Self-doping in YBa2Cu3Oy starts to switch from a charge balancing of chain metal reduction and plane oxidation to one of chain ligand oxidation (O-) and plane reduction on quenching from >600K. Amongst the responses are plane expansions and types of unusually strong superconductivity such as elevated temperature superconductivity (ETS), observed through laser pulsing (Tc=552K*) and upon shot quenching (Tc=200K*). We ascribe ETS to limited 3-D superconductivity due to a correlated system of bond ordering within chain-plane sandwiches and propose how to stabilize it. Accordingly, plane expanding n-doping arises from self-doping charge equilibration with local chain Cu of two-fold O coordination (2). The dumbbell type bonds of both apical O- are a result of high-energy environment and comparable in their metric with electron pairs on the plane. Following empirical Tc=%(2)x11 we suggest increasing %(2) to cause the observed retrograde rise in Tc (photo-induced reflectivity edge) to a theoretical limit of Tc=1100K* at 100%(2). We propose compositions and heat treatments based on charge-lattice commensurability. Paired charge concentrations on planes, determined by bond ordering based on magic number counts, suggest several promising candidates such as c=0.22=2/3a0x3b0, c=0.17=2/3x4 or c=0.080=2/5x5. The latter could be achieved with 32%(2) and display Tc=352K* not only in laser pulsed but in shot quenched materials.

The complex phenomenology of shot quenched YBa2Cu3O6.5 with Tc=100K and 200K levels is compared with laser pulsed analogs with an eye on explaining the presumed Tc=552K of the latter. Shot quenching can produce metastable states with pronounced increases in plane metric and cell volume, accompanied by a rough doubling of Tc to a 100K level of an orthorhombic with 3-fold O coordinated chain Cu (O3 type). These states decay over a non-superconducting transition range to the conventional Tc=50K level of O24. We consider the plane expanded laser pulsed materials to contain aspects of O42 plane n-doped counterparts of the O3 n-doped version of shot quench preparations. In addition, we assume that highly charged p-doped chains of 4-fold O coordination form hole pairs at trijugate position, allowing close approach of the apical O to the electron-doped planes. They are now capable of participating in the bonding with the plane pairs at corresponding 3a0/2 location. The overall pair number is therefore multiplied, and the coupling strengthened, by limited 3-D effects within the Plane-Chain-Plane sandwich. The latter can be seen as an extended chemical bonding system that has the potential to equilibrate contractive and expansive pairs and so obviate the need for distinction of doping type as it may exchange it dynamically. It is argued that indications for a Tc=200K level on shot quenching has a related origin and represents one in series of predicted Tc levels based on bond order principles. Predictions are made where similar effects can be expected in other compound classes.

The distance of apical O to planes, d, is introduced as serving as an arbiter in the dispute between different local O coordination (n) in determining charge equilibration in YBa2Cu3Oy. We assign reported cell volume and plane expansion (V+P+) on shot quenching (SQ) from above 600K to O- connected with (3) at a critical cluster size for increased d, maximizing at 673K and y=6.44. This and a Tc=100K level is ascribed to self-doped apical O-, acting as a plane reducer and expander (P+). By contrast, slow cooling to 260K produces conventional cell volume contracted varieties (V-P-), based on plane oxidizing (4) with its small d=2.3A at a Tc=50K level. V+P+ to V-P- transformation is slow due to electronic rearrangement involving O-, compared to the primarily structural one within V-. A SQ minority at Tc=200K* level and related effects observed on laser pulsing (for y=6.5 Tc=552K*), termed as elevated temperature superconductivity (ETS), are also explained as due to plane expanding n-doping. We assume that central (2) connect p-doped pairs in the bonds of both apical O- with plane Cu, in line with retrograde increases in Tc with increasing %(2). 3-D superconductivity is a result of d now being comparable to plane dimensions.

Analysis of kinetic literature suggests several electronic rearrangements above 600K involving O- (subperoxides) in YBa2Cu3Oy. Slow cooling to 260K produces a Tc=50K level with conventional plane and cell volume contracted varieties (P-V-), based on plane oxidizing (4) where (n) denotes local O coordination. When these materials are quenched from <600K, the subsequent changes at 298K of structural parameters or Tc have activation energies E=92kJ and A=1.0x10-12s. The changes saturate at temperatures where they are faster than the time constant t of quenching. This temperature is extended to 473K with SQ, indicating t=0.1s. SQ of y near 6.44 from >600K leads to increased axial ratios, plane and V expansion (P+V+), in a process which is complete near 670 and extending to 950K. P+V+ effects can far exceed P0V0 of the respective semiconductor. The relative stability at elevated temperatures indicates another intrinsically slower transformation mechanism of primarily electronic nature with E=280kJ, involving O-. V+ and its Tc=100K level, is ascribed to (3) with doped charge on apical O-, acting as a plane expander and n-doper. Similar slowing of kinetic through O- also hold for the more complex range of Tq>950K. It can produce a c-axis contracted non-superconductor (P+C-) and indications for elevated temperature superconductivity (ETS) with Tc>150K*. Kinetic data are embedded into general thermodynamic arguments concerning peroxide stability belts.

A phenomenological bond order model predicting doping curves [Tc vs doped charge, c] of cuprates is found to have wider applicability. In this model Tc is dependent on the density of electronic pair crystals [EC] in a covalently bonding layer structure and on a layer Isolation factor, f [ECI model]. Characteristic doping curve events such as optima are correlated with a select number of EC with pair repeats corresponding to multiples of lattice parameters such as c=2/3x4=0.167, where 3x4 represent pair periodicity of 3a0 and 4b0. At these EC all doped charge is converted into pairs according to c=2np. For Tc prediction one writes Tc=2npfTe, where Te=600K and 300K as empirical constants for hole and electron doping. Doping curves for YBa2Cu3Oy with their sharp optima or kinks, separated by near linear ranges, or Tc plateaus on different preparations, can express the stability of special EC. Examples are c=0.22=2/32 for the sharp optimum or the Tc=90K plateau, and c= 0.17 for the 60K plateau, the latter depicting also the optimum for other systems such as La2-wSrwCuO4. For oxypnictides R[O1-xFx]FeAs one writes Tc=300x and expects EC with optimal dopings at x=0.11 and 0.17, as corroborated experimentally. Other examples include HfN derivatives such as Li0.17HfNCl.

The degree of the isolation of the CuO2 planes (e.g. distance or bond valence to the apical coordination) has been shown by quantitative algorithms to be the major factor in determining aspects of the doping curves. They include the magnitude of the optimal number of doped holes (hop) and the corresponding T cop. It is shown that the roots of these phenomenological laws lie in a related structural dependence of super-exchange. The latter is expressed in the pseudo-gap or Neel temperature of the undoped parent compound. A fruitful language can be developed which deals with a buildup of complex quantum chemical features by bringing two holes into vicinity of a super-exchange O, forming a “local” Cu2O7 pair. Structural considerations also dictate that stress is relieved by alternate orthogonal pair orientation. This leads to plaid patterns with primary and secondary channels of charge. The presence of these two types of charge channels is involved in the mechanism of superconducting charge transport. Similar structuring of doped charge into plaid patterns of “local” pairs has been proposed for “all” high T c superconductivity. STM now gives pictorial representation of the remnants of such an electronic crystal structure. The response of these bond-ordering motifs to structural details is further discussed. These ideas supply organization to the manifold experimental situation and provide opportunities for a unifying theory for high T c superconductivity in terms of real space structuring of “local” pairs, largely on crystal-chemical principles.

Phenomenology indicates that doping curves are quantitatively given by the filling of bond orders (BO) of super-exchange pairs. This filling is related to the degree of isolation of the plane. We discuss the existence of different BO families, their mutual transformations and aspects of the mechanism of charge transport as block movements within the BO.

An empirical bond order model indicates that a high degree of plane isolation increases both optimal Tc and optimal hole concentrations. Within this plane isolation model Y Ba2CuCu2Oy is analyzed with respect to structural literature data concerning distance to the apical O, dc. From dc the bond valences in the c-direction, sc, are calculated. They extrapolate to a finite intercept for the undoped parent, scp. Subtracting scp from sc, yields extra holes beyond the equilibrium distribution of the parent. This part is here identified to correspond to the inert part of the total holes, hc that extend into the c-direction. The remaining holes in the planes are effective in fixing the optimal Tc. Accordingly a physically meaningful basis for the empirical rules is found and ‘all planar’ cuprates can be modeled purely on structure. As examples materials with high [Hg analogs] and low dc [Bi analogs] are successfully dealt with in this modified bond order model.

The compound of RuSr2GdCu2O8 shows distinct magnetic transitions, which occur on independent sublattice. Comparison is made between measurements in the cell at no pressure and maximum 10 kbar of quasi-hydrostatic pressure. The chain site ruthenium oxide layer has a weakly ferromagnetic transition of 133 K and increases to 139 K under pressure. The plane site copper oxide layer has an intra-granular superconducting critical temperature of 49 K and increases to 51 K under pressure. The response to pressure is related to anisotropic changes in lattice parameters. The bulk or inter-granular superconducting transition also shows a significant increase with applied pressure. With low frequency (0.2Hz) AC susceptibility, the peak in the imaginary component increases from 21 K to 24 K under pressure.

STM and ARPES display a partly disordered electronic crystal state that is here shown to corroborate a bond order model. This model predicts characteristic plaid structures for bond centered pairs at 3a0/2. We show that indications for some of these predicted patterns are now seen in experiments. The elastic energy as given by the period of the electronic crystal is connected with a quantitative algorithm for Tc vs. holes. Accordingly Tc=2fa600/Pab. In the bond order model parameters such as optimal holes, Tc, or pseudo‐gaps are enhanced by high isolation of the planes (fa). Accordingly high Tc superconductivity and the electronic crystal state are predictable purely on structural data.

Within the rules of a pair plaid model charge-lattice lock-in patterns are identified, which are responsible for the trends to characteristic hole values for a variety of features in the doping curves [onsets, kinks or optima,] of cuprates and related materials. Examples are the prevalence of optimal hole values of 0.16, 0.22 or 0.25. Selection of one of these values depends on the degree of isolation of the plane. Periods of pair plaid represent a central aspect for an algorithm of Tc or doping curve predictions when combined with the plane isolation model. Aspects of the theoretical concept of pair plaids have been made visible in recent STM graphs indicating electronic crystal behavior for the related pseudo-gap region. Pair plaids are in competition with stripes of non-superconducting singles and can be transformed into them. This competition is further elucidated with emphasis on the regions, where both orders can coexist. This further defines over and under-doping.

A distinction is made between extreme types, such as high T c cuprates and soft-metal superconductors concerning the extended, relatively exchange frustration-free covalent ring structures (eight-membered) in the former. Phenomenology indicates for cuprates that bond order (BO) effects within a given number of doped bonds can create real space organization of pairs around O super-exchange centers (trijugate position) within a mobile pair kernel. Indications for this postulated new quantum chemical principle have now been found in related electronic crystal behavior by STM. This situation creates small coherence lengths (∼4 atoms) and unusually high pair numbers. For optimal doping, all holes are converted into pairs and these pairs show trends to geometric checkerboard patterns due to characteristic charge-lattice lock-ins, such as configurations with configurations with hop = 0.25 or hop = 0.16. Period of BO and the degree of isolation of the planes determine T c. Doping curves reflect BO events and are roughly predictable from structural data alone. It is suggested that a variety of related materials with large member rings (e.g. C60) follow the relevant BO phenomenology. By contrast, soft metal superconductors (e.g. Pb) are based on 3D close packed structures with small triangular rings in which exchange interactions are frustrated and small. “Normal” BCS isotope effects suggest the operation of phonons in pair formation over extended coherence lengths (>100 atoms). Very small pair numbers are created through phonons.

Doping curves for as quenched YBa2Cu3Oy are discussed as prototype examples of bond ordering (BO) phenomenology, based on charge-lattice commensurabilities of holes (h) in the CuO2 planes. Literature data for YBa2Cu3Oy show extended linear Tc ranges with y up to a ‘sharp’ Tc optimum (designated Source region). There are relatively pronounced changes in slope at critical hole-concentrations. The sequence in the doping curve involves Tc onset at h∼1/24, a kink at h∼1/12 (in annealed samples a Tc∼60K plateau corresponds to h∼1/6), and the optimum at about h∼1/4.5. The unusually large extent of the Source region and the relatively high values for h (or Tc) for kink and optimum, compared with other materials such as La2−xSrxCuO4, are related to the relatively large lattice parameter. This behavior is discussed in terms of a BO model. Accordingly, Tc scale universally with the number of superconducting pairs, np, and an elasticity-related parameter. Analytical functions are given for np, based on critical hole concentrations, which reflect BO transformations. In the Source region towards the optimum, Tc is based directly on the number of holes, h (e.g. obtained by Knight shift), as in this region h=2np. A factor f accounts for the deleterious influence of the apical O. Pair generation out of a BO of single holes is discussed as a general crystal chemical problem, involving the lamination of stripes of single holes into strands of pairs. In addition, unusual cell volume expansion effects are dealt with as special manifestations of variety in hole placement into various bond systems.

ChemInformVolume 35, Issue 18 Physical Inorganic Chemistry YBa2Cu3Oy as Prototypes for the Empirical Bond Order Rules for High Tc Superconductors. H. Oesterreicher, H. Oesterreicher Dep. Chem., Univ. Calif., San Diego, La Jolla, CA 92093, USASearch for more papers by this author H. Oesterreicher, H. Oesterreicher Dep. Chem., Univ. Calif., San Diego, La Jolla, CA 92093, USASearch for more papers by this author First published: 07 April 2004 https://doi.org/10.1002/chin.200418020AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinked InRedditWechat No abstract is available for this article. Volume35, Issue18May 4, 2004 RelatedInformation

Superconducting Tc is modeled over the doping range for the three prototype cuprate families (with respect to apical coordination). The model is based on a competition of elastic and exchange energies (ExEl model). Data for these energies are taken from direct observation such as Tc and the pseudo-gap Tp. An additional penalty for charge concentration in pairs is introduced for the low pair concentration region. These energies are internally calibrated. The rather different observed curve shapes and quantitative features in the doping curves of different materials can be related to the relative magnitude of Tc and Tp. Both linear and parabolic curve shapes near the Tc optimum can be explained on the ExEl model. The basis of the relevant phenomenology is indicated in bond ordering effects, for which new concepts, e.g. for resonating pair kernels, are developed. Accordingly, stripes of single holes are dimerized into pair strands through super-exchange. Conclusions are drawn about the limits of phenomenology for cuprates and other high Tc materials.