CH.2 Geoscience Basics: Understanding Minerals and Crystallography

⚛ Atomic Substitution

Ionic Substitution: The replacement of one ion by another in a mineral's crystal structure. This happens when ions have similar sizes and charges, and are available during mineral formation. Think of it like LEGOs – similar-sized bricks can fit in the same spot.

Simple Substitution: Complete replacement of one ion by another in any proportion. Olivine ((Mg,Fe)₂SiO₄) is a great example: Magnesium (Mg²⁺) and iron (Fe²⁺) can substitute freely. This creates a solid solution series between the end members forsterite (Mg₂SiO₄) and fayalite (Fe₂SiO₄). End members are the pure forms of a mineral with only one type of ion in a specific site.

Coupled Substitution: Simultaneous substitution of ions with different charges in different sites to maintain electrical neutrality. Plagioclase feldspars are a classic example. Sodium (Na⁺) and calcium (Ca²⁺) substitute in one site, balanced by aluminum (Al³⁺) and silicon (Si⁴⁺) substitution in another. This keeps the overall charge balanced.

Limited Substitution: Partial replacement of one ion by another due to significant size or charge differences. The substitution between calcite (CaCO₃) and magnesite (MgCO₃) is limited because Ca²⁺ is much larger than Mg²⁺. This can lead to miscibility gaps, where certain compositions don't exist in nature.

Solid Solution Series: A continuous range of compositions between two end-member minerals due to complete substitution. The olivine series is a perfect example.

End Members: The pure forms of a mineral in a solid solution series. Forsterite and fayalite are the end members of the olivine solid solution series.

Miscibility Gaps: Ranges of compositions within a solid solution series that do not occur naturally due to limited substitution. These gaps represent compositions that are unstable.

📊 Phase Diagrams

Phase: A physically distinct and homogeneous part of a system. A mineral, a liquid, or a gas are all phases.

Phase Rule: A fundamental principle governing the number of phases that can coexist in equilibrium in a system. The rule is expressed as: P = C + 2 - F, where: - P = Number of phases - C = Number of components (chemical elements or compounds) - F = Degrees of freedom (variables like temperature and pressure that can change without altering the number of phases)

Liquidus: The temperature above which a substance is entirely liquid.

Solidus: The temperature below which a substance is entirely solid.

Eutectic: A point on a phase diagram where a liquid cools to form two solid phases simultaneously.

Peritectic: A point on a phase diagram where a solid phase reacts with a liquid to form a new solid phase.

Solvus: A boundary on a phase diagram separating regions of complete solid solution from regions of limited solid solution.

Lever Rule: A method used to determine the relative proportions of phases in a two-phase region of a phase diagram.

Continuous Reaction Series: A series of minerals that change composition continuously during crystallization or melting. Plagioclase feldspars are an example.

Discontinuous Reaction Series: A series of minerals that change abruptly during crystallization or melting. Bowen's reaction series is a classic example.

Silica Saturation: The relative abundance of silica (SiO₂) in a system, which influences mineral formation. Systems can be silica-undersaturated, silica-saturated, or silica-oversaturated.

⏳ Isotopes and Radiometric Dating

Isotopes: Atoms of the same element with different numbers of neutrons. This leads to different atomic masses. Some isotopes are stable, while others are radioactive.

Isotopic Ratios: The relative abundance of different isotopes of an element. These ratios are used in various geological applications. Examples include δ¹⁸O (oxygen isotopes) and δ¹³C (carbon isotopes).

Radioactive Decay: The spontaneous transformation of an unstable (radioactive) isotope into a more stable isotope. Three main types are: - Alpha (α) decay: Loss of two protons and two neutrons. - Beta (β) decay: Conversion of a neutron to a proton. - Electron capture: Addition of an electron to a proton, converting it to a neutron.

Half-life: The time it takes for half of the atoms in a radioactive sample to decay.

Decay Constant (λ): A measure of the rate of radioactive decay.

Age Calculation: The age of a rock can be calculated using the following equation: t = (1/λ)ln[(D+P)/P], where: - t = age - λ = decay constant - D = number of daughter atoms - P = number of parent atoms

Uranium-Lead Dating: A radiometric dating method using the decay of uranium isotopes (²³⁸U and ²³⁵U) to lead isotopes (²⁰⁶Pb and ²⁰⁷Pb).

Rubidium-Strontium Dating: A radiometric dating method using the decay of rubidium-87 (⁸⁷Rb) to strontium-87 (⁸⁷Sr).

Potassium-Argon Dating: A radiometric dating method using the decay of potassium-40 (⁴⁰K) to argon-40 (⁴⁰Ar).

Concordia Diagram: A graphical representation used in Uranium-Lead dating to determine the age of a sample.

Isochron: A line on a graph representing samples of the same age in Rubidium-Strontium dating.

💎 Crystallography

Crystallography: The study of the structure and symmetry of crystals.

Coordination Polyhedra: Geometric shapes formed by the arrangement of atoms or ions around a central atom or ion in a crystal structure.

Unit Cell: The smallest repeating unit of a crystal lattice. There are seven basic unit cell shapes in three dimensions.

Bravais Lattices: The 14 unique ways to arrange points in three-dimensional space while maintaining symmetry.

Crystal Systems: Seven categories of crystals based on their unit cell symmetry: cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, and trigonal.

Miller Indices: A system of three numbers used to identify crystallographic planes.

Crystal Forms: The external shapes of crystals, determined by the arrangement of crystal faces. Examples include cubes, octahedra, prisms, pyramids, and rhombohedra.

Twinning: The intergrowth of two or more crystals of the same mineral with a symmetrical relationship.

Facts to Memorize

1. Ionic substitution requires similar ion sizes and charges.

2. Simple substitution creates solid solution series between end members.

3. Coupled substitution maintains electrical neutrality.

4. Limited substitution leads to miscibility gaps.

5. The phase rule is P = C + 2 - F.

6. The liquidus is the temperature above which a substance is entirely liquid.

7. The solidus is the temperature below which a substance is entirely solid.

8. Eutectic points involve simultaneous crystallization of two solids.

9. Peritectic points involve a solid reacting with a liquid to form a new solid.

10. Isotopes have the same number of protons but different numbers of neutrons.

11. Radioactive decay transforms unstable isotopes into stable ones.

12. Half-life is the time for half of a radioactive isotope to decay.

13. Uranium-Lead dating uses the decay of uranium to lead.

14. Rubidium-Strontium dating uses the decay of rubidium to strontium.

15. Potassium-Argon dating uses the decay of potassium to argon.

16. Crystallography studies crystal structure and symmetry.

17. There are seven crystal systems and 14 Bravais lattices.

18. Miller indices describe crystallographic planes.

19. Twinning involves the symmetrical intergrowth of crystals.

20. The lever rule helps determine phase proportions in phase diagrams.