The fractional part of a period through which the time variable of a periodic quantity (alternating electric current, vibration) has moved, as measured at any point in time from an arbitrary time origin. In the case of a sinusoidally varying quantity, the time origin is usually assumed to be the last point at which the quantity passed through a zero position from a negative to a positive direction.
In comparing the phase relationships at a given instant between two time-varying quantities, the phase of one is usually assumed to be zero, and the phase of the other is described, with respect to the first, as the fractional part of a period through which the second quantity must vary to achieve a zero of its own (see illustration). In this case, the fractional part of the period is usually expressed in terms of angular measure, with one period being equal to 360° or 2π radians. See Phase-angle measurement, Sine wave
the argument of the function cos (ωt+ φ), describing a harmonic oscillatory process, where ω is the angular frequency, t is the time, and φ is the initial phase of oscillations, that is, the phase at the initial time t = 0. The phase can be determined with an accuracy up to the value of an arbitrary term that is a multiple of 2π. Usually, the only values of interest are the phase differences in various harmonic processes. For oscillations that have the same frequency, the phase difference is always equal to the difference between the initial phases φ1 – φ2 and does not depend on the time reference point. For oscillations that have differing frequencies ωl and ω2, the phase relationships are characterized by the reduced phase difference
which similarly is not dependent on the time reference point. The auditory perception of the direction from which a sound approaches is associated with the difference in the phase of acoustic vibrations arriving at each ear.
in thermodynamics, a state of thermodynamic equilibrium of a substance, the physical properties of which differ from those of other equilibrium states—that is, other phases—of the same substance (seeEQUILIBRIUM, THERMODYNAMIC). A nonequilibrium metastable state of a substance is sometimes called a phase or, more explicitly, a metastable phase.
A transition of a substance from one phase to another, which is called a phase transition, is associated with a qualitative change in the properties of the substance. For example, the gaseous, liquid, and crystalline states, or phases, of a substance are substantially different with respect to the nature of the motion of particles (molecules) and the presence or absence of ordered structure (seeSTATES OF AGGREGATION). At high temperatures and pressures, a substance undergoes a transition to the plasma state. Various crystalline phases may differ from one another in, for example, electrical conductivity, the presence of an electric or magnetic moment, the type of crystal structure, and the existence of superconductivity. Various liquid phases may differ from one another in, for example, the concentration of components, the presence or absence of superfluidity (as in liquid 3He and 4He; seeQUANTUM FLUID), and the anisotropy of elastic and electrical properties (as in liquid crystals).
In most cases, phases are spatially homogeneous. However, there are some exceptions, such as ferromagnets in weak magnetic fields (seeDOMAINS) and the mixed state of type II superconductors (seeSUPERCONDUCTIVITY).
V. L. POKROVSKII