Geothermometry and geobarometry

Geothermometry and geobarometry use the difference in chemistry of minerals that exist together to estimate the temperature and pressure at which some geological processes occur. The estimation of temperatures and pressures is crucial to the understanding of such complex phenomena as the melting of the rocks that ultimately result in volcanic eruptions on the earth's surface and the mechanical properties of rocks that are involved in ruptures that result in earthquakes.

Basic Principles of Chemical Thermodynamics

Geothermometry and geobarometry are methodologies used by geologists to determine the temperature and pressure attending igneous and metamorphic processes. The temperatures below the earth's surface at which magma (molten rock) is generated and subsequently crystallizes (solidifies) is an example of one type of information that may be obtained through geothermometry and geobarometry. Another is the temperature at which the constituent mineral phases of large masses of sediments are metamorphosed to different compositions or structures. To understand how geologists have developed the methodologies of geothermometry and geobarometry, one needs to understand some of the basic principles of chemical thermodynamics and how these principles are applied to rocks.

Temperature, along with pressure and bulk composition, largely controls the macroscopic physical and chemical properties of most materials. Based on experience, scientists know that certain substances behave in predictable ways under certain conditions. The substance may be as simple as a glass of water or a single grain of homogeneous iron metal, or it may be as complex as an igneous or metamorphic rock. For example, at atmospheric pressure (the pressure of the atmosphere at sea level, or 14.69 pounds per square inch), pure water will become solid ice at a temperature of 0 degrees Celsius (its freezing point) and gaseous steam at a temperature of 100 degrees Celsius (its boiling point). The behavior outlined above, however, may not be commonly observed, because pure water is rarely encountered in communities or homes. In the colder regions of the United States and Canada, many communities spread sodium chloride (common household salt) on the streets during the winter months. The introduction of salt to a pure water system changes its properties such that at atmospheric pressure, the water freezes at a temperature below 0 degrees Celsius. The new freezing point is a function of the salted water's composition and pressure. The addition of small amounts of salt to pure liquid water also raises its boiling point to a temperature above 100 degrees Celsius that, again, depends on the amount of salt and pressure. Many recipes in which food is cooked in boiling water call for small amounts of salt, allowing the liquid to attain a higher temperature, and hence heat content, before reaching its boiling point.

To discuss these concepts in greater detail, it helps to define which system is under investigation and where it exists. In the first example described earlier, the system is the ice and liquid water on a road surface, where water existed in one of two distinct phases, either solid or liquid, depending on the temperature. In the ice-water system, salt spread on the road will primarily dissolve into the water phase, changing its composition from pure water to a saltwater solution. The composition is fixed by the amount of salt relative to the amount of water present, which is defined as the salt concentration in solution and is generally expressed in units of grams per liter. When the system obtains its minimum energy configuration for the specified set of conditions, it is at equilibrium.

For fixed temperature and pressure, equilibrium is characterized by a minimum in the Gibbs free energy function, which balances the heat content of the system against energy unavailable to the system to perform work on its surroundings. (The Gibbs free energy function takes its name from American theoretical physicist Josiah Willard Gibbs.) The type of work may be mechanical—for example, pushing a piston as a result of the rapid expansion of a gas—or electrochemical—for example, oxidation and reduction of chemical species at the positive and negative electrodes of a battery to produce an electric current. Gibbs formalism relies on the principle of chemical equilibrium, which allows scientists to relate changes in a chemical system, such as the ice-water-steam examples outlined previously, to specific thermodynamic properties. The principle of chemical equilibrium states that the chemical potential of each component in every phase in the system must be equal. Chemical potentials are used by scientists to relate the reactivity of individual chemical species at some specified temperature and pressure. At equilibrium, then, the component chemical potentials are equal and the total Gibbs free energy of the system under consideration is at a minimum. As a consequence, one would expect to observe no net change in the status of the system. A description of a well-defined chemical system in terms of classical thermodynamics is referred to as the study of the phase equilibria of that system.

When scientists analyze phase equilibria in terms of thermodynamics, they develop relationships between the composition of constituent phases and the temperature and pressure conditions under which they formed. In the saltwater system described earlier, if one could experimentally determine the relationship between the amount of freezing point depression and the concentration of salt in solution, one could then easily predict the temperature at which the road surface would freeze, given the amount of salt added to the system. The appropriate relationships applied to systems of geologic interest are commonly referred to as geothermometers, if they are used to determine temperature, or geobarometers, if they are used to determine pressure.

Application of Thermodynamics to Petrology

For the last 250 years, scientists from a variety of disciplines have carefully gathered experimental data to characterize the behavior of many materials of variable composition under a wide range of temperature and pressure conditions. These experimental data may be analyzed using a formalism called classical thermodynamics, which was largely developed by J. Willard Gibbs in the 1870s, based on the pioneering experiments and ideas of S. Carnot and E. Clapeyron. In the 1910s, N. L. Bowen, a geologist, pioneered the application of classical thermodynamics to the study of rocks. Bowen and his coworkers began a long and productive career of careful experimental characterization of geological systems. During this period, they developed experimental apparatus and techniques that are still in use presently with only moderate modification. Bowen mainly focused on examining the phase equilibria of silicate systems comprising two to three oxide components. Many of his original experimental investigations form the basis of modern igneous petrology.

Although Bowen and his coworkers did extensive experimental work to characterize the phase equilibria of many important geologic systems, the development and application of the methodologies of geothermometry and geobarometry did not gain wide acceptance until the 1960's. During the 1960's and 1970's, four common types of chemical reactions were developed and applied to rocks as both geothermometers and geobarometers: solid-solid exchange reactions, solid-liquid exchange reactions, solid-gas buffer reactions, and stable isotope exchange reactions. Each type of reaction is based on slightly different thermodynamic data and therefore has a somewhat different application to geological systems.

Solid-Solid Geothermometry and Geobarometry

Solid-solid geothermometry or geobarometry is based on the exchange of one or more chemical components in the formation of coexisting solid phases that depends on temperature and pressure. In most igneous and metamorphic rocks, silicate phases (solids whose structure and properties are dominantly controlled by the presence of silicon, usually coordinated by four oxygens at the apexes of a tetrahedron) represent more than 90 percent of the rock's weight. The other 10 percent is composed of oxide phases (solids whose structure and properties are dominantly controlled by oxygen, usually in a close-packed arrangement). The exchange of a magnesium component between two similar silicate phases, clinopyroxene and orthopyroxene, is the basis of a commonly applied geothermometer. The exchange of an aluminum component between orthopyroxene and garnet (another common silicate mineral) is the basis of a commonly applied geobarometer.

There are several prerequisites for the application of either a geothermometer or a geobarometer to rocks. First, both phases must be present in the system of interest. Second, the two phases must be in demonstrable chemical equilibrium. Often, that is quite difficult to prove. However, evidence of disequilibrium is usually discernible in the form of compositionally zoned phases. Third, the thermodynamic properties of each of the phases must be known. Fourth, the composition of the two phases must be determined by chemical analysis. Last, to apply the geothermometer, one needs an independent determination of the pressure at which the two pyroxene phases formed, because the thermodynamic relations for the two pyroxenes are a function of pressure. Often, a geologist would use a geobarometer to obtain an estimate of the pressure. Concomitantly, to apply the geobarometer, one needs an independent determination of the temperature. Armed with these data, one may easily calculate the temperature at which the pyroxenes formed.

Geotherms

Only the uppermost 10-20 kilometers of the earth's continental crust have been directly sampled by drilling; direct observation of the oceanic crust is even less extensive because of the extreme difficulty and expense of drilling from the ocean's surface through 5 kilometers of water prior to reaching the oceanic crust. There often are pieces of rock called xenoliths, however, that are accidentally entrained in magmas that originate from depths of 5 kilometers to as great as 200 kilometers below the earth's surface. Many of these xenoliths contain several mineral phases that are in equilibrium. The compositions of the constituent minerals are determined either by chemical analysis using traditional wet chemical methods, which require separation of individual phases, or by electron microprobe microanalysis, which allows direct determination of the composition of a spot with a diameter on the order of 1-10 microns. By examining these xenoliths in detail and applying a geothermometer and a geobarometer in concert, geologists have been able to determine temperature versus depth profiles for parts of the earth that are inaccessible to direct observation. Temperature-depth profiles are called geotherms, and they provide the link between the region of the earth where its composition is reasonably well known and the much deeper region where its composition and temperature are poorly constrained and subject to debate.

Solid-Liquid Geothermometry

The principles of solid-liquid geothermometry are much the same as those outlined previously for solid-solid geothermometry. In contrast to the simple example offered earlier, in which salt dissolved only in the liquid water phase, the chemical components in silicate systems tend to be soluble in several solid phases and the liquid phase simultaneously. That complicates the thermodynamic analysis considerably, and significantly more experimental data are needed to fully characterize the system. In addition, unlike the application of the two-pyroxene solid-solid geothermometer, where both phases are examined directly to obtain the temperature at which they formed, application of a solid-liquid geothermometer requires extensive assumptions about the composition and state of the liquid in equilibrium with the solid, as that liquid is no longer present in the rock. Plagioclase is a common silicate mineral found in rapidly frozen lavas that span a wide compositional spectrum. Because the plagioclase phase incorporates both sodium oxide and calcium oxide, which are both components in the liquid phase as well, the composition of plagioclase may be used to infer the composition of the coexisting liquid and the temperature at which the plagioclase formed. This method has been applied extensively to lavas that range from basaltic (silica poor) to andesitic (silica rich) in composition.

Solid-Gas Buffer Reactions

The reaction between one or more solid phases and a gas phase also yields information about temperature and the partial pressure of some gas species. One example of a solid-gas buffer reaction defines the coexistence of magnetite and hematite (oxide phases composed of iron). If both phases are pure— that is, they contain only iron and oxygen in the appropriate ratio that defines the phase—then their equilibrium with each other is directly related to their theoretical coexistence with an oxygen-bearing gas phase, which is defined by the partial pressure of oxygen (the amount of oxygen present, expressed as a percentage of the total pressure of the system).

The concept of a buffer arises because if oxygen is added to or subtracted from the system, the relative proportions of magnetite and hematite in the system will change to maintain internal equilibrium. This type of reaction does not specify the temperature explicitly, since magnetite and hematite may coexist over a range of temperatures and oxygen contents. Thus, if both pure solid phases are present and the temperature is varied, then the oxygen partial pressure will change sympathetically. Similarly, if the oxygen partial pressure is varied, then the temperature must also change. The observed coexistence of magnetite and hematite in many silica-rich igneous systems has been used to infer either the temperature or oxygen partial pressure attending formation, depending on which parameter may be fixed by independent information.

Stable Isotope Exchange Geothermometry

The exchange of different stable isotopes of oxygen between coexisting phases forms the basis of the last common type of reaction used as a geothermometer. The isotopes of any chemical element—for example, oxygen—have the same number of protons but a different number of neutrons in their nuclei. Oxygen has two stable isotopes; one contains 8 protons and 8 neutrons, and one contains 8 protons and 10 neutrons. These two isotopes are referred to as oxygen-16 and oxygen-18. Their exchange between two coexisting phases in general is a function of temperature. At present, very few solid-solid, solid-liquid, or solid-gas exchange equilibria have been experimentally calibrated as a function of temperature and isotopic concentration of oxygen, however, and in the absence of such experimental calibrations, stable isotope exchange geothermometry has seen little application to igneous or metamorphic systems.

Understanding of Volcanoes and Earthquakes

Many geologic processes can affect people's daily lives. Examples include potentially devastating earthquakes and the rapid and oftentimes catastrophic eruptions of volcanoes at the surface of the earth. By applying geothermometry and geobarometry methods to rocks, geologists have developed a much better understanding of how some aspects of these complex phenomena are initiated and how they evolve.

By determining temperature-depth profiles for the upper 200 kilometers of the earth, geologists have gained valuable information on the composition and state of regions of the earth that are not accessible to direct observation. This information is crucial to the understanding of how and why rocks deform during earthquakes. In fact, for rocks of fixed composition, ambient temperature is the primary variable that determines whether rocks will be able to deform in such a way as to produce an earthquake. In addition, temperature may be important in controlling the magnitude of some earthquakes.

The second and perhaps more direct application of geothermometry is in an effort to gain a greater understanding of the causes and warning signs of potentially catastrophic igneous eruptions, such as the one that occurred in 1980 at Mount St. Helens, Washington. Studies of volcanic rocks, for example, that generally integrate geothermometry, geobarometry, geochemistry, and field geology, have revealed that the processes that governed the eruption of Mount St. Helens continue to operate there as well as at other sites worldwide where oceanic crust is subducted below continental crust. In the Cascade province of the western United States, for example, Mount Shasta, Mount Bachelor, and Mount Rainier share many characteristics with Mount St. Helens, so scientists suspect that these volcanoes should erupt in a similar manner. Mount Rainier and Mount Bachelor represent a potential danger to the large population centers of Seattle and Portland, which are in close proximity to these volcanoes.

Principal Terms

component: a chemical entity used to describe compositional variation within a phase

igneous rock: any rock that forms by the solidification of molten material, usually a silicate liquid

metamorphic rock: any rock whose mineralogy, mineral chemistry, or texture has been altered by heat, pressure, or changes in composition; metamorphic rocks may have igneous, sedimentary, or other, older metamorphic rocks as their precursors

mineral: a naturally occurring solid compound that has a specific chemical formula or range of composition; minerals normally have regular crystal structures such that their internal arrangement of atoms is predictable

phase: a chemical entity that is generally homogeneous and distinct from others in the system under investigation

phase equilibria: the properties of chemical systems described in terms of classical thermodynamics; systems of specified composition are generally investigated as a function of temperature and pressure

thermodynamics: the area of science that deals with the transformation of energy and the laws that govern these changes; equilibrium thermodynamics is especially concerned with the reversible conversion of heat into other forms of energy

volcanic rock: a type of igneous rock that is erupted at the surface of the earth; volcanic rocks are usually composed of larger crystals inside a fine-grained matrix of very small crystals and glass

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