chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a physical science within the natural sciences that studies the chemical elements that make up matter and chemical compound, compounds made of atoms, molecules a ...

, isomorphism has meanings both at the level of crystallography and at a molecular level. In

crystallography Crystallography is the branch of science devoted to the study of molecular and crystalline structure and properties. The word ''crystallography'' is derived from the Ancient Greek word (; "clear ice, rock-crystal"), and (; "to write"). In J ...

, crystals are isomorphous if they have identical symmetry and if the atomic positions can be described with a set of parameters (unit cell dimensions and fractional coordinates) whose numerical values differ only slightly. Molecules are isomorphous if they have similar shapes. The

coordination complex A coordination complex is a chemical compound consisting of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of chemical bond, bound molecules or ions, that are in turn known as ' ...

es tris(acetylacetonato)iron (Fe(acac)₃) and tris(acetylacetonato)aluminium (Al(acac)₃) are isomorphous. These compounds, both of ''D''₃ symmetry have very similar shapes, as determined by bond lengths and bond angles. Isomorphous compounds give rise to isomorphous crystals and form

solid solution A solid solution, a term popularly used for metals, is a homogeneous mixture of two compounds in solid state and having a single crystal structure. Many examples can be found in metallurgy, geology, and solid-state chemistry. The word "solutio ...

s. Historically, crystal shape was defined by measuring the angles between crystal faces with a

goniometer A goniometer is an instrument that either measures an angle or allows an object to be rotated to a precise angular position. The term goniometry derives from two Greek words, γωνία (''gōnía'') 'angle' and μέτρον (''métron'') ' me ...

. Whereas crystals of Fe(acac)₃ are deep red and crystals of Al(acac)₃ are colorless, a solid solution of the two, i.e. Fe_1−xAl_x(acac)₃ will be deep or pale pink depending on the Fe/Al ratio, x. Double sulfates, such as Tutton's salt, with the generic formula M^I₂M^II(SO₄)₂.6H₂O, where M^I is an alkali metal and M^II is a divalent ion of Mg, Mn, Fe, Co, Ni, Cu or Zn, form a series of isomorphous compounds which were important in the nineteenth century in establishing the correct

atomic weight Relative atomic mass (symbol: ''A''; sometimes abbreviated RAM or r.a.m.), also known by the deprecated synonym atomic weight, is a dimensionless physical quantity defined as the ratio of the average mass of atoms of a chemical element in a giv ...

s of the transition elements.

Alum An alum () is a type of chemical compound, usually a hydrated double salt, double sulfate salt (chemistry), salt of aluminium with the general chemical formula, formula , such that is a valence (chemistry), monovalent cation such as potassium ...

s, such as KAl(SO₄)₂.12H₂O, are another series of isomorphous compounds, though there are three series of alums with similar external structures, but slightly different internal structures. Many

spinel Spinel () is the magnesium/aluminium member of the larger spinel group of minerals. It has the formula in the cubic crystal system. Its name comes from the Latin word , a diminutive form of ''spine,'' in reference to its pointed crystals. Prop ...

s are also isomorphous. In order to form isomorphous crystals two substances must have the same chemical formulation (i.e., atoms in the same ratio), they must contain atoms which have corresponding chemical properties and the sizes of corresponding atoms should be similar. These requirements ensure that the forces within and between molecules and ions are approximately similar and result in crystals that have the same internal structure. Even though the space group is the same, the

unit cell In geometry, biology, mineralogy and solid state physics, a unit cell is a repeating unit formed by the vectors spanning the points of a lattice. Despite its suggestive name, the unit cell (unlike a unit vector In mathematics, a unit vector i ...

dimensions will be slightly different because of the different sizes of the atoms involved.

Mitscherlich's law

Mitscherlich's law of isomorphism, or the law of isomorphism, is an

approximate An approximation is anything that is intentionally similar but not exactly equal to something else. Etymology and usage The word ''approximation'' is derived from Latin ''approximatus'', from ''proximus'' meaning ''very near'' and the prefix ...

law Law is a set of rules that are created and are enforceable by social or governmental institutions to regulate behavior, with its precise definition a matter of longstanding debate. It has been variously described as a science and as the ar ...

suggesting that crystals composed of the same number of similar elements tend to demonstrate isomorphism. Mitscherlich's law is named for German chemist Eilhard Mitscherlich, who formulated the law and published it between 1819 and 1823. According to Ferenc Szabadváry, one of the clues that helped Berzelius determine the atomic weights of the elements was "the discovery of Mitscherlich that compounds which contain the same number of atoms and have similar structures, exhibit similar crystal forms (isomorphism)."

References

{{Authority control Crystallography Mineralogy concepts

Mitscherlich's law

See also

References