Earth Materials. John O'Brien

range, we can define low magnesium calcite and high magnesium calcite in terms of their proportions of calcite (Ct) and magnesite (Ms) end members. Low magnesium calcites generally contain less than 4% magnesium (Mg⁺²) substituting for calcium (Ca⁺²) in this structural site and so have compositions in the range Ct_96–100 = Ms_0–4 (Figure 3.5). High magnesium calcites have more than 4% magnesium substituting for calcium and therefore have compositions in the range Ct_75–96 = Ms_4–25. Some workers further subdivide these compositions into medium magnesium and high magnesium calcite with a boundary at 10% magnesium (James and Jones 2016). Compositions from Ms_40–55 = Ct_45–60 actually have a different structure – that of the double carbonate mineral dolomite whose average composition is CaMg(CO₃)₂. Many other examples exist of limited substitution series with miscibility gaps. The importance of mineral compositional variations that result from variations in substitution can be more fully understood in the context of phase stability diagrams, as discussed in the following section.

3.2 PHASE STABILITY (EQUILIBRIUM) DIAGRAMS

The behavior of materials in Earth systems can be modelled using thermodynamic calculations and/or empirical results from laboratory investigations. The results of such calculations and/or investigations are commonly summarized on phase stability diagrams. A phase is a mechanically separable part of the system. Phase stability (equilibrium) diagrams display the stability fields (conditions under which a phase is stable) for various phases in a system of specified composition. These fields are separated by phase stability boundary lines that represent the conditions under which phase changes from one phase to another occur. Phase stability diagrams related to igneous systems and processes summarize relationships between liquids (melts) and solids (crystals) in a system. Such diagrams usually have temperature increasing upward on the vertical axis and composition shown on the horizontal axis. At high temperatures the system is completely melted. The stability field for 100% liquid is separated from the remainder of the phase diagram by a phase boundary line called the liquidus that represents the temperature above which the system exists as 100% melt and below which it contains some crystals. The low temperature stability field for 100% solid crystals is separated from higher temperature conditions by a phase boundary line called the solidus. At intermediate temperatures between the solidus and liquidus, the system consists of two types of stable phases in equilibrium, both liquid and solid crystals. Phase equilibrium diagrams, based on both theoretical and laboratory analyses, exist for a variety of multicomponent systems. A one‐component and five representative two‐component systems related to the discussion of igneous rocks and processes (Chapters 7–10) are discussed below. Metamorphic phase diagrams are discussed in Chapter 18. For discussions of systems that are beyond the scope of this text, including three‐ and four‐component systems, the reader is referred to mineralogy books by Wenk and Bulakh (2016), Nesse (2016), Dyer et al. (2008) and Klein and Dutrow (2007) and to petrology books by Frost and Frost (2019), Philpotts and Ague (2009), Winter (2009) and Best (2000). Some of the more important terms you will encounter in this discussion are defined in Table 3.1.

Table 3.1 A list of some common terms used in discussing phase diagrams.

Terms	Definitions
Liquidus	Phase boundary (line) that separates the all‐liquid (melt) stability field from stability fields that contain at least some solids (crystals)
Solidus	Phase boundary (line) that separates the all‐solid (crystal) stability field from stability fields that contain at least some liquid (melt)
Eutectic	Condition under which liquid (melt) is in equilibrium with two different solids
Peritectic	Condition under which a reaction occurs between a pre‐existing solid phase and a liquid (melt) to produce a new solid phase
Phase	A mechanically separable part of the system; may be a liquid, gas or solid with a discrete set of mechanical properties and composition
Invariant melting	Occurs when melts of the same composition are produced by melting rocks of different initial composition
Incongruent melting	Occurs when a solid mineral phase melts to produce a melt and a different mineral with a different composition from the initial mineral
Discontinuous reaction	Mineral crystals and melt react to produce a completely different mineral; negligible solid solution exists between the minerals
Continuous reaction	Mineral crystals and melt react to continuously and incrementally change the composition of both; requires a mineral solid solution series
Solvus	Phase boundary (line) that separates conditions in which complete solid solution occurs within a mineral series from conditions under which solid solution is limited

      3.2.1 The phase rule

      The phase rule (Gibbs 1928) governs the number of phases that can coexist in equilibrium in any system and can be written as:

      where

       P represents the number of phases present in a system. Phases are mechanically separable varieties of matter that can be distinguished from other varieties based on their composition, structure and/or state. Phases in igneous systems include minerals of various compositions, and crystal structures, amorphous solids (glass) and fluids such as liquids or gases. All phases are composed of one or more of the components used to define the composition of the system.

       C designates the minimum number of chemical components required to define the phases in the system. These chemical components are usually expressed as proportions of oxides. The most common chemical components in igneous reactions include SiO2, Al2O3, FeO, Fe2O3, MgO, CaO, Na2O, K2O, H2O, and CO2. All phases in the system can be made by combining components in various proportions.

       F refers to the number of degrees of freedom or variance. Variance means the number of independent factors that can vary, such as temperature, pressure, and the composition of each phase, without changing the phases that are in equilibrium with one another. We will use the first phase diagram in the next section to show how the phase rule can be applied to understanding phase diagrams. A discussion of the phase rule and of phase diagrams related to metamorphic processes is presented in Chapter 18.

      3.2.2 One component phase diagram: silica polymorphs

Pure silica (SiO₂) occurs as a number of different mineral phases, each characterized by a different crystal structure. These silica minerals include low quartz (alpha quartz), high quartz (beta quartz),