SELECTED PRINCIPLES: INTRODUCTION - METALLIC BONDING
An element (E) is defined as 'a pure substance which cannot be broken 
down into simpler substances by chemical means'. Of the 111 elements so 
far characterized, 81 are stable (H ... Mo, Ru ... Nd, and Sm ... Bi),
whereas 30 occur only as radioactive isotopes (Tc, Pm, and Po ... Uuu);
extensive compilations of various data for most elements are included 
in reference books (e.g., The Handbook of Physics and Chemistry).
This first Table shows selected data for 13 of the 81 stable elements,
including those for the best electrical conductor (silver).
 
   CE /
 MW cm-
    CT /
 W m- K-
 TM /
  K
 TB /
  K
   r
 g cm-
  DH1 /
 kJ mol-
  DH2 /
 kJ mol-
 Ag 
  68.0
    428
 1235
 2433
  10.5
    289
    731
 Cu
  64.5
    403
 1356
 2853
   8.9
    339
    745
 Au
  48.8
    319
 1337
 3080
  19.3
    369
    890
 Al
  40.0
    236
  933
 2623
   2.7
    314
    578
 Mg
  25.4
    157
  922
 1363
   1.7
    150
    938
 Na
  23.8
    142
  371
 1173
   0.97
    109
    496
 In
  12.5
     84
  430
 2323
   7.3
    244
    558
 Pt
  10.2
     72
 1995
 3993
  21.5
    565
    868
 Ga
   7.4
     41
  302
 2342
   5.9
    289
    579
 As
   3.8
     39
  886-subl.
   5.7
    290
    946
 Hg
   1.1
      8
  234
  630
  13.6
     61
   1007
 Mn
   0.7
      8
 1517
 2393
   7.4
    279
    717
 Te
   0.001
      - 
  723
 1263
   6.3
    199
    869
Electrical conductivity (CE); Thermal conductivity (CT); Melting point
(TM); Boiling point (TB); Density (r) at 293 K. Heat of sublimation
(DH1), defined as the energy required to separate a gaseous atom from
the solid element; i.e., E(s)  E(g). First ionization energy (DH2),
defined as the energy required to remove one electron from an isolated
gaseous atom; i.e., E(g)  E1+(g) + 1e-. Conductivity values refer
to data obtained at ambient temperatures (288 - 298 K).
These compilations show that no element has an electrical conductivity
between 0.001 MW cm- (Te) and 0.7 MW cm- (Mn), and so a metallic
element can be precisely defined as 'a pure substance which cannot be
broken down into simpler substances by chemical means, and which has an 
electrical conductivity greater than or equal to 0.7 MW cm- at ambient
temperatures'. This definition may appear unduly pedantic, but its use
results in 62 of the 81 stable elements being classified as metallic
and 19 as non-metallic (H, He, B, C, N, O, F, Ne, Si, P, S, Cl, Ar, Se, 
Br, Kr, Te, I, and Xe). Furthermore, this definition tacitly recognizes
the occurrence of elements whose conductivities are increased either by
photo- or thermal-excitation or by the presence of trace impurities
(e.g., 'semi-conductors' such as silicon), as well as those which show 
'superconductivity' at very low temperatures (e.g., hydrogen).
Three initial problems arise when attempting to introduce an overview of metallic elements. First, they do show typical properties, such as high electrical and thermal conductivities, high melting and boiling points, and high densities: but there are several anomalies which are difficult to explain; e.g., the melting points of caesium, gallium, mercury, potassium, rubidium, and sodium are all lower than several non-metallic elements. Second, there is a reasonably acceptable linear relationship between electrical and thermal conductivities (i.e., CE k CT + c): but, as is clearly apparent from inspection of those data in the above Table, there are no correlations between any other pair of physical quantities. And third, their typical properties are invariably attributed to metallic bonding: but simple descriptions of this phenomenon, which are not misleading, have proven elusive ...

The following description of a metal, or minor variants thereof, has
been commonly included in introductory texts: 'a metal consists of a 
lattice of positive ions embedded in a sea of electrons'. However, for
at least three reasons, this description must be firmly eschewed.
First, the term 'lattice' refers strictly to the solid state: but, as
evinced by conductivity data (see, for examples, those shown in this
second Table), metallic bonding clearly persists in the liquid state.
 
 Hg
 Cs
 Ga
 Rb
   K
  Na
Conductivity at 293 K / MW cm-
 1.0
 5.0
 7.5
 8.0
 16.5 
 24.0 
Melting point / K
 234
 301
 303
 312
  336
  371
Conductivity at 373 K / MW cm-
 1.0
 2.0
 3.5
 3.5
  5.5
 10.5
Second, researchers do not invoke 'ionization' in their descriptions of
metals; the experimental data, together with theoretical calculations,
support a bonding model which is fundamentally covalent in character. *
And third, 'a sea of electrons' is a peculiarly mixed metaphor; thus,
conduction in aqueous solutions occurs via free-moving ions, whereas
conduction in metals occurs via free-moving delocalized electrons. #
Quite reasonably, one would expect, as a minimum, a description of the bonding in metallic elements to provide at least partial explanations for two observations: first, the 100-fold difference in electrical conductivity between silver and manganese; and second, the 700-fold difference in electrical conductivity between manganese and tellurium. Unfortunately, however, such expectations probably cannot be realized from a simple qualitative description of metallic bonding. Furthermore, there may not be such a description which is illuminating without being misleading: so the following attempt may only score marks 'for effort'.
'A metal consists of a giant covalent structure, in which each atom has contributed one or more of its valence electrons to the formation of omnidirectional, delocalized covalent bonds that extend throughout the structure.'
Strictly speaking, this description of a metal does not 'explain' its characteristic properties: but advanced theories of metallic bonding indicate that it is concordant. In particular, it is consistent with two platitudes: 'a metal is a good conductor of electricity because of the presence of free-moving delocalized electrons', and 'a non-metal is a poor conductor of electricity because of the absence of free-moving delocalized electrons'.
* See, for example, R. Hoffmann, Solids and Surfaces, VCH Publishers, New York, 1988 (and references cited therein). # An extended critique of this description would be inappropriate here and, indeed, unnecessary because a beautifully balanced summary of both historical and contemporary bonding theories in metals has been written by J. D. Lee [Concise Inorganic Chemistry (pp. 114 - 118), Harper Row, London, 1991]. However, the student is invited to consider constructing and testing various hypotheses, using the electrical conductivity, heat of sublimation, and first ionization data shown in the first Table. The following notes should provide a slightly deeper perspective ... Each sodium atom has one electron in its outermost atomic energy level: so 1 mole of sodium metal contains 6.022 10 valence electrons which contribute to the formation of covalent bonds. A covalent bond contains two electrons which occupy the same molecular energy level: so 1 mole of electrons contains half this number of covalent bonds. In principle, each of these (very closely spaced) levels encompasses the 6.022 10 nuclei: so there are 3.011 10 omnidirectional, delocalized covalent bonds extending throughout 1 mole of sodium metal.
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