Phase matter: Encyclopedia II - Phase matter - Definition

Phase matter - Definition

Even though the concept of phases is widely-used in the physical sciences, it is not easy to define precisely. Before presenting the general definition, we will provide two common examples of phase phenomena: firstly, the ordinary solid, liquid, and gas phases of matter; secondly, the paramagnetic and ferromagnetic phases of magnetic materials.

Phase matter - Example 1: Solid liquid and gas phases

Water (H₂O) 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 (or "melting" if we go in the opposite direction), 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.

Phase matter - Example 2: Magnetic phases

A second example of phases occurs in magnetic materials. In these materials, each atom possesses a magnetic moment that produces a tiny magnetic field pointing in a certain direction. The atoms are free to rotate, so their magnetic fields can point anywhere, but the magnetic fields of neighboring moments tend to make them line up with one another. At high temperatures, and in the absence of an external magnetic field, individual moments tend to be aligned with only a few neighbors, so the moments tend to point in random directions. There is no net magnetic field, i.e. zero magnetization. This is known as the paramagnetic phase.

If we lower the temperature below a certain point, called the Curie point, the moments abruptly line up over large regions (usually many thousands of atoms). Within these regions, called "magnetic domains", almost all the moments are pointing in the same direction. This is known as spontaneous magnetization. The appearance of magnetic domains is a phase transition, and the new phase is known as a ferromagnet.

Phase 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 quantities. 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.

Phase matter - Other examples of phases

Main article: List of phases of matter

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 phase intermediate between solids and liquids. The atoms in an amorphous solid are aligned in a rigid disorderly structure, instead of a regular lattice like an ordinary ("crystalline") solid. Liquid crystals are another phase intermediate between solids and liquids; the atoms are held in place, but are free to rotate.

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 cubic array. 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. (It is commonly stated that plasmas are the "fourth state of matter", but the above discussion shows that this statement is false. There are a huge variety of phases, or "states of matter", depending on what physical properties you are looking at.)

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 take place inside stars that have used up their nuclear fusion "fuel", such as white dwarfs and neutron stars.

Phase transitions also play an extremely important role in 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.

Adapted from the Wikipedia article "Definition", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki