Editorial for Special Issue “Isomorphism, Chemical Variability and Solid Solutions of Minerals and Related Compounds, 2nd Edition”

1. Introduction: General Definitions and Regularities

The concepts of isomorphism and solid solutions are closely related to each other. Isomorphism in mineralogy refers to the ability of different minerals to have the same crystal structure. Crystals of isostructural minerals may have different habit shapes, but are characterized by similar interfacial angles. The term solid solution refers to a solid homogeneous mixture of two compounds with a single crystal structure. Isomorphic series, comprising two isostructural minerals, or isomorphic systems, comprising more than two, between pure end-members can be complete or partial.

Most minerals are ionic compounds or oxides. Ions with similar radii and identical charges usually easily replace each other at the same site of the crystal structure, which contributes to the formation of continuous series and systems of solid solutions. The smaller the radius of a cation and its coordination number in a given structure, the higher its force characteristics.

Table 1. Kinds of cations and their selected properties [CN—coordination number, r—ionic radius (Å), ν—wavenumber of stretching vibrations of coordination polyhedra (cm⁻¹)].

Cation Type	CN	r	Examples	Trend to Isomorphous Substitutions	Trend to Site Vacancies	Trend to Site Splitting	ν
T	4	<0.5	Si4+, Al3+, P5+, B3+, Be2+	-	-	-	850–1100
M	5–6	0.6–0.7	W6+, Nb5+, Ta5+, Ti4+, Sn4+, Zr4+, Fe3+, Y3+, Mn3+	+	-	-	550–750
D	6	0.7–1.0	Mg2+, Zn2+, Fe2+, Mn2+, Ca2+	+	+	-	400–500
A	>6	1.1–1.5	Na+, Ca+, Sr2+, Ba2+, Pb2+, K+, H3O+	+	+	+	<400

shows the selected properties of some cations, arranged in order of decreasing force strength. Within each group of cations, with the exception of T-cations, isomorphic substitutions are common. T-cations are usually ordered in different positions of the crystal structure (the exception is the pair Si⁴⁺ and Al³⁺).

There are several types of isomorphic substitutions. In the simplest mechanism (homovalent isomorphism), an ion is replaced by an ion of the same charge in the same position of the crystal structure. Typical examples of such substitutions include the substitutions Mg²⁺ ↔ Fe²⁺ in the continuous isomorphic series magnesite MgCO₃—siderite FeCO₃, and F⁻ ↔ Cl⁻ in the continuous isomorphic series fluorapatite Ca₅(PO4)₃F—chlorapatite Ca₅(PO₄)₃Cl. However, the continuous isomorphic series magnesite MgCO₃—calcite CaCO₃ is not realized under equilibrium conditions due to the large difference in the ionic radii of calcium and magnesium cations: in the middle part of this series, calcium and magnesium are ordered in different positions to form a dolomite structure.

In heterovalent isomorphism, the R^q1 ion, which has a charge q1, is replaced by a R^q2 ion of a different charge, which requires compensation of the charge in another position. The general scheme of coupled heterovalent substitution with a change in charge by the value i is as follows: ^Site1R^q1 + ^Site2R^q2 ↔ ^Site1R^q1+i + ^Site2R^q2−i.

Isomorphic substitutions may involve not individual atoms, but groups in which the atoms are linked by covalent bonds. In particular, the tetrahedral groups PO₄³⁻, AsO₄³⁻, and VO₄³⁻ easily replace each other in the structures of various minerals. In some cases, such substitutions may change not only the charge of the polyatomic anion, but also the coordination number of the central atom (a case of heteropolyhedral isomorphism). For example, in apatite, some of the PO₄³⁻ tetrahedra may be replaced by triangular CO₃²⁻ groups. According to the classical definition, such a substitution is not isomorphic, since it is accompanied by the appearance of new positions in the crystal structure; however, heteropolyhedral isomorphism has recently been considered within the framework of the general concept of solid solutions. One example of the heteropolyhedral isomorphism of oxides is minerals of the columbite group. Unlike other columbite-supergroup minerals containing only octahedrally coordinated metal atoms, members of the samarskite group contain a relatively large cation at the A site with a 6+2-fold coordination [1]. This is due to the distortion of the crystal structure without changing its topological type.

Blocky isomorphism is the most complex kind of site substitution in minerals. It is defined as the ability of groups of atoms or ions having different configurations to replace each other in crystal structures [2]. Such substitutions are known for a large number of alkaline zircono- and titanosilicates [3]. In particular, eudialyte-group minerals exhibit an ability to blocky isomorphism involving several sites of high-force-strength cations belonging to the framework, and at numerous sites of extra-framework cations and anions [4]. In these minerals, the M2 micro-region situated between six-membered rings of octahedra, M1₆O₂₄, can be populated by ^IVFe²⁺, ^VFe²⁺, ^VFe³⁺, ^VIFe³⁺, ^VMn²⁺, ^VIMn²⁺, ^IVZr, ^IVTa, ^IVNa, ^VNa, ^VINa, ^VIINa, ^VIK, ^VIIK, and ^VIIIK, where Roman numerals denote coordination numbers, whereas micro-regions at the central parts of the ^IVSi₉O₂₇ nine-membered rings of tetrahedra can contain NbO₆ octahedra, SiO₄ tetrahedra, or be vacant. These substitutions result in the rearrangement of atoms in the local environments of corresponding micro-regions, whereas the framework topology and unit–cell dimensions remain almost unchanged.

New data on the crystallochemical properties of minerals expand our understanding of the mechanisms of isomorphic substitutions in crystals. A number of such examples are described in articles included in the Special Issue titled “Isomorphism, Chemical Variability and Solid Solutions of Minerals and Related Compounds, 2nd Edition”.

2. Overview of the Special Issue Contributions

Crystal structures of most microporous and mesoporous materials are stabilized by large low-force-strength cations (type A cations: see Table 1). Such materials are widely used in different technologies due to a high ion mobility of A-cations. The crystal structures and properties of minerals and their synthetic analogs with ion-exchange and ion-conducting properties are discussed in [5]. It was shown therein that fast ionic transport is related to the combination of steric factors (including relationships between the sizes of extra-framework cations and the diameter of conduction channels) and the activation energy of the ion transfer. In an ideal crystal, all extra-framework sites are completely occupied. As a result, in such crystals, ionic transport is impossible. However, several kinds of heterovalent isomorphic substitution impurities may result in the appearance of partially occupied positions.

In homovalent isomorphism, the impurity cation or anion often enters selectively into one of two or more positions of the main ion. This situation occurs in the case of calcioveatchite, a Ca-Sr-ordered analog of veatchite. Its general formula is Sr(Ca,Sr)B₁₁O₁₆(OH)₅·H₂O, where Ca for Sr substitution occurs mainly at one of two cation sites: 11-fold cation polyhedron is occupied mainly by Sr, whereas the 10-fold polyhedron is Ca-dominant [6].

Similarly, in the crystal structure of V-bearing silicocarnotite, Ca₅[(PO₄)(SiO₄)](PO₄,VO₄), the vanadate anion preferably substitutes one of two nonequivalent PO₄ tetrahedra [7]. Ca position splitting observed in silicocarnotite may be related to the partial ordering of Si and P.

An example of heterovalent isomorphism is the coupled substitution ^VIFe²⁺ + ^IVSi⁴⁺ ↔ ^VI(Al³⁺,Fe³⁺) + ^IVAl³⁺ in Fe-bearing serpentines and chlorites with the simplified general formula (Fe²⁺,Fe³⁺,Al)₃[(Si,Al)₂O₅](OH)₄. Direct methods were used to solve the crystal structure of a representative of this solid-solution series with a serpentine structure (the 2H₁ polytype) and composition close to that of the berthierine end-member, (Fe²⁺₂Al)[(SiAl)O₅](OH)₄ [8]. It was shown that berthierine crystallizes metastably in the stability field of chamosite.

Isomorphic substitutions of extra-framework anions and neutral molecules in microporous structures often occur according to a heteropolyhedral or blocky mechanism. This fact is strikingly illustrated by the sodalite group of minerals, in which the sodalite cavity can contain variable amounts of particles such as Cl⁻, F⁻, OH⁻, HS⁻, S²⁻, SO₄²⁻, S₂⁻, S₄⁻, SO₄²⁻, S₃, S₄, MoO₄²⁻, WO₄²⁻, AsO₄³⁻, and COS. In particular, it was shown in [9] that vladimirivanovite (an orthorhombic analog of haüyne with a commensurately modulated structure) contains SO₄²⁻, S₃⁻, and S₄ groups, the contents of which vary over wide limits. The general formula of vladimirivanovite is (Na⁺_6.0–6.4Ca²⁺_1.5–1.7)(Al₆Si₆O₂₄)(SO₄²⁻,S₃⁻,S₄)_1.7–1.9(CO₂)_0–0.1·nH₂O (n = 1–3). The commensurate structural modulations of this mineral can be associated with the regular alternation of sulfate anions with S₃⁻ or S₄.

Isomorphic substitutions in minerals are accompanied by significant changes in physical properties such as density, optical characteristics, and the nature of thermal expansion. This is especially evident when hydrogen-free ions are replaced by hydrogen-containing groups with the formation of additional hydrogen bonds. Typical cases of such substitutions in minerals are Na+ → H₂O, K⁺ → H₃O⁺, K⁺→ NH₃⁺, and F⁻ → OH⁻. For example, boussingaultite, (NH₃)₂Mg(SO₄)₂·6H₂O, differs from the microstructural picromerite, K₂Mg(SO₄)₂·6H₂O, in its lower density (1.72 g/cm³ vs. 2.03 g/cm³) and somewhat higher mean refractive index. In addition, boussingaultite shows anomalous thermal behavior with thermal contraction along the c parameter at temperatures below −50 °C [10].