Solutions and the Nonmetal-to-Metal Transition

Na-NH3, 1.02 x 108 ohm-1 cm2 mol-1 for Hg, 0°C, 0.16 x 10 ohm-1 cm2 mol-1). In the intermediate composition range 1 to 7 MPM, a NM-M transition occurs, and changes in the electronic, thermodynamic, and mechanical properties of the system are equally impressive (35, 37, 124, 154). A detailed discussion of the concentration dependence of various properties of metal-ammonia solutions is given in the book by Thompson (164). In addition, a recent review (60) at Colloque Weyl V also summarizes the available data for lithium-methylamine solutions (10, 11, 63, 127, 128, 166). 

Our canvas here is to provide a qualitative description of current models for the NM-M transition, developed for both metal-ammonia and metal-methylamine solutions. For this purpose we also draw upon interpretations from other systems in which the transition from localized to itinerant electron regimes is well recognized (78). 

Models for the Nonmetal-to-Metal Transition 1. The Herzfeld Theory of Metallization 

In 1927, K. F. Herzfeld published a paper (93) in which he proposed a simple criterion for determining when an element or system will ex- 

If (RIV) = 1, the resultant force on the localized electron vanishes, the electron is set free, and the system acquires metallic status. The previous statements may be recast in slightly different form using the venerable Clausius-Mossotti relationship (81), where 

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However, this scheme does present major conceptual difficulties and has been criticized recently (160). In particular, the formation of specific diamagnetic (cluster) units at these very low metal concentrations might be considered unrealistic in view of the extremely large (average) electron-electron separation (—100 A). Clustering phenomena are well established for concentrations close to the nonmetal-to-metal transition in these systems (33, 155), but for sodium-ammonia solutions this does not occur until approximately 4 MPM (Section IV). 

Fig. 24. The electronic and thermodynamic phase transitions at the nonmetal-to-metal transition a schematic representation of the free energy of a metal-ammonia solution in the temperature range of the miscibility gap, showing the NM-M transition as a function of metal concentration for increasing temperatures.

Freshly prepared films show the absorption peak of K. This tends to anneal with time to a combination of a localized electron peak at 1250 nm and an absorbance that rises steadily with increasing wavelength. The spectra are remarkably similar to those of concentrated metal-ammonia solutions as they move through the nonmetal to metal transition.The rising absorbance is attributed to the plasma edge that is characteristic of metallic behavior. The electrical conductivity of powders and films of this electride is far greater than that of other electrides, as shown in Fig. 5. Whether these conductivities are intrinsic or defect-dominated is uncertain but clearly, the open-channel nature of... 

Ti) solid solution and simple transition metal nitrides are classified using the radius ratio of nonmetal to metal atoms and the number of valence electrons. The relationship of the generalized number of valence electrons instead of the average number of valence electrons per atom to the thermal stability of transition metal nitride has been discussed. 

The M-NM transition has been a topic of interest from the days of Sir Humphry Davy when sodium and potassium were discovered till then only high-density elements such as Au, Ag and Cu with lustre and other related properties were known to be metallic. A variety of materials exhibit a transition from the nonmetallic to the metallic state because of a change in crystal structure, composition, temperature or pressure. While the majority of elements in nature are metallic, some of the elements which are ordinarily nonmetals become metallic on application of pressure or on melting accordingly, silicon is metallic in the liquid state and nonmetallic in the solid state. Metals such as Cs and Hg become nonmetallic when expanded to low densities at high temperatures. Solutions of alkali metals in liquid ammonia become metallic when the concentration of the alkali metal is sufficiently high. Alkali metal tungsten bronzes... 

Edwards, Lusis, and Sienko have recently reported an ESR study (60) of frozen lithium-methylamine solutions which suggests the existence of a compound tetramethylaminelithium(O), Li(CH3NH2)4, bearing all the traits (60) of a highly expanded metal lying extremely close to the metal-nonmetal transition. Specifically, both the nuclear-spin and electron-spin relaxation characteristics of the compound, although nominally metallic, cannot be described in terms of the conventional theories of conduction ESR (6,15, 71) and NMR in pure metals (60, 96, 169). 

A, causing the decrease in density of the metal solutions compared to ammonia and the paramagnetism of the solutions. At intermediate concentrations (0.01 MPM to 2MPM), the electronic and magnetic properties are dominated by spinpaired species, for example, peanut-shaped bipolarons. These species account for about 90% of the excess electrons at 1 MPM. A metal-nonmetal transition takes place at around... 

Sources of transition metals Copper, silver, gold, platinum, and palladium are the only transition metals that are unreactive enough to be found in nature uncombined with other elements. All other transition metals are found in nature combined with nonmetals in minerals such as oxides and sulfides. Recall that minerals are mixed with other materials in ores. Metallurgy is the branch of applied science that studies and designs methods for extracting metals and their compounds from ores. The methods are divided into those that rely on high temperatures to extract the metal, those that use solutions, and those that rely on electricity. Electricity also is used to purify a metal extracted by high temperatures or solutions. 

Figures 3 and 4 show diagrams for the transition metals vanadium and chromium and for the nonmetal nitrogen, all in l.OM aqueous acid solution. The slopes of lines joining redox couples represent the potentials for the halfreactions in question, a positive slope representing a reduction potential and a negative slope an oxidation potential. An intermediate state above tie lines joining higher and lower states will be unstable to disproportionation [e.g., Cr(V) and NO2] while species below such tie lines are stable [e.g., Cr(III) and N2]. The diagrams are a convenient way to postulate the feasibility of various possible one-and two-electron pathways in multistep redox processes involving a particular element.

It is apparent from Figs. 2.3 and 2.4 that there is a close correlation between the behavior of the density and that of the conductivity. As we discuss in later chapters, the density variation is the single most influential factor governing the MNM transition in mercury and the alkali metals. In this important respect the MNM trcmsition in fluid metals is similar to the continuous MNM transitions observed in other systems where the density or concentration of a metallic component can be varied. These include heavily doped semiconductors, metal-ammonia solutions, metal-nonmetal aggregates like mercury-xenon, molten metal-salt solutions, etc. (see, e.g., Edwards and Rao, 1985). 

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