phase

—phaseless, adj. —phasic, phaseal, adj.

/fayz/, n., v., phased, phasing.

n.

1. any of the major appearances or aspects in which a thing of varying modes or conditions manifests itself to the eye or mind.

2. a stage in a process of change or development: Each phase of life brings its own joys.

3. a side, aspect, or point of view: This is only one phase of the question.

4. a state of synchronous operation: to put two mechanisms in phase.

5. Astron.

a. the particular appearance presented by the moon or a planet at a given time.

b. one of the recurring appearances or states of the moon or a planet in respect to the form, or the absence, of its illuminated disk: the phases of the moon. See diag. under moon.

6. Zool. See color phase.

7. Chem. a mechanically separate, homogeneous part of a heterogeneous system: the solid, liquid, and gaseous phases of a system.

8. Physics. a particular stage or point of advancement in a cycle; the fractional part of the period through which the time has advanced, measured from some arbitrary origin often expressed as an angle (phase angle), the entire period being taken as 360°.

v.t.

9. to schedule or order so as to be available when or as needed.

10. to put in phase; synchronize: to phase one mechanism with another.

11. phase down, to reduce by gradual stages.

12. phase in, to put or come into use gradually; incorporate by degrees: to phase in new machinery.

13. phase out, to bring or come to an end gradually; ease out of service: to phase out obsolescent machinery.

[1805-15; (n.) back formation from phases, pl. of PHASIS]

Syn. 1. form, shape; facet, side.

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I

In thermodynamics, a chemically and physically uniform quantity of matter that can be separated mechanically from a nonhomogeneous mixture.

It may consist of a single substance or of a mixture of substances. The three basic phases of matter are solid, liquid, and gas; other phases that are considered to exist include crystalline (see crystal), colloidal (see colloid), glass, amorphous, and plasma. The different phases of a pure substance are related to each other in terms of temperature and pressure. For example, if the temperature of a solid is raised enough, or the pressure is reduced enough, it will become a liquid.

II

In wave motion, the fraction of the time required to complete a full cycle that a point completes after last passing through the reference position.

Two periodic motions are said to be in phase when corresponding points of each reach maximum or minimum displacements at the same time. If the crests of two waves pass the same point at the same time, they are in phase for that position. If the crest of one and the trough of the other pass the same point at the same time, the phase angles differ by 180° and the waves are said to be of opposite phase. Phase differences are important in alternating electric current technology (see alternating current).

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▪ astronomy

      in astronomy, any of the varying appearances of a celestial body as different amounts of its disk are seen (from the Earth, ordinarily) to be illuminated by the Sun. The Moon displays four main phases: new, first quarter, full, and last quarter. Earth, as seen from the Moon, shows the same phases in opposite order; e.g., Earth is full when the Moon is new. Planets more distant than the Earth from the Sun display only full or gibbous (more than half but not entirely full) phases to an observer on the Earth; i.e., they are always seen with more than half of their apparent disks in sunlight. However, only Mars is noticeably gibbous. The two planets closer to the Sun than Earth, Mercury and Venus, show full cycles of phases like the Moon's. The Italian astronomer Galileo's discovery of the phases of Venus was the first direct observational evidence for the Sun-centred solar system.

▪ mechanics

      in mechanics of vibrations, the fraction of a period (i.e., the time required to complete a full cycle) that a point completes after last passing through the reference, or zero, position. For example, the reference position for the hands of a clock is at the numeral 12, and the minute hand has a period of one hour. At a quarter past the hour the minute hand has a phase of one-quarter period, having passed through a phase angle of 90°, or π/2 radians. In this example the motion of the minute hand is a uniform circular motion, but the concept of phase also applies to simple harmonic motion such as that experienced by waves and vibrating bodies.

      If the position y of a point or particle changes according to a simple harmonic law, then it will change in time t according to the product of the amplitude, or maximum displacement, r, of the particle and a sine or cosine function composed of its angular speed, symbolized by the Greek letter omega (ω), the time t, and what is called the angle, symbolized by the Greek letter epsilon (ε): y = r sin (ωt + ε). The angle (ωt + ε) is called the phase angle at time t, which at zero time is equal to ε. Phase itself is a fractional value—the ratio of elapsed time t to the period T, or t/T—and is equal to the ratio of the phase angle to the angle of the complete cycle, 360°, or 2π radians. Thus, phase for uniform circular or harmonic motion has the value (ωt + ε)/2π. Applying this expression to the example of the moving minute hand cited above, ε is zero (zero phase angle at zero time), angular speed is 2π radians per hour, and time t is ¹/₄ hour, giving a phase of ¹/₄.

      When comparing the phases of two or more periodic motions, such as waves (wave motion), the motions are said to be in phase when corresponding points reach maximum or minimum displacements simultaneously. If the crests of two waves pass the same point or line at the same time, then they are in phase for that position; however, if the crest of one and the trough of the other pass at the same time, the phase angles differ by 180°, or π radians, and the waves are said to be out of phase (by 180° in this case).

 The measurement of phase difference is of central importance in alternating-current (alternating current) technology. In the diagram—>, two curves represent the voltage (E) and the current (I) in an alternating-current (AC) circuit with pure inductance. The difference in phase angle between the voltage and the current is 90°, and the current is said to lag one-quarter cycle in phase. This lag may be seen from the diagram. In AC power transmission the terms multiphase and polyphase are applied to currents that are out of phase with one another. In a two-phase system there are two currents with a phase-angle difference of 90°; in a three-phase system the currents differ in phase angle by 120°.

 

▪ state of matter

Introduction

      in thermodynamics, chemically and physically uniform or homogeneous quantity of matter that can be separated mechanically from a nonhomogeneous mixture and that may consist of a single substance or of a mixture of substances. The three fundamental phases of matter are solid, liquid, and gas (vapour), but others are considered to exist, including crystalline, colloid, glassy, amorphous, and plasma phases. When a phase in one form is altered to another form, a phase change is said to have occurred.

General considerations

      A system is a portion of the universe that has been chosen for studying the changes that take place within it in response to varying conditions. A system may be complex, such as a planet, or relatively simple, as the liquid within a glass. Those portions of a system that are physically distinct and mechanically separable from other portions of the system are called phases.

      Phases within a system exist in a gaseous, liquid, or solid state. Solids are characterized by strong atomic bonding and high viscosity, resulting in a rigid shape. Most solids are crystalline, inasmuch as they have a three-dimensional periodic atomic arrangement; some solids (such as glass) lack this periodic arrangement and are noncrystalline, or amorphous. Gases (gas) consist of weakly bonded atoms with no long-range periodicity; gases expand to fill any available space. Liquids (liquid) have properties intermediate between those of solids and gases. The molecules of a liquid are condensed like those of a solid. Liquids have a definite volume, but their low viscosity enables them to change shape as a function of time. The matter within a system may consist of more than one solid or liquid phase, but a system can contain only a single gas phase, which must be of homogeneous composition because the molecules of gases mix completely in all proportions.

System variables

      Systems respond to changes in pressure, temperature, and chemical composition, and, as this happens, phases may be created, eliminated, or altered in composition. For example, an increase in pressure may cause a low-density liquid to convert to a denser solid, while an increase in temperature may cause a solid to melt. A change of composition might result in the compositional modification of a preexisting phase or in the gain or loss of a phase.

The phase rule

      The classification and limitations of phase changes are described by the phase rule, as proposed by the American chemist J. Willard Gibbs (Gibbs, J Willard) in 1876 and based on a rigorous thermodynamic relationship. The phase rule is commonly given in the form P + F = C + 2. The term P refers to the number of phases that are present within the system, and C is the minimum number of independent chemical components that are necessary to describe the composition of all phases within the system. The term F, called the variance, or degrees of freedom, describes the minimum number of variables that must be fixed in order to define a particular condition of the system.

Phase diagrams (phase diagram)

Unary systems

      Phase relations are commonly described graphically in terms of phase diagrams (see Figure 1). Each point within the diagram indicates a particular combination of pressure and temperature, as well as the phase or phases that exist stably at this pressure and temperature. All phases in Figure 1 have the same composition—that of silicon dioxide (silica), SiO₂. The diagram is a representation of a one-component (unary) system, in contrast to a two-component (binary), three-component (ternary), or four-component (quaternary) system. The phases coesite, low quartz, high quartz, tridymite, and cristobalite are solid phases composed of silicon dioxide; each has its own atomic arrangement and distinctive set of physical and chemical properties. The most common form of quartz (found in beach sands and granites) is low quartz. The region labeled anhydrous melt consists of silicon dioxide liquid.

      Different portions of the silicon dioxide system may be examined in terms of the phase rule. At point A a single solid phase exists—low quartz. Substituting the appropriate values into the phase rule P + F = C + 2 yields 1 + F = 1 + 2, so F = 2. For point A (or any point in which only a single phase is stable) the system is divariant—i.e., two degrees of freedom exist. Thus, the two variables (pressure and temperature) can be changed independently, and the same phase assemblage continues to exist.

      Point B is located on the boundary curve between the stability fields of low quartz and high quartz. At all points along this curve, these two phases coexist. Substituting values in the phase rule (2 + F = 1 + 2) will cause a variance of 1 to be obtained. This indicates that one independent variable can be changed such that the same pair of phases will be retained. A second variable must be changed to conform to the first in order for the phase assemblage to remain on the boundary between low and high quartz. The same result holds for the other boundary curves in this system.

      Point C is located at a triple point, a condition in which three stability fields intersect. The phase rule (3 + F = 1 + 2) indicates that the variance is 0. Point C is therefore an invariant point; a change in either pressure or temperature results in the loss of one or more phases. The phase rule also reveals that no more than three phases can stably coexist in a one-component system because additional phases would lead to negative variance.

Binary systems

      Consider the binary system (Figure 2) that describes the freezing and melting of the minerals titanite (CaSiTiO₅) and anorthite feldspar (CaAl₂Si₂O₈). The melt can range in composition from pure CaSiTiO₅ to pure CaAl₂Si₂O₈, but the solids show no compositional substitution. All phases therefore have the composition of CaSiTiO₅, CaAl₂Si₂O₈, or a liquid mixture of the two. The system in the figure has been examined at atmospheric pressure; because the pressure variable is fixed, the phase rule is expressed as P + F = C + 1. In this form it is called the condensed phase rule, for any gas phase is either condensed to a liquid or is present in negligible amounts. The phase diagram shows a vertical temperature coordinate and a horizontal compositional coordinate (ranging from pure CaSiTiO₅ at the left to pure CaAl₂Si₂O₈ at the right).

      The phase fields (separated by the solid curves) contain either one or two phases. Any point in a one-phase field corresponds to a single phase whose composition is indicated directly below on the horizontal axis. For example, point A presents a liquid whose composition is 70 percent CaAl₂Si₂O₈ and 30 percent CaSiTiO₅. The compositions of phases in a two-phase field are determined by construction of a horizontal (constant-temperature) line from the point of interest to the extremities of the two-phase field. Thus, a sample with composition B consists of liquid C (43 percent CaSiTiO₅ and 57 percent CaAl₂Si₂O₈) and solid anorthite D. A sample at point E at a lower temperature consists of the solids titanite (F) and anorthite (G).

      Liquid CaAl₂Si₂O₈ cools to produce solid anorthite at 1,550° C, whereas liquid CaSiTiO₅ cools to produce solid titanite at 1,390° C. If the batch were a mixture of the two components, the freezing (freezing point) temperature of each of these minerals would be depressed. In a melt consisting of a single component, such as CaSiTiO₅, all atoms could add to titanite nuclei to form crystals of titanite. If, however, the melt contained 30 percent CaAl₂Si₂O₈, the rate of formation of titanite nuclei would be decreased, as 30 percent of the melt could not contribute to their formation. In order to increase the rate of formation of titanite nuclei and promote crystallization, the temperature of the melt must be decreased below the freezing point of pure CaSiTiO₅. When cooled, liquid A does not begin crystallization until temperature H is reached. Pure anorthite crystals precipitate from the melt. Depletion of CaAl₂Si₂O₈ from the melt causes the melt composition to become relatively enriched in CaSiTiO₅, with consequent additional depression of the anorthite freezing point. As freezing continues, the liquid composition changes until the minimum point is reached at I. This point is called the eutectic. It is the lowest temperature at which a liquid can exist in this system. At the eutectic, both anorthite and titanite crystallize together at a fixed temperature and in a fixed ratio until the remaining liquid is consumed. All intermediate liquid compositions migrate during crystallization to the eutectic. The melting sequence of titanite-anorthite mixtures is exactly the opposite of the freezing sequence (i.e., melting of any anorthite-titanite mixture begins at the eutectic).

      Depression of the freezing point of a compound by the addition of a second component is common in both binary and more complex systems. This usually occurs when the solid phases either have a fixed composition or show limited solid solution. Common examples are the mixing of ice and salt (NaCl) or the use of ethylene glycol (antifreeze) to depress the freezing point of water.

Applications to petrology

      Systematic investigation of the phase changes of the more common anhydrous mineral groups was initiated by the Canadian-born American petrologist Norman L. Bowen (Bowen, Norman L.) and his coworkers at the Geophysical Laboratory of the Carnegie Institution of Washington, D.C., in the early 20th century. This work was generally limited to systems at atmospheric pressure. Subsequent advances in technology have permitted the examination of rock systems in the presence of water pressure and ultrahigh confining pressures. Materials can now be systematically examined under conditions that range from those at the Earth's surface to those simulating conditions that exist at the core. This has led to a vast increase in knowledge about the conditions of formation of both igneous (igneous rock) and metamorphic rocks (metamorphic rock). Synthetic equivalents of almost every mineral or rock system can now be produced in the laboratory. Even gemstones such as diamonds are routinely synthesized.

  Typical of the data now available are the freezing-melting curves (Figure 3—>) of the common volcanic rock basalt (and its coarse-grained equivalent, gabbro). Figure 3A—> shows the crystallization range (shaded) for basaltic melts as a function of lithostatic pressure; this pressure is due to depth of burial. The two short lines show the approximate position of a transition region between gabbro and its denser solid equivalent, eclogite (a sodium-pyroxene + garnet rock). The melting curves have a positive slope, as the solids are denser than their equivalent melts and are thus favoured (enlarged) with increasing pressure.

 In the presence of water pressure (P_H2O), the freezing-melting curves are depressed (Figure 3B—>) because the water acts as another component. The slope of the curves is also influenced by the presence of a hydrous solid phase, hornblende, whose approximate stability field is indicated by the dashed line. The changes in liquid composition and crystallization sequences have been determined. Similar information is available for most common igneous rocks.

      In 1915 the Finnish petrologist Pentii E. Eskola set up a classification scheme for metamorphic rocks that was based on metamorphic facies. Each facies was defined by the presence of one or more common mineral assemblages. The stability limits of these assemblages subsequently have been determined by laboratory studies. As a result, placing a metamorphic rock within a particular facies indicates the broad pressure-temperature region in which the rock formed. (See metamorphic rock: Metamorphic facies (metamorphic rock) for the pressure-temperature regions of the major metamorphic facies.) For example, a rock containing sodium-rich pyroxene and garnet is placed within the eclogite facies, which indicates that it formed at pressures greater than about 12 kilobars and temperatures above approximately 600° C. Rocks in the blueschist facies (glaucophane facies) contain the blue amphibole glaucophane; such rocks are stable at high pressures and relatively low temperatures.

      A large variety of schemes are available to provide more detailed information on the temperatures and pressures of formation of both igneous and metamorphic rocks. These may use phase relations, stable isotopes, or the compositions of coexisting mineral pairs.

Ernest G. Ehlers

Additional Reading

Gerhard L. Salinger and Francis Weston Sears, Thermodynamics, Kinetic Theory, and Statistical Thermodynamics (1975), is a classic introduction. A detailed application of thermodynamic principles to phases, phase changes, and phase diagrams is given in Mats Hillert, Phase Equilibria, Phase Diagrams, and Phase Transformations: Their Thermodynamic Basis (1998).Works focusing on phase equilibria in geology and petrology include W.G. Ernst, Petrologic Phase Equilibria (1976), a concise introduction to phase equilibria that assumes some knowledge of thermodynamics; Ernest G. Ehlers and Harvey Blatt, Petrology: Igneous, Sedimentary, and Metamorphic (1982), an introduction to phase equilibria of petrologic systems; and Ernest G. Ehlers, The Interpretation of Geological Phase Diagrams (1972, reprinted 1987), which provides step-by-step nonmathematical procedures for understanding phase diagrams. A more-recent work is Thomas M. Will, Phase Equilibria in Metamorphic Rocks: Thermodynamic Background and Petrological Applications (1998).Simeon Potter

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