Room temperature ambient pressure superconductors and method of preparing same

Abstract

The invention relates to a computer-implemented method of identifying candidate elements or compounds for use in constructing a superconductive material. The method comprises computationally screening candidate elements or compounds by modelling electronic- structure, chemical-bonding and crystallographic properties and by applying orbital-spacing constraints compatible with dissipationless tunnelling. During the screening, materials that are incapable of undergoing a metal–insulator transition or that exhibit purely metallic conduction without an intervening insulating phase are excluded. The method enables efficient identification of physically viable superconductive candidates. The invention further relates to a superconductive material obtainable by the disclosed method.

Description

[0001] ROOM TEMPERATURE AMBIENT PRESSURE SUPERCONDUCTORS AND METHOD OF PREPARING SAME

[0002] INTRODUCTION TO THE INVENTION

[0003] In the quest for construction of high Tc superconducting materials an engineering design method is necessary. Such a method is hereby provided. The invention further provides a computer-implemented modelling system and evaluation framework enabling execution of the described calculation on a computing system and provide a synthesis workflow enabling the practical manufacture of superconducting materials.

[0004] BACKGROUND TO THE INVENTION

[0005] The BCS theory (Bardeen Cooper Schrieffer) is the first accepted microscopic theory for the explanation of superconduction. It gave reasonably accurate results for superconducting metals, but also implied that the maximum critical temperature (Tc) below which the relevant material would superconduct, should be an order of magnitude less than the Debye temperature (which is the point of crystal’s highest normal mode of vibration) which is about room temperature for most metals. This means that the maximum attainable critical temperature would be about 30°K.[1]

[0006] In 1986 Bednorz and Muller discovered superconductivity in cuprates (superconductors containing copper oxide). Since then, many cuprates with temperatures above the 30°K threshold have been synthesized. Perhaps the most well-known is YBCO (Yttrium Barium Copper Oxide) on which a huge amount of research has been done. With a Tc of about 93°K the BCS theory is unable to explain this and moreover cannot be used by engineers to construct new “high temperature” (i.e. Tc>30°K) superconductors, predicting that superconduction is essentially a low temperature phenomenon. Thus, the discovery of YBCO was in fact made by using the crystal chemistry of perovskites which teaches that, to sustain the basic crystal structure, the ionic radii of the metal ions have to fall within certain constraints. Therefore, amongst other modifications, by choosing Yttrium rather than e.g. Lanthanum, YBCO was discovered. It must also be noted that this discovery was accompanied by massive experimentation, making YBCO a largely empirical discovery [2], Another case in point which cannot be explained by current insights is that the application ofpressure to certain superconductors raises the Tc considerably, in some cases very near to 300°K. The pressures that have to be applied are enormous (up to Gigapascals) (as reference, diamonds are created under pressure of 5 GPa) and therefore render the materials all but useless for industrial application. The bottom line is that one is still left with superconductors which require at least liquid nitrogen refrigeration. Such superconductors are widely used e.g. in medicine for MRI scans to attain the huge magnetic fields necessary for this diagnostic technique.

[0007] These considerations show that engineers are left without a sound method for designing and characterizing superconductors and has to rely heavily on experimentation, crystal chemistry considerations, ionic radii choices and empirical optimisation. Thus, to attain the ultimate goal of constructing an industrially useful room temperature superconductor (under simple achievable pressures) has not been achieved although many alternative theories have been published (see [1], p.11 et seq.).

[0008] OBJECT OF THE INVENTION

[0009] It is therefore the object of the invention to provide a method for designing and characterizing classes of high temperature superconductors with an aim to finding a member of the class with the highest critical temperature to provide a design procedure for the ab initio creation / manufacture of a room temperature ambient pressure superconductor / s. A further object of the invention is to provide a method configured for implementation on a computing system adapted to execute quantum-mechanical modelling routines and to evaluate candidate materials through computational-chemistry analysis.

[0010] BRIEF DESCRIPTION OF THE ACCOMPANYING DRAWINGS

[0011] Figure 1 is an illustration of a Mott metal to insulator transition by the formation of localised Wigner orbital;

[0012] Figure 2 is a graph illustrating the results portrayed in Table 1 depicting Tc (°K) on the horizontal axis and eV on the vertical axis;Figure 3 is a graph showing lower Tc values for higher values of R0;

[0013] Figure 4 is a graph which illustrates the increase in superconductive critical temperature Tc when increasing the oxygen content y within YBCO;

[0014] Figure 5 is a graph of the curve found by plotting Tc as a function of the stoichiometric values 6.4 < y < 7 using Eq. (18);

[0015] Figure 6 is a graph of the varying critical temperature when suitably heavily doped diamond with boron becomes superconducting; and

[0016] Figure 7 shows a graph use Eq. (23) in accordance with the invention.

[0017] SUMMARY AND DESCRIPTION OF THE INVENTION

[0018] The following description first outlines relevant physical principles and phenomena underlying superconductivity, including metal–insulator transitions and electron localisation, which form part of the general scientific background. The description then sets out the specific design method and computational framework according to the invention, by which candidate superconductive materials are identified, evaluated, and optimised.

[0019] The inventors have found that, for superconduction to occur in a suitable solid material, an externally supplied electric field must be cancelled within so that the charge carriers of the superconductor cannot be accelerated, since accelerated charges is normal conduction and generate heat and waste energy via resistance, the property of zero resistance being one of the hallmarks of superconductivity. In fact, this type of conduction is a different phase from normal conduction that involves resistance.

[0020] The design method described herein is implemented and executable on a computing system configured to perform the required calculations, modelling operations and iterative optimisation steps, thereby providing a technical tool that outputs candidate superconducting materials based on the physical parameters disclosed. The stepwise procedure described insteps A–H below is performed by the computing system as part of the modelling and evaluation workflow.

[0021] This, the inventors have found, demands that the material must first undergo a phase transition from conductor to insulator or be an insulating material so that the applied electric field be cancelled, which will occur if the material responds to the applied electric field like an insulator. Thus, within the theoretical framework applied by the present invention, any material that possesses the ability to become a superconductor, will also have the ability (pre requisite) to become an insulator first. This unique phase in superconduction is a Mott transition, well known in Condensed Matter Physics, but has never been applied to superconduction.

[0022] Some materials called Type II “high temperature” superconductors are already insulators or very weak electrical conductors. In metals that can superconduct, a metal-insulator (Mott) transition is necessary which occurs at very low near absolute zero temperatures.

[0023] Eugene Wigner showed the possibility of localised electron states forming at low temperatures. In 1938, Eugene Wigner did a theoretical analysis of how charge correlation might change the e-spectrum of a metal and concluded that at low temperatures, in suitable “non-ideal” metals, some of the delocalized waves form time-independent, localized orbitals. These are called localized, harmonic time-independent waves postulated by Wigner i.e., “Wigner orbitals”.

[0024] Philip Anderson also predicted localised states in the case of adequate crystallographic disorder in a metal, causing a metal-to-insulator transition.

[0025] As shown in figure 1, the shaded oblong spheres represent electron wave packets. The notion of wave packets comes from the formalism of Quantum Wave Mechanics and these packets were constructed to accommodate experimental difficulties of materials, especially on the atomic and sub-atomic scale, that show both particle and wave properties.

[0026] These wave-packets are modelled by adding sourceless, coherent, harmonic running-waves with different frequencies to form a “localised” wave-entity. That such wave-packets can physically manifest within a material is a well-known and experimentally-proven fact inphysics. “W” is the symbol denoting localised orbitals. For clarity in the context of the present invention: the term “Wigner orbital” denotes a localised electron wave-packet bound to a positive charge at low temperature; “jump distance R” denotes the spatial separation between neighbouring Wigner orbitals; “critical jump distance Rc” denotes the maximum allowable separation for dissipationless tunnelling as defined by Eq. (7); and “superconductive phase” denotes the state in which the Wigner-orbital chain satisfies the tunnelling conditions derived in Eqs. (4)-(8). These definitions apply consistently throughout the description and claims.

[0027] As illustrated by figure 1, a Mott metal to insulator transition by the formation of localised Wigner orbitals:

[0028] (a) Any thermodynamically stable solid-state material is electrically neutral, i.e. the atomic positive charges and matching electrons are so arranged that the charges cancel. At high temperature (e.g. room temperature) there are enough wave-packets to screen the positivecharges. In a metal, the wave-packets are assumed to be a gas (so-called free electron model) hence the random distribution of the oblong structures;

[0029] (b) At intermediate temperatures (lower than room temperature, depends on the material) localised Wigner orbitals form to screen localised positive charges (Wigner orbital consists of positive charge with negative localised electron wave in orbit). This is necessary since the density of mobile wave packets now also becomes lower as a result of lowering the temperature and cannot adequately screen the positive charges due to polarization. It is then that it becomes energetically more favourable to form localised time-independent Wigner-orbitals;

[0030] (c) At the metal-insulator transition a gap (as can be seen in Fig 1 (c)) opens up within which the Wigner orbitals form “donor-like” states with a binding-energy AES. Note that the Fermi energy level EFhas now entered the gap (EFis the highest energy level that an electron can occupy at the absolute zero temperature). This situation is similar to semiconductor behaviour in that the Fermi level now resides within the gap and an activation energy is needed to excite electrons into the upper edge of the gap. Since the Fermi level EFis related to the probability of an electron in the upper (mobility) edge of the gap, it plays a role in the calculation of the binding energy of an electron residing on a Wigner orbital.

[0031]

[0032] disturbance under electric field

[0033] When an electric field is now supplied via contacts to the material in condition (c) above, the energetic situation of the orbitals (i.e., the Wigner orbitals) is now disturbed. In normal conduction this disturbance is handled by normal conduction to restore the energetic condition of the material to a time before the applied field.

[0034] The inventors have thus found that, although the localised orbitals are now time-independent in the sense that they remain situated on a positive charge they can still borrow just enough energy AE in a small time At to break free from their donor sites and then move on at speed “v”. This means that they must borrow the required kinetic energy to move in addition to the energy required to scale the energy barrier within the time interval (At) allowed. Each wave packet can thus instantaneously borrow energy to move over a barrier with the required kinetic-energy within a time-interval At without using any of its own energy. This non-dissipative “borrow-and-return” dynamic underpins the superconductive transport mechanism described herein.

[0035]

[0036] orbital i

[0037] This means that current is transported in a superconductor by an external wave packet charge injected from outside to replace an orbital which then borrows energy to replace the next one and so jumps across an orbital array up to the target contact. At each orbital “jump” the energy is returned to from where it came so that there is no gain in energy and no dissipation. The direction of the wave packets is determined by the polarization of the applied electric field and the electron wave packets being injected at one contact impress a direction.

[0038] Not to put too fine a point on this statement: The energy with which electrons arrive at the superconductor after passing through contact above where boundary conditions and electric field was still active, is the same energy with which the electrons arrive at the other side of the superconductor target contact, travelling back into normal conductor. None of this energy is lost during the movement via superconductor Wigner Orbital jumps in the bulk as these jumps are none dissipative in a superconductor.

[0039]

[0040] '-time relation

[0041] The principle whereby this occurs is the Heisenberg relation:

[0042] A

[0043]

[0044] EAt=g / z g > 1 / 2. (1)

[0045] For a minimum uncertainty state g=½ it can thus never be less than ½.

[0046] This quantum-mechanical constraint is explicitly incorporated into the computational framework of the invention when determining feasible orbital-jump conditions.

[0047] Incorporating the complex of ideas above, the loan energy must thus be AE and this must be equal to the sum of the kinetic energy (speed “v” above) required to jump plus the bindingenergy AEs:

[0048] ΔE=ΔEs + ½mv². (2)

[0049]

[0050] 2 The kinetic energy (1 / 2)mv2(m = mass) in Eq. (2) is the kinetic energy needed to move at speed v through distance R. Realising that therefore

[0051] At=R / v,

[0052] one obtains from (2) by substitution for At in (1) and algebraic manipulation the following quadratic equation

[0053] mR?

[0054] - v“ - gfrv + AESR = 0.

[0055] Solving (3) for v 2

[0056] V“

[0057]

[0058] ' niK / J wh, ere a =, 1 - 2mAEsR —2

[0059] (. (4)Eq. (4) sets boundaries for superconduction to occur. To see this, Eq. (4) may be written as follows:

[0060] v = (gℏ / mR)[1 ± √a] where a = 1 - 2mΔEsR² / (gℏ)²

[0061]

[0062] If a is negative, i.e., a < 0, v will be non-physical. For such values superconduction cannot occur. This has profound implications in the sense that the prohibition of negative values under the square root places restrictions on the possible parameters for superconduction as will be seen below. (Note in addition that if one takes in the square brackets 1 + positive square root, the equation (3) will also be satisfied, but the result will also be non-physical).

[0063] According to Eq. (4), therefore, the cut-off point is

[0064] when

[0065] 2mΔEsR² / (gℏ)² = 1

[0066]

[0067] (g^)2

[0068] > (5) Eq. (5) in (4) yields

[0069] mRc.

[0070]

[0071] (6)

[0072] where C subscript means “critical.” As explained below, in this case it means vcis the velocity that may not be exceeded.

[0073] From (5):

[0074] (7)

[0075]

[0076] As in FIG.1, the AE is the binding energy of the Wigner orbitals. The subscript S merely denotes “superconduction”.

[0077] Eq. (4) implies that for R > Rc, superconduction will be impossible, thus i.t.o. Eq. (7),gℏ

[0078]

[0079] will ensure that superconduction be possible.

[0080] Therefore, as discussed with reference to Eq. (1) to (8), the inventors have set the boundary conditions for candidate materials that are suitable choices to achieve superconduction at any selected temperatures.

[0081] The properties of jump speed vcare not so easily discernible from (4) but it is clear that if R (jump distance) increases, v must increase to do the jump in the time At required. Thus vcis the maximum speed achievable for superconduction.

[0082] Electrons are fermions (Fermions include protons, neutrons, electrons, neutrinos, and quarks) and therefore they distribute themselves over many energy-levels according to the Fermi-Dirac distribution function:

[0083]

[0084] 1 + exp[-(E-EF) / kT]

[0085] . (9) where P(E) is the probability that a fermion (e.g. electron) will have an energy E at temperature T. EFis the Fermi-energy (or Fermi level as shown in FIG 1), k=Boltzmann’s constant and T is the temperature in Kelvin. For all E higher than 3 * kT above EFthis may be approximated by:

[0086] P(E) = exp[-(E-EF) / kT]

[0087]

[0088] kT | > (10)

[0089] Considering 3kT « 75meV (milli electron volt) and bandgap energies of superconductors very often are lower than that, the use of Eq. (10) in the engineering application, is suspect.Nevertheless, the validity of the Boltzmann distribution as in Eq. (10) is known to depend on the specific system and the energy levels involved. Thus, even when the gap (in FIG 1) AES< 3kT, the Boltzmann distribution can still provide a reasonable approximation. The accuracy of the approximation can be assessed by comparing the predictions of the Boltzmann distribution with experimental data or more rigorous theoretical models. In the examples section below, the experimental validity of the engineering application is demonstrated.

[0090] For each energy E, we can have g, possible quantum states. Thus f, where

[0091] no. of occupied states

[0092] g.

[0093] is the probability occupying a state at energy E,.

[0094] Taking into account that only one electron per state is allowed according to the Pauli exclusion principle, since e~ is a fermion, the probability P(E) similar to f, may be calculated and is given by Eq. (9) above.

[0095] Thus P(E) is the fraction of the density of fermions that will have energy E. Thus the density n is given by nref*P(E) where nrefis a chosen reference density (usually at 0°K).

[0096] The number of orbitals at absolute zero is determined by the density of the sub-surface donor charges that can eject electrons into the vacuum level. Some donors could be donating electrons to lower acceptor states in the bulk. These, however, do not participate in the formation of the dipole layer. Thus neo=nDo. constitute the band equivalent to the valence band in semiconductor physics and the active donors nDo an empty “conduction band” (since at 0°K the Fermi-Dirac probability P(E)=1 since E=EF).

[0097] In the case of a gap opening up as in FIG. 1c, EF= EV+(1 / 2)(EC- Ev) = (1 / 2)( Ev+ Ec) = (1 / 2) Eg= (1 / 2) AESThus the effective activation barrier is (1 / 2) AESThis is similar to the well-known bandgap formation in semiconductors. When 0°K< T< Tc the external electron density is obviously now different from neo since at T>0 electrons will be excited back and forth. Thus, we have

[0098] nD0= active donor density at T=0°K

[0099] ne0= active external electron density at T=0°K

[0100] ne= external electron at density T > 0°K

[0101] Now applying equation 10:

[0102] AES

[0103] > (11)

[0104]

[0105] 2kT At superconducting temperature (T < Tc) dynamic equilibrium will be established such that external electrons will have an average density of ne provided by donors neD such that ne + neD = neO. (12) whence

[0106] ne= ne0- neD.........(13)

[0107] (11) into (13)

[0108] > >

[0109]

[0110] However, at 0°K ne0= nD0

[0111] so

[0112] >

[0113] ne0

[0114]

[0115] or

[0116] ne= ne0( 1 - exp[...] ) .........(15)

[0117]

[0118] The invention describes design and characterization methods to ultimately design and manufacture a high temperature (which may include room temperature), ambient pressure superconductor. To this end, Eq. (7) is employed to find the maximum dissipationless jump distance Rcbetween orbitals

[0119] (7)

[0120]

[0121] Next, in Eq. (15) the variable Tc must become the dependent Variable:

[0122]

[0123] where n0= (1 / R0)2and nc= (1 / Rc)2where

[0124] R0is the jump distance between orbitals at 0°K;

[0125] Rcis the maximum jump distance that will allow superconduction;

[0126] No is the orbital density at 0°K;

[0127] ncis the minimum orbital density that will allow superconduction.

[0128] The relationship in Eq. (16) may be written in terms of R0and Rcby substituting n0= (1 / R0)2and nc= (1 / Rc)2in Eq. (16):

[0129]

[0130] 2

[0131] However, this gives an equation of Tc in terms of R² (i.e., a two-dimensional quantity), whereas orbital densities are essentially linear rows (i.e., one dimensional quantities). Indeed, when the above equation is matched to experimental data, the results do not fit experiment. When, however, the R² terms are replaced by R, the correct equation emerges. It is2kln( 1

[0132]

[0133] > (17)

[0134] Thus, a method is provided to engineer candidate materials exhibiting superconduction at a specific chosen transition temperature Tc.

[0135] In addition, the invention provides a method to establish the Tc when the distances R in A (Angstrom) between orbitals are known (Eq. 17).

[0136] In this case, a molecule of which the stereochemical formula (as opposed to empirical formula) is available can be used to determine the R values. This would be especially convenient for designs in which doping is used to effect superconduction in non-superconducting materials (e.g. doping diamond with boron) because the R values are, together with the value AES, the determining factor for the Tc (Eq. 17). Doping in this context refers to the addition of impurities after the initial synthesis of the candidate material.

[0137] In accordance with the invention, and based on the principles described above, the following steps (A-H) are provided to identify candidate elements or compounds for use in engineering a high-temperature superconductor. Thus, to identify candidate elements or compounds for use in engineering a high temperature superconductor the following steps (A - H) are provided:

[0138] Step A:

[0139] The user will determine and / or choose the specific temperature for the superconduction to occur at. Thus, as a first step, the user sets, as an input parameter, a target critical temperature between 93°K and 300°K.

[0140] The temperature range provided in step A is between the temperature of 93°K (at which superconduction in YBCO has been shown and which thus provides a workable / possible temperature for superconduction). The upper end of the temperature range will include room temperature (i.e., 300°K) which would be an excellent workable and preferential temperature which provides many applications. The invention may however also be workable at highertemperatures and will be dependent on the requirements of a particular installation i.e., if cooling to 300°K would be feasible.

[0141] The temperature range of 93°K and 300°K is constrained by the interatomic distances that determine the minimum achievable Wigner-orbital spacing Ro. Since Rocannot be less than the lattice-defined spacing of the orbital array, feasible superconducting transition temperatures are bounded accordingly, with 93°K representing an empirically validated lower bound and 300°K representing an upper design objective corresponding to room temperature.

[0142] Step B:

[0143] Once the temperature is set, the user determines, using a computational physics model, a Wigner-orbital binding energy AES for a minimum non-dissipative orbital-jump distance of RC = 3 A which was chosen based on quantum-jump constraints for a minimum Wigner-orbital spacing of approximately 3 A.

[0144] In terms of step B, it will be appreciated that the Wigner orbital jump distance can be anywhere between 0 (i.e, more than 0) and 3 A. As mentioned, the ideal minimum practical distance (not to be confused with Rcwhich is the maximum distance for a specific AES) is 3 A. There is no possibility that the range could possibly include Rc=0, because then AES = «. Although 0< Rc^3A mathematically, practically an Rcof 3 A is the minimum. Thus AES < 0.11 eV. It is conceivable that AES may come very close to 0, thus 0< AES<0.11eV, whereas Rc may be larger than 3 A with no theoretical limit. The Wigner jumping distance R therefore has to be 0< R<3 A. Obviously AES does not change, since AES determines a maximum. If AES were to change or have a range there would be a constantly varying maximum, leading to the untenable conclusion that there is no maximum. It must be remembered that AES is an ionisation energy of an electron in a localised orbital. This is determined by the molecular structure of the superconductor. By regarding AES as variable, electrons can go totally and chaotically haywire because of no fixed bond strength, including the possibility of no bond strength when AES=0. In the latter case the electrons can fly off their anchored positions into space leaving behind a positively charged superconducting material which cannot manifest the Meissner or any other magnetic effect whatsoever since no electrons - an extremely strange and non-functional “superconductor”.Step C:

[0145] Now that the Wigner-orbital binding energy AESis determined, the user calculates, using the determined AES and Rc, a Wigner-orbital spacing Roat 0°K.

[0146] Step D:

[0147] The next step is to identify, through computational modelling that incorporates electronic-structure data, chemical-bonding characteristics and crystallographic properties, one or more candidate elements and / or compounds capable of forming a crystal structure having Wigner-orbital spacing substantially equal to the calculated Ro.

[0148] As provided in step D, the selection of the elements will be done by noting that, employing the periodic table, there are 43 probable cationic elements and 20 probable anionic elements that could form ionic bonds. By surveying the literature, it will be appreciated that high temperature superconductors usually depend on a choice of 3-5 cationic elements and 1-3 anionic elements. Thus, the available choices are: Cationic 1x106elements and anionic 1350 choices. For each choice of 3 cationic combinations there are 1350 choices of 1-3 anionic elements so that there are 1.5x109compounds that must be evaluated for superconduction. This can be done using computational routines implementing DFT (Density Functional Theory) where a subroutine incorporating the Wigner orbital Eqs. 7, 17 for a selection of possible compounds is added as well as a database of electronic and chemical characteristics (i.e. insulating or otherwise, crystal or amorphic). The computer model, using e.g. DFT calculations, may evaluate the possibilities of compound candidates according to the above criteria. It will be understood that although a standard database is extremely difficult to construct due to the endless requirements of the invention’s high Tc superconductor that may be necessary for the designer, the invention’s application does provide some critical exclusions. For example, as shown below, cuprate ceramics will be excluded for any superconductor of Tc>250 K. Ideal metals are also excluded since they maintain standard non-superconductor behaviour right down to almost 0 K. For superconduction to occur, there must first be a metal-to-insulator transition - in ideal metals this does not occur. Accordingly, these exclusions will be taken into account. The term “database” as used herein is therefore considered in the widest possiblesense in terms of available elements and compounds. Also, the materials most likely to superconduct are insulators or near-insulators.

[0149] It will be understood that many Quantum Mechanical methods can be used to predict and understand chemical properties. In this instance, the inventors have identified that Density Functional Theory (DFT) and related electronic-structure methods are particularly suitable for this purpose, as they enable predictive evaluation of orbital arrangements, energetics, and bonding configurations across large combinatorial chemical design spaces. DFT thus provides a practical and reliable means for screening candidate materials prior to synthesis. It will be understood however that any quantum-mechanical or electronic-structure modelling technique suitable for predicting orbital spacing and energetic parameters may be used.

[0150] In one implementation of the design method, the computational screening step itself constitutes a distinct materials-selection process. In this process, candidate compounds are evaluated using electronic-structure, chemical-bonding and crystallographic data, and materials that are incapable of undergoing a metal-insulator transition within the selected temperature range are excluded at an early stage. Likewise, materials exhibiting purely metallic conduction without an intervening insulating phase are computationally excluded, as such materials are physically incapable of supporting the formation of a superconductive Wigner-orbital array. This screening step substantially reduces the candidate search space and provides a technically efficient method for identifying physically viable superconductive materials.

[0151] Step E:

[0152] The next step is to generate, for each candidate element and / or compound, a stoichiometric crystal model comprising an array of Wigner orbitals that complies with the calculated values of Ro and Rc. Similar computational modelling method, as provided in step D, will be applied.

[0153] Step F:

[0154] The next step is to compute, from a stoichiometric density relationship of the form neo=C(y-yo), electron densities associated with Wigner-orbital participation in the superconductive phase.In other words, from a total density of electrons y for each of the stoichiometric crystal model generated in step E, determine / compute the density of electrons y0not participating in the superconductive phase. From this, the density in the Wigner-orbital participation neo=C(y-yo) may be determined.

[0155] Step G:

[0156] Based on the computed electron-density relationship determined above, the user can now construct a linearised Arrhenius-type representation corresponding to a temperaturedependent critical-state transition.

[0157] In this regard, refer to Eq. (15). The linearised Arrhenius-type representation constructed in Step G provides a practical tool for parameter optimisation as the user will be confronted with varying chemical stoichiometries and it is not all orbitals that participate in the Wigner line-up as was clearly demonstrated by the inventor’s analysis of YBCO below. Thus, the Arrhenius equation enables determination of:

[0158] (i) the stoichiometric fraction y0of electrons not participating in the Wigner-orbital chain, (ii) the Wigner-orbital binding energy AES, and

[0159] (iii) the stoichiometry expected to yield the highest critical temperature.

[0160] The Arrhenius straight line is obtained from Eq. (15) where:

[0161] neo = C(y-yo), C a constant (disappears in the calculation of the Arrhenius straight line); ne= C(yc- yo), yc = minimum orbital density that will allow superconduction.

[0162] Inserting these values into Eq. (15) and taking the natural logarithm on both sides, yields

[0163] ln| 1 - (yc- y0) / (y - y0) | = S·Tc-1

[0164]

[0165] (y - y0) 2k·Tc

[0166] This represents a straight-line Y=SX whereY = -ln[ 1 - (yc- y0) / (y - y0) ]

[0167]

[0168] v y - y0>

[0169] And

[0170] X = Tc-1

[0171] Then S can be obtained from this straight line:

[0172] S = AEs / 2k

[0173] This representation allows efficient computational extrapolation when optimising material composition.

[0174] Step H:

[0175] Finally, the user can output, based on the Arrhenius-type representation, material parameters or synthesis conditions for obtaining a superconductive material predicted to exhibit superconductivity at or above the target critical temperature Tc. These synthesis conditions may include stoichiometric ratios, annealing temperatures, doping levels, or predicted crystal structures.

[0176] The foregoing steps collectively define the design method according to the invention, while the preceding discussion provides the physical and theoretical context within which the method operates.

[0177] The design method described in steps A-H above is implemented and executable on a computing system configured to perform the required calculations, modelling operations and iterative optimisation steps, thereby providing a technical tool that outputs candidate superconducting materials based on the physical parameters disclosed.

[0178] Each chosen compound calculated by the method given must in the end be manufactured guided by the results obtained from the computational chemistry data. These must then besubjected to experimental procedures to establish the accepted standard requirements for a material to be superconductive. From these superconductive materials the one that has the best characteristics for engineering applications (e.g. cost of manufacture, current density, diamagnetic flux pinning) must be chosen despite a high number of possibilities. In this respect, it will be understood that although further investigations may have to be employed by a skilled person, the invention nevertheless provides a list of possibilities of manufacturing a superconductive material which have previously not been known. The further investigations etc., to arrive at the superconductive material does not require any inventive steps but merely the application of knowledge known in this particular field of technology to provide the best and most effective method of manufacturing of a new superconductive material, and may include capturing deviations observed during manufacture and measurement and using such deviations as feedback to refine the underlying computational and mathematical analysis within the routine competence of a skilled person.

[0179] EXAMPLE EMBODIMENTS OF THE INVENTION

[0180] In the example embodiments below, it is shown how the invention is utilised to design and characterize classes of high temperature superconductors with an aim to finding a member of the class with the highest critical temperature to provide a design procedure for the ab initio creation of a room temperature ambient pressure superconductor. The invention also enables a skilled person to identify limitations of certain materials (such as cuprate ceramics described below) which makes them unsuitable for superconduction.

[0181] 1. Characterization of the cuprate ceramics

[0182] Cuprate ceramics have attracted a huge amount of research and interest. It is thus important to find out what their limitations are. The methods described in this invention will be applied.

[0183] The lowest value for Ro(the jump distance between orbitals at 0°K) is taken to be 3 A which is very low: for YBCO the lattice constants are in the order of 3.8 A.

[0184] Thus, a curve is generated by plotting:2klnj 1

[0185]

[0186] Here

[0187] • ΔESis in eV (electron Volt) converted to J (Joules) by multiplying with 1.602x10-19• k=Boltzmann’s constant = 1.38x10'23J / K

[0188] • For Rc(the maximum critical distance for dissipationless jump), m=electron mass is needed i.e. 9.11x10-31kg;

[0189] • h=Planck’s reduced constant = 6.63x10'34Js / (2fl) = 1.054571817x10’34Js

[0190] • g=1 / 2

[0191] The results are portrayed in the following table (Table 1) to be read with the graph provided in figure 2:

[0192] eV TcfK)

[0193] 0 0

[0194] 0.0125 172.4307

[0195] 0.025 218.2077

[0196] 0.0375 240.8834

[0197] 0.05 249.9

[0198] 0.0625 248.2983

[0199] 0.075 236.4908

[0200] 0.0875 212.169

[0201]

[0202] 0.1 163.2131

[0203] Table 1

[0204] According to the graph of figure 2, no matter how one engineers the gap AESthe Tc will never go higher than 250°K. This rules out the ceramic superconductors in their pure crystal form as room temperature superconductors. In fact, for all Ro> 3 A one has, not surprisingly, the graph shown in figure 3

[0205] shows much lower Tc values for higher values of Ro. The dot in the graph of figure 3 shows the situation for YBCO.

[0206] 2. Analysis of YBCO utilizing the design modelAs an example of the utilization of the design model according to the invention the characteristics of the ceramic superconductor YBCO (YBa2Cu3O7- δ) is shown. The method used will be a modification of Eq. (15), presented here for convenience:

[0207] ne= ne0^l - exp

[0208]

[0209] The two important parameters to be inserted into the equation above are:

[0210] ne0= active external electron density at T=0°K

[0211] ne= external electron at density T > 0°K

[0212] The density of electrons that participate in superconduction are equated to the stoichiometric density y of oxygen atoms:

[0213] Ne0= C(y-y0)

[0214] C is a constant and y0is the stoichiometric fraction of electrons that do not form part of the superconducting chain since they are not situated along Wigner (linear) chains.

[0215] At temperature T=0 then ne= ncwhich is the minimum orbital density that will allow superconduction at any temperature. Inserting this into the above equation:

[0216] C(yc- y0) = C(y - y0) 1 — exp

[0217]

[0218] 2kT

[0219] The above equation is transformed into an Arrhenius plot (for Arrhenius plot, see e.g.

[0220] Wikipedia)

[0221] > (18)

[0222]

[0223] This allows the relevant parameters to be plotted as a straight line so that extrapolation becomes easier, in this case as the lineY=SX where

[0224] Y = -Infl- v

[0225]

[0226] y-y0>

[0227] and

[0228] X=Tc-1

[0229] The value of yccan be estimated from the curve shown in figure 4 which illustrates the increase in superconductive critical temperature Tc when increasing the oxygen content y within YBCO as adapted from K. Segawa and Y Ando, Phys. Rev. Lett. 86 (2001) 4907)

[0230] Here it can be seen that by manufacturing YBCO to form molecules YBa2Cu3O6.4,

[0231]

[0232] YBa2Cu3O6.5 YBa2Cu3Oy i.e. stoichiometric content y of oxygen of each molecule is varied and the Tc experimentally determined, the Tc varies according to the content y. The y in this graph differs from the y in Eq. (18), because it includes yo, the non-chain oxygen. When y exceeds 7, the Tc starts to drop.

[0233] By plotting the negative logarithm in Eq. (18) for this value of yc and 6.4 < y < 7 as a function of Tc1and varying ycas well as y0on this straight line to find the best line though the origin, the values yc= 6.448 and y0= 5.348 were found. For these values S = 108.54.

[0234] By plotting Tc as a function of the stoichiometric values 6.4 < y < 7 the curve shown in figure 5 is found using Eq. (18):

[0235] It can be seen that some experimental points do not lie on the graph of figure 5. These points are caused by the added oxygen occupying sites from which electrons cannot be donated.

[0236] At y=6.95, Eq. (18) predicts a Tc = 93.5°K. This agrees well with the experimental result of Segawa and Ando of 93.4°K: a difference of 0.1 °K is not going to have any real consequence in this design model, being a 0.1% deviation from experimental data.This example shows excellent results with the experimental data found when different oxygen content in the empirical formula YBa2Cu3O7-5 is measured, i.e., different values of 6 are studied experimentally. Unfortunately, Example 1 shows the cuprate ceramics to be unlikely to have Tc’s higher than 250 °K = -25°C.

[0237] 3. Treatment of doped materials

[0238] It was experimentally found that diamond, when suitably heavily doped with boron becomes superconducting (T. Klein, P. Achatz, J. Kacmarcik, C. Marcenat, F. Gustafson, J. Marcus, E. Bustarret, J. Pernot, F. Omnes, Bo. F. Semelius, C. Persson, A. Ferreira da Silva, C. Cyterman, Metal-insulator transition and superconductivity in boron-doped diamond. Phys. Rev. B. 75 (2007) 165313-1-4.). The critical temperature varies with doping concentration as can be seen in the graph of figure 6.

[0239] Again, this scenario can be modelled by noting that an impurity band forms by doping and a gap (like figure 1) between the valence-band edge and the impurity band edge opens up owing to Wigner-orbital formation. The following symbols will be used:

[0240] NA= boron density

[0241] C = constant

[0242] AEib = impurity band gap

[0243] NH= Total density of acceptor states

[0244] NH’(T) = non-ionised density at temperature T that can barrier-jump

[0245]

[0246] It is now assumed that the ionised acceptors = hole density (a hole represents the absence of an electron). Thus

[0247] NH(T) = NH - P. (19)

[0248] Since the donor levels should still increase with an increase in NA(boron density):

[0249] <-AE p = CNAexp^^-^J. (20)

[0250]

[0251] If the acceptor states are those below a mobility edge, then only a fraction NH of NA would be tunnelling:

[0252] NH= QNA, Q < 1 > (21)

[0253] Eq. (21) and (20) into Eq. (19) yields

[0254] NH' (T) = QNA- CNAexp — > > (22)

[0255]

[0256] k 2k 1

[0257] By Eq. (21), at any critical temperature Tc, a critical density NH’(T)=QNA(O) must be present.

[0258] NA(0) is the required boron density at 0°K for that specific Tc.

[0259] Thus

[0260] QNA(0) = QNA- CNAexpf- >^M

[0261]

[0262] k 2kl J

[0263] Changing the dependent variable in the above equation to Tc,

[0264] T =AElb> (23) 2 Jk: I.n — - i m Gi 1 -NA;-(°)1

[0265]

[0266] To test the above formula against the experimental data, a straight line may be obtained from (23):

[0267] > (24)

[0268]

[0269] c - m xFrom the experimental graph,

[0270] NA(0) ≈ 4.5x1020cm-3

[0271] K

[0272]

[0273] = 1.38x1 O’23J / °K

[0274] If any 2 more values for nB- NAon the graph are inserted in (24), 2 equations will result: y = c - mx

[0275] y2 = c - mx2

[0276] Y1 - Y2 = m(xi - X2)

[0277] m=Zl —

[0278]

[0279] X1 -X2

[0280] From these known values C / Q, AEibcan be determined. These were fixed on:

[0281] C / Q = 1.25

[0282] AEib= 0.14meV.

[0283] It is now possible to use Eq. (23) to draw a graph as shown in figure 7.

[0284] Comparison with the experimental graph of figure 7 shows excellent fit.

[0285] These examples show excellent agreement with experimental results. The mathematical techniques are within the competence of a skilled artisan.

[0286] The design model is, admittedly, dependent on information about the physical and chemical properties of available materials. It can, however, as demonstrated here, help to identify materials (i.e., elements and / or compounds and combinations thereof) for construction of high temperature superconductors, as well as an aid to characterize superconductive materials. Thorough characterization of the design parameters and specifications will be required but which will be within the competence of a skilled artisan.

[0287] 4. Low temperature superconductivity: non-superconduction of ideal metalsIt is well known that certain metals like gold and copper will not superconduct. The theory here espoused shows the reason: there must first be a metal-to-insulator transition, which obviously does not occur in ideal metals that maintain standard non-superconducting conduction throughout the cooling process right down to almost absolute zero. Thus, the model here presented in accordance with the invention is perfectly consistent with these experimental results also.

[0288] The invention offers an improved method for designing superconductors by integrating advanced modelling techniques and analytical frameworks. This approach enhances the accuracy and efficiency of the design process, enabling users to better predict performance outcomes and optimize parameters. By leveraging innovative methodologies, the invention facilitates more informed decision-making and fosters the development of superior products across various applications to leverage the unique properties of superconductors to enhance performance and efficiency across various technologies.

[0289] The invention thus offers various options or approaches that allow the skilled person to create an optimal superconductor tailored for specific applications. The invention presents multiple strategies, materials, or methods for designing superconductors. This variety can cater to different performance characteristics, such as temperature range, critical current capacity, or mechanical properties. It therefore enables a skilled person to create a superconductor that performs best for its intended use, whether that is in power transmission, medical imaging (like MRI), or magnetic levitation. Different applications may have unique requirements, and the provided options allow for customization. The choice of design thus depends on the specific use case. Overall, the invention provides flexibility and adaptability, empowering skilled persons to optimize superconductors based on real-world needs.

[0290] For clarity and to assist in the interpretation of the present specification and the accompanying claims, certain terms used herein are defined below. These definitions are provided to ensure consistent understanding of the physical concepts, modelling terminology, and computational parameters employed in the described design method. Unless the context clearly indicates otherwise, the terms defined in this section shall apply uniformly throughout the specification, figures, examples, and claims.DEFINITIONS:

[0291] Orbital:

[0292] A Wigner orbital is a localised, harmonic, time-independent electron state that forms under low-temperature charge-correlation conditions. It represents a spatially localised electron wave-packet bound to a positive charge such as an ion or dopant centre. Wigner orbitals may form linear or quasi-linear sequences (“orbital arrays”) within suitable crystal structures and participate in dissipationless tunnelling when the separation and binding-energy constraints described herein are satisfied. “Wigner orbital” refers to the localized, harmonic, time-independent electron orbitals predicted by Eugene Wigner (E. Wigner, Trans. Faraday Soc. 34 (1938) 678). In non-ideal metals at sufficiently low temperature, electron correlation causes delocalisation breakdown and formation of these bound localized orbitals around lattice ions. These orbitals define the binding energy AESrelevant to equations (7), (15) and (17).

[0293] Orbital Array of Wigner Orbitals:

[0294] An orbital array of Wigner orbitals refers to a sequence of neighbouring Wigner orbitals arranged along a crystallographic direction, such that each orbital is separated by a distance permitting non-dissipative tunnelling. The geometry and periodicity of the array are determined by the underlying lattice parameters, dopant spacing, or stoichiometric configuration.

[0295] Orbital Jump Distance (R):

[0296] The orbital jump distance R is the spatial separation between neighbouring Wigner orbitals. This distance governs the tunnelling probability of an electron moving between adjacent orbitals and forms a key physical parameter in determining whether superconductive behaviour can be achieved.

[0297] Critical Orbital Jump Distance (Rc):

[0298] The critical orbital jump distance Rcis the maximum permissible separation betweenneighbouring Wigner orbitals for which dissipationless tunnelling can occur. Rcis determined from the quantum-mechanical tunnelling constraints and the Wigner-orbital binding energy AES. When R exceeds Rc, the tunnelling probability drops below the threshold required for superconductivity.

[0299]

[0300] -Orbital:oL

[0301] Ro is the calculated orbital separation at absolute zero, derived from the binding-energy relationships described herein. Rorepresents the idealised spacing of the Wigner-orbital array at 0 K and serves as a design target when screening and modelling candidate materials.

[0302]

[0303] -Orbital

[0304] AESis the binding energy associated with a Wigner orbital. It influences the tunnelling characteristics and determines, together with R and Rc, the temperature range over which dissipationless transport can occur. AESis determined from the quantum-jump conditions and lattice-dependent parameters.

[0305] Stoichiometric Orbital

[0306]

[0307] The stoichiometric orbital density y represents the fraction of atoms or ions in the crystal that contribute electrons participating in the superconductive Wigner-orbital phase. y0denotes the fraction that does not participate. ycdenotes the minimum participating stoichiometric fraction required to sustain the superconductive tunnelling chain at the target critical temperature. These parameters are related through the density equations described in the specification.

[0308]

[0309] Dissipationless tunnelling refers to the quantum-mechanical movement of electrons between Wigner orbitals without energy loss. This behaviour arises only when both the orbital spacing and binding-energy constraints are satisfied, and it forms the physical basis of the superconductive phase described herein.Arrhenius-' Linearisation:

[0310] An Arrhenius-type linearisation refers to the transformation of the temperature-dependent electron-density relations into a linear form of the type Y = S X, where S = AESI (2k). This linear representation provides a practical means for determining AES, yo and yc, extrapolating Tc, and guiding material optimisation and synthesis.

[0311]

[0312] Computational chemistry or computational modelling refers to any computer-implemented method for predicting electronic, structural or energetic properties of materials, including but not limited to density functional theory (DFT). These tools may be used to identify candidate materials, estimate orbital spacing, calculate AEs and evaluate crystal configurations.

[0313] Database of Electronic and Chemical Characteristics:

[0314] A database of electronic and chemical characteristics refers to any organised dataset comprising electronic-structure parameters, chemical-bonding characteristics, crystallographic properties, or related material descriptors, accessible by the computational routines for screening and evaluating potential superconductive compounds.

[0315]

[0316] Phase:

[0317] The superconductive phase refers to the state in which a Wigner-orbital array satisfies both the binding-energy and spacing constraints required for dissipationless tunnelling, enabling zero-resistance current transport at or above the calculated critical temperature.References

[0318] [1] Andrei Mourachkine Room-Temperature Superconductivity Cambridge international Science Publishing 7 Meadow Walk, Great Abington, Cambridge CB1 6AZ, UK (2004) ©Andrei Mourachkine

[0319] [2] Jim Ashburn: First-Hand: Discovery of Superconductivity at 93 K in YBCO Engineering and Technology History Wiki (Url: https: / / ethw.org / First- Hand: Discovery __of__Superconductivity__at__93__KJn__YBCO)

Claims

CLAIMS1. A computer-implemented method of designing and identifying a superconductive material, the method comprising:A. setting, as an input parameter, a target critical temperature between 93°K and 300° K;B. determining, using a computational physics model, a Wigner-orbital binding energy AESfor a minimum non-dissipative orbital-jump distance of Rc= 3 A which was chosen based on quantum-jump constraints for a minimum Wigner- orbital spacing of approximately 3 A;C. calculating, using the determined AESand Rc, a Wigner-orbital spacing Roat 0°K;D. identifying, through computational modelling that incorporates electronic- structure data, chemical-bonding characteristics and crystallographic properties, one or more candidate compounds capable of forming a crystal structure having Wigner-orbital spacing substantially equal to the calculated Ro; E. generating, for each candidate compound, a stoichiometric crystal model comprising an array of Wigner orbitals that complies with the calculated values of Ro and Rc;F. computing, from a stoichiometric density relationship of the form neo=C(y-yo), electron densities associated with Wigner-orbital participation in the superconductive phase;G. constructing, from the computed electron-density relationship, a linearised Arrhenius-type representation corresponding to a temperature-dependent critical-state transition; andH. outputting, based on the Arrhenius-type representation, material parameters or synthesis conditions for obtaining a superconductive material predicted to exhibit superconductivity at or above the target critical temperature.

2. A computer-implemented method of identifying candidate compounds for use in constructing a superconductive material, the method comprising:identifying, by computational modelling incorporating electronic- structure data, chemical-bonding characteristics and crystallographic properties, one or morecandidate compounds capable of forming a crystal structure comprising an array of Wigner orbitals having an orbital spacing compatible with dissipationless tunnelling; andexcluding, during the computational modelling, candidate compounds that are incapable of undergoing a metal-insulator transition within a selected temperature range or that exhibit purely metallic conduction without an intervening insulating phase.

3. The method of claim 1, wherein, in step B, the critical Wigner-orbital jump distance is selected as a distance corresponding to non-dissipative tunnelling.

4. The method of claim 1, wherein, in step C, candidate elements or compounds are rejected if the calculated Wigner-orbital spacing at 0 K exceeds the critical Wigner- orbital jump distance.

5. The method of claim 1, wherein, in step D, candidate elements or compounds that are incapable of undergoing a metal-insulator transition within the selected temperature range are excluded.

6. The method of claim 1, wherein, in step D, materials exhibiting purely metallic conduction without an intervening insulating phase are excluded.

7. The method of claim 1, wherein, in step D, the computational screening employs electronic-structure modelling selected from density-functional theory, tight-binding methods, molecular-dynamics simulations, or combinations thereof.

8. The method of claim 1, wherein, in step G, the Arrhenius-type linear representation is used to extract at least one of:a) Wigner-orbital binding energy;b) a non-participating stoichiometric fraction; orc) a minimum stoichiometric fraction required to sustain a superconductive phase.

9. The method of claim 1, wherein, in step H, the predicted synthesis conditions comprise at least one of stoichiometric ratios, dopant concentrations, annealing temperatures, or crystal-structure parameters.

10. A superconductive material obtainable by the method of claim 1.

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