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Phase (matter)

2007 Schools Wikipedia Selection. Related subjects: General Physics

   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".

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
   Enlarge
   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 behaviour, 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 ionization, occurs abruptly upon raising the
   temperature and lowering the pressure, and thus displays the hallmarks
   of a phase transition.

   Bose-Einstein condensate is a phase of matter that occurs 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.

   Phases can also exist in two dimensions. The boundaries between two
   different three-dimensional phases, the surfaces of materials, and the
   grain boundaries between different crystallographic orientations of a
   single material can also show distinct phases. For example, surface
   reconstructions on metal and semiconductor surfaces are two dimensional
   phases.

   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.

Phase diagrams

   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
   Enlarge
   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 called 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.

Metastable phases

   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.

   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.

Phase equilibrium

   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
   phenomenon 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.

Emergence and universality

   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 -- even, say, a thousand atoms
   -- 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 behaviour 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 -- resistance to deformation -- 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.

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