A New Classification of Metallic Solids


In the scientific literature electrically-conducting solids are usually described as either "metallic" (having an inverse conductivitytemperature relationship) or as "semiconducting" (having a direct conductivitytemperature relationship) . For almost two decades I've been studying metallic solids in a chemistry context , examining the crystal and electronic structures of a wide range of electrically-conducting materials . My original objective was to try to understand the nature of superconductors in chemical , rather than physical terms . By definition , all superconductors are metallic solids (although the converse obviously isn't true) . By understanding the nature of the metallic bond in a wide variety of superconductors , I hoped to understand the functioning of this unique class of materials , and thereby be able to predict and design new superconductors .

In my survey of metallic solids I discovered that they spanned all of the many varieties of chemical compounds (including the elementary metals , of course) . Both inorganic and organic compounds could contain metallic bonds ; they could be found in crystals with covalent and ionic bonds , and in molecular and nonmolecular (extended atomic / infinite lattice) solids . Metallic solids in general , and the metallic bond in them , proved to be endlessly fascinating subjects to study . In fact , I wrote an "ebook", Exploring the Chemistry of Metallic Solids , including Superconductors , 417 pp. , which is available for free as a PDF document download (6.00 MB) from this website .

In my survey of metallic solids I found it useful to classify them in a more detailed manner than in the usual rather broadly-stated categories of "metallic" or "semiconducting" materials . I renamed the former group the True Metals , with four subtypes , and the latter class the Pseudometals , also with four corresponding subclasses : eight classes in all . In the following essay I'll discuss these classes of metallic solids , with numerous examples to illustrate the diversity of the classes and of metallic solids in general .


The Eight Classes of Metallic Solids


Let's proceed with the classification ; then I'll discuss the background theory as we go along , using individual case studies to examine the various types of metallic solids . The eight classes are listed in the following Table :

In the Valency column , "homovalent" means that the metal atoms in the compound all have the same formal charge ; this would also include zerovalent solids , such as the elementary metals – obviously – but also the occasional zerovalent compound , such as CuTi2S4 [Cu0 Ti4+ Ti4+ (S2-)4 ] . In mixed-valent compounds the metal atom components are formally in two different valence states . I say "formally", because in practice the two valences are usually blended perfectly together to form a third averaged valence , often a non-integral number . For example , in the famous high temperature superconductor YBCO (YBa2Cu3O7) , the two formal copper cation valences are 2+ and 3+ : (Y3+ Ba2+ Ba2+)(Cu2+ Cu3+ Cu2+) O714 - ; ultrafast resonance of the copper(II) 3d9 valence electrons in the crystal structure results in a non-integral valence in the copper cations of (7+)/3 = Cu(2.33+) .

My new general classification of metallic solids was inspired partly by the Robin-Day classes of mixed-valent compounds : I , II , IIIA , and IIIB , of which the II and IIIB types are of interest here , as they include the electrically-conductive varieties . Classes I and IIIA are essentially all insulators . (The references are listed at the end of this web page . Underlined blue hyperlinks can be clicked when online to download the PDF or HTML file , which will open in a new window) . In Robin-Day Class II mixed-valent compounds , the electronically-active cations are separated by anions ; in Class IIIB the cations have direct metal-metal bonds , with the anions "off to the side". These two different arrangements of the cations in the crystal result in dramatically different electronic structures and physical and chemical properties of Classes II and IIIB compounds . The former are often intensely coloured (dark blue or black) semiconductors or poor conductors ; the latter are commonly referred to as synthetic metals (two of which are discussed below) , having metallic colours (coppery , bronze , silvery , golden) , a noticeable metallic luster (a high light reflectivity) , and high conductivities . Nevertheless , all of the high transition temperature superconductors (the cuprates) are Class II materials , while none of the Class IIIB synthetic metals are ; some have Tc values close to Absolute Zero , while others are pseudometals and never become superconducting .

An explanation of the properties in the Metallic Bond column of the Table requires a little background discussion of how the valence shell orbitals of the metal cations and nonmetal anions can combine in the crystal lattice to form the metallic bond in it .


Atomic , Molecular , and Crystal Orbitals


The overlapping of valence shell atomic orbitals (AOs) between the atoms in a solid , together with their associated electrons , forms the chemical bonds between those atoms . The four different types of AOs (s , sharp ; p , principal ; d , diffuse ; and f , fine) can overlap with each other and with the other types in many ways , to provide a wide array of chemical bonds . Orbitals can be considered in two ways : first , as a "picture" of where a particular electron is located near its atomic kernel ; it's a sort of measurement of the electron probability density . Second , an orbital can be thought of as a standing electron wave around the kernel , with the different orbitals having different shapes and sizes . As with water waves , electron waves can interact together to produce a wide variety of composite wave patterns .

The AOs , as wave patterns , also have a symmetry property ; they have a region , or regions of positive and/or negative symmetry . The overlapping of positive + positive or negative + negative symmetry regions will produce an energetically stabilizing bond ; if a positive and negative symmetry region (lobe) overlap , an energetically-destabilizing antibond will be formed .

Another important feature of AO overlap , not generally discussed in chemistry textbooks , is their orbital topography . When AOs overlap to produce a molecular orbital (MO) , a small volume of interatomic space around the kernel may contain essentially no electron density . Such electron-empty spaces are called nodal surfaces or planes , or simply nodes . An example of nodes in covalent bond MOs is provided by the methane molecule , CH4 :

There are four nodes between the carbon atom kernel and the electron density in the sigma MOs , which form the C–H covalent bonds . This is contrasted to the nodeless sigma MO covalent bond in the hydrogen molecule . The concept of nodal and nodeless MOs can be applied to the chemical bonds in extended atomic solids , where it will affect the electrical behaviour of metallic materials .

In certain crystalline solids with an infinite atomic lattice , the individual MOs between the atoms can blend together and "polymerize" into a crystal-wide orbital , which I have called a crystal orbital (XO) . Metallic bonds (physics : conduction band) are XOs . Pauling described metallic bonds as resonating valence bonds , but I think the molecular orbital description of them is undoubtedly the most accurate one . A metallic bond can occur in a solid when one or more "extra" valence electrons remain after the formation of the strong covalent bonds in it ; in some cases , there are extra valence electrons above a very stable Inert Gas kernel (as with the Alkali and Alkaline Earth elementary metals) . The extra electron enters an energetically-favourable frontier orbital above the covalent skeleton or crystal framework , or Inert Gas kernel . If the frontier orbitals , together with their extra electrons , can overlap and polymerize successfully into a crystal orbital , then the material can become an electrically-conducting metallic solid ; and in some cases , it might even become superconducting at a lower temperature .

The metallic bond has been described as a partial covalent bond , but I think this is an erroneous picture . These two types of chemical bonds are actually very different , as the following example shows . Consider the two materials gold and diamond (1) , which have been the mainstays of jewellery for millennia . The atomic weight of gold is 196.967 g/mol ; that of carbon is 12.011 g/mol . In a mole (as a nugget , ingot , or other object) of gold weighing 196.967 g there is only one single metallic bond , but there are an Avogadro Number (NA = 6.022142 x 1023 ) of energy levels for the corresponding number of its 6s1 "extra" valence electrons in that bond . In a pure diamond weighing 12.011 g there are 2NA sp3 sigma covalent bonds between the carbon atoms , but they are all at essentially the same energy level . Metallic and covalent bonds are therefore the converse of each other : very different , indeed !

So a metallic bond is really a single crystal-wide XO formed by a continuous overlapping of the frontier orbitals with their "extra", unused valence shell electrons . Since the Pauli Exclusion Principle restricts the population of any one orbital to only two electrons (and those two must have opposite spins) , the XO has a vast number of energy levels corresponding to one level for each electron in it . A mole of atoms in a sample of a univalent metal will have a mole of extra electrons in the XO and a mole , i.e. NA , of energy levels . The extra electrons are mostly paired off in these energy levels ; typically 99% are paired off in energy space , even though they may be widely separated in physical space in the crystal lattice . The remaining 1% of electrons are singlets at higher energy levels . The energy level dividing the paired (lower) from the singlet (upper) electrons is the Fermi level , EF . The singlet electrons above EF are responsible for the physical properties so typical of metals : their high electrical and thermal conductivities , metallic luster (reflectivity) and colours , opacity , and Pauli paramagnetism . The metallic bond is one of the weaker of the five types of chemical bonds ; it is really only a feeble , flashy sort of "afterthought", added on over the really strong "workhorse" covalent bonds . The frontier orbitals forming the XO are energetically and physically higher than the atomic kernels and covalent bonds . I like to compare the metallic and covalent bonds to the human body : the covalent bonds are like the strong , hard skeleton , while the metallic bonds are like the softer flesh covering the bones , and the free electrons above EF are like the blood circulating in the flesh .

The above analogy is applicable to the true metals , with their nodeless XOs . However , a different situation would apply to the pseudometals , which include the semiconductors . In these cases , the metallic bonds are in the skeletons themselves , and not in the "flesh" (in the analogy , there wouldn't be any flesh with the pseudometals) . The "joints" in between the "bones" of the skeleton would be the MO nodes . Referring to the sketch of of the methane molecule above , suppose we change the carbon atom to silicon , and after removing the hydrogen atoms , polymerize the silicons into a mass of pure silicon crystal :

A small (30 x 15 x 13 mm) piece of industrial grade silicon , "photographed" in my scanner . Silicon has the diamond crystal structure , with tetrahedral sp3 covalent bonds .

As in methane , there would be four nodes around each silicon atom . Perfectly pure silicon would be essentially nonmetallic , since there are no "extra" valence electrons available under ordinary circumstances . If silicon is doped with electron-rich donors (n-type) or electron-deficient elements (p-type) , it will become semiconducting , either by the added extra electrons , or by the one-electron Si–Si bonds (which can resonate in the lattice as empty vacancies , conventionally called "positive holes") produced in it by the p-type dopants .

Unlike the nodeless true metals , in the nodal pseudometals the free electrons in the XO are obliged to "jump across" (tunnel through) the nodes as they are pulled downfield by the electrical potential difference (p.d.) . Tunneling requires a small but finite energy input to the mobile free electrons above EF . This energy must come from the environment , usually thermally , but sometimes from light (generally , electromagnetic) , supplied naturally or artificially . As more and more external energy is supplied to the pseudometal , more and more of its mobile free electrons gain enough kinetic energy to tunnel through the periodic nodes in the XO , and its electrical conductivity gradually rises . Thus , pseudometals always have a direct temperature–electrical conductivity relationship . This is nicely illustrated by the graph of the electrical conductivity of gray tin , which has the diamond type of crystal structure , like that of silicon :

The situation is different for the true metals . Because their XOs are nodeless , their mobile free electrons don't need any thermal energy to move downfield through the crystal lattice under the applied p.d. . Electrical conductivity in true metals is controlled by the electron–kernel interactions . As the solid warms up , its component atoms vibrate more and more , and the mobile free electrons in the XO bounce off them (scatter) more and more . Their progress through the lattice is slowed down as its temperature increases , and conversely , the electrons move more readily , with less scattering off the kernels , as the crystal is cooled . So for true metals we always observe an inverse electrical conductivity–temperature relationship , as is clearly shown in the following graph of the electrical conductivity of gold :

Using data from the CRC Handbook of Chemistry and Physics I plotted similar graphs for other elementary metals , and they all have the same sort of rounded curve , asymtotic at the ends like that of gold . Twenty-nine of the elementary metals become superconducting at very low temperatures , close to Absolute Zero ; the three coinage metals – copper , silver , and gold – while having extremely high electrical conductivities in the liquid helium range , never become superconducting .

All the elementary metals have at least one or two valence shell electrons in an s AO , and may also have additional valence electrons in p AOs . Palladium is an exception ; its formal valence shell configuration is 4d10 5s0 , although undoubtedly there is some leakage of the 4d electrons into the 5s-p AOs . This same sort of leakage occurs in other metals with ns2 electronic configurations , such as in magnesium , zinc , mercury , etc. ; the resulting vacancies in the sigma XO permit the extra electrons to become mobile in it . The s AOs are large , spherical , and omnidirectional , and can overlap throughout the crystal lattice to form a nodeless XO , a "polymerized MO" :

Thus , all of the elementary metals are true metals . Nodeless MOs , and by extension , XOs , can also be formed by p AOs and d AOs :

The sigma XOs are nodeless in three dimensions ; the pi XOs can be nodeless in two dimensions (for example , in the sheets of carbon atoms in graphite , or in the sheets of boron atoms in MgB2 ) ; and the delta XOs could be nodeless along only one major crystal axis . In practice I don't know of any examples of metallic solids with delta XOs , although they could conceivably be found in Transition metals such as iron , which have many d-orbital valence electrons . A delta MO is thought to be one of the metal-metal quadruple bonds in the dimeric compound molybdenum(II) diacetate , formed from the face-to-face overlap of its 4dxy AOs with their valence electrons [Mo2+ is 4d4] . The other three d-d sigma bonds in the compound are nodal MOs formed by the end-to-end overlapping of the 4d xz , yz , and z2 AOs (the 4dx2-y2 AOs are used in coordinate covalent bonding of the Mo with the acetate ligands) .

In my study of metallic solids , as discussed in the ebook mentioned near the top of this web page , I introduced what I thought was a useful guiding principle , Krebs's Theorem , in the understanding of these materials . I named this rule after the German solid-state chemist , Heinz Krebs (University of Stuttgart) , who studied the chemistry of superconductors some forty or so years ago . In one of his reviews of the crystal chemistry of superconductors , he observed ,

“The rule that superconductivity is only possible if there exists at least one space direction not intersected by plane or conical nodal surfaces can only be verified for a limited number of superconductors . On the other hand , in no case does anything point against the validity of this rule . In those cases in which the condition of the rule is fulfilled , superconductivity is found with very few exceptions . We can thus assume that the principle condition for the occurrence of superconductivity is in fact the absence of these nodal surfaces”.

I believe that Professor Krebs was the first person to study the electronic structure of superconductors in orbital terms , and to try to correlate the orbital location of the free , mobile electrons in metallic solids with the presence or absence of superconductivity in them .

However , he was wrong . The recent discovery of superconductivity in several classic semiconductors (PDF , 293 KB) such as diamond (2) (heavily doped with boron) , silicon (PDF , 507 KB) , and silicon carbide (PDF , 1480 KB) , conclusively disproved the theorem he stated four decades ago . We have two options : first , retain Krebs's Theorem for superconductors , but try to devise a new orbital configuration for these semiconductors in which their XOs are nodeless in the superconducting state ; or second , we must accept the fact that Cooper pairs can tunnel through nodes in an energy-free manner (i.e. they require no environmental energy for tunneling) . The latter picture is the more reasonable one , since we know that Cooper pairs in the superconducting state can indeed tunnel through very thin insulating layers in an energy-free manner ; this is the basis of the Josephson effect and the Josephson junction .

Although Kreb's original theorem no longer applies to superconductors , it is still valid – in my opinion – for "ordinary electrical conduction", that is , for singlet electrons above EF in the XO . Extended to metallic solids in general , it could be re-phrased something like this :

“True metals have a metallic bond consisting of a nodeless crystal orbital along at least one crystal axis , while in pseudometals the metallic bond consists of a crystal orbital that is periodically intersected by nodes”.

Note that true metals may also have , simultaneously , other conduction pathways that utilize nodal crystal orbitals , but the XO that makes them a true metal will always be nodeless . Pseudometals , by comparison , have no nodeless XOs at all .


Monolayer and Bilayer Metallic Bonds


In an elementary metal the atoms are identical , and the metallic bond XO in it should be homogeneous throughout the lattice . In chemical compounds with a metallic bond , one of the atomic components will supply the "extra" valence electrons , while the other atomic components will often be inert links between the "active" atoms (which are usually derived from the elementary metals) . In some cases , though , the "inactive" atoms , while not supplying extra valence electrons to the XO , may participate in the metallic bond indirectly , by providing some of their unused lone pairs to it . For example , in a metal oxide the metal atoms provide the extra valence electrons and the oxygen atoms linking them furnish one or more of their 2s and/or 2px,y,z AOs with their lone pairs to the XO as well . The requirement here is that the metal atoms must locate their extra electrons in their outermost s and/or p frontier orbitals . The metal atom and oxygen atom s and p AOs must also have the correct size , shape , symmetry , and orientation to overlap continuously in the lattice , forming a s (sigma) or p (pi) XO , respectively , and sometimes both .

I discussed the excellent example of rhenium trioxide , ReO3 , in another web page to which I'll refer the interested reader , as a metallic solid with a bilayer XO . Because of the great disparity in the energy levels of the metal atoms (Re extra electrons are located in the 6py,z frontier AOs) and oxygen linking atoms (lone pairs are in the 2py,z AOs) , the oxygen lone pair electrons don't "blend in" with the rhenium extra electrons . Instead , the oxygen electron pairs form a lower layer in the Re–O XO , while the rhenium electrons are in its upper layer . Since by definition the Fermi level EF separates the energy levels with the spin-paired electrons from the higher energy levels with the unpaired singlet electrons , ALL of the rhenium extra electrons will be located above EF in ReO3 . In rhenium metal with its monolayer metallic bond , the extra electrons are subjected to the Fermi-Dirac distribution , with the result that most of them are spin-paired below EF , and relatively few of them are the active singlet electrons above EF . The result is that there are many times the number of charge-carrying electrons in ReO3 compared to rhenium metal [the valence electrons in rhenium(0) are 5d5 6s2 , so there are probably two or more extra electrons provided to the XO per Re atom] . As strange as it seems at first glance , the oxide compound ReO3 actually has a higher electrical conductivity (149,300 ohm-1cm1 , ambient) than its parent element Re (58,140 ohm-1cm1 , 273 K) , which we can now understand in terms of the very different metallic bonds in the two materials .

Rhenium trioxide , which has an inverse(1) temperature-electrical conductivity relationship , is a true metal ; it is homovalent ; and it has a nodeless 2p-6p , bilayer pi XO . It is assigned to Class 1 (Table near the top of this web page) .

The tungsten bronzes are somewhat similar to ReO3 . The parent compound WO3 has the same sort of "supercubic" crystal structure as ReO3 , but it's distorted from the latter's cubic symmetry . Tungsten is the element (no. 74) before rhenium (no. 75) in the Periodic Table , and its valence shell electrons are 5d4 6s2 , with one less electron than in Re ; that is , WO3 has the same electronic structure as ReO3 , but lacks the seventh "odd" valence electron that makes ReO3 a metallic solid . As a result , WO3 (yellow , m.p. 1473 ºC) is effectively an electrical insulator . However , a wide assortment of elementary metal atoms can be inserted into the central cavities of the "supercubes" in tungsten trioxide , thus producing the tungsten bronzes , which have the perovskite structure :

In the above sketch , the small red spheres represent the tungsten atoms (M) ; the blue spheres are the oxygen linking atoms (X) ; and the green spheres stand for the inserted metal atoms (A) such as the Alkali metals . Two ways are shown of portraying the perovskite AMX3 crystal structure , the A-type (more common) and the B-type . The octahedral coordination of the tungstens by the oxygens is clearly shown in the B-type structure . There are no covalent bonds (black lines) between the A cations (green) in the B-type unit cell ; they are included only to outline the cubic unit cell .

The insertion of reactive elementary atoms such as those of the Alkali metals into the WO3 cavities adds electrons to the compound . But rather than chemically reducing it , the added electrons enter the tungstens' empty 6p frontier orbitals , in effect becoming their extra valence electrons . A crystal-wide 2p-6p bilayer pi XO is created , as in ReO3 , with the participation of the oxygen linking atoms . The resulting tungsten bronzes are metallic solids with bright colours and a noticeable metallic luster (hence their "bronze" name) . They have an inverse (2) temperature–electrical conductivity relationship ; a few bronzes become superconducting near Absolute Zero . In the cubic NaxWO3 series those sodium tungsten bronzes with x>0.8 can have conductivities of up to 70,000 ohm-1cm-1 ; by comparison the ambient (293 K) electrical conductivity of tungsten metal is 189,394 ohm-1cm-1 . The tungsten bronzes are true metals with a nodeless bilayer XO , but they are mixed-valent , formally having W(V,VI) atoms . They are assigned to Class 3 in the Table near the top of this web page .

The high temperature superconductor YBCO (idealized empirical formula , YBa2Cu3O7) can also be placed in Class 3 , even though chemically it's very different from the tungsten bronzes . YBCO has a layered structure , consisting of alternating layers of copper oxide with the inert yttrium and barium spectator cations nesting betweeen them . The yttrium cations are somewhat small for the lattice , which folds around them , forming periodic "kinks" in the surrounding Cu–O layers . The copper cations have two coordinations by the linking oxide anions : four , in the planar CuO2 structures commonly called "diamonds"; and five , in the CuO3 groups called "pyramids" :

In the above sketch , the small red spheres represent Cu2+ / Cu3+ and the green spheres are oxide anions . The large violet spheres stand for Ba2+ , and the smaller yellow sphere is Y3+ . My M3D model is based on the nice sketch of YBCO by Ourmazd and Spence .

The Valence Bond theory was first developed around 1930 to describe the covalent bonds in small organic molecules , which it did so quite successfully before eventually being replaced by the more advanced and computational Molecular Orbital theory (with assistance from VSEPR theory for the shapes of molecules) . Lacking any sort of mathematical sophistication , at least at the level required by MOT , I have retained VBT and have extended it for use in describing the covalent bond framework that may exist in extended atomic structures of interest . Using VBT , we can readily predict that the metallic bond XO in YBCO will be in the copper 4pz and 5px,y,z AOs , as the upper layer , and in the oxides' 2py,z AOs as the lower layer :

The resulting nodeless , bilayer Cu–O pi XO permits YBCO to act as a true metal ; it becomes superconducting below 93 K , and above that temperature it has an inverse temperature–electrical conductivity relationship , with an ambient conductivity of about 500 ohm-1cm-1 :

The above graph was prepared using data from the influential paper by M.K. Wu et al. , describing YBCO's preparation and properties . The researchers presented their results in sample-specific conductance terms , rather than in the universal conductivity units , but the principle is the same . Note that below about 90 K the sample became superconducting ; this part of the curve deviated from linearity and was omitted in my graph .

The bilayer metallic bond in YBCO and its cuprate superconductor relatives is primarily responsible for its exceptionally high transition temperature in the liquid nitrogen range of temperatures . All the Cu2+ 3d9 valence electrons are located in the upper layer of the XO , above the Fermi level EF . Thus , neighbouring 3d9 electrons become the mobile , free electrons in the XO (they are now in the coppers' 4pz and 5px,y,z frontier orbitals) . The parent copper(II) oxide compounds such as CuO and La2CuO4 are strongly antiferromagnetic . When they are doped in an oxidative procedure , a Robin-Day Class II mixed-valent Cu2+ / Cu3+ composite is formed , which creates vacancies ("holes") in the 4pz and 5px,y,z frontier orbitals , permitting an ultrafast resonance of the mobile free electrons over the oxide links and between the Cu3+ base cations , which are spin-paired and diamagnetic . The antiferromagnetic ordering régime is also imposed on the mobile , free electrons above EF , giving an alternating spin orientation to each of the neighbouring free electrons . As outlined in another web page , if electrons can approach each other closely enough , and if they have antiparallel spin orientations , they can magnetically couple together like two macroscopic magnets of our everyday experience . This can occur because the magnetic attractive force between two antiparallel electrons is roughly 1200 times as strong as the simultaneous electric repulsive force existing between them . The absolute net attractive force between the neighbouring pairs of mobile , free , antiparallel electrons in the XO of YBCO is apparently great enough to permit the formation of Cooper pairs at unusually high temperatures . A convergence of three crucial conditions is required for the realization of high temperature superconductivity in a compound :

– a bilayer metallic bond (XO) in it , so ALL of the extra valence electrons entering the frontier orbitals will be located above EF . We will then have a rich population of mobile , free electrons , with the singlet electrons on neighbouring metal-atoms ;

– an antiferromagnetic parent compound to the metallic solid , so that an antiferromagnetic ordering régime will also be imposed on the mobile , free electrons above EF in the metallic derivative , giving them an alternating antiparallel spin orientation ; and ,

– a Robin-Day Class II mixed-valent compound , which makes the antiferromagnetic parent compound metallic , permitting the extra valence electrons to resonate in the lattice . This really narrows down the field of metallic solids as high Tc superconductor candidates to those materials in Class 3 , in the Table near the top of this web page .

Niobium monoxide has a bilayer XO , but it's homovalent and isn't antiferromagnetic . NbO is a true metal , having an ambient electrical conductivity of about 50,000 ohm-1cm-1 (that of its parent element , niobium metal , is 65,789 ohm-1cm-1 at 273 K) , and its superconducting Tc is 1.38 K (niobium's is 9.3 K) . NbO is black as a powder , but it has a silvery , metallic sheen as a fused button . It exhibits Pauli paramagnetism over a wide temperature range , typical of true metals , but not Curie paramagnetism (which rules out discrete Nb2+ cations in the lattice) . For a long time NbO was thought to have an ionic rocksalt crystal structure with periodic atomic vacancies , but a computational study of it in 1993 by Schulz and Wentzcovitch concluded that , “[NbO] is stabilized through strong M–M bonds” (p. 16,990) . These authors proposed that the Nb–Nb covalent bonds were formed by a combination of p and d orbitals . A simple , non-mathematical Valence Bond analysis of NbO can rationalize its crystal structure as consisting of an infinite atomic lattice of niobium octahedron "metal cages", around which oxide anions are nested :

In the above M3D molecular model , the small red spheres represent the niobium atoms , while the larger green spheres are the oxide anions . The black lines are Nb–Nb covalent bonds , but there are no Nb–O covalent bonds ; black lines are shown between the red and green spheres only for clarity , because without them the perspective is lost and the structure becomes confusing and difficult to follow (for me , anyway) .

The following sketch outlines the Valence Bond description of the Nb–Nb covalent bonds in NbO , with the resultant prediction of the location and nature of its XO metallic bond :

Each niobium atom has eight covalent bonds to neighbouring Nb atoms , requiring sixteen electrons for completion . To form the required square prism hybrid AO Nb uses all of its normal 4d and 5s valence shell orbitals plus two lower energy 4p AOs with their four hypervalent electrons . Niobium(0) has five electrons plus four hypervalent electrons from the 4p AOs , but has donated two of them to an oxygen atom to become Nb(II) , for a total of seven electrons . Another hypervalent electron is taken from the third (unhybridized) 4p AO , and the eight Nb–Nb covalent bonds are completed , forming the octahedron metal cage framework . That leaves the 4s2 4p1 AOs as the outermost orbitals – in effect , the frontier orbitals – of the niobiums . They are both at approximately the same energy level , and there is electron leakage – and exchange – from the 4s to the 4p AOs . The 4s and 4pz AOs (which are perpendicular to the NbO4 plane) can overlap continuously with the oxide anions' corresponding 2s2 and 2p2z native (unhybridized) AOs to form the Nb-O sigma-pi XO , which is predicted to be its bilayer metallic bond . NbO is a homovalent true metal with a bilayer , nodeless XO ; it is assigned to Class 1 in the Table above .

I referred to the simple compound iron monophosphide , FeP , in the Iron web page . It's a true metal (ambient electrical conductivity of 12,500 ohm-1cm-1 rising to around 3.3 million ohm-1cm-1 at 4.2 K) , exhibiting Pauli paramagnetism - typical of true metals - and is also antiferromagnetic (TN = 123 K) . FeP has the nickel arsenide crystal structure :

In the above M3D model of FeP , the iron atoms are represented by the smaller blue spheres , and the phosphorus atoms by the larger brown spheres .

The iron atoms (blue) are octahedrally coordinated by the phosphorus atoms (brown) , which in turn have a trigonal prismatic coordination by the iron atoms :

The trigonal antiprismatic coordination is somewhat like the octahedral coordination , although the bond angles are a little different .

Iron monophosphide has covalent Fe-P bonds , with the added metallic bond over the layers of hexagonally-packed iron atoms . There are six Fe-P bonds per formula unit , requiring twelve valence electrons for completion . Iron(0) [3d6 4s2] can supply eight electrons ; phosphorus(0) [3s2 4p3] can provide five . Of these thirteen valence electrons , twelve form the six Fe-P bonds , while the thirteenth "odd" electron is located in an iron frontier orbital :

Iron , as a Transition metal element , strongly favours its d AOs in the formation of hybrid AOs . The d5s octahedral hybrid AO is common in many Transition metal compounds (for example , in ReO3 above and in CrO2 below) . Phosphorus , a post-Transition metal element in the p-block of the Periodic Table , tries to use as many of its p AOs as possible along with s AOs , which are a sort of "universal orbital" involved in a wide array of hybrid orbitals . The p-block elements are well-known for avoiding the use of d AOs in the formation of hybrid AOs . The prediction from Valence Bond Theory , then , is that the metallic bond in FeP will be the 4p pi XO over the layers of iron atoms in the lattice . FeP has a monolayer XO with homovalent iron and a direct Fe-Fe metallic bond ; it is therefore assigned to Class 2 in the Table above .

Chromium dioxide [chromium (IV) oxide , CrO2] is another Transition metal oxide that can be classified as a true metal . It's a brownish-black or dark gray powder which has been used for several decades as the recording medium in magnetic ribbon for tape recorders and compact cassettes , considered superior to its competitor iron(III) oxide . Chromium dioxide has been widely described as a half-metallic ferromagnet (review , PDF , 2947 KB) . Its electrical conductivity at room temperature is about 2500 ohm-1cm-1, and rises steadily as the material is cooled toward absolute zero :

The above graph looks a lot like that of gold , shown near the top of this web page , with that familiar curve and the asymtotic ends . It was drawn using data from Chamberland's review (his Figure 9 , p. 13 ) of the physical and chemical properties of CrO2 .

Chromium dioxide displays a Curie paramagnetism which is three-dimensionally ordered into a ferromagnetic state (although it's not a strong ferromagnetism like that of iron , cobalt , and nickel , for example) with a Curie temperature (TC ) around 393 K (or 391 K) . Chromium dioxide has an ambient magnetic susceptibility of 2.0 BM (Bohr magnetons) , a value typical of many Transition metal salts and compounds . Using the simple formula for calculating spin only magnetic moments ,

m = [n (n+2)] ½  ,

where m is the magnetic susceptibility in Bohr magnetons , and n is the number of unpaired valence electrons in the Transition metal atoms in the solid , if n = 1 , then m = 1.73 BM , while if n = 2 , then m = 2.83 BM . The value for chromium dioxide is closer to n = 1 than 2 , so there seems to be only one extra , unpaired chromium valence electron generating the Curie paramagnetism . The simple magnetic susceptibility formula above is reasonably accurate for magnetically dilute compounds , that is , those in which there is no significant interaction between the unpaired singlet electrons . Possibly the ferromagnetic ordering in CrO2 boosts its Curie paramagnetism from the theoretical n = 1 , m = 1.73 BM , to the observed m = 2.0 BM .

Chromium dioxide has the MX2 rutile crystal structure , in which the metal atom M is octahedrally coordinated by the nonmetal atoms , X ; they have a trigonal planar coordination by the M atoms :

Blue spheres : octahedral Cr(IV) [in rutile , TiO2 , Ti(IV)] ; green spheres , trigonal planar oxygen linking atoms in both CrO2 and in TiO2 . This M3D model is based on the illustration of the rutile structure in Wold and Dwight's textbook .

Valence Bond theory can be applied to the analysis of chromium dioxide , providing a simple , qualitative picture of its electronic structure :

In CrO2 there are six covalent (not ionic) Cr-O bonds per formula unit , requiring twelve valence electrons for completion . Chromium(0) , which is 3d5 4s1 , can provide six . Each covalent trigonal oxygen linking atom - not an oxide anion - which is 2s2 2p4 , can provide four (with two left over in the unhybridized 2pz orbital) , or eight for the two formula unit oxygens . Of those fourteen available valence shell electrons , twelve complete the Cr-O covalent bonds , leaving two extra , unused electrons on the chromium atoms . Chromium's 3d and 4s AOs are "taken" for the d5s hybrid AO , leaving its 4p AOs as the lowest energy available frontier orbitals . Only the 4pz AOs have the correct orientation to overlap with the oxygen links' 2pz AOs . These combine throughout the lattice to form the 2pz- 4pz pi XO , which is predicted to be the bilayer metallic bond in CrO2 . The second extra , unused valence electrons are located in the isolated 4px,y AOs , where they are localized (pinned) , and provide the magnetic spins resulting in the Curie paramagnetism and ferromagnetism in the material .

The question arises : why don't both extra Cr valence electrons go into the "magnetic" 4px,y AOs , or both into the "metallic" 4pz AOs ? The answer is that singlet electrons tend to have the same spin orientations in the native valence shell orbitals (Hund's Rule) , so they will "spread themselves out" as singlets with the same spin to the maximum extent in them . This is certainly the case in the d shell AOs , and it's probably true for the p shell electrons also . Several explanations have been proposed as the basis of Hund's Rule , eg. a decrease in electron-nucleus attractions , or a reduction of inter-electron repulsion energy . I pointed out in the Iron web page that antiparallel spin electrons can magnetically couple together into pairs , because the attractive magnetic coupling force between them is about 1200 times as strong as the repulsive electrical force separating them . Conversely , two electrons with parallel spin orientations should strongly repel each other , as the magnetic force now becomes strongly repulsive . Electrons fill up the available AOs according to the Aufbau Principle ; they will enter the orbitals as singlets with a parallel spin orientation . Adding additional valence electrons to the singlets to create pairs requires energy , which must be provided by an external influence . Lacking such a "pairing energy", the valence electrons remain singlets , spread out to the maximum extent in their orbitals , whether d or p AOs .

If some external influence "squashed" the two Cr extra electrons together into a spin pair , forcing them to magnetically couple , the resulting material would have quite different physical properties than CrO2 . If the electron pair was located into the "magnetic" 4px,y AOs , they would in effect act as an "inert pair", and the compound wouldn't be magnetic (or metallic) any more . If the pair was located in the "metallic" 4pz AOs , the compound might be a superconductor , especially if the pair was in a bilayer metallic bond , and located above the Fermi level , EF . Also as discussed in the Iron web page , chalcogenide (and probably also pnictide) anions are natural reducing agents , and are able to donate an electron pair to neighbouring metal cations . This likely isn't a "clean" donation - more of a "resonating" exchange - but it would act to "squash down" the two extra electrons into a spin pair . So possibly if reducing chalcogenide anions were combined with Cr(IV) - which is a very strong oxidizer in any case - we might see one or other of these effects taking place . The compounds CrX2 (X = S , Se , and Te) would be very interesting to examine in this regard (assuming they can be synthesized in pure form and with the rutile crystal structure , of course) .


Two Synthetic Metals : KCP and Poly(sulfur nitride)


Chemical compounds , both inorganic and organic , generally have only covalent or ionic bonds , which are the "workhorse" bonding forces in most solids . I'm writing this web page in mid-Winter , so as I look out the window I see a lot of hydrogen bonding in the snow and ice outside , too ; and there is another weak bond , van der Waals dipolar bonds , in many liquids and solids . So when a new compound is prepared , almost always by chance - serendipity - that has a metallic shininess (luster) and colour , and is a tolerable electrical conductor , there is a buzz of excitement about it , with a flurry of research into its properties and into related materials . Of course , it has some sort of metallic bond in it that gives it this extraordinary appearance and its electrical properties . Inorganic and organic compounds having a direct M-M metallic bond are called "synthetic metals", two of which , KCP and poly(sulfur nitride) , I'll briefly review in the following section .

KCP is the abbreviation for a remarkable platinum-based coordinate covalent compound that is bonded into long chains , or stacks of molecules , by a continuous Pt-Pt metallic bond . It has the appearance of reddish , coppery coloured crystals with a noticeable metallic luster . KCP is composed mostly of tetracyanoplatinite anions , [Pt(CN)4]2- . About one fifth of these anions have been oxidized by bromine to tetracyanodibromoplatinate , [Pt(CN)4Br2]2- (the bromine atoms are displaced by the forming metallic bond when the platinite(II) and platinate(IV) are co-crystallized) . The two different varieties of Pt-CN anions crystallize in tall stacks , like poker chips or dinner plates , with the electronically inert spectator cations (in this case , potassium) , anions (bromides) , and water molecules "off to the side" :

Large aqua spheres : platinum atoms ; black spheres : carbon ; blue spheres : nitrogen , which form the cyanide (CN) ligands . The spectator cations (K) , anions (Br) , and water molecules are omitted for clarity . The yellow spray paint represents the metallic bond XO (5dz2 AOs on the platinums) . To minimize steric repulsion the molecules stack with their cyanide ligands rotated with a 45º turn relative to their neighbours .

The chemical formula of KCP is K2Pt(CN)4Br0.3 . 3H2O , and by valence counting we see that the average valence on the platinum atoms is a non-integral number , 2.3+ ; the platinums are said to be in a non-integral oxidation state (NIOS) . KCP is thus a mixed-valent compound , with both Pt(II) and Pt(IV) together in the same crystal ; and the platinum atoms are connected directly in a continuous Pt-Pt metallic bond , with the Pt(II) and Pt(IV) valences blended together - reproportionated - at room temperature into the NIOS Pt(2.3+) . KCP is a Robin-Day Class IIIB mixed-valent compound . Because of its direct conductivity-temperature relationship (see below) , I've assigned it to Class 8 of the metallic solids (Table above) .

The platinum atoms in KCP and its related compounds (called Krogmann Salts after the German researcher who established their crystal structure by X-ray crystallography in 1969) have that peculiar NIOS valence because of a fine balance in the molecular stacks between the coulombic charge on the Pt(CN)4 anions , which will cause electrostatic repulsion , versus the attractive forces (Pt-Pt metallic bond , van der Waals , and hydrogen bonds) , which will keep them bonded together . Most (about 80%) of the stack components are tetracyanoplatinite anions , [Pt(CN)4]2-, with Pt(II) . To "dilute down" the repulsive anionic charges and allow the metallic bond to hold the stacks together , about 20% of the stack components are neutral , uncharged Pt(CN)4 molecules , with Pt(IV) . It so happens that this 80% (II) : 20% (IV) mix results in a precise balance between the repulsive coulombic force and the attractive bonds in the stacks . This same situation is also observed in other stack compounds with a metallic bond , and whose component molecules have unusual NIOS valences .

Such a NIOS valence is also beneficial in that the neutral Pt(CN)4 molecules provide platinum atoms with empty 5dz2 AOs , as opposed to the full 5dz2 AOs on the anions' platinums . The empty 5dz2 AOs produce "holes" (orbital vacancies) in the sigma XO (or conduction band) which are essential for permitting the singlet electrons above the Fermi level to become free and mobile in the XO . If all the 5dz2 AOs were filled with electron pairs (as in the anions) , the material would be an insulator , or at best , a semiconductor . The pure compound K2Pt(CN)4 is in fact a rather ordinary salt-like substance , colorless and water-soluble , not at all metallic , nor does it form molecular stacks in the crystalline state . But if neutral Pt(CN)4 molecules are mixed in with it :

K2Pt(CN)4 + Br2 -------------> K2Pt(CN)4Br2 -------------> Pt(CN)4 + 2 KBr ,

a metallic compound will form . Another technique is to remove some of the potassium cations from K2Pt(CN)4 by electrocrystallization - anodic oxidation of the [Pt(CN)4]2-anions - thus producing the related compound K1.75Pt(CN)4.1.5 H2O , in the form of slender , shiny , brass-coloured needles on the anode . For a colour photograph of this compound , see the article by Epstein and Miller , cited in KCP .

The ambient (293 K) electrical conductivity of KCP is about 830 ohm-1cm-1 , compared with that of platinum metal at 95,238 ohm-1cm-1 . However , unlike that of platinum , the electrical conductivity of KCP declines with decreasing temperature ; below 60 K , its conductivity rapidly plummets and it almost becomes an insulator :

By comparison , the conductivity of platinum at 60 K has risen to 903,342 ohm-1cm-1 (CRC Handbook of Chemistry and Physics , 87th edition , 2006) . Of course , platinum is a true metal with a nodeless XO metallic bond and an inverse temperature-electrical conductivity relationship . KCP clearly has a direct temperature-electrical conductivity relationship and so is a pseudometal , a result of its nodal sigma XO metallic bond , as sketched below :

The metallic bond in KCP is the XO formed by the continuous overlapping in the stacks of [Pt(CN)4] of the stereochemically prominent 5dz2 AOs on the platinums . They have the correct positive symmetry to form sigma covalent Pt-Pt bonds , which have nodes around the platinum atom kernels . These nodes , which act as "band gaps" in the stacks , are undoubtedly very narrow in a large , heavy atom such as platinum , so that while KCP is a pseudometal like semiconductors such as doped silicon and germanium , its ambient electrical conductivity is vastly greater than theirs (this is also true of gray tin , another pseudometal ; tin is a larger , heavier atom than either silicon or germanium ; its XO nodes are narrower than theirs , and its electrical conductivity is correspondingly higher than theirs ) .

KCP is a nice example of the chemical phenomenon of reproportionation-disproportionation , which can occur in mixed-valent compounds with nodal XOs . In reproportionation two different valences are "blended together" to obtain a third intermediate one : Pt(II) + 1/5 Pt(IV) = Pt(2.3+) . In electronic terms , the electron pairs in the Pt(II) 5dz2 AOs are "spreading out" and partly filling the empty 5dz2 AOs on the Pt(IV) . That creates the very narrow 5dz2 "band" (sigma XO metallic bond) in the stacks . As KCP is cooled down - and especially below 60 K - disproportionation occurs , and the the single Pt(2.3+) valence reverts into distinct Pt(II) and Pt(IV) . The mobile free electrons in the 5dz2 band lose some of their kinetic energy and are unable to tunnel through the nodes ; they are pinned on their parent platinum kernels . Below 60 K the Pt-Pt bonds become more like regular , ordinary covalent bonds , with little electronic activity around them , and the metallic bond , and electrical conductivity , fades away from the material . KCP , and generally the pseudometals with nodal XOs , have reversible metallic bonds which form and strengthen with heating , and weaken and disappear with cooling of the material .

KCP has also been cited as a prime example of Peierls distortion , in which a one-dimensional conduction band is thought to be inherently unstable , and subject to collapse into insulating segments . However , the example of poly(sulfur nitride) - see below - caused confusion , since it was also thought to be a one-dimensional conductor that defied Peierls distortion . We see that the chemical cause for the physical effect , Peierls distortion , is disproportionation , and that in metallic solids with nodal XOs it may be reversed by heating and reproportionation . We also understand the difference between the metallic bonds in KCP and poly(sulfur nitride) : KCP has a nodal XO , subject to disproportionation-reproportionation , while poly(sulfur nitride) has a nodeless XO , which is stable from Absolute Zero up to the decomposition point of the material (and based on a sigma XO , it's really three-dimensional and not one-dimensional) . Peierls distortion is now generally recognized as being three-dimensional , for example affecting the crystal structures of various elements such as As , Sb , Bi , Se , and Te . Their "original" metallic structures with a simple cubic symmetry (polonium) underwent an irreversible Peierls distortion , collapsing into more complex structures with covalent M-M bonds and having lone pairs of electrons in non-bonding orbitals .

The simplest example of three-dimensional Peierls distortion is the disproportionation of metallic hydrogen (and deuterium) back into gaseous hydrogen molecules ; conversely , liquid hydrogen can be shock compressed to metallic hydrogen (its electrical conductivity at 2000 K and 1.8 MBar is around 2000 ohm-1cm-1) .

Reproportionation is a very useful chemical technique for synthesizing novel , unique inorganic structures , including new metallic solids under the appropriate conditions . For example , niobium(II) oxide (see above) was prepared by combining niobium(0) metal and niobium(V) oxide in a reproportionation reaction , fusing the two precursors together in an arc furnace . The resulting NbO product had very strong Nb-Nb bonds in a stable crystal structure . However , the attempted reproportionation of aluminum(0) metal and aluminum(III) oxide was unsuccessful in that the desired lower-valent aluminum(I) and (II) oxides couldn't be isolated at room temperature . There is some evidence they were briefly stable at very high temperatures , but promptly disproportionated to the starting materials as the reaction mixture was cooled down . Quite possibly there were no reasonably accessible frontier orbitals available for the promoted extra aluminum valence electrons in the crystal lattice . The next example of a synthetic metal illustrates another successful reproportionation of two stable , common valence states of an element into a third intermediate valence state . This results in the promotion of extra valence electrons into marginally accessible frontier orbitals , which can then form a metallic bond XO .

The inorganic polymer poly(sulfur nitride) [also called poly(thiazyl) ; I'll abbreviate it as PSN] has been extensively studied by solid state scientists since its serendipitous discovery in 1910 by the English researcher F.P. Burt . PSN has the form of acicular crystals with a golden colour and metallic luster when viewed from above , or dark blue when viewed from their ends . The crystals are soft and malleable , and can be rolled into thin sheets . If left exposed to atmospheric oxygen and humidity , pure PSN crystals will tarnish like a conventional metal . PSN is somewhat unstable ; it sublimes at 135 ºC in vacuo , and detonates when heated in air to around 240 ºC (a thermal instability typical of most , if not all sulfur-nitrogen compounds) , and will also explode if it is strongly compressed mechanically .

PSN is a true metal , with an ambient electrical conductivity of pure and well-formed crystals of about 4000 ohm-1cm-1 ; it becomes superconducting at 0.26 K . It also forms black , highly conductive salts with one-electron oxidizers such as bromine . PSN consists of long chains of alternating sulfur and nitrogen atoms , in a crenellated (all-Z) pattern . The chains are packed together in bundles with a parallel orientation in the needle-like crystals . The stronger sigma bonds form the "spines" of the chains , with resonating pi bonds over them , and the metallic bond surrounds the covalent bonds at a higher energy level . I think a more accurate name for the polymer would be poly(sulfur imide) , if the reader will pardon my hairsplitting . The word "nitride" implies an ionic nature ; PSN is a covalent-metallic material .

In this "organic chemistry" representation , the two original sulfur valences , II and IV , are reproportionated into the "unnatural" sulfur(III) valence , permitting the pi electron resonance , which helps to stabilize the molecules . The sulfur(II) valence is found in many organosulfur compounds , for example in the mercaptans (thiols) and sulfides (thioethers) . The well-known compounds sulfur dioxide , thionyl chloride , and sulfur tetrafluoride have the sulfur(IV) valence . However , sulfur(III) compounds are very rare ; they may be the basis of sulfur-containing metallic solids . In PSN this sulfur(III) reproportionation has the effect of promoting the "sixth" valence electrons on the sulfurs to another higher energy frontier orbital , since the sigma-pi bonds can utilize only five valence electrons per atom , both for the sulfur and for the nitrogen linking atoms (which are like the nitrogen atom in the pyridine molecule , for example) . The sixth sulfur valence electrons in their frontier orbitals then combine throughout the chains to form the metallic bond XO in them .

There has been considerable discussion over the years about the electronic structure of PSN , with several theories about where the sixth valence electrons are located . For a long time I've thought they are in sulfur's 4s AOs : 3s2 3p4 (II and IV) --------> 3s2 3p3 4s1 (reproportionated to III) :

The remarkable metal-like properties of PSN , indeed the very fact that it's a true metal , all point to the 4s AOs as the frontier orbital that receives the sixth sulfur valence electrons . In this picture , PSN is isoelectronic with potassium metal (4s1) , and in fact PSN behaves somewhat both physically and chemically like potassium , but is much less reactive and energetic than it , of course .

One theory of the sixth electron location , proposed by MacDiarmid and co-workers , is that they are in the S-N pi* ABMO (antibonding molecular orbital) at a higher energy level than the S-N pi bond , by analogy with the singlet electron in the p* ABMO in nitric oxide , NO . However , ABMOs are nodal in nature , so the resulting material would be a pseudometal , which PSN definitely isn't :

It could be that in PSN the S-N pi* ABMO energy level is only a little bit higher than that of the 4s AOs , so that at ambient temperature the sixth sulfur electrons are preferentially located in the latter orbitals , and PSN becomes metallic . However , as its temperature is raised , more and more 4s electrons are promoted higher into the S-N pi* ABMOs . Since electrons in ABMOs lower the bond order in the compound - in essence , "cancelling out" bonds - the material becomes more and more unstable , until the remaining "bonding bonds" are too weak to hold the atoms together . Then they fly apart , and PSN goes BANG ! The inference from the fact that PSN explodes at the relatively low temperature of about 240 ºC is that the 4s and S-N pi* ABMO energy levels are probably quite close together (and that's likely true for most , if not all sulfur-nitrogen compounds - such as S2N2 and S4N4 - which are quite thermally unstable) .

I could write much more about the metallic bond and metallic solids (in fact I have , in the ebook , to which interested readers are referred) , but space on this web page is limited . Nevertheless , I hope this brief review will inspire teachers , students , and researchers to continue their study of these fascinating topics and to expand our knowledge of them .


References , Notes , and Further Reading


metal : 1297, from the Old French métal ; from the Latin metallum “metal , mine , quarry , mineral , what is got by mining” ; from the Greek metallon “metal , ore”, originally “mine , quarry , pit” ; probably from metalleuein “to mine , to quarry”, of unknown origin , but related somehow to metallan “to seek after”. Metallic is first recorded in 1567, from the Greek metallikos . My thanks to Douglas Harper of Etymonline.com for this reference .

Robin-Day : M.B. Robin and P. Day , “Mixed Valence Chemistry – A Survey and Classification”, Adv. Inorg. Chem. Radiochem. 10 , pp. 247-422 , H.J. Emeléus and A.G. Sharpe (eds.) , Academic Press , New York , 1967 ; P. Day , “Mixed Valence Chemistry and Metal Chain Compounds”, pp. 191-214 in  Mixed-Valence Compounds : Theory and Applications in Chemistry , Physics , Geology , and Biology , D.B. Brown (ed.) , NATO Advanced Study Institute , Series C , Mathematical and Physical Sciences Series no. 58 , Reidel-Holland (Kluwer Academic Publications , Hingham , MA) , 1980 ; P. Day , “Les Composés à Valence Mixte”, La Recherche 12 (120) , pp. 304-311 (mars 1981) ; A.J. Markwell , “Mixed-Valency Compounds”, Educ. Chem. 25 (1) , pp. 15-17 (January , 1988) . I discussed the Robin-Day classes of mixed-valent compounds in my web page , “New Solar Cells from Mixed-Valent Metallic Compounds”.

crystal orbital : I use the term "crystal orbital" to mean a "polymerized molecular orbital" , which spans the entire crystal dimensions (in a macroscopic sample of metal there is only one single metallic bond) . Thus , "crystal orbital" is synonymous with the terms "metallic bond" (chemistry) and "conduction band" (physics) . I abbreviate crystal orbital as XO , since "Xal" is sometimes used as shorthand for crystal (and I don't want to use CO , which stands for carbon monoxide !) . The term crystal orbital has been used in two excellent solid state chemistry textbooks : P.A. Cox , The Electronic Structure and Chemistry of Solids , Oxford University Press , Oxford , UK , 1987 ; Ch. 4 , pp. 79-133 ; R. Hoffmann , Solids and Surfaces , A Chemist’s View of Bonding in Extended Structures , VCH Publishers , New York , 1988 ; pp. 43-55 . See also A.B. Ellis et al. below (typically 99%) , Figure 7.3 , p. 190 , showing the polymerization of the 3s AOs in sodium metal to form a continuous conduction band in the solid , i.e. the sigma XO metallic bond .

resonating valence bonds : L. Pauling , “The Nature of the Interatomic Forces in Metals”, Phys. Rev. 54 (11) , pp. 899-904 (1938) ; idem. , “The Resonating-Valence-Bond Theory of Metals”, Physica 15 (1-2) , pp. 23-28 (1949) ; idem. , “The Resonating Valence-Bond Theory of Metals and Intermetallic Compounds”, Proc. Roy. Soc. Lond. A196 (1046) , pp. 343-362 (1949) ; idem. , “The Resonating-Valence-Bond Theory of Superconductivity : Crest Superconductors and Trough Superconductors”, Proc. Natl. Acad. Sci. 60 (1) , pp. 59-65 (1968) [PDF , 716 KB] ; idem. , “The Nature of Metals”, Pure & Appl. Chem. 61 (12) , pp. 1271-1274 (1989) [PDF , 384 KB] ; also in Pauling's textbook , The Nature of the Chemical Bond and the Structure of Molecules and Crystals : An Introduction to Modern Structural Chemistry , 3rd edition , Cornell University Press , Ithaca (NY) , 1960 ; Ch. 11 , “The Metallic Bond”, pp. 393-448 .

partial covalent bond : A.P. Sutton , Electronic Structure of Materials , Clarendon Press , Oxford (UK) , 1993 : According to the above picture , the metallic bond is an unsaturated covalent bond (p. 110) .

gold : W.J. Moore , Seven Solid States , An Introduction to the Chemistry and Physics of Solids , W.A. Benjamin , New York , 1967 ; Ch. 2 , “Gold”, pp. 41-72 .

diamond (1) : H.C. Miller , “Diamond , Natural”, pp. 666-675 in the Kirk-Othmer Encyclopedia of Chemical Technology , 3rd edition , Vol. 4 , M. Grayson and D. Eckroth (eds.) , John Wiley , New York (1978) .

typically 99% : A.B. Ellis et al. , Teaching General Chemistry , A Materials Science Companion , American Chemical Society , Washington , D.C. , 1993 ; pp. 191-192 (example of sodium metal) .

Fermi level : A.R. Mackintosh , “The Fermi Surface of Metals”, Scientific American 209 (1) , pp. 110-120 (July , 1963) ; also in Moore's excellent textbook [gold above] , pp. 47-51 .

five types of chemical bonds : covalent , ionic (coulombic, electrostatic) , van der Waals dipolar , hydrogen , and metallic ; S.T. Matsuo , J.S. Miller , E. Gebert , and A.H. Reis , Jr. , “One-Dimensional K2Pt(CN)4Br0.3 . 3 H2O , A Structure Containing Five Different Types of Bonding”, J. Chem. Educ. 59 (5) , pp. 361-362 (1982) .

silicon : W.J. Moore [see above for gold] , Ch. 3 , Silicon, pp. 73-99 ; W. Runyan , “Silicon and Alloys (Pure Silicon)”, pp. 826-845 in the Kirk-Othmer Encyclopedia of Chemical Technology , 3rd edition , Vol. 20 , M. Grayson and D. Eckroth (eds.) , John Wiley , New York (1982) .

one-electron : L. Pauling , The Nature of the Chemical Bond (op. cit.) , p. 340 , for a discussion of the one-electron bond in the hydrogen molecule-cation , H2+ ; also in A. Holden , The Nature of Solids , Dover Publications , New York , 1992 [reprint of the Columbia University Press textbook , 1965] , p. 91 . The convention in semiconductor science and technology is to consider silicon doped with electron-deficient dopants (such as boron) as containing “positive holes” ; in fact there are NO positive charges produced on either the silicon or boron atoms . The doped silicon remains electrically neutral . From a chemical point of view , there would be a few orbital vacancies empty spaces in the sp3 sigma MOs , with singlet electrons instead of electron pairs : that is , one-electron bonds , resonating in the lattice in the MOs (SiSi covalent bonds) , which form the nodal XO in the doped silicon .

electrical conductivity of gray tin : A.W. Ewald and E.E. Kohnke, “Measurements of Electrical Conductivity and Magnetoresistance of Gray Tin Filaments”, Phys. Rev. 97 (3) , pp. 607-613 (1955) ; see Figure 2 , p. 609 for the graph of the electrical conductivity of gray tin over a range of temperatures . A photograph of gray tin can be found on Theodore Gray's excellent website , at http://www.theodoregray.com/PeriodicTable/Elements/050/index.html .

electrical conductivity of gold : D.R. Lide (ed.) , CRC Handbook of Chemistry and Physics , 82nd edition , CRC Press , Boca Raton (FL) , 2001 ; data for the electrical conductivity of gold over a range of temperatures are listed on p. 12-45 .

Twenty-nine : C.P. Poole Jr. , H.A. Farach , and R.J. Creswick , Superconductivity , Academic Press , San Diego , CA , 1995 ; Table 3.1 , “Properties of the Superconducting Elements”, pp. 60-61 . The twenty-nine elements listed are superconducting at ambient pressure (one atmosphere) ; several more elements become superconducting near Absolute Zero under extremely high pressures .

leakage : see A.B. Ellis et al. above (typically 99%) , Figure 7.2 , p. 189 , showing simple band structures for sodium and magnesium metals .

molybdenum(II) diacetate : F.A. Cotton and G. Wilkinson , Advanced Inorganic Chemistry , 5th edition , John Wiley , New York , 1988 ; quadruple bonds in molybdenum compounds , pp. 839-845 ; Mo(OAc)2 on pp. 840-841 (also in Table 9-C-5 , p. 840) .

reviews : H. Krebs , “Superconductivity in Metals , Alloys , Semiconductors , and Glasses as a Result of Particular Bond Systems”, Prog. Solid State Chem. 9 , pp. 269-296 , Pergamon Press , Oxford , UK , 1975 ; pp. 294-295 . Also in Krebs's textbook : idem , Fundamentals of Inorganic Crystal Chemistry , transl. by P.H.L. Walter , McGraw-Hill , London , UK , 1968 ; pp. 231-232 .

diamond (2) : Y. Takano et al. , Superconductivity in Diamond Thin Films Well Above Liquid Helium Temperature, Appl. Physics Lett. 85 (14) , pp. 2851-2853 (2004) ; K.-W. Lee and W.E. Pickett , Superconductivity in Boron-Doped Diamond, Phys. Rev. Lett. 93 , 237003 (2004) ; E.A. Ekimov et al. , Superconductivity in Diamond, Nature 428 (6982) , pp. 542-545 (2004) . This last paper can be downloaded for free , PDF document (279 KB) .

Fermi-Dirac distribution : see Fermi level above .

inverse(1) : H.K. Bowen , “Ceramics as Electrical Materials”, pp. 290-314 in the Kirk-Othmer Encyclopedia of Chemical Technology , 3rd edition , Vol. 5 , M. Grayson and D. Eckroth (eds.) , John Wiley , New York (1979) ; Figure 5 , p. 299 .

tungsten bronzes : P.G. Dickens and M.S. Whittingham , “The Tungsten Bronzes and Related Compounds”, Quart. Rev. 22 (1) , pp. 30-44 (1968) .

distorted : A.F. Wells , Structural Inorganic Chemistry , 3rd edition , Clarendon Press , Oxford (UK) , 1962 ; pp. 469-471 .

perovskite : R.M. Hazen , “Perovskites”, Scientific American 258 (6) , pp. 74-81 (June , 1988) ; O. Fukunaga and T. Fujita , “The Relation Between Ionic Radii and Cell Volumes in the Perovskite Compounds”, J. Solid State Chem. 8 (4) , pp. 331-338 (1973) ; R.W.G. Wyckoff , Crystal Structures , 2nd edition , vol. 2 , Interscience Publishers , New York , 1964 ; “Perewskite-Like Compounds”, pp. 390-402 ; Michael W. Davidson , The Perovskite Collection , at http://micro.magnet.fsu.edu/micro/gallery/perovskite/perovskite.html ; WolfWikis , Perovskite, at http://wikis.lib.ncsu.edu/index.php/Perovskite .

inverse (2) : Bowen (see inverse(1) above) , Figure 11 , p. 307 ; M.J. Sienko , “Electric and Magnetic Properties of the Tungsten and Vanadium Bronzes”, Ch. 21 , pp. 224-236 in Nonstoichiometric Compounds , R. Ward (ed.) , Adv. Chem. Series 39 , American Chemical Society , Washington , D.C. (1963) ; Figure 3 , p. 229 .

conductivities : H.R. Shanks , P.H. Sidles , and G.C. Danielson , “Electrical Properties of the Tungsten Bronzes”, Ch. 22 , pp. 237-245 in Nonstoichiometric Compounds (immediately above) ; especially Figure 2 , p. 240.

Ourmazd and Spence : A. Ourmazd and J.C.H. Spence , “Detection of Oxygen Ordering in Superconducting Cuprates”, Nature 329 (6138) , pp. 425-427 (1987) .

Valence Bond : L. Pauling , “The Nature of the Chemical Bond – Application of  Results Obtained from the Quantum Mechanics and from a Theory of Paramagnetic Susceptibility to the Structure of Molecules”, J. Amer. Chem. Soc. 53 (4) , pp. 1367-1400 (1931) . This first exposition of the VB theory was later incorporated into Pauling’s well-known textbook , The Nature of the Chemical Bond and the Structure of Molecules and Crystals , Cornell University Press , Ithaca (NY) , becoming Ch. 4 , “The Directed Covalent Bond : Bond Strengths and Bond Angles”, pp. 108-144 in the 3rd edition (1960) ; See also G.E. Kimball , Directed Valence, J. Chem. Phys. 8 (2) , pp. 188-198 (1940) ; and R.T. Sanderson , Inorganic Chemistry , Reinhold Publishing , New York , 1967 ; Table 8-2 , “Directional Characteristics of Some Valence Orbitals”, p. 112 .

ambient conductivity : C.P. Poole , Jr. , T. Datta , and H.A. Farach , Copper Oxide Superconductors , John Wiley , New York , 1988 ; Table X-1 , p. 198 .

M.K. Wu : M.K. Wu et al. , “Superconductivity at 93 K in a New Mixed-Phase Y-Ba-Cu-O Compound System at Ambient Pressure”, Phys. Rev. Lett. 58 (9) , pp. 908-910 (1987) .

fused button : T.B. Reed and E.R. Pollard , “Niobium Monoxide”, Inorg. Synth. 14 , pp. 131-134 , A. Wold and J.K. Ruff (eds.) , McGraw-Hill , New York , 1973 . This was reprinted in Inorg. Synth. 30 , Nonmolecular Solids , pp.108-110 , D.W. Murphy and L.V. Interrante (eds.) , John Wiley , New York , 1995 . An excellent review of the arc furnace method of inorganic syntheses with , and preparing , refractory materials : T.B. Reed , “Arc Techniques for Materials Research”, Mater. Res. Bull. 2 (3) , pp. 349-367 (1967) .Theodore Gray describes a home-made arc furnace in “Melting the Unmeltable”, Popular Science , May , 2004 ; available online here .

Pauli paramagnetism : H.R. Khan et al. , “Magnetic and Superconductivity Properties of Niobium Oxides”, Mater. Res. Bull. 9 (9) , pp. 1129-1135 (1974) .

rocksalt crystal structure : J.K. Burdett and T. Hughbanks , “NbO and TiO : Structural and Electronic Stability of Structures Derived from Rock Salt”, J. Amer. Chem. Soc. 106 (11) , pp. 3101-3113 (1984) ; A. Simon , “Metal-Rich Compounds”, Ch. 4 , pp. 112-165 in Solid State Chemistry , Compounds , A.K. Cheetham and P. Day (eds.) , Clarendon Press , Oxford , UK (1992) ; NbO and TiO are discussed on p. 140 : “Clearly , both structures are defect rocksalt structures …..” . Simon also discussed NbO as a metal cluster compound .

Schulz and Wentzcovitch : W.W. Schulz and R.M. Wentzcovitch , “Electronic Band Structure and Bonding in Nb3O3”, Phys. Rev. B 48 (23) , pp. 16986-16991 (1993) ; Fig. 1 , p. 16986 .

iron monophosphide : D. Bellavance , M. Vlasse , B. Morris , and A. Wold , “Preparation and Properties of Iron Monophosphide”, J. Solid State Chem. 1 (1) , pp. 82-87 (1969) ; see Figures 3 and 4 , p. 86 , for temperature–conductivity graphs . See also D. Bellavance and A. Wold , "Single Crystals of Iron Monophosphide", Inorg. Synth. 14 , pp. 176-182 , A. Wold and J.K. Ruff (eds.) , McGraw-Hill , New York , 1973 .

avoiding the use of d AOs : “It was discovered that the d orbitals in some states of atoms like sulfur could be so diffuse that they could not reasonably be expected to participate to a significant extent in bonding” : R.G.A.R. Maclagan , “Symmetry , Ionic Structures and d Orbitals in SF6”, J. Chem. Educ. 57 (6) , pp. 428-429 (1980) ; the quotation is from p. 428 . “Models of SF6 requiring sp3d2 hybridization should be discarded” : A.E. Reed and F. Weinhold , “On the Role of d Orbitals in SF6”, J. Amer. Chem. Soc. 108 (13) , pp. 3586-3593 (1986) ; the quotation is from p. 3586 . See also W. Kutzelnigg , “Chemical Bonding in Higher Main Group Elements”, Angew. Chem. Internat. Ed. Engl. 23 (4) , pp. 272-295 (1984) [especially pp. 288-290] ; R.P. Messmer and R.B. Murphy , “Valence Bond Theory and Superconductivity”, Ch. 2 , pp. 13-24 in Chemistry of High Temperature Superconductors , D.L. Nelson , M.S. Whittingham , and T.F. George (eds.) , ACS Symposium Series 351 , American Chemical Society , Washington , D.C. (1987) [especially pp. 20-23] .

half-metallic ferromagnet : H. van Leuken and R.A. de Groot , Electronic Structure of the Chromium Dioxide (001) Surface, Phys. Rev. B 51 (11) , pp. 7176-7178 (1995) [available free online , PDF , 462 KB] ; J.M.D. Coey and M. Venkatesan , Half-Metallic Ferromagnetism : Example of CrO2 (Invited), J. Appl. Phys. 91 (10) , pp. 8345-8350 (2002) . These latter authors have provided a classification of metallic solids (ten classes) , based on the spin orientation of the free , mobile electrons at the Fermi level , EF : Table I , “Summary of the Classification of Half-Metals”, p. 8346 .

Chamberland's review : B.L. Chamberland , “The Chemical and Physical Properties of CrO2 and Tetravalent Chromium Oxide Derivatives”, CRC Crit. Rev. Solid State Mater. Sci. 7 (1) , pp. 1-31 (1977) ; Figure 9 , p. 13 . Chromium dioxide is also discussed by J.B. Goodenough , “Transition Metal Oxides with Metallic Conductivity”, Bull. Soc. Chim. France (4) , pp. 1200-1206 (1965) ; pp. 1204-1205 .

simple formula : F.A. Cotton , G. Wilkinson , and P.A. Gaus , Basic Inorganic Chemistry , 3rd edition , John Wiley , New York , 1995 ; p. 68 , and Table 2.5 , p. 68 . The equation is presented there as m = 2[S(S+1)] ½ , where S is the electron spin in ½ units and n = 2S . meff works out to the same value with both formulas . More complex formulas for calculating meff for paramagnetic compounds are presented and discussed by B.N. Figgis and J. Lewis , “The Magnetic Properties of Transition Metal Complexes”, Prog. Inorg. Chem. 6 , pp. 37-239 , F.A. Cotton (ed.) , Interscience / John Wiley , New York , 1964 . See also this web page from the University of Oxford , UK .

Wold and Dwight's textbook : A. Wold and K. Dwight , Solid State Chemistry , Synthesis , Structure , and Properties of Selected Oxides and Sulfides , Chapman and Hall , New York , 1993 ; Fig. 7.4 , p. 97 .

very strong oxidizer : the reduction of CrO2 to Cr3+ in acid can be written as :

CrO2   +  4 H+   +  e-  -----------> Cr3+  +   2  H2O  ;  E0red  = 1.48 V

This redox half-reaction is from the CRC Handbook of Chemistry and Physics , D.R. Lide (ed.) , 87th edition , CRC Press/Taylor & Francis , Boca Raton (FL) , 2006 , p. 8-21 . Compare the standard reduction potential of CrO2 to that of chromic acid , which is a well-known oxidizing agent :

H2CrO4   +  6 H+   +  3e-  -----------> Cr3+  +   4 H2O  ;  E0red = 1.35 V

KCP : J.M. Williams and A.J. Schultz , “One-Dimensional Partially Oxidized Tetracyanoplatinate Metals : New Results and Summary”, pp. 337-368 in Molecular Metals , W.E. Hatfield (ed.) , Plenum Press , New York , 1979 ; J.S. Miller and A.J. Epstein , “One Dimensional Inorganic Complexes”, Prog. Inorg. Chem. 20 , pp. 1-151 , S.J. Lippard (ed.) , John Wiley , New York , 1976 ; A.J. Epstein and J.S. Miller , “Linear Chain Conductors”, Scientific American 241 (4) , pp. 52-61 (October , 1979) ; a colour photograph of K1.75Pt(CN)4.1.5 H2O is on p. 54 .

oxidized by bromine : J.A. Abys et al. , pp. 1-5 in Ch. 1 , “Electrically Conducting Solids”, Inorg. Synth. 19 , pp. 1-58 , D.F. Shriver (ed.) , John Wiley , New York (1979) .

German researcher : K. Krogmann , “Planar Complexes Containing Metal-Metal Bonds”, Angew. Chem. Internat. Ed. Engl. 8 (1) , pp. 35-42 (1969) .

electrocrystallization : J.M. Williams , Organic Superconductors, Prog. Inorg. Chem. 33 , pp. 183-220 (especially pp. 188-190) , S.J. Lippard (ed.) , John Wiley , New York , 1985 ; J.M. Williams et al. , Rational Design of Synthetic Metal Superconductors, Prog. Inorg. Chem. 35 , pp. 51-218 (especially pp. 77-83) , S.J. Lippard (ed.) , John Wiley , New York , 1987 .

electrical conductivity of KCP : H.R. Zeller and A. Beck , “Anisotropy of the Electrical Conductivity in the One-Dimensional Conductor K2[Pt(CN)4] Br0.30 . 3 (H2O)”, J. Phys. Chem. Solids 35 (1) , pp. 77-80 (1974) .

Peierls distortion : R.E. Peierls , Quantum Theory of Solids , Clarendon Press , Oxford (UK) , 1955 (reprinted in 2001) ; pp. 108-112 . It follows that for a one-dimensional metal with a partly filled band the regular chain structure will never be stable , since one can always find a distortion with a suitable value of r for which a break will occur at or near the edge of the Fermi distribution (pp. 110-111) . This is generally referred to as Peierls's Theorem .

various elements : U. Müller , Inorganic Structural Chemistry , John Wiley , Chichester (UK) , 1993 ; pp. 100-101 .

metallic hydrogen : S.T. Weir , A.C. Mitchell , and W.J. Nellis , “Metallization of Fluid Molecular Hydrogen at 140 GPa (1.4 Mbar)”, Phys. Rev. Lett. 76 (11) , pp. 1860-1863 (1996) ; P.M. Celliers et al. , “Shock-Induced Transformation of Liquid Deuterium into a Metallic Fluid”, Phys. Rev. Lett. 84 (24) , pp. 5564-5567 (2000) .

aluminum(0) metal and aluminum(III) oxide : M. Hoch and H.L. Johnston , “Formation , Stability and Crystal Structure of the Solid Aluminum Suboxides : Al2O and AlO”, J. Amer. Chem. Soc. 76 (9) , pp. 2560-2561 (1954) ; C.N. Cochran , “Aluminum Suboxide Formed in Reaction of Aluminum with Alumina”, J. Amer. Chem. Soc. 77 (8) , pp. 2190-2191 (1955) . See also T. Forland et al. , “Measurements of Phase Equilibria in the Aluminum – Aluminum Sulfide System”, Acta. Chem. Scand. , Series A28 (2) , pp. 226-228 (1974) . The compound AlS has a narrow window of stability between 1010 ºC and its m.p. of 1060 ºC .

poly(sulfur nitride) : M.M. Labes , P. Love , and L.F. Nichols , “Polysulfur Nitride – A Metallic , Superconducting Polymer”, Chem. Rev. 79 (1) , pp. 1-15 (1979) ; R.T. Oakley , “Cyclic and Heterocyclic Thiazenes”, Prog. Inorg.Chem. 36 , pp. 299-391 , S.J. Lippard (ed.) , John Wiley , New York , 1988 ; G.B. Street and W.D. Gill , “The Chemistry and Physics of Polythiazyl , (SN)x , and Polythiazyl Halides”, pp. 301-326 in Molecular Metals , W.E. Hatfield (ed.) , Plenum Press , New York (1979) .

MacDiarmid and co-workers : A.G. MacDiarmid et al. , “Synthesis and Selected Properties of  Polymeric Sulfur Nitride (Polythiazyl) , (SN)x”, Ch. 6 , pp. 63-72 in Inorganic Compounds with Unusual Properties , R.B. King (ed.) , Adv. Chem. Series 150 , American Chemical Society , Washington , D.C. (1976) .



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