The Interior of the Earth

Planetary geologists spend much of their time trying to understand how planets initially form and how their internal structures evolve. The temperatures and compositions of the interior of the Earth are well understood at shallow depths, and are less well understood as depth increases. The development of this knowledge has taken a lot of ingenuity and time because there are few ways to study the composition of the Earth directly.

The crust itself can be sampled at its surface, and volcanic eruptions sometimes bring up small pieces of the mantle. At certain places on the Earth's surface, rocks from the upper mantle have been pushed up onto the continents, either by collision or by deep volcanic explosions, and can be inspected directly. In these ways, there is direct evidence of only the very shallowest parts of the Earth, which may also be the parts of the Earth that have gone through the most alteration: repeated episodes of heating, melting, and mixing.

Other information on the Earth's composition comes from meteorite compositions, and from replicating deep-earth conditions in labs with high-pressure and high-temperature experimental equipment (see the sidebar "High-Pressure Experiments" on page 36). Scientists can begin to make estimates about what the mantle is made of based on the minerals that are stable in experiments at various pressures and temperatures. Experiments can give a large-scale idea of mineralogy, but the variation in compositions and therefore the variation in less common, or accessory, minerals in the Earth's mantle is not known. Gravity, magnetism, and seismic waves can be measured at the Earth's surface and allow scientists to learn more about the Earth's deep interior. Through the analysis of earthquake waves moving in the deep interior, scientists have been able to determine that the Earth's outer core is liquid, a crucial step in understanding the interior of the Earth.

Deep mines give us some information about composition and heat at depth, but even the deepest hole on Earth, the 7.5-mile- (12-km-) deep drill hole in Russia's Kola Peninsula, is still well within the crust and fails to approach even the upper mantle. As the writer Brad Lemley put it in Discover magazine, using the Kola drill hole to investigate the deep interior of the Earth is like learning about Alaska by driving from St. Petersburg, Florida, to nearby Tampa. Though 7.5 miles (12 km) is very deep by human standards, it does not reach through even the outermost, thinnest layer of the Earth.

Heat radiates away from the Earth into space, and the Earth is cooling through time. If the Earth had only the heat from its initial formation it could be calculated that the planet would have completely cooled by this time. Radioactive decay of atoms throughout the Earth produces heat, and the interior of the Earth is hotter than the surface. Heat flowing out of the Earth can be measured by placing thermal measuring devices in holes dug deeply into the soil, and heat flux (the amount of heat moving through a unit of surface area in a unit of time) has been found to be different in different parts of the world. Heat flux in areas of active volcanism, for example, is higher than heat flux in quiet areas. The likely internal temperatures of the Earth can be calculated based on heat flux at the surface. Such calculations lead to the conclusion that the Earth's shallow interior, not much deeper than the hard, cold crust, is 2,190 to 2,640°F (1,200 to 1,450°C).

Rocks at that temperature are able to flow over geologic time. Although they are not liquid, there is enough energy in the atoms that the crystals can deform and "creep" in response to pressure, over thousands or millions of years. The interior of the Earth is indeed creeping in this way, in giant circulation patterns driven by heat from the interior escaping toward the surface and radiating into space. This movement in response to heat is called convection. A small example of convection occurs in heating soup: In a glass pot, you can see upwelling plumes of hot soup, as well as soup that, having cooled at the surface, is now returning to the bottom of the pan.

Plate tectonics, the movement of the brittle outside of the Earth, is caused in part by these internal convective movements. At the surface this movement is only an inch or two (a few centimeters) a year, but over geologic time the movement is enough to give us the San

Andreas fault in California, where the edges of two plates are scraping past each other, along with the volcanoes around different parts of the Pacific Ocean's rim, where one plate is bending and being pushed beneath another.

Plate movement includes not only the crust at the surface, but also some portion of the Earth that lies beneath it. Below the crust, the planet's material is called the mantle. The uppermost mantle is too cool to be able to flow easily, even over millions of years, and so it moves as a unit with the crust. Together, these cool, connected layers are called the lithosphere. Beneath the lithosphere, the remaining mantle is hot enough to flow more quickly, perhaps at centimeters to tens of centimeters per year on average.

Seismologists studying the way earthquake waves move through the Earth have long known that the Earth has a core made of very different material than the mantle. Based on an analysis of the bulk silicate Earth (the mantle and crust, made mostly of minerals based on silicon atoms) compared to the composition of primitive meteorites that represent the material the inner planets were made of, we know that the silicate Earth is clearly missing a lot of iron and some nickel. Models of planetary formation also show that the heat of accretion (the original assembly of the planet) will cause iron to melt and sink into the deep interior of the Earth. Scientists are fairly certain, then, that the core of the Earth is made of iron with some nickel and a few percent of other elements. The density structure this implies also matches the planet's moment of inertia, which is a measure of the density structure inside a planet (for more, see the sidebar "Moment of Inertia" on page 26).

The structure of the Earth, used as the starting point in understanding the structures of other terrestrial planets, begins with the outermost cool, thin veneer of the Earth, the crust. The crust is coupled to the coolest, uppermost mantle, and together they are called the lithosphere. Under the lithosphere is the convecting mantle, and beneath that, the core. The outer core is liquid metal, and the inner core is solid metal. Though this structure is used as the starting point for understanding other terrestrial planets, it is different in one very important way:The Earth is the only known planet with plate tectonics (Mars may have had plate tectonics very early in its history). Mercury,Venus, and Mars are one-plate planets: Their crust and lithosphere form a single, solid spherical shell. Without

Moment of Inertia

The moment of inertia of a planet is a measure of how much force is required to increase the spin of the planet. (In more technical terms, the angular acceleration of an object is proportional to the torque acting on the object, and the proportional constant is called the moment of inertia of the object.)

The moment of inertia depends on the mass of the planet and on how this mass is distributed around the planet's center. The farther the bulk of the mass is from the center of the planet, the greater the moment of inertia. In other words, if all the mass is at the outside, it takes more force to spin the planet than if all the mass is at the center. This is similar to an example of two wheels with the same mass: one is a solid plate and the other is a bicycle wheel, with almost all the mass at the rim. The bicycle wheel has the greater moment of inertia and takes more force to create the same angular acceleration. The units of the moment of inertia are units of mass times distance squared; for example, lb X ft2 or kg X m2.

By definition, the moment of inertia I is defined as the sum of mr2 for every piece of mass m of the object, where r is the radius for that mass m. In a planet, the density changes with radius, and so the moment of inertia needs to be calculated with an integral:

where rg is the center of the planet and r is the total radius of the planet, p(r) is the change of density with radius in the planet, and r is the radius of the planet and the variable of integration. To compare moments of inertia among planets, scientists calculate what is called the moment of inertia factor. By dividing the moment of inertia by the total mass of the planet M and the total radius squared R2, the result is the part of the moment of inertia that is due entirely to radial changes in density in the planet.

plate tectonics, there are no volcanic arcs such as Japan or the Cascades, and there are no mid-ocean ridges from which oceanic crust is produced. Surface features on one-plate planets are therefore different from those on Earth.

What all the terrestrial planets seem to have in common are a cool outer crust and lithosphere, a silicate mantle, and an iron-rich core

This division also produces a non-dimensional number because all the units cancel. The equation for the moment of inertia factor, K, is as follows:

The issue with calculating the moment of inertia factor for a planet is that, aside from the Earth, there is no really specific information on the density gradients inside the planet. There is another equation, the rotation equation, that allows the calculation of moment of inertia factor by using parameters that can be measured. This equation gives a relationship between T, the rotation period of the planet; K, the moment of inertia factor of the planet; M, the mass of the planet; G, the gravitational constant; R, the planet's polar radius; D, the density for the large body; a, the planet's semimajor axis; i, the orbital inclination of the planet; m, the total mass of all satellites that orbit the large body; d, the mean density for the total satellites that orbit large body; and r,the mean polar radius of all satellites that orbit the large body:

By getting more and more accurate measures of the moment of inertia factor of Mars, for example, from these external measurements, scientists can test their models for the interior of Mars. By integrating their modeled density structures, they can see whether the model creates a moment of inertia factor close to what is actually measured for Mars. On the Earth, the moment of inertia factor can be used to test for core densities, helping constrain the percentage of light elements that have to be mixed into the iron and nickel composition.

(see figure on page 28). How the crusts formed seems to differ among the planets, as does the composition of the mantle (though always silicate) and core (though always iron-dominated), and the heat and convective activity of the mantle. Theorizing about the degree of these differences and the reasons for their existence is a large part of planetary geology.

The Brittle Crust

The crust, the part of the Earth that humans tend to think of as the Earth, makes up only 0.5 percent of the Earth's total mass. The crust is made up of igneous rocks, metamorphic rocks, and sedimentary rocks. Sedimentary rocks, such as shale and limestone, can only be made at the surface of the planet, by surface processes such as rivers, glaciers, oceans, and wind.They make up the majority of rock outcrops at the surface but are not found at any depths in the planet. The crust of the Earth is significantly different from the crusts of other planets. On other terrestrial planets, the crust seems to made largely of igneous rocks low in silica and high in magnesium, like the dark lavas that erupt in Hawaii.There are exceptions: On the Moon, the white highlands seen so clearly from Earth seem to be made largely of the high-silica mineral plagioclase. In general, though, other planets are not covered with metamorphic rocks or high-silica igneous rocks, like

The fundamental layers of the Earth are the inner and outer core, the lower and upper mantle, and the lithosphere and crust. (Zaranek, modified after Beatty et al., 1999)

Structure of Earth's Interior

Inner core Outer core D" layer Mantle (solid) (liquid)

Crust and lithosphere —

Inner core Outer core D" layer Mantle (solid) (liquid)

Crust and lithosphere —

granites and andesites (these water-rich, high-silica magmas erupt at subduction zones).There are some sedimentary rocks on Mars, formed by ancient water movement and current wind storms.

On the Earth, oceanic crust consists of basalt, a dense, dark-colored igneous rock produced by melting the mantle, and of sediments deposited on the sea floor.The thickest oceanic lithosphere is about 40 miles (70 km) thick, and oceanic crust attains that thickness at an age of about 10 million years. Continental crust, on the other hand, is thicker and more buoyant, being made mainly of rocks that have a lower density than oceanic crust. Oceanic crust is eventually subducted back into the mantle, and so no oceanic crust is much older than 200 million years. Continental crust, on the other hand, has a wide range of ages. The oldest crustal rocks are almost 4 billion years old (discovered in the Canadian northwest by Sam Bowring, a professor at the Massachusetts Institute of Technology).There are no known crustal rocks older than 4 billion years, which raises the question: What was the Earth like in its first 560 million years? Was there little or no crust? Why was crust first formed? These questions remain unresolved. The lithosphere is divided into about 12 plates that move as individual units. There are a number of kinds of boundaries between plates. At one type of boundary, a transform boundary (see figure above), the plates move parallel to each other, creating long faults at the boundary (shown in the upper color insert on page C-2) where they meet.The San Andreas fault on the United States' west coast is one such place; movement at these boundaries create earthquakes.

At a transform boundary, plates slip horizontally past each other without significant convergence or divergence. The San Andreas fault between the North American and Pacific plates is an example of a right-lateral transform boundary.

At mid-ocean ridges, new crust is formed by upwelling and melting mantle, and the plates on each side of the ridge move away from each other.

At mid-ocean ridges, plates move away from each other (see figure below). These are called extensional boundaries. Mid-ocean ridges are marked by jagged lines of mountains down the center of the Atlantic, Pacific, and some other oceans, with a deep rift valley between the mountains. Beneath these rifts the mantle is flowing upward, and it melts as it depressurizes. This melt rises to the surface and cools as new oceanic crust. A total of about one cubic mile (~4 km3) of new oceanic crust is produced each year at mid-ocean ridges. As new melt rises, the crust moves away from the mid-ocean ridge, cooling, thickening, and settling more deeply into the mantle as it ages and moves away from the ridge. In this way, the deepest basins in the oceans are formed, by cooling, settling oceanic plates.

At compressional boundaries, the plates are moving toward each other.This kind of boundary creates a subduction zone, shown in the figure on page 31: Thinner, denser oceanic crust is pressed down underneath thicker, more buoyant continental crust, and the oceanic crust descends into the mantle (for more on subduction zones, see the mantle section below). Subduction zones create both earthquakes and volcanic eruptions, like those almost ringing the Pacific Ocean, including the Cascades, with many volcanoes, including Mount Saint Helens (shown in the lower color insert on page C-2); the Japanese islands, including Mount Fuji; and the Philippines, including Mount Pinatubo. When the oceanic plate subducts

Mantle flows away with plate

Mantle flows away with plate

Mantle flows away with plate

Upwelling mantle

Mantle flows away with plate

Mantle flow

Fluids rise from Mantle flow dehydrating minerals and cause mantle melting and formation of volcanoes

Possible pressure-release melting

Mantle flow

Fluids rise from Mantle flow dehydrating minerals and cause mantle melting and formation of volcanoes

Possible pressure-release melting beneath the continent, it sinks through its inherent density into the mantle and pulls the rest of the plate with it; this is thought to be the driving force for the formation of new crust at mid-ocean ridges, and is also thought to create the pattern of convection in the upper mantle. Clint Conrad, a researcher with Carolina Lithgow-Bertelloni at the University of Michigan, has created a model showing that some slabs remain attached as they sink into the mantle, pulling the plate behind them, and others detach but mantle flow continues to pull the plate down.

At some compressional boundaries the intervening ocean has been completely subducted and the two continents once separated by the ocean basin have collided. Neither can easily subduct beneath the other, and so large plateaus and mountain ranges are thrown up along complex systems of faults as the two continents are forced into each other. The collision of the Indian plate with the Asian plate is an example of this kind of compressional boundary, and has produced high mountains, including the Earth's highest, Mount Everest. Mount Everest is 5.5 miles (8.8 km) high. Astronaut Dan Bursch, a member of the Expedition 4 crew on the International Space Station, took this

At subduction zones, thinner, denser oceanic crust slides under more buoyant continental crust and sinks gradually into the mantle beneath.

Astronaut Dan Bursch, a member of the Expedition 4 crew on the International Space Station, took this photograph of Mount Everest from the space station in late March 2002. (Earth Sciences and Image Analysis Laboratory, NASA Johnson Space Center,, ISSO4-E-8852)

photo of Mount Everest in late March 2002. In this image early morning light shines on the mountain's eastern Kangshung Face.

The Solid but Moving Mantle

It is necessary to stress here that the upper mantle of the Earth is not molten because this is a falsehood that has been propagated through textbooks for years. The uppermost mantle, in general, is solid, but because it is warm and at low pressure compared to the rest of the mantle, it is softer and flows more easily. Only small parts of the upper mantle melt as they rise and depressurize, or as they have water injected into them at subduction zones.The addition of water lowers the melting temperature of the mantle, and so melting and subsequent volcanism is triggered by the addition of water from sediments on the subducting slab. Only a small percent of the upper mantle is molten at any one time, and that melt rapidly moves upward through buoyant forces. Further, the areas of the mantle with melt in them are in specific geologic settings scattered around the Earth.

Based on what is suspected about the bulk composition of the Earth, what is known about the seismic properties of the mantle, and what is known from pieces of the mantle that are carried to the surface in volcanic eruptions (these are called xenoliths), the bulk composition of the mantle is approximately 46 percent silica (SiO2), 38 percent magnesium oxide (MgO), 7 percent iron oxide (FeO), 4 percent alumina (Al O ), 3 percent calcium oxide (CaO), 0.5 percent sodium oxide (Na2O), and about 1 percent all other elements. Note that all these compounds are expressed as oxides: there is enough oxygen in the Earth to balance the charges of all the positively charged ions, such as silicon, magnesium, and so on.The oxides that make up the bulk composition are all organized into crystalline mineral grains in the mantle. Oxygen (O) and silicon (Si) form the framework of almost all the minerals that make up the mantle. Oxygen and silicon bonded together is called silica, and minerals with silica-based crystal structures are called silicates. These minerals determine the mantle's viscosity, density, seismic speed, and its melting behavior, which in turn determines the types and volumes of magma that erupt to the surface.

The mantle is divided into the upper mantle, including all material shallower than about 415 miles (670 km), and the lower mantle, reaching from 415 miles (670 km) to the core-mantle boundary at 1,800 miles (2,900 km) depth.The boundary between the upper and lower mantles, at 415 miles (670 km), is known throughout the geologic community as the 670 discontinuity. The upper mantle, which can be sampled through xenoliths, is made mainly of the minerals olivine ((Mg, Fe)2SiO4), clinopyroxene ((Ca,Mg,Fe,Al)2(Si,Al)20g), orthopyroxene ((Mg, Fe)SiO ), and one of several minerals that contains alumina, which cannot fit into the other three minerals in any great amount. The aluminous minerals change according to the pressure they are at. At the shallowest depths and lowest pressures, the aluminous mineral is plagioclase. At greater depths, the plagioclase (NaAlSi O to CaAl Si O ) transforms into spinel (MgAl O ), and then at greater depths, into the beautiful mineral garnet ([Ca,Mg,Fe Mn]3[Al,Fe,Cr,Ti]2[SiO4]3). Because of this mineralogy, the mantle is an exceptionally beautiful material:The olivine is a bright olive green, usually making up over 50 percent of the rock, and the remainder of the mantle is made up of black orthopyroxenes, bottle-green clinopy-roxenes, and brilliant ruby-colored garnets.

The boundary between the upper and lower mantle is clearly seen in seismic studies. Waves bounce off the boundary and change their qualities if they pass through the surface. This type of boundary is called a seismic discontinuity, and the 670 discontinuity is observed worldwide.To understand the nature of this boundary, how materials react to increasing pressure must be understood. The more pressure placed on a material, the closer the atoms are forced together. Some materials are compressible: With increasing pressure, their atoms move closer and the volume of the material decreases. Gases are compressible. They can be pushed into pressurized tanks, and balloons filled with gases expand as they go up in altitude, because the air pressure around them is lessening and allowing the interior gas to expand. Water is almost incompressible: Its molecules have slight charges, and the electrical charges repel each other, preventing water from being compressed too much. Crystalline substances, like the minerals that make up rocks, are generally close to incompressible. The crystal lattices are very stiff and are able to withstand large pressures without changing their shape or allowing their atoms to press more closely together (though pressure may cause defects, such as empty spaces or offsets in the crystal lattice, to migrate through the crystal, creating the creep phenomenon that leads to the mantle's ability to flow).

Raising temperature along with pressure enhances crystal's ability to change its properties.With increased temperature, the atoms in the crystal lattices vibrate faster and are more able to move out of position. As pressure and temperature are raised, the material eventually reaches a point where its current crystal structure is no longer stable, and it metamorphoses into a new, more compact crystal structure. The first such transformations in the mantle are in the aluminous phases, which transform from plagioclase to spinel to garnet with increasing pressure. These make up only a small percentage of the mantle, though, and their transformations do not change the way seismic waves travel through the Earth in any significant way. Olivine makes up the majority of the mantle, and when it transforms to a different crystal structure, the seismic properties of the mantle are significantly changed.

Within the upper mantle as pressure increases with depth olivine transforms to a higher-pressure phase called j-olivine, and the pyroxene and garnet minerals transform into a garnet-like mineral with lower silica, called majorite. The pressures and temperatures for these transformations have been measured experimentally in high-pressure laboratory devices (see the sidebar "High-Pressure Experiments" on page 36), and they seem to correspond to a layer in the Earth weakly seen in seismic studies at 255 miles (410 km) and about 140,000 atmospheres pressure (14 GPa) (see the table "Derived Units" in appendix 1). The big transformation occurs at higher pressure when j-olivine transforms to perovskite.This transformation makes a great change in seismic qualities of the mantle, and it occurs at a pressure and temperature that corresponds to 415 miles (670 km) depth and about 220,000 atmospheres pressure (22 GPa) in the Earth. Seismologists have thus measured the internal properties of the Earth, and experimental scientists have recreated the changes in the laboratory, so scientists have a good idea of the cause of the seismic transformations in the mantle.

Perovskite, then, is probably the most common mineral in the Earth, since it is thought to make up the bulk of the mantle between 415 miles (670 km) and 1,800 miles (2,900 km) depth. The volume of mantle is more than half the volume of the Earth. Our knowledge of the deep mantle is sketchy, though. There is tremendous ongoing debate over how well mixed the mantle is, and though perovskite is thought to make up by far the bulk of the lower mantle, there may be many other high-pressure mineral phases that are not yet identified. High-pressure experimentalists regularly find new minerals, though they are hard to characterize in the tiny amounts that are made in experiments.They receive letters instead of names, such as phase L, phase M, and phase N, pending further information.

Other seismic boundaries can be seen in the deep mantle, including an especially interesting deep layer called D'' (pronounced "D double prime"), found at about 1,700 miles (2,700 km) depth.There is significant topography on its surface, so its depth varies from place to place.The changes in seismic speed across this boundary cannot be explained entirely by a change in temperature, but require a change in composition as well. Is this a deep, sequestered layer that has not been mixed into the rest of the mantle? Louise Kellogg, Brad Hager, and Rob van der Hilst, three of the most noted geophysicists working today, believe that this layer may be the starting point of hot, buoyant

High-Pressure Experiments

T hough it is possible to estimate the pressure, temperature, and even the bulk composition of materials in the Earth's deep interior, it is difficult to know the minerals that would exist deep inside the mantle. Even if the deep mantle moves upward through convection, and pieces are erupted onto the surface in volcanoes, the deep minerals would have reequilibrated into lower-pressure phases before they could be examined.

Scientists in a branch of geology called experimental petrology seek to answer questions about the Earth's unreachable interior. Over the course of the 20th century, scientists slowly developed sophisticated equipment to re-create conditions deep in the Earth. The apparatus that puts material under the greatest pressure is called a diamond anvil. Two small circular plates, each bearing a diamond with a flattened tip, are screwed together until the tips of the diamonds meet and press an experimental sample between them. The diamond anvil can create pressures up to about 100 GPa, close to the pressure at the core-mantle boundary in the Earth. The sample, however, can only be about 20 microns in diameter, so the means to inspect and analyze the experiment are largely limited to X-ray diffraction studies of crystal structure. In addition, diamond anvil cells cannot be heated significantly.

mantle plumes that rise through the entire mantle and create melt that erupts onto the surface (the Hawaii island chain is thought to be the product of such a plume).

The topic of plumes brings us to another subject: mantle convection. At the temperatures and pressures in the mantle, the rock can flow slowly over time. Heat escaping from the core heats the lower mantle, which makes it less dense. (In general, heating a substance increases its volume slightly, which makes it less dense.) The less dense parts of the mantle are then buoyant when compared to their cooler neighboring areas, and the hotter material rises, displacing cooler material downward.This is the process of convection. The mantle is thought to move at a few centimeters per year near the surface (this is estimated from plate motions and subduction zone speeds), and it may move faster at depth. The motions of

An apparatus called the multi-anvil is used to create high pressures and temperatures simultaneously. A huge press frame, weighing perhaps 10 tons, houses a hydraulic system. The hydraulic system pushes a set of carbide blocks together in such a way that they all press equally on a tiny octahedron in their center. This octahedron contains about a tenth of a gram of experimental sample inside a graphite tube that acts as a heater. Graphite has high resistance to electrical current, so when a current is passed through the graphite it heats up. This simple principle allows the sample to be heated to 3,200°F (1,800°C) or more, and to be controlled within about 10 degrees by placing thermocouple wires next to the experiment and running them out through the carbide blocks to an electrical controller. The experimental sample is large enough to be examined in an optical microscope or analyzed in an electron microprobe, but usually the apparatus can only reach about 30 GPa.

The multi-anvil, the diamond anvil, and a lower-pressure but more common apparatus called the piston-cylinder are the tools that allow experimental petrologists to approximate conditions inside the Earth and attempt to determine the mineral phases present and their behaviors. Using these techniques, scientists have discovered the mineral phase changes that create the 410 and 670 discontinuities in the Earth's mantle, the processes that may have formed the Earth's core, as well as the compositions and mineral assemblages that make up the interior of the Moon (much of the author's research has been in this area).

convection are controlled by viscosity, which is a measure of the ability of a material to flow (see the sidebar "Rheology, or How Solids Can Flow" on page 38).

The viscosity of the mantle cannot be measured directly, and could not be even if it could be reached with a drill.Viscosity of the mantle is strongly controlled by temperature. As soon as the mantle is cooled, it stops flowing, and in any case it only flows a few centimeters a year. However, scientists thought of a very clever method to help measure mantle viscosity. About 10,000 years ago, the Northern Hemisphere was covered by ice sheets as thick as two miles (3 km). The edge of one of the Earth's two current ice sheets, the Greenland ice sheet, is shown in this image from NASA's Terra satellite (the second ice sheet in existence today is the far larger Antarctic sheet).The Greenland ice sheet is two miles (3 km) thick at its greatest extent,

Rheology, or How Solids Can Flow

IRheology is the study of how materials deform, and the word is also used to describe the behavior of a specific material, as in "the rheology of ice on Ganymede." Both ice and rock, though they are solids, behave like liquids over long periods of time when they are warm or under pressure. They can both flow without melting, following the same laws of motion that govern fluid flow of liquids or gases, though the timescale is much longer. The key to solid flow is viscosity, the material's resistance to flowing.

Water has a very low viscosity: It takes no time at all to flow under the pull of gravity, as it does in sinks and streams and so on. Air has lower viscosity still. The viscosities of honey and molasses are higher. The higher the viscosity, the slower the flow. Obviously, the viscosities of ice and rock are much higher than those of water and molasses, and so it takes these materials far longer to flow. The viscosity of water at room temperature is about 0.001 Pas (pascal seconds), and the viscosity of honey is about 1,900 Pas. By comparison, the viscosity of window glass at room temperature is about 1027 Pas, the viscosity of warm rocks in the Earth's upper mantle is about 1019 Pas.

The viscosity of fluids can be measured easily in a laboratory. The liquid being measured is put in a container, and a plate is placed on its surface. The liquid sticks to the bottom of the plate, and when the plate is moved, the liquid is sheared (pulled to the side). Viscosity is literally the relationship between shear stress a and the rate of deformation e. Shear stress is pressure in the plane of a surface of the material, like pulling a spatula across the top brownie batter.

The higher the shear stress needed to cause the liquid to deform (flow), the higher the viscosity of the liquid.

The viscosity of different materials changes according to temperature, pressure, and sometimes shear stress. The viscosity of water is lowered by temperature and raised by pressure, but shear stress does not affect it. Honey has a similar viscosity relation with temperature: The hotter the honey, the lower its viscosity. Honey is 200 times less viscous at 160°F (70°C) than it is at 57°F (14°C). For glass, imagine its behavior at the glasshouse. Glass is technically a liquid even at room temperature, because its molecules are not organized into crystals. The flowing glass the glassblower works with is simply the result of high temperatures creating low viscosity. In rock-forming minerals, temperature drastically lowers viscosity, pressure raises it moderately, and shear stress lowers it, as shown in the accompanying figure.

Latex house paint is a good example of a material with shear-stress dependent viscosity. When painting it on with the brush, the brush applies shear stress to the paint, and its viscosity goes down. This allows the paint to be brushed on evenly. As soon as the shear stress is removed, the paint becomes more viscous and resists dripping. This is a material property that the paint companies purposefully give the paint to make it perform better. Materials that flow more easily when under shear stress but then return to a high viscosity when undisturbed are called thixotropic. Some strange materials, called dilatent materials, actually obtain higher viscosity when placed under shear stress. The most common example of a dilatent


These graphs show the relationship of fluid flow to shear stress for different types of materials, showing how viscosity can change in the material with increased shear stress.

Relation of Fluid Flow with Shear Stress

Newtonian viscosity

Recall that viscosity (T|) is defined as shear stress (O) divided by shear rate (£):

and so the slopes of these lines show the viscosities of the materials being graphed.

Shear stress

Shear stress divided by shear rate is constant: Viscosity does not depend upon shear stress.

Shear rate

Bingham plastic viscosity

Power-law viscosity

Low viscosity

Shear stress

Materials called Bingham plastics do not begin to flow until a certain threshold stress is applied.

Shear stress

Mantle materials have •¡J^/ stess-dependent viscosities: The / higher the stress, the lower their viscosity becomes and the Faster they shear (deform).

Shear rate

Shear rate

Rheology, or How Solids Can Flow (continued) material is a mixture of cornstarch and water. This mixture can be poured like a fluid and will flow slowly when left alone, but when pressed it immediately becomes hard, stops flowing, and cracks in a brittle manner. The viscosities of other materials do not change with stress: Their shear rate (flow rate) increases exactly with shear stress, maintaining a constant viscosity.

Temperature is by far the most important control on viscosity. Inside the Earth's upper mantle, where temperatures vary from about 2,000°F (1,100oC) to 2,500°F (1,400oC), the solid rocks are as much as 10 or 20 orders of magnitude less viscous than they are at room temperature. They are still solid, crystalline materials, but given enough time, they can flow like a thick liquid. The mantle flows for a number of reasons. Heating in the planet's interior makes warmer pieces of mantle move upward buoyantly, and parts that have cooled near the surface are denser and sink. The plates are also moving over the surface of the planet, dragging the upper mantle with them (this exerts shear stress on the upper mantle). The mantle flows in response to these and other forces at the rate of about one to four inches per year (2 to 10 cm per year).

Rocks on the planet's surface are much too cold to flow. If placed under pressure, cold, brittle surface rocks will fracture, not flow. Ice and hot rocks can flow because of their viscosities. Fluids flow by molecules sliding past each other, but the flow of solids is more complicated. The individual mineral grains in the mantle may flow by "dislocation creep," in which flaws in the crystals migrate across the crystals and effectively allow the crystal to deform or move slightly. This and other flow mechanisms for solids are called plastic deformations, since the crystals neither return to their original shape nor break.

and so is a modern analog to the last ice age, though at that time the ice sheets were far more extensive.

In Norway, Sweden, and Finland (together called Fennoscandia) in particular, because of the relatively small size and round shape of this land mass, the thick ice sheets pressed the continental crust down into the mantle just as one's hand can press a toy boat down into a bath of water. Now, with the ice sheets gone, Fennoscandia is rebounding, rising up again to its equilibrium height in the mantle. Since the mantle is highly viscous this rebound occurs slowly, unlike in the toy boat analogy. The viscosity of the mantle can be calculated by the speed of rebound of Fennoscandia.The area is rebounding about one-third of an inch (8 mm) per year at its center, and it is estimated that it has about 656 feet (200 m) of rebound to go. By using the following equation, the viscosity of the underlying mantle can be calculated:

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