Fick, Roult and Henry’s law in petrogenesis

Fick’s Law of Diffusion in Igneous Petrology

Fick’s law describes the movement of elements and ions due to concentration gradients, crucial for understanding magmatic differentiation and element transport –

1. Fick’s First Law
   • J = -D*dC/dx
   • States that the flux of a species is proportional to its concentration gradient (dC/dx), where D is the diffusion coefficient.
   • In igneous systems, this governs how elements like Fe, Mg and trace elements diffuse in a cooling magma.
2. Fick’s Second Law
   • dC/dt = D(d²C/dx²)
   • Predicts how concentration changes over time, important for crystal zoning and magma chamber evolution.
   • Helps in estimating cooling rates of magma and interpreting diffusion profiles in minerals.

Examples

1. Zoned Crystals in Igneous Rocks
   • Olivine in Basaltic Magma : Mg-Fe diffusion in olivine shows compositional zoning, reflecting changes in magma composition and cooling rates
   • Faster cooling – Sharp compositional gradients, Slower cooling – Gradual diffusion and homogenization
2. Diffusive Equilibration in Magma Chambers
   • Plagioclase Zoning in Andesites : Plagioclase crystals often show normal (Ca-rich core, Na-rich rim) or reverse (Na-rich core, Ca rich rim) zoning due to diffusion driven with changing magma composition
3. Magma Mixing and Hybridization
   • Andesitic Magma Formation : When basaltic and rhyolitic magmas mix, diffusion-controlled exchange of major elements (Si, Mg, Fe) occurs, leading to hybrid magma compositions

Activity-Composition relations in Igneous Petrology

Roult’s Law (Ideal Solutions)

• a_i = X_i (Activity a_i equals mole fraction X_i)
• Applicable to silicate melts where components mix ideally (simple binary systems)
• Albite-Anorthite in plagioclase feldspar

Examples

1. Binary Feldspar Solid Solutions
   • Examples : Plagioclse (Anorthite-Albite Series)
   • The activity of albite (Ab) and anorthite (An) in plagioclase feldspar follows Roult’s law at high tempeartes in an ideal system
   • Important in understanding phase equilibria and crystallization paths in basaltic to granitic melts
2. Silicate Melt Behavior
   • Examples : Dry Granite Melt
   • At high temperature, major components like SiO₂, Al₂O₃ behave ideally, allowing models to predict liquidus and solidus relations.

Henry’s Law (Dilute Solutions)

• a_i = KX_i , Where K is Henry’s constant
• Governs the solubility of volatile components (H₂O, CO₂) in magma
• Crucial for understanding volcanic degassing, buble formation and explosive eruptions

Examples

1. Dissolution of Volatiles in Magma
   • Examples : H₂O, CO₂ in basaltic magma
   • The solubility of water in basalt follows Henry’s Law at low concentrations, impacting magma viscosity and explosivity
   • High water content lowers the loquidus temperature, promoting early crystallization of minerals like amphibole
2. Vocanic Degassing and eruption Mechanics
   • Example : Explosive Eruption of Andesitic Magmas
   • As magma rises, pressure decreases, reducing gas solubility (Henry’s law) leading to bubble nucleation and explosive eruptions (Mount St. Helens, Karaktoa)