Where does phase collide?

A physically distinct, homogeneous region of matter, such as solid, liquid, or gas, that can coexist with other such regions across a boundary. Gibbs set this out in On the Equilibrium of Heterogeneous Substances (1876), where the phase rule F = C - P + 2 counts the degrees of freedom left to a system given its number of components C and the number of coexisting phases P. In a modern account such as Atkins' Physical Chemistry the referent is a bulk sample of matter and its state, and a phase transition is a change from one such region to another at a fixed temperature and pressure. What marks this meaning is that phase names a region of matter and the state it is in, not a position, an angle, or a stage in time.[1][2]

Unit

A homogeneous region of matter in one state

Recovery means

Not applicable

Measured by

Observed coexistence of phases and the degrees of freedom set by the phase rule F = C - P + 2

The angular position of a periodic signal within its cycle, fixing how far the oscillation has advanced at a given instant. For a sinusoid written as A sin(ωt + φ), the phase is the whole argument ωt + φ, and the constant φ is the phase at t = 0; a phase difference between two waves of the same frequency is the fixed offset between their arguments. French's Vibrations and Waves (1971) develops this for oscillators and travelling waves, where phase is read in radians or degrees and two signals a quarter cycle apart differ by 90 degrees. Here the referent is a point within a repeating cycle, an angle, not a region of matter and not a span of time.[3]

Unit

Radians or degrees within one cycle

Recovery means

Not applicable

Measured by

Phase angle read from a signal in radians or degrees, and the phase difference between two signals

The fraction of the Moon's disc that appears lit as seen from Earth, running from new through crescent, quarter, and gibbous to full and back. The named phases track the changing angle between the Sun, the Earth, and the Moon as the Moon orbits, and Meeus's Astronomical Algorithms (1998) gives the illuminated fraction as k = (1 + cos i) / 2, where i is the phase angle at the Moon. The referent is the appearance of a body in the sky and how much of it is lit, reported as a number between 0 and 1 or as a named shape. It shares the word with the wave meaning, and even borrows the phrase phase angle, but it names how much of a disc is visible, not a state of matter and not a stage in a plan.[4]

Unit

Illuminated fraction from 0 to 1, or a named phase

Recovery means

Not applicable

Measured by

The illuminated fraction k computed from the Sun-Earth-Moon phase angle i

In archaeology, phase refers to an archaeological unit of similar finds limited in space and time, the basic unit for comparing sites. This meaning comes from Willey (1958) in Method and theory in American archaeology.[5]

Unit

Recovery means

Measured by

In entomology, phase refers to the solitary and gregarious forms of locusts, which differ in colour, shape and behaviour and switch with crowding. This meaning comes from Uvarov (1921) in Bulletin of Entomological Research.[6]

Unit

Recovery means

Measured by