Model Answer
0 min readIntroduction
The study of rocks and minerals necessitates understanding the conditions under which they form and remain stable. Thermodynamic principles play a vital role in deciphering these conditions. The Gibbs Phase Rule, a cornerstone of physical chemistry, provides a quantitative relationship between the number of components, phases, and degrees of freedom in a system at equilibrium. This rule is extensively used in petrology to interpret mineral assemblages and understand the evolution of igneous, metamorphic, and sedimentary rocks. Understanding the ACF diagram is crucial for interpreting the composition of magmatic and metamorphic rocks.
Thermodynamic Phase Rule: Definition and Mathematical Expression
The Gibbs Phase Rule states the number of independent intensive variables (degrees of freedom, F) that can be changed without altering the number of phases (P) in a system at equilibrium, given the number of components (C). It is mathematically expressed as:
F = C - P + 2
Where:
- F = Degrees of Freedom (number of independent variables like temperature and pressure)
- C = Number of Components (minimum number of chemical constituents needed to describe the composition of all phases)
- P = Number of Phases (physically distinct and homogeneous portions of the system)
- The '+2' represents the two intensive variables, typically temperature and total pressure.
Degree of Freedom Calculation for the Given System
For a system under equilibrium with 8 components (C = 8) and 5 mineral phases (P = 5), the degree of freedom (F) can be calculated using the Gibbs Phase Rule:
F = C - P + 2
F = 8 - 5 + 2
F = 5
Therefore, the system has 5 degrees of freedom. This means that five independent variables (e.g., temperature, pressure, and the chemical potentials of five components) can be varied without changing the number of phases present.
Principle of the ACF Diagram
The ACF diagram (Alkali – Calcium – Feldspar diagram) is a triangular diagram used in petrology to represent the relative proportions of three end-member components in plagioclase feldspars and alkali feldspars. It’s particularly useful in interpreting the composition of igneous and metamorphic rocks, especially those containing feldspars.
The three apexes of the triangle represent the end-member compositions:
- A – Albite (NaAlSi3O8)
- C – Anorthite (CaAl2Si2O8)
- F – Orthoclase/Sanidine (KAlSi3O8)
Any point within the triangle represents a specific feldspar composition, defined by its relative proportions of albite, anorthite, and orthoclase. The diagram is based on the principle that the total composition of the feldspar is fixed, and therefore, knowing the proportions of two components automatically defines the proportion of the third.
Applications of ACF Diagram:
- Determining the composition of coexisting feldspars in igneous and metamorphic rocks.
- Inferring the P-T conditions of rock formation based on feldspar compositions.
- Understanding the evolution of magmatic series.
The ACF diagram is a simplified representation and doesn't account for other components that might be present in feldspars (e.g., Ba, Sr). However, it remains a valuable tool for quick and efficient compositional analysis.
Conclusion
The Gibbs Phase Rule is a fundamental principle governing the behavior of multi-component systems at equilibrium, with significant applications in petrology and geochemistry. Calculating the degree of freedom allows us to understand the variability within a system. The ACF diagram provides a visual and practical method for interpreting feldspar compositions, aiding in the reconstruction of geological processes. These tools, when used in conjunction, provide a powerful framework for understanding the formation and evolution of rocks.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.