Phase (matter)
In the
physical sciences, a
phase is a
set of states of a macroscopic physical system that have relatively uniform chemical composition and physical properties (i.e.
density,
crystal structure,
index of refraction, and so forth). The most familiar examples of phases are
solids,
liquids, and
gases. Less familiar phases include:
plasmas and
quark-gluon plasmas;
Bose-Einstein condensates and
fermionic condensates;
strange matter;
liquid crystals;
superfluids and
supersolids; and the
paramagnetic and
ferromagnetic phases of
magnetic materials.
Phases are sometimes called
states of matter, but this term can lead to confusion with
thermodynamic states. For example, two gases maintained at different pressures are in different thermodynamic states, but the same "state of matter".
Example 1: Solid, liquid, and gaseous phases
Water (H
2O) is composed of water
molecules, each of which is an
oxygen atom attached to two
hydrogen atoms. At
room temperature, the molecules are packed closely together, and interact weakly. They do not stick together, and are able to slide past one another like the sand grains in an
hourglass. This microscopic behavior of water molecules gives rise to the physical properties of liquid water with which we are all familiar. Because the molecules do not form any rigid structure, water has no fixed shape, and adapts to the shape of any container in which it is placed. Because the molecules are very close to one another, water resists
compression; try squeezing a
water balloon, and you will find that it is practically impossible to reduce its volume, unlike an ordinary air balloon.
If we make slight changes in the physical conditions, such as lowering the
temperature, we will observe no abrupt changes in the properties of water. Cold water behaves little differently from lukewarm water. For instance, its compressibility changes slightly with temperature, but remains very low.
However, if we reduce the temperature below a certain point, an abrupt and dramatic change occurs. At the microscopic level, the molecules suddenly align with one another to form a rigid
hexagonal lattice, losing the ability to slide past one another. The system as a whole acquires rigidity, and can hold a definite shape (though it may deform or fracture into pieces if sufficient force is applied.) This is the solid phase of water, commonly known as
ice. The transition from a liquid phase to a solid phase is called freezing, and it is a type of phenomenon known as a
phase transition.
Another phase transition, known as
boiling, occurs if we raise the temperature of liquid water past a certain point. The water abruptly enters a gaseous phase, where it is called
water vapor. In the gaseous phase, the molecules are spread far apart, and interact extremely weakly. Like a liquid, a gas has no fixed shape, but unlike a liquid, it has little resistance to compression because there is enough space for the molecules to move closer to one another. Whereas a liquid placed in a container will form a puddle at the bottom of the container, a gas will expand to fill the container.
We can use other physical parameters, not just temperature, to produce these phase transitions. For example, we can change a liquid into a gas by decreasing the pressure, or, equivalently, increasing the volume. As before, small changes do not have much effect; the phase transition occurs abruptly when the change exceeds a certain amount.
General definition of phases
In general, we say that two different states of a system are in different phases if there is an abrupt change in their physical properties while transforming from one state to the other. Conversely, two states are in the same phase if they can be transformed into one another without any abrupt changes.
An important point is that different types of phases are associated with different physical qualities. When discussing the solid, liquid, and gaseous phases, we talked about rigidity and compressibility, and the effects of varying the pressure and volume, because those are the relevant properties that distinguish a solid, a liquid, and a gas. On the other hand, when discussing
paramagnetism and
ferromagnetism, we looked at the magnetization, because that is what distinguishes the ferromagnetic phase from the paramagnetic phase. Several more examples of phases will be given in the following section.
Not all physical quantities are relevant when we are looking at a certain system. For example, it is generally not useful for us to compare the magnetization of liquid water to the magnetization of ice. In this sense, what constitutes a "phase" depends on what parameters you are looking at, and vice versa. It is this idea that allows us to generalize the concept of phases to encompass a wide variety of phenomena.
In more technical language, a phase is a region in the
parameter space of
thermodynamic variables in which the
free energy is
analytic. As long as the free energy is analytic, all thermodynamic properties (such as
entropy,
heat capacity,
magnetization, and
compressibility) will be
well-behaved, because they can be expressed in terms of the free energy and its
derivatives. For example, the
entropy is the first derivative of the free energy with
temperature.
When a system goes from one phase to another, there will generally be a stage where the free energy is non-analytic. This is a
phase transition. Due to this non-analyticity, the free energies on either side of the transition are two different functions, so one or more thermodynamic properties will behave very differently after the transition. The property most commonly examined in this context is the
heat capacity. During a transition, the heat capacity may become infinite, jump abruptly to a different value, or exhibit a "kink" or discontinuity in its
derivative. See also
differential scanning calorimetry.
|
Possible graphs of heat capacity (C) against temperature (T) at a phase transition |
Other examples of phases
In this section, we will present several systems that exhibit phase phenomena.
We have discussed the solid, liquid, and gaseous phases of ordinary matter. It turns out that other configurations of molecules are possible, corresponding to novel phases.
Amorphous solids, or
glasses, are a solid phase in terms of mechanical behavior, but lack the structural order of an ordinary ("
crystalline") solid, so that the arrangement of atoms within them resembles a liquid.
Liquid crystals are another phase intermediate between solids and liquids; the molecules of such a substance have an orderly orientation and in some cases (that is, for
smectic liquid crystals) even an orderly position in one direction, but are free to flow past one another. Liquid crystals are liquids in the mechanical sense, but have structural features that are normally seen in solids.
In many materials, there are actually a variety of solid phases, each corresponding to a unique
crystal structure. These varying crystal phases of the same substance are called "
allotropes" if intramolecular bonding changes or "polymorphs" if only intermolecular bonding changes. For instance, there are at least nine different polymorphs of
ice that manifest under different temperature and pressure conditions. To take another example,
diamond and
graphite are allotropes of
carbon. Graphite is composed of layers of hexagonally arranged carbon atoms, in which each carbon atom is strongly bound to three neighboring atoms in the same layer and is weakly bound to atoms in the neighboring layers. By contrast, in diamond each carbon atom is strongly bound to four neighboring carbon atoms in a
diamond cubic array, with tetrahedral bonding. The unique crystal structures of graphite and diamond are responsible for the vastly different properties of these two materials.
In an ordinary gas phase, the
electrons are tightly bound to the
atomic nuclei. In contrast, in the
plasma phase the atoms are dissociated, i.e. the electrons are separated from the atomic nuclei. This dissociation, or , occurs abruptly upon raising the temperature and lowering the pressure, and thus displays the hallmarks of a phase transition.
Superfluids,
supersolids, and
Bose-Einstein condensates are phases of matter that occur at extremely low temperatures, near
absolute zero. These temperatures are too low to occur anywhere on Earth except in laboratory experiments. The very slow motion of molecules at these temperatures allow some of the more bizarre aspects of quantum mechanics to manifest themselves in the form of novel macroscopic properties.
Under extremely high pressure, ordinary matter undergoes a transition to a series of exotic phases collectively known as
degenerate matter. These phases are of great interest to
astrophysics, because these high-pressure conditions are believed to exist inside
stars that have used up their
nuclear fusion "fuel", such as
white dwarves and
neutron stars.
Phase transitions also play an extremely important role in
physical cosmology. It is believed that the universe as a whole underwent a series of important phase transitions during its early history, shortly after the
Big Bang. A major branch of theoretical cosmology,
inflation theory, seeks to explain various aspects of the modern universe, such as
why the universe is so flat, as the effect of one or more of these transitions. These transitions are of great interest to
particle physics as well, as it has been hypothesized that the
quantum field that fills
spacetime (a particle physics concept that incorporates "material" particles like electrons as well as "field-like" particles such as
photons and
gluons) underwent a series of transitions from a highly "symmetric" phase in which all
fundamental forces were unified into a single entity, into the "
broken symmetry" phase that we observe today, in which there are four fundamental forces with very different strengths.
Main article: Phase diagram
The different phases of a system may be represented using a
phase diagram. The axes of the diagrams are the relevant thermodynamic variables. For simple mechanical systems, we generally use the
pressure and
temperature.
|
A phase diagram for a typical material exhibiting solid, liquid and gaseous phases |
The markings on the phase diagram show the points where the free energy is non-analytic. The open spaces, where the free energy is analytic, correspond to the phases. The phases are separated by lines of non-analyticity, where phase transitions occur, which are called
phase boundaries.
In the diagram, the phase boundary between liquid and gas does not continue indefinitely. Instead, it terminates at a point on the phase diagram called the
critical point. At temperatures and pressure above the critical point, the physical property differences that differentiate the liquid phase from the gas phase become less defined. This reflects the fact that, at extremely high temperatures and pressures, the liquid and gaseous phases become indistinguishable. In water, the critical point occurs at around 647
K (374 °C or 705 °F) and 22.064
MPa.
The existence of the liquid-gas critical point reveals a slight ambiguity in our above definitions. When going from the liquid to the gaseous phase, one usually crosses the phase boundary, but it is possible to choose a path that never crosses the boundary by going to the right of the critical point. Thus, phases can sometimes blend continuously into each other. This new phase which has some properties that are similar to a liquid and some properties that are similar to a gas is call a
supercritical fluid. We should note, however, that this does not always happen. For example, it is impossible for the solid-liquid phase boundary to end in a critical point in the same way as the liquid-gas boundary, because the solid and liquid phases have different
symmetry.
An interesting thing to note is that the solid-liquid phase boundary in the phase diagram of most substances, such as the one shown above, has a positive slope. This is due to the solid phase having a higher density than the liquid, so that increasing the pressure increases the melting temperature. However, in the phase diagram for
water the solid-liquid phase boundary has a negative slope. This reflects the fact that ice has a lower density than water, which is an unusual property for a material.
Sometimes a substance or mixture can be heated, compressed, etc., beyond the point at which it would normally exhibit a phase change, but without actually triggering the change. Examples include
supercooling,
superheating, and
supersaturation.
Metastable states are sometimes referred to as phases although strictly speaking they are not because they are unstable. Usually each polymorph of a given substance is only stable over a specific range of conditions. For example,
diamond is the stable form of
carbon at extremely high pressures while
graphite is the stable form at normal atmospheric pressures. Regardless, diamonds appear stable at normal temperatures and pressures, but, in fact, are very slowly converting to graphite. Heat increases the rate of this transformation, but at normal temperatures the diamond is practically stable.
Another important example of metastable polymorphs occurs in the processing of
steel. Steels are often subjected to a variety of thermal treatments designed to produce various combinations of stable and metastable iron phases. In this way the steel properties, such as hardness and strength can be adjusted by controlling the relative amounts and crystal sizes of the various phases that form.
The distribution of kinetic energy among molecules is not uniform, and it changes randomly. This means that at, say, the surface of a liquid, there may be an individual molecule with enough kinetic energy to jump into the gas phase. Likewise, individual gas molecules may have low enough kinetic energy to join other molecules in the liquid phase. This phenomena means that at any given temperature and pressure, multiple phases may co-exist.
For example, under
standard conditions for temperature and pressure, a bowl of liquid water in dry air will evaporate until the
partial pressure of gaseous water equals the
vapor pressure of water. At this point, the rate of molecules leaving and entering the liquid phase becomes the same (due to the increased number of gaseous water molecules available to re-condense). The fact that liquid molecules with above-average kinetic energy have been removed from the bowl results in
evaporative cooling. Similar processes may occur on other types of phase boundaries.
Gibbs' phase rule relates the number of possible phases, variables such as temperature and pressure, and whether or not an equilibrium will be reached.
Phases are
emergent phenomena produced by the self-organization of a macroscopic number of particles. Typical samples of matter, for example, contain around 10
23 particles (of the order of
Avogadro's number). In systems that are too small the distinction between phases disappears, since the appearance of non-analyticity in the free energy requires a huge, formally infinite, number of particles to be present.
One might ask why real systems exhibit phases, since they are not actually infinite. The reason is that real systems contain thermodynamic fluctuations. When a system is far from a phase transition, these fluctuations are unimportant, but as it approaches a phase transition, the fluctuations begin to grow in size (i.e. spatial extent). At the ideal transition point, their size would be infinite, but before that can happen the fluctuations will have become as large as the system itself. In this regime, "finite-size" effects come into play, and we are unable to accurately predict the behavior of the system. Thus, phases in a real system are only well-defined away from phase transitions, and how far away it needs to be is dependent on the size of the system.
There is a corollary to the emergent nature of phase phenomena, known as the principle of
universality. The properties of phases are largely independent of the underlying microscopic physics, so that the same types of phases arise in a wide variety of systems. This is a familiar fact of life. We know, for example, that the property that defines a solid is exhibited by materials as diverse as
iron,
ice, and
Silly Putty. The only differences are matters of scale. Iron may resist deformation more strongly than Silly Putty, but both maintain their shape if the applied forces are not too strong.
*
2005-06-22, MIT News: MIT physicists create new form of matter Citat: "... They have become the first to create a new type of matter, a gas of atoms that shows high-temperature superfluidity."
*
2003-10-10, Science Daily: Metallic Phase For Bosons Implies New State Of Matter*
2004-01-15, ScienceDaily: Probable Discovery Of A New, Supersolid, Phase Of Matter Citat: "...We apparently have observed, for the first time, a solid material with the characteristics of a superfluid...but because all its particles are in the identical quantum state, it remains a solid even though its component particles are continually flowing..."
*
2004-01-29, ScienceDaily: NIST/University Of Colorado Scientists Create New Form Of Matter: A Fermionic Condensate*
French physicists find a solution that reversibly solidifies with a rise in temperature - α-
cyclodextrin,
water, and
4-methylpyridine*
Condensed matter physics*
Cooling curve*
Supercooling*
Superheating*
Multiphasic liquid
