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