Title of Invention: Cathode materials for secondary (rechargeable) lithium batteries Abstract: The invention relates to materials for use as electrodes in an alkali-ion secondary (rechargeable) battery, particularly a lithium-ion battery. The invention provides transition-metal compounds having the ordered-olivine or the rhombohedral NASICON structure and the polyanion (PO4)3− as at least one constituent for use as electrode material for alkali-ion rechargeable batteries. Detailed Description: Part general_description_paragraphs: This is a continuation of application Ser. No. 13/269,299, filed Oct. 7, 2011; which is a continuation of application Ser. No. 12/952,978, filed Nov. 23, 2010, now U.S. Pat. No. 8,067,117; which is a continuation application of application Ser. No. 11/179,617, filed Jul. 13, 2005 (now abandoned), which is a continuation of application Ser. No. 10/902,142, filed Jul. 30, 2004 (now abandoned), which is a continuation of application Ser. No. 10/307,346, filed Dec. 2, 2002 (now abandoned), which is a continuation of application Ser. No. 08/998,264, filed Dec. 24, 1997 (now U.S. Pat. No. 6,514,640, issued Feb. 4, 2003), which is a continuation-in-part of application Ser. No. 08/840,523 (now U.S. Pat. No. 5,910,382, issued Jun. 8, 1999), filed Apr. 21, 1997. This application claims priority through the above-identified applications to provisional patent Application No. 60/032,346, filed Dec. 4, 1996, and provisional patent Application No. 60/016,060, filed Apr. 23, 1996. The entire text of each of the above-referenced disclosures is specifically incorporated by reference herein without disclaimer. The Robert A. Welch Foundation, Houston, Tex., supported research related to the present invention. Part BACKGROUND OF THE INVENTION: 1. Field of the Invention The present invention relates to secondary (rechargeable) alkali-ion batteries. More specifically, the invention relates to materials for use as electrodes for an alkali-ion battery. The invention provides transition-metal compounds having the ordered olivine, the modified olivine or the rhombohedral NASICON structure and containing the polyanion (PO4)3− as at least one constituent for use as an electrode material for alkali-ion rechargeable batteries. 2. Description of the Related Art Present-day lithium batteries use a solid reductant as the anode and a solid oxidant as the cathode. On discharge, the metallic anode supplies Li+ ions to the Li+-ion electrolyte and electrons to the external circuit. The cathode is typically an electronically conducting host into which Li+ ions are inserted reversibly from the electrolyte as a guest species and charge-compensated by electrons from the external circuit. The chemical reactions at the anode and cathode of a lithium secondary battery must be reversible. On charge, removal of electrons from the cathode by an external field releases Li+ ions back to the electrolyte to restore the parent host structure, and the addition of electrons to the anode by the external field attracts charge-compensating Li+ ions back into the anode to restore it to its original composition. Present-day rechargeable lithium-ion batteries use a coke material into which lithium is inserted reversibly as the anode and a layered or framework transition-metal oxide is used as the cathode host material (Nishi et al., U.S. Pat. No. 4,959,281). Layered oxides using Co and/or Ni are expensive and may degrade due to the incorporation of unwanted species from the electrolyte. Oxides such as Li2±x[Mn2]O4, which has the [M2]O4 spinel framework, provide strong bonding in three dimensions and an interconnected interstitial space for lithium insertion. However, the small size of the O2− ion restricts the free volume available to the Li+ ions, which limits the power capability of the electrodes. Although substitution of a larger S2− ion for the O2− ion increases the free volume available to the Li+ ions, it also reduces the output voltage of an elementary cell. A host material that will provide a larger free volume for Li+-ion motion in the interstitial space would allow realization of a higher lithium-ion conductivity σLi, and hence higher power densities. An oxide is needed for output voltage, and hence higher energy density. An inexpensive, non-polluting transition-metal atom within the host structure would make the battery environmentally benign. Part SUMMARY OF THE INVENTION: The present invention meets these goals more adequately than previously known secondary battery cathode materials by providing oxides containing larger tetrahedral oxide polyanions forming 3D framework host structures with octahedral-site transition-metal oxidant cations, such as iron, that are environmentally benign. The present invention provides electrode material for a rechargeable electrochemical cell comprising an anode, a cathode and an electrolyte. The cell may additionally include an electrode separator. As used herein, “electrochemical cell” refers not only to the building block, or internal portion, of a battery but is also meant to refer to a battery in general. Although either the cathode or the anode may comprise the material of the invention, the material will preferably be useful in the cathode. Generally, in one aspect, the invention provides an ordered olivine compound having the general formula LiMPO4, where M is at least one first-row transition-metal cation. The alkali ion Li+ may be inserted/extracted reversibly from/to the electrolyte of the battery to/from the interstitial space of the host MPO4 framework of the ordered-olivine structure as the transition-metal M cation (or combination of cations) is reduced/oxidized by charge-compensating electrons supplied/removed by the external circuit of the battery in, for a cathode material, a discharge/charge cycle. In particular, M will preferably be Mn, Fe, Co, Ti, Ni or a combination thereof. Examples of combinations of the transition-metals for use as the substituent M include, but are not limited to, Fe1−xMnx, and Fe1−xTix, where 0<x<1. Preferred formulas for the ordered olivine electrode compounds of the invention include, but are not limited to LiFePO4, LiMnPO4, LiCoPO4, LiNiPO4, and mixed transition-metal compounds such as Li1−2xFe1−xTixPO4 or LiFe1−xMnxPO4, where 0<x<1. However, it will be understood by one of skill in the art that other compounds having the general formula LiMPO4 and an ordered olivine structure are included within the scope of the invention. The electrode materials of the general formula LiMPO4 described herein typically have an ordered olivine structure having a plurality of planes defined by zigzag chains and linear chains, where the M atoms occupy the zigzag chains of octahedra and the Li atoms occupy the linear chains of alternate planes of octahedral sites. The present invention additionally provides electrode material for a rechargeable electrochemical cell including an anode, a cathode and an electrolyte where the material has a modified olivine structure. The pristine olivine structure of LiMPO4 may be modified either on the anionic site or on the cationic site to provide an alternative lithium insertion-type. It is also envisioned that the pristine olivine structure may be modified on both the anionic and the cationic sites. Preferably, the structure is modified by aliovalent or isocharge substitutions to provide better lithium ion diffusivity and electronic conductivity. In general, “isocharge substitutions” refers to substitution of one element on a given crystallographic site with an element having a similar charge. For example, Mg2+ is considered similarly isocharge with Fe2+ and V5+ is similarly isocharge with P5+. Likewise, PO43− tetrahedra can be substituted with VO43− tetrahedra. “Aliovalent substitution” refers to substitution of one element on a given crystallographic site with an element of a different valence or charge. One example of an aliovalent substitution would be Cr3+ or Ti4+ on an Fe2+ site. Another example would be Li+ on a Fe2+ site. These cathode materials will generally have an olivine structure based on iron or manganese derivatives whose general formula is: Lix+yM1−(y+d+t+q+r)DdTtQqRr[PO4]1−(p+s+v)[SO4]p[SiO4]s[VO4]v where: M may be Fe2+ or Mn2+ or mixtures thereof; D may be a metal in the +2 oxidation state, preferably Mg2+, Ni2+, Co2+, Zn2+, Cu2+, or Ti2+; T may be a metal in the +3 oxidation state, preferably Al3+, Ti3+, Cr3+, Fe3+, Mn3+, Ga3+, Zn3+, or V3+; Q may be a metal in the +4 oxidation state, preferably Ti4+, Ge4+, Sn4+, or V4+; and R may be a metal in the +5 oxidation state, preferably V5+, Nb5+, or Ta5+. In this preferred embodiment, M, D, T, Q and R reside in octahedral sites. The additional coefficients may be defined as follows: x represents the degree of intercalation during operation of the electrode material; y represents the fraction of lithium ions on the (for example) initial Fe2+ sites; d represents the fraction of divalent ions (noted as D) on the initial Fe2+ sites; t represents the fraction of trivalent ions (noted as T) on the initial Fe2+ sites; q represents the fraction of tetravalent ions (noted as Q) on the initial Fe2+ sites; r represents the fraction of pentavalent ions (noted as R) on the initial Fe2+ sites; p represents the fraction of hexavalent sulfur (as discrete SO42− tetrahedra) on the initial P5+ sites; s represents the fraction of tetravalent silicon (as discrete SiO42− tetrahedra) on the initial P5+ sites; and v represents the fraction of pentavalent vanadium ions on the initial P5+ sites. The conditions for site occupancy and electroneutrality imply the following: 0≦x≦1; y+d+t+q+r≦1; p+s+v≦1; and 3+s−p=x−y+2+t+2q+3r. x, y, d, t, q, r, p, s, and v may be between 0 (zero) and 1 (one), with at least one of y, d, t, q, r, p, s, or v differing from 0. In a preferred embodiment y, d, t, q, r, and v may vary between 0 (zero) and 0.2 ( 2/10) and p and s may vary between 0 (zero) and 0.5 (½). The invention further provides an electrochemical cell or battery having at least one positive and one negative electrode. At least one positive electrode in this embodiment contains the Lix+yM1−(y+d+t+q+r)DdTtQqRr[PO4]1−(p+s+v)[SO4]p[SiO4]s[VO4]v material described above. Further, at least one negative electrode contains a source of lithium ion at a high chemical activity. The phrase “high chemical activity” is generally understood in the art to refer to an electrode whose mean voltage during operation is not more positive than 2 volts versus the Li+/Li0 couple. Preferably, at least one negative electrode will contain metallic lithium, a lithium alloy, a lithium-carbon intercalation compound, a lithium-transition metal mixed nitride of antifluorite, or a lithium-titanium spinel Li1+x+zTi2−xO4, where 0≦x≦⅓ and 0≦z≦1−2x. It will be understood by those of skill in the art that the term “a” used before a compound encompasses structures containing more than one of that type of compound. For example, “a lithium-transition metal mixed nitride of antifluorite” encompasses mixtures of more than one of this type of compound and “a lithium-titanium spinel” encompasses solid solutions and/or mixtures of more than one of this type of compound with other spinels. Alternatively, the electrochemical cell of the invention may contain an intercalation material with fast diffusion kinetics in the positive electrode containing the Lix+yM1−(y+d+t+q+r)DdTtQqRr[PO4]1−(p+s+v)[SO4]p[SiO4]s[VO4]v material described above. The phrase “fast diffusion kinetics” is generally understood in the art as referring to a material able to sustain a specific current of at least 10 mA per gram of material with more than 80% utilization of the capacity at the temperature of operation. Preferably, the intercalation material with fast diffusion kinetics may be a lamellar dichalcogenide, a vanadium oxide VOx where 2.1≦x≦2.5, or a NASICON-related material such as Li3Fe2(PO4)3 or Li3−xFe2−xTix(PO4)3 where x represents the degree of substitution of Fe3+ by Ti4+. In other preferred aspects, the electrochemical cell of the invention will include a conductive additive in at least one positive electrode. The conductive additive may preferably be carbon. In other aspects, it is envisioned that the electrochemical cell of the invention includes at least one positive electrode containing the Lix+yM1−(y+d+t+q+r)DdTtQqRr[PO4]1−(p+s+v)[SO4]p[SiO4]s[VO4]v material described above and a polymeric binder. In certain preferred aspects, this positive electrode may additionally include a conductive additive, such as carbon. Preferably, the polymeric binder may be a homopolymer or copolymer of tetrafluoroethylene, an ethylene-propylene-diene terpolymer, a polyether, a polyester, a methylmethacrylate-based polymer, an acrylonitrile-based polymer, or a vinylidene fluoride-based polymer. It is contemplated that the polymeric binder for use in conjunction with the present invention may be crosslinked, but those of skill in the art will appreciate that cross-linkage is not essential. The term “crosslinked” refers to the presence of physical or chemical bonds between the polymer chains. Generally, those skilled in the art measure crosslinkage in terms of the number of crosslinks per cubic centimeter. The polymeric binder for use in conjunction with the present invention will preferably have a cross-linkage of between 1018 and 1020 inter-chain bonds per cubic centimeter. Alternatively, the polymeric binder may possess ionic conductivity. Ionic conductivity is generally understood in the art to be the ability to carry a current due to the motion of ions. Preferred values of ionic conductivity are between about 10−7 and about 10−2 (Scm−1). In certain embodiments, the polymeric binder may be swollen by an aprotic solvent which contains a salt, the cation of which is at least in part Li+. The aprotic solvent may preferably be ethylene carbonate, propylene carbonate, dimethylcarbonate, diethylcarbonate, methyl-ethylcarbonate, γ-butyrolactone, a tetraalkylsulfamide, or a dialkylether of a mono-, di-, tri-, tetra- or higher oligo-ethylene glycol of molecular weight lower or equal to 2000 and mixtures thereof. The invention further provides a variable optical transmission device which is constructed from transparent semi-conductor coated glass or plastic and includes two electrodes separated by a solid or gel electrolyte. In this embodiment, at least one electrode contains the Lix+yM1−(y+d+t+q+r)DdTtQqRr[PO4]1−(p+s+v)[SO4]p[SiO4]s[VO4]v material as described above. Preferably, the Lix+yM1−(y+d+t+q+r)DdTtQqRr[PO4]1−(p+s+v)[SO4]p[SiO4]s[VO4]v compound of the invention is layered on a transparent semiconductor coated glass or plastic in a thin film. It is preferred that the semi-conductor be coated onto the glass or plastic at a thickness of between 200 and 104 Ångstroms (Å) or between 20 and 103 nanometers (nm). The material of the invention may be placed onto the glass or plastic, for example, using a vacuum deposition technique, by sputtering, or from a sol-gel precursor. The techniques for placing the compound of the invention onto the glass or plastic are well known to those skilled in the art. Preferred techniques include sputtering, chemical vapor deposition (CVD) from organometallic precursors like metal hexafluoroacetylacetonates and organic phosphates or silicates, sol-gel from hydrolysis-condensation of metal alkoxides in water-organic solutions in the presence of phosphoric acid and organosiloxanes. It is preferred that the glass for use in conjunction with the present invention be conventional optical quality glazing. Preferred plastics include high transparency, high mechanical strength material like polyethylene terephthalate (Mylar®). The transparent semi-conductor is contemplated to be virtually any transparent semi-conductor but is preferably antimony- or fluorine-doped tin oxide, tin- or fluorine-doped indium oxide, or non-stoichiometric zinc oxide. In another aspect, the invention provides electrode materials for a rechargeable electrochemical cell comprising an anode, a cathode and an electrolyte, with or without an electrode separator, where the electrode materials comprise a rhombohedral NASICON material having the formula YxM2(PO4)3, where 0≦x≦5. Preferably, the compounds of the invention will be useful as the cathode of a rechargeable electrochemical cell. The alkali ion Y may be inserted from the electrolyte of the battery to the interstitial space of the rhombohedral M2(XO4)3 NASICON host framework as the transition-metal M cation (or combination of cations) is reduced by charge-compensating electrons supplied by the external circuit of the battery during discharge with the reverse process occurring during charge of the battery. While it is contemplated that the materials of the invention may consist of either a single rhombohedral phase or two phases, e.g. orthorhombic and monoclinic, the materials are preferably single-phase rhombohedral NASICON compounds. Generally, M will be at least one first-row transition-metal cation and Y will be Li or Na. In preferred compounds, M will be Fe, V, Mn, or Ti and Y will be Li. Redox energies of the host M cations can be varied by a suitable choice of the XO4 polyanion, where X is taken from Si, P, As, or S and the structure may contain a combination of such polyanions. Tuning of the redox energies allows optimization of the battery voltage with respect to the electrolyte used in the battery. The invention replaces the oxide ion O2− of conventional cathode materials by a polyanion (XO4)m− to take advantage of (1) the larger size of the polyanion, which can enlarge the free volume of the host interstitial space available to the alkali ions, and (2) the covalent X—O bonding, which stabilizes the redox energies of the M cations with M-O—X bonding so as to create acceptable open-circuit voltages Voc with environmentally benign Fe3+/Fe2+ and/or Ti4+/Ti+ or V4+/V3+ redox couples. Preferred formulas for the rhombohedral NASICON electrode compounds of the invention include, but are not limited to those having the formula Li3+xFe2(PO4)3, Li2+xFeTi(PO4)3, LixTiNb(PO4)3, and Li1+xFeNb(PO4)3, where 0<x<2. It will be understood by one of skill in the art that Na may be substituted for Li in any of the above compounds to provide cathode materials for a Na ion rechargeable battery. For example, one may employ Na3+xFe2(PO4)3, Na2+xFeTi (PO4)3, NaxTiNb (PO4)3 or Na1+xFeNb (PO4)3, where 0<x<2, in a Na ion rechargeable battery. In this aspect, Na+ is the working ion and the anode and electrolyte comprise a Na compound. Compounds of the invention having the rhombohedral NASICON structure form a framework of MO6 octahedra sharing all of their corners with XO4 tetrahedra (X═Si, P, As, or S), the XO4 tetrahedra sharing all of their corners with octahedra. Pairs of MO6 octahedra have faces bridged by three XO4 tetrahedra to form “lantern” units aligned parallel to the hexagonal c-axis (the rhombohedral [111] direction), each of these XO4 tetrahedra bridging to two different “lantern” units. The Li+ or Na+ ions occupy the interstitial space within the M2(XO4)3 framework. Generally, YxM2(XO4)3 compounds with the rhombohedral NASICON framework may be prepared by solid-state reaction of stoichiometric proportions of the Y, M, and XO4 groups for the desired valence of the M cation. Where Y is Li, the compounds may be prepared indirectly from the Na analog by ion exchange of Li+ for Na+ ions in a molten LiNO3 bath at 300° C. For example, rhombohedral LiTi2(PO4)3 may be prepared from intimate mixtures of Li2CO3 or LiOH.H2O, TiO2, and NH4H2PO4.H2O calcined in air at 200° C. to eliminate H2O and CO2 followed by heating in air for 24 hours near 850° C. and a further heating for 24 hours near 950° C. However, preparation of Li3Fe2(PO4)3 by a similar solid-state reaction gives the undesired monoclinic framework. To obtain the rhombohedral form, it is necessary to prepare rhombohedral Na3Fe2(PO4)3 by solid-state reaction of NaCO3, Fe{CH2COOH}2 and NH4H2PO4.H2O, for example. The rhombohedral form of Li3Fe2(PO4)3 is then obtained at 300° C. by ion exchange of Li+ for Na+ in a bath of molten LiNO3. It will be understood by one of skill in the art that the rhombohedral Na compounds will be useful as cathode materials in rechargeable Na ion batteries. In another aspect of the invention, the rhombohedral NASICON electrode compounds may have the general formula YxM2(PO4)y(XO4)3−y, where 0<y≦3, M is a transition-metal atom, Y is Li or Na, and X═Si, As, or S and acts as a counter cation in the rhombohedral NASICON framework structure. In this aspect, the compound comprises a phosphate anion as at least part of an electrode material. In preferred embodiments, the compounds are used in the cathode of a rechargeable battery. Preferred compounds having this general formula include, but are not limited to Li1+xFe2(SO4)2(PO4), where 0≦x≦1. The rhombohedral NASICON compounds described above may typically be prepared by preparing an aqueous solution comprising a lithium compound, an iron compound, a phosphate compound and a sulfate compound, evaporating the solution to obtain dry material and heating the dry material to about 500° C. Preferably, the aqueous starting solution comprises FeCl3, (NH4)2SO4, and LiH2PO4. In a further embodiment, the invention provides electrode materials for a rechargeable electrochemical cell comprising an anode, a cathode and an electrolyte, with or without an electrode separator, where the electrode materials have a rhombohedral NASICON structure with the general formula A3−xV2(PO4)3. In these compounds, A may be Li, Na or a combination thereof and 0≦x≦2. In preferred embodiments, the compounds are a single-phase rhombohedral NASICON material. Preferred formulas for the rhombohedral NASICON electrode compounds having the general formula A3−xV2(PO4)3 include, but are not limited to those having the formula Li2−xNaV2(PO4)3, where 0≦x≦2. The rhombohedral NASICON materials of the general formula A3−xV2(PO4)3 may generally be prepared by the process outlined in FIG. 9. Alternatively, Li2NaV2(PO4)3 may be prepared by a direct solid-state reaction from LiCO3, NaCO3, NH4H2PO4.H2O and V2O3. In a further aspect, the invention provides a secondary (rechargeable) battery where an electrochemical cell comprises two electrodes and an electrolyte, with or without an electrode separator. The electrodes are generally referred to as the anode and the cathode. The secondary batteries of the invention generally comprise as electrode material, and preferably as cathode material, the compounds described above. More particularly, the batteries of the invention have a cathode comprising the ordered olivine compounds described above or the rhombohedral NASICON compounds described above. Part DESCRIPTION OF ILLUSTRATIVE EMBODIMENTS: Present-day secondary (rechargeable) lithium batteries use a solid reductant as the anode, or negative electrode, and a solid oxidant as the cathode, or positive electrode. It is important that the chemical reactions at the anode and cathode of a lithium secondary battery be reversible. On discharge, the metallic anode supplies Li+ ions to the Li+-ion electrolyte and electrons to the external circuit. The cathode is a host compound into/from which the working Li+ ion of the electrolyte can be inserted/extracted reversibly as a guest species over a large solid-solubility range (Goodenough 1994). When the Li+ ions are inserted as a guest species into the cathode, they are charge-compensated by electrons from the external circuit. On charge, the removal of electrons from the cathode by an external field releases Li+ ions back to the electrolyte to restore the parent host structure. The resultant addition of electrons to the anode by the external field attracts charge-compensating Li+ ions back into the anode to restore it to its original composition. The present invention provides new materials for use as cathodes in lithium secondary (rechargeable) batteries. It will be understood that the anode for use with the cathode material of the invention may be any lithium anode material, such as a reductant host for lithium or elemental lithium itself. Preferably, the anode material will be a reductant host for lithium. Where both the anode and cathode are hosts for the reversible insertion or removal of the working ion into/from the electrolyte, the electrochemical cell is commonly called a “rocking-chair” cell. An implicit additional requirement of a secondary battery is maintenance not only of the electrode/electrolyte interfaces, but also of electrical contact between host particles, throughout repeated discharge/recharge cycles. Since the volumes of the electrode particles change as a result of the transfer of atoms from one to another electrode in a reaction, this requirement normally excludes the use of a crystalline or glassy electrolyte with a solid electrode. A non-aqueous liquid or polymer electrolyte having a large energy-gap window between its highest occupied molecular orbital (HOMO) and its lowest unoccupied molecular orbital (LUMO) is used with secondary lithium batteries in order to realize higher voltages. For example, practical quantities of very ionic lithium salts such as LiClO4, LiBF4 and LiPF6 can be dissolved in empirically optimized mixtures of propylene carbonate (PC), ethylene carbonate (EC), or dimethyl carbonate (DMC) to provide acceptable electrolytes for use with the cathodes of the invention. It will be recognized by those of skill in the art that the (ClO4)− anion is explosive and not typically suitable for commercial applications. General Design Considerations The power output P of a battery is the product of the electric current I delivered by the battery and the voltage V across the negative and positive posts (equation 1). P=IV (1) The voltage V is reduced from its open-circuit value Voc (I=0) by the voltage drop IRb due to the internal resistance Rb of the battery (equation 2). V=Voc−IRb (2) The open-circuit value of the voltage is governed by equation 3. Voc=(μA−μC)/(−nF)<5V (3) In equation 3, n is the number of electronic charges carried by the working ion and F is Faraday's constant. The magnitude of the open-circuit voltage is constrained to Voc<5V not only by the attainable difference μA−μC of the electrochemical potentials of the anode reductant and the cathode oxidant, but also by the energy gap Eg between the HOMO (highest occupied molecular orbital) and the LUMO (lowest unoccupied molecular orbital) of a liquid electrolyte or by the energy gap Eg between the top of the valence band and the bottom of the conduction band of a solid electrolyte. The chemical potential μA, which is the Fermi energy εF of a metallic-reductant anode or the HOMO of a gaseous or liquid reductant, must lie below the LUMO of a liquid electrolyte or the conduction band of a solid electrolyte to achieve thermodynamic stability against reduction of the electrolyte by the reductant. Similarly, the chemical potential μA−μC, which is the LUMO of a gaseous or liquid oxidant or the Fermi energy of a metallic-oxidant cathode, must lie above the HOMO of a liquid electrolyte or the valence band of a solid electrolyte to achieve thermodynamic stability against oxidation of the electrolyte by the oxidant. Thermodynamic stability thus introduces the constraint μA−μC≦Eg (4) as well as the need to match the “window” Eg of the electrolyte to the energies μA and μC of the reactants to maximize Voc. It follows from equations 1 and 2 that realization of a high maximum power Pmax (equation 5) requires, in addition to as high a Voc as possible, a low internal battery resistance Rb (see equation 6). Pmax=ImaxVmax (5) Rb=Re1Rin(A)+Rin(C)+Rc(A)+Rc(C) (6) The electrolyte resistance Re1 to the ionic current is proportional to the ratio of the effective thickness L to the geometrical area A of the interelectrode space that is filled with an electrolyte of ionic conductivity σi (equation 7). Re1=(L/σiA) (7) Since ions move diffusively, σi (see equation 8) increases with temperature. A σi≦0.1 Scm−1 (the maximum σi represents the room-temperature protonic conductivity σH in a strong acid) at an operating temperature Top dictates the use of a membrane separator of large geometrical area A and small thickness L. σLi=(B/T)exp(−Ev/kT) (8) The resistance to transport of the working ion across the electrolyte-electrode interfaces is proportional to the ratio of the geometrical and interfacial areas at each electrode: Rin≈A/Ain (9) where the chemical reaction of the cell involves ionic transport across an interface, equation 9 dictates construction of a porous, small-particle electrode. Achievement and retention of a high electrode capacity, i.e., utilization of a high fraction of the electrode material in the reversible reaction, requires the achievement and retention of good electronic contact between particles as well as a large particle-electrolyte interface area over many discharge/charge cycles. If the reversible reaction involves a first-order phase change, the particles may fracture or lose contact with one another on cycling to break a continuous electronic pathway to the current collector. Loss of interparticle electrical contact results in an irreversible loss of capacity. There may also be a reversible capacity fade. Where there is a two-phase process (or even a sharp guest-species gradient at a diffusion front) without fracture of the particles, the area of the interface (or diffusion front) decreases as the second phase penetrates the electrode particle. At a critical interface area, diffusion across the interface may not be fast enough to sustain the current I, so not all of the particle is accessible. The volume of inaccessible electrode increases with I, which leads to a diffusion-limited reversible capacity fade that increases with I. This problem becomes more important at lower ionic conductivity σLi. The battery voltage V vs. the current I delivered across a load is called the polarization curve. The voltage drop (Voc−V)≡η(I) of a typical curve, FIG. 1, is a measure of the battery resistance (see equation 10). Rb(I)=η(I)/I (10) On charging, η(I)=(Vapp−Voc) is referred to as an overvoltage. The interfacial voltage drops saturate in region (i) of FIG. 1; therefore in region (ii) the slope of the curve is dV/dI=Re1+Rc(A)+Rc(C) (11) Region (iii) is diffusion-limited; at the higher currents I, normal processes do not bring ions to or remove them from the electrode/electrolyte interfaces rapidly enough to sustain an equilibrium reaction. The battery voltage V vs. the state of charge, or the time during which a constant current I has been delivered, is called a discharge curve. Cathode Materials The cathode, or positive electrode, material of the present invention, for use in a secondary lithium battery, consists of a host structure into which lithium can be inserted reversibly. The maximum power output, Pmax (see equation 5) that can be achieved by a cell depends on the open-circuit voltage Voc=ΔE/e and the overvoltage η(I) at the current Imax of maximum power Vmax=Voc−η(I) (12) ΔE is the energy difference between the work function of the anode (or the HOMO of the reductant) and that of the cathode (or the LUMO of the oxidant). In order to obtain a high Voc, it is necessary to use a cathode that is an oxide or a halide. It is preferable that the cathode be an oxide in order to achieve a large Voc and good electronic conductivity. To minimize η(Imax), the electrodes must be good electronic as well as ionic conductors and they must offer a low resistance to mass transfer across the electrode/electrolyte interface. To obtain a high Imax, it is necessary to have a large electrode/electrolyte surface area. In addition, where there is a two-phase interface within the electrode particle, the rate of mass transfer across this interface must remain large enough to sustain the current. This constraint tends to limit the electrode capacity more as the current increases. Oxide host structures with close-packed oxygen arrays may be layered, as in Li1−xCoO2 (Mizushima, et al. 1980), or strongly bonded in three dimensions (3D) as in the manganese spinels Li1−x[Mn2]O4 (Thackeray 1995; Thackeray et al. 1983; Thackeray et al. 1984; Guyomard and Tarascon 1992; and Masquelier et al. 1996). Li intercalation into a van der Waals gap between strongly bonded layers may be fast, but it can also be accompanied by unwanted species from a liquid electrolyte. On the other hand, strong 3D bonding within a close-packed oxygen array, as occurs in the spinel framework [Mn2]O4, offers too small a free volume for the guest Li+ ions to have a high mobility at room temperature, which limits Imax. Although this constraint in volume of the interstitial space makes the spinel structure selective for insertion of Li+ ions, it reduces the Li+-ion mobility and hence Li+-ion conductivity σLi. The oxospinels have a sufficiently high σLi, to be used commercially in low-power cells (Thackeray et al., 1983) but would not be acceptable for the high power cells of the insertion. The present invention overcomes these drawbacks by providing cathode materials containing larger tetrahedral polyanions which form 3D framework host structures with octahedral-site transition-metal oxidant cations. In the cathode materials of the invention having the NASICON structure, the transition-metal ions are separated by the polyanions, so the electronic conductivity is polaronic rather than metallic. Nevertheless, the gain in σLi more than offsets the loss in electronic conductivity. Variation of the energy of a given cation redox couple from one compound to another depends on two factors: (a) the magnitude of the crystalline electric field at the cation, which may be calculated for a purely ionic model by a Madelung summation of the Coulomb fields from the other ions present, and (b) the covalent contribution to the bonding, which may be modulated by the strength of the covalent bonding at a nearest-neighbor counter cation. The stronger is the negative Madelung potential at a cation, the higher is a given redox energy of a cation. Similarly the stronger is the covalent bonding of the electrons at a transition-metal cation, the higher is a given redox energy of that cation. The lower the redox energy of the cation host transition-metal ion, the larger is Voc. The redox couples of interest for a cathode are associated with antibonding states of d-orbital parentage at transition-metal cations M or 4f-orbital parentage at rare-earth cations Ln in an oxide. The stronger is the cation-anion covalent mixing, the higher is the energy of a given LUMO/HOMO redox couple. Modulation of the strength of the cation-anion covalence at a given M or Li cation by nearest-neighbor cations that compete for the same anion valence electrons is known as the inductive effect. Changes of structure alter primarily the Madelung energy as is illustrated by raising of the redox energy within a spinel [M2]O4 framework by about 1 eV on transfer of Li+ ions from tetrahedral to octahedral interstitial sites. Changing the counter cation, but not the structure, alters primarily the inductive effect, as is illustrated by a lowering of the Fe3+/Fe2+ redox energy by 0.6 eV on changing (MoO4)2− or (WO4)2− to (SO4)2− polyanions in isostructural Fe2(XO4)3 compounds. Raising the energy of a given redox couple in a cathode lowers the voltage obtained from cells utilizing a common anode. Conversely, raising the redox energy of an anode raises the cell voltage with respect to a common cathode. The invention provides new cathode materials containing oxide polyanions, including the oxide polyanion (PO4)3− as at least one constituent, for use in secondary (rechargeable) batteries. For example, the cathode materials of the present invention may have the general formula LiM(PO4) with the ordered olivine structure, the modified olivine structure of LiM(PO4), or the more open rhombohedral NASICON framework structure. The cathode materials of the present invention have the general formula LiM(PO4) for the ordered olivine structure, the general formula Lix+yM1−(y+d+t+q+r)DdTtQqRr[PO4]1−(p+s+v)[SO4]p[SiO4]s[VO4]v for the modified olivine structure or YxM2(PO4)y(XO4)3−y for the rhombohedral NASICON framework structure. The parameters for the modified olivine structure are as follows: M may be Fe2+ or Mn2+ or mixtures thereof; D may be a metal in the +2 oxidation state, preferably Mg2+, Ni2+, Co2+, Zn2+, Cu2+, or Ti2+; T may be a metal in the +3 oxidation state, preferably Al3+, Ti3+, Cr3+, Fe3+, Mn3+, Ga3+, Zn3+, or V3+; Q may be a metal in the +4 oxidation state, preferably Ti4+, Ge4+, Sn4+, or V4+; R may be a metal in the +5 oxidation state, preferably V5+, Nb5+, or Ta5+. In this preferred embodiment x is the degree of intercalation during operation of the electrode material; y is the fraction of lithium ions on the initial Fe2+ sites; d is the fraction of divalent ions (noted as D) on the initial Fe2+ sites; t is the fraction of trivalent ions (noted as T) on the initial Fe2+ sites; q is the fraction of tetravalent ions (noted as Q) on the initial Fe2+ sites; r is the fraction of pentavalent ions (noted as R) on the initial Fe2+ sites; p is the fraction of hexavalent sulfur (as discrete SO42− tetrahedra) on the initial P5+ sites; and s is the fraction of tetravalent silicon (as discrete SiO42− tetrahedra) on the initial P5+ sites; v is the stoichiometric coefficient for V5+ residing in tetrahedral sites; and M, D, T, Q and R reside in octahedral sites. The conditions for site occupancy and electroneutrality imply: 0≦x≦1; y+d+t+q+r≦1; p+s+v≦1; and 3+s−p=x−y+2+t+2q+3r. Generally, x, y, d, t, q, r, p, s, and v may be between 0 (zero) and 1 (one), with at least one of y, d, t, q, r, p, s, or v differing from 0. Preferably, y, d, t, q, r and v may vary between 0 (zero) and 0.2 ( 2/10) and p and may vary between 0 (zero) and 0.5 (½). In the rhombohedral NASICON framework structure, 0<y≦3, M is a transition-metal atom, Y is Li or Na and X═Si, As or S and acts as a counter cation. The olivine structure of Mg2SiO4 consists of a slightly distorted array of oxygen atoms with Mg2+ ions occupying half the octahedral sites in two different ways. In alternate basal planes, they form zigzag chains of corner-shared octahedra running along the c-axis and in the other basal planes they form linear chains of edge-shared octahedra running also along the c-axis. In the ordered LiMPO4 olivine structures of the invention, the M atoms occupy the zigzag chains of octahedra and the Li atoms occupy the linear chains of the alternate planes of octahedral sites. In this embodiment of the present invention, M is preferably Mn, Fe, Co, Ni or combinations thereof. Removal of all of the lithium atoms leaves the layered FePO4-type structure, which has the same Pbnm orthorhombic space group. These phases may be prepared from either end, e.g., LiFePO4 (triphylite) or FePO4 (heterosite), by reversible extraction or insertion of lithium. FIG. 2A, FIG. 2B and FIG. 2C show discharge/charge curves vs. benjamin01@example.org mA·cm−2 (0.95 mA·g−1 and 1.13 mA·g−1, respectively) for Li1−xFePO4, Li1−xFe0.5Mn0.5PO4 and LiFePO4, respectively, where 0≦x≦0.5. A benjamin01@example.org V corresponds to the Fe3+/Fe2+ redox couple and a benjamin01@example.org V corresponds to the Mn3+/Mn2+ couple. With LiClO4 in PC and DME as the electrolyte, it is only possible to charge up a cathode to 4.3 V vs. a lithium anode, so it was not possible to extract lithium from LiMnPO4, LiCoPO4 and LiNiPO4 with this electrolyte. However, in the presence of iron, the Mn3+/Mn2+ couple becomes accessible. The inaccessibility is due to the stability of the Mn3+/Mn2+, Co3+/Co2+ and Ni3+/Ni2+ couples in the presence of the polyanion (PO4)3−. The relatively strong covalence of the PO4 tetrahedron of the compounds of the present invention stabilizes the redox couples at the octahedral sites to give the high Voc's that are observed. Insertion of lithium into FePO4 was reversible over the several cycles studied. FIG. 3 shows discharge/charge curves of FePO4/LiClO4+PC+DME/Li coin cell at 185 mA·g−1 for FePO4 prepared by chemical extraction of Li (delithiation) from LiFePO4. The LixFePO4 material of the present invention represents a cathode of good capacity and contains inexpensive, environmentally benign elements. While a nearly close-packed-hexagonal oxide-ion array apparently provides a relatively small free volume for Li+-ion motion, which would seem to support only relatively small current densities at room temperature, increasing the current density does not lower the closed-circuit voltage V. Rather, it decreases, reversibly, the cell capacity. Capacity is easily restored by reducing the current. As illustrated schematically in FIG. 4, lithium insertion proceeds from the surface of the particle moving inwards behind a two-phase interface. In the system shown, it is a LixFePO4/Li1−xFePO4 interface. As the lithiation proceeds, the surface area of the interface shrinks. For a constant rate of lithium transport per unit area across the interface, a critical surface area is reached where the rate of total lithium transported across the interface is no longer able to sustain the current. At this point, cell performance becomes diffusion-limited. The higher the current, the greater is the total critical interface area and, hence, the smaller the concentration x of inserted lithium before the cell performance becomes diffusion-limited. On extraction of lithium, the parent phase at the core of the particle grows back towards the particle surface. Thus, the parent phase is retained on repeated cycling and the loss in capacity is reversible on lowering the current density delivered by the cell. Therefore, this loss of capacity does not appear to be due to a breaking of the electrical contact between particles as a result of volume changes, a process that is normally irreversible. Moreover, the problem of decrease of capacity due to the particles' breaking of electrical contact may be overcome by reducing the particle size of the cathode material to the nanometer scale. Electrode materials with the olivine structure LiFePO4 (triphylite) and the quasi-isomorphous delithiated material FePO4, have the advantage of an operating voltage of 3.5V vs. Li+/Li0, i.e. in the stability window of both liquid and polymer electrolytes with a flat discharge (lithium intercalation) plateau (as seen in FIGS. 2A-2C). It may be possible to increase the diffusion kinetics and electronic conductivity by using a modified olivine structure in an electrode. The absence of non-stoichiometry or mutual miscibility for both phases (LiFePO4 and FePO4) in the materials with a pristine olivine structure may contribute to lower electronic conductivity than the materials having a modified olivine structure and to slower diffusion kinetics than may be achieved using materials with a modified olivine structure. Thus, the invention additionally provides cathode materials where the pristine olivine structure of LiM(PO4) (M=Fe or Mn or their solid solutions) is modified either on the anionic site or on the cationic site, or on both, by aliovalent or isocharge substitutions, to provide better lithium ion diffusivity and electronic conductivity. These substitutions allow for the coexistence of iron or manganese in two different oxidation states in the same phase. These substitutions may further introduce specific interactions with other elements having redox levels close to those of Fe and Mn (e.g., Fe2+/Ti4+Fe3+/Ti3+, Mn2+/V5+Mn3+/V4+, etc. . . . ). Both of these situations are favorable to electronic conductivity. Further, disorder on the anionic site provides preferential diffusion sites for Li+. Similarly, partial substitution of phosphorus by vanadium, or to some extent by silicon, increases the lattice parameters, thereby increasing the size of the bottlenecks which tend to slow diffusion. The formation of non-stoichiometry domains with mixed valence states and/or transition-metal mediated electron hopping, as well as partial substitution of phosphorus sites, differentiates the modified olivine compounds from the LiMPO4/MPO4 compounds in which the totality of Fe (Mn) is either in the +2 or +3 oxidation state. The invention further provides new cathode materials exhibiting a rhombohedral NASICON framework. NASICON, as used herein, is an acronym for the framework host of a sodium superionic conductor Na1+3xZr2(P1+xSixO4)3. The compound Fe2(SO4)3 has two forms, a rhombohedral NASICON structure and a related monoclinic form (Goodenough et al. 1976; Long et al. 1979). Each structure contains units of two FeO6 octahedra bridged by three corner-sharing SO4 tetrahedra. These units form 3D frameworks by the bridging SO4 tetrahedra of one unit sharing corners with FeO6 octahedra of neighboring Fe2(SO4)3 elementary building blocks so that each tetrahedron shares corners with only octahedra and each octahedron with only tetrahedra. In the rhombohedral form, the building blocks are aligned parallel, while they are aligned nearly perpendicular to one another in the monoclinic phase. The collapsed monoclinic form has a smaller free volume for Li+-ion motion which is why the rhombohedral form is preferred. In these structures, the FeO6 octahedra do not make direct contact, so electron transfer from an Fe2+ to an Fe3+ ion is polaronic and therefore activated. LixFe2(SO4)3 has been reported to be a candidate material for the cathode of a Li+-ion rechargeable battery with a Voc=3.6 V vs. a lithium anode (Manthiram and Goodenough 1989). While the sulfates would seem to provide the desired larger free volume for Li, batteries using sulfates in the cathode material tend to exhibit phase-transition problems, lowering the electronic conductivity. The reversible lithium insertion into both rhombohedral and monoclinic Fe2(SO4)3 gives a flat closed-circuit voltage vs. a lithium anode of 3.6 V (Manthiram and Goodenough 1989; Okada et al. 1994; Nanjundaswamy et al. 1996). Neither parent phase has any significant solid solution with the orthorhombic lithiated phase Li2Fe2(SO4)3, which is derived from the rhombohedral form of Fe2(SO4)3 by a displacive transition that leaves the framework intact. Powder X-ray diffraction verifies that lithiation occurs via a two-phase process (Nanjundaswamy et al. 1996). Increasing the current density does not change significantly the closed-circuit voltage V, but it does reduce reversibly the capacity. The reduction in capacity for a given current density is greater for the motion of the lithiated interface. The interstitial space of the framework allows fast Li+-ion motion, but the movement of lithium across the orthorhombic/monoclinic interface is slower than that across the orthorhombic/rhombohedral interface, which makes the reversible loss of capacity with increasing current density greater for the monoclinic than for the rhombohedral parent phase. The cathode materials of the invention avoid the phase transition of known sulfate cathode materials by incorporating one or more phosphate ions as at least one of the constituents of the cathode material. The rhombohedral R3c (NASICON) and monoclinic P21/n framework structures of Li3Fe2(PO4)3 are similar to those for the sulfates described above, as illustrated in FIG. 5A and FIG. 5B. A further embodiment of the invention is a rhombohedral NASICON cathode material having the formula A3−xV2(PO4)3, where A may be Li, Na or a combination thereof. Rhombohedral A3−xV2(PO4)3 reversibly intercalates 1.5 Li per formula unit for a discharge capacity of 100 mAh·g−1 with average closed-circuit voltage being 3.8 V vs. a lithium anode (see FIG. 8). The voltage and capacity performances of the rhombohedral A3−xV2(PO4)3 compounds of the invention are comparable to the high-voltage cathode materials LiMn2O4 (4.0 V), LiCoO2 (4.0 V) and LiNiO2 (4.0 V). The large, open three-dimensional framework of VO6 octahedra and PO4 tetrahedra allows an easy diffusion of the lithium ions, making it attractive for high-power batteries. A further advantage of this material is that it includes a cheaper and less toxic transition-metal element (V) than the already developed systems using Co, Ni, or Mn. Part EXAMPLES: Part Example 1: Part Ordered Olivine LiMPO: The ordered-olivine compound LiFePO4 was prepared from intimate mixtures of stoichiometric proportions of Li2CO2 or LiOH.H2O, Fe(CH2CO2)2 and NH4H2PO4.H2O; the mixtures were calcined at 300-350° C. to eliminate NH3, H2O, and CO2 and then heated in Ar at about 800° C. for 24 hours to obtain LiFePO4. Similar solid-state reactions were used to prepare LiMnPO4, LiFe1−xMnxPO4, LiCoPO4 and LiNiPO4. FePO4 was obtained from LiFePO4 by chemical extraction of Li from LiFePO4. Charge/discharge curves for Li−xFePO4 and discharge/charge cycles for LixFePO4 gave similar results with a voltage of almost 3.5 V vs. lithium for a capacity of 0.6 Li/formula unit at a current density of 0.05 mA·cm2− (See FIG. 2A and FIG. 2C). The electrolyte used had a window restricting voltages to V<4.3 V. Li extraction was not possible from LiMnPO4, LiCoPO4, and LiNiPO4 with the electrolyte used because these require a voltage V>4.3 V to initiate extraction. However, Li extraction from LiFe1−xMnxPO4 was performed with 0≦x≦0.5, and the Mn3+/Mn2+ couple produced a voltage benjamin01@example.org V vs. lithium. Arsenate may be substituted for at least some of the phosphate in LiFePO4. The iron in LiFePO4 may be supplemented up to 10% by other metals such as those filled with two electron shells, manganese or titanium, for example. This iron-based material is non-toxic, inexpensive, non-hygroscopic, easy to prepare and has good electronic conductivity compared to existing high voltage cathode materials. There is a decrease in the volume of the unit cell with the extraction of lithium from LiFePO4. At higher current densities, there is a decrease of capacity on repeated cycling associated with movement of a two-phase interface, a feature characteristic of cathodes that traverse a two-phase compositional domain in a discharge cycle. The volume change across the two-phase interface causes the particles to crack and lose electrical contact with the current collector. This problem can be overcome by reducing the particle size of the cathode material to the nanometer scale. Part Example 2: Part Modified Olivine LiMPO: The modified olivine compounds, LiMPO4, were prepared from intimate mixtures of stoichiometric proportions of Fe(C2O4).2H2O (Aldrich), LiH2PO4, Li2C2O4 (Alpha Inorganics), (NH4)2TiO(C2O4)2.H2O and polydiethoxy-siloxane (Gelest) in isopropanol. In particular, 12.95 grams of iron oxalate (Fe(C2O4).2H2O), 8.31 grams of lithium dihydrogen phosphate (LiH2PO4), 1.52 grams of lithium oxalate (Li2C2O4), 2.94 grams of ammonium titanyl oxalate monohydrate (NH4)2TiO(C2O4)2T2O) and 2.68 grams of poly-diethyoxysiloxane in 120 milliliters (ml) of isopropanol were ball-milled in a polyethylene container with sintered zirconia balls for two days. The resulting slurry was evaporated to dryness and treated in a vacuum furnace at 350° C., the 700° C. under argon (<6 ppm oxygen) to yield a compound with olivine structure of formula Li1.1Fe0.8Ti0.1P0.8Si0.2O4. The compound was delithiated with a solution of bromine in acetonitrile to Li0.1Fe0.8Ti0.1P0.8Si0.2O4. A solid-state button type cell was constructed using a 106 molecular weight polyethylene oxide-lithium bis(trifluoromethanesulfonylimide) electrolyte at an oxygen/lithium ratio of 20:1; the positive electrode was made from a 45/5/50 v/v composite of respectively the olivine material, Ketjenblack and an ionic binder of composition similar to that of the electrolyte, coated on a nickel current collector. The capacity was 1.2 mAh·cm−2. The negative electrode was a lithium disc. At 80° C., 85% of the stoichiometric discharge capacity could be obtained and cycled reversibly at 100 mAh·cm−2. Part Example 3: Part Rhombohedral NASICON Li: The inventors compared redox energies in isostructural sulfates with phosphates to obtain the magnitude of the change due to the different inductive effects of sulfur and phosphorus. Rhombohedral Li1+xTi2(PO4)3 has been shown to exhibit a flat open-circuit voltage Voc=2.5 V vs. lithium, which is roughly 0.8 V below the Ti4+/Ti3+ level found for FeTi(SO4)3. The flat voltage V(x) is indicative of a two-phase process. A co-existence of rhombohedral and orthorhombic phases was found for x=0.5 (Delmas and Nadiri 1988; Wang and Hwu 1992). Li2+xFeTi(PO4)3 of the present invention remains single phase on discharge. All three phosphates Li3M2(PO4)3, where M=Fe, Fe/V, or V, have the monoclinic Fe2(SO4)3 structure if prepared by solid-state reaction. The inventors have found that these compounds exhibit a rhombohedral structure when prepared by ion exchange in LiNO3 at 300° C. from the sodium analog Na3Fe2(PO4)3. The discharge/charge curve of FIG. 6A for lithium insertion into rhombohedral Li3+xFe2(PO4)3 exhibits an average Voc of 2.8 V. This is surprisingly different from the curves for the monoclinic form (See FIG. 6B). The inventors have found that up to two lithiums per formula unit can
{'bibliographic_information': "{'country': 'US', 'doc-number': '13645341', 'kind': 'B2', 'date': '20121004', 'disclaimer_text': 'This patent is subject to a terminal disclaimer.', 'invention_title': 'Cathode materials for secondary (rechargeable) lithium batteries'}", 'source_file': './grant/2014/ipg140722.xml', 'source_data': 'USPTO-Grant'}