'... a metal conducts and a non-metal doesn't'

In a letter to one of the authors, Sir Nevill Mott, then in his tenth decade, highlighted the fact that the statement '... a metal conducts, and a non-metal doesn't' can be true only at the absolute zero of temperature, T=0 K. But, of course, experimental studies of metals, non-metals and, indeed, the electronic and thermodynamic transition between these canonical states of matter must always occur above T=0 K, and, in many important cases, for temperatures far above the absolute zero. Here, we review the issues-theoretical and experimental-attendant on studies of the metal to non-metal transition in doped semiconductors at temperatures close to absolute zero (T=0.03 K) and fluid chemical elements at temperatures far above absolute zero (T>1000 K). We attempt to illustrate Mott's insights for delving into such complex phenomena and experimental systems, finding intuitively the dominant features of the science, and developing a coherent picture of the different competing electronic processes. A particular emphasis is placed on the idea of a 'Mott metal to non-metal transition' in the nominally metallic chemical elements rubidium, caesium and mercury, and the converse metallization transition in the nominally non-metal elements hydrogen and oxygen. We also review major innovations by D. A. Goldhammer (Goldhammer 1913 Dispersion und absorption des lichtes) and K. F. Herzfeld (Herzfeld 1927 Phys. Rev. 29, 701-705. (doi:10.1103/PhysRev.29.701)) in a pre-quantum theory description of the metal-non-metal transition, which emphasize the pivotal role of atomic properties in dictating the metallic or non-metallic status of the chemical elements of the periodic table under ambient and extreme conditions; a link with Pauling's 'metallic orbital' is also established here.