Minerals: concept and classification

List the conditions a solid must meet to be considered a mineral and apply this criterion to decide whether glacier ice and fossil amber are minerals.

What is the difference between a mineral and a rock? Give an example of a rock formed by a single mineral and another formed by several different minerals.

Distinguish between an isolated crystal and an aggregate or crystalline mass. Why do many quartz samples not show perfect faces?

What is the difference between the essential minerals and the accessory minerals of a rock? Give an example of each in a granite.

What is the crystalline structure of a mineral and how is it manifested externally in the habit or shape of its crystals?

Graphite and diamond are composed exclusively of carbon and yet their properties are opposite. Based on crystal structure, explain how this is possible (polymorphism).

What is an isomorphous series? Explain, using ion substitution in the crystal lattice, why olivine can vary in composition between forsterite ($\text{Mg}_2\text{SiO}_4$) and fayalite ($\text{Fe}_2\text{SiO}_4$).

The colour of olivine varies from pale green to dark brown according to its iron content. Relate this variation to the isomorphism of the forsterite–fayalite series and explain why colour is not an absolute diagnostic criterion.

During an electron microprobe analysis of a zoned plagioclase crystal from an andesite, you obtain the following cationic data between the core and the rim: in the core, the molar ratio $\text{Ca}/(\text{Ca}+\text{Na}) = 0,72$; in the outermost rim, this ratio drops to $0,28$.

1. a) Justify what coupled ionic substitution mechanism has taken place as the crystal grew and explain why it would be electrostatically unfeasible to substitute only $\text{Ca}^{2+}$ for $\text{Na}^+$ without modifying the proportion of $\text{Si}^{4+}$ and $\text{Al}^{3+}$ in the tetrahedral network.
2. b) A classmate argues that the atomic ratio $\text{Si}/\text{Al}$ must be greater in the core than in the rim of the crystal. Demonstrate why their claim is incorrect using the stoichiometric formulas of anorthite ($\text{CaAl}_2\text{Si}_2\text{O}_8$) and albite ($\text{NaAlSi}_3\text{O}_8$), and deduce what thermal trend the magma chamber experienced during crystallization.

In a petrology laboratory, two silica-rich ($\text{SiO}_2$) rock samples are analyzed:

• Sample A: Comes from a cavity in a rhyolitic lava flow erupted at over $950\text{ }^\circ\text{C}$; it contains microcrystals of tridymite and cristobalite coexisting at room temperature.

• Sample B: Comes from a quartzitic sandstone subjected to ultra-high-pressure metamorphism in a deep subduction zone; it contains coesite partially enclosed in garnets.

1. a) Based on the concept of polymorphism and the stability fields in the silica phase diagram, justify why minerals with identical chemical formulas provide such different geodynamic information about the pressure ($P$) and temperature ($T$) at which they formed.
2. b) Reason why high-temperature or high-pressure phases such as cristobalite and coesite can persist at room temperature and pressure without immediately transforming into $\alpha$-quartz, which is the thermodynamically stable phase at the surface. What kinetic factor is involved in this metastable persistence?

The general formula of garnets is $X_3Y_2(\text{SiO}_4)_3$. Two main solid solution series are distinguished:

• Pyralspites ($Y = \text{Al}^{3+}$; $X = \text{Mg}^{2+}, \text{Fe}^{2+}, \text{Mn}^{2+}$).

• Ugrandites ($X = \text{Ca}^{2+}$; $Y = \text{Al}^{3+}, \text{Fe}^{3+}, \text{Cr}^{3+}$).

You have the following ionic radii in VIII-fold coordination: $\text{Mg}^{2+} = 0,89\text{ Å}$; $\text{Fe}^{2+} = 0,92\text{ Å}$; $\text{Mn}^{2+} = 0,96\text{ Å}$; $\text{Ca}^{2+} = 1,12\text{ Å}$.

1. a) Apply the crystal-chemical rules for isomorphic substitution (percentage difference in ionic radius and charge) to justify why complete solid solution exists between pyrope ($\text{Mg}$), almandine ($\text{Fe}$), and spessartine ($\text{Mn}$), whereas between these and grossular ($\text{Ca}$) there is a pronounced miscibility gap at moderate temperatures.
2. b) In a metapelite, a garnet crystal with concentric zonation is analyzed: the core has $22\,\%$ molar spessartine ($\text{Mn}$) and $4\,\%$ pyrope ($\text{Mg}$), while the rim shows $2\,\%$ spessartine and $26\,\%$ pyrope. Knowing that $\text{Mn}$ enters preferentially at low temperatures and $\text{Mg}$ requires high temperatures, deduce the thermal evolution experienced by the rock during crystal growth and justify why garnet is ideal for recording this metamorphic history.

In a borehole in Cretaceous marine sediments, ammonite fossils whose original shells were made of aragonite (density $2,93\text{ g/cm}^3$, orthorhombic system) are recovered. Petrographic analysis reveals that the external morphology and suture lines are perfectly preserved, but the mineral mass consists entirely of a mosaic of sparry calcite (density $2,71\text{ g/cm}^3$, trigonal system).

1. a) Interpret the mineralogical process that took place (pseudomorphism by polymorphic inversion) and justify, based on the relationship between density, molar volume, and pressure, why aragonite is the stable phase at high pressures whereas under surface conditions it is metastable and tends to transform into calcite.
2. b) If you find primary aragonite preserved without transforming into calcite in a blueschist facies metamorphic rock, deduce what type of exhumation path (rapid cooling vs. slow decompression or hot isothermal decompression) the rock must have experienced to prevent aragonite from reverting to calcite during its ascent to the surface.

Name one representative mineral of each of these chemical groups: carbonates, sulphates, sulphides, oxides and halides.

Classify the following minerals according to their chemical group and state the characteristic anion of each group: quartz ($\text{SiO}_2$), calcite ($\text{CaCO}_3$), pyrite ($\text{FeS}_2$), and gypsum ($\text{CaSO}_4 \cdot 2\ \text{H}_2\text{O}$).

In the laboratory, three unknown silicate minerals (M1, M2, and M3) are analyzed. The following results are obtained:

• M1: Cationic ratio $\text{Si}:\text{O} = 1:4$; lacks cleavage planes (exhibits conchoidal fracture); high density ($3,3\text{ g/cm}^3$).

• M2: Cationic ratio $\text{Si}:\text{O} = 2:5$; perfect and easy cleavage into thin, flexible sheets; medium density ($2,8\text{ g/cm}^3$).

• M3: Cationic ratio $\text{Si}:\text{O} = 1:2$; lacks cleavage; hardness 7 on the Mohs scale and low density ($2,65\text{ g/cm}^3$).

1. a) Reasonably deduce which structural subgroup of silicates each mineral belongs to based on the number of oxygen atoms shared by each $[\text{SiO}_4]^{4-}$ tetrahedron, and propose a representative mineral example for each.
2. b) Justify why the presence of anisotropic chemical bonds (strong in two directions and very weak in the third) explains the sheet cleavage of M2, whereas the isotropic three-dimensional arrangement of M3 prevents the formation of preferential planes of breakage.

Silicates are the most abundant group of minerals in the Earth's crust. Look at the diagram: its basic unit appears on the left, and two linked units on the right. Explain what the $\text{SiO}_4^{4-}$ tetrahedron is, what each sphere represents, and why the ability of tetrahedra to share oxygen atoms gives rise to so many different silicates.

Mica, feldspar, amphibole, pyroxene, olivine and quartz are all silicates. State what they have in common and name at least two subgroups of silicates according to the arrangement of their tetrahedra.

Micas cleave into extremely thin sheets. Relate this property to their phyllosilicate structure, in which the tetrahedra form sheets, and explain why they flake apart with a fingernail.

Pyroxenes and amphiboles are single-chain and double-chain inosilicates, respectively. Explain how this structural difference translates into different cleavage angles ($90°$ versus $60°$ and $120°$).

Quartz, a tectosilicate, lacks cleavage and breaks with conchoidal fracture. Explain why its three-dimensional network of tetrahedra makes it so resistant and compare it with calcite.

Garnet, staurolite and andalusite are typical minerals of metamorphic rocks. Explain why they are called "index minerals" and what information their presence in a schist provides.

During field work on a basalt outcrop, you collect a mafic rock with abundant idiomorphic phenocrysts of an olive-green color, vitreous luster, and conchoidal fracture (no observable cleavage), which scratch common glass (hardness around $6,5-7$). A classmate hypothesizes that they are a variety of green quartz (prase) or green pyroxene.

1. a) Devise a petrological and crystal-chemical argument to completely rule out the presence of primary quartz in equilibrium with that mafic rock, based on silica saturation and the reaction relating olivine to quartz ($\text{Mg}_2\text{SiO}_4 + \text{SiO}_2 \rightleftharpoons 2\text{MgSiO}_3$).
2. b) Justify what diagnostic physical property allows you to unequivocally distinguish whether those green crystals correspond to olivine (nesosilicate) or a clinopyroxene (inosilicate), explaining how this property reflects the internal architecture of their silicon tetrahedra.

The sand fraction of two different sedimentary basins originating from the erosion of the same granitic batholith composed of quartz, K-feldspar, plagioclase, and biotite is studied:

• Basin 1: The sand contains $50\,\%$ angular quartz, $35\,\%$ poorly altered plagioclase and K-feldspar, and $15\,\%$ fresh biotite.

• Basin 2: The sand contains $97\,\%$ well-rounded quartz and barely $3\,\%$ residual K-feldspar, with no detectable presence of plagioclase or biotite.

1. a) Justify the differential disappearance of minerals in Basin 2 by applying Goldich's weathering series and relate it to the thermodynamic crystallization conditions in Bowen's reaction series: why are the minerals formed at higher temperatures in magma the most vulnerable to surface weathering?
2. b) Deduce the environmental conditions of each basin (arid/cold climate versus humid/warm, relief, and length of sedimentary transport) using the concepts of mineralogical and textural maturity.

In a contact metamorphic aureole over pelitic slates, petrographic study shows that as the igneous pluton is approached, muscovite progressively disappears by reacting with quartz according to the reaction:

In that same zone of the aureole, biotite ($\text{K}(\text{Mg},\text{Fe})_3(\text{AlSi}_3\text{O}_{10})(\text{OH})_2$) remains stable in equilibrium with quartz.

1. a) Explain at a crystal-chemical level why biotite exhibits dark coloration and strong pleochroism under a petrographic microscope, whereas muscovite is colorless/light-colored, indicating which octahedral sites of the sheet the cations responsible for this difference occupy.
2. b) A student argues that, since both are phyllosilicates with the same $\text{Si}:\text{O}$ ratio, they should decompose at the same temperature. Refute this argument by justifying the difference in thermal stability based on the distinction between dioctahedral (muscovite) and trioctahedral (biotite) micas, and interpret which aluminosilicate phase ($\text{Al}_2\text{SiO}_5$) you would expect to find in this low-pressure context.