Spinel group

{{Short description|Mineral supergroup}} [[File:Spinel Mineral New York State Museum.jpg|thumb|Spinel (MgAl₂O₄) on display at the New York State Museum in Albany, NY]] The '''spinels''' are any of a class of minerals of general formulation {{chem|A|B|2|X|4}} which crystallise in the cubic (isometric) crystal system, with the X anions (typically chalcogens, like oxygen and sulfur) arranged in a cubic close-packed lattice and the cations A and B occupying some or all of the octahedral and tetrahedral sites in the lattice.<ref>Robert J. Naumann: [https://books.google.com/books?id=7wLLBQAAQBAJ&dq=spinel+ab2x4&pg=PA118 Introduction to the Physics and Chemistry of Materials] CRC Press, 2008, {{ISBN|978-1-4200-6134-5}}. Retrieved 15 April 2018.</ref><ref name=meyer>H-J Meyer: [https://books.google.com/books?id=bW7cxciPCv4C&dq=spinellstruktur&pg=PA316 Festkörperchemie] in: H-J Meyer (ed.), ''Riedel Moderne Anorganische Chemie'', Walter de Gruyter, 2012, {{ISBN|978-3-11-024900-2}}. Retrieved 15 April 2018.</ref> Although the charges of A and B in the prototypical spinel structure are +2 and +3, respectively ({{chem|A|2+|B|2|3+|X|4|2−}}), other combinations incorporating divalent, trivalent, or tetravalent cations, including magnesium, zinc, iron, manganese, aluminium, chromium, titanium, and silicon, are also possible. The anion is normally oxygen; when other chalcogenides constitute the anion sublattice the structure is referred to as a thiospinel.

A and B can also be the same metal with different valences, as is the case with magnetite, {{chem2|Fe3O4}} (as {{chem|Fe|2+|Fe|2|3+|O|4|2−}}), which is the most abundant member of the spinel group.<ref>{{cite book|last=Ernst |first=W. G. |title=Earth Materials |url=https://archive.org/details/earthmaterials0000erns |url-access=registration |location=Englewood Cliffs, NJ |publisher=Prentice-Hall |date=1969 |edition=Print |page=[https://archive.org/details/earthmaterials0000erns/page/58 58]}}</ref> It is even possible for them to be alloys, as seen for example in {{chem|Li|Ni|0.5|Mn|1.5|O|4}}, a material used in some high energy density lithium ion batteries.<ref>{{cite journal | last=Liu | first=D. | last2=Zhu | first2=W. | last3=Trottier | first3=J. | last4=Gagnon | first4=C. | last5=Barray | first5=F. | last6=Guerfi | first6=A. | last7=Mauger | first7=A. | last8=Groult | first8=H. | last9=Julien | first9=C. M. | last10=Goodenough | first10=J. B. | last11=Zaghib | first11=K. | title=Spinel materials for high-voltage cathodes in Li-ion batteries | journal=RSC Adv. | volume=4 | issue=1 | date=2014 | issn=2046-2069 | doi=10.1039/C3RA45706K | doi-access=free | pages=154–167 | url=https://pubs.rsc.org/en/content/articlepdf/2014/ra/c3ra45706k | access-date=2025-05-14}}</ref> Spinels are grouped in series by the B cation.

The group is named for spinel ({{chem|Mg|Al|2|O|4}}), which was once known as "spinel ruby".<ref>{{cite web|url=https://www.britannica.com/science/ruby-spinel|title=ruby spinel|publisher=Encyclopædia Britannica|access-date=2022-11-25}}</ref> (Today the term ''ruby'' is used only for corundum.)

==Spinel group members== Members of the spinel group include:<ref>[http://www.mindat.org/min-29156.html Spinel group at Mindat]</ref> *Aluminium spinels: **Spinel: {{chem2|MgAl2O4}}, after which this class of minerals is named **Gahnite: {{chem2|ZnAl2O4}} **Hercynite: {{chem2|FeAl2O4}} **Galaxite: {{chem2|MnAl2O4}} **Pleonaste: {{chem2|(Mg,Fe)Al2O4}} *Iron spinels: **Cuprospinel: {{chem2|CuFe2O4}} **Franklinite: {{chem2|(Fe,Mn,Zn)(Fe,Mn)2O4}} **Jacobsite: {{chem2|MnFe2O4}}<ref>{{Cite book|chapter-url=https://doi.org/10.1063/1.5112943|doi = 10.1063/1.5112943|chapter = Facile synthesis and temperature dependent dielectric properties of MnFe2O4 nanoparticles|title = Dae Solid State Physics Symposium 2018|year = 2019|last1 = Rawat|first1 = Pankaj Singh|last2 = Srivastava|first2 = R. C.|last3 = Dixit|first3 = Gagan|last4 = Joshi|first4 = G. C.|last5 = Asokan|first5 = K.|volume = 2115|issue = 1|page = 030104|s2cid = 199183122}}</ref><ref>{{Cite journal|doi = 10.1021/ja035474n|title = Effects of Surface Coordination Chemistry on the Magnetic Properties of MnFe2O4 Spinel Ferrite Nanoparticles|year = 2003|last1 = Vestal|first1 = Christy R.|last2 = Zhang|first2 = Z. John|journal = Journal of the American Chemical Society|volume = 125|issue = 32|pages = 9828–9833|pmid = 12904049}}</ref> **Magnesioferrite: {{chem2|MgFe2O4}} **Magnetite: {{chem2|FeFe2O4}}, where one Fe is +2 and two Fe's are +3, respectively. **Trevorite: {{chem2|NiFe2O4}} **Ulvöspinel: {{chem2|TiFe2O4}} **Zinc ferrite: {{chem2|(Zn,Fe)Fe2O4}} *Chromium spinels: **Chromite: {{chem2|FeCr2O4}} **Magnesiochromite: {{chem2|MgCr2O4}} **Zincochromite: {{chem2|ZnCr2O4}} *Cobalt spinels: **Manganesecobaltite: {{chem2|Mn1.5Co1.5O4}}<ref>{{cite book |title=American Elements, Manganese Cobalt Oxide, Spinel Powder |url=https://www.americanelements.com/manganese-cobalt-oxide-spinel-powder}}</ref> *Vanadium spinels: **Coulsonite: {{chem2|FeV2O4}} **Magnesiocoulsonite: {{chem2|MgV2O4}} *Others with the spinel structure: **Ringwoodite: {{chem2|(Mg,Fe)2SiO4}}, an abundant olivine polymorph within the Earth's mantle from about 520 to 660&nbsp;km depth, and a rare mineral in meteorites ** Musgravite: {{chem2|Be(Mg,Fe,Zn)2Al6O12}} a type of "multi-spinel".

There are many more compounds with a spinel structure, e.g. the thiospinels and selenospinels, that can be synthesized in the lab or in some cases occur as minerals.

The heterogeneity of spinel group members varies based on composition with ferrous and magnesium based members varying greatly as in solid solution, which requires similarly sized cations. However, ferric and aluminium based spinels are almost entirely homogeneous due to their large size difference.<ref>{{cite book|last=Ernst |first=W. G. |title=Earth Materials |url=https://archive.org/details/earthmaterials0000erns |url-access=registration |location=Englewood Cliffs, NJ |publisher=Prentice-Hall |date=1969 |edition=Print |page=[https://archive.org/details/earthmaterials0000erns/page/59 59]}}</ref>

==The spinel structure== thumb|right|Crystal structure of spinel The space group for a spinel group mineral may be Fd{{overline|3}}m (the same as for diamond), but in some cases (such as spinel itself, {{chem|MgAl|2|O|4}}, beyond 452.6 K<ref>{{Cite journal |last1=Zhang |first1=Liang |last2=Ji |first2=Guang-Fu |last3=Zhao |first3=Feng |last4=Meng |first4=Chuan-Min |last5=Wei |first5=Dong-Qing |date=February 2011 |title=The first-principle studies of the crystal phase transitions: Fd3m-MgAl2O4→F4-3m-MgAl2O4 |url=https://linkinghub.elsevier.com/retrieve/pii/S0921452610010100 |journal=Physica B: Condensed Matter |language=en |volume=406 |issue=3 |pages=335–338 |doi=10.1016/j.physb.2010.10.054|bibcode=2011PhyB..406..335Z |url-access=subscription }}</ref>) it is actually the tetrahedral F{{overline|4}}3m.<ref>{{cite web |last1=Robert John Lancashire |title=Normal Spinels |url=http://wwwchem.uwimona.edu.jm/courses/spinel.html |website=CHEM2101 (C 21J) Inorganic Chemistry - Chemistry of Transition Metal Complexes |publisher=University of the West Indies|archive-url=https://web.archive.org/web/20230808174808/http://wwwchem.uwimona.edu.jm/courses/spinel.html |archive-date=2023-08-08 }}</ref><ref>{{cite journal |display-authors=etal|last1=N. W. Grimes |title=New Symmetry and Structure for Spinel |journal=Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences |volume=386 |issue=1791 |pages=333–345 |date=Apr 8, 1983 |doi=10.1098/rspa.1983.0039 |jstor=2397417 |bibcode=1983RSPSA.386..333G |s2cid=96560029 }}</ref><ref>{{cite journal |display-authors=etal|last1=L. Hwang |title=On the space group of {{chem|MgAl|2|O|4}} spinel |journal=Philosophical Magazine |date=Jul 1973 |doi=10.1080/14786437308217448 |url=https://www.researchgate.net/publication/233373497}}</ref> <ref>{{cite journal | last1 = Assadi | first1 = M. Hussein N. | last2 = H. | first2 = Katayama-Yoshida | date = 2019 | title = Covalency a Pathway for Achieving High Magnetisation in TMFe₂O₄ Compounds | journal = J. Phys. Soc. Jpn. | volume = 88 | issue = 4 | article-number = 044706 | doi = 10.7566/JPSJ.88.044706 | arxiv= 2004.10948 | bibcode = 2019JPSJ...88d4706A | s2cid = 127456231 }}</ref>

Normal spinel structures have oxygen ions closely approximating a cubic close-packed latice with eight tetrahedral and four octahedral sites per formula unit (but eight times as many per unit cell). The tetrahedral spaces are smaller than the octahedral spaces. B ions occupy half the octahedral holes, while A ions occupy one-eighth of the tetrahedral holes.<ref>{{Cite journal |last=Verwey |first=E.J.W. |last2=Heilmann |first2=E.L. |date=April 1, 1947 |title=Physical Properties and Cation Arrangement of Oxides with Spinel Structures I. Cation Arrangement in Spinels |url=https://pubs.aip.org/aip/jcp/article-abstract/15/4/174/291439/Physical-Properties-and-Cation-Arrangement-of?redirectedFrom=fulltext |journal=The Journal of Chemical Physics |volume=15 |issue=4 |pages=174-180 |via=AIP Publishing}}</ref><ref>{{Cite journal |last1=Sickafus |first1=Kurt E. |last2=Wills |first2=John M. |last3=Grimes |first3=Norman W. |date=2004-12-21 |title=Structure of Spinel |url=https://onlinelibrary.wiley.com/doi/10.1111/j.1151-2916.1999.tb02241.x |journal=Journal of the American Ceramic Society |language=en |volume=82 |issue=12 |pages=3279–3292 |doi=10.1111/j.1151-2916.1999.tb02241.x|url-access=subscription }}</ref> The mineral spinel {{chem2|MgAl2O4}} has a normal spinel structure.

In a normal spinel structure, the ions are in the following positions, where i, j, and k are arbitrary integers and δ, ε, and ζ are small real numbers (note that the unit cell can be chosen differently, giving different coordinates):<ref>See [http://aflowlib.org/prototype-encyclopedia/A2BC4_cF56_227_d_a_e.html Spinel Structure] in the Encyclopedia of Crystallographic Prototypes, which gives coordinates for the Fd{{overline|3}}m case.</ref>

X: (1/4-δ, δ, δ ) + ((i+j)/2, (j+k)/2, (i+k)/2) ( δ, 1/4-δ, δ ) + ((i+j)/2, (j+k)/2, (i+k)/2) ( δ, δ, 1/4-δ) + ((i+j)/2, (j+k)/2, (i+k)/2) (1/4-δ, 1/4-δ, 1/4-δ) + ((i+j)/2, (j+k)/2, (i+k)/2) (3/4+ε, 1/2-ε, 1/2-ε) + ((i+j)/2, (j+k)/2, (i+k)/2) (1-ε, 1/4+ε, 1/2-ε) + ((i+j)/2, (j+k)/2, (i+k)/2) (1-ε, 1/2-ε, 1/4+ε) + ((i+j)/2, (j+k)/2, (i+k)/2) (3/4+ε, 1/4+ε, 1/4+ε) + ((i+j)/2, (j+k)/2, (i+k)/2) A: (1/8, 1/8, 1/8) + ((i+j)/2, (j+k)/2, (i+k)/2) (7/8, 3/8, 3/8) + ((i+j)/2, (j+k)/2, (i+k)/2) B: (1/2+ζ, ζ, ζ ) + ((i+j)/2, (j+k)/2, (i+k)/2) (1/2+ζ, 1/4-ζ, 1/4-ζ) + ((i+j)/2, (j+k)/2, (i+k)/2) (3/4-ζ, 1/4-ζ, ζ ) + ((i+j)/2, (j+k)/2, (i+k)/2) (3/4-ζ, ζ, 1/4-ζ) + ((i+j)/2, (j+k)/2, (i+k)/2)

The first four X positions form a tetrahedron around the first A position, and the last four form one around the second A position. When the space group is Fd{{overline|3}}m then δ=ε and ζ=0. In this case, a three-fold rotoinversion with axis in the 111 direction is centred on the point (0,&nbsp;0,&nbsp;0) (where there is no ion) and can also be centred on the B ion at (1/2,&nbsp;1/2,&nbsp;1/2), and in fact every B ion is the centre of a three-fold rotoinversion (point group ''D''{{sub|3''d''}}). Under this space group the two A positions are equivalent. If the space group is F{{overline|4}}3m then the three-fold rotoinversions become simple three-fold rotations (point group ''C''{{sub|3''v''}}) because the inversion disappears, and the two A positions are no longer equivalent.

Every ion is on at least three mirror planes and at least one three-fold rotation axis. The structure has tetrahedral symmetry around each A ion, and the A ions are arranged just like the carbon atoms in diamond. There are another eight tetrahedral sites per unit cell that are empty, each one surrounded by a tetrahedron of B as well as a tetrahedron of X ions.

Inverse spinel structures have a different cation distribution in that all of the A cations and half of the B cations occupy octahedral sites, while the other half of the B cations occupy tetrahedral sites. An example of an inverse spinel is {{chem2|Fe3O4}}, if the Fe²⁺ (A²⁺) ions are d⁶ high-spin and the Fe³⁺ (B³⁺) ions are d⁵ high-spin.

In addition, intermediate cases exist where the cation distribution can be described as (A_1−''x''B_''x'')[A_{{{frac|''x''|2}}}B_{1−{{frac|''x''|2}}}]₂O₄, where parentheses () and brackets [] are used to denote tetrahedral and octahedral sites, respectively. The so-called inversion degree, ''x'', adopts values between 0 (normal) and 1 (inverse), and is equal to {{frac|2|3}} for a completely random cation distribution.

The cation distribution in spinel structures are related to the crystal field stabilization energies (CFSE) of the constituent transition metals. Some ions may have a distinct preference for the octahedral site depending on the ''d-electron'' count. If the A²⁺ ions have a strong preference for the octahedral site, they will displace half of the B³⁺ ions from the octahedral sites to tetrahedral sites. Similarly, if the B³⁺ ions have a low or zero ''octahedral site stabilization energy'' (OSSE), then they will occupy tetrahedral sites, leaving octahedral sites for the A²⁺ ions.

Burdett and co-workers proposed an alternative treatment of the problem of spinel inversion, using the relative sizes of the s and p atomic orbitals of the two types of atom to determine their site preferences.<ref>{{cite journal|doi=10.1021/ja00365a019|author=J.K. Burdett, G.L. Price and S.L. Price|journal=J. Am. Chem. Soc.|volume=104|year=1982|pages=92–95|title=Role of the crystal-field theory in determining the structures of spinels}}</ref> This is because the dominant stabilizing interaction in the solids is not the crystal field stabilization energy generated by the interaction of the ligands with the d electrons, but the σ-type interactions between the metal cations and the oxide anions. This rationale can explain anomalies in the spinel structures that crystal-field theory cannot, such as the marked preference of Al³⁺ cations for octahedral sites or of Zn²⁺ for tetrahedral sites, which crystal field theory would predict neither has a site preference. Only in cases where this size-based approach indicates no preference for one structure over another do crystal field effects make any difference; in effect they are just a small perturbation that can sometimes affect the relative preferences, but which often do not.

== Common uses in industry and technology == Spinels commonly form in high temperature processes. Either native oxide scales of metals,<ref>{{cite journal|last1=Hyun Park |first1=Joo |date=2007 |title=Formation Mechanism of Spinel-Type Inclusions in High-Alloyed Stainless Steel Melts |journal=Metallurgical and Materials Transactions B |volume=38 |issue=4 |pages=657–663 |doi=10.1007/s11663-007-9066-x|bibcode=2007MMTB...38..657P |s2cid=135979316 }}</ref> or intentional deposition of spinel coatings<ref>{{Cite thesis |title=On the degradation of porous stainless steel |first=L. |last=Rose |pages=144–168 |year=2011 |doi=10.14288/1.0071732 |publisher=University of British Columbia }}</ref> can be used to protect base metals from oxidation or corrosion. The presence of spinels may hereby serve as thin (few micrometer thick) functional layers, that prevent the diffusion of oxygen (or other atmospheric) ions or specific metal ions such as chromium, which otherwise exhibits a fast diffusion process at high temperatures.

=== Magnetoelectric and multiferroic properties of spinels === It is widely known that magnetism and electricity are interrelated from Maxwell's equations. However, these properties are usually studied independently in materials.These special materials exhibit Magnetoelectric effect such that there is a linear coupling between electric and magnetic fields, with the firstof its kind being Cr2O3. The magnetoelectric behaviour of spinel oxides can be understood by starting from the basic idea of ferroelectricity. A ferroelectric material develops electric polarization that can be reversed by an external electric field, usually because small ionic shifts break inversion symmetry in the crystal structure.<ref>R. E. Cohen, "Origin of ferroelectricity in perovskite oxides", ''Nature'' 358, 136–138 (1992).</ref> Multiferroics combine electric order with magnetic order. In many spinel oxides, the polarization does not already exist but only appears after a particular magnetic structure forms, placing them among type-II multiferroics where magnetism creates the polar state.<ref>S.–W. Cheong and M. Mostovoy, "Multiferroics: a magnetic twist for ferroelectricity", ''Nature Materials'' 6, 13–20 (2007).</ref><ref>Y. Tokura, S. Seki and N. Nagaosa, "Multiferroics of spin origin", ''Reports on Progress in Physics'' 77, 076501 (2014).</ref>

The magnetoelectric effect requires the simultaneous breaking of inversion symmetry and time-reversal symmetry.<ref>M. Fiebig, "Revival of the magnetoelectric effect", ''Journal of Physics D: Applied Physics'' 38, R123–R152 (2005).</ref> Spinels crystallize in the centrosymmetric space group Fd3̅m, but their magnetic structures often break inversion symmetry even when the lattice does not. This is connected to the spinel B-site sublattice, which forms a pyrochlore network of corner-sharing tetrahedra, a geometry known for strong magnetic frustration.<ref>J. S. Gardner, M. J. P. Gingras and J. E. Greedan, "Magnetic frustration in rare-earth pyrochlores", ''Reviews of Modern Physics'' 82, 53–107 (2010).</ref><ref>L. Balents, "Spin liquids in frustrated magnets", ''Nature'' 464, 199–208 (2010).</ref> Because a simple up–down antiferromagnetic order is impossible, spins often form spirals, helices, or canted states that remove inversion symmetry, allowing magnetically induced ferroelectricity.

Two main microscopic mechanisms explain how magnetic structures produce polarization in spinels. The first is the inverse Dzyaloshinskii–Moriya mechanism, where non-collinear spins generate a local electric dipole proportional to the spiral's chirality.<ref>H. Katsura, N. Nagaosa and A. V. Balatsky, "Spin current mechanism of multiferroicity", ''Physical Review Letters'' 95, 057205 (2005).</ref><ref>M. Mostovoy, "Ferroelectricity in spiral magnets", ''Physical Review Letters'' 96, 067601 (2006).</ref> The second is exchange striction, where parallel and antiparallel spin pairs refer different bond lengths; an asymmetric arrangement of these distortions generates a net polarization.<ref>L. C. Chapon et al., "Structural origin of the magnetoelectric effect in frustrated magnets", ''Physical Review Letters'' 93, 177402 (2004).</ref><ref>A. Garcia et al.,"Magnetostrictive and multiferroic effects in spinels", ''Physical Review B'' 82, 180401 (2010).</ref> In vanadium spinels, orbital ordering of the V³⁺ ions further modifies the lattice and enhances this mechanism.<ref>Y. Nishihara et al., "Orbital ordering and multiferroicity in vanadium spinels",''Physical Review B'' 85, 064412 (2012).</ref>

Several examples highlight these mechanisms. In CoCr₂O₄, a conical spin spiral forms below about 26 K and produces a ferroelectric polarization whose sign reverses with the chirality of the spiral.<ref>Y. Yamasaki et al., "Magnetic reversal of the ferroelectric polarization in a multiferroic spinel oxide", ''Physical Review Letters'' 96, 207204 (2006).</ref> In ZnCr₂Se₄, a long-wavelength helical magnet produces a magnetic-field-tunable polarization, illustrating continuous magnetoelectric control.<ref>I. Kezsmarki et al., "Enhanced directional dichroism in the conical spin state of ZnCr₂Se₄",''Physical Review Letters'' 106, 057403 (2011).</ref> Vanadium spinels such as MnV₂O₄ display strong coupling between lattice distortion, orbital order, and spin arrangement, producing multiferroicity through cooperative exchange striction.<ref>V. O. Garlea et al., "Noncollinear spin ordering in MnV₂O₄", ''Physical Review Letters'' 100, 066404 (2008).</ref>

Spin–phonon coupling also plays a central role. Phonon anomalies detected in Raman or infrared spectra at magnetic transition temperatures show that lattice vibrations are strongly affected by spin ordering.<ref>B. Poojitha et al., "Spin–phonon coupling in ferrimagnet spinel CoMn₂O₄", ''Journal of Chemical Physics'' 156, 204401 (2022).</ref><ref>K. Wakamura and T. Arai, "Phonon anomalies in magnetically ordered spinel compounds", ''Journal of Physics and Chemistry of Solids'' 51, 771–776 (1990).</ref> These effects demonstrate how the crystallographic structure, magnetic frustration, and non-collinear ordering in spinels work together to produce magnetoelectric and multiferroic behaviour.

=== Thermo-electric (thermochromic) properties of spinels === Some AB₂O₄ spinels exibit thermochromism]. {| class="wikitable" |+Thermochromism of spinels; AB₂O₄ <ref>{{Cite book |last=Rost |first=Florian |url=https://www.academia.edu/164955847/Untersuchungen_der_Thermochromie_von_Spinellen_Sammelband_PDF_Pack_ |title=Untersuchungen der Thermochromie von Spinellen (Sammelband; PDF-Pack) |date=2026-03-05}}</ref> !Systematic name ↓ & molecular formula !Thermochromism (Y/N, Intensity) |- |'''C'''opper aluminate; CuAl₂O₄ |N→x |- |Copper chromite; CuCr₂O₄ |Y→+ |- |Copper ferrite; CuFe₂O₄ |Y→+++ |- |'''M'''agnesio chromite; MgCr₂O₄ |Y→+ |- |Magnesio ferrite; MgFe₂O₄ |Y→+ |- |Magnesio spinel; MgAl₂O₄ |N→x |- |'''Z'''inc aluminate; ZnAl₂O₄ |N→x |- |Zinc chromite; ZnCr₂O₄ |Y→+ |- |Zinc ferrite; ZnFe₂O₄ |Y→++ |} The table below is ordered in descending order, in regards to thermochromism of +II-cations Cu²⁺ ↑ > Zn²⁺ > Mg²⁺ ↓ & +III-cations Fe³⁺ ↑ > Cr³⁺ > Al³⁺ ↓.

{| class="wikitable" |+Thermochromism of cations in AB₂O₄ <ref>{{Cite book |last=Rost |first=Florian |url=https://www.academia.edu/164955847/Untersuchungen_der_Thermochromie_von_Spinellen_Sammelband_PDF_Pack_ |title=Untersuchungen der Thermochromie von Spinellen (Sammelband; PDF-Pack) |date=2026-03-05}}</ref> !A²⁺/B³⁺ !Fe³⁺ ↑ !Cr³⁺ !Al³⁺ ↓ |- |Cu²⁺ ↑ |CuFe₂O₄→+++ |CuCr₂O₄ →+ |CuAl₂O₄ →x |- |Zn²⁺ |ZnFe₂O₄→++ |ZnCr₂O₄ →+ |ZnAl₂O₄ →x |- |Mg²⁺ ↓ |MgFe₂O₄ →+ |MgCr₂O₄ →+ |MgAl₂O₄ →x |}

== References == {{reflist}}

== Further reading == *{{cite journal|last1=Biagoni |first1=C. |last2=Pasero |first2=M |date=2014 |title=The systematics of the spinel-type minerals: An overview |journal=American Mineralogist |volume=99 |issue=7 |pages=1254–1264 |doi=10.2138/am.2014.4816|bibcode=2014AmMin..99.1254B |s2cid=102231166 }}

Category:Spinel group