Notes

Equilibrium, Crystal Nucleation and

Growth, and such Related Topics

Geology 3020 Petrology

Spring Semester 2004

Copyright Lisa R. Lytle 2004 All Rights Reserved

Equilibrium Stability – Metastability – Instability Equilibrium is achieved by minimizing the energy of the system (free energy, chemical energy, potential energy, etc.). These conditions are defined by thermodynamics.

Go = xi µi + xj µj + .....

Metastability – Energy of the system is greater than the lowest state, but an energy barrier exists to a change to that lowest state. Phase Rule F = C + 2 - P F = degrees of freedom (T,P,X, etc.) C = number of components (choose minimum # to describe system) P = number of phases (phases are separated by an interface, such as Solid-Liquid-Gas, separate minerals, etc.) 2 comes from the equation: dE = TdS - PdV + µa dna + µb dnb + .... The TdS and PdV are the two terms which give the “2” of the equation. The number of “µa dna” terms are the number of components C The phase rule can help describe a system. CIPW Norms

♦ gives potential minerals implied by the chemical anaylses ♦ 1st used in early 1900’s to estimate mineralogy of very fine grained rocks that could not

be identified in thin section ♦ allows comparison between laboratory experimental studies and natural occurences ♦ can be used to describe a system in terms of expected chemical reactions, without the

complications of a natural system

Phase Diagrams Phase diagrams used in petrology usually compare composition of a mineral (or mineral system) with changes in temperature or pressure (or both) to predict which mineral phases will be in equilibrium with the conditions. There are several treatments of phase diagrams in the literature. Best (class recommended text) does cover this, and there is a very good text by S.A.Morse (Basalts and Phase Diagrams, Springer-Verlag, 1980). In this class, you will be expected to recognize and use the simple phase diagrams, such as the solid solution phase diagram for plagioclase or olivine, or the k-feldspar or pyroxene diagrams that contain a solvus separating a one-phase from a two-phase field. More complex diagrams exist and are useful – and we may see them in the course of our investigations, but your detailed use of these can be postponed for graduate-level courses. Silicate Minerals Silicate minerals are formed by various combinations of the silica tetrahedron: isolated, pairs, single chains, double chains, sheets, and framework structures of tetrahedra. This structure defines how a mineral will behave in a melt, how easily it will crystallize, how fast it will weather, etc. Melts When we think of a magma, we think of a liquid, and our mental picture of a liquid is something like water. This gives us an unrealistic picture of a silicate melt. Silicate melts retain a resemblance to silicate solids, and exist as melted olivine, plagioclase, quartz, etc., fragments in ordered polymerized molecules. These fragments still retain mineral identity within the melt. Melts are not made up of isolated silica tetrahedra floating around ready to form into chains, sheets, etc. Melts also contain volatiles (H2O, CO2, H2S, F, etc.), and may contain crystals (solids) as well. There may be more than one liquid phase, perhaps immiscible liquids. Polymerization (and viscosity of melt) increases with increased structural complexity of silicate minerals. Volatiles, especially water, decrease polymerization of a melt by breaking bridging-O bonds. The less structured silicate liquids exist at a higher temperature than the more structured (framework) silicate liquids. It is “easier” for the isolated tetrahedra to move quickly and independently in a higher T melt.

Crystal Stability Example: NaCl – Unit Crystal

The bonds are partially unsatisfied, resulting in a large energy – therefore not at maximum stability. (Satisfied bonds are lower energy and more stable.)

from Klein, 2003 A larger crystal or array has proportionally fewer unsatisfied surface bonds, therefore a lower surface energy and more stable than the “embyonic” crystal. In nature, crystals are not isolated but have interfaces (surfaces) between crystals or crystal-liquids. Atoms at surfaces are more loosely bonded or have unbalanced bonds – which have a higher energy and are less stable. There is therefore an energy advantage for a crystal to add atoms onto its surface (to grow). Either euhedral crystal faces or larger crystals minimize surface energy of a crystal.

Crystal Nucleation Homogeneous Nucleation A crystal forms when its free energy becomes less than the free energy of the melt. This change can be due to changes in T, P, or concentration of a component. But, as we’ve just seen above, embryonic crystals are not very stable. Embryonic nuclei have very high surface energy compared to larger crystals Thermal vibrations can destroy embryonic crystal nuclei VS Attractive forces of crystallization A phase transformation requires some degree of overstepping (energy input) to initiate nucleation. The most common is Undercooling.

[Best, p.134, fig. 6.11] Gmelt = free energy of the melt Gcrystal = free energy of the crystal Gγ = embryo nucleus surface energy – which becomes very small (negligable) at a critical radius ∆T = undercooling = the difference between T at Gmelt < Gcrystal and T at Gmelt < Gcrystal +Gγ The T at which a crystal is stable is higher than the T at which a crystal will

nucleate. So, even though the melt has cooled to the point that the solid is stable, it does not mean that nucleation will automatically occur at that T

As T decreases, we reach Gcrystal +Gγ < Gmelt and crystals may nucleate. ∆T changes for different minerals. Homogeneous nucleation is easier with less polymerized melt (related to ∆S). This is the basis for Bowen’s Reaction series where the nesosilcates nucleate and grow 1st as a melt crystallizes.

Heterogeneous Nucleation Nucleation on an existing surface. Activation energy barrier is overcome by existing contrasting interface. Crystals may nucleate more easily on another surface than directly from the melt. It is possible that this is a common phenomenon in igneous rocks. Crystal Growth As increase ∆T , increase crystal growth Decrease of T increases melt viscosity, whcih retards ion mobility [Best p.137. fig 6.14]

Crystal shape and form are determined by a combination of cooling rate degree of ∆T Crystals go from tabular to skeletal to dendritic (xls become less compact) as you increase cooling rate, increase ∆T, or take heat away from xls more quickly. Compact xls: growth at xl face; higher T, slower cooling so that more heat next to the xl and diffusion is still rapid bringing ions to face of xl.

Dendritic xls: growth at corners of xl; faster cooling so that heat is dissipating away from xl decreasing diffusion of ions to face of xl. Crystal Shape – see Best p.138, fig. 6.15 Crystal Size and Rock Texture Crystal size depends on nucleation density vs growth. High nucleation rate & slow growth = many small xls Fast rate of cooling = volcanic Low nucleation rate & fast growth = fewer but large xls Heat loss slow = deep plutonic Nucleation may be supressed with presence of volatiles, as in pegmatites, allowing xls to grow quite large.