like P or As which have five valence electrons) or of the elements which have less than 4 valence electrons (for example Group 13 elements like Ga which have three valence electrons).

Thus, the impurities added may be electron-rich or deficit. The defects thus introduced in the crystals are called electronic defects.

a) Doping with electron-rich impurities-

• Group 14 elements like silicon or germanium have four electrons in the outermost orbit. Hence, it normally forms four covalent bonds with the neighbouring atom.
• Group 14 elements have four electrons in their outermost orbit. Consider, that a group 14 element in a crystal structure is replaced by any of the elements of the 15 group which have five electrons in their outermost orbit. Group 15 element will use only four of its electrons for bonding and the fifth electron is completely free to move and conduct electricity of the group14 elements of silicon and germanium.
• As the increase in conductivity is due to negatively charged electrons, the silicon or germanium crystals doped with higher electron-containing elemental impurities are known as n-type conductors.

b) Doping with electron deficit impurities-

• When group 14 element like Si or Ge is doped with group 13 elements like B, Al, or Ga, the Si or Ge atom at some lattice are substituted by those of B, Al, or Ga.
• Now, as Group 13 elements have only 3 valence electrons, they can form three covalent bonds with the neighbouring silicon atoms.
• Thus, a hole is created at the site where the fourth electron is lost. The vacancy is known as electron vacancy or a hole
• An electron with a neighbouring atom jump to fill up this electron's hole but then an electron hole is created at the site from where electrons jumped.
• As this jumping continues, electrons and holes will be moving in opposite directions
• Now, when an electric field is applied, the electrons move towards the positively charged plate and electron holes will move towards the cathode like a cation. Hence, silicon and germanium doped with electron-deficit impurities are called p-type semiconductors.

Practice Problems

Q1. ZnS has a theoretical density of d gcm^-3. If the crystal has a 4% Frenkel defect, then the actual density of ZnS should be:

A. d gcm^-3
B. 0.04d gcm^-3
C. 0.96d gcm^-3
C. 1.0 d gcm^-3

Answer: A)

Solution: The theoretical density of ZnS is d gcm^-3. If the crystal has a 4% Frenkel defect,

then the actual density of ZnS does not change because cations missing from

their lattice sites occupies the interstitial sites. Therefore, it should be d $\frac{\mathit{g}}{\mathit{c}{\mathit{m}}^3}$

Q2. Silver bromide AgBr(s) crystals exhibit which of the following point defect and why?

A. Schottky defect
B. Frankel defect
C. Metal excess defect
D. Metal deficiency defect

1. i & ii
2. iii & iv
3. i & iii
4. ii & iv

Answer: A)

Solution: Schottky defects occur when ions are missing from their lattice point, while Frenkel defects occur when missing ions occupy interstitial sites. In the case of AgBr, both silver and bromide ions have almost similar radii with a radius ratio that is neither too large nor too close, So it exhibits both Frenkel and Schottky defects. The Frenkel defect is the most common defect in AgBr. It has a ccp lattice, in which Br atoms coexist with Ag atoms in all octahedral holes. When Ag transitions from octahedral to tetrahedral sites, only cations precipitate.

Q3. When a solid is heated, what kind of defect can occur? Which physical attribute is altered, and how?
Answer: When a solid is heated, the Crystal develops a vacancy defect. Because some atoms and ions completely leave the lattice site when heated, some lattice sides become vacant. The density of the substance decreases as some atoms/ions completely leave the Crystal as a result of this defect.

Q4. Which of the following is not a point defect

A. Stoichiometric defect
B. Non-stoichiometric defect
C. Impurity defect
D. None of the above.

Answer: (D)

Solution: defects in crystals have been classified into two categories

• Point defect
• Line defect

Point defect is further classified into 3 categories that is

• Stoichiometric defect
• Non-stoichiometric defect
• Impurity defect

Frequently Asked Questions (FAQs)

Q1. Why is there no Frankel defect in pure alkali metal halides?
Answer: Due to the large size of alkali metal ions it would be difficult to fit the ions in the interstitial sites of crystals. Hence, alkali metal halides don’t show a Frankel defect.

Q2. Why Stoichiometric defects are also called intrinsic defects?
Answer: Stoichiometric defects are so called because they do not alter the stoichiometry of the Crystal. they are called intrinsic defects because it is due to the deviation from the regular arrangement of atoms or ions within the Crystal and no external substance is added.

Q3. Is it possible to make a perfect crystal i.e, with zero defects?
Answer: No it is almost impossible to make a perfect crystal. Because only at absolute zero temperature a crystal will be defectless and attending 0 K is not possible. So crystal will have some amount of defect.

Q4. What is the difference between the interstitial defect of ionic and nonionic solids?
Answer: In ionic solids, an interstitial defect is also called a Frankel defect, the ions present at the lattice point vacate it and move to the interstitial position. In the interstitial defect non-ionic solids , foreign material come and occupy the interstitial positions