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# Case Study: Non-Stoichiometric Materials

Stoichiometric coefficients are very convenient with normal chemical equations and their reactions.  However, these coefficients are innaccurate in certain compounds due to missing or extra atoms of a specific element.  In these compounds, we have a special way of writing the formulas to account for the missing/extra particles.

### Non-Stoichiometric Compounds

Non-stoichiometric compounds are usually caused by compounds with non-integral coefficients or varying ratios of atoms.  Their ratios cannot be defined by integral numbers, and therefore they defy the law of definite proportions.  The law of definite proportions states that a chemical compound always contains  elements in the same proportions by mass and the number of atoms.  Stoichiometric coefficients are used in chemical equations to know how much of an element is needed to react with the other element(s).  They are very useful in stoichiometric equations, for example finding how many moles of a specific atom are produced in a chemical reaction.  However, in nonstoichiometric compounds these coefficients cannot be determined due to:

• An atom is missing from the lattice structure of a solid, causing the other atoms to change their oxidation states to maintain neutrality in the atom.
• Extra atoms are found in excess in the solid
• The missing atoms are replaced by atoms of a different element to maintain the neutral charge.

This phenomenon is most common in ionic compounds of transition metals, specifically Oxides, Hydrides, Carbides, and Borides.  It occurs most often in solids due to defects in the lattice of their crystalline structures.  The structure of a crystalline solid has uniform atoms forming rows of cubes called a lattice strucure, which means that these compounds are caused by defects to the structure of the cubes, and therefore the perfect crystal.  They are sometimes called Berthollide compounds in contrast to Daltonides, or compounds with small interger ratios of elements (a normal stoichiometric compound).

In these compounds there are specific ways to account for the missing or extra atoms.  A variable is added to the coefficients to show that the compound is not entirely stoichiometric.

1. If the metal/nonmetal ratio is greater than stoichiometric, then there is either excess metal or missing nonmetal.

•     If there is excess metal(interstitial atoms) it is represented as, for example Fe1+xO.
•     If there is missing nonmetal, it is represented as, for example, MoO3-x

2. If the metal/nonmetal ratio is less than stoichiometric, then the situation is the opposite.

•     Missing metal is represented by the compound Rh1-xO
•     Extra nonmetal is represented by the compound WO2+x

3. If another element replaces the missing atoms, called impurity materials, it is best to consider it as a simple solid solution.

This diagram exemplifies the three most common causes of non-stoichiometric compounds.  The dots represent atoms in the lattice structure of a solid.  The vacancies are the missing atoms that can throw off the proportions of the compound.  The interstitial atoms are the extra atoms that wedge themselves in the framework of the solid and prevent the use of stoichiometric coefficients.  The colored and oddly shaped dots are the substitutional atoms, or atoms of a different element that fill the empty spaces caused by vacancies.

Group 13 and Group 15 elements can enter the crystalline structure of group 14 elements, causing the substitutions seen as yellow in the above figure.  Since group 13 atoms have one less valence electron than group 14 atoms, it is common for group 13 solids to have holes, which increase electrical conductivity.  When group 14 and 15 elements combine it forms n-type semiconductors, n for negative charge flow.  when group 13 and 14 elements combine it forms p-type semiconductors (positive hole movement).

### Applications

Many of these Berthollides are important in electronic devices such as rectifiers, thermistors, photodetectors, magnets useful in high-frequency circuits, and thermoelectric generators.  They are also common in alloys, ceramics, and glasses and are considered to be semiconductors.

### References

1. Clark, George, and Hawley, Gessner. The Encyclopedia of Chemistry. 2nd ed. New York: Reinhold Publishing Corporation, 1966.
2. Pettrucci, Ralph H. General Chemistry: Principles and Modern Applications. 9th. Upper Saddle River: Pearson Prentice Hall, 2007

### Problems

1. What are nonstoichiometric compounds?
2. What are 3 causes of nonstoichionetric compounds?
3. What types of compounds normally form nonstoichiometric compounds?
4. When is the metal/nonmetal ratio greater than stoichiometric? (2 answers)
5. When is the metal/nonmetal ratio less than stoichiometric? (2 answers)
6. What are some uses of nonstoichiometric compounds in real life?

1. compounds with noninterger coefficients
2. missing atoms, extra interstitial atoms, atoms of different elements taking the place of missing elements
3. transitional metal Oxides, Hydrides, Carbides, and Borides
4. when there is excess metal or missing nonmetal
5. when there is missing nonmetal or excess metal
6. rectifiers, thermistors, photodetectors, magnets useful in high-frequency circuits, alloys, ceramics, glass, and thermoelectric generators

### Contributors

• Rachel Feldman, UC Davis