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Mathematics for Physics

219 Matter

A collection of atoms that is used to form solids, liquids, and gases, where a condensed phase is a dense form of matter whose many constituents interact strongly.

Phase. A phase is a macroscopic state of matter that is uniform in chemical composition and physical state. This principle is used to name the uniform macroscopic state of a sample.

Phase transition. A phase transition is the transformation of a substance from one physical state to another. This principle is used to describe melting, freezing, boiling, and condensation.

Condensed phases. Neighboring molecules attract at moderate distances and cannot occupy the same space. This principle is used to explain why solids and liquids stay compact instead of expanding to fill a container.

Lattice periodicity. A crystalline solid has a repeating three-dimensional array of atoms. An amorphous solid has only short-range structural order and lacks that repeating array. This principle is used to explain sharp Bragg peaks in crystals and diffuse scattering from glasses.

Positional order of the atoms. A solid has long-range crystalline order. A liquid is dense but disordered, with only local, temporary arrangement. A gas has no lasting positional order: the molecules are separated and free. This principle is used to tell the three familiar states of matter apart.

The radial distribution function \(g(r)\) is used to read that order from the density of neighbors at distance \(r\). See Radial Distribution Function.

Note: Condensed phases are the familiar solid and liquid forms of matter. There is no fundamental liquid-gas distinction beyond density and compressibility.

219.1 References

  1. Simon, S. H. The Oxford Solid State Basics. Oxford University Press, 2013. Ch. 7 — disordered liquid and gas configurations; density and compressibility. §1.1 — condensed phases.
  2. Feynman, R. P., Leighton, R. B., & Sands, M. The Feynman Lectures on Physics, Vol. I. §1-2 — crystalline long-range order distinguishes solid from liquid.
  3. Atkins, P., de Paula, J., & Keeler, J. Atkins’ Physical Chemistry. — phase as a uniform macroscopic state; \(g(r)\) spikes in crystals; short-range liquid order.
  4. Levine, I. N. Physical Chemistry. — liquid coordination shells; gas \(g(r)\) beyond the collision diameter.
  5. Kittel, C. Introduction to Solid State Physics. Wiley — lattice periodicity of crystals; amorphous solids.