Antiferromagnetic Induction in High Temperature Superconductors

 

While superconductors are fascinating materials to study , they are very practical , too ; think of the Magnetic Resonance Imaging (MRI) machines in hospitals , so invaluable in medical diagnostics . MRIs have large coils of a superconducting intermetallic compound made of niobium and titanium (Nb0.6Ti0.4 ; Tc = 9.8 K) , or of niobium and tin (Nb3Sn ; Tc = 18 K) , immersed in a bath of ultracold (4.2 K) liquid helium . These superconducting coils generate the intense magnetic fields required to completely permeate the human body .

Scientists study superconductors in many ways . Most of the research with superconductors is carried out by condensed matter physicists , who examine their many varied properties . Crystallographers determine their crystal structures . Materials scientists and technologists develop practical applications for superconductors ; for example , how the brittle , poorly malleable and ductile intermetallics NbTi and Nb3Sn can be formed into wires used for superconduction .

The preparation of superconductors is done by solid state chemists , who also try to devise new chemical compounds that might have that property . That's where the problem arises . There are no chemical theories or models of superconductivity , as it's considered to be a physical and not a chemical phenomenon . The long-reigning BCS theory (from Bardeen , Cooper , and Schrieffer) , is a lengthy mathematical treatise that makes no mention of chemistry or of any chemical substances (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) . However , all superconductors – and “ordinary” electrical conductors , of course – are elements and chemical compounds which can be described in chemistry terms . How

can we associate the physical phenomenon of superconductivity with the chemical description of the materials in which it occurs ?

The earliest attempt to correlate superconductivity with the chemical attributes of superconductors was made by B. T. Matthias , who in the mid to late 1950s proposed several guidelines (now generally referred to as Matthias's Rules) for optimizing the superconducting transition temperature , Tc , in alloys of elements and in binary intermetallic compounds . At that time the superconductors with the highest Tc values , and consequently of greatest research interest , were intermetallic compounds with the general formula M3X and having the A15 , or beta-tungsten crystal structure :

The A15 (beta-tungsten) crystal structure for an M3X intermetallic compound . Red spheres : M atoms ; blue spheres : X atoms . Examples : Nb3Sn (see above) , Nb3Ge , V3Si . This molecular model is based on the sketch of the A15 structure in Simon and

Smith's book .

Matthias observed that the higher Tc A15 superconductors always had a Transition metal element as the M atom (d shell valence electrons were involved) , and the optimum average number of valence electrons per atom per formula unit was a maximum of five or seven . In later years and decades researchers refined and broadened Matthias's Rules , but never succeeded in extending them to ternary and quaternary compounds (the high Tc cuprate superconductors , for example) . The highest Tc ~ 22 K for an M3X A15 intermetallic compound (and for superconductors generally) was achieved for Nb3Ge films in 1973 , and that record stood until 1986–87 with the discovery of the cuprate family of superconductors .

A second approach to explaining superconductivity in chemical , rather than in physical terms was made in the mid 1970s by the German solid state chemist Heinz

Krebs (University of Stuttgart) . He attempted to correlate the appearance of superconductivity in solids with the types of atomic orbitals in which the conduction electrons were located . Krebs summed up his findings as follows :

“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”.

Krebs seems to have been one of the few scientists to study the electronic structures of nonmolecular solids and superconductors from an orbital point of view . Unfortunately , his concepts apparently were ignored at the time and forgotten (except by me) . Recently , his rule about nodes in metallic bond orbitals has been overturned by the remarkable discovery of an ephemeral superconductivity in heavily-doped (with boron) semiconductors such as diamond , silicon (PDF , 507 KB) , and silicon carbide (PDF , 1480 KB) . However , his nodal principle still remains valid for metallic solids and electrical conduction in general ; I refer to it as Krebs's Theorem , and have restated it for the metallic bond this way :

“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”.

As is well known , Cooper pairs in superconductors have the surprising ability to tunnel through thin layers of electrical insulators (the Josephson effect and the Josephson junction) . They are thus able to tunnel through the periodic nodes in the XOs of semiconductors (XO = crystal orbital = metallic bond = conduction band) in an energy-free manner , unlike the singlet conduction electrons in semiconductors in the normal state . Superconductors can thereby circumvent Krebs's Theorem , which nevertheless remains valid for “normal” electrical conductors . I've discussed these orbital concepts of the metallic bond , and various types of metallic solids , in another Chemexplore web page , “A New Classification of Metallic Solids”, to which the interested reader is referred .

I think it's safe to say that up to now , all of the known “synthetic” (chemical compounds , not elements , which are “natural”) superconductors have been discovered in a serendipitous manner . Serendipity is a lucky or unexpected discovery , and it often plays an important role in scientific research . Someone will produce a material that has an extraordinary property that makes it of great interest .

That material is then widely studied , and usually many of its analogues are prepared and examined . I believe this is true for every new type of superconductor discovered so far . None were designed and synthesized from first principles , simply because there are no first principles , in the chemical sense , for superconductors . In scientific philosopic terms , Matthias's Rules and Krebs's Theorem are inductive (deriving a general law from specific examples) ; they followed from a study and classification of existing materials , which were obtained from serendipitous discoveries . What is needed is a deductive model (a predictive law , from which specific examples are derived) , one that is based on a broader approach to understanding the phenomenon . Combining basic physical and chemical concepts , an entirely new model is constructed , from which novel superconductor candidate compounds can be designed , synthesized , and tested . The results from these predictions can then be used to refine and extend the model , or to refute it . If the model is successful , scientists will no longer have to rely on serendipity to obtain a fresh supply of new superconducting materials for their research . The objective of this web page is to bring forward such a deductive model of high temperature superconductors and from it make several predictions for the design and synthesis of new high Tc compounds .

 

The Antiferromagnetic Model of High Temperature Superconductors

 

I began studying superconductors in 1990 after reading about the new high Tc cuprates in the popular press , but quickly became frustrated with the total lack of any sort of chemical explanation for them . What chemistry there was of the cuprate materials merely involved chemical “cooking”, without any significant theoretical input from chemists . As mentioned above , the dominant BCS theory was purely mathematical and completely divorced from the actual chemical materials (elements and compounds) comprising the various superconductors .

The high Tc cuprates provided two important clues about their physical and chemical natures , and how they could be linked together . The first clue was the antiferromagnetism in the copper oxide precursors . The key ingredient in synthesizing all of the cuprates is copper(II) oxide , CuO , a jet black , refractory (m.p. 1326 ºC) solid which is known to be antiferromagnetic (TN = 230 K , – 43 ºC) . This antiferromagnetism was often retained when CuO was chemically combined with one or more other compounds to form more complex cuprates , such as La2CuO4 .

The copper(II) in La2CuO4 is 3d9 electronically , so it will have at least one unpaired singlet valence electron . According to the simple equation for calculating the spin-only magnetic moment for n unpaired electrons , = [n (n+2)] ½ , the ninth singlet electron in La2CuO4 should produce in it a magnetic moment of 1.73 BM (Bohr magnetons) . However , Arjomand and Machin measured a much lower magnetic moment for the compound : 0.69 BM at room temperature (300 K) , and 0.34 BM at liquid nitrogen temperature (80 K) . These results suggested that La2CuO4 is indeed strongly antiferromagnetic , even at room temperature . Many subsequent studies of it confirmed these early findings and provided much more information about La2CuO4 .

Lanthanum copper(II) oxide is non-metallic , but it can be converted by the chemical

process of oxidative doping into a metallic solid . When La2CuO4 is doped with Ba2+ cations (i.e. replacing some of the La3+ with Ba2+) , an equivalent amount of Cu2+ must be oxidized to Cu3+ in order to maintain electrical neutrality in the system . Thus , the doping process created a copper(II)–copper(III) mixed-valent compound which proved to be metallic . The German-Swiss researchers Bednorz and Müller discovered in 1986 that this barium-doped La2CuO4 was superconducting at a new record high temperature of around 30 K . Several months later , by substituting smaller Sr2+ cations for the larger Ba2+ , they prepared the analogous cuprate (La0.925 Sr0.075)2 CuO4 , whose Tc was somewhat higher , at 38 K .

In the Spring of 1987 the combined Chu and Wu research teams announced their synthesis and study of YBCO , the first liquid nitrogen range cuprate superconductor (Tc ~ 93 K) . Their discovery began a frantic search for more high temperature superconducting cuprates with even higher transition temperatures . YBCO is also a copper(II)–copper(III) mixed-valent compound with the ideal empirical formula YBa2Cu3O7 . Its Cu(II)–Cu(III) can be quickly seen by displaying YBCO's “valence counting formula” : (Y3+ Ba2+ Ba2+)(Cu2+ Cu3+ Cu2+)(O2-)7 . It's interesting to note in this regard that Arjomand and Machin prepared the two pure , homovalent precursors to YBCO , BaCuO2 and YCuO3 , back in 1975 . They found the former compound to be – astonishingly ! – ferromagnetic , and the latter material had high spin octahedral Cu3+, that while paramagnetic , became mildly antiferromagnetic when cooled to 80 K . However , YBCO has a completely different crystal structure than either BaCuO2 and YCuO3 , with radically different magnetic and electrical properties than them .

All of the high Tc superconductors were found to have mixed-valent metal cations (mostly Cu2+ and Cu3+) , and that provided the second important clue – the “chemistry” one – about high temperature superconductivity . Before reviewing the role of mixed-valent chemistry , though , I'll first outline the significance of the “physics” clue , that of antiferromagnetism .

The Transition metals and their compounds display a wide range of magnetic properties such as Curie paramagnetism , Pauli paramagnetism , ferromagnetism , ferrimagnetism , and antiferromagnetism , to name five of the commoner magnetic ordering states in the solids . Such conditions are produced by the valence shell d orbital electrons in the metal atoms and their cations . The second type of magnetism , Pauli paramagnetism , is produced by the spins of the mobile , free electrons above the Fermi level EF in the metallic bond . Strong ferromagnetism in metals such as iron , cobalt , and nickel is associated with the magnets of everyday experience , although a weaker ferromagnetism can also be found in certain Transition metal compounds such as chromium dioxide .

All electrical conductors and superconductors are metallic solids , having a metallic bond (or conduction band , for the physicists) throughout their lattice . In any one given sample of a metallic solid there is a single metallic bond , comprised of continuously overlapping atomic orbitals , which form one single lattice-wide crystal orbital , XO , containing the valence shell electrons associated with the metallic bond . The Fermi-Dirac distribution assigns these electrons to a vast number of energy levels corresponding to the number of participating metal atoms , pairing them two by two according to the Pauli exclusion principle . In most common metals , about 99% of the electrons in the metallic bond are thus spin-paired at room temperature , while about 1% of them remain as unpaired singlets in higher energy levels . The boundary between the paired and unpaired electrons in the XO is the Fermi level , EF . The unpaired electrons above EF are the free , mobile electrons that are responsible for all the properties so typical of the metallic solids : electrical conduction and superconduction , high thermal conduction , metallic luster (high reflectivity) , metallic colours , opacity , and Pauli paramagnetism , as noted above .

While it's the mobile singlet electrons above EF that are the electrical charge and energy carriers in ordinary conductors , it's pairs of electrons – the famous Cooper pairs – that are the electrical carriers in superconductors . The electrons in the Cooper pairs are spin-paired , that is , their magnetic spins have an antiparallel orientation , in a manner similar to the spin-paired electrons in the atomic kernels and in the covalent bond , for example . At first glance , it would seem that the static electric field around the electrons would cause them to be repelled from one another . However , a simple calculation involving High School physics (Coulomb's Laws of Electric Force and Magnetic Force) shows that the magnetic field around the electrons , derived from their spins , is much stronger than the corresponding electric field :

Coulomb's Law of Electric Force is simple and straightforward , and is in all of the physics textbooks I reviewed on the subject . However , Coulomb's Law of Magnetic Force is by comparison little known . It turns out that the force relationship between two (macroscopic) magnets is rather complex , and the equation for the magnetic force used above is a simplification , as explained in the competent Wikipedia article , “Magnetic Field” :

“The force between two magnets is quite complicated and depends on the orientation of both magnets and the distance of the magnets relative to each other . The force is particularly sensitive to rotations of the magnets due to magnetic torque .

 In many cases , the force and the torque on a magnet can be modeled quite well by assuming a “magnetic charge” at the poles of each magnet and using a magnetic

equivalent to Coulomb's law . In this model , each magnetic pole is a source of an H-field that is stronger near the pole . An external H-field exerts a force in the direction of H on a north pole and opposite to H on a south pole . In a nonuniform magnetic field , each pole sees a different field and is subject to a different force . The difference in the two forces moves the magnet in the direction of increasing magnetic field and may also cause a net torque .

 Unfortunately, the idea of “poles” does not accurately reflect what happens inside a magnet (see ferromagnetism) . For instance , a small magnet placed inside of a larger magnet feels a force in the opposite direction . The more physically correct description of magnetism involves atomic sized loops of current distributed throughout the magnet” .

A magnetic force equation , more complicated than that of Coulomb's Law , is provided in another Wikipedia article , “Magnetic Moment”. The discussion of magnetic force in these two Wikipedia articles is more relevant to the macroscopic (eg. bar and horseshoe) magnets of of our common experience . Keep in mind that the electrons in a Cooper pair are the simplest , smallest , and most fundamental magnets that can exist ; in fact , their magnetic pole strength (magnetic flux) is considered to be the quantum unit and is called the “fluxoid” (2.0678 x 10-15 weber) . Also , in Cooper pairs the two electrons are locked into a perfectly antiparallel orientation to each other , so there is no magnetic torque between them . In such a simple , elementary situation I believe Coulomb's Law of Magnetic Force can be correctly applied to derive a reasonably accurate comparison – the Fm / Fe ratio – of the magnetic and electric forces between the two electrons .

The critical requirement is that the two electrons are in an antiparallel orientation to each other in order for the magnetic field force to surpass that of the electric field . That being the case , the two electrons can associate with each other in the Cooper pair . In fact , the Fm / Fe ratio may be double that indicated in the calculation above , which applies to a single set of magnetic poles :

I'm speculating here , but possibly the Fm / Fe ~ 2400 case might apply to Cooper pairs below Tc , while at Tc the magnetic spins reorient to the weaker Fm / Fe ~ 1200 case . Then , as the Cooper pairs scatter off lattice atoms , their magnetic spins interact with those of neighbouring lattice atom electrons , and the pairs are torn apart :

Another possibility might be the thermal promotion by energy packets (kT) of the antiparallel electrons into singlet electrons with a parallel orientation , which forces them apart and breaks up the Cooper pairs :

The Fm / Fe ratio , which is overwhelmingly favourable for the attractive magnetic fields about antiparallel electrons , might also explain pairing of electrons in other environments , such as in the atomic orbitals of the kernels (hence a rationale for the Pauli exclusion principle) and as a minor contributor to the strength of the covalent bond . Since the strength of both the magnetic and electric forces is inversely proportional to the square of the separation distance between them , the closer together the two associating antiparallel electrons are , the much stronger the attractive magnetic force between them will be . The range of transition temperatures of superconductors , from near Absolute Zero to the present-day record of 138 K (at ambient pressure) , is closely related to this separation distance (coherence length) between the two electrons in the Cooper pairs .

The pairing of electrons participating in the metallic bond occurs both in physical space (across the lattice dimensions) and in energy space ; that is , each pair of electrons is at the same energy level . However , they may be very widely separated physically , at opposite ends of the crystal , or they may be near to each other , maybe even on neighbouring atoms . This applies to both the electron pairs below EF , and to the Cooper pairs that form above EF . Because the Fermi-Dirac distribution limits the population of mobile , free electrons above EF to roughly 1% of the entire population of metallic bond electrons , they are widely distributed , statistically , across the crystal lattice . Thus , their coherence lengths tend to be very long . The absolute value of the magnetic force between any two sets of antiparallel electrons above EF , which might otherwise be able to couple them , must be virtually nil . The pairing

mechanism in such superconductors will therefore be that of phonon mediation , as described in the BCS theory . Once the phonons have pushed the electron pairs together , the magnetic coupling force can then link them together into Cooper pairs .

In effect , the Fermi-Dirac distribution in conventional metallic solids inhibits the formation of Cooper pairs . The Fermi-Dirac distribution is a fundamental attribute of metallic bonds and is unavoidable , but we can circumvent it by inserting anions between the metal atoms (now cations) . The anions' valence shell electrons will participate in the metallic bond and increase its population . Even better , the anions' electron pairs will form the paired electron population below EF , leaving the cations' singlet valence electrons above EF . We can now have neighbouring singlet electrons above EF , which will bring them very close together , i.e. with short coherence lengths :

“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) .

A striking example of how non-metal atoms can provide their electron pairs to the metallic bond is that of rhenium trioxide , ReO3 , whose electrical conductivity is a remarkable 149,300 ohm-1cm1 (ambient) , comparable to that of many common metallurgical metals . Its parent element rhenium , with a hexagonal close-packed (hcp) crystal structure , has a much lower electrical conductivity , 58,140 ohm-1cm1 (ambient) . Rhenium trioxide has a very simple cubic crystal structure :

Rhenium trioxide . Blue spheres , octahedral rhenium(VI) ; green spheres , linear oxygen . ReO3 has a strong framework of Re–O covalent bonds , covered with a Re–O

metallic bond .

It's quite obvious that the oxygen linking atoms are participating with the rhenium atoms in the metallic bond in ReO3 . Rhenium trioxide is discussed at some length in the Iron web page . I've proposed it as an excellent example of a compound having a bilayer metallic bond , in which the nonmetal (oxygen) atoms provide the paired electrons for the lower layer (below EF) , and the metal atoms' (rhenium) singlet valence electrons occupy the upper layer (above EF) . Despite its high ambient electrical conductivity , ReO3 never becomes superconducting (PDF , 258 KB) , even very close to Absolute Zero . This is because it isn't antiferromagnetic ; rather , it has the Pauli paramagnetism so typical of the common metallurgical metals .

Metallic solids with direct metal–metal bonds , such as all the metallurgical metals of common experience , their alloys and intermetallic compounds , and synthetic metals , will thus be adversely affected by the Fermi-Dirac distribution in the sense of being unable to superconduct at higher temperatures (or at all) . Twenty-nine metal elements are known to superconduct at ambient pressure (several more , and a few non-metal elements as well , can superconduct when highly compressed) , but only at a few kelvins above Absolute Zero . On the other hand , all of the genuine high temperature superconductors (the cuprates) have a bilayer Cu–O metallic bond . I've discussed several examples of compounds with a bilayer metallic bond , including that of YBCO , in another web page , “A New Classification of Metallic Solids”, to which the interested reader is referred .

The third prominent feature of all high Tc superconductors is that they have mixed-valent cations as the electronically-active components of the materials , i.e. they participate in the metallic bond . There are four recognized types of mixed-valent compounds , which are now universally referred to as the Robin-Day classes , named for the most prominent researchers in that field , M. Robin and P. Day , whose wide-ranging survey of mixed-valent compounds , published in 1967 , is still the definitive review of the topic .

Only Class II is able to provide high temperature superconductor candidates . Classes I and IIIA are insulating or poorly semiconducting materials ; the Class IIIB synthetic metals , while highly conductive , either become insulating when they are cooled down , or they may superconduct , but only near Absolute Zero . They have direct metal–metal bonds with no participating anions , so all of their metallic bond valence electrons are subject to the Fermi-Dirac distribution , which greatly reduces the population of their free , mobile electrons above EF , as mentioned above . In Class II , the anions or non-metal atoms separating the electronically-active cations are able to participate in the metallic bond , donating their valence shell electron pairs to the lower layer of the bilayer metallic bond in which they participate . In my web page , “A New Classification of Metallic Solids”, I expanded Robin-Day Classes II and IIIB

into eight new types of metallic solids . Superconductors can be found in all four of the true metal classes , but only Class 3 can provide high temperature superconductors . Participation of the anions or non-metal linking atoms in the metallic bond , i.e. a bilayer metallic bond , is an essential condition for high transition temperature superconductivity .

In Robin-Day Class II mixed-valent compounds the valence electrons have an extremely fast resonance over the anions and between the cations . For example , in magnetite [Fe3O4 , (Fe3+

tet – Fe2+oct – Fe3+

oct) O4] the 3d6 valence electron on the octahedral Fe2+ cations can resonate with the octahedral Fe3+ cations (but not with the orbitally mismatched tetrahedral Fe3+ cations) :

“......the magnetic fields at the octahedral sites are indistinguishable , indicating an oscillation of valence [electrons] more rapid than 108/sec . On the other hand , at 85 K , the Fe(II) and Fe(III) ions in the octahedral holes can be distinguished as expected for a Class II system” (Robin and Day , wide-ranging survey , p. 304) .

There is no thermodynamic barrier to such an electron resonance . Consider the redox situation in a sample of a homovalent copper(II) oxide compound . Suppose an electron is transferred by resonance from copper(II) cation A to copper(II) cation B . Cu2+

A becomes Cu3+A , while Cu2+

B becomes Cu1+B . The redox equations for this

electron transfer are as follows :

Cu2+A – e- -------------> Cu3+

A ........... E0ox = – 2.4 V

Cu2+B + e- -------------> Cu1+

B ........... E0red = 0.153 V

Net reaction : Cu2+A + Cu2+

B -------------> Cu3+A + Cu1+

B ........... E0T = – 2.247 V

The very large negative cell potential for this reaction – the disproportionation of copper(II) to copper(I) and copper(III) – indicates that it is highly unfavourable thermodynamically at STP and is essentially impossible . The copper(II) 3d9 valence electrons are strongly pinned on their respective kernels , and thus homovalent copper(II) oxide compounds are insulators (or poor semiconductors) .

Now consider what happens in a typical Robin-Day Class II mixed-valent copper compound , for example in YBCO , with its Cu2+ – Cu3+ – Cu2+ . The copper(II) 3d9 valence electron will resonate with the 3d8 copper(III) . When that happens , the Cu2+

A

will become Cu3+A as before . However , now the Cu3+

B becomes Cu2+B , as represented

in the following redox equations :

Cu2+A – e- -------------> Cu3+

A ........... E0ox = – 2.4 V

Cu3+B + e- -------------> Cu2+

B ........... E0red = + 2.4 V

Net reaction : Cu2+A + Cu3+

B -------------> Cu3+A + Cu2+

B ........... E0T = 0 V

We see from this simple redox analysis that there is no thermodynamic barrier to the electron resonance in Robin-Day Class II (Class 3) mixed-valent compounds . That's why they have such extraordinary optical , electrical , and magnetic properties , compared to their corresponding homovalent parent compounds , in which the valence electrons are pinned on their atomic kernels . This extremely fast electron resonance permits the free electrons in the metallic bond to closely approach other nearby free electrons ; and , if the two electrons have an antiparallel orientation with respect to each other , they can magnetically couple together , as discussed above .

A Robin-Day Class II (Class 3) mixed-valency is the “chemical trick” required to unpin the frozen valence electrons in the metal oxide precursors , thus installing in them the bilayer metallic bond essential for high temperature superconductivity . Elementary metals , their alloys and intermetallic compounds , and synthetic metals , already have unpinned mobile electrons in their metallic bonds , but because they lack any participating anions or non-metal atoms , their free electron populations have been drastically reduced by the Fermi-Dirac distribution , preventing them from ever becoming high temperature superconductors (if at all) .

A mechanism is now required to arrange the electrons above EF into an antiparallel spin order . One way to do this is to create a metallic bond within an antiferromagnetic compound . Then , the antiferromagnetic ordering will also be imposed on the free electrons , just as it is on the pinned valence electrons in the parent homovalent compound . This is exactly what Bednorz and Müller did in their pioneering research with the doping of the strongly antiferromagnetic La2CuO4 . Its antiferromagnetic ordering translated into an antiparallel spin ordering of the free electrons in the newly created metallic bond in the doped La2CuO4 , which now contained both copper(II) and copper(III) , and was a Robin-Day Class II mixed-valent compound . The antiparallel resonating free electrons were able to approach each other fairly closely , and magnetically “clicked together” like a pair of refrigerator magnets (although the resulting Cooper pairs were stable only at relatively low temperatures , ~ 30–40 K , in that crystal environment) .

The same situation occurred again with YBCO not long after . The compound YBa2Cu3O6.5 with homovalent copper(II) was partially oxidized in an atmosphere of pure oxygen to YBa2Cu3O7 , which is a Robin-Day Class II mixed-valent compound . YBCO is a true metal , with an inverse temperature–electrical conductivity relationship (its ambient electrical conductivity is around 500 ohm-1cm-1 ) . It has a bilayer metallic bond , with the linear oxygen linking atoms providing their 2pz

electron pairs to the pi XO . The copper(II) oxide matrix in which the metallic bond is located in YBCO is strongly antiferromagnetic over a wide temperature range ; thus , a strong antiparallel spin orientation was induced in the mobile , free electrons above EF in the XO . Since virtually all the Cu2+ 3d9 valence electrons were above EF (because of the bilayer XO) , they were on neighbouring copper atoms and so their coherence lengths were extraordinarily short . The magnetic coupling force was therefore quite strong , and the resulting Cooper pairs were remarkably stable . As a result of all these converging factors , YBCO proved to have a record (at the time , in early 1987) transition temperature , Tc ~ 93 K , well into the liquid nitrogen (>77 K) range .

If we examine various superconductors in the other three classes of true metals , we see that there is little, if any , antiferromagnetic ordering in them . That is , their kernels are mostly diamagnetic , and they exhibit Pauli paramagnetism , which is common in “ordinary” metallic bonds . Since there is no antiferromagnetic ordering in them , their transition temperatures are all very low , usually close to Absolute Zero . Their superconductivity can be attributed to the BCS phonon-mediated association mechanism .

The family of ferropnictide (LaOFeAs) superconductors , which I have surveyed in another web page , is a noteworthy exception . These compounds have direct Fe–Fe metallic bonds (they can be thought of as iron synthetic metals) , and so are prevented by the Fermi-Dirac distribution from becoming high Tc superconductors . However , their pnictide atom components do seem to have a mild , modest sort of antiferromagnetic ordering capability on their iron atom neighbours , and the ferropnictide transition temperatures are in a “medium” range of about 30–50 K , with a current (February , 2010) record high Tc = 56 K for several related compounds . Because the ferropnictides have a monolayer metallic bond (i.e. direct metal–metal bonding) , we can predict that they will never be high Tc superconductors . Possibly by various chemical adjustments (discussed in the Doping web page) their transition temperatures might be raised into the low end of the liquid nitrogen range , but they are unlikely ever to exceed 100 K , in my opinion . Selenium also seems to have the “magic touch” for inducing antiferromagnetic ordering in certain of the Transition metal atoms (such as cobalt) to which it is bonded .

Summarizing , the physical basis of all superconductivity is the magnetic coupling of pairs of free electrons above EF in any environment and at any temperature . For low temperature superconductivity the BCS phonon-mediated enabling mechanism “pushes together” the metallic bond free electrons , which are widely separated across the crystal lattice . For high temperature superconductivity a Robin-Day Class II mixed-valence resonance unpins the valence electrons , which are in close proximity

on neighbouring cations , and thereby creates a bilayer metallic bond in the solid . Once the free electrons are brought fairly close together – by whatever mechanism – they can magnetically couple together into Cooper pairs . However , they must have an antiparallel spin orientation relative to each other in order for the magnetic force to apply and be effective .

There are several chemical prerequisites for high temperature superconductivity :

* First , the material must be a true metal [inverse temperature–electrical conductivity relationship] , with a nodeless XO . Yes , superconductivity can also occur in pseudometals (because Cooper pairs can tunnel through nodes) as we have seen in samples of heavily boron-doped diamond , silicon , and silicon carbide , but this superconductivity occurs only at very low temperatures , close to Absolute Zero .

* Second , the material must have a bilayer metallic bond , so that all the valence electrons concerned from the electronically active metal atoms will be located above EF . They will then be located on neighbouring metal atoms and will have very short coherence lengths , and can strongly couple together magnetically to form reasonably stable Cooper pairs .

* Third , nonmetallic compounds with homovalent cations must be chemically converted into Robin-Day Class II (Class 3) mixed-valent compounds with a bilayer metallic bond ; and ,

* Fourth , there must be antiferromagnetism in the material , either naturally in its precursor , or induced in it by an external agent . The stronger its antiferromagnetic ordering , the stronger will be the antiparallel ordering of the free electrons above EF in the XO and the stronger its Cooper pairs will be . In the following section of this web page I'll discuss the possibility , with several examples , of modifying non-antiferromagnetic (i.e. diamagnetic) Robin-Day Class II mixed-valence systems by intercalating them with nonmetallic antiferromagnetic layers . The metallic bond will remain in the mixed-valent layers , but hopefully the additive will induce an antiparallel ordering into its free electrons . Then they'll be able to form Cooper pairs at a much higher temperature than they would without the antiferromagnetic layers . A substantially higher Tc of the layered composite compared to the original mixed-valent compound would be very encouraging for researchers in their study of these new superconductor candidates .

Any theory is of little value unless it can be tested by various experimental methods , by which it is verified , or refined , or refuted . In the following section of this web page I'll outline the syntheses of several new types of potential high temperature

superconductors , which may provide some evidence to support the antiferromagnetic induction model described above .

 

Intercalating Robin-Day Class II Mixed-Valent (and Generally , Metallic) Substrates with Antiferromagnetic Induction Layers

 

The first step in a chemical approach to designing new high temperature superconductors is to select a suitable antiferromagnetic precursor which can be modified by some chemical technique or other into a metallic solid . This latter material should then have a good chance of being a superconductor , and possibly with a reasonably high Tc . The following Table presents a selection of well-known antiferromagnetic compounds , together with their Néel temperatures (TN) . Generally , the higher the TN the better , since below TN the valence electrons are being organized into their characteristic antiparallel spin régime . Therefore , the higher the TN the higher the temperature at which there will be an antiparallel ordering imposed on the mobile , free electrons above EF in the newly-created metallic bond in the solid . Hopefully any Cooper pairs created at that higher temperature will also be stable within that particular crystal environment :

A more complete list is provided in the CRC Handbook of Chemistry and Physics , as noted immediately above in the Table .

It's convenient to think of the mixed-valent cations in Robin-Day Class II compounds selected for superconductor candidates in terms of triads . The copper triad can be readily seen in YBCO , YBa2Cu3O7 : (Y3+ Ba2+ Ba2+)(Cu2+ Cu3+Cu2+)(O2-)7 . Materials in the superconducting state are known to be strongly diamagnetic , which means that all the electrons in the the electronically-active metal atoms or cations must be completely spin-paired . In YBCO , the 3d9 valence electrons in the copper(II) cations form the Cooper pairs , while the Cu3+ base cations ( 3d8) are spin-paired : Cu3+

spCu3+spCu3+

sp e22- . Meanwhile , the yttrium and barium cations , and the oxide

anions , are also diamagnetic , so YBCO in the superconducting state is entirely diamagnetic .

We could also consider a lower-valent , mixed-valent copper triad : Cu0–Cu1+–Cu0 , with copper(I) base cations , which are 3d10 electronically : Cu1+

spCu1+spCu1+

sp e22- .

This triad might furnish some interesting new metallic solids to study , but they would probably not be high Tc superconductors (if at all) , because copper(I) compounds are well-known to be diamagnetic , and therefore are incapable of inducing an antiparallel ordering in their valence electrons . A metallic solid containing such a lower-valent copper triad would undoubtedly need to be layered with an antiferromagnetic induction agent in order to become superconducting .

In the Iron web page I proposed the mixed-valent Fe1+–Fe2+–Fe1+ triad , for example in the novel compounds Fe3OX (X = a chalcogenide anion , i.e. sulfide , disulfide , selenide , and telluride) , for incorporation into new superconductor candidates . If the base of iron(II) cations , 3d6 , can be kept in a low-spin condition (the chalcogenide anions should ensure that this happens) , the “extra” 3d7 valence electrons on the iron(I) cations can form the Cooper pairs : Fe2+

sp Fe2+sp Fe2+

sp e22- . The FeO matrix of

this system is antiferromagnetic [TN = 198 K (–75 ºC)] , so there is a good chance of it being superconducting at a reasonably high Tc . On the other hand , iron(III) cations , 3d5 , are permanently paramagnetic because of their odd number of valence electrons , so they can never be used as the electronically-active cations in the metallic bond , where they would prevent the formation of Cooper pairs . Thus , while the compound LaFeO3 is antiferromagnetic with an extraordinarily high TN = 750 K (477 ºC) , its iron(III) cations disqualify it from consideration as an antiferromagnetic precursor compound .

In actual practice , there are few usable triads that can be derived from the elements whose antiferromagnetic compounds are listed in the above Table (copper is , of course , the outstanding exception) . The concept of chemically creating a metallic bond within an existing antiferromagnetic compound thus turns out to be of rather limited scope . A more practical approach – and one with a much wider scope – would be to combine an existing diamagnetic mixed-valent triad with an external antiferromagnetic induction compound . While most elements have multiple valence states (especially the Transition metals) and so could theoretically provide us with many mixed-valence triads – refer to Robin and Day's comprehensive review of mixed-valence chemistry – I'll discuss only several of the better known ones , because of the limited available length of this web page .

The first one is the bismuth triad , which is found in the high Tc superconductor BSCCO-2212 (bismuth strontium calcium copper oxide , Bi2Sr2Ca2Cu3O10+y ; Tc ~ 110 K) :

This molecular model was based on the sketch of BSCCO-2212 by G.-H. Gweon .

It's generally thought that superconduction in BSCCO is in the copper oxide layers :

“The present work on the Bi compounds , as well as similar work on the high-Tc thallium phases , whose structures also do not contain Cu–O chains , indicates that superconductivity resides in the CuO2 planes” (Tarascon et al. , p. 8891) .

This might not be correct , as the following simple redox analysis shows . First , here's a Table of common oxidizing metal species and their standard reduction potentials :

The standard reduction potentials , E0red , for the metal species are all versus the SHE

at STP . However , they were derived either from measurements in aqueous media or from thermodynamic calculations , so we should be cautious about applying them in a solid state environment . Nevertheless , they can provide some useful guidance to the chemist in the design of new superconductor candidates .

Copper(III) , with the highest E0red , is the most powerfully oxidizing metal cation

known . YBCO , with mixed-valent Cu(II)–Cu(III) , is a strong oxidizer , and when exposed to atmospheric humidity it can oxidize water to oxygen gas and hydroxide anions . The bismuth triad is Bi(V)–Bi(III)–Bi(V) [Bi(4.33+)] , which is 6s0–6s2–6s0 electronically . The Bi(V) component of the triad is a remarkably powerful oxidizer , with E0

red ~ 1.8 V ; the mixed-valent triad Bi(4.33+) would have a somewhat lesser E0

red . Consider the unoxidized parent precursor to BSCCO , Bi2Sr2Ca2Cu3O10 . By valence-counting we see that all of its metal atom components are homovalent : (Bi3+)2(Sr2+)2(Ca2+)2(Cu2+)3O10

20- . Using oxidizing conditions in its preparation (such as a flowing atmosphere of pure oxygen gas) a small mole fraction , y , of oxide can be added to the precursor material to obtain BSCCO , Bi2Sr2Ca2Cu3O10+y ; the actual value of y has never been specified , to the best of my knowledge . This added increment of oxygen removes some of the valence electrons from the metal atom components . Will the electron donor be the bismuth(III) or the copper(II) ? Redox considerations suggest that bismuth(III) is easier to oxidize to Bi(V) than copper(II) is to oxidize to copper(III) . So the superconductor triad in BSCCO is Bi(V)–Bi(III)–Bi(V) , not the copper triad .

I should mention an alternate possibility here : that of a pseudo mixed-valent resonance in BSCCO , in which the strongly oxidizing Bi(V) components try to “take” the copper(II) 3d9 valence electrons , while the resulting copper(III) kernels simultaneously try to pull them back from the bismuth atoms . This sets up an ultrafast resonance between the bismuth(V) and copper(III) centers , with the 3d9 valence electrons participating in the “tug-of-war” between them . In other words , the 3d9 electrons have been “activated”, just as they are in the genuine Robin-Day Class II Cu2+–Cu3+–Cu2+ triad :

Bi(V)   +   2  Cu(II)   <------------->   Bi(III)   +   2  Cu(III)  ; E0T ~ | 0.6 V |

The electron exchange equilibrium is expected to lie well to the left in the above equation . The absolute difference between the two E0

red values for Bi(V) and Cu(III) is roughly 0.6 V , written between vertical bars to indicate that it is neither a positive nor negative value . In this picture , the homovalent copper(II) cations have been redox-activated by the bismuth(V) components , and so superconductivity would indeed occur in the CuO2 planes , as claimed by Tarascon and co-workers .

However , I'm interested in exploring the alternate explanation of superconductivity in BSCCO , provided by the antiferromagnetic induction concept . In this model , the actual electronic activity is in the bismuth–oxygen layers , with the bismuth triad , Bi(V)–Bi(III)–Bi(V) , providing the Cooper pairs for the superconduction . The copper–oxygen layers are electronically inert , but are strongly antiferromagnetic in nature , and they impress an antiparallel spin ordering on the adjacent mobile , free

electrons in the Bi–O bilayer metallic bond . Without this external influence , a diamagnetic Bi–O superconductor would have only a low Tc ; but with a neighbouring antiferromagnetic induction , much stronger Cooper pairs should be produced , resulting in a significantly higher transition temperature (which is about 110 K , in the case of BSCCO-2212) .

Magnetic induction of any sort in crystalline solids is accomplished orbitally , by an electron superexchange process . Cox comments ,

“Direct through-space magnetic dipole interaction of spins is far too small to account for most magnetic-ordering phenomena” (p. 148) .

The electron spin orientations of the cations are mediated by the p orbital electron pairs of the intervening anions , as shown below for the Cu–O–Bi atoms in BSCCO , for example :

Superexchange in this particular case may be facilitated by the p–p overlap of the Cu 5pz –O 2pz –Bi 7pz orbitals to form a linear nodeless Cu–O–Bi pi XO . The spin orientations of the Cu and Bi valence electrons will be synchronized by superexchange , with bismuths' free electrons copying the antiparallel orientations of their copper 3d9 partners , which are pinned in the Cu–O lattice .

Generally , the free electrons' spins will mimic those of any sort of magnetic ordering in the adjacent induction layers . For example , if the induction agent was ferromagnetic , the spin ordering in the free electrons above EF would be identical , i.e. parallel . This is reminiscent of their precise reflection of incident light wavelengths , which is the physical basis of mirrors .

Such a diamagnetic bismuthate superconductor was discovered by two independent research groups in 1988 and had a medium range Tc = 29.8 K (onset) . It was a cubic symmetry perovskite , and was prepared in strongly oxidizing conditions :

0.6 BaO +  0.4 KO2  +  ½ Bi2O3 --------- (1)  heat at 675 ºC , 3 days ---------

--------- (2)  anneal in pure O2 , 475 ºC ---------> Ba0.6K0.4BiO3

Its valence-counting formula is Ba2+0.6K1+

0.4Bi3+0.3Bi5+

0.7O36- , with a NIOS (non-integral

oxidation state) bismuth valence of Bi(4.4+) , which is quite close to the Bi(V)–Bi(III)–Bi(V) triad valence of Bi(4.33+) ; the exact triad would be present in Ba0.67K0.33BiO3 , i.e. 4–5–4 , which is equivalent to 5–3–5 . Ba0.6K0.4BiO3 is a true metal with a nodeless Bi–O bilayer metallic bond (probably Bi 7px,y,z– O 2py,z) , and it's a Robin-Day Class II (Class 3) mixed-valence compound . All the ingredients are in place for the appearance of superconductivity in it , but one key component is missing for high temperature superconductivity in the bismuthate . Bismuth and its compounds are diamagnetic , which limits the Tc of Ba0.6K0.4BiO3 to about 30 K . Suppose we intercalated layers of a strongly antiferromagnetic copper(II) oxide compound between layers of the bismuthate perovskite . Would they induce an antiparallel ordering into its metallic bond free electrons , thereby permitting them to form much stronger Cooper pairs ? In a sense this has already been accomplished in BSCCO-2212 , with its alternating layers of partially oxidized Sr2Bi2O5 and Ca2Cu3O5 (refer to the sketch of BSCCO-2212 above) .

Lanthanum copper(II) oxide , mentioned above in connection with Bednorz and Müller's breakthrough discoveries in 1986–87 , could be examined for this application . The layered composite from the combination of equimolar quantities of Ba0.6K0.4BiO3

and La2CuO4 , Ba0.6K0.4La2BiCuO7 , might have the following crystal structure :

The syntheses of La2CuO4 , La2NiO4 , and La2CoO4 were first reported in 1960 by French researchers . La2NiO4 has the K2NiF4 crystal structure , while La2CuO4 and La2CoO4 have distorted variants of it . In particular , La2CuO4 was tetragonally distorted ; that is , its copper(II) atoms have a “4+2 distorted octahedral” [tetragonal] coordination by the oxygen , with four short Cu–O bonds in the x-y plane , and two longer vertical Cu–O bonds . This tetragonal distortion is caused by the Jahn-Teller effect , which is ever-present in copper(II) compounds :

This molecular model was based on the sketch by B.M. Klein et al. .

As mentioned above , Arjomand and Machin prepared La2CuO4 and thought it might be antiferromagnetic :

“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) .

They also prepared La2NiO4 in another study of ternary nickel oxides , and similarly found it to be antiferromagnetic . For typical high spin Ni2+, eff ~ 3.1 BM ; at 300 K , they found eff = 1.70 BM ; at 80 K , they found eff = 1.09 BM (Table 3 , p. 1057) .

“Although there is no direct indication of antiferromagnetism [in La2NiO4] , these observations suggest that such an interaction does occur below 80 K . Compounds with the K2NiF4 structure are commonly antiferromagnetic” (p. 1057) .

Bednorz and Müller's success with Ba- and Sr-doped La2CuO4 resulted in it being extensively studied from the late 1980s onward . La2CuO4 , La2NiO4 , and La2CoO4 are now recognized as being quite strongly antiferromagnetic , with Néel temperatures of around 350 K , 330 K , and 270 K respectively (mentioned by Blundell et al. , PDF , 116 KB ; but see the refs. in Several investigations for various different TN

values . Magnetic susceptibilty and TN are very sensitive to the sample preparation history and to the compound's stoichiometry) .

Several investigations of how partially oxidizing La2CuO4 and La2NiO4 affects their magnetic susceptibilty and TN are very pertinent to this present report . It was generally found that partial oxidation of the copper(II) and nickel(II) in the compounds substantially degraded their antiferromagnetism , flattening their magnetic susceptibility curves and lowering their TNs . This should come as no surprise in light of the above discussion of mixed-valent compounds . Partial oxidation is chemically creating mixed-valent Cu(II)–Cu(III) and Ni(II)–Ni(III) ; the 3d valence electrons in the Cu(II) and Ni(II) , previously pinned in the homovalent compounds , are now resonating in the mixed-valent materials . This electron resonance is degrading the antiferromagnetic ordering of the 3d electrons in the lattice .

We can now clearly see the dilemma of high temperature superconductivity : on the one hand , we need the Robin-Day Class II (Class 3) mixed-valent resonance to unpin the valence electrons in the homovalent insulators and create a bilayer metallic bond in them ; but on the other hand , such a resonance destroys the antiferromagnetism we need to ensure the free electrons have the antiparallel orientation they require for magnetic coupling into Cooper pairs . Chemists trying to synthesize such superconductors must therefore find the precise balance between optimizing the mixed-valency and yet retaining sufficient antiferromagnetism in the modified material . We will always be confronted by this dilemma as long as we try to design a superconductor by creating a Robin-Day Class II mixed-valent metallic compound within an antiferromagnetic homovalent precursor .

However , we might be able to avoid the dilemma by intercalating layers of an antiferromagnetic induction agent between layers of all sorts of metallic substrates . For high temperature superconductor candidates any substrate with a bilayer metallic bond is still preferred , for the reasons outlined above . Electrical conductivity and superconductivity can first be optimized in that layer if a mixed-valent compound is the selected substrate . Then , layers of La2CuO4 or La2NiO4 (depending on the system's redox chemistry) can be intercalated between layers of the metallic solid .

Antiferromagnetism is optimized in stoichiometric La2CuO4 or La2NiO4 , that is , neither partially oxidized nor reduced , so researchers should prepare in advance samples of pure , stoichiometric La2CuO4 or La2NiO4 . They should carry out the intercalation reactions in an atmosphere of pure , dry argon or nitrogen to avoid any partial oxidation of the Cu(II) or Ni(II) . Also , the La2CuO4 composites should not be overheated ; Foëx and co-workers (French researchers) discovered that above 1200 ºC copper(II) oxidizes some of the oxides to oxygen , and La2CuO4 is converted into a mixture of La2O3 and Cu2O (Arjomand and Machin prepared CuAlO2 by heating CuO

– not Cu2O – and Al2O3 at 1100ºC for five days) . A moderate reaction temperature of ~ 800–900 ºC for the preparations is therefore recommended . On the other hand , La2NiO4 is thermally stable , and can be melted at 1750 ºC without decomposition . These redox reactions occur (or not) because Cu(II) is a natural oxidizer , with E0

red = 0.153 V to Cu(I) , while Ni(II) is a low energy redox species , neither oxidizing nor reducing in nature .

While copper(II) is resistant to the Bi(V) in Ba0.6K0.4BiO3 , nickel(II) can be oxidized (at 1.17 V) to nickel(III) by Bi(V) , at ~1.8 V . Therefore , La2CuO4 could be tried as an antiferromagnetic induction agent with Ba0.6K0.4BiO3 , while La2NiO4 would be unsuitable for this application .

Wells has pointed out the similarity of the K2NiF4 crystal structure with that of the perovskites :

“The structure of a number of complex oxides X2YO4 is closely related to the perovskite structure , which is that of the corresponding oxide XYO3” (p. 499) .

Layers of La2CuO4 should thus be able to intercalate smoothly with alternating perovskite layers of the mixed-valent bismuthate to form the new composite La2Ba0.6K0.4BiCuO7 . If the antiferromagnetic induction model is valid , this latter material should have a substantially enhanced Tc compared to the original Ba0.6K0.4BiO3 .

Referring to the Table of Oxidizers above , we note that cobalt(II) oxide can't be oxidized by Bi(V) , so La2CoO4 could also be tried as an antiferromagnetic induction agent with Ba0.6K0.4BiO3 . Yamada and co-workers measured TN = 275 K for La2CoO4 .

Normally , researchers would carefully avoid the inclusion of high spin cations with any superconductor material or candidate . However , they should remember that high spin copper(II) is found in BSCCO-2212 , for example . I pointed out in the Doping web page that in the YBCO series of cuprates , MBa2Cu3O7 , superconductivity was still observed even when M was a paramagnetic Rare Earth cation such as Dy3+, 4f9 ; Gd3+, 4f7 ; Sm3+, 4f5 ; and Nd3+, 4f3 . These are all inert spectator cations , nested between the electronically active CuO2 sheets and CuO3 pyramids . The Rare Earth cations in the YBCO series are off to the side and don't participate in the Cu–O bilayer metallic bond in them . Their f electron Curie paramagnetism is undoubtedly much weaker than the d electron antiferromagnetism in the copper(II) cations . They therefore don't disrupt the formation of the Cooper pairs and are quite innocuous . Similarly , the layers of La2CuO4 intercalated between the bismuthate layers – in which the electronic activity actually occurs – shouldn't interfere with the Bi–O

superconductivity , so long as their Cu2+ doesn't mix into the bismuth layers . The two different layers are somewhat like “oil and water”, and probably would remain cleanly separated , like the complex layers in BSCCO-2212 .

A second mixed-valent triad that would be interesting to investigate in this new context is the titanium trio , Ti3+–Ti4+–Ti3+ , which is 3d1– 3d0– 3d1 electronically . Verwey studied this titanium system in his pioneering research with mixed-valent compounds and the controlled valence technique of synthesizing them . The electrical conductivity of strontium titanate rose dramatically from 10-7 ohm-1cm-1 to 0.6 ohm-

1cm-1 when doped with 1% lanthanum(III) .

Three decades later Johnston prepared a series of Li1+xTi2-xO4 spinel compounds (x = 0 to 0.33) , studying their electrical conductivities from 0–300 K . Superconductivity was optimized at Tc ~ 13.7 K in the x = 0 compound , LiTi2O4 . Its valence counting formula , Li 1+ Ti3+ Ti4+ O8-

4 , reveals the presence of the Ti3+–Ti4+–Ti3+ triad in the material . LiTi2O4 was a mediocre semiconductor with a normal state electrical conductivity of about 10 ohm-1cm-1 , a value which remained remarkably level from Tc

to 300 K [Johnston's Fig. 5 , p. 158] .

Titanium(III) compounds are mildly reducing , so La2NiO4 and La2CoO4 would be compatible with them (but not the oxidizing La2CuO4) . Electrical conductivity and superconductivity in Verwey's SrTiO3 – LaTiO3 mixed perovskites would first be optimized . LaTiO3 , described as “black , slightly iridescent crystals”, is a metallic solid (Rao) that supplies free electrons to the metallic bond in the Sr–La composites . It would be doped into the non-metallic substrate SrTiO3 , a cubic perovskite , at various mole ratios to obtain a series of composites for testing :

x  LaTiO3   +   (1– x)  SrTiO3  ---------->  Lax Sr1-xTiO3 ; x = 0 to 1 .

The titanium triad would be present in this system in the composition La0.67Sr0.33TiO3 , although that might not be the optimum formula . The optimized LaxSr1-xTiO3 would then be combined with an equimolar quantity of stoichiometric La2NiO4 to obtain the layered La/Sr–Ti–Ni–O structure , which hopefully would have a significantly enhanced superconducting transition temperature relative to the original LaxSr1-xTiO3 . N. Bergeal and co-workers recently reported that epitaxial films of LaxSr1-xTiO3 they prepared had a Tc ~ 0.3 K (PDF , 1592 KB) .

The superconducting properties of a third group of mixed-valent compounds , the tungsten bronzes (and possibly other bronzes , such as the molybdenum bronzes) might also benefit from the presence in them of an antiferromagnetic induction agent . Some tungsten bronzes have the cubic perovskite structure while others have related non-cubic forms . They can be thought of as the insertion of zerovalent metal atoms

into the tungsten trioxide precursor structure . The metal atoms donate their valence electrons to the WO3 , but rather than reducing it to tungsten metal , the electrons enter the oxide's frontier orbitals and create a metallic bond XO in the crystal . The inserted metal atoms remain as electronically inert spectator cations nested in periodic cavities in the lattice .

The tungsten (and other) bronzes are brightly coloured with a metallic luster , and they can have high electrical conductivities . For example , the cubic bronze Na0.85WO3 has an ambient conductivity of around 70,000 ohm-1cm-1 . Despite these remarkably high conductivities , few of the tungsten (or other) bronzes become superconducting , even near Absolute Zero . Matthias and co-workers studied the electrical conductivity near Absolute Zero of a dark blue sample of tungsten bronze having the approximate composition Na0.3WO3 , whose Tc ~ 0.57 K (onset) . Rubidium tungsten bronzes have the highest transition temperatures of the alkali metal tungsten bronzes , with the Tc = 1.98 K for RbxWO3 (x = 0.27–0.29) reported in 1965 . An efficient synthesis of rubidium tungsten bronzes in a microwave furnace was recently described by J. Guo and co-workers . All the conductive bronzes display Pauli paramagnetism , with no evidence of any antiferromagnetism .

The mixed-valent triad in the tungsten bronzes is W(V)–W(VI)–W(V) , which is 5d1– 5d0– 5d1 electronically . Tungsten(VI) in the parent material , WO3 , is a very mild oxidizer [Table of Oxidizers above] , so as with the titanium triad only La2NiO4 and La2CoO4 could be combined with them for the preparation of new high Tc superconductor candidates . Apparently the tungsten bronzes , with their bright , lustrous colours , are used industrially in paint pigments (Microsoft Word document , 259 KB) , but I was unable to locate any of their commercial suppliers .

Tungsten bronzes were first prepared in 1823 by the prominent German chemist Friedrich Wöhler (1800–1882) , and several synthesis routes to them have been developed since then . In a typical procedure described in detail in Inorganic Syntheses , W(0) and W(VI) are reproportionated to mixed-valent W(V,VI) using a mixture of tungsten metal powder , tungsten trioxide , and sodium tungstate salt . This classical method was recently modernized by carrying it out in a microwave furnace . Another interesting preparation of a barium tungsten bronze was published by Conroy and Yokokawa :

x BaCl2 + x WO2 + WO3 ---- (900 ºC , 15 hrs , in vacuo) ------> BaxWO3 + x WO2Cl2

(g) .

The by-product WO2Cl2 was sublimed from the mixture , thus driving the reaction to completion . However , this resulted in a deplorable loss of valuable metal reagent from the system . Here's a suggestion for a simple route to sodium tungsten bronzes ,

also involving the evolution of a gaseous by-product – but an expendable one – and using only relatively inexpensive reagents :

x NaH + WO3 ---- (warm in a stream of pure flowing nitrogen) ------> NaxWO3 + ½ x H2 (g) ; and ,

x NaBH4 + WO3 ---- (pure flowing nitrogen) ------> NaxWO3 + ½ x H2 (g) + ½ x B2H6

(g) .

Both sodium hydride and sodium borohydride are well-known reagents in organic chemistry , the former as a strong but non-nucleophilic base , and the latter as a mild reducer of numerous organic functional groups . The corresponding lithium and potassium compounds are also known and are commercially available , but are less frequently used than the sodium chemicals . Hydride is a remarkably strong reducing agent , and it should readily transfer one of its 1s2 valence electrons to the mildly-oxidizing W(VI) in the WO3 :

2 W(VI) + 2e- -------------> 2 W(V) ............ E0red = 0.26 V ;

2 H1- – 2e- -------------> H2 (g) ............ E0ox = 2.23 V ;

Net : 2 W(VI) + 2 H1- -------------> 2 W(V) + H2 (g) ............ E0T = 2.49 V

The substantial E0T suggests that the NaH–WO3 reaction could be strongly exoergic ,

so the two compounds should not be compressed into a pellet , but rather gently mixed together as loose powders . Caution : please take the appropriate safety precautions if attempting these reactions ! Use of eye protection (safety glasses , with goggles or a visor) is obligatory , and a safety screen and leather gloves are strongly advised . Only semi-micro quantities of the reagents (no more than a gram or two) should be combined in exploratory work , until the researcher is confident that the reaction – if successful , of course – can be safely scaled up to a preparative level .

The powerful base potassium hydride , KH , is now available in the form of a 50 : 50 blend with solid paraffin wax . In this form it is very stable and easy to manipulate , with no loss of its basic properties (PDF , 35 KB) . KH-paraffin could be very useful in the synthesis of KxWO3 , where the paraffin might dilute down the KH , and so moderate the addition reaction .

Borohydride isn't as strong a reducer (1.24 V in alkaline aqueous media) as hydride anion , but NaBH4 is easier to handle than NaH (although it's somewhat hygroscopic , which can be a nuisance on those humid summer days) . Aldrich supplies NaH in a dry powder form (95% pure) , which is more convenient than the mineral oil

dispersions of the Alkali metal hydrides commonly available commercially . The tungsten bronzes are chemically quite robust , so the reaction products can be thoroughly washed with water or even dilute mineral acid to remove excess alkali and water-soluble sodium tungstate impurities without harming the bronze .

The tungsten triad would be represented in the bronze [Na1+]2 [W(V)O3 –W(VI)O3 –W(V)O3] ; dividing by 3 , we have Na0.67WO3 , which is in the “mid-range” of sodium-doped WO3 . This may or may not represent the optimum doping level for superconductor candidates , so I would suggest adding a less doped bronze , say Na0.35WO3 , and a more highly doped one , say the conductive cubic bronze Na0.85WO3

mentioned above , to the research study of these materials . These three sodium tungsten bronzes would then be combined with an equimolar quantity of La2NiO4 to produce the composites La2NaxNiWO7 (x = 0.35 , 0.67 , and 0.85) for physical testing . A “shake-'n-bake” technique , with an inert atmosphere of pure , dry argon , and moderate baking temperatures (~ 800–900 ºC) , would be used in their preparation . Chemical bonding in La2NiO4 is entirely ionic in nature , while the W–O bonds in the bronzes are covalent , so hopefully the W–O and Ni–O layers would remain completely separated in the new W–O–Ni composites .

Molybdenum trioxide , a pale green powder , m.p. 795 ºC , could similarly be reacted with NaH and/or NaBH4 to produce the corresponding sodium molybdenum bronzes . The molybdenum triad is 4d1– 4d0– 4d1 for Mo(V)–Mo(VI)–Mo(V) , and the exact triad would be present in the bronze Na0.67MoO3 [tetragonal K0.5MoO3 has an unusually high Tc = 4.2 K (Sleight and co-workers)] . MoO3 is somewhat more strongly oxidizing [Mo(VI) / Mo(V) ~ 0.7 V] than WO3 . It might therefore be possible to try the more oxidizing La2CuO4 , as well as La2NiO4 and La2CoO4 , as antiferromagnetic induction agents with the NaxMoO3 bronzes .

Rhenium trioxide , briefly discussed above , would also provide an excellent test of the antiferromagnetic induction theory . As mentioned earlier , although it has a remarkably high ambient electrical conductivity , it never becomes superconducting . It's really a type of bronze , with a cubic crystal structure similar to the tungsten bronze perovskites [hexagonal K0.3ReO3 has a Tc = 3.6 K (Sleight and co-workers)] . Its Re(VI) is 5d1 electronically . Rhenium trioxide has a bilayer Re–O metallic bond , but it displays Pauli paramagnetism and isn't antiferromagnetic at all . ReO3 could be layered with an equimolar quantity of La2NiO4 to form the composite La2NiReO7 , whose electrical properties would be carefully studied and compared with those of the parent compound .

The tin triad , Sn(IV)–Sn(II)–Sn(IV) , which is 5s0–5s2–5s0 electronically , would also be interesting to study in this context . A well-known cubic perovskite , BaSnO3 , would provide Sn(IV) . Tin(III) is found in the metallic rocksalt SnP , whose cubic

form superconducts at Tc ~ 2.8–4.8 K . Sn(III) might be stabilized in the compound LaSnO3 , which could be a metallic perovskite . The series of Ba1-x Lax SnO3 composites could be prepared in the following one-pot reaction :

(1–x) BaCO3 + ½ x La2O3 + ½x SnO + (1– ½x) SnO2 --------- (flowing argon) --------->

Ba1-x Lax SnO3 + (1–x) CO2 (g) [or ¼x Sn0 + (1– ¼x) SnO2] , where x = 0 to 1 ,

and their electrical conductivities determined . The composite Ba0.33 La0.67 SnO3 [i.e. 3–4–3 , which is equivalent to 4–2–4] would represent the tin triad , although it might not be optimized with respect to electrical conductivity and superconductivity (if any) . Tin(II) is very easily oxidized to tin(IV) [0.151 V] , so all of the synthesis procedures should be carried out in an inert (argon) atmosphere . The optimum Ba1-x Lax SnO3 composite would then be intercalated with stoichiometric La2NiO4 and/or La2CoO4 (but not with the oxidizing La2CuO4) to obtain Ba/La–Sn–O–Ni/Co layered structures for further electrical testing .

The layering of antiferromagnetic induction compounds with metallic solids could be a very general sort of chemical process , leading to the production of many remarkable new systems to investigate as potential superconductor candidates . For example , graphite is a fairly good electrical conductor (about 25,000 ohm-1cm-1 for virgin , undoped graphite at room temperature) . Its conductivity can be dramatically increased by the reaction with it of both electron donors and acceptors . The intercalation compound of graphite with 75% by weight of SbF5 (an electrophilic acceptor) has the astonishing ambient conductivity of around one million ohm-1cm-1 , which I believe is the world record for room temperature electrical conductivity . Could layers of an antiferromagnetic induction agent be added to this material to make it an ambient superconductor ?

Another example is titanium disulfide , TiS2 , which I've discussed in the Layered web page . It has a lamellar morphology like that of graphite , with a golden-yellow colour and a metallic luster . Its ambient electrical conductivity is about 1400 ohm-1cm-1 , and while it has an inverse temperature–conductivity relationship , TiS2 apparently never becomes superconducting , although many of its intercalation products do (but only close to Absolute Zero) . Suppose a layer of an antiferromagnetic induction agent was intercalated between each layer of TiS2 ; would the composite then become superconducting at an appreciable Tc ? Here's a suggestion : equimolar quantities of TiS2 and the compound tetrakis(triethylphosphite)nickel(0) , [(EtO)3P]4Ni , both of which are commercially available , could be reacted together . After distillation of the complexing (EtO)3P ligands from the solid , the nickel atoms would bond with the sulfurs to form a coating of NiS over the TiS2 layers . Nickel(II) sulfide is known to be

a fairly strong antiferromagnetic material [TN = 263 K (–10 ºC) , Table above] , so possibly the nickel-intercalated product TiS2Ni might prove to be a superconductor , with a Tc well above Absolute Zero .

Combinations of antiferromagnetic induction agents with the wide array of available metallic solids (with a compatible redox chemistry between the two combining materials being carefully respected , of course) could in theory provide an large host of superconductor candidates , and many interesting new materials generally , for investigation . If supported by experimental evidence , the antiferromagnetic induction model of high temperature superconductivity would give chemists the ability and confidence to assume a leadership role in future superconductivity research , in partnership with solid state physicists , crystallographers , materials scientists , and technologists .

The study of AFM induction in layers of metallic solids continues in the web page , “New Layered Compounds for High Temperature Superconductivity”, with more examples of metallic–AFM composites .

 

References , Notes , and Further Reading

 

mathematical treatise : J. Bardeen , L. N. Cooper , and J. R. Schrieffer , “Microscopic Theory of Superconductivity”, Phys. Rev. 106 (1) , pp. 162-164 (1957) ; idem , “Theory of Superconductivity”, Phys. Rev. 108 (5) , pp. 1175-1205 (1957) .

Matthias's Rules : B.T. Matthias , “Empirical Relation between Superconductivity and the Number of Valence Electrons per Atom”, Phys. Rev. 97 (1) , pp. 74-76 (1955) ; see Fig. 3 , p. 75 for a graph of several A15 compounds ; B. T. Matthias , T. H. Geballe , and V. B. Compton , “Superconductivity”, Rev. Mod. Phys. 35 (1) , pp. 1-22 (1963) ; see Table IV , p. 12 for a list of superconducting A15 compounds . For an interesting biographical article about Matthias , see : T.H. Geballe and J.K. Hulm , “Bernd Theodor Matthias” (unknown source , undated , PDF , 153 KB) . Matthias's Rules are mentioned on pp. 249-251 .

Simon and Smith's book : R. Simon and A. Smith , Superconductors , Conquering Technology’s New Frontier , Plenum Press , New York , 1988 ; the A15 crystal structure sketch is on p. 115 . Note that the labeling of the A and B atoms has been erroneously reversed in this drawing , i.e. it shows A2B6 (2 x AB3) instead of the correct A6B2 (2 x A3B) . Matthias's Rules are discussed on pp. 112-114 .

refined and broadened : W.E. Pickett , “Probing Room Temperature Superconductivity in a Parallel , Wiser Universe . Metaphysical Considerations” (PDF , 893 KB) , p. 3 (no date) ; idem , “Electron–Phonon Coupling : When Conventional Becomes Unconventional” (PDF , 8633 KB) ; p. 16 (August , 2009) .

was achieved : J.R. Gavaler , “Superconductivity in Nb–Ge Films Above 22 K”, Appl. Phys. Lett. 23 (8) , pp. 480-482 (1973) . Matthias had also investigated Nb3Ge earlier : B.T. Matthias et al. , “Superconductivity of Nb3Ge”, Phys. Rev. 139 (5A) , pp. A1501-A1503 (1965) . They found that for a bulk sample of stoichiometric Nb3Ge the Tc ~ 17 K (onset) .

Krebs summed up : 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 : 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 (23) , 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 (279 KB) .

Arjomand and Machin : M. Arjomand and D. J. 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 ; Table 3 , p. 1062 .

non-metallic : P. Ganguly and C.N.R. Rao , “Electron Transport Properties of Transition Metal Oxide Systems with the K2NiF4 Structure”, Mater. Res. Bull. 8 (4) , pp. 405-412 (1973) . The electrical conductivity of La2CuO4 is discussed on pp. 408-409 , and is shown in Fig. 3 , p. 408 . It remains fairly constant (at about 5 ohm-1cm1) over a wide temperature range (125–1000 K) . I would call it a semiconductor . I suspect that a very pure sample of La2CuO4 prepared in an inert atmosphere and completely devoid of any Cu(III) impurity would indeed be an insulator . For example , very pure NiO is a green insulator , but commercial NiO is a black semiconductor containing some Ni(III) impurity , thus making it a mixed-valent compound . Okajima , Yamada , and Yamaya (Several investigations , below) state , “....... La2CuO4 ......... with no excess oxygen is an antiferromagnetic insulator with a Néel temperature TN of 315 K” (p. 1319) .

Bednorz and Müller : 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) .

Several months later : 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) .

Chu and 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) .

frantic search : R.M. Hazen , The Breakthrough , The Race for the Superconductor , Summit Books , New York , 1988 . See also : B. Schechter , The Path of No Resistance , The Story of the Revolution in Superconductivity , Simon and Schuster , New York , 1989 ; J.L. Mayo , Superconductivity , The Threshold of a New Technology , TAB Books , Blue Ridge Summit (PA) , 1988 ; J. Langone , Superconductors  , The New Alchemy , Contemporary Books , Chicago (IL) , 1989 ; Simon and Smith (see above) also provide a good account (“Breakthrough” , Ch. 13 , pp. 247-265) of the world-wide research efforts in the high temperature superconductivity of the cuprates around 1986–87 .

Fermi-Dirac distribution : A.R. Mackintosh , “The Fermi Surface of Metals”, Scientific American 209 (1) , pp. 110-120 (July , 1963) . The electron theory of metals is discussed by 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 ; see Fig. 2.4 , p. 49 for a sketch of a typical Fermi-Dirac distribution curve .

strength of the covalent bond : R.T. Sanderson , Inorganic Chemistry , Reinhold Publishing , New York , 1967 ; p. 142 .

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

wide-ranging survey : 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 ; see also : 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've discussed the four Robin-Day classes in my web page , “New Solar Cells from Mixed-Valent Compounds”, with various examples of each class , and illustrated with sketches of the examples .

magnetite : The electronic situation in magnetite is quite complex , and there have been many studies of it over the past decades . For reviews of the physics and chemistry of magnetite , see the following two articles : F. Walz , “The Verwey Transition – A Topical Review”, J. Phys. : Condens. Matter 14 (12) , pp. R285-R340 (2002) ; J. García and J. Subías , “The Verwey Transition – A New Perspective”, J. Phys. : Condens. Matter 16 (7) , pp. R145-R178 (2004) .

Selenium : 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) : “ …… Se substitution [in CoS2] introduces strong antiferromagnetic interactions between cobalt atoms” (p. 216) ; 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) : CoS2 is ferromagnetic , CoSe2 is antiferromagnetic .

Tarascon et al. : J.M. Tarascon et al. , “Preparation , Structure , Properties of the Superconducting Compound Series Bi2Sr2Can-1CunOy with n = 1,2, and 3”, Phys. Rev. B38 (13) , pp. 8885-8892 (November , 1988) . See also H. Maeda et al. , “A New High Tc Oxide Superconductor Without a Rare Earth Element”, Jpn. J. Appl. Phys. (Lett.) 27 (2) , pp. L209-L210 (February , 1988) .

oxidize water : M.F. Yan et al. , “Water Interaction with the Superconducting YBa2Cu3O7 Phase”, Appl. Phys. Lett. 51 (7) , pp. 532-534 (1987) .

Cox : P.A. Cox , Transition Metal Oxides , An Introduction to Their Electronic Structure and Properties , Clarendon Press , Oxford (UK) , 1995 ; electron superexchange is discussed on pp. 148-153 , and is illustrated in Figs. 3.21 (p. 150) , 3.22 (p. 151) , and 3.33 (p. 152) . See also A. Tressaud and J.M. Dance , “Ferrimagnetic Fluorides”, Adv. Inorg. Chem. Radiochem. 20 , pp. 133-188 ; H.J. Emeléus and A.G. Sharpe (eds.) , Academic Press , New York , 1977 ; electron superexchange is discussed on pp. 136-142 , and is illustrated in Fig. 1 , p. 137 .

bismuthate superconductor : R.J. Cava et al. , “Superconductivity Near 30 K Without Copper : The Ba0.6K0.4BiO3 Perovskite”, Nature 332 (6167) , pp. 814-816 (1988) ; L.F.

Mattheis , E.M. Gyorgy , and D.W. Johnson , Jr. , “Superconductivity Above 20 K in the Ba–K–Bi–O System”, Phys. Rev. B37 (7) , pp. 3745-3746 (1988) ; J.J. Krajewski , “Synthesis of Superconducting Oxides”, pp. 192-201 in Inorg. Synth. 30 , Nonmolecular Solids , D.W. Murphy and L.V. Interrante (eds.) , John Wiley , New York , 1995 ; the preparation of Ba1-xKxBiO3 is described on pp. 198-199 ; J.C. Stark et al. , “The Preparation of BaBiO3 and the Superconductor K0.4Ba0.6BiO3 from Mixed Metal Alkoxide Precursors”, Mater. Res. Bull. 26 (7) , pp. 623-630 (1991) .

French researchers : M. Foëx , A. Mancheron , and M. Liné , “Sur une Combinaison du Sesquioxyde de Lanthane avec le Protoxyde de Nickel” , Comptes Rendus 250 (18) , pp. 3027-3028 (1960) .

B.M. Klein et al. : B.M. Klein et al. , “Electronic Structure and High Critical Temperature in Oxide Superconductors”, Ch. 3 , pp. 26-43 in Chemistry of High-Temperature Superconductors II , D.L. Nelson and T.F. George (eds.) , ACS Symposium Series 377 , American Chemical Society , Washington , DC , 1988 ; Figure 1 , p. 28 ; ibid. , J. DiCarlo et al. , “Determination of the Homogeneity Range of La2CuO4”, Ch. 11 , pp. 140-144 ; Figure 2 , p. 144 . The La2CuO4 structure was also sketched by J.B. Goodenough , “Ceramic Superconductors , Single-Valent versus Mixed-Valent Oxides”, Ch. 16 , pp. 287-321 in Electron Transfer Biology and the Solid State , Inorganic Compounds with Unusual Properties , M.K. Johnson et al. (eds.) , Adv. Chem. Series 226 , American Chemical Society , Washington , D.C. , 1990 ; Fig. 15 , p. 318 .

ternary nickel oxides : M. Arjomand and D. J. Machin , “Oxide Chemistry . Part I . Ternary Oxides Containing Nickel in Oxidation States II , III , and IV”, J. Chem. Soc. Dalton Trans. 1975 (11) , pp. 1055-1061 .

Several investigations : Y. Okajima , M. Yamada , and K. Yamaya , “Magnetic Properties of La2CuO4 with Slight Amounts of Excess Oxygen”, Physica C 282-287 , Part 3 , pp. 1319-1320 (1997) ; J. Saylor et al. , “Néel Temperature of Stoichiometric La2CuO4”, Phys. Rev. B40 (10) , pp. 6854-6861 (1989) : “The most significant result of our work is the conclusion that stoichiometric La2CuO4 has the highest TN [317 K] ” (p. 6860) ; J. Shimizu , M. Nakagawa , and Y. Oda , “The Normal State Magnetic Susceptibility of La2CuO4+d with Excess Oxygen”, Physica C 388-389 , pp. 263-264 (2003) ; P. Gopalan et al. , “Influence of Oxygen Stoichiometry on the Antiferromagnetic Ordering of Single Crystals of La2NiO4+d”, Phys. Rev. B45 (1) , pp. 249-255 (1992) ; R.A.M. Ram , P. Ganguly , C.N.R. Rao , and J.M. Honig , “Preparation and Characterization of La2CoO4+ ”, Mater. Res. Bull. 23 (4) , pp. 501-506 (1988) . These latter researchers reported a broad TN ~ 150 K for partially-oxidized La2CoO4 ; stoichiometric La2CoO4 has a TN = 275 K (Yamada and co-workers , below) . It's noteworthy that in none of these physics-related papers is the

chemistry subject of mixed-valence cations , compounds or resonance ever mentioned ; an unfortunate oversight , in my opinion .

Wells : A.F. Wells , Structural Inorganic Chemistry , 3rd edition , Clarendon Press , Oxford (UK) , 1962 . The K2NiF4 structure is sketched in Fig. 166 , p. 499 .

Yamada and co-workers : K. Yamada et al. , “Successive Antiferromagnetic Phase Transitions in Single-Crystal La2CoO4”, Phys. Rev. B39 (4) , pp. 2336-2343 (1989) .

Verwey : E.J.W. Verwey , “Valence Induite”, Bull. Soc. Chim. France , mises au point D122 (1949) [“Induced Valence”, Chem. Abs. 43 , 6015g (1949)] .

Johnston : D.C. Johnston , “Superconducting and Normal State Properties of Li1+xTi2-

xO4 Spinel Compounds . I . Preparation , Crystallography , Superconducting Properties , Electrical Resistivity , Dielectric Behaviour , and Magnetic Susceptibility”, J. Low Temp. Physics 25 (1&2) , pp. 145-175 (1976) .

iridescent crystals : M. Kestigan and R. Ward , “The Preparation of Lanthanum Titanium Oxide , LaTiO3”, J. Amer. Chem. Soc. 76 (23) , p. 6027 (1954) .

Rao : C.N.R. Rao , “Localized Versus Collective Behaviour of d-Electrons in Transition Metal Oxide Systems of Perovskite Structure”, J. Indian Chem. Soc. 51 (12) , pp. 979-987 (1974) ; see Figure 3 , p. 982 .

tungsten bronzes : P.G. Dickens and M.S. Whittingham , “The Tungsten Bronzes and Related Compounds”, Quart. Rev. 22 (1) , pp. 30-44 (1968) ; H.R. Shanks , P.H. Sidles , and G.C. Danielson , “Electrical Properties of the Tungsten Bronzes”, Ch. 22 , pp. 237-245 in Nonstoichiometric Compounds , R. Ward (ed.) , Adv. Chem. Series 39 , American Chemical Society , Washington , D.C. 1963 ; M.J. Sienko , “Electric and Magnetic Properties of the Tungsten and Vanadium Bronzes”, Ch. 21 , pp. 224-236 in Nonstoichiometric Compounds ; C.T. Hauck , A. Wold , and E. Banks , “Sodium Tungsten Bronzes”, pp. 153-158 in Inorg. Synth. 12 , R.W. Parry (ed.) , McGraw-Hill , New York , 1970 [republished by R.E. Krieger , Huntington , NY] .

ambient conductivity : Shanks , Sidles , and Danielson in Nonstoichiometric Compounds (immediately above) ; Fig. 2 , p. 240 .

Matthias and co-workers : Ch. J. Raub et al. , “Superconductivity of Sodium Tungsten Bronzes” , Phys. Rev. Lett. 13 (25) , pp. 746-747 (1964) ; N. N. Garif'yanov et al. , “Superconductivity of Sodium Tungsten Bronze with Cubic Structure”, Czech. J. Phys. 46 (suppl. S2) , pp. 855-856 (1996) . They reported a maximum T ~ 1.7 K for Na0.15WO3 .

Rubidium tungsten bronzes : A.R. Sweedler , Ch. J. Raub , and B.T. Matthias , “Superconductivity of the Alkali Tungsten Bronzes”, Phys. Lett. 15 (2) , pp. 108-109

(1965) ; R.K. Stanley , R.C. Morris , and W.G. Moulton , “Conduction Properties of the Hexagonal Tungsten Bronze , RbxWO3”, Phys. Rev. B20 (5) , pp. 1903-1914 (1979) .

J. Guo and co-workers : J. Guo et al. , “Crystal Structure and Superconductivity of Rubidium Tungsten Bronzes RbxWO3 Prepared by a Hybrid Microwave Method”, Mater. Res. Bull. 43 (4) , pp. 779-786 (2008) . They reported a maximum T = 5.3 K (onset) for Rb0.14WO3 .

Inorganic Syntheses : Hauck , Wold , and Banks , “Sodium Tungsten Bronzes”, in tungsten bronzes above .

microwave furnace : J. Guo et al. , “A Green Route for Microwave Synthesis of Sodium Tungsten Bronzes NaxWO3 (0<x<1)”, J. Solid State Chem. 178 (1) , pp. 58-63 (2005) .

Conroy and Yokokawa : L.E. Conroy and T. Yokokawa , “The Preparation and Properties of a Barium Tungsten Bronze”, Inorg. Chem. 4 (7) , pp. 994-996 (1965) .

reagents in organic chemistry : L. F. Fieser and M. Fieser , Reagents for Organic Syntheses , vol. 1 , John Wiley , New York , 1967 . NaH , pp. 1075-1081 ; NaBH4 , pp. 1049-1055 .

Sleight and co-workers : A.W. Sleight , T.A. Bither , and P.E. Bierstedt , “Superconducting Oxides of Rhenium and Molybdenum with Tungsten Bronze Type Structures”, Solid State Commun. 7 (2) , pp. 299-300 (1969) .

SnP : P.C. Donohue , “The Synthesis , Structure , and Superconducting Properties of New High-Pressure Forms of Tin Phosphide”, Inorg. Chem. 9 (2) , pp. 335-337 (1970) .

intercalation compound of graphite : J.-M. Lalancette and J. Lafontaine , “Intercalation of Antimony Pentafluoride in the Lattice of Graphite”, J.C.S. Chem. Commun. 1973 , p. 815 ; J.-M. Lalancette , “Graphite Intercalated Antimony Pentafluoride”, U.S. Patent 3950262 , April 13 , 1976 ; F.L. Vogel , “The Electrical Conductivity of Graphite Intercalated with Superacid Fluorides : Experiments with Antimony Pentafluoride”, J. Mater. Sci. 12 (5) , pp. 982-986 (1977) ; idem , “Intercalation Compounds of Graphite”, pp. 261-279 in W.E. Hatfield (ed.) , Molecular Metals , Plenum Press , New York , 1979 ; see especially Table III , “Acceptor Intercalated Compounds of Graphite”, p. 269 ; idem , “Process for

Conducting Electricity Utilizing a Specifically Defined Graphite Intercalation Compound ”, U.S. Patent 4293450 , October 6 , 1981 ; P.G. Rodewald , “Graphite Intercalation”, U.S. Patent 4035434 , July 12 , 1977 (see especially examples 3 and 4) .

tetrakis(triethylphosphite)nickel(0) : the zerovalent Ni compound tetracarbonylnickel(0) , Ni(CO)4 , might also be tried in the reaction , but it's a very toxic , volatile (b.p. 43 ºC) , thermally unstable chemical . Tetrakis(triethylphosphite)nickel(0) is a stable solid (m.p. ~106 ºC) , and is easier and safer to handle than Ni(CO)4 . Other zerovalent Transition metal (M) carbonyls could be reacted with TiS2 to deposit layers of MS in the flakes . For example , Cr(CO)6 (stable , m.p. ~154 ºC) , should deposit CrS , which is strongly antiferromagnetic [TN = 460 K (187 ºC)] . Pentacarbonyliron(0) , Fe(CO)5 [stable but air-sensitive , b.p. 103 ºC , not as toxic as Ni(CO)4] , should deposit antiferromagnetic FeS [TN = 428 K (155 ºC) ; T. Takahashi , “Magnetic Properties of Stoichiometric Iron Sulfide Single Crystals near the Alpha Transition Temperature”, Solid State Commun. 13 (9) , pp. 1335-1337 (1973)] . Graphite could be treated with Fe(CO)5 , then exposed to air or even pure oxygen to leave a deposit of Fe2O3 [TN = 948 K (675 ºC)] on the surfaces of the flakes . The iron(III) oxide layers might induce superconduction in the graphite at an elevated transition temperature .

 

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