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. 2010 Mar 13;368(1914):941-65.
doi: 10.1098/rsta.2009.0282.

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

P P Edwards  1 , M T J Lodge, F Hensel, R Redmer
Affiliations

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

P P Edwards et al. Philos Trans A Math Phys Eng Sci. .

Abstract

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.

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Figures

Figure 1.
Figure 1.
Sir Nevill Mott: ‘… a metal conducts and a non-metal doesn’t’. A letter from Sir Nevill Mott to P. P. Edwards 9 May 1996: Nevill answers the question, ‘What is a metal?’. (Reproduced with permission from Edwards 1998.)
Figure 2.
Figure 2.
The room-temperature electrical resistivity of materials and substances is one of the most widely varying of all physical properties, encompassing 28 orders of magnitude difference between metals and non-metals. At the absolute zero of temperature, non-metals do not conduct, while metals do (excluding here the phenomenon of superconductivity). (Adapted from Ehrenreich 1967.)
Figure 3.
Figure 3.
Energy band diagrams for (a) a metal, (b) an insulator (non-metal), (c) an intrinsic semiconductor and (d) an impurity semiconductor. (Adapted from Shockley 1950.)
Figure 4.
Figure 4.
The metal–non-metal transition at T=0 K, whereby free (conduction) electrons become localized at individual sites. The system transforms discontinuously from a metal to a non-metal as the mean distance between centres continuously increases.
Figure 5.
Figure 5.
The measured electrical conductivities of a range of bulk crystals of silicon doped with phosphorus (Si : P). The electron (or donor atom) density supplied by the phosphorus donor atoms is indicated on each curve in units of electrons per cubic centimetre.
Figure 6.
Figure 6.
A semi-logarithmic plot of the zero temperature conductivity, σ (0), versus the donor atom content for Si : P. The transition from non-metal to metal is extremely sharp, but probably continuous. Mott’s minimum metallic conductivity is also indicated for this particular example. The critical density for the metal–non-metal transition is 3–4×1018 cm−3 (Rosenbaum et al. 1980).
Figure 7.
Figure 7.
The electrical conductivity of fluid caesium, rubidium, mercury, oxygen and hydrogen versus atom density, n. The tag lines on the atom density axis denote the predicted metallization densities for each element, based on the Goldhammer–Herzfeld model (see text). Note that the experimented atom densities range from 1021 cm−3 for rubidium and caesium to over 1023 cm−3 for oxygen and hydrogen. (Adapted from Edwards & Hensel 2002.)
Figure 8.
Figure 8.
Linus Pauling offers his visionary insights and remarkable intuition into the success of the Goldhammer–Herzfeld criterion in rationalizing the occurrence of metallic character in the periodic table of the chemical elements. He also establishes the direct link with the concept of the metallic orbital (Edwards & Sienko 1983c). Photograph courtesy of California Institute of Technology.
Figure 9.
Figure 9.
The transition to the metallic state for high-temperature (T> 1000 K) fluid caesium, rubidium, mercury and hydrogen: the dependence of the electrical conductivity on the scaling parameter n1/3aH*. The dotted line drawn at n1/3aH* indicates the common metallization condition for these chemical elements. To the left of the metallization condition, we have the non-metallic form of the four elements (non-metallic fluids); to the right, we have the corresponding metallic state (the metallic fluids). Above the metallization threshold, we anticipate conduction based on the theory put forward by Ziman (1961).
Figure 10.
Figure 10.
Room-temperature electrical conductivities for the majority of chemical elements of the s-, p- and d-blocks of the periodic table. The inset represents one conventional designation of elements as metals, metalloids and semiconductors, as non-metals. (Adapated from Logan & Edwards 1985.)
Figure 11.
Figure 11.
Metallization of elements of the periodic table under ambient conditions imposed on the Earth. The figure shows the ratio (R/V) for elements of the s-, p- and d-blocks of the periodic table. Here, R is the molar refractivity and V is the molar volume. The shaded circles represent elements for which both R and V are known experimentally. The open circles are for elements in which R is calculated and V is known experimentally. (Adapted from Edwards & Sienko , 1983b).
Figure 12.
Figure 12.
A possible form of the periodic table of the chemical elements at a pressure close to 3 million atmospheres. This table is not yet complete—certain elements have not been investigated to these high pressures (e.g. F2, etc.). Notice now the absence of the traditional demarcation separating metals from non-metals (grey background) under normal conditions on Earth. Fluid hydrogen is shown as a metal; solid hydrogen does not attain metallic states, even at these high-imposed pressures. A new development could be that certain prototypical ‘metals’ (e.g. Li) could become non-metals at these high pressures (Ashcroft 2009)! We do not discuss such a possibility here. (Adapted from Edwards & Hensel 2002.)
Figure 13.
Figure 13.
Miscibility gap in the hydrogen–helium system for constant pressures as a function of the hydrogen concentration, y=NH/(NH+NHe) (see Lorenzen et al. 2009). The calculated melting temperatures, Tm, of solid helium are indicated on the right-hand side for each pressure. The strong increase in the demixing temperatures occurs at critical hydrogen concentrations yc, which are in accordance with Mott’s criterion, formula image. We conclude that the thermodynamics that drives the phase separation in the mixture is caused by a continuous non-metal to metal transition in the hydrogen subsystem.
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