Prediction of Superconductivity in Transition Metal Chalcogenide Oxides

 

 

Until recently it was generally thought that even traces of iron or other paramagnetic impurities in a metallic solid prevented the appearance of superconductivity in that material . That belief , only partially true , inhibited solid state scientists from investigating iron compounds as possible superconductor candidates . A serendipitous discovery in 2006 by a Japanese research team , of superconductivity in the compound LaOFeP (Tc = 4 K) , and subsequently in the related layered structure , LaOFeAs (Tc = 26 K , fluoride-doped) , dispelled the myth of the "impossibility of iron" in superconductors . (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) . Since these initial discoveries , a multitude of new LaOFeAs analogues have been prepared and reported . The transition temperatures of the derivatives have been steadily rising , with that of the current (August , 2008) record holder , SmO0.9F0.1FeAs , being 55 K .

Another remarkable advance in the development of iron-based superconductors was recently made as I was in the middle of writing this web page . On July 15 , 2008 , a team of Chinese researchers announced the discovery of superconductivity (Tc = 8 K) in FeSe . This simple compound has been known for a long time (coincidently I noted its crystal structure [it has both the litharge and nickel arsenide structures ; the former one was the superconductor] in the standard reference [1962] by A.F. Wells about a week before) . It thus occupies in the ongoing development of superconductors the same sort of position as the now-iconic magnesium diboride (MgB2 , Tc = 39 K) , another simple compound also long known but overlooked in the search for new superconductors . Had magnesium diboride's electrical conductivity properties been studied , say in the early 1960s , the erroneous belief in a 30 K upper limit of the transition temperature for superconductors would never have arisen . Similarly , if superconductivity in FeSe had been discovered , again in the 1960s , the equally erroneous belief of the ineligibility of iron compounds as superconductor candidates would be unknown . As the title of a review of MgB2 says , "Better late than never" !

In 2004 I published online an ebook , Exploring the Chemistry of Metallic Solids , including Superconductors , which is available for free from this website , Chemexplore . A new approach to understanding superconductivity , this time from a chemist's point of view , was described in the ebook . Since all superconductors are metallic solids , the scope of the book was expanded to include a wide range of metallic compounds in the discussion . I found an appreciation of metallic bonds and metallic solids in general was very helpful in understanding the nature of superconductors .

In the course of investigating known and potential metallic solids and superconductors from across the Periodic Table I concluded it might be possible to design and synthesize new high temperature superconductors based on several of the Transition metal elements , such as iron , cobalt , nickel , copper , and zinc . Given the rapid pace of progress in the development of new iron-based superconducting compounds at this time , I thought it might be helpful if I joined in the discussion of these materials with my own contribution , of a theoretical nature , with ideas drawn from my ebook cited above . The copper structures studied there are quite different from those of iron and the others , so I won't be discussing them in this web page .

 

Low Spin Iron Compounds

 

All materials in the superconducting state are strongly diamagnetic . This is the basis of the Meissner effect , by which a superconducting pellet can be levitated above a strong magnet . Thus , all the atomic components of the material in the superconducting state must be in a spin-paired (low spin) condition . For example , in the famous high Tc superconductor YBCO , all of its component ions are in a low spin state below 93 K , its Tc . This is obvious for the yttrium , barium , and oxide ions , but what about the copper cations , which are mostly copper(II) , having a 3d9 configuration ? We can write YBCO's ideal empirical formula as follows : (Y3+Ba2+Ba2+)(Cu2+Cu3+Cu2+)(O2-)7 . We see that YBCO is a Robin-Day Class II mixed-valent compound with respect to its copper component . As such , the copper 3d9 electrons can resonate through the lattice between the copper cations and over the oxide anions by superexchanging . The "true" valence of copper in YBCO is therefore +7/3 = +2.33 .

Below Tc the itinerant and antiparallel 3d9 electrons begin to condense into Cooper pairs , which are diamagnetic . Underneath them the copper "base" cations are all Cu3+ , which are 3d8 electronically and are in a low spin state . So , when YBCO is in its superconducting state , all of its components , the anions , cations , and Cooper pairs , are completely spin-paired and diamagnetic .

It's similarly possible to formulate new superconductor candidate compounds from a wide range of elements across the Periodic Table , but care must be taken to avoid using as "base cations" those metal cations which exhibit a Curie paramagnetism , having unpaired singlet electrons in their valence shell . Such singlet electrons have a residual magnetic moment which can uncouple the Cooper pairs passing nearby them . Traces of paramagnetic iron (or other) impurities in a material may indeed prevent the appearance of superconductivity in it , even though it's a metallic solid .

Taking iron as an example , its three common valences are Fe(0) [3d6 4s2] , Fe(II) [3d6] , and Fe(III) [3d5] . Because of its odd number of valence shell electrons and resultant paramagnetism , Fe(III) is unsuitable for designing into superconductor candidate compounds . However , it might be possible to use Fe2+ cations as base cations , like the Cu3+ in the YBCO example above . In this case , we would create an iron triad , and add two "extra" itinerant electrons to the three Fe(II) cations , to obtain Fe2+(e-) – Fe2+ – Fe2+(e-) , which can also be written formally as Fe1+–Fe2+–Fe1+. If the ferrous cations can be kept in a low spin condition , and if the two extra electrons can condense into Cooper pairs at a certain Tc , then the iron compound will become superconducting and strongly diamagnetic .

A number of low spin iron(II) compounds are well-known . The simple salt potassium ferrocyanide , K4Fe(CN)6 , with octahedrally-coordinated iron , is diamagnetic , as is the covalent organometallic compound ferrocene [bis(cyclopentadienyl)iron(II)] . Two infinite lattice iron compounds are particularly relevant to our discussion here : iron pyrites – the common mineral "fool's gold" – which chemically is iron(II) disulfide , FeS2 , and has a cubic rocksalt crystal structure ; and iron monophosphide , FeP . Iron pyrites is a diamagnetic semiconductor ; clearly its octahedrally-coordinated iron(II) cations are in a low spin condition .

Iron monophosphide has the nickel arsenide crystal structure , with octahedral iron atoms and trigonal prismatic phosphorus atoms . It's a metallic solid with an ambient electrical conductivity of 12,500 ohm-1cm-1 rising to around 3.3 million ohm-1cm-1 at 4.2 K , in liquid helium . It almost becomes superconducting , but not quite . As a metallic solid FeP exhibits Pauli paramgnetism , but not Curie paramagnetism . While its formula looks like Fe3+P3-, the primary bonding in the compound is best described as covalent . Note that iron(III) is a mild oxidizer : Fe3+  +  e-  ------->  Fe2+  ;  E0red = 0.771 V . Any Fe3+ in the material would strip electrons off the reducing phosphide anions . Each iron atom in the lattice has six covalent Fe–P bonds , which require twelve electrons for completion . The iron(0) uses all eight of its valence shell electrons (3d6 4s2) ; its phosphorus(0) partner atom supplies all five of its valence shell electrons (3s2 4p3) . Wait , that's thirteen electrons in total ! Twelve of the electrons will go into the six low energy sigma covalent Fe–P bonds , while the thirteenth one will become "extra" and itinerant in the lattice : the metallic bond electron . The nickel arsenide structure consists of alternating layers of nickel atoms and arsenic atoms :

In the above molecular model of FeP , the iron atoms are represented by the smaller blue spheres , and the phosphorus atoms by the larger brown spheres . The metallic bond in FeP is over the layers of iron atoms , which are in a hexagonal packing arrangement .

I'd like to return to the iron pyrites example for a moment . The iron atoms in this compound are all in a low spin condition . In this case it may be the redox nature of the coordinating anions , the disulfides , S22-, that causes the spin pairing of the iron(II) 3d6 valence electrons . The chalcogenide anions are known to be chemically reducing :

Note that while oxygen is in the same family (VIB/16) as the chalcogenide elements (S, Se , and Te) , its redox behaviour is radically different from them to the point where it can't really be considered a chalcogenide element . Iron(II) oxide , FeO , has a rocksalt crystal structure like iron pyrites , but its iron(II) cations are in a high spin condition and FeO exhibits Curie paramagnetism , which however is strongly affected by an antiferromagnetic ordering of its singlet valence electrons .

If we write the redox half-reactions for iron(II) and disulfide , we see that the iron(II) is almost reduced to iron(0) :

Fe2+  +  2e-  --------->  Fe0    E0red = – 0.447 V

S22-   –   2e-  --------->  2 S0   E0ox =  0.428 V

 Net :  Fe2+  +  S22-  -------->  Fe0(S0)2 (c)   E0T = – 0.019 V

The small negative value for the reaction cell potential , E0T , suggests that a full , clean transfer of the disulfide electrons to the iron(II) cation would be thermodynamically unfavourable at STP . However , there is likely some sort of partial charge transfer or electron resonance from the disulfide anions into the valence orbitals of the iron(II) cations . This movement of ligand electrons to the iron atoms will "push down" the high spin Fe2+ 3d6 electrons into spin pairs , making the iron(II) diamagnetic , which is experimentally observed in iron pyrites .

The same situation will probably occur in the other iron chalcogenides , even when their E0T values are positive : FeS (0.029 V) , FeSe (0.477 V) , and FeTe (0.696 V) . Another example of this interesting phenomenon is the beautiful mineral galena , which chemically is lead(II) sulfide , PbS . In this latter case the cell potential E0T is calculated to be 0.35 V , suggesting an internal reduction of the lead(II) to lead(0) ; that is , the mineral is a mass of lead and sulfur zerovalent atoms ! As a macroscopic crystal galena is bluish-gray (like lead metal) with a metallic luster ; it's black in powder form . Ng and Zuckerman have commented about the X-ray diffraction data for galena :

“The direct integration of charge density , the observed atomic scattering factors , and the population analysis of the valence electrons all indicate that the lead atom is negatively charged , i.e. electrons are transferred from sulfur to lead” (p. 313) .

Despite that , galena is a semiconductor . At one time it was used in the electronics of early radios , as the crystal in "crystal sets" to detect radio waves . I think the answer here is the same as with iron monophosphide : the formal valences in PbS , as in FeP , are irrelevant , as the chemical bonding in galena is covalent and not ionic . I stress this point , as I believe the same situation occurs in LaOFeAs and all of its multitude of relatives . The compound is likely a "sandwich" of covalently bonded FeAs between ionic layers of La3+ and O2-. Normally FeAs alone would assume the nickel arsenide structure shown above ; most of the pnictides and chalcogenides of Fe , Co , and Ni have such a structure (A.F. Wells) . During the formation of LaOFeAs the ionic components force the covalently bonded phase into sandwich-like layers . As we will see , this is advantageous electronically for the iron , assisting it in eventually becoming the superconducting part of LaOFeAs . The second advantage of the LaO ionic layer is its contribution to the "controlled valence process" in the iron , in effect providing extra , itinerant electrons in iron's frontier orbitals that become Cooper pairs below Tc . Now let's take a closer look at the structure of LaOFeAs .

 

The Crystal and Electronic Structure of LaOFeAs

 

The crystal structure of LaOFeAs consists of anionic layers of FeAs bonded to alternating cationic layers of LaO ; it has been crystallographically classified in the ZrCuSiAs family :

Black spheres : iron atoms ; yellow : arsenic ; aqua : La3+ ; green : oxides . This molecular model is based on the structure of LaOFeAs found in several publications , for example the nice drawing in the Nature paper by Takahashi et al. . Note that the coordination of the lanthanums is unlikely to be tetrahedral as shown in the sketch , as lanthanide and actinide cations are well-known to prefer very high coordination numbers , generally a minimum of sixfold or greater . However , the correct oxide coordination of La3+ is relatively unimportant and will have no influence on the electronic structure of the FeAs layer , which is central to its electrical conductivity properties . In an interesting paper Hiroi argued for an alternative nomenclature for LaOFeAs ; he suggested that the compound is really an arsenate , and so should be named LaFeAsO to reflect this chemical reality . In this web page I am retaining the original and more familiar designation of LaOFeAs (which I think is a more accurate description for it anyway ; as you can see in the sketch above , there are no AsO chemical bonds . If anything , there might be AsLa bonds of some sort . Unquestionably there are strong AsFe covalent bonds in LaOFeAs) .

The FeAs layers are undoubtedly the electronically active part of the compound . Even in them the arsenics are really just inert connecting links , with the planar sheets of iron atoms being the free electron conduits . The arsenics could in theory be replaced with various other nonmetal elements , while still retaining the metallic properties of the compound . Note that the iron arsenide part of LaOFeAs has the anti-litharge (anti-PbO) crystal structure :

A side view of the litharge/anti-litharge structure .

For PbO (litharge) : the small black spheres represent lead(II) . The larger yellow spheres stand for oxygen linking atoms . The very small gray spheres portray electron lone pairs , which in the heavy metal lower valent cations are called inert pairs . The presence of inert pairs in such structures is a sure sign of covalent bonding (as it is in small molecules like water and ammonia) . The chemical bonding in PbO is entirely covalent , not ionic . The stereochemically prominent inert pairs force the lead(II) to adopt the tetragonal (or square) pyramid configuration , a sort of flattened tetrahedron . When joined together by tetrahedral oxygen linking atoms the resulting PbO structure assumes a two-dimensional sheet form . If all the A and B atoms were tetrahedral , the AB crystal would have the three-dimensional wurtzite or zinc blende (sphalerite) structure .

The FeAs layer in LaOFeAs has the anti-litharge crystal structure , with the yellow spheres representing the iron atoms , and the black spheres being the arsenic atoms . Again , the chemical bonding in the FeAs is covalent , with the metallic bond covering the iron layers . The sketch below is the valence bond description of the electronic structure of the FeAs layer . Throughout my ebook I have used classical Valence Bond (VB) theory , developed primarily by Pauling around 1930 , with later refinements by other contributors . I have found it to be a simple , easy , nonmathematical approach to understanding , in a qualitative manner , the electronic structures of many metallic solids and superconductors , as expounded in the ebook .

From the above analysis , two extra electrons are predicted to enter the 4p unhybridized frontier orbitals on the iron atoms in LaOFeAs . Of course , "an electron is an electron is an electron" ; that is , they are all identical and indistinguishable , but I've labelled them x , o , and y to clarify their origin for the reader . We see that one electron (formally donated by the arsenic atom) , and the electron donated by the LaO layer , will be located in the 4p frontier AOs . Creation of the strong , low energy level , covalent FeAs bonds is given top priority when LaOFeAs is formed . Arsenic uses all five of its valence shell electrons (plus two hypervalent 3dz2 electrons) in its square pyramid (dsp3) hybrid AOs , but iron has a total of eight valence electrons , so the "odd" electron will be located in a frontier orbital when the other twelve electrons are spin-paired . The 4px,y,z AOs can overlap side-by-side continuously in the planar sheets of iron atoms in the FeAs layers to form a p XO [XO = crystal orbital , a "polymerized molecular orbital (MO)"] , which is predicted to be the metallic bond in the material . My ball-and-stick molecular models are "exploded" structures meant to clearly show the atomic coordinations ; in reality the atoms are close-packed in these infinite atomic lattices . So there are probably very short Fe–Fe distances in the layers , permitting a reasonably strong overlapping of the 4p AOs . In the related superconducting compound LiFeAs (Tc = 18 K) the Fe–Fe distance , as measured by X-ray diffraction , was found to be 2.68 Å . The Fe–Fe bond length is 2.48 Å in iron metal at room temperature . LaOFeAs could be considered as a synthetic metal of iron . Recall the compound KCP [K2Pt(CN)4Br0.3 . 3H2O] with Pt–Pt bonds forming its metallic bond . In my proposed new classification of metallic solids , I've placed LaOFeAs and its relatives in Class 2 , which also includes the elementary metals , alloys , and most intermetallic compounds .

The related compound LaOFeP was metallic and had a very low Tc of 4 K . LaOFeAs , while metallic , apparently didn't become superconducting even close to absolute zero . However , when it was doped with fluoride anions , it was found to become superconducting at Tc = 26 K (for LaO0.89F0.11FeAs) . When it was doped with Ca2+, no Tc was noted :

"Further , Tc was not observed for Ca2+-doped samples , suggesting that a critical factor for induction of superconductivity is electron doping , and not hole doping" (Kamihara et al. , p. 3297) .

Lowering the negative charge in the anion layer has the chemical effect , by the controlled valence process , of lowering the positive charge (valence) on the iron atoms , that is , adding electrons to them , and into their 4p frontier orbitals . Referring to the VB sketch above , fluoride doping will add a third extra electron ; let's call it "z" . Ca2+ doping will have the effect of removing the "y" electron from the 4p AOs . That will still leave the extra Fe "x" electron in them . Kamihara et al. found that while the x+y (undoped) and the x (Ca2+) conditions failed to produce superconductivity , the x+y+z (F1-) combination was successful (Tc = 26 K) . In order to observe and indeed enhance superconductivity in the LaOFeAs family of compounds , additional electrons must be added to the planar layers of iron atoms in them , and into their 4p pi XO metallic bond .

A number of researchers in the late 1980s experimented with fluoride doping of ternary copper oxide compounds , with unverified claims of Tc enhancements of up to 155 K . Apparently there were problems with "mixed-phases" in these materials ; it seems the fluoride chemicals didn't blend in smoothly with their oxide counterparts , and complex mixtures were formed . Personally , I would choose cation doping to create new compounds , and avoid oxide/fluoride mixtures .

The lanthanum oxide layer in LaOFeAs acts as a chemical reducing agent to donate electrons to the iron layer : [La2+O2-] = [La3+O2-] + e- ----- + FeAs --------> [La3+O2-]1+ [FeAs]1- . Therefore , in order to add two additional extra electrons to the iron atoms , per formula unit , a tetravalent metal cation dopant should be used to form the "sandwich" composite .

Uranium(IV) oxide , UO2 (brown-black , m.p. 2500 ºC) , could be used to synthesize the compound UOFeAs , which should have three electrons in the iron atoms' 4p frontier orbitals :

½ UO2  + ½ U0  +  ½ Fe0  + ½ FeAs2  -------------> UOFeAs , i.e. [U(IV)O2-]2+ [FeAs]2- .  

(fuse a pellet of reaction mixture in an arc furnace under an argon atmosphere)

Uranium(IV) has a crystal ionic radius , per Shannon-Prewitt , of 1.00 Å (8-coordinate ; UO2 has the fluorite crystal structure , with 8-coordinated uranium atoms) . Uranium metal powder (m.p. 1132 ºC) and UO2 reagent are commercially available (Alfa-Aesar) . It's difficult to locate a commercial supplier of the precursor compound FeAs ; many researchers prepare it directly from the elements . As arsenic is a volatile , toxic substance I've instead suggested the use of one of its commercially available , non-volatile compounds , FeAs2 , as the arsenic source in the preparation of UOFeAs .

A second interesting possibility would be to use the strong reducing agent titanium monoxide [titanium(II) oxide , TiO] to add two extra electrons to the iron atom layers :

TiO +  ½ Fe0  + ½ FeAs2  -------------> TiOFeAs , i.e. [Ti(IV)O2-]2+ [FeAs]2- .

Titanium(II) oxide has been described as a golden yellow or bronze coloured solid , quite refractory (m.p. 1750 ºC) , which can be prepared from the reproportionation of titanium metal and titanium dioxide at very high temperatures . It is said to have a "defect rocksalt" crystal structure , and undoubtedly has M–M metal bonds , as does NbO (see the sketch of NbO below) . TiO is commercially available (eg. Alfa-Aesar ) as a very fine , 325 mesh powder . The best technique for reacting it with the iron and arsenic components would probably be the arc furnace method , as the reaction mix materials are very refractory in nature . A protective atmosphere of pure , dry argon is essential at all stages of the synthesis , as TiO and presumably the product TiOFeAs are strong reducing agents that would react rapidly with atmospheric oxygen (and probably moisture , as well) .

Arsenic is one of several non-metal elements that could form the iron-based anti-litharge layer in MOFeX compounds : phosphorus (which has already been used in LaOFeP , for example) , arsenic (which could be extended to analogue compounds) , antimony , and the three chalcogenide elements sulfur , selenium , and tellurium . These non-metal elements must be able to form a square pyramid dx2-y2sp3 hybrid AO in which they place all of their valence shell electrons . I mentioned near the beginning of this web page that FeSe had two known crystal structures , the nickel arsenide one (FeP sketch above) and the litharge one (I suspect that it is actually the anti-litharge structure) . This suggests that selenium can form the square pyramid structure . The lighter elements in the 2 s-p level such as B , N , C , etc. can't form the square pyramid hybrid AO because they don't have access to hypervalent d electrons and orbitals , or more generally , any additional orbitals to form a square pyramid hybrid AO required by the anti-litharge structure . There is no problem for the metal component ; tetrahedral hybrid orbitals , either d3s for the d-block Transition metals , or sp3 for the p-block elements , are readily accessible . For example , phosphorus can form the required hybrid orbital , while its neighbour silicon apparently can't . Sulfur is known to have the square pyramid coordination , with tetrahedral iron , in the mineral mackinawite (tetragonal FeS , anti-litharge structure) . Sulfur might be forced into this coordination in the "sandwich layer reaction", for example in the combination , TiO + FeS -----> [TiO]2+ [FeS]2-.

The square pyramid hybrid AO , with four bonding lobes , obliges the iron atoms to use four of their own valence electrons to complete the covalent Fe–X bonds . The X element may or may not donate an electron to the iron atom . Also , the ionic oxide layer will donate one or two electrons to the iron atoms' 4p frontier orbitals , creating a metallic bond pi XO in them . For each non-metal element a different and unique electronic configuration will be established for the iron atoms' XO . The following sketch illustrates several of these configurations :

In the example of the hypothetical compound LaOFeSe , selenium , as a 4 s-p element , has access to empty 4d AOs , one of which (the 4dx2-y2 AO) it can use with its 4s and 4p valence shell orbitals to form the sp3d hybrid AO for the required square pyramid geometry on the selenium atoms . This results in one less electron being relocated to the iron atom's 4p frontier orbitals than with the arsenic analogue . The prediction is that LaOFeSe and TiOFeSe would be metallic solids , but – disappointingly – not superconducting at any temperature .

The more promising compound in the sketch , TiOFeAs , would be interesting to compare with the less-electron-doped LaOFeAs . Similarly , the compound TiOFeP could prepared by fusing together equimolar quantities of TiO and FeP , and compared to the superconducting LaOFeP (Tc = 4 K) . Unfortunately , the chalcogenide analogues of LaOFeAs , while undoubtedly being metallic solids , don't appear to be as fruitful as superconductor candidates as their pnictide cousins , at least according to VB predictions . However , that might be disproved experimentally . Chemistry is full of surprises !

 

The Bilayer Metallic Bond

 

A key feature of high Tc superconductors is their bilayer metallic bond , among other important characteristics . The best way to define a bilayer bond is to describe one in actual practice . An excellent example of such a metallic bond can be found in rhenium trioxide :

Blue spheres : rhenium atoms ; red spheres : oxygen atoms .

Compare the electrical conductivities of rhenium trioxide and its parent metal element , rhenium :

rhenium metal : 58,140 ohm-1cm1 (ambient) ; superconductor at Tc = 2.4 K ; has the hexagonal close-packed (hcp) crystal structure .

rhenium trioxide : 149,300 ohm-1cm1 (ambient) ; doesn't become superconducting , even close to absolute zero .

At first glance these are astonishing figures . How is it possible for a metal oxide compound – especially one with a fairly "open" crystal structure like ReO3 – to have a higher electrical conductivity than its parent element , with very closely packed , all-metal atoms ? The answer lies in a comparison of the metallic bonds in both materials .

First , we recognize that the strong chemical bonds in ReO3 are covalent , not ionic . It's simply not possible to have a Re6+ cation in a crystal lattice (trivalent cations , such as Al3+ , are probably the limit) . Again using a VB analysis , and noting that Re(0) is 5d5 6s2 electronically , we can write :

The oxygens aren't oxide anions ; rather , they are covalent linking atoms having a linear sp hybrid AO (like the carbon atoms in acetylene , for example) . The octahedral rhenium hybrid AO lobes overlap with the oxygen linear AO lobes to form the ReO3 structure , with six Re–O covalent bonds per unit formula . However , rhenium(0) has an odd number of valence shell electrons , and the "leftover" seventh electron will be located in the rhenium 6p native , unhybridized AOs .

Because of the rectilineal geometry of the crystal structure , the rhenium 6py,z AOs and the oxygen 2py,z AOs , which are also unhybridized , can overlap continuously throughout the lattice . Note that the rhenium 6px orbitals have nothing to overlap with , as the oxygens' 2px AOs are used to form the linear spx hybrid AOs and so are unavailable . However , the 2py,z and 6py,z orbitals have the right shape , size , symmetry , and orientation to continuously overlap , but their energy levels are very different . The oxygen 2p electrons stay spin-paired in the lower energy levels of the composite p XO , while the rhenium 6p electrons stay as singlets in the higher energy levels of the XO . By definition , the Fermi level EF occurs at the boundary between the spin-paired electrons in the metallic bond (XO) and its higher energy level singlet electrons . Here's a sketch of the bilayer metallic bond in ReO3 :

A different situation occurs in rhenium metal . Its metallic bond will be formed by a continuous overlapping in the lattice of the Re 6 s-p native AOs , to form the s-p XO (some of rheniums' 6s2 electrons will "leak" into its 6p AOs) . However , these valence electrons will be energetically distributed in the XO by the Fermi-Dirac distribution , with the result that only about 1% or so of them will be located above EF . It is this relatively small population of energetic singlet electrons in the metallic bond that is responsible for its electrical conduction properties (and others , such as Pauli paramagnetism , metallic luster and colour , and heat capacity) .

We see from this simple analysis that the singlet electron population in the metallic bond of ReO3 will be much greater (maybe by almost 100 times) than that in the parent rhenium metal . The electrical conductivity , which is dependent on the number of charge carriers , is thus considerably higher in ReO3 than in Re . In the bilayer metallic bond the oxide layer and the metal layer remain more or less separate , like oil and water , because of their greatly different energies . The extra , leftover metal singlet electrons "float" in the upper layer above the lower level oxygen spin pairs .

Undoubtedly the same situation occurs in the high Tc cuprate superconductors , with their rectilinear Cu–O planes and the coppers' 3d9 electrons located in their 4pz AOs , which overlap with the oxygens' 2pz AOs . I don't have enough space in this web page for a fuller treatment of this topic , so I'll refer the interested reader to my ebook (pp. 190-195) for that . According to conventional superconductivity theory , an increase in the electron population above EF (density of states) should result in an increase in Tc , so that may at least partially explain the high transition temperatures of the cuprate superconductors .

Returning to LaOFeAs and related materials , we see that there is no participation by the arsenic , or other X linking atoms , in the metallic bond in the FeAs layers . The metallic bond is restricted to the planes of iron atoms , so there is no bilayer metallic bond in LaOFeAs and its analogues . We should realistically expect , therefore , that the Tcs for any compound or doped composite in this general class will never be as high as those for the cuprate superconductors . I'll propose , further down this web page , another series of iron-based superconductor candidates in which there could well be participation by the oxide anion components in the metallic bond , which consequently may be a bilayer bond . Before that , however , I'd like to briefly discuss another important characteristic of high Tc superconductors , that of the effect of antiferromagnetic ordering in their parent compounds .

 

Magnetic Polar Coupling , Antiferromagnetism , and Superconductivity

 

Researchers have long suspected an intimate link between superconductivity and magnetism . Hundreds of research papers have been published describing various magnetic aspects of superconductors . In the following section I'll present a remarkably simple picture of how singlet electrons above the Fermi level in a metallic bond can associate together in Cooper pairs . This fundamental mechanism is magnetic polar coupling , and is the electron equivalent of what we can see in our kitchens : two refrigerator magnets sticking together in a strong – and for me , still mysterious and awesome – magnetic bond .

Electrons inside matter have a magnetic spin property – possibly induced in them by the nuclei of their atomic kernels – which is manifested by their magnetic moments . That is , the electrons are behaving like tiny spherical magnets , surrounded by a magnetic field , with a north and south pole . Possibly electrons located outside matter , like static electricity electrons , don't have this magnetic spin , but just display their fundamental electrical charge . Because of the Pauli Exclusion Principle , atomic electrons all have a unique orientation with respect to each other , either "up" or "down". Pairs of electrons in covalent bonds , non-bonding lone (inert) pairs , and the Cooper pairs in superconductors , have an "up" electron and a "down" electron in the same orbital . The idea here is that the "up" and "down" electrons are stuck to each other like the macroscopic magnets of common experience . However , electrons universally also have an enveloping electrical field , with its fundamental electronic charge , which will cause two electrons to be repelled from one another . Is it possible for the attractive magnetic force , Fm , between a pair of "up" and "down" electrons to overcome the repulsive electrical force , Fe , between them ? Yes it is ! The following sketch shows the simple calculation involved :

That is , the attractive magnetic force Fm is almost 1200 times as strong as the repulsive electrical force Fe . However , the absolute value of these two forces must be extremely low , and of course their magnitude varies as the inverse square of the separation distance between the two electrons .

Magnetic polar coupling and the bilayer metallic bond provide clues to the differences between superconductivity in the "classical" BCS types of superconductors and the high Tc superconductors such as the cuprates . In the BCS types , we see that there is only a monolayer metallic bond , as there is in all the metallurgical metals . Their metallic bond electron energies are "crunched" in the Fermi-Dirac distribution , with only a small population of singlet electrons remaining above the Fermi level . These electrons are scattered across the metal crystal , with very long distances (coherence lengths) between them . The absolute values for the attractive magnetic force between any two of them must be virtually zero . The BCS mechanism of phonon-assisted coupling is required for the appearance of superconductivity in those metallic solids .

In materials with a bilayer metallic bond , the population of the singlet electrons is much greater than in the BCS metals , with neighbouring electrons above EF . This is where the orientation – "up" or "down" – of the singlets becomes critical . We saw above that the compound ReO3 has a bilayer metallic bond , yet it never becomes superconducting , even close to absolute zero . Rhenium trioxide exhibits the magnetism typical of most metallic solids , that of Pauli paramagnetism , caused by the combined magnetic moments of the unpaired singlet electrons above EF . The very fact that ReO3 has such a paramagnetism , and never becomes superconducting , shows that its singlets are virtually either all "up" or "down". The magnetic attractive force applies only to a set of "up" and "down" electrons , whose magnetic poles are oriented in the correct north-south and south-north positions . We now need some sort of mechanism to make the singlets assume alternating "up" and "down" orientations .......... antiferromagnetism !

In antiferromagnetic compounds the valence shell electrons are in a high spin (spin-free) condition , and are oriented , with respect to neighbouring atoms , in an alternating "up" and "down" pattern throughout the crystal lattice . As a result , the overall magnetic susceptibility of the material is considerably reduced from the value calculated for the compound if it was magnetically dilute (without internal magnetic interactions) . As the compound is warmed , its singlet electrons become more randomly oriented , which decreases its magnetic susceptibility (as in Curie paramagnetism) ; as it is cooled , the singlets become more and more alternately oriented , which again causes a decline in the magnetic susceptibility . The maximum susceptibility for the antiferromagnetic compound is observed at its Néel temperature , TN . In experiments with antiferromagnetic precursor superconductor candidate compounds , a high TN is desired , since below that temperature the singlets are in their alternating "up" and "down" pattern ; and – the key point here – this same antiferromagnetic régime is imposed on the singlet electrons above EF . In the following tabulation a list of antiferromagnetic compounds with fairly high TN values is presented :

One compound not found on the above list is La2CuO4 , which played a key role in the discovery of the high Tc cuprate superconductors . In their wide-ranging survey in the mid-1970s of the magnetic properties of various ternary copper oxide compounds , Arjomand and Machin noted that La2CuO4 had an anomalously low magnetic susceptibility :

"La2CuO4 has a very low magnetic susceptibility ........ which remains relatively constant over the temperature range 8–300 K . It is not clear why this behaviour occurs , unless there is a very strong antiferromagnetic interaction" (p. 1064) .

Ten years later Bednorz and Müller doped La2CuO4 , first with barium(2+) , to obtain a doped composite with a Tc of around 30 K , then shortly after with strontium(2+) to obtain an improved Tc = 38 K in the doped composite (La0.925 Sr0.075)2 CuO4 . Of course , La2CuO4 certainly is a strongly antiferromagnetic material , as are many Cu(II) oxide compounds , including CuO itself . La2CuO4 has a latent bilayer metallic bond , which can be – and was – activated by converting its homovalent copper(II) cations into mixed-valent copper(II–III) by doping . In Robin-Day Class II mixed-valent compounds the "extra" valence electrons can resonate throughout the lattice , hopping from cation to cation . In semiconductors , that's all they can do : hop back and forth . But in compounds with a true metallic bond (eg. the copper 4pz– oxygen 2pz p XO) the "extra" electrons are the singlet electrons above EF , and they can flow through the solid as an electrical current . AND they now have an antiferromagnetic "up" and "down" alternating orientation relative to one another , AND they are neighbouring valence electrons , with a relatively short coherence length :

“These new pairs [in the high Tc cuprates ] differ from BCS pairs [in the low Tc classical superconductors] in one respect at least : the distance between the charge carriers of each pair in the new superconductors is much shorter , by a factor of around 100" (G. Vidali , p. 137) .

The magnetic attractive force is strong enough at liquid nitrogen temperatures to permit a polar coupling between the "up" and "down" singlets above EF , with the formation of Cooper pairs . A bilayer metallic bond , and mixed-valent resonance and an antiferromagnetic ordering in its itinerant free electrons , are the three prerequisites for high Tc superconductivity in metallic solids :

Even in these optimized conditions in the mixed-valent cuprates the absolute value of the magnetic coupling force Fm must be extremely small , and as the superconductor is warmed eventually the phonon vibrations become too great , overwhelm it , and break up the Cooper pairs . There is undoubtedly an upper temperature limit to the magnetic polar coupling mechanism of high Tc superconductivity , and I suspect that researchers have arrived at or near it with the current record high Tc value of 138 K , set in 1995 for the mercury cuprate with the complex formula Hg0.8Tl0.2Ba2Ca2Cu3O8.33 . I believe that for genuine "high temperature superconductivity" – at STP and warmer – we'll need a third mechanism for the formation of Cooper pairs . I've speculated about such a third mechanism , and have written about two possible approaches to ambient superconductivity . In the first , I've proposed the synthesis of a new type of polymer that might fulfil the requirements , described by W.A. Little in 1964 , for his "excitonic mechanism" of Cooper pair formation . In the second approach to ambient superconductivity I've outlined the preparation of a hypothetical molecular metal in which a stable aromatic pair of electrons (like the p electron pairs in the benzene molecule) is promoted above the Fermi level into the s XO metallic bond of the crystal lattice .

 

Designing a Possible High Tc Superconducting Iron-based Antiperovskite

 

With the various attributes of high Tc superconductors discussed above in mind , I'll outline the design and synthesis of new iron-based compounds which might be superconducting in the liquid nitrogen range of temperatures . First , examining the list of antiferromagnetic compounds above , iron(II) oxide , FeO , is selected as the base structure . The suitable iron triad for Fe(II) is the reducing one , Fe1+– Fe2+ – Fe1+ , i.e. Fe2+(e-) – Fe2+ – Fe2+(e-) , mentioned near the top of this web page . We need to have a chalcogenide anion (sulfide , disulfide , selenide , or telluride) present in the compound , to ensure that the iron cations will be in their low spin configuration ; in FeO the oxides don't donate their electrons to the iron cations , which are high spin as a result . The chalcogenide anions , as chemical reducers , can donate charge to the Fe(II) cations and thus keep their valence shell electrons (3d6) spin paired , as explained above .

The compound could thus be Fe1+– Fe2+ – Fe1+ + oxide anion + chalcogenide anion , for example Fe3OX , where X is a chalcogenide anion (S2-, Se2-, Te2-, and possibly disulfide , S22-) . Such a compound could conceivably have the antiperovskite crystal structure :

Black spheres : iron(II) cations ; green spheres : oxide anions ; central yellow sphere : chalcogenide anion . The left model is the typical perovskite A-type structure . In the right model the oxides are shown as uncoordinated anions , while the chalcogenide anion forms some sort of covalent or coordinate covalent bond to the iron atoms , in order to feed charge into them .

The perovskite crystal structure , and its converse , the antiperovskite structure , are remarkably compact forms with tightly packed atoms in the extended atomic lattice . Assuming only ionic bonding in Fe3OX , we can calculate its tolerance factor "t" from the known values of the crystal ionic radii , per Shannon-Prewitt , of its component ions :

I've also calculated the tolerance factors for several other Transition metal analogues of Fe3OX . The sulfide values are on the low side , and could indicate some distortion of the structure away from the ideal cubic symmetry . The tolerance factors for the selenides and tellurides are in the cubic symmetry range of t = 0.89 to 1.00 .

Synthesis of Fe3OX and its analogues should be straightforward ; for example :

Fe0  +  FeO  +  FeS  --------------->  Fe3OS

(shake-‘n-bake in an argon atmosphere ,

or fuse a pellet of reaction mixture in an arc furnace)

Exothermic variation :

2 Zn0  +  ZnO  +  S0  --------------->  Zn3OS + heat

Reproportionation method :

7/3 Fe0  +  1/3 Fe2O3  +  Se0  -------------->  Fe3OSe + heat

The reagent iron(II) oxide is surprisingly expensive , so it might be possible to use the much cheaper iron(III) oxide , Fe2O3 , reproportionating its iron(III) with iron(0) to obtain Fe(1.33+) , as indicated above . The chalcogenide elements could be combined directly with the finely divided elementary metal to provide the FeX component in situ in an exothermic reaction . CAUTION : these reactions can sometimes be quite violent ; for example , the combination of zinc dust with flowers of sulfur can actually detonate ! The finer the particle size of reactant , usually the more reactive it is ; micron-sized metal powders can be spontaneously pyrophoric with atmospheric oxygen . So researchers should be very careful with M0 + X reactions ! However , they might be useful in fusing the reaction mixture together into a sintered lump , assisting in the diffusion of the atomic components . In an alternate technique more suitable for refractory solids , the reaction mixture – after a thorough grinding together in a mortar with a pestle – could be compressed into a pellet and melted into a button in an arc furnace , a method used in the preparation of the metallic compound niobium monoxide by the reproportionation of niobium metal with niobium pentoxide .

Since all these chemical systems are oxygen-sensitive , the reactions and products should be protected from the air by an inert gas blanket such as argon . Another procedure might be to carry out the reaction in an expendable crucible , eg. porcelain or fireclay , with a layer of inert powder such as alumina , Al2O3 , tamped down over the top of the reaction mixture :

After completion of the reaction , the crucible and its contents are cooled to room temperature , and the alumina is removed . The crucible is broken with a hammer blow , and the lumps of fused product (those uncontaminated by surface diffusion of the alumina) are recovered for further treatment , X-ray and chemical analysis , and physical testing .

Because the primary chemical bonding in the Fe3OX series is ionic and not covalent , a VB analysis of their electronic structure is inappropriate . The Crystal Field theory (CFT) is more suitable , although it produces results similar to what would be predicted by VB for a covalently bonded lattice . Each iron(II) cation is surrounded octahedrally by six anions (two oxides and four chalcogenides) . These anions energetically destabilize any of the irons' AOs that point directly at them , making those AOs unsuitable to receive the "extra" electrons in frontier orbitals . This situation is sketched below :

The empty 3dz2 and 4s AOs on the iron cations point at , and have the correct positive symmetry to overlap with the chalcogenides' ns2 AOs . They can form coordinate covalent Fe–X bonds through which charge can be transferred from the reducing chalcogenides to the iron cations . The empty 4pz AOs also point at the chalcogenide anion , but they have the wrong symmetry for Fe–X bond formation , and so are destabilized . The irons' 4d AOs (not shown on the sketch) are at roughly the same energy level as the 5 s-p AOs . Generally , d atomic orbitals are smaller and closer to the kernel than are s and p AOs . However , Fe3OX is a chemically reducing system . In reducers , the kernels try to push the "extra" electrons away from them (in oxidizers , the kernels try to pull them in) . Therefore , in the Fe3OX series the extra electrons are predicted to be located in the 5 s-p frontier AOs , which are further out from the kernels than the inner 4d AOs . These can overlap with the oxide anions' 2 s-p AOs to form a bilayer s-p XO , the anticipated metallic bond in the solid . In simpler terms , the octahedrally coordinating anions about the iron(II) cations have the effect of promoting the extra electrons from the 4 s-p AOs to the next level , the 5 s-p AOs . This is the same result as would be predicted for a covalently-bonded system , using an inner octahedral hybrid AO (d2sp3) . It's also the same sort of geometry and electronic configuration as with the low spin Fe2+ in iron pyrites , mentioned above .

A similar analysis can be applied to the Fe3OX analogues . In the cobalt case , Co2+ is 3d7 electronically, so the kernels will be Curie paramagnetic , which is fatal for superconductivity . The Co3OX compounds are predicted to be metallic solids which never become superconducting . For the nickel series , Ni2+ is 3d8 ; these cations can be spin-paired and diamagnetic . The Ni3OX compounds are predicted to be metallic and possibly high Tc superconductors . The zinc antiperovskites , assuming they can be formed , are somewhat different from the iron , cobalt , and nickel series . The base compound , zinc oxide , is diamagnetic . The Zn3OX series could provide some confirmation of the role of antiferromagnetism , and the magnetic polar coupling mechanism , in high Tc superconductivity . With no antiferromagnetism to align the metallic bond free electrons in an alternating antiparallel oriention , we wouldn't expect to observe a high Tc in the Zn3OX series . These zinc compounds should be metallic , but will require deep cryogenic cooling to become superconducting . Rosenberg has commented ,

 “The list of compounds which become antiferromagnetic , however , is very large , as most paramagnetic substances become antiferromagnetic at a sufficiently low temperature” (p. 204) .

The Zn3OX compounds would have the benefit of a bilayer metallic bond , and would be Robin-Day Class II mixed-valent compounds , so they have a good chance of becoming superconducting , but not in the liquid nitrogen range (my guesstimate is the 20–40 K range) .

The selenide compounds would be especially interesting . Two independent studies demonstrated that the selenide anion can induce antiferromagnetism in neighboring transition metal cations :

 “ …… Se substitution [in CoS2] introduces strong antiferromagnetic interactions between cobalt atoms” (Johnson and Wold , p. 216) .

 Adachi , Sato , and Takeda found that while CoS2 is ferromagnetic , CoSe2 is antiferromagnetic . They concluded that “….. selenides are more metallic than sulfides in the nickel and cobalt dichalcogenides with pyrite structure” (p. 637) . This may have assisted FeSe in becoming superconducting at 8 K . The selenium in Zn3OSe might help to boost its Tc somewhat .

Synthesis and study of the hypothetical oxide-chalcogenide antiperovskites M3OX ( M = Fe , Co , Ni , and Zn ; X = S , Se , Te , and maybe S22-) would be beneficial in advancing our understanding of high Tc superconductivity , and in expanding the horizons of this important field of study in solid state science .

 

A Brief Note on the Antiperovskite MgCNi3

 

The metallic compound MgCNi3 was first synthesized and studied in 2001 by R.J. Cava's research group at Princeton University . Its ambient electrical conductivity was found to be about 11,000 ohm-1cm-1, increasing smoothly to 26,300 ohm-1cm-1 at 8 K , at which point it abruptly became superconducting . It has an antiperovskite crystal structure , and at first glance it seems to resemble the proposed oxide-chalcogenide compounds , M3OX , discussed above . However , its chemical bonding is undoubtedly quite different than theirs . In the Ni3OX antiperovskites , the nickel component would be present as nickel cation , Ni2+ , while (I propose) the nickel in MgCNi3 is covalently bonded in the form of octahedron "metal cages" :

Because the carbon atoms are octahedrally coordinated by the nickel atoms , they must be spherical anions nested in the structure's cavities (carbon has only four valence shell orbitals and so can't form a hybrid AO with six positive symmetry bonding lobes) . The magnesium cation , Mg2+ , balances the negative charge on the C2- anion . The zerovalent nickel atoms form the octahedron "metal cages" , surrounded by the magnesium cations :

Small blue spheres : nickel atoms ; violet spheres : carbide anions ; large aqua spheres : magnesium cations . Similar octahedron metal cage structures are well-known in Transition metal chemistry , for example that of the metallic compound niobium monoxide , NbO (red spheres , niobium) :

Formation of the octahedron nickel cages in MgCNi3 with their covalent NiNi bonds has the effect of promoting the nickel(0) 4s2 valence electrons to the next energy level , the 5 s-p AOs . While unable to form six covalent s CNi bonds , the carbide anions' 2 s-p AOs can overlap with nickels' 5 s-p AOs to form a s-p XO , which is predicted to be the bilayer metallic bond in MgCNi3 . However , the compound is homovalent and lacks an antiferromagnetic ordering (both like ReO3) , so it's not surprising that its Tc is so low . As an interesting variation , I would suggest the combination of nickel and MgO in an attempt to reproduce the compound , but substituting oxide for the carbide :

MgO (m.p. 2852 ºC) + 3 Ni0 (m.p. 1453 ºC) -------------> MgONi3

Given the refractory nature of the reactants , the arc furnace technique would seem to be the most appropriate synthetic method to try in this case . MgONi3 has a NiO base which might induce an antiferromagnetic ordering into its metallic bond free electrons and so help to raise its Tc . Because of the metal cage structure , doping would be problematic . One possibility might be to synthesize the MgOCo3 and MgOFe3 analogues , with one less and two less free electrons than MgONi3 , respectively . The substrate MgOCo3 (one extra electron) would be doped with increasing mole fractions of the "empty" dopant , MgOFe3 :

x MgOCo3 + (1-x) MgOFe3 --------------> MgOCo3xFe3-3x (x = 1 to 0)

This doping procedure should have the effect of introducing "holes" (vacancies) into the cobalt substrate's s-p XO . That should help to raise its Tc a little more . The chalcogenide anions could also be tried (MgS is commercially available - Alfa-Aesar - but apparently not MgSe and MgTe ; they would have to be synthesized by the researcher . ZnO/S/Se/Te and CdO/S/Se/Te , all commercially available , and with covalent rather than ionic bonding , might also be tried in place of MgO) . As noted above , selenide anion seems to induce antiferromagnetism in Transition metal cations , for example in CoSe2 . It might do so again in the antiperovskite MgSeCo3 and its doped composites . These new variations of MgCNi3 would be very interesting to synthesize and study , as they could provide yet more confirming evidence for the picture of high Tc superconductivity presented above .

I would also like to mention in passing a third type of Ni3OX compound that might be a high Tc superconductor : this is where X = O , that is , a second oxide . In this case the compound Ni3O2 might have the anticorundum crystal structure :

Small blue spheres : Ni2+ cations (square planar coordination) ; larger green spheres : oxide anions (octahedral coordination) . This molecular model is based on a sketch of the corundum crystal structure in Cox's textbook , but is its "converse", of course . NiO bonds (black lines) are shown for clarity , to highlight the coordinations , but the strong bonding in the compound would be entirely ionic and not covalent . The extra electrons in the Ni1+–Ni2+–Ni1+ triad in Ni3O2 should be located in their 4pz AOs , which can overlap with the oxides' 2pz AOs to form a bilayer p XO (this system is isoelectronic with YBCO , but is reducing , not oxidizing) :

Ni3O2 would be a Robin-Day Class II mixed-valent compound , and should have an antiferromagnetic ordering (from the base NiO) in its metallic bond mobile free electrons . These are all positive indicators for high Tc superconductivity in a suitably cooled sample of the material . Its nickel(1.33+) might be prepared by the reproportionation of nickel(0) and nickel(II) :

Ni0 (m.p. 1453 ºC) + 2 NiO (m.p. 1984 ºC) ----------------> Ni3O2

As the reactants are quite refractory , the arc furnace method with a protective argon atmosphere would probably be the best synthesis technique for this reaction , as with NbO . Chalcogenide analogues might also be prepared using the commercially-available (Alfa-Aesar) NiS , NiSe , and NiTe . It would be a most interesting project !

 

References and Notes

 

LaOFeP : Y. Kamihara et al. , Iron-based Layered Superconductor : LaOFeP, J. Amer. Chem. Soc. 128 (31) , pp. 10012-10013 (2006) .

LaOFeAs : Y. Kamihara , T. Watanabe , M. Hirano , and H. Hosono , Iron-Based Layered Superconductor La[O1-xFx]FeAs (x = 0.05–0.12) with Tc = 26 K”, J. Amer. Chem. Soc. 130 (11) , pp. 3296-3297 (2008) .

A.F. Wells : A.F. Wells , Structural Inorganic Chemistry , 3rd ed. , Clarendon Press , Oxford (UK) , 1962 . The sulfides , selenides , and tellurides of iron , cobalt , and nickel mostly have the nickel arsenide structure (Fig. 168 , p. 514) . FeSe can also have the litharge (PbO) structure (Fig. 160 , p. 477) .

upper limit : T.P. Sheahen , Introduction to High Temperature Superconductivity , Plenum Press , New York , 1994 ; see section 7.1 , pp. 117-119 , “Why It was Impossible”, for a discussion of the fallacy of the 30 K upper limit for the transition temperatures of superconductors . “By their discovery , Bednorz and Müller proved again that experiment always prevails over theory” [p. 119 ; my emphasis : an invaluable lesson !] .

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 . The Robin-Day classification of mixed-valent compounds is also discussed , with examples and illustrations , in my web page , “New Solar Cells from Mixed-Valent Metallic Compounds.

potassium ferrocyanide : F.A. Cotton , G. Wilkinson , and P.L. Gaus , Basic Inorganic Chemistry , 3rd ed. , John Wiley , New York , 1995 ; p. 566 .

ferrocene : G. Wilkinson , M. Rosenblum , M.C. Whiting , and R.B. Woodward , “The Structure of Iron Bis-Cyclopentadienyl”, J. Amer. Chem. Soc. 74 (8) , pp. 2125-2126 (1952) . Its magnetic susceptibility is cmol = – 125 x 10-6 cgsu at ambient temperature .

iron pyrites : H. Haraldsen and W. Klemm , “Magnetochemical Investigations . XV . The Magnetic Behaviour of Some Sulfides of Pyrites Structure”, Chem. Abs. 29 , 71365 (1935) ; L. Néel and R. Benoit , “Magnetic Properties of Certain Disulfides”, Chem. Abs. 48 , 3084c (1954) . “FeS2 is practically diamagnetic” ;  A. Wold and K. Dwight , Solid State Chemistry , Synthesis , Structure , and Properties of Selected Oxides and Sulfides , Chapman and Hall , New York , 1993 ; “3d Transition Metal Disulfides with the Pyrite Structure”, pp. 179-182 . “FeS2 is a diamagnetic semiconductor”, p. 180 .

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 . FeP is antiferromagnetic , with TN = 123 K . 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 .

Ng and Zuckerman : S.-W. Ng and J.J. Zuckerman , “Where are the Lone-Pair Electrons in Subvalent Fourth Group Compounds ? ”, Adv. Inorg. Chem. Radiochem. 29 , pp. 297-325 , H.J. Emeléus and H.G. Sharpe (eds.) , Academic Press , Orlando (FL) , 1985 .

Pauling : 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) .

other contributors : For example , G.E. Kimball , Directed Valence, J. Chem. Phys. 8 (2) , pp. 188-198 (1940) ; for a comprehensive list of VB hybrid orbitals , see Table XXIV , p. 198 . A similar list is provided by R.T. Sanderson , Inorganic Chemistry , Reinhold Publishing , New York , 1967 ; Table 8-2 , “Directional Characteristics of Some Valence Orbitals”, p. 112 .

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 .

strong overlapping : It was generally thought for a long time that the formation of p-p p MOs was restricted to the 2 s-p valence shell elements , and possibly also silicon , sulfur and phosphorus . In the last several decades theorists have extended the concept of p MOs to heavier elements ; for example : R. Hoffmann , J. Li , and R.A. Wheeler , “YCoC : A Simple Organometallic Polymer with Strong Co–C p Bonding”, J. Amer. Chem. Soc. 109 (22) , pp. 6600-6602 (1987) . In certain Transition metal elements quadruple bonds are thought to occur , formed by the overlapping of native d orbitals (one of the quadruple bonds is the interesting delta bond , created by the side-by-side overlapping of two 4dxy AOs , for example in the dimeric compound molybdenum diacetate) . The d AOs are smaller than the corresponding p AOs ; so if 4d AOs can form delta bonds , surely 4p AOs can form p MOs and XOs .

KCP : 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) ;   K. Krogmann , “Planar Complexes Containing Metal-Metal Bonds”, Angew. Chem. Internat. Ed. Engl. 8 (1) , pp. 35-42 (1969) ; A.J. Epstein and J.S. Miller , “Linear Chain Conductors”, Scientific American 241 (4) , pp. 52-61 (October , 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 .

fluoride doping : S.R. Ovshinsky et al. , “Superconductivity at 155 K”, Phys. Rev. Lett. 58 (24) , pp. 2579-2581 (1987) ; M. Xian-Ren et al. , “Zero Resistance at 148.5 K in Fluorine Implanted Y-Ba-Cu-O Compound”, Solid State Commun. 64 (3) , pp. 325-326 (1987) ; K. Fukushima , H. Kurayasu , T. Tanaka , and S. Watanabe , “The Influence of Fluorine Addition on the Crystal Structure and Electrical Properties of a YBa2Cu3O7-d Oxide Superconductor”, Jpn. J. Appl. Phys. 28 (9) , pp. L1533-L1536 (1989) ; C.H. Chen et al. , “Superlattice Modulation and Superconductivity in the Electron-Doped Nd2CuO4-xFx and Nd2-xCexCuO4 Systems”, Physica C 160 (3&4) , pp. 375-380 (1989) .

arc furnace : 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 . The button might also be fused simply by arc-welding it (a knowledgeable arc welder from a local metal fabrication shop might be employed for this) in an argon atmosphere .

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

Fermi-Dirac distribution : A.R. Mackintosh , “The Fermi Surface of Metals”, Scientific American 209 (1) , pp. 110-120 (July , 1963) .

only about 1% : 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) .

Arjomand and Machin : M. Arjomand and D. Machin , “Oxide Chemistry . Part II . Ternary Oxides Containing Copper in Oxidation States-I , -II , -III , and -IV”, J. Chem. Soc. Dalton Trans. 1975 (11) , pp. 1061-1066 .

with barium(2+) : J.G. Bednorz and K.A. Müller , “Possible High Tc Superconductivity in the Ba-La-Cu-O System”, Z. Phys. B64 (2) , pp. 189-193 (1986) .

with strontium(2+) : J.G. Bednorz , K.A. Müller , and M. Takashige , “Superconductivity in Alkaline Earth-Substituted La2CuO4-y”, Science 236 (4797) , pp. 73-75 (April , 1987) . The following report was published three months earlier : R.J. Cava , R.B. van Dover , B. Batlogg , and E.A. Reitman , “Bulk Superconductivity at 36 K in La1.8Sr0.2CuO4”, Phys. Rev. Lett. 58 (4) , pp. 408-410 (January , 1987) .

semiconductors : O. Berkooz , M. Malamud , and S. Shtrikman , “Observation of Electron Hopping in 151Eu3S4 by Mössbauer Spectroscopy”, Solid State Commun. 6 (3) , pp. 185-188 (1968) . A beautiful demonstration of a hopping semiconductor ! Eu3S4 [with Eu3+Eu2+Eu3+] is a Robin-Day Class II mixed-valent compound , but apparently lacks a suitable overlapping of its valence electron orbitals to form a true metallic bond . Its 4f7 valence electron (formally on the Eu2+) can hop over the sulfide anion to a neighbouring Eu3+ cation , but no further . This hopping is a thermally-dependent process , so that when Eu3S4 is cooled , the 4f7 electrons gradually become localized ("pinned") on their parent Eu2+ kernels , which is clearly shown by Mössbauer spectroscopy .

electrical current : YBCO is a true metal , with an inverse temperatureelectrical conductivity relationship , typical of all the metallurgical metals . Its electrical conductivity at room temperature is about 500 ohm-1cm-1 : C.P. Poole , Jr. , T. Datta , and H.A. Farach , Copper Oxide Superconductors , John Wiley , New York , 1988 ; Table X-1 , p. 198 .

G. Vidali : G. Vidali , Superconductivity : The Next Revolution ? , Cambridge University Press , Cambridge (UK) , 1993 .

mercury cuprate : P. Dai et al. , “Synthesis and Neutron Powder Diffraction Study of the Superconductor HgBa2Ca2Cu3O8 by Tl Substitution”, Physica C 243 (3&4) , pp. 201-206 (1995) .

W.A. Little : W.A. Little , “Possibility of Synthesizing an Organic Superconductor”, Phys. Rev. 134 (6A) , pp. A1416-A1424 (1964) ; idem , “Superconductivity at Room Temperature”, Scientific American 212 (2) , pp. 21-27 (February 1965) ; idem , “The Exciton Mechanism in Superconductivity”, pp. 17-26 in W.A. Little (ed.) , Proceedings of the International Conference on Organic Superconductors , J. Polymer Sci. , Part C , Polymer Symposia 29 , Interscience , New York , 1970 ; p. 26 .

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 .

tolerance factor : U. Müller , Inorganic Structural Chemistry , John Wiley , Chichester (UK) , 1993 , p. 200 ; A.F. Wells (see above) , p. 497 . It's also mentioned in the WolfWikis "Perovskite" web page cited immediately above (the formula is generally known as the Goldschmidt equation) .

detonate : J.R. Partington , A Textbook of Inorganic Chemistry , 6th edition , Macmillan , London (UK) 1957 ; p. 783 ;  see also C.A. Jacobson and C.A. Hampel , Encyclopedia of Chemical Reactions , Vol. 8 , Reinhold Publishing , New York , 1959 ; p. 183 .

same energy level : F. Basolo and R.C. Johnson , Coordination Chemistry , The Chemistry of Metal Complexes , W.A. Benjamin , New York , 1964 ; Figure 2-1 , p. 28 . This energy level diagram can be found in many inorganic chemistry textbooks in various forms .

Rosenberg : H.M. Rosenberg , The Solid State , Clarendon Press , Oxford (UK) , 1975 .

Johnson and Wold : V. Johnson and A. Wold , “Crystal Growth and Magnetic Properties of Compositions in the CoS2 : CoSe2 System”, J. Solid State Chem. 2 (2) , pp. 209-217 (1970) .

Adachi , Sato , and Takeda : K. Adachi , K. Sato , and M. Takeda , “Magnetic Properties of Cobalt and Nickel Dichalcogenide Compounds with Pyrite Structure”, J. Phys. Soc. Japan 36 (3) , pp. 631-638 (1969) .

metal cage : The NbO molecular model was based on the sketch of NbO in Krebs's excellent textbook : H. Krebs , Fundamentals of Inorganic Crystal Chemistry , transl. by P.H.L. Walter , McGraw-Hill , London (UK) , 1968 ; Fig. 14.14 , p. 191 . See also 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 . Sketches of similar-looking octahedron metal cage compounds are shown in Pauling's textbook (see above) : p. 440 , Fig. 11-16 , [Mo6Cl8]4+ ; Fig. 11-17 , [Ta6Cl12]2+. Niobium carbide , NbC (Tc = 10.3 K) , seems to have the rocksalt crystal structure : R. Hoffmann , “Carbides”, American Scientist 90 (4) , pp. 318-320 (July-August , 2002) ; Figure 2 , p. 319 . However , as with MgCNi3 , its carbon atoms are bonded to the enclosing niobium octahedron cages , not by s covalent NbC bonds , but by the s-p XO metallic bond in which it participates .

Cox : P.A. Cox , Transition Metal Oxides , An Introduction to Their Electronic Structure and Properties , Clarendon Press , Oxford (UK) , 1995 ; Fig. 1.7(b) , p. 20 .

 

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