Abstract:
The composition of compounds containing a multiplicity of different elements are optimized in general by full or partial substitutions of one or more of the atoms in such compounds so as to effect an Ne/χ value which represents a peak or near peak value in λ (the electron-phonon coupling constant) so as to maximize T c  for such compositions of matter.

Description:
FIELD OF THE INVENTION 
     This invention relates to superconductor materials and in particular to compositions that result in superconductive characteristics at relatively high temperatures. 
     DESCRIPTION OF THE PRIOR ART 
     The Phenomenon of superconductivity occurs with certain metals and alloys when cooled to a very low characteristic transition temperature, superconductive elements, alloys or compounds will conduct electricity without resistance below a critical temperature T c . Resistance is undesirable because it causes loss in energy flow through the material. Superconductivity, which was first discovered by Onnes in 1911, is characterized by the disappearance of all electrical resistance in a material below the transition temperature. 
     Superconductor materials have been found to be useful for various applications, such as superconducting magnets, magnetic resonance imaging, high sensitivity bolometer, and magnetoencephalography, among others. However, a major problem is the necessity to operate the superconductor material at a very low temperature, such as 4.2° K, which would require the use of liquid helium for example. Large and costly equipment is required and maintenance and repair are major problems. 
     In the article “Theory of Superconductivity” published in Physical Review, Dec. 1, 1957, page 1175, Bardeen, Cooper and Schrieffer proposed a theory of superconductivity (known as the BCS Theory) that delineates the properties of superconductors. The theory postulates that the interaction between electrons resulting from a virtual exchange of phonons is attractive when the energy difference between the electrons states involved is less than the phonon energy. The BCS theory, for which they were presented with a Nobel Prize in Physics, expresses the relation between T c , a typical phonon energy (ω), and the interaction strength N(O)V as
 
 T   c =1.14(ω)exp[−1 N[O]V] 
 
     This BCS equation for T c  has been modified to include μ*, the coulomb pseudopotential. The modified equation
 
 T   c =1.14(ω)exp[−1 /N[O]−μ*].  
 
     It should be noted that in the framework of the BCS theory, there is a formula for estimating the T c . However, it is a general formula which does not take into account any specific feature of the superconducting materials. 
     In the 1975 publication by Allen-Dynes, Physical Review B, Vol. 18, #3, page 913, the value of μ* is treated as a constant of 0.10, which value will be used in the explanation of the present invention. 
     In pages 75-77 of the text of Volume 21 of Physical Chemistry, published by Academic Press, R. T. Sanderson sets forth a principle of electronegativity equalization. The principle is that “When two or more atoms are initially different in electronegativity combine chemically, they become adjusted to the same intermediate electronegativity within the compound”. The intermediate electronegativity may be defined as the geometric mean of the individual electronegativities of all of component atoms that make the compound formula. For example, if the A 2 B 3  represents a compound of two atoms of A and three atoms of B, the electronegativity may be expressed as
 
χ (A2B3) =(χ 2   a χ 3   b ) 1/5 
 
     Andre Mourachkine points out in the text “Room-Temperature Superconducitivity”, published in 2004 by International Science Publishing, at pages 21-22, that there is no theoretical formula for predicting the value of critical temperature in a given compound and that there is no rule for predicting whether a certain substance will undergo a superconducting transition at a particular temperature. The publication points out that a major problem in the field of superconductivity is how to calculate the critical temperature T c  value in different materials by taking into account the specific features of a material. 
     In an article “Transition Temperatures of Strong Coupled Superconductors” by W. L. McMillan, Physical Review, Vol. 167, pg 334-367 (1968), McMillan provides a set of equations that allows for the calculation of λ values from experimental values of θ D  and T c  for a wide variety of superconductors. The McMillan article is incorporated herein by reference. 
     McMillan provides two principle equations:
 
 T   c =θ D /1.45exp[1.04(1+λ)/λ−μ*(1−0.62λ)]
 
and λ=1.04 μ*ln(θ/1.45 T   c )/(1−0.62 μ*)ln(θ/1.45 T   c )−1.04
 
     The above equations are solved for a variety of superconductors (elements and compounds) using a constant μ*=0.10. McMillan&#39;s equations are valid only for λ values between 0.33 and 0.90. Beyond those limits, error greater than 10% occurs for the calculated λ values. 
     SUMMARY OF THE INVENTION 
     An object of this invention is to provide selected superconductor compositions that exhibit superconductivity at relatively high temperatures. 
     According to this invention novel superconductor compositions are established by taking into account the value of Ne/χ of any arbitrary composition where Ne is the average number of valance electrons in the composition of matter in question and χ is the absolute value of the electronegativity of such a composition. By utilizing prior experimental work by McMillan and Allen-Dynes we establish a new universal relationship which allows for the calculation of λ (electron phonon coupling constant) and, from a universal equation developed from the McMillan and Allen-Dynes publication which is λ=[(ln θ D /2T c )/2] −1 . From these parameters we can construct the response of λ (electron-phonon coupling constant) to Ne/χ for any composition of matter. The λ response vs. Ne/χ is depicted in  FIGS. 1   a - 1   d  and illustrates maxima in λ at specific values of Ne/χ. By design or selection of compositions of matter which possess peak (near peak) λ values we are able to create novel compositions of matter that possess maximal values of T c  for their atomic properties as defined by Ne and χ of such a composition and by the consequence of a peak or near peak value of λ. Additionally we have developed a relationship by which we can estimate the value of the Debye temperature for any arbitrary composition of matter. This relationship is θ D  (Debye Temperature)=exp[10.0−0.64(ln at. wt.+ln at. vol)]. Additionally if the composition of matter is amorphous the θ D  as calculated above is modified to be equal to 0.70 θ D  (crystalline). 
     The values of Ne, χ (absolute electronegativity) and the (In at. wt.+ln at. vol) of selected elements as used in this invention are depicted in Table 1. Additionally, Table 2 illustrates the Ne/χ values at peak positions of λ and the peak value of λ and limits thereof. 
     
       
         
               
               
               
               
               
               
             
               
               
               
               
               
               
             
           
               
                 TABLE I 
               
               
                   
               
               
                   
                   
                   
                   
                 ln At. 
                   
               
               
                   
                   
                   
                 Metallic 
                 wt. + ln 
                 Absolute 
               
               
                 Atomic 
                   
                   
                 Valence 
                 At. 
                 Electronegativity 
               
               
                 no. 
                 Symbol 
                 Element 
                 Ne 
                 Vol. 
                 Electron Volts (χ) 
               
               
                   
               
             
             
               
                   
               
             
          
           
               
                 1 
                 H 
                 Hydrogen 
                 1 
                 2.67 
                 7.18 
               
               
                 2 
                 He 
                 Helium 
                 2 
               
               
                 3 
                 Li 
                 Lithium 
                 1 
                 4.5 
                 3.00 
               
               
                 4 
                 Be 
                 Beryllium 
                 2 
                 4.25 
                  4.6 ± 0.1 
               
               
                 5 
                 B 
                 Boron 
                 3 
                 4.5 
                 4.29 
               
               
                 6 
                 C 
                 Carbon 
                 4 
                 4.34 
                 6.26 
               
               
                 7 
                 N 
                 Nitrogen 
                 5 
                 5.49 
                 7.3 
               
               
                 8 
                 O 
                 Oxygen 
                 6 
                 5.41 
                 7.54 
               
               
                 9 
                 F 
                 Fluorine 
                 7 
                 5.79 
                 10.41 
               
               
                 10 
                 Ne 
                 Neon 
                 8 
               
               
                 11 
                 Na 
                 Sodium 
                 1 
                 6.30 
                 2.84 
               
               
                 12 
                 Mg 
                 Magnesium 
                 2 
                 5.83 
                 3.28 ± 0.5 
               
               
                 13 
                 Al 
                 Aluminum 
                 3 
                 5.60 
                 3.21 
               
               
                 14 
                 Si 
                 Silicon 
                 4 
                 5.82 
                 4.77 
               
               
                 15 
                 P 
                 Phosphorus 
                 5 
                 6.26 
                 5.62 
               
               
                 16 
                 S 
                 Sulfur 
                 6 
                 6.26 
                 6.22 
               
               
                 17 
                 Cl 
                 Chlorine 
                 7 
                 6.50 
                 8.3 
               
               
                 18 
                 Ar 
                 Argon 
                 8 
               
               
                 19 
                 K 
                 Potassium 
                 1 
                 7.48 
                 2.42 
               
               
                 20 
                 Ca 
                 Calcium 
                 2 
                 6.94 
                 3.07 
               
               
                 21 
                 Sc 
                 Scandium 
                 3 
                 6.49 
                 3.37 
               
               
                 22 
                 Ti 
                 Titanium 
                 4 
                 6.23 
                 3.46 
               
               
                 23 
                 V 
                 Vanadium 
                 5 
                 6.08 
                 3.64 
               
               
                 24 
                 Cr 
                 Chromium 
                 6 
                 5.94 
                 3.72 
               
               
                 25 
                 Mn 
                 Manganese 
                 7 
                 6.04 
                 3.72 
               
               
                 26 
                 Fe 
                 Iron 
                 8 
                 5.98 
                 4.02 
               
               
                 27 
                 Co 
                 Cobalt 
                 9 
                 5.87 
                 4.27 
               
               
                 28 
                 Ni 
                 Nickel 
                 10 
                 5.96 
                 4.39 
               
               
                 29 
                 Cu 
                 Copper 
                 11 
                 6.11 
                 4.48 
               
               
                 30 
                 Zn 
                 Zinc 
                 12 
                 6.39 
                 4.47 ± 0.1 
               
               
                 31 
                 Ga 
                 Gallium 
                 3 
                 6.70 
                 3.21 
               
               
                 32 
                 Ge 
                 Germanium 
                 4 
                 6.89 
                 4.56 
               
               
                 33 
                 As 
                 Arsenic 
                 5 
                 6.89 
                 5.31 
               
               
                 34 
                 Se 
                 Selenium 
                 6 
                 7.17 
                 5.89 
               
               
                 35 
                 Br 
                 Bromine 
                 7 
                 7.54 
                 7.59 
               
               
                 36 
                 Kr 
                 Krypton 
                 8 
               
               
                 37 
                 Rb 
                 Rubidium 
                 1 
                 8.47 
                 2.33 
               
               
                 38 
                 Sr 
                 Strontium 
                 2 
                 8.01 
                 2.87 
               
               
                 39 
                 Y 
                 Yttrium 
                 3 
                 7.27 
                 3.26 
               
               
                 40 
                 Zn 
                 Zirconium 
                 4 
                 7.16 
                 3.53 
               
               
                 41 
                 Nb 
                 Niobium 
                 5 
                 6.93 
                 3.83 
               
               
                 42 
                 Mo 
                 Molybdenum 
                 6 
                 6.8 
                 3.92 
               
               
                 43 
                 Tc 
                 Technetium 
                 7 
                 4.6 
                 3.92 
               
               
                 44 
                 Ru 
                 Ruthenium 
                 8 
                 6.74 
                 4.2 
               
               
                 45 
                 Rh 
                 Rhodium 
                 9 
                 6.74 
                 4.3 
               
               
                 46 
                 Pd 
                 Palladium 
                 10 
                 6.84 
                 4.45 
               
               
                 47 
                 Ag 
                 Silver 
                 11 
                 7.01 
                 4.44 
               
               
                 48 
                 Cd 
                 Cadmium 
                 12 
                 7.28 
                 4.43 ± 0.1 
               
               
                 49 
                 In 
                 Indium 
                 3 
                 7.50 
                 3.1 
               
               
                 50 
                 Sn 
                 Tin 
                 4 
                 7.81 
                 4.23 
               
               
                 51 
                 Sb 
                 Antimony 
                 5 
                 7.70 
                 4.84 
               
               
                 52 
                 Te 
                 Tellurium 
                 6 
                 7.87 
                 5.49 
               
               
                 53 
                 I 
                 Iodine 
                 7 
                 8.09 
                 6.76 
               
               
                 54 
                 Xe 
                 Xenon 
                 8 
               
               
                 55 
                 Cs 
                 Cesium 
                 1 
                 9.15 
                 2.18 
               
               
                 56 
                 Ba 
                 Barium 
                 2 
                 8.59 
                 2.67 
               
               
                 57 
                 La 
                 Lanthanum 
                 3 
                 8.05 
                 3.02 
               
               
                 58 
                 Ce 
                 Cerium 
                 4 
                 7.95 
                 3.25 
               
               
                 59 
                 Pr 
                 Praseodymium 
                 3 
                 8.03 
                 3.21 
               
               
                 60 
                 Nd 
                 Neodymium 
                 3 
                 8.00 
                 3.15 ± 0.1 
               
               
                 61 
                 Pr 
                 Promethium 
                 3 
                 8.09 
                 3.21 ± 0.1 
               
               
                 62 
                 Sm 
                 Samarium 
                 3 
                 8.00 
                 2.97 ± 0.1 
               
               
                 63 
                 Eu 
                 Europium 
                 3 
                 8.05 
                 3.09 ± 0.1 
               
               
                 64 
                 Gd 
                 Gadolinium 
                 3 
                 8.05 
                  3.1 ± 0.1 
               
               
                 65 
                 Tb 
                 Terbium 
                 3 
                 8.02 
                 2.98 ± 0.1 
               
               
                 66 
                 Dy 
                 Dysprosium 
                 3 
                 8.03 
                 3.02 ± 0.1 
               
               
                 67 
                 Ho 
                 Holmium 
                 3 
                 8.04 
                 3.06 ± 0.1 
               
               
                 68 
                 Er 
                 Erbium 
                 3 
                 8.03 
                 3.16 ± 0.1 
               
               
                 69 
                 Tm 
                 Thulium 
                 3 
                 8.03 
                 3.61 
               
               
                 70 
                 Yb 
                 Ytterbium 
                 3 
                 8.36 
                 3.63 
               
               
                 71 
                 Lu 
                 Lutetium 
                 3 
                 8.04 
                 2.89 
               
               
                 72 
                 Hf 
                 Hafnium 
                 4 
                 7.79 
                  3.7 ± 0.1 
               
               
                 73 
                 Ta 
                 Tantalum 
                 5 
                 7.59 
                 4.11 
               
               
                 74 
                 W 
                 Tungsten 
                 6 
                 7.46 
                 4.4 
               
               
                 75 
                 Re 
                 Rhenium 
                 7 
                 7.44 
                 4.02 
               
               
                 76 
                 Os 
                 Osmium 
                 8 
                 6.10 
                 4.89 
               
               
                 77 
                 Ir 
                 Iridium 
                 9 
                 7.41 
                 5.33 
               
               
                 78 
                 Pt 
                 Platinum 
                 10 
                 7.48 
                 5.56 
               
               
                 79 
                 Au 
                 Gold 
                 11 
                 7.60 
                 5.77 
               
               
                 80 
                 Hg 
                 Mercury 
                 12 
                 7.99 
                 5.12 
               
               
                 81 
                 Tl 
                 Thallium 
                 3 
                 8.17 
                 3.24 
               
               
                 82 
                 Pb 
                 Lead 
                 4 
                 8.23 
                 3.89 
               
               
                 83 
                 Bi 
                 Bismuth 
                 5 
                 8.41 
                 4.12 
               
               
                 84 
                 Po 
                 Polonium 
                 6 
               
               
                 85 
                 As 
                 Astatine 
                 7 
               
               
                 86 
                 Rn 
                 Radon 
                 8 
               
               
                 87 
                 Fr 
                 Francium 
                 1 
               
               
                 88 
                 Ra 
                 Radium 
                 2 
               
               
                 89 
                 Ac 
                 Actinium 
                 3 
               
               
                 90 
                 Th 
                 Thorium 
                 3, 4 
                 8.47 
                 3.55 ± 0.1 
               
               
                 91 
                 Pr 
                 Protactinium 
                 3 
               
               
                 92 
                 U 
                 Uranium 
                 3 
                 8.01 
                 3.15 ± 0.1 
               
               
                 93 
                 Np 
                 Neptunium 
                 3 
               
               
                 94 
                 Pu 
                 Plutonium 
                 3 
                 28.2 
                 3.25 ± 0.1 
               
               
                   
               
             
          
         
       
     
     If no range is noted for the electronegativity the range is ±0.1 cv 
     
       
         
               
               
               
             
               
               
               
             
           
               
                   
                 TABLE II 
               
               
                   
                   
               
               
                   
                 Ne/χ values at peak 
                 (max λ) at indicated peak 
               
               
                   
                   
               
             
             
               
                   
               
             
          
           
               
                   
                 0.465 ± .005  
                 0.8 
               
               
                   
                 0.595 ± 0.004 
                 1.0 
               
               
                   
                 0.655 + 0.001, −0.004 
                 1.0 
               
               
                   
                  0.69 ± 0.003 
                 0.80 
               
               
                   
                  0.74 ± 0.005 
                 0.60 
               
               
                   
                 0.848 ± 0.001 
                 0.55 
               
               
                   
                 0.875 ± 0.002 
                 1.3 
               
               
                   
                  0.91 ± 0.002 
                 1.2 
               
               
                   
                 0.971 ± 0.001 
                 1.45 
               
               
                   
                 1.015 ± 0.002 
                 2.85 
               
               
                   
                  1.07 ± 0.007 
                 3.35 
               
               
                   
                 1.12 + 0.004, −0.01 
                 2.6 
               
               
                   
                  1.17 ± 0.008 
                 3.0 
               
               
                   
                 1.215 ± 0.002 
                 2.45 
               
               
                   
                  1.28 ± 0.005 
                 0.94 
               
               
                   
                 1.34 ± 0.01 
                 0.95 
               
               
                   
                  1.36 ± 0.002 
                 0.60 
               
               
                   
                 1.408 ± 0.003 
                 0.90 
               
               
                   
                  1.45 ± 0.003 
                 1.25 
               
               
                   
                 1.473 ± 0.002 
                 0.75 
               
               
                   
                 1.508 ± 0.002 
                 0.90 
               
               
                   
                 1.525 ± 0.002 
                 0.55 
               
               
                   
                 1.578 ± 0.002 
                 0.68 
               
               
                   
                 1.596 ± 0.002 
                 0.55 
               
               
                   
                 1.642 + 0.005, −0.002 
                 0.86 
               
               
                   
                 1.704 ± 0.005 
                 0.68 
               
               
                   
                 1.80 + 0.00, −0.005 
                 0.68 
               
               
                   
                 1.86 + 0.005 −0.01 
                 0.74 
               
               
                   
                 1.97 ± 0.02 
                 0.48 
               
               
                   
                 2.166 ± 0.01  
                 0.65 
               
               
                   
                 2.16 ± 0.01 
                 0.7 
               
               
                   
                 2.34 ± 0.01 
                 0.90 
               
               
                   
                   
               
             
          
         
       
     
     All of the essential elements required to estimate the T c  of new and novel superconductors are now present and examples of their use for specific examples follows. 
     The actual novel compositions which are referred to later and in the claims are arrived at by tuning a particular composition of say, AB by selection of A′ or B′ or both from within the same class of elements constituting A or B such that A 1−x A′B or AB 1−y B′ or A 1−x A x ′B 1−y B y ′ such that the resultant composition is tuned to a single peak or near peak value of Ne/χ shown in Table 2 or  FIG. 1   a - 1   d , so as to maximize the electron phonon coupling constant. The natural result of such tuning exercise is to convert ternary to quaternary compositions or pentanary compositions and, to convert nominal ternary compositions to quaternary or pentanary compositions by the act of tuning to maximize the electron phonon coupling constant, and by the act of full or partial substitutions of A&#39;s and B&#39;s with elements of differing electronegativity such as to arrive a peak or near peak value of Ne/χ of such substituted composition of matter. 
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     The invention will be described in greater detail with reference to the drawing in which  FIG. 1   a - 1   d  which is a plot of the electron phonon coupling constant λ against the values of Ne/χ which is dependent on the number of electron per atom in the composition and the absolute electronegativity. 
     By utilizing both the McMillan and the Allen-Dynes experimental results, and by limiting the values of λ derived from the McMillan equation to its range of validity, we arrive at a universal relationship between θ, T c , and λ. The plot of ln(θ D /2 T c ) versus λ −1  results in a (0,0) intercept, and in a universal equation for T c  which is
 
 T   c =θ D /2exp[−2/λ]
 
     Similarly, using Allen-Dynes experimental results in amorphous superconductors and plotting ln(ωlog/2 T c ) vs. λ −1 , we arrive at
 
 T   c =ωlog/2exp[−2/λ], wherein θ D , and ωlog are in units of ° K
 
     The only difference in the two equations is the pre-exponential factor which represents the difference between crystalline superconductors in the McMillan case and amorphous superconductors in Allen-Dynes case. The dependence of T c  on λ remains in the same exponential form, that is, T c{EMBED Equation.3} exp[−2/λ]. 
     With the above equation, we can calculate reliable values of λ for cuprate superconductors and a variety of other superconductors which heretofore has not been possible. For example, we calculate the λ values for several well-known superconductors, which are crystalline in nature, by both our universal equation and the McMillan equation, recalling that both equations are utilized at μ*=0.10. For La 1.85 Sr 0.15 CuO 4  whose T c =38° K and whose θ D =365° K, the McMillan equation results in λ=1.68 whereas for our universal equation λ=1.27. The McMillan result is ˜32% greater than that derived from the universal equation. 
     For YBa 2 Cu 3 O 7  whose T c =92° K and whose θ D =425 T c  the McMillan equation yields λ=24.1 whereas the universal equation yields a value if 2.39. The McMillan equation, which in this case is used well beyond its limits of validity, i.e. λ=0.90 differs from the universal equation value by an extremely high 1.008%. 
     For the highest T c  element Niobium, whose T c =9.2° K and whose θ D =277° K, the McMillan derived value of λ=0.745, whereas the value derived from the universal equation is λ=0.737 an insignificant difference of 1%. 
     In accordance with the present invention, we can calculate reliable values of λ. The λ values for various superconductors of arbitrary compositions can be connected to electronic properties of individual atoms which, in combination or individually, possess determinable atomic electronic properties. The two atomic properties we choose are Ne [the number of valence electrons/atoms] and χ the absolute electronegativity of individual atomic species
 
Where, χ[electronegativity]= I+A/ 2
 
Where I=ionization energy [ev]/atom and A is the electron affinity/atom in units of electron volts or [ev]/atom
 
     From the preceding, we now note that an atomic property Ne/χ relevant to the electronic properties of atoms produce a reliable and reproducible response of λ vs. Ne/χ. The value λ can be shown to achieve peak values at particular values of Ne/χ, with either crystalline or amorphous superconductors as exemplified by the Allen-Dynes compounds or the elements of McMillan, and the cuprates as well. This accommodation of both amorphous and crystalline compounds illustrates the robustness of λ vs. Ne/χ. This robustness allows for the estimation of the λ value for any arbitrary compound by calculating the value of its Ne/χ value from its constituents and the use of the universal equation for T c  if θ D  is also known. 
     A reasonable estimate of θ D  can be made from the correlation of θ D  with the term [ln(atomic weight)+ln(atomic volume)]. Each element possesses unique values of the above terms. The value of ln(atomic weight)+ln(atomic volume) for any arbitrary compound is simply the geometric means of its constituents. The correlation equation is θ D =e 10−0.64 ln[(atomic weight)+ln(atomic volume)] . As an example, the θ D  for YBa 2 Cu 3 O 7  is equal to θ χ   10−0.64(6.11) =441° K and the experimental values is 447° K. For YBa 2 Cu 3 O 7  (ln atomic weight+ln atomic volume) Y123 =7.27×(8.59) 2 ×(6.111 3 ×(541) 7 , the product thereof=[1.65×10 10 ] 1/13 =6.11 which is the geometric mean of the combined ln&#39;s of the atomic weight and atomic volume for the atomic constituents of YBa 2 Cu 3 O 7 . A simpler example is that of Niobium whose (ln atomic weight+ln atomic volume)=6.93 Therefore,
 
θ D ( Nb )= e   10−0.64(6.93) =261° K,
 
whereas the literature value for Nb=277° K.
 
     A more recent discovery relating to superconductor MgB 2  is found in an article by Akamitsu, Nature (London) 410, 63 (2001), which is incorporated herein by reference. The discovery of MgB 2  in 2001 by Akamitsu Lab was the result of a screening of compounds that had previously not been investigated for superconductivity. Commercially available samples of MgB 2  were available as early as the 1950&#39;s. There were succeeding attempts by the superconductor community to discover and produce other Magnesium Diborides. The compounds MgB 2  did not fit the Mathias rule, and there was no evidence of other similar compounds being superconductive. The discovery of MgB 2  was not based on scientific theory or available methodology to guide or to explore such a compound for superconductivity. As it turned out, MgB 2  which is superconductive at 40° K, has proven to be a useful discovery and maintains to this day the T c  record temperature for simple noncuprate superconductors. Directly after the discovery of MgB 2 , there was a flurry of activity in the scientific community and two principle approaches were taken.
         1. Doping of MgB 2  by substitution (either Mg substituted by Al or Boron substituted by Carbon or Be) effects for both Mg and B, while maintaining the MgB 2  structure. Examples were Mg 1-x Al χ B 2  and MgB 2-χ  with χ being either Be or C.   2. The second approach was to screen or make isostructural compounds which included the Borides of the elements (Li, Be, Al) and the transition metal Borides Sc, Ti, Zr, Hf, V, Ta, Cr, Mo and Nb. The report on TaB 2  by Rosner and Pickett in September 2001 with Ta borides. They produced two samples of Ta borides namely, TaB 1.26  and TaB 2.03.          

     Both approaches provided no superconductivity. 
     For the above two specific samples, if we calculate the values of Ne/χ and θ D  from our graphical data, we can estimate the values of χ for these compositions and the values of θ D , and hence the expected superconducting critical temperature. 
     From the above values for these two compositions, we can calculate the estimated T c  in ° K. 
     For composition (1), graphically with the reference to  FIGS. 1A-1D , λ is found to be 0.25 and θ D =654° K and T c =0.11° K by solving our universal equation. For composition (2), we find similarly that λ=0.25 and θ D =718° K. Therefore, T c =0.13° K. The referred paper by Rosner and Pickett provided measurements of these compounds to only 1.5° K. Thus superconductivity was not observed and according with our calculations, it should not have since, both estimated T c  values were less than 1.5° K. 
     A TaB 2  composition can be made to have a superconductor characteristic. For example, Ta 1-χ Ti χ B 2  is found in the ternary composition range and also Ti 0.65 Ta 0.35 B 2  which has λ value graphically of ˜1.03 and an (Ne/χ) of about 0.847 and θ D =829° K. Thus it can be computed that
 
 T   c (Ti 0.65 Ta 0.35 B 2 )≈88.9° K.
 
     In accordance with this invention, we can establish accurate λ values if θ D  and T c  are known. The two equations that delineate the relationships are
 
 T   c =θ D /2exo[−2/λ] and
 
λ=[θ D /2 T   c /2] −1  
 
     The following four examples satisfy these equations: 
     
       
         
               
               
               
               
               
             
           
               
                   
               
               
                 Composition 
                 Ne/χ 
                 θ D   
                 Estimated λ 
                 T c   
               
               
                   
               
             
             
               
                 Nb 1.95 Ti 1.05 Sn 
                 1.174 
                 259° K 
                 2.7 
                  61° K 
               
               
                 Zr 2.12 Nb 0.88 Sn 
                 1.122 
                 210° K 
                 2.5 
                  41° K 
               
               
                 La 1.20 Tm 0.55 Sr 0.15 CuO 4   
                 1.069 
                 426° K 
                 3.3 
                 116° K 
               
               
                 Sc 1.0 La 0.85 Ca 0.15 CuO 4   
                 1.071 
                 486° K 
                 3.3 
                 132° K 
               
               
                   
               
             
          
         
       
     
     Examples 1 and 2 are in the class of A-15 type compounds, i.e., AB 3  and should posses a high critical field ≧10 Telsa. The practical applications could be in the form of wires carrying large current densities at higher temperature than now realized. The advantage would be the relaxed refrigeration requirement; other refrigerants instead of Helium could be useful, liquid refrigerant instead of helium which could be useful in MRI type applications. The wires currently used are NbTi alloys having a T c  of ˜10-11° K and can operate only at liquid Helium temperatures. 
     Example 3 is a compound related to the original Bednorz-Mueller discovery of La 1.85 Ba 0.15 CuO 4  for which they won the Nobel Prize. The novel composition disclosed herein optimizes the Copper layer structure having nontoxic elements in its composition to achieve a T c ˜132° K which heretofore has only been obtained with compounds containing toxic elements, such as Mercury (Hg) and Thallium (Tl). Such compounds were more complex, containing three Copper layers per composition in contrast to the single Copper layer used in the novel composition disclosed herein. For example 3 and 4, the preparation process would preferably be conducted under high pressure to ensure the desired structure. 
     Another Example is the same class as preceding Examples 1 and 2. 
     EXAMPLE 4 
     
       
         
               
               
               
               
               
             
           
               
                   
               
               
                 Composition 
                 Ne/χ 
                 θ D   
                 λ 
                 T c   
               
               
                   
               
             
             
               
                 V 2.655 Nb 0.345 Si 
                 1.215 
                 449° K 
                 ~2.45 
                 99° K 
               
               
                   
               
             
          
         
       
     
     This represents a composition in the A-15 class which has the potential to be refrigerated by liquid Nitrogen i.e. ˜77° K and would be expected to have a high critical field as well. 
     The following lists Examples of optimized Superconductive compositions: 
     EXAMPLES OF OPTIMIZED SUPERCONDUCTIVE COMPOSITIONS 
     Example 1 
     A-15 Type, V 2.655 Nb 0.345 Si 0.885 Ge 0.115    
     Ne/χ=1.216; λ˜2.45; θ D ˜440° K; T c ˜97° K 
     Example 2 
     A-15 Type, Nb 3 Ge 0.245 Al 0.755    
     Ne/χ=1.216; λ˜2.45; θ D ˜307° K; T c ˜62° K 
     Example 3 
     MgB 2  Type, Mg 0.8 Sc 0.1 Na 0.1 B 2    
     Ne/χ=0.656; λ˜1.0; θ D ˜940° K; T c ˜63° K 
     Example 3a 
     Cuprate, La 1.33 Tm 0.52 Sr 0.15 CuO 4    
     Ne/χ=1.07; λ˜3.3; θ D ˜420° K; T c ˜109° K 
     Example 4 
     Cuprosulfide, Sc 1.85 Sr 0.15 CuS 4    
     Ne/χ=1.175; λ˜3; θ D ˜391° K; T c ˜100° K 
     Example 5 
     Cuproselenide, Sc 1.85 Ba 0.15 CuSe 4    
     Ne/χ=1.214; λ˜2.3; θ D ˜270° K; T c ˜56° K 
     Example 6 
     Intermetallic, Mg 2 Ni 0.53 Pt 0.47    
     Ne/χ=1.125; λ˜2.5; θ D ˜457° K; T c ˜101° K 
     Example 6a 
     Intermetallic, Mn 0.90 Mo 0.10 Al 12    
     Ne/χ=1.016; λ˜2.7; θ D ˜596° K; T c ˜142° K 
     Example 7 
     Cuprate, Mg 0.765 Be 0.135 CuO 2    
     Ne/χ=1.12; λ˜2.6; θ D ˜605° K; T c ˜140° K 
     Example 8 
     Bismuth Sulfide, Ba 0.6 Na 0.30 K 0.10 BiS 3    
     Ne/χ=1.015; λ˜2.5; θ D ˜269° K; T c ˜60° K 
     Example 8a 
     Bismuth Selenide, Ba 0.65 Rb 0.35 BiSe 3    
     Ne/χ=1.063; λ˜3.0; θ D ˜163° K; T c ˜42° K 
     Example 9 
     Titanium Selenide, RbTi 2 Se 4    
     Ne/χ=1.064; λ˜3.0; θ D ˜241° K; T c ˜61° K 
     Example 10 
     Cuprate, ScMg 1.5 Ca 0.5 Cu 3 O 7    
     Ne/χ=1.124 λ˜2.5; θ D ˜557° K; T c ˜125° K 
     Example 11 
     Intermetallic, Mg 3 Au 0.81 Ag 0.19    
     Ne/χ=1.016; λ˜2.7; θ D ˜415° K; T c ˜99° K 
     Example 12 
     Cuprate, PdMgBe 2 Cu 3 O 8.45    
     Ne/χ˜1.074; λ˜3.3; θ D ˜652° K; T c ˜177° K 
     Example 13 
     Pd Mg 1.12 Be 0.88 CuO 4.15    
     Ne/χ˜1.069; λ˜3.3; θ D ˜626° K; T c ˜170° K 
     Example 14 
     Silicide, V 0.59 Mo 0.4 Si 2    
     Ne/χ˜1.017; λ˜2.6; θ D ˜477° K; T c ˜110° K 
     Example 15 
     Intermetallic, Cr 0.914 V 0.086 Al 3    
     Ne/χ˜1.12; λ˜2.50; θ D ˜578° K; T c ˜129° K 
     Example 16 
     Intermetallic Aluminum deficient, MoAl 2.9    
     Ne/χ˜1.115; λ˜2.5; θ D ˜509° K; T c ˜114° K 
     Example 17 
     Cuprate (oxide) YMg 2 Cu 3 O 7    
     Ne/χ˜1.117; λ˜2.5; θ D ˜552° K; T c ˜124° K 
     Example 18 
     CuproSulfide, YBe 1.06 Mg 0.94 Cu 3 S 7    
     Ne/χ˜1.215; λ˜2.45; θ D ˜476° K; T c ˜105° K 
     Example 19 
     Diboride, Sc 0.6 La 0.4 RuB 2    
     Ne/χ˜1.069; λ˜3.3; θ D ˜621° K; T c ˜169° K 
     Example 20 
     Transition Metal MonoBoride, Ti 0.98 V 0.02 B 
     Ne/χ˜0.91; λ˜1.2; θ D ˜744° K; T c ˜70° K 
     Example 21 
     Transition Metal Monoboride, V 0.47 Cr 0.53 B 
     Ne/χ˜1.073; λ˜3.3; θ D ˜790° K; T c ˜215° K 
     Example 22 
     Transition Metal Pentaboride, Mo 1.16 W 0.84 B 5    
     Ne/χ˜0.91; λ˜1.2; θ D ˜831° K; T c ˜78° K 
     Example 23 
     Transition Metal Pentaboride, Mo 1.78 Ti 0.22 B 5    
     Ne/χ˜0.91; λ˜1.2; θ D ˜870° K; T c ˜82° K 
     Example 24 
     Transition Metal Tetraboride, Cr 2.78 Mn 0.22 B 4    
     Ne/χ˜1.07; λ˜3.3; θ D ˜858° K; T c ˜234° K 
     Example 25 
     Boron Deficient Transition Metal Tetraboride, Cr 3 B 3.95    
     Ne/χ˜1.065; λ˜3.0; θ D ˜857° K; T c ˜220° K 
     Example 26 
     Intermetallic, Mg 2 Si 0.885 Sn 0.115    
     Ne/χ˜0.652; λ˜1.0; θ D ˜510° K; T c ˜34° K 
     Example 27 
     Au 0.95 Cu 0.05 Be 3    
     Ne/χ˜0.876; λ˜1.3; θ D ˜956° K; T c ˜102° K 
     Example 28 
     Intermetallic, Ti 0.59 Nb 0.25 V 0.16 Al 3    
     Ne/χ˜1.016; λ˜2.6; θ D ˜543° K; T c ˜126° K 
     Example 29 
     Cuprate, TmBe 2 Cu 3 O 7    
     Ne/χ˜1.077; λ˜3.0; θ D ˜640° K; T c ˜161° K 
     Example 30 
     Boride, TiB 0.98    
     Ne/χ˜0.91; λ˜1.2; θ D ˜907° K; T c ˜91° K 
     Example 31 
     Monoboride, Zr 0.90 V 0.10 B 
     Ne/χ˜0.91; λ˜1.2; θ D ˜600° K; T c ˜56° K 
     Example 32 
     Monoboride, Cr 0.60 Nb 0.40 B 
     Ne/χ˜1.07; λ˜3.3; θ D ˜725° K; T c ˜186° K 
     Example 33 
     Intermetallic, IrSn 2.96-2.98    
     Ne/χ˜1.171; λ˜3.0; θ D ˜159° K; T c ˜41° K 
     Example 34 
     Intermetallic, Ir 3 Sn 6.9    
     Ne/χ˜1.215; λ˜2.6; θ D ˜161° K; T c ˜37° K 
     Example 35 
     A composition of matter specified by Re 0.925 B 2 , 
     Ne/χ=1.015, θ D  is 752° K, λ=2.8 and whose Tc=184° K. 
     Example 36 
     A composition of matter specified by Re 0.55 B 2 , 
     Ne/χ=0.913, θ D  is 893° K, λ=1.20 and whose Tc=84° K. 
     Example 37 
     A composition of matter whose composition is V 0.82 B 2    
     Ne/χ=0.876, θ D  is 950° K, λ=1.3 and whose Tc=101° K. 
     Example 38 
     A composition of matter where composition is V 0.655 B 2    
     Ne/χ=0.848, θ D  is 990° K, λ=1.3 and whose Tc=106° K. 
     Example 39 
     Alloys of Cu, Ni, Pt, Pd, Ir, Au, Ag C Ne/χ=2.34 
     
       
         
               
               
               
               
               
             
           
               
                   
               
               
                 Alloys 
                 Compound 
                 Ne/χ 
                 θ D   
                 T c   
               
               
                   
               
             
             
               
                 Binary 
                 Ag .785 Au 0.215   
                 2.34 
                 233° K 
                 12.7° K 
               
               
                   
                 Pd 0.55 Cu .45   
                 2.34 
                 314° K 
                 20.2° K 
               
               
                   
                 Cu .81 Au .19   
                 2.34 
                 374° K 
                   20° K 
               
               
                 Ternary 
                 Cu .40 Pd .275 Ni 0.325   
                 2.34 
                 402° K 
                   22° K 
               
               
                   
                 Cu 0.75 Pt 0.1575 Ag 0.925   
                 2.34 
                 369° K 
                   20° K 
               
               
                 Quaternary 
                 Cu 3 Ag 0.30 Au .385 Pt .315   
                 2.34 
                 365° K 
                 19.7° K 
               
               
                 Peranary 
                 Cu 3 Ag 0.225 Ir 0.275 Au 0.32 Pd 0.18   
                 2.34 
                 340° K 
                 18.4° K 
               
               
                 Hexanary 
                 Cu 3 Ag 0.2625 Au 0.3525 Pt 0.1575 Ir 0.1375 Pd 0.09   
                 2.34 
                 368° K 
                 19.9° K 
               
               
                   
               
             
          
         
       
     
     Example 40 
     A composition of matter where composition is Ta 0.93 Zr 0.07 , 
     Ne/χ=1.212, θ D ˜175° K, λ˜2.4 and whose T c ˜38° K. 
     Example 41 
     A composition of matter where composition is Ta 0.93 Zr 0.035 Ti 0.035 , 
     Ne/χ=1.213, θ D ˜179° K, λ˜2.4 and whose T c ˜39° K. 
     Example 42 
     A composition of matter where composition is Mg 0.88 Sc 0.06 Na 0.06 B 2 , 
     Ne/χ=0.653, θ D =943° K, λ˜1.0 and whose Tc˜63.8° K.