chemistry Chemistry is the scientific study of the properties and behavior of matter. It is a natural science that covers the elements that make up matter to the compounds made of atoms, molecules and ions: their composition, structure, proper ...

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. M ...

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 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 wor ...

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'') ' m ...

. 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 sulfate salt of aluminium with the general formula , where is a monovalent cation such as potassium or ammonium. By itself, "alum" often refers to potassium alum, with the ...

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

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 Hun ...

, 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

{{reflist Crystallography Mineralogy concepts

Mitscherlich's law

See also

References