New Solar Cells from Mixed-Valent Metallic Compounds
This web page is intended as an update to an earlier report in which the possibility of fabricating a new type of solar cell (photovoltaic diode , pvd) was discussed . The novelty of the device was its bilayer design : an upper layer receiving the incident radiation , usually sunlight , and a lower layer . The upper layer would be made from a "zerovalent" (uncharged) compound , whose photochemically active atoms would be excited by the light energy received by them . The lower layer of the assembly would consist of a corresponding mixed-valent compound with a similar chemical composition as the top layer , but in a partially oxidized state . The free electrons from the zerovalent compound , excited by the incident light , would be transferred to the lower layer , where they could be temporariliy trapped or absorbed by the similar but partially oxidized atoms .
A hypothetical example was provided , that of a metallic silver(0) compound in the upper layer , and a mixed-valent Ag(0)Ag(I) compound , also metallic , underneath . Silver compounds such as AgBr have been used in photography for over a century and a half , as they are very light-sensitive and undergo fast photoinduced chemical reduction to metallic silver particles . Photoexcitation of the Ag0 valence electrons (nominally 5s1) into the lower layer , where they are trapped by the Ag1+ cations , should produce a measurable potential difference (p.d. , voltage) between the two layers , as long as the upper layer is illuminated . It might similarly be possible to use organic semiconductors such as pentacene , which are currently being investigated as pvd materials , in such a bilayer solar cell . A pure pentacene compound would form the upper layer , and its corresponding Wurster Blue derivative which has a delocalized radical cation in its p MO might form the lower layer , in essence having "holes" into which the photoexcited electrons from the upper layer can fall .
A Single Layer PVT (Photovoltaic Transducer)
The question posed in this essay is : would it be possible to dispense with the upper layer of zerovalent compound , and use only the single layer of mixed-valent compound as the photovoltaic material in the solar cell ? The principle is illustrated in the following simplified sketch :
The free electrons in the metallic bond of the compound are able to move through the crystalline solid under an applied potential difference (p.d.) across it , hence the material is an electrical conductor . In the absence of a p.d. , they will remain close to their parent atomic kernels . In the sketch above , the 5s1 free electrons (black dots) are normally associated with the silver(0) atoms [dark blue] . The light energy falling on the upper surface of the compound excites (or "pushes") them downward into the atomic layers below , where they are trapped , or absorbed , by the silver(I) atoms [light blue] , which temporarily become silver(0) , dark blue . Note that while the free electrons in the metallic bond are mobile , the atomic kernels (silver cations) and spectator anions and cations are fixed rigidly in place in the crystal structure . Thus , when the photoexcited free electrons move from the outer illuminated surface layer down into the dark interior layers , they transport their negative charge with them , and the solid becomes electrically unbalanced . The outer layer , depleted in free electrons , becomes positively charged , and the inner "dark" layers become negatively charged . This charge imbalance should be measurable as a potential difference , or voltage , between the upper and lower surfaces .
The success of this scheme will depend on two main factors : first , the compound must be photochemically active , with mobile free electrons capable of being photoexcited or "pushed" from a lower-valent atom to a higher-valent atom ; and second , the candidate material must be a mixed-valent compound with metal atoms in two different valence states , connected orbitally so that the solid is electrically conductive . In essence , the lower-valent atoms provide the free electrons to be temporarily (under illumination) transferred to the higher-valent atoms , which have the vacancies (empty orbitals) to accept them .
We can see from this simple picture why conventional metals such as iron , copper , aluminum , etc. don't exhibit a photovoltaic effect when illuminated : they consist entirely of zerovalent atoms , without any "holes" to accept the photoexcited free electrons .
Since the layer of mixed-valence compound is homogeneous , there is no "n-type" or "p-type" distinction between chemical species in the material . Strictly speaking , it isn't a diode , which does have distinguishable n- and p-type components . In general terms the mixed-valence compound layer could be referred to as a photovoltaic transducer , PVT (assuming it actually is found to be one) . The word "transducer" in this context is defined as a device that converts one form of energy (electromagnetic radiant energy) into another form of energy (electrical) .
Whether or not a monolayer of mixed-valent compound will be photovoltaic when illuminated must be determined experimentally on a case-by-case basis . Let's look at mixed-valent compounds in general , and consider specific examples of possible candidates for photovoltaic activity .
Mixed-valent compounds have been known for centuries . The mineral magnetite (Fe3O4) , with Fe(II) and Fe(III) , was used as a compass component ("lodestone") by medieval mariners . The inorganic compound Prussian Blue a complex Fe(II) / Fe(III) cyanide was discovered in 1704 and subsequently employed as a paint pigment . In the last two decades many mixed-valent copper oxide derivatives have been prepared and studied as superconductors . YBCO , with the empirical formula YBa2Cu3O7 , has mixed-valent copper(II) and (III) .
The first comprehensive study of mixed-valence compounds was made by Robin and Day in 1967 (the references are below , at the end of this web page) . They proposed an organization of mixed-valence compounds into four classes :
Class I : The compound's metal atoms are of the same element in two different valence states , but there is no electron exchange between them . This is because the two different types of cations have different coordinations by anions or other ligands . Verwey's Rule states that in mixed-valent compounds the cations must be in crystallographically equivalent sites in order for any valence electron exchange to occur . When the metal atoms have a similar coordination by ligands , their valence electron orbitals will usually be able to overlap properly , forming a conduit through which the electrons can resonate between the metal atom kernels . Gallium dichloride , GaCl2 , is a good example of a Class I mixed-valent compound :
The compound consists of equimolar quantities of eight-coordinated gallium(I) and tetrahedrally coordinated gallium(III) . GaCl2 is a white crystalline solid melting at 170.5 ║C , with covalent GaCl bonding and no electron exchange between the gallium atoms .
Red lead oxide (whose old-fashioned name is "minium") is a Robin-Day Class I mixed-valent compound with electronically-isolated lead(II) and lead(IV) atoms , and with covalent leadoxygen bonds :
Class II : The mixed-valent cations have a similar coordination , are separated by anions, and the valence electrons can resonate between them through the anion bridges . Prussian Blue , mentioned above , is a Class II compound , with octahedrally coordinated iron atoms . It can be prepared in various forms , but they are all chemically iron(II,III) cyanide with a cubic crystal structure :
The iron(II) cations (green) are coordinated by the carbon ends (black) of the cyanide anions (with triple bonds) ; the iron(III) cations (red) are coordinated by the nitrogen ends (blue) of the CN ligands . The water-dispersible form of Prussian Blue contains potassium or ammonium cations (aqua) nesting in the "supercube" cavities of the lattice . There are also water molecules of hydration trapped in some of the empty cavities too , but these have been omitted in the sketch for clarity . As its name suggests , Prussian Blue is a deep blue crystalline solid . I haven't been able to find any electrical conductivity data for it , but I suspect that Prussian Blue is at best a semiconductor .
Magnetite is another compound with mixed-valent iron atoms . It has the AB2X4 spinel structure , of the "inverse" type :
My rather crude molecular model above poorly represents the complex spinel structure , which was too large to construct with my modeling software . For a more accurate picture of the spinel crystal structure , see this GIF image from the web page , "Ionic Crystals" (University of Kiel , Germany) . The following is a reproduction of a sketch of the spinel structure by Verwey and Heilmann , who determined its atomic arrangement by X-ray crystallography in the mid 1940s :
This close-packed spheres representation provides a wider view of the spinel structure , showing the regular packing order of the tetrahedral and octahedral cations among the anions .
Magnetite has the empirical formula Fe3O4 , or Fe2+(Fe3+O2)2 , ferrous ferrite . Its formula as a spinel would be Fe3+tetFe2+octFe3+octO4 , where "tet" and "oct" stand for tetrahedral and octahedral coordinations by the oxide anions . In the above model , the blue spheres represent the tetrahedral iron(III) cations , and the red spheres are the octahedrally coordinated iron(II) and (III) cations . The oxide anions are shown as the green spheres . Because of the fortuitous inverse nature of the magnetite structure , ferrous and ferric cations are both in the similar octahedral coordination by oxides . In "normal" spinels , such as the mineral spinel itself (magnesium aluminate) , the A cation is tetrahedral and the M cations are both octahedral :
In the magnetite lattice the base iron cations are all Fe(III) , and the "extra" valence electrons , formally the 3d6 electrons from the iron(II) cations , can resonate over the octahedrally coordinated iron atoms but not with the tetrahedral iron(III) cations . This resonance is facilitated by the intermediate oxide anions , in a "superexchange" process . M÷ssbauer spectra of Fe3O4 show that
"......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 , p. 304) .
Crystal field splitting of the 3d orbitals' energy levels is very different in tetrahedral coordinations than in octahedral coordinations , and only in the latter environment will the iron orbitals be able to overlap properly with those of the the oxide bridges , forming a molecular orbital through which the "extra" Fe(II) electrons can resonate . Magnetite is an electrical conductor , although not a particularly good one , having an ambient conductivity of about 100 ohm-1cm-1 . This value remains fairly constant over a wide temperature range . However , when magnetite is cooled below 120 K , its conductivity suddenly plummets , and it becomes almost insulating below that temperature (known as the Verwey temperature , after the Dutch solid state physicist E.J.W. Verwey , who studied magnetite and other ferrites , and who developed doping techniques to produce mixed-valent compounds) . The likely explanation is that the mixed-valence resonance of the 3d6 electrons between the octahedral iron(II,III) cations is temperature-dependent ; that is , it requires heat energy from the crystal environment to function , and when that heat energy is removed , the resonance ceases and the 3d6 electrons become localized , or "pinned" , onto their parent iron(II) kernels .
The tungsten bronzes are a third example of Class II mixed-valent compounds . They have a perovskite AMX3 crystal structure , with WO3 forming a supercube lattice , and with various large A cations trapped in the cage-like cavities :
Blue spheres : W(V,VI) ; red spheres : oxygen ; green spheres : large "A" cations . With half of the cavities filled , the tungsten bronze above would have the empirical formula A0.5WO3 . The family of tungsten bronzes is very large ; many metallic elements "A" have been inserted into WO3 , although the most widely studied have been the alkali metal tungsten bronzes . In fact , ten elements are generally considered to form "bronzes" : Ti , Zr , V , Nb , Ta , Cr , Mo , W , Re , and U , so the scope of these Class II compounds is very wide .
In contrast to magnetite , the tungsten bronzes can have remarkably high electrical conductivities , which are dependent on the doping level . For example , in the cubic NaxWO3 series , when "x" is below 0.3 , the compounds are poor semiconductors . The Na0.5WO3 bronze has an ambient electrical conductivity of around 18,000 ohm-1cm-1 , and those with higher doping levels of x>0.8 can have conductivities of up to 70,000 ohm-1cm-1 , well in the metallic range (Shanks et al. , 1963) . This is because , when the "A" element enters the WO3 lattice , it donates its valence electrons to the tungstenoxygen p orbitals , creating a pi XO (crystal orbital , metallic bond , conduction band) throughout the WO lattice . The more "A" element is used to dope the WO3 lattice , the richer the XO becomes in mobile free electrons , and the higher is the compound's electrical conductivity . The bronzes are all brightly coloured solids with a noticeable metallic luster .
Robin and Day considered the tungsten bronzes to be IIIB compounds , with direct W-W bonds . However , I respectfully disagree with their analysis , and have assigned the tungsten (and other) bronzes to Class II . Robin and Day placed mixed-valent compounds in the Classes II or IIIB according to whether or not the metal cations were distinguishable or indistinguishable , usually by spectroscopic means . However , I prefer and have adopted the practice for this and other essays on the subject to assign mixed-valence compounds to either Class II or IIIB on a structural basis . In Classes I and II the metal cations are separated by anions or other ligands ; in Classes IIIA and IIIB there is direct metal-metal bonding between the cations . For example , in the the superconducting cuprates , the copper(II) and (III) valences are reproportionated , such as to Cu(2.33+) in YBCO . Robin and Day would have called YBCO a Class IIIB compound . However , direct CuCu bonding in this material is highly unlikely . Its XO is undoubtedly over the entire CuO lattice ; therefore I have assigned YBCO to Class II .
Class IIIA : These are metal cluster compounds , with direct metal-metal bonds . Niobium monoxide (which is homovalent , not mixed-valent) is good example of a metal cluster compound :
Small red spheres : niobium atoms ; larger green spheres : oxygen atoms . NbO has an extended atomic lattice structure , with NbO p orbitals participating in the metallic bond XO throughout the solid . It has an excellent ambient electrical conductivity of 50,000 ohm-1cm-1 , and it becomes superconducting at 1.38 K . On the other hand , the IIIA compounds are molecular , with little if any resonance of the metal atoms' valence electrons between the molecules . They resemble NbO in their metal-metal bonding and cage-like structures , but are halides such as [Mo6Cl8]4+ , Nb6Cl14.8H2O , and [Ta6Cl12]2+. Described as "deeply coloured" solids , they are poor semiconductors or insulators , in contrast to NbO . The structure of [Ta6Cl12]2+ resembles that of NbO above ; the structure of [Mo6Cl8]4+ is somewhat similar , with the familiar "metal cage" structure of the Mo6 octahedron (red) , square-coordinated by chlorine atom ligands (blue) :
Class IIIB : These compounds are often called the "synthetic metals" , having metal-metal bonds in an extended atomic lattice . The classic example of a synthetic metal is KCP , a platinum compound with the formula K2Pt(CN)4Br0.3 . 3H2O . At room temperature the platinum valences in KCP - about five parts Pt(II) and one part Pt(IV) - are perfectly blended together (reproportionated) to form the non-integral oxidation state (NIOS) of Pt(2.30+) . X-ray diffraction studies of KCP and related compounds (sometimes called "Krogmann Salts" after the German researcher who first determined their structure in the late 1960s) revealed them to be composed of stacks of square planar platinum(II,IV) cyanide molecules :
Aqua spheres : platinums ; black spheres : carbons , which are triply-bonded to the nitrogens (blue) . Bromide anions and water molecules of hydration are omitted for clarity . The yellow spray paint represents the metallic bond in KCP .The 5dz2 platinum orbitals overlap continuously along the vertical (z) axis , producing the sigma XO which bonds the Pt(CN)4 molecules together in the linear stacks .
Electrical conduction in the Class IIIB synthetic metals is usually quite high . Actually this isn't the case with KCP ; its ambient electrical conductivity is only 830 ohm-1cm-1 , compared with that of platinum metal at 101,523 ohm-1cm-1 ; this might be attributed to its rather narrow sort of XO . The conductivity in KCP is also anisotropic . That is , it is excellent along the major axes of the crystals , which run along the PtPt metallic bonds , but very poor semiconducting across them . Isotropic mixed-valent candidate compounds , identical along all their crystal axes in structure and physical properties , would be preferable for the photovoltaic testing . KCP is also what I refer to as a "pseudometal" [in conventional literature , a semiconductor , but it's much more conductive than the classic semiconductors like doped silicon] . It has a direct temperature-electrical conductivity relationship , in contrast to the "true metals" , which all have an indirect relationship . As KCP is cooled down , its electrical conductivity gradually declines . Below 60 K , its conductivity rapidly falls like magnetite's at 120 K and it becomes a genuine semiconductor .
I mentioned at the beginning of this web page the hypothetical silver-fluoride perovskite compound suggested as a candidate for examination as a photovoltaic material . There is a well-known silver-based synthetic metal , silver subfluoride , Ag2F , with Ag(0) and Ag(1+) perfectly reproportionated into Ag(0.5+) . Silver subfluoride is readily prepared from silver and AgF . It has been described as a very hard , crystalline material , brass-colored with a greenish tinge and a metallic luster . . Its ambient electrical conductivity is 42,000 ohm-1cm-1 (that of pure silver is 618,430 ohm-1cm-1) , and it becomes superconducting at 0.058 K . Silver subfluoride has the anti-CdI2 structure , with alternating layers of silver atoms and fluorides :
Aqua spheres : silver(0.5+) cations ; green spheres : fluoride anions . Unlike KCP , Ag2F is isotropic and a true metal , and it might be worthy of examination for a possible photovoltaic effect . In particular , it would be interesting to try to form an extremely thin layer of Ag2F on a sheet or foil of silver or other metal substrate (eg. silver-plated glass [mirror] or plastic) , and examine this composite for a photovoltaic effect between the outer Ag2F surface (exposed to the light source) and the under side of the metal substrate .
Molecular beam epitaxy (MBE) is a high-tech method for coating substrates with layers of "sprayed-on" atoms . It should be possible to deposit a layer of silver subfluoride , several atoms thick , on a suitable metal surface such as a thin silver foil or silver-plated glass or plastic . Presumably fluorine atoms (as molecules) would be sprayed over the silver(0) surface , forming an ultrathin coating of AgF ; then an outer layer of silver(0) atoms would be added , completing the Ag2F film . Although silver subfluoride seems to be a unique compound among the coinage metals , it might be possible to create analogue coatings of metal subhalides using MBE . For example , Ag2X films , with X = Cl , Br , and I , could be similarly examined . In the case of copper , CuF is apparently unknown , so the analogue material Cu2F might be too unstable to isolate . However , the Cu2X compounds (X = Cl , Br , and I) would be interesting to study for possible PVD properties , if they could be synthesized as ultrathin films on a copper foil substrate by MBE .
Properties of the four classes of mixed-valent compounds , as categorized by Robin and Day , are summarized in the following Table :
Clearly , the most desirable type of mixed-valent compounds for our application to solar cells will be found in Class IIIB , the synthetic metals , with their excellent electrical conductivies . However , we shouldn't rule out the Class II compounds . The IIIB materials , as synthetic metals , have a noticeable metallic luster ; they reflect light fairly well , so they correspondingly don't absorb a significant amount of it . That will translate into a low conversion efficiency of light energy into electricity . On the other hand , while the Class II mixed-valent compounds are usually poor electrical conductors , they are all intensely coloured , often dark blue or black . Magnetite , for example , is jet black , as are the cuprate superconductors such as YBCO . That suggests they absorb a relatively high percentage of their incident light energy across all or most of the visible spectrum (the black compounds may reflect some of it away as infrared light , though) .
I think it's important to note that while there is a strong valence electron exchange , or resonance , in both Class II and IIIB mixed-valent compounds , which is driven by environmentally-derived energy (heat and light) , such an exchange doesn't necessarily result in electrical conductivity in the former materials . For example , while Prussian Blue has a deep blue colour , it's probably only a poor semiconductor at best . Another excellent example of this is the mineral crocidolite , which is an amphibole type of asbestos . The most important source of crocidolite is (or was) South Africa , where it is commercially referred to as "Cape Blue" ; the milled fibre is rather stiff and spiky , and has a deep sapphire blue colour . Crocidolite is (or was) also mined in Cochabamba , Bolivia , and is called "Bolivian Blue" . This latter form of the mineral consists of long , soft , silky fibres with a silvery-lavender colour . Crocidolite's mineralogical name is "fibrous riebeckite" , and it's a sodium iron(II,III) silica hydroxide with the formula Na2(Fe2+)3(Fe3+)2[Si8O22](OH)2 . Bolivian Blue is "fibrous magnesioriebeckite" , with Mg2+ substituting for some of the Fe2+ cations in the crystal lattice . That "dilutes down" the Fe(II)Fe(III) resonance , reducing the intensity of the blue colour of the mineral . However , I am unaware of any type of crocidolite being an electrical conductor , or even semiconductor . The Fe(II) 3d6 electrons can resonate through bridging oxygen anions between the iron atoms , but there is no actual metallic bond in crocidolite .
The three Class II mixed-valent compounds mentioned above having a significant ambient electrical conductivity are magnetite , the tungsten (and other) bronzes , and the superconducting cuprates such as YBCO . Magnetite's conductivity is fairly constant over a wide range of temperatures , but it seems to slowly rise with increasing temperature , suggesting that it is a pseudometal . Magnetite has been called a hopping semiconductor , referring to the way in which its iron(II) 3d6 electrons seem to jump from one iron atom to another via oxygen bridges . It's possible that light energy on the surface of magnetite and for that matter , any mixed-valent compound will only cause the mobile valence electrons to resonate even faster between their respective cations , and won't push them deeper into the solid , even temporarily .
The tungsten bronzes , such as those in the cubic sodium series , are true metals (a few even become superconducting near Absolute Zero) with high electrical conductivities in the metallic range when they contain higher amounts of sodium dopant . They might be more promising candidates for examination of a photovoltaic effect . A series of NaxWO3 compounds , with x = 0.3 to 0.9 , could be tested as follows . Ideally , a thin film of candidate compound should be deposited on an inert metal substrate (sheet or foil) , but this might be difficult to do in a simple experiment . Instead , the researcher could prepare small , thin discs of the compound using a "KBr disc" press . This procedure will be familiar to organic chemists , who grind a sample of solid organic compound with potassium bromide (KBr) powder , then make a small , thin disc of the mixture by compressing it in a mold in a strong press . The translucent disc so produced is secured in a holding plate , which slides into place in an infrared (IR) spectrophotometer , to obtain the IR spectrum of the organic compound dispersed in the KBr . In our case , the test disc of NaxWO3 would be examined for any photovoltaic activity by shining a suitable light on its upper surface , while measuring any resulting potential difference (p.d.) . A suggested setup is sketched below :
The test apparatus could be fabricated from an insulator such as wood or plastic (red in the above sketch) . A circular cavity with a diameter slightly greater than the test disc would be machined in its surface . A metal disc (blue) is placed in the receptacle , with the test disc (yellow) on top of it . A metal screw (gray) is tapped through the tester's side , to contact the metal disc . A second screw is tapped into the top side of the tester , securing a small metal plate or clip pressing on the upper side of the test disc . The two screws are the contact electrodes of the apparatus , to which the electrical multimeter's testing leads are attached .
The superconducting cuprates would also be interesting to examine as PVT candidates . They are black in appearance , indicating a strong absorption of incident light , and are modest electrical conductors at room temperature . For example , YBCO's ambient electrical conductivity is about 500 ohm-1cm-1 ; it's a true metal , as shown by its inverse temperature-conductivity relationship :
The above graph was prepared using data from the influential paper by M.K. Wu et al. , describing YBCO's preparation and properties . The researchers presented their results in sample-specific conductance terms , rather than in the universal conductivity units , but the principle is the same . Note that below about 90 K the sample became superconducting ; this part of the curve deviated from linearity and was omitted in my graph . YBCO has a layers of copper(II,III) oxide with electronically-inert Y3+ and Ba2+ spectator cations nesting in cavities in between the layers :
Small red spheres : copper cations ; green : oxide anions ; yellow : yttrium cation ; larger violet spheres : barium cations . The small test disc of the compound could be prepared in the usual manner , with sintering , annealing , and cool-down in an atmosphere of pure , flowing oxygen .
Class IIIB Perovskites
Desirable properties of a PVT will include a high ambient electrical conductivity , in the range of the common metallurgical metals ; true metal behaviour (inverse temperature-conductivity relationship) ; direct metal-metal bonds in an extended atomic lattice ; a NIOS valence for the metal cations (i.e. a Class IIIB mixed-valent compound) ; be isotropic (similar properties along all crystal axes) ; and have a high light absorption and retention (i.e. a black appearance) . It might be difficult to reconcile all these beneficial properties in a single material . For example , Class IIIB compounds usually have a high electrical conductivity and a strong metallic reflectivity ; the Class II compounds are often dark blue or black but have a poor electrical conductivity .
Existing mixed-valence compounds could be examined for any possible photovoltaic effect in them , as discussed above . It might also be possible to design new mixed-valent materials in which several of the desirable properties noted might be present . The most promising materials are inorganic compounds in which the resonant "extra" valence electrons are in the voluminous s AOs . This is the situation in silver subfluoride , described above . However , Ag2F is a rather unusual substance , and is likely specific only to the coinage metal group of elements , if not exclusive to silver itself . A more general example was provided in the hypothetical silver-fluoride perovskite mentioned at the beginning of this web page .
Mixed-valent perovskites could be formulated in which the resonant "extra" valence electrons are in the large "A" cations of the AMX3 compound . If one of the component A cations was actually a zerovalent A atom , then the resonant electrons should be in the voluminous s AOs . The resulting sigma XO in the crystalline solid should resemble that in the corresponding elementary metal to a certain extent (the metallic bonds in all the elementary metals are primarily sigma XOs , formed from valence , or frontier , s AOs) .
Perovskites can be portrayed in several ways . The following is the commoner A-type structure :
The A cation (green sphere) is in the middle of the supercube "MX3 cage" , with smaller M (red) cations and X (blue) anions . However , the A cations can be shown preferentially in the B-type structure :
In this sketch we can see that direct metal-metal bonds could theoretically form between the A cations . Of course , these are "exploded" ball-and-stick models , with the component atoms spread well apart and connected by bonds for easy viewing . The close-packed spheres representation of crystal structures , such as are shown in the excellent textbooks by Sanderson and Wyckoff , are more realistic and "truer" than my sketches . However , they are much more difficult for me to visualize and understand , and in any case I can't draw them with my chemistry software ! The presence of the anions (blue) in the layers of A cations (green) will undoubtedly attenuate to a certain extent any metallic bond that may form between the latter atoms , as the negative charge of the anions will repel the free electrons in the XO surrounding the A cations .
The mixed-valent perovskites with A0 and Ay+ metal species might be synthesized from the two components A0MaX3 and Ay+MbX3 , which are also perovskites . They would have to be prepared separately , then in a third step , one would be "doped" into the other in varying mole ratios , producing a range of composites with varying properties of interest to the researcher :
x A0MaX3 + (1-x) Ay+MbX3 ----------------> A(y-xy)+(Ma)x(Mb)1-xX3
In this formula , x is a mole ratio taken experimentally from zero to unity . Thus , a series of composite compounds from pure A0MaX3 to pure Ay+MbX3 could be made ; how many of them would depend on the researcher's particular program .
Many AMX3 compounds are known , but not all are perovskites . The relative sizes of the A , M , and X components will determine which kind of crystal structure the compound adopts . A tolerance factor formula , sometimes called the Goldschmidt equation after its inventor , has been devised to provide some idea as to what sort of structure the particular AMX3 compound will have :
The radii in the equation are the crystal ionic radii of the component ions in the compound . This "tolerance factor" equation is only an approximation to be applied cautiously , because we will also use other atomic radii with it , depending on the chemical bonding in the solid . For example , in the well-known piezoelectric perovskite , barium titanate , the Ti-O bonds are covalent , not ionic , as the discrete Ti4+ cation doesn't exist ; it is usually represented as Ti(IV) , where the Roman numerals indicate covalent bonding . The salt potassium iodate , KIO3 , is a perovskite , with covalent I-O bonds . In these cases we should really use the values for the covalent radius of the atoms involved . With the A0MaX3 compounds I'll use the metallic radii values for the A0 atoms in calculating their tolerance factors .
Tolerance factors are helpful in giving us an idea of whether or not a hypothetical compound we design will indeed be a perovskite or not , and if so , what its crystal symmetry will be . The range of tolerance factors for perovskites is thought to be from 0.78 to 1.05 . Below 0.78 another type of crystalline solid will form , usually an ilmenite (after the mineral ilmenite , FeTiO3 , an important ore of titanium) . Ilmenites will often result when the "A" cation is too small for the MX3 cavity , causing the MX layers to shift diagonally to permit them to close more tightly about the A cations . In the case of very small A cations , the corundum crystal structure will result (after that of alumina , Al2O3 = Al3+AlO3 , also known as corundum) . I don't know what crystal structures will form at tolerance factors greater than 1.05 .
Cubic symmetry of perovskites is favoured by tolerance factors ranging between 0.89 and 1.00 . Outside those values a lower symmetry of the crystal will be observed . Although non-cubic perovskites may exhibit a photovoltaic effect and be quite satisfactory for use in solar cells , I have tried to design , for simplicity , only the cubic variety in this study . This is basically a "mix-and-match" process , juggling the A , M , and X atoms until a suitable tolerance factor for them is found .
Although various anions can theoretically be used in the synthesis of perovskites , in reality the oxides are by far the commonest sort encountered (and indeed are the most useful in practical applications) . However , the low valences (0 to 2) involved for the A and M cations in my proposed Class IIIB perovskites require the use of halide anions as the X component , in order to keep all the valence charges balanced . In actual practice , I have examined only fluorides in this report , although the other corresponding halides may also be acceptable (the chlorides are usually the cheapest of the series , as well : an economic factor that might eventually need to be considered) .
Let's first look at the zerovalent series of A0MaX3 compounds . The insertion of zerovalent atoms into host lattices is fairly well-known , although it remains a HUGE uncharted region of inorganic chemistry , as its scope is very wide . Two much studied host materials for the intercalation of many different types of inserted species (both atomic and molecular) are graphite and the MX2 chalcogenide compounds (M = Ti , Zr , Hf , V , Nb , Ta , Mo , W , and Sn ; X = S and Se) . For example , potassium metal can be inserted into graphite , and lithium metal can be doped into TiS2 .
Several years ago , while visiting one of those "New Age" boutiques (called "l'Age du Verseau" , the "Age of Aquarius") , I noticed a pretty pink quartz crystal among their mineral specimens for sale as "magic crystals" . According to its card , it had been doped with gold atoms . Since gold doesn't react with silicon dioxide , it would remain as zerovalent atoms in the silica lattice . That made me think : would it be possible to form a stoichiometric compound of gold(0) and SiO2 ? If so , would the gold atoms be electronically linked , and would the compound be a metallic solid ? What would its crystal structure be ? And then : would it be generally possible to insert zerovalent metal atoms into a vast range of unreactive acceptor inorganic lattices , thus forming many fascinating new metallic compounds ? Maybe some of them could be doped with the corresponding metal cations , to form Class II and IIIB mixed-valent compounds . A few of those new compounds might even be superconductors ! I have discussed this topic at length in my ebook , available without charge by download from this website .
Again , for the sake of simplicity and brevity , I'll restrict the metal atom candidates to those of the "soft metals" (sometimes called "poor metals") on the right-hand side of the Periodic Table . The Alkali and Alkaline Earth elements are too reactive for the fluorides ; for example , aluminum was isolated in 1827 by the reduction of aluminum chloride with potassium metal . The refractory Transition metals are for the most part too "hard" (probably) to serve as reagents here , although their volatile carbonyls - for example , pentacarbonyliron(0) , Fe(CO)5 , b.p. 103 ║C - might be suitable precursors for metal insertion . I've compiled a list of possible metal atom candidates for insertion into fluorides , below :
The elements shown in red are those I think are the most practical , in that it might be possible to form their corresponding Ay+MbX3 perovskites , which will of course be necessary when preparing the mixed-valent Class IIIB compounds . The "n/a" designation means that the metal's boiling point is so high that it need not be taken into consideration when designing the experimental procedure for it (in my opinion , but the interested researcher should of course verify all this data for him/herself) .
In a second table I have listed possible MX3 candidate lattices (mostly fluorides) into which the above metal atoms might be inserted , in a 1:1 stoichiometric ratio , to form an A0MaX3 compound :
Consider the possible insertion of copper into AlF3 to produce the compound Cu0AlF3 . The AlF3 host lattice has large cavities in which zerovalent guest atoms might nest :
This model of AlF3 is in the polyhedral style , which I often find somewhat confusing and difficult to understand . I prefer the ball-and-stick representations of crystal structures , but in this case the back-and-forth and up-and-down tilting of the AlF6 polyhedra made a ball-and-stick model very difficult for me to draw with my chemistry software . The small greenish spheres represent fluoride anions , with the aluminum cations hidden at the centers of the octahedrons .
The MF3 fluorides tabulated above are mostly ionic , with the exception of those of bismuth and antimony , which have covalent bonds (SbF3 is known to be a molecular solid , with a relatively low melting point) . Aluminum fluoride is a high melting ionic solid , compared to AlCl3 , which is a low melting (or subliming) molecular compound . The high melting points of the MF3 fluorides are advantageous , as their reaction mixtures with the metal reagents may require heating at a high temperature to effect a diffusion of the metal atoms into the host lattices . All of these MF3 fluorides are commercially available , for example from Alfa-Aesar and Aldrich Chemicals (and probably from the fluorine chemical company , Ozark Fluorine Specialties ) .
May I suggest to any interested researcher that he/she conduct a microscale "pilot experiment" for each insertion reaction , using the helpful technique of differential thermal analysis (dta) . Typically in a dta run about 25 to 50 mg of reaction mix are placed into a tiny quartz test tube , which is heated at a steady rate from room temperature to the desired higher temperature . A thermocouple (usually made of a platinum/rhodium alloy) is placed in the reaction mix , and a second test tube with an inert "control" or reference material (often calcined alumina) and thermocouple is placed in the heating block with the reaction mix test tube . Dta measures energy changes in the reaction mix as it is heated up , with reference to the inert control material . Such energy changes will be produced by the melting of a component , a chemical reaction , or a recrystallization . These physical and chemical changes are usually either exothermic or endothermic , and can be monitored by the dta equipment . Thus , dta can provide valuable information to the researcher , while only using a very small amount of reaction mixture . This advance "pilot experiment" can then guide the researcher in designing a macroscale preparation , if desired (of course , the reaction product from the dta run can usually be recovered and examined , to provide more information as well) .
The reaction mixture , thoroughly ground in a mortar with a pestle , would be pressed into a cylindrical pellet , which is then heated to the appropriate temperature . An inert atmosphere of nitrogen or argon should be used in the furnace , since most of the metals tabulated above will oxidize in air . Special techniques would have to be devised for the more volatile metals such as mercury , zinc , and cadmium (and probably thallium) . Their reaction mixtures would have to be encapsulated in an ampoule or autoclave , for heating under pressure . Such encapsulation would also keep the very toxic metal vapour from infiltrating the furnace and laboratory (and eventually , the chemist !) .
Using the radii values of 1.28 ┼ for Cu0 , 0.54 ┼ for Al3+ , and 1.33 ┼ for F- , the tolerance factor for Cu0AlF3 is calculated to be 0.99 , so it could be a cubic symmetry perovskite . With the formation of an XO from the direct overlapping in the solid of the copper 5s AOs (Cu0 is 5s1 electronically) , the compound could be a synthetic metal . However , it is homovalent , not mixed-valent . It requires the corresponding Cu1+M2+F3 (or Cu2+M1+F3) dopant compound to complete the Class IIIB mixed-valent composite for examination as a photovoltaic material . These latter compounds , while they might actually exist or could be made , probably wouldn't be perovskites , as both copper(I) and copper(II) are very small cations .
Here's a tabulation of a number of A0MaX3 compounds I think would be interesting to investigate :
The lists of silver and thallium compounds are shown to illustrate how use of the different MX3 host lattices might "tweak" the structures of the resulting adducts . The insertion technique would be a neat method of preparing synthetic metals of Cu , Zn , Al , Cd , Tl , Sn , Pb , and Bi for the first time . The aluminum(0) compound would be quite exceptional if it could be made . Note that aluminum metal is a fairly strong reducing agent (1.662 V ; in a fluoride environment , 2.069 V) ; that would sharply limit the number of host lattices it might be inserted into . Its zerovalent perovskite , Al0AlF3 , should be a Class I mixed-valent compound with no electronic communication between the Al0 and Al3+ atoms , yet it could still be a metallic solid from the XO formed between the Al0 3s AOs (Al0 is 3s2 3p1 electronically , but electron density can "leak" from the filled 3s to the unfilled 3p AOs , permitting the partially-opened 3s AOs to overlap in the solid and act as the metallic bond XO in it) . I'm assuming that the Al0AlF3 , if it forms , will retain its perovskite structure and doesn't reproportionate to another structure , such as (Al0,3+)2F3 , possibly a corundum [but Al0 octahedrally-coordinated by fluorides would probably be very unstable] .
The second step if the first is successful would be to prepare the Ay+MbX3 component of the mixed-valent composite . This should be fairly straightforward , since many fluoride (and other halide) perovskites are well-known . Probably the simplest technique for preparing them would be the chemie douce method of metathesis of the metal cations in water solutions at room temperature , with precipitation of the insoluble double-fluoride perovskite . This procedure , suitable as a student experiment , was described for the preparation of the series of KMF3 perovskites , with M a Transition metal divalent cation (Mn , Fe , Co , Ni , Cu , and Zn) . In our case , if the A and M fluorides are very soluble in water , they can be used directly ; if not , the universally soluble nitrate salts could serve as the reagent . The fluoride source could be the neutral salt , ammonium fluoride . For example :
AgF + 2 NH4+F- -------- (1) dissolve in water (2) add Mg(NO3)2 . 6 H2O (aq) --------> AgMgF3 (c) + 2 NH4+NO3- + 6 H2O . Silver(I) fluoride is very water-soluble (1820 g/L) ; MgF2 is very insoluble (0.076 g/L) . AgZnF3 is known(1) to be a cubic symmetry perovskite (t = 0.89) .
Pb(NO3)2 + LiNO3 --------- (1) H2O (2) add 3 NH4+F- (aq) --------> PbLiF3 (c) + 3 NH4NO3 . Lead(II) fluoride is slightly soluble in water (0.64 g/L) ; LiF is sparingly water-soluble (2.7 g/L) . BaLiF3 is known(2) to be a cubic symmetry perovskite (t = 0.99) .
Direct combination of lower-melting A and M fluorides might also be possible , in a "shake-'n-bake" procedure :
PbF2 (m.p. 855 C) + LiF (m.p. 842 C) ---------- (1) grind together (2) press a pellet (3) heat in furnace under argon atm. --------------> PbLiF3 (c) . Dta would be very helpful here as a "microscale pilot experiment" , to determine the optimum reaction conditions for the macroscale preparation .
The A0MaF3 and Ay+MbF3 sets of perovskites would then be combined in separate series of doping trials . The direct combination method would have to be used , with a shake-'n-bake technique as noted above . In certain cases with lower-melting components the mixed-valent composite might be synthesized in a one-pot (one step) reaction ; for example :
x Pb0 + x CeF3 + (1-x) PbF2 + (1-x) LiF ---------------> Pb(2-2x)+CexLi(1-x) F3
Note : "x" is a mole ratio taken experimentally from zero to unity , with as many composite test specimens synthesized as the researcher considers necessary .
I have studied many A0MaF3 / Ay+MbF3 combinations , finally selecting six of the more useful ones based on two criteria . I wanted both compounds in the sets to be cubic symmetry perovskites (assuming they can actually be synthesized , of course) , and I wanted them to be practical , in the economic sense and in the chemical sense of being stable , "reasonable" materials . These six sets of A0MaF3 / Ay+MbF3 Class IIIB fluoroperovskites are tabulated below :
Since gold(I) and indium(I) are unstable with respect to disproportionation to M(0) and M(III) , I didn't include them in the survey . Both elements and their compounds are in any case very expensive ; the price of gold just topped $700 U.S. per Troy ounce as I was writing this web page (mid-September , 2007) . This is rather discouraging for any future prospects of their large-scale application in actual solar energy panels . Gold is even more expensive than the gallium in the costly gallium arsenide PVDs that are the "best" of the current solar cells (about 35% energy conversion efficiency) .
In the case of Hg2+LiF3 , I calculated its tolerance factor , 0.84 , based on a crystal ionic radius of 1.14 ┼ ; however , this is for an 8-coordinated cation , and the radius for a 12-coordinated cation , as in the A cations of perovskites , is expected to be significantly larger . So I "guesstimated" its reported tolerance factor at t = >0.89 . The Ag1+ radius value I used , 1.28 ┼ , was similarly for an 8-coordinated cation , but in this case (for Ag1+MgF3 ) I retained the calculated tolerance factor of t = 0.90 . All other A cation radii values used were for 12-coordinated cations (from the CRC Handbook of Chemistry and Physics , cited above) . The tin(II) radius wasn't listed in there ; I found a value for it , 1.36 ┼ , in Smart and Moore's excellent textbook . I believe the radii values they give are for 8-coordinated cations .
The thallium couple is most interesting . The metallic radius of Tl0 (6p1) and the crystal ionic radius of Tl1+ (6p0) are both 1.70 ┼ . The M cations in the thallium perovskites , Ce3+ and Ca2+ , have almost identical radii (1.01 ┼ and 1.00 ┼ , respectively , 6-coordinated) , and of course the fluorides are identical . Thus , the two suggested Tl perovskites are nearly similar , so that when they are combined together to form the mixed-valent Class IIIB composite material , they should form a completely homogeneous blend . Other more dissimilar couples may form "mixed phases" of partially blended components , and so might not function as efficiently as the thallium couple .
Unfortunately , most of the heavy metals in this survey are very toxic to humans and other life . A possible exception is tin , which may be less hazardous than the others . Tin(II) fluoride was used for decades as an anticaries additive in toothpaste under the tradename "fluoristan" (it has since been replaced by the more innocuous sodium fluoride) . The tin perovskite couple looks feasible , but the lead couple is undoubtedly more economical , assuming it actually demonstrates a photovoltaic effect , of course . Lead metal and lead compounds are very cheap and are universally available , while tin metal and its compounds are considerably more expensive . There has been a great outcry in the news media as I write this web page about toxic lead in paint on children's toys manufactured in China . Yes , lead compounds are toxic , but I don't hear people complaining about the lead and lead compounds in their car batteries , do you ? This is because the lead is securely sealed in the batteries , and there is little or no human exposure to the lead in them in normal usage . In the battery manufacturing industry , and in the lead recycling and recovery business at the end of the consumer usage cycle , precautions are taken to prevent , or at least minimize , exposure of the workers involved to lead . Similarly for any hypothetical use of the lead perovskite couple in solar cells : it would be tightly sealed into the panels and couldn't infiltrate into the environment or humans . After all , the panels are electrical units , requiring a tight weatherproof seal against water and the weather in general . The seal that keeps water out of the panels will similarly keep the lead in them from escaping , too .
A host of variations of the six couples tabulated above are possible . For example , in the silver couple the Al3+ , Mg2+ , and F- components are "colourless" , with any photovoltaic activity in the mixed-valent composite occurring between the Ag1+ cations and Ag0 atoms . The researcher could use Transition metal M cations to alter the photochemistry of the couples in a subtle and possibly beneficial manner . For example , an alternate A0 compound could be prepared and studied , such as Ag0FeF3 (t = 1.05) . The Fe3+ cation , octahedrally-coordinated by fluoride anions , would be in a high-spin state , with its five 3d valence electrons as unpaired singlets . Compounds with such iron(III) cations are brightly coloured , so in Ag0FeF3 the iron cations will act as a sort of chromophore , absorbing the light energy received on the surface of the compound . They might also act as a photosensitizer , transmitting the absorbed radiant energy to the silver atoms . Similarly , the A1+ compound Ag1+CoF3 (t = 0.93) could be prepared and studied , in combination with both Ag0AlF3 and Ag0FeF3 in a separate series of experiments . Many such permutations are possible with the other perovskite couples suggested above .
As you can see , there is a very wide scope for research in this field of solid state chemistry . Although the immediate aim would be to synthesize new metallic compounds for examination as possible photovoltaic materials , their electrical and magnetic properties and photochemistry might also reveal other interesting facets of the mixed-valent compounds . In effect , they are chemical compounds whose metallic bonds have been designed to resemble those of their parent metals , but which have "holes" (orbital vacancies) interspersed throughout their lattices . These Class IIIB perovskite synthetic metals would undoubtedly be remarkable and fascinating new materials to study .
References and Notes
Robin and Day : M.B. Robin and P. Day , Mixed Valence Chemistry A Survey and Classification, Adv. Inorg. Chem. Radiochem. 10 , pp. 247-422 , H.J. EmelÚus and A.G. Sharpe (eds.) , Academic Press , New York , 1967 ; P. Day , Mixed Valence Chemistry and Metal Chain Compounds, pp. 191-214 in Mixed-Valence Compounds : Theory and Applications in Chemistry , Physics , Geology , and Biology , D.B. Brown (ed.) , NATO Advanced Study Institute , Series C , Mathematical and Physical Sciences Series no. 58 , Reidel-Holland (Kluwer Academic Publications , Hingham , MA) , 1980 ; P. Day , Les ComposÚs Ó 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) .
Gallium dichloride : in Robin and Day's review (above) , Fig. 40 , p. 367 ; L.S. Forster , Gallium(II) Chloride, Inorg. Synth. 4 , pp. 111-114 , J.C. Bailar , Jr. (ed.) , McGraw-Hill , New York , 1953 .
Prussian Blue : Robin and Day , pp. 294-300 . Dr. Joe Schwarcz of McGill University , Montreal , Canada , has written an engaging account of the discovery of Prussian Blue in 1704 by two German tradesmen , Dipple and Diesbach , in somewhat alchemical conditions : J.A. Schwarcz , The Genie in the Bottle , 64 All New Commentaries on the Fascinating Chemistry of Everyday Life , ECW Press , Toronto , ON , Canada (2001) ; pp. 168-172 .
Magnetite : Robin and Day , pp. 302-304 .
Verwey and Heilmann : E.J.W. Verwey and E.L. Heilmann , Physical Properties and Cation Arrangement of Oxides with Spinel Structures . I . Cation Arrangement in Spinels , J. Chem. Phys. 15 (4) , pp. 174-180 (1947) ; from Fig. 1 , p. 174 .
doping techniques : E.J.W. Verwey , Induced Valence, Chem. Abs. 43 , 6015g (1949) ; E.J.W. Verwey , P.W. Haayman , and F.C. Romeijn ,Electrical Properties of Metallic Oxides Containing Other Metals as Impurities, Chem. Abs. 46 , 3424e (1952) .
ten elements : P.G. Dickens and M.S. Whittingham , The Tungsten Bronzes and Related Compounds, Quart. Rev. 22 (1) , pp. 30-44 (1968) .
Shanks et al. : 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 ; 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] ; M.J. Sienko , Electric and Magnetic Properties of the Tungsten and Vanadium Bronzes, Ch. 21 , pp. 224-236 in Nonstoichiometric Compounds (see above) ; A. Kleiman , Tungsten Bronzes : Electrochromic Properties and Metal Insulator Transitions, 22 pp. (November , 2005) , can be downloaded from the Web without charge (PDF document , 672 KB) from http://www.mrl.ucsb.edu/~seshadri/2005_286G/Alan286.pdf .
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 Chemists View of Bonding in Extended Structures , VCH Publishers , New York , 1988 ; pp. 43-55 .
structure : L. Pauling , The Nature of the Chemical Bond and the Structure of Molecules and Crystals : An Introduction to Modern Structural Chemistry , third ed. , Cornell U.P. , Ithaca (NY) , 1960 ; pp. 439-440 . Fig. 11-16 , [Mo6Cl8]4+ ; Fig. 11-17 , [Ta6Cl12]2+ ; Robin and Day (above) , pp. 321-330 ; Fig. 23 , p. 323 .
that of NbO : H. Krebs , Fundamentals of Inorganic Crystal Chemistry , transl. by P.H.L. Walter , McGraw-Hill , London , UK , 1968 ; Fig. 14-14 , p. 191 ; W.W. Schulz and R.M. Wentzcovitch , Electronic Band Structure and Bonding in Nb3O3, Phys. Rev. B 48 (23) , pp. 16986-16991 (1993) ; 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 .
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) ; J.M. Williams and A.J. Schultz , One-Dimensional Partially Oxidized Tetracyanoplatinate Metals : New Results and Summary, pp. 337-368 in Molecular Metals , W.E. Hatfield (ed.) , Plenum Press , New York , 1979 ; J.A. Abys et al. , pp. 1-5 in Ch. 1 , Electrically Conducting Solids, Inorg. Synth. 19 , pp. 1-58 , D.F. Shriver (ed.) , John Wiley , New York , 1979 .
Krogmann : K. Krogmann , Planar Complexes Containing Metal-Metal Bonds, Angew. Chem. Internat. Ed. Engl. 8 (1) , pp. 35-42 (1969) .
overlaps : 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 ; Fig. 26 , p. 53 .
very poor : H.R. Zeller and A. Beck , Anisotropy of the Electrical Conductivity in the One-Dimensional Conductor K2[Pt(CN)4] Br0.30 . 3 (H2O), J. Phys. Chem. Solids 35 (1) , pp. 77-80 (1974) ; Fig. 3 , p.80 .
silver subfluoride : Robin and Day (above) , pp. 359-360 .
readily prepared : A. Hettich , The Nature of Silver Hypofluoride, Chem. Abs. 22 , p. 520 (1928) ; H. Terrey and H. Diamond , The Crystal Structure of Silver Subfluoride, J. Chem. Soc. 1928 , pp. 2820-2824 ; L. Poyer et al. , Disilver Fluoride, Inorg. Synth. 5 , T. Moeller (ed.) , McGraw-Hill , New York , 1957 ; pp. 18-21 .
silver-plated : depositing a smooth silver deposit on glass might be accomplished by the "Tollen's Test" , which is used in analytical organic chemistry and biochemistry to test for reducing sugars , such as glucose . It is discussed in many organic chemistry laboratory textbooks , and in Web articles . A description of the Tollen's Test (including the "recipe" of the required chemicals) , with an accompanying video clip , is provided by Peter Keusch , on his web page , Tollen's Reaction Silver Mirror Test.
Molecular beam epitaxy : Wikipedia , Molecular Beam Epitaxy, http://en.wikipedia.org/wiki/Molecular_beam_epitaxy ; Alex Anselm , An Introduction to MBE Growth, http://projects.ece.utexas.edu/ece/mrc/groups/street_mbe/mbechapter.html ; I. Amato , Stuff , The Materials the World is Made Of , Avon Books , New York , 1997 ; see especially pp. 119-125 for a description of the molecular beam epitaxy (MBE) technique , including a photograph of the industrial apparatus used for it (Figure 21 , p. 125) .
Molecular beam epitaxy is only one of a number of chemical vapour deposition (CVD) methods , used to deposit thin films of atoms on surfaces . A brief review of these techniques is provided by U. Schubert and N. HŘsing , Synthesis of Inorganic Materials , Wiley-VCH , Weinheim , Germany , 2000 ; pp. 71-112 , especially Table 3-2 , p. 84 ; MBE , p. 88 .
The Condensed Matter Physics Group in the School of Physics & Astronomy at the University of Leeds , UK , operates an MBE apparatus and three sputtering machines in their laboratories . They provide an excellent description of these techniques , as well as photos of the equipment . See their web page , Thin Film Deposition, at : http://www.stoner.leeds.ac.uk/facilities/thin%20film%20deposition .
Table : Robin and Day (above) , Table III , p. 268 .
asbestos : Wikipedia , Asbestos, at http://en.wikipedia.org/wiki/Asbestos . There are photos of blue asbestos on this web page .
slowly rise : H.K. Bowen , Ceramics as Electrical Materials, pp. 290-314 in the Kirk-Othmer Encyclopedia of Chemical Technology , Vol. 5 , M. Grayson and D. Eckroth (eds.) , John Wiley , New York (1979) ; Figure 5 , p. 299 and Figure 10 , p. 306 .
hopping semiconductor : Eu3S4 is an excellent example of a mixed-valent compound that behaves electronically much like magnetite , as a "hopping semiconductor " : O. Berkooz , M. Malamud , and S. Shtrikman , Observation of Electron Hopping in 151Eu3S4 by M÷ssbauer Spectroscopy, Solid State Commun. 6 (3) , pp. 185-188 (1968) .
ambient : C.P. Poole , Jr. , T. Datta , and H.A. Farach , Copper Oxide Superconductors , John Wiley , New York , 1988 ; Table X-1 , p. 198 .
M.K. Wu : M.K. Wu et al. , Superconductivity at 93 K in a New Mixed-Phase Y-Ba-Cu-O Compound System at Ambient Pressure, Phys. Rev. Lett. 58 (9) , pp. 908-910 (1987) ; Fig. 3 , p. 909 .
layers : My model of YBCO was based on the nice clear sketch of it in the research paper by A. Ourmazd and J.C.H. Spence , Detection of Oxygen Ordering in Superconducting Cuprates, Nature 329 (6138) , pp. 425-427 (1987) ; Figure 1 , p. 426 .
usual manner : for example , see the experimental descriptions in the papers : C.W. Chu et al. , Evidence for Superconductivity Above 40 K in the La-Ba-Cu-O System, Phys. Rev. Lett. 58 (4) , pp. 405-407 (1987) ; 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 (1987) . Note : yttrium barium copper oxide (YBCO , "1-2-3") is now offered commercially , as very pure , fine powders , by Aldrich Chemicals and Alfa-Aesar .
perovskite : R.M. Hazen , Perovskites, Scientific American 258 (6) , pp. 74-81 (June , 1988) ; 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 .
Sanderson : R.T. Sanderson , Inorganic Chemistry , Reinhold Publishing , New York , 1967 .
Wyckoff : R.W.G. Wyckoff , Crystal Structures , second ed. , several volumes , Interscience Publishers , New York , 1964 .
Goldschmidt equation : U. MŘller , Inorganic Structural Chemistry , John Wiley , Chichester , UK , 1993 ; p. 200 ; A.F. Wells , Structural Inorganic Chemistry , third ed. , Clarendon Press , Oxford , UK , 1962 ; p. 497 . It's also mentioned in the WolfWikis Perovskite web page cited above .
range : these values vary somewhat according to the author . See the three references immediately above for this information .
graphite : U. Schubert and N. HŘsing (see above) ; intercalation reactions are briefly reviewed on pp. 45-60 , including graphite and MX2 compounds .
TiS2 : Zerovalent copper has been inserted into the flaky lattice of titanium disulfide . At a molar ratio of one copper to two TiS2 , the intercalated product rearranged to the thiospinel , Cu0Ti2S4 . This was a normal spinel [see the spinel model above] with Ti(IV) octahedrally coordinated , and the Cu0 tetrahedrally coordinated by the sulfide anions . It proved to be an electrically conducting metallic solid . Related thiospinels with Cu1+ instead of Cu0 were also made , and were found to be nonmetallic : J. Padiou , D. Bideau , and J.P. Troadec , Magnetic and Electrical Properties of Quaternary Thiospinels, Chem. Abs. 92 , 225778j (1980) . Original article , which I havent been able to obtain : J. Solid State Chem. 31 (3) , pp. 401-405 (1980) .
poor metals : Wikipedia , Poor Metal, at http://en.wikipedia.org/wiki/Poor_metals .
model : Wikipedia , Aluminum Fluoride, at http://en.wikipedia.org/wiki/Aluminum_fluoride . I thank the author of this sketch , and Wikipedia , for implied permission to reproduce it here on this web page .
molecular : Wells , Structural Inorganic Chemistry (see above) : .....crystalline SbF3 .....[is] a molecular crystal (p. 664) .
differential thermal analysis : R.C. Mackenzie (ed.) , Differential Thermal Analysis , vol. 1 , Fundamental Aspects, Academic Press , London (UK) , 1970 ; vol. 2 , Applications, idem. , 1972 ; M.E. Brown (ed.) , Introduction to Thermal Analysis , Techniques and Applications , Kluwer Academic , Dordrecht (Netherlands) , 2001 ; T. Hatakeyama and Z. Liu , Handbook of Thermal Analysis , John Wiley , Chichester (UK) , 1998 ; P.D. Garn , Thermoanalytical Methods of Investigation , Academic Press , New York , 1965 ; W.W. Wendlandt , Thermal Analysis , third ed. , John Wiley , New York , 1991 ; H.K.D.H. Bhadeshia , Thermal Analysis Techniques , can be downloaded without charge from the Web (PDF document , 128 KB) at http://www.msm.cam.ac.uk/phase-trans/2002/Thermal1.pdf .
The French company Setaram offers a compact dta apparatus : http://www.setaram.com/Differential-Scanning-Calorimetry-DSC-Differential-Thermal-Analysis-DTA.htm
well-known : Wyckhoff , Crystal Structures (see above) , vol. 2 , 1964 ; perovskites are discussed on pp. 390-402 , and many examples are presented in Table VIIA 7 in that section . Wells , Structural Inorganic Chemistry (see above) discusses perovskites , with examples , on pp. 494-499 .
chemie douce : F.J. DiSalvo , Solid State Chemstry, Solid State Commun. 102 (2-3) , pp. 79-85 (1997) ; see pp. 81-82 ; A. Stein , S.W. Keller , and T.E. Mallouk , Turning Down the Heat : Design and Mechanism in Solid-State Synthesis, Science 259 (5101) , pp. 1558-1564 (1993) ; C.N.R. Rao , Chemical Approaches to the Synthesis of Inorganic Materials , Wiley Eastern Ltd. , New Delhi , India , 1994 ; pp. 11-13 (and elsewhere in this textbook) ; C.N.R. Rao and J. Gopalakrishnan , New Directions in Solid State Chemistry , second ed. , Cambridge University Press , Cambridge , UK , 1997 ; p. 128-137 ; Ohio State web page at http://www.chemistry.ohio-state.edu/~woodward/ch754/syn_cd.htm .
student experiment : R.H. Langley , C.K. Schmitz , and M.B. Langley , The Synthesis and Characterization of Some Fluoride Perovskites , An Undergraduate Experiment in Solid State Chemistry, J. Chem. Educ. 61 (7) , pp. 643-645 (1984) ; D.M. Adams and J.B. Raynor , Preparation of potassium trifluoronickelate , KNiF3, p. 57 , in Advanced Practical Inorganic Chemistry , John Wiley , London (UK) 1965 .
known (1) : R. C. DeVries and R. Roy , Fluoride Models for Oxide Systems of Dielectric Interest : The KFMgF2 and AgFZnF2 Systems, J. Amer. Chem. Soc. 75 (10) , pp. 2479-2484 (1953) ; especially pp. 2482-2483 .
known (2) : W.L.W. Ludekens and A.J.E. Welch , Reactions Between Metal Oxides and Fluorides : Some New Double-Fluoride Structures of Type ABF3, Acta. Cryst. 5 , p. 841 (1952) .
shake-'n-bake : This is the preparative technique in ceramic chemistry where stoichiometric quantities of reagents , usually the oxides or carbonates (sometimes hydroxides and oxalates) of the desired elements , are combined together to form complex compounds . The materials are generally quite refractory , and require repeated cycles of grinding together , pelletizing , heating in a furnace , and cooldown . YBCO and related copper oxide superconductors are often prepared this way . See the references above for usual manner for typical shake-'n-bake procedures . A detailed recipe and procedure for making YBCO can be found on the web page , Making High-Temperature Superconductors, by John Wiltbank , and on this web page , Preparation , Structure and Properties of a High-Temperature Supeconductor, by M.S. Whittingham , Institute for Materials Research , State University of New York at Binghampton .
gold : Gold(I) readily disproportionates according to the redox reaction : 3 Au1+ -------> 2 Au0 + Au3+ ; E0T = 0.291 V . The positive cell potential indicates that the reaction is thermodynamically favourable at STP . Disproportionation of gold(I) will occur in the absence of reasonably strong coordinating anions or other ligands (fluoride is a very weak coordinating ligand) . Similarly for copper(I) : 2 Cu1+ -------> Cu0 + Cu2+ ; E0T = 0.368 V . This is why AuF and CuF are apparently unknown compounds : they can't exist as purely ionic lattices like AlF3 , but require some coordinate covalent bonding from a strong ligand to stabilize their univalent state .
indium : D.G. Tuck , The Lower Oxidation States of Indium, Chem. Soc. Rev. 22 (4) , pp. 269-276 (1993) .
Smart and Moore : L.E. Smart and E.A. Moore , Solid State Chemistry , third ed. , CRC Press/Taylor & Francis , Boca Raton (FL) , 2005 ; Table 1.9 , Crystal Radius, p. 47 .
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