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chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds made of atoms, molecules and ions ...
isomorphism has meanings both at the level of crystallography and at a molecular level. In
crystallography Crystallography is the experimental science of determining the arrangement of atoms in crystalline solids. Crystallography is a fundamental subject in the fields of materials science and solid-state physics (condensed matter physics). The wor ...
, compounds are isomorphous if their symmetry is the same and their unit cell parameters are similar Molecules are isomorphous if they have similar shapes. The
coordination complex A coordination complex consists of a central atom or ion, which is usually metallic and is called the ''coordination centre'', and a surrounding array of bound molecules or ions, that are in turn known as ''ligands'' or complexing agents. Many ...
es
tris(acetylacetonato)iron Tris(acetylacetonato) iron(III), often abbreviated Fe(acac)3, is a ferric coordination complex featuring acetylacetonate (acac) ligands, making it one of a family of metal acetylacetonates. It is a red air-stable solid that dissolves in nonpolar ...
(Fe(acac)3) and
tris(acetylacetonato)aluminium Aluminium acetylacetonate, also referred to as Al(acac)3, is a coordination complex with formula Al(C5H7O2)3. This aluminium complex with three acetylacetone ligands is used in research on Al-containing materials. The molecule has D3 symmetry, be ...
(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 homogenous mixture of two different kinds of atoms in solid state and have a single crystal structure. Many examples can be found in metallurgy, geology, and solid-state chemistry. The word ...
s. Historically, crystal shape was defined by measuring the angles between crystal faces with a goniometer. 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. Fe1−xAlx(acac)3 will be deep or pale pink depending on the Fe/Al ratio, x. Double sulfates, such as
Tutton's salt Tutton's salts are a family of salts with the formula M2M'(SO4)2(H2O)6 (sulfates) or M2M'(SeO4)2(H2O)6 (selenates). These materials are double salts, which means that they contain two different cations, M+ and M'2+ crystallized in the same regular ...
, with the generic formula MI2MII(SO4)2.6H2O, where MI is an alkali metal and MII 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 , where is a valence (chemistry), monovalent cation such as potassium or a ...
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 , which means ''spine'' in reference to its pointed crystals. Properties S ...
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, for example) does not necessaril ...
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,Robertson, ''Crimes against humanity'', 90. with its precise definition a matter of longstanding debate. It has been vario ...
suggesting that crystals composed of the same number of similar elements tend to demonstrate isomorphism. Mitscherlich's law is named for
German German(s) may refer to: * Germany (of or related to) ** Germania (historical use) * Germans, citizens of Germany, people of German ancestry, or native speakers of the German language ** For citizens of Germany, see also German nationality law **Ge ...
chemist
Eilhard Mitscherlich Eilhard Mitscherlich (; 7 January 179428 August 1863) was a German chemist, who is perhaps best remembered today for his discovery of the phenomenon of crystallographic isomorphism in 1819. Early life and work Mitscherlich was born at Neuende ...
, who formulated the law and published it between 1819 and 1823. According to
Ferenc Szabadváry Ferenc Szabadváry (1 September 1923 – 21 May 2006) was a Hungarian chemist and historian. From 1971 he was director at the Hungarian National Museum for Science and Technology. In 1960 he published a history of analytical chemistry in Hunga ...
, 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)."


See also

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Asterism (gemology) An asterism () is a star-shaped concentration of reflected or refracted light from a gemstone. Asterisms can appear when a suitable stone is cut ''en cabochon'' i.e. shaped and polished (not faceted). A gemstone that exhibits this effect is re ...
*
Polymorphism (materials science) In materials science, polymorphism describes the existence of a solid material in more than one form or crystal structure. Polymorphism is a form of isomerism. Any crystalline material can exhibit the phenomenon. Allotropy refers to polymorphism ...
*
Goldschmidt tolerance factor Goldschmidt's tolerance factor (from the German word ''Toleranzfaktor'') is an indicator for the stability and distortion of crystal structures. It was originally only used to describe the perovskite ABO3 structure, but now tolerance factors are a ...
*
Solid solution A solid solution, a term popularly used for metals, is a homogenous mixture of two different kinds of atoms in solid state and have a single crystal structure. Many examples can be found in metallurgy, geology, and solid-state chemistry. The word ...
*
Vegard's law In crystallography, materials science and metallurgy, Vegard's law is an empirical finding (heuristic approach) resembling the rule of mixtures. In 1921, Lars Vegard discovered that the lattice parameter of a solid solution of two constituents is ...


References

{{reflist Crystallography Mineralogy concepts