Layered Cuprates Containing Flat Fragments: High-Pressure Synthesis, Crystal Structures and Superconducting Properties

High-pressure synthesis and crystal structures of the homologous series AuBa2(Ca,Ln)n−1CunO2n+3 (n = 1–4; Ln = rare-earth cations) are described. Their crystal structures and superconducting properties are compared with the corresponding members of the Hg-homologous series. Numerous cuprates containing flat structural fragments (CuO4, CO3 and BO3) synthesized mainly at high pressure are compared in terms of structural peculiarities and superconducting properties. Importance and future prospects of high-pressure application for the preparation of new superconducting oxides are discussed.


Introduction
Numerous high-temperature superconducting cuprates have complex perovskitebased intergrowth crystal structures. In these structures, it is possible to select different blocks, for example, perovskite-like (CaTiO 3 ), halite-like (NaCl), fluorite-like (CaF 2 ) and/or other ones stacking along the four-fold axis of the perovskite sublattice [1]. The first member of series of Ruddlesden-Popper (RP) phases La 2 CuO 4 has a simple intergrowth structure consisting of perovskite-like and halite-like fragments (K 2 NiF 4 structural type). High-temperature superconductivity at T c = 36 K was discovered in this material after hole doping by Ba 2+ [2]. T c was shown to increase up to 52.5 K when measured in situ under a hydrostatic pressure of 1.68 GPa [3].
The crystal structures of Hg-containing series of superconducting cuprates, HgBa 2 Ca n−1 Cu n O 2n+2+δ (n = 1-6), can be described as intergrowth ones [4][5][6][7][8][9]. Defect halite-like fragments and perovskite-like fragments are stacking along the four-fold axis, which coincides with the crystallographic c-axis ( Figure 1). Hg 2+ cations have typical dumbbelllike coordination with a significant range of oxygen stoichiometries in the HgO δ layers. In the crystal structures of compounds with n = 2-6, the corresponding amounts of CuO 2 layers are separated by Ca 2+ cations forming repeated perovskite-like blocks. It is important to note that the highest T c (up to 138 K) was reported for the compound with n = 3. Moreover, at ultrahigh pressures above 20 GPa T c increased remarkably and reached 166 K in fluorinated Hg-1223 [10][11][12].
Since the first high-pressure device was invented by Bridgeman in the 1940s, highpressure has been extensively used in solid state sciences. It is established that ultrahigh pressure deals with the pressures greater than 1.01 GPa, and now the pressure scale is extended up to 500 GPa at temperatures exceeding 3000 • C. The most frequently used apparatus in high pressure research is the diamond-anvil cell (DAC) in a piston-cylinder design. It allows one to achieve pressures as high as 4 GPa or even more. The disadvantage of the Bridgeman device in a piston-cylinder design is the small sample size. That problem was solved by the belt-like apparatus invented in the 1960s, that can generate 10 GPa at temperatures up to 2000 • C. The modern devices are multianvil cells, where the anvils are usually made from materials with high hardness, preferably from diamond. This review is dedicated mainly to the application of high pressure for the synthesis and superconducting properties optimization of layered cuprates. However, superconductivity at T c > 200 K in H 3 S (T c = 203 K at 150 GPa) [14] and in LaH 10 (T c~2 50 K at 170 GPa) [15] was recently discovered. These new exciting materials belong to conventional superconductors with properties that can be described by the Bardeen-Cooper-Schrieffer and the Migdal-Eliashberg theories. In addition, first-principles calculations based on density functional theory and recently developed non-adiabatic theory are used for explanation and prediction of properties of new superconducting materials [16][17][18][19][20][21][22][23]. The latest results increase significantly interest in high pressure research and one can hope for further rapid progress in this direction.

Au-Containing Cuprates: High-Pressure Synthesis and Characterization
High pressure applications is strongly required for the synthesis of these materials because it is only way to stabilize gold oxides which are thermally very unstable at ambient pressures. The general formula of the homologous series is as follows: AuBa 2 (Ca,Ln) n−1 Cu n O 2n+3 (n = 1-4; Ln = rare-earth trivalent cations). The second member AuBa 2 Y 1−x Ca x Cu 2 O 7 was synthesized in polycrystalline and single crystal form at 1.8 GPa/950 • C and at 6 GPa/1380 • C, respectively [24,25]. Its crystal structure was determined from single crystal X-ray diffraction data in space group Pmmm (Jana 2000 software; R, R w (I >3 σ (I)) = 0.0260, 0.0219; R, R w (all data) = 0.0443, 0.0225; the details are given in [25]); a = 3.8260(2) Å, b = 3.8501(2) Å, c = 12.075 (1) Å. The samples exhibited bulk superconductivity with T c = 82-84 K. The crystal structure of Au-1212 compound is shown in Figure 2.  2(1) obtained from electron probe microanalysis (EPMA) data is in agreement with that obtained from X-ray single crystal diffraction, indicating ca. 20% substitution of Cu 1+ cations on the Au 3+ site, it was associated with approximately the same amount of oxygen vacancies in the corresponding plane. It should be noted that no superstructure related to possible Cu/Au ordering was revealed from the X-ray single crystal diffraction data. Au 3+ is located in square-planar coordination with Au-O distances 1.980 Å and 2.027 Å. AuO4 squares share corners and they are forming zigzag chains along the short a-axis, and that is different from YBa2Cu3O7 where CuO4 squares ran along the longer b-axis. The coordination of the in-plane Cu is square pyramidal with an apical distance of 2.41 Å, it is typical for layered cuprate superconductors.
A HRTEM image of Au-1223 phase along the b-axis is shown in Figure 3. It is confirmed the 1223 stacking along the c-axis: BaO-AuO-BaO-CuO2-Ca-CuO2-Ca-CuO2. Attempts to synthesize next members (n = 5, 6) were not successful both at 1.8 GPa and at 6 The cation stoichiometry Au: Ba: Y: Ca: Cu = 0.8(1): 1.9(1): 0.7(1): 0.4(1): 2.2(1) obtained from electron probe microanalysis (EPMA) data is in agreement with that obtained from X-ray single crystal diffraction, indicating ca. 20% substitution of Cu 1+ cations on the Au 3+ site, it was associated with approximately the same amount of oxygen vacancies in the corresponding plane. It should be noted that no superstructure related to possible Cu/Au ordering was revealed from the X-ray single crystal diffraction data. Au 3+ is located in square-planar coordination with Au-O distances 1.980 Å and 2.027 Å. AuO 4 squares share corners and they are forming zigzag chains along the short a-axis, and that is different from YBa 2 Cu 3 O 7 where CuO 4 squares ran along the longer b-axis. The coordination of the in-plane Cu is square pyramidal with an apical distance of 2.41 Å, it is typical for layered cuprate superconductors.
A HRTEM image of Au-1223 phase along the b-axis is shown in Figure 3. It is confirmed the 1223 stacking along the c-axis: BaO-AuO-BaO-CuO 2 -Ca-CuO 2 -Ca-CuO 2 . Attempts to synthesize next members (n = 5, 6) were not successful both at 1.8 GPa and at 6 GPa. AuBa 2 Ca 3 Cu 4 O 11 showed bulk superconductivity with T c~9 9 K, but Au-1223 showed only a weak diamagnetic signal at T c~3 0 K. In order to understand the possible reason, crystal structure of Au-1223 was determined from single crystal X-ray diffraction data (SHELXL-97 software; S.G. Pmmm; R1, wR2 (I > 2 σ (I)) = 0.0188, 0.0437; R, R w (all data) = 0.0301, 0.0484; the details are available in [27].
GPa. AuBa2Ca3Cu4O11 showed bulk superconductivity with Tc ~ 99 K, but showed only a weak diamagnetic signal at Tc ~30 K. In order to understand the reason, crystal structure of Au-1223 was determined from single crystal X-ray di data (SHELXL-97 software; S.G. Pmmm; R1, wR2 (I > 2 σ (I)) = 0.0188, 0.0437; R data) = 0.0301, 0.0484; the details are available in [27]. The cation stoichiometry Au: Ba: Ca: Cu = 0.9(1): 1.91(6): 2.10(6): 3.1(1) was o from EPMA. The crystal structure is similar to Hg-1223, but the cation stoichio indicative of some possibility of Cu/Au disorder. The refinement of the oc yielded 4.1% of Cu in Au site. Au-O in-plane distance is 2.055 Å and it is noticeabl than typical Cu-O in-plane distances that correlate with their ionic radii differenc Contrary to Hg-1223, oxygen in the AuO layer is located at (x,1/2,0), it lead mation of AuO4 zigzag chains as in Au-1212. Electron diffraction revealed the w perstructure with bs = 2b in Au-1223, however, the corresponding intensities in X gle crystal diffraction data were extremely weak. This suggests no ordering of zig chains and/or their irregularity.
Related to the suppression of superconductivity, some incorporation of Au f the CuO2 planes (6-8%) should be taken into consideration. Although the degr substitution is very moderate, even this level can lead to superconductivity supp Au-1201 is the less known member of the Au-series. Au(Ba,La)2CuO5±δ was as a principal phase in the polyphasic sample prepared at 6 GPa and 1250 °C [28] tallizes in an orthorhombic primitive cell with the parameters a = 3.7976(3) Å, b = 3 Å, c = 8.5749(9) Å. EPMA shown the cation stoichiometry Au: Ba: La: Cu = 0.75(8 1.2(1): 1.25 (8), therefore, the approximate formula of Au-1201 can be expre Au0.75Ba0.8La1.2Cu1.25O5±δ. Therefore, it suggests that ca. 25% of Au positions are o by Cu. HRTEM indicated that this is a first member of AuBa2(Ca,Ln)n−1CunO2n+3 se ure 4). However, an ED study revealed a weak superstructure with as = 5a, bs = b, could be due to possible Au/Cu ordering. Samples of Au-1201 showed a weak netic signal with Tc = 19 K and low level of diamagnetic Meissner fraction. Contrary to Hg-1223, oxygen in the AuO layer is located at (x,1/2,0), it leads to formation of AuO 4 zigzag chains as in Au-1212. Electron diffraction revealed the weak superstructure with b s = 2b in Au-1223, however, the corresponding intensities in X-ray single crystal diffraction data were extremely weak. This suggests no ordering of zigzaglike chains and/or their irregularity.
Related to the suppression of superconductivity, some incorporation of Au for Cu in the CuO 2 planes (6-8%) should be taken into consideration. Although the degree of the substitution is very moderate, even this level can lead to superconductivity suppression.
Au-1201 is the less known member of the Au-series. Au(Ba,La) 2 CuO 5±δ was obtained as a principal phase in the polyphasic sample prepared at 6 GPa and 1250 • C [28]. It crystallizes in an orthorhombic primitive cell with the parameters a Therefore, it suggests that ca. 25% of Au positions are occupied by Cu. HRTEM indicated that this is a first member of AuBa 2 (Ca,Ln) n−1 Cu n O 2n+3 series ( Figure 4). However, an ED study revealed a weak superstructure with a s = 5a, b s = b, c s = 2c. It could be due to possible Au/Cu ordering. Samples of Au-1201 showed a weak diamagnetic signal with T c = 19 K and low level of diamagnetic Meissner fraction.

Au and Hg-containing Series: Structural Details and Superconductivity
Crystal structures of corresponding members of Au and Hg-series are rather similar (except for the first member), however, there are some important differences. First, maximum Tc was achieved in the Hg-series but not in the Au-series [26,29]. Moreover, only first four members of Au-series were identified in comparison with six members of Hgseries (the n = 7 member was obtained only if doped in the Hg site). The possible reason could be a noticeable mismatch between Au-O and Cu-O in-plane distances that lead to formation of zigzag chains consisting of corner-shared AuO4 square-planar units along a and/or b crystallographic axis. That mismatch can impede the formation of higher members of this series and their synthesis may require higher pressures application.
The extra oxygen in HgOδ layer of Hg-series members is located in the central position (1/2,1/2,0) and is very weakly bonded with Hg. This results in a rather extended oxygen stoichiometry range and a possibility to optimize Tc using various thermal treatments of these materials [4][5][6][7]. Oxygen in Au-containing layers is located in more general positions and the oxygen stoichiometry in Au-series members is practically fixed and can vary in the very limited range only due to some doping caused by Cu incorporation resulting in Au/Cu disorder in Au-O plane. It may create serious difficulties to achieve the appropriate hole concentration, and, therefore, for Tc optimization.
It should be particularly taken into account some extent of Au incorporation in CuO2 layers that was not revealed for Hg in Hg-series. It is a possible reason of suppression of bulk superconductivity in Au-1201 and Au-1223. In Au-1201 it might be also due to an insufficient hole concentration. Additional studies preferably based on X-ray single crystal diffraction data are required to verify these hypotheses.
The ultimate member (n = ∞) of both series, CaCuO2, has so-called "infinite-layer" structure, which is very simple. It contains only corner-shared square planar CuO2 units

Au and Hg-Containing Series: Structural Details and Superconductivity
Crystal structures of corresponding members of Au and Hg-series are rather similar (except for the first member), however, there are some important differences. First, maximum T c was achieved in the Hg-series but not in the Au-series [26,29]. Moreover, only first four members of Au-series were identified in comparison with six members of Hg-series (the n = 7 member was obtained only if doped in the Hg site). The possible reason could be a noticeable mismatch between Au-O and Cu-O in-plane distances that lead to formation of zigzag chains consisting of corner-shared AuO 4 square-planar units along a and/or b crystallographic axis. That mismatch can impede the formation of higher members of this series and their synthesis may require higher pressures application.
The extra oxygen in HgO δ layer of Hg-series members is located in the central position (1/2,1/2,0) and is very weakly bonded with Hg. This results in a rather extended oxygen stoichiometry range and a possibility to optimize T c using various thermal treatments of these materials [4][5][6][7]. Oxygen in Au-containing layers is located in more general positions and the oxygen stoichiometry in Au-series members is practically fixed and can vary in the very limited range only due to some doping caused by Cu incorporation resulting in Au/Cu disorder in Au-O plane. It may create serious difficulties to achieve the appropriate hole concentration, and, therefore, for T c optimization.
It should be particularly taken into account some extent of Au incorporation in CuO 2 layers that was not revealed for Hg in Hg-series. It is a possible reason of suppression of bulk superconductivity in Au-1201 and Au-1223. In Au-1201 it might be also due to an insufficient hole concentration. Additional studies preferably based on X-ray single crystal diffraction data are required to verify these hypotheses.
The ultimate member (n = ∞) of both series, CaCuO 2 , has so-called "infinite-layer" structure, which is very simple. It contains only corner-shared square planar CuO 2 units and its unit cell consists of only two stacking layers (Ca 2+ ) (CuO 2 ) along the c-axis. At ambient pressures, this structure is stable in the very narrow x range of Ca 1-x Sr x CuO 2 solid solution (0.10 ≤ x ≤ 0.16) [30]. High-pressure application results in extension its stability range up to 0 ≤ x ≤ 1. Syntheses of CaCuO 2 with "infinite-layer" structure were reported by using a belt-type apparatus at 6 GPa and high Ar pressure of 1,4-1,6 GPa [31,32]. Using the last technique, single crystals were grown. It showed a weak diamagnetic signal at T c = 78 K, however, superconducting transition was not supported by the resistivity measurements and was attributed to some A-deficient domains. Bulk superconductivity was observed only after the electron doping by large rare-earth cations.
It should be noted that the "infinite-layer" structure was also reported for reduced nickelates as LaNiO 2 [33] and Nd 1−x Sr x NiO 2 [34] containing Jahn-Teller cation Ni 1+ . These compounds were prepared using soft chemistry methods and they did not show superconducting properties.

La 2 CuO 4 -Related Superconductors in Sr-Cu-O and Ba-Cu-O Systems
Sr 2 CuO 3 crystal structure is stable at normal pressure and is heavily oxygen deficient. Cu is in square-planar coordination and CuO 2 units are corner-shared along the a-axis [35]. At pressures as high as 6 GPa, 800-900 • C and in a strongly oxidizing atmosphere (created by adding KClO 4 ) it was reported to transform into a layered structure of K 2 NiF 4 structural type related to La 2 CuO 4 and, moreover, a new series of copper oxide superconductors Sr n+1 Cu n O 2n+1+δ was discovered [36]. The initial stoichiometry of the n = 1 member corresponds to Sr 2 CuO 3.1 , and the main peaks were indexed in tetragonal unit cell with a = 3.764 Å, c = 12.548 Å. A superlattice with a s = 4 × √ 2a, c s = c was revealed from electron diffraction data. The member with n = 2 was characterized but it was not obtained as single or dominant phase sample. According to X-ray diffraction data, it has a tetragonal unit cell with a = 3.902 Å, c = 21.085 Å. The samples exhibited bulk superconductivity at 70 K and a weak diamagnetic signal at~100 K was attributed to a minor phase, a series member with n = 2. Higher members (n = 4, 5) were identified by electron diffraction but were not reported in bulk form.
Another research group published the synthesis of Sr 2 CuO 3+δ at 5.7 GPa and 900 • C using KClO 4 as an internal oxidizer [37]. The as-prepared material was nearly single phase with unit cell parameters a = 3.7556(3) Å, c = 12.521(2) Å (I4/mmm) and it exhibited bulk superconductivity at T c = 70 K. No X-ray evidence of other series Sr n+1 Cu n O 2n+1+δ members was found. Heat treatment under flowing N 2 and 310 • C for 1 h resulted in enhancement of T c up to 94 K, unit cell parameters of Sr 2 CuO 3+δ changed to a = 3.7591(1) Å, c = 12.518(9) Å. Based on these data, the as-prepared sample is considered to be in an overdoped state, so δ > δ opt [38].
The average crystal structures of superconducting and non-superconducting samples of Sr 2 CuO 3+δ with the tetragonal unit cell were refined using neutron powder diffraction data [39]. Superconducting sample (T c = 65 K, Meissner fraction volume~6%, δ~0.1) was prepared by treatment of orthorhombic Sr 2 CuO 3 at 6 GPa and 850 • C using an internal oxidizer KClO 3 . Tetragonal normal pressure phase Sr 2 CuO 3+δ was synthesized in flowing oxygen at 350 • C from hydroxometallate precursor Sr 2 Cu(OH) 6 , the obtained material did not show any diamagnetic signal above 4 K. In both crystal structures oxygen vacancies in CuO 2 layers were revealed. It can be a reason why both samples did not exhibit bulk superconductivity. A weak diamagnetic signal in the "high-pressure" sample can be attributed to some superconducting clusters without these vacancies. However, more experimental data are required for verification of this assumption.
Another explanation of superconductivity in Sr 2 CuO 3+δ (δ~0.1-0.6) was proposed in later publications [40,41]. Sr 2 CuO 3+δ single phase samples were prepared at 6 GPa and 1100 • C. Only La 2 CuO 4 -like phase was detected. As a source of oxygen SrO 2 was used instead of KClO 4 or KClO 3 , as it permits one to avoid the formation of another superconducting phase (Sr,K)CuO 2 Cl 2 as an impurity [42]. Then the samples were annealed The TEM and electron energy loss spectroscopy (EELS) techniques have been utilized to characterize superconducting Sr 2 CuO 3+δ (with nominal δ = 0.4) samples, both in the as-prepared state and post-annealed at different temperatures in order to reveal the superconducting phases. It was demonstrated that with raising the annealing temperature, T c increased from 75 K (as-prepared) to 89 K (post-annealed at 150 • C) and 95 K (postannealed at 250 • C). In the last stage the superconductivity disappeared when the annealing temperature exceeded 250 • C. TEM investigations revealed two types of modulated phase, Fmmm and C2/m, in the sample. The structure phase transitions are as follows. It starting from C2/m modulated phase → Cmmm modulated phase (annealed at 150 •C) → Pmmm modulated phase (annealed at 250 •C) → unmodulated orthorhombic structure (annealed at 350 •C), while no obvious changes are found for the Fmmm modulated phase up to 250 •C. The experimental results show that the C2/m modulated phase is responsible for T c at 75 K, the Cmmm modulated phase exhibited T c at 89 K, and for the Pmmm modulated phase T c was observed at 95 K. Fmmm modulated phase is non-superconducting. That was attributed to the oxygen vacancies located at the Cu-O planes. It was concluded that, besides the hole doping level, the reordering of apical oxygen in those superconducting modulated phases is the important factor that governs the T c in Sr 2 CuO 3+δ . Moreover, Ba-substitution led to increase T c up to 98 K in Sr 1.4 Ba 0.6 CuO 3+δ [43].
The detailed analysis of structure and superconducting properties in Sr 1−x Ba x CuO 3+δ system was performed in [44]. The authors pointed out that there is no direct experimental evidence of the absence of oxygen vacancies in Cu-O planes. On the contrary, there is a clear evidence of oxygen vacancies (estimated in~30%) from neutron powder diffraction data [39]. The simulation of the electron diffraction data also revealed an average commensurate superstructure (Fmmm) with orthorhombic supercell 5 √ 2a p × 5 √ 2a p × c p (p belongs to tetragonal I4/mmm K 2 NiF 4 -type structure) and two different Cu-Cu distances in Cu-O plane [45,46]. This is in agreement with the oxygen vacancies in this plane deduced from with the neutron diffraction data. It is remarkable that T c is almost triple in comparison with La 2 CuO 4 -based superconductors [2,47], therefore, the author concluded the existence of an enhancement of superconductivity.
Two new possible mechanisms of enhanced superconductivity were assumed: negative U-centers and optimum inhomogeneity. The concepts of negative U-centers deal with a band of paired electrons formed by the overlap of negative −U oxygen vacancies [48][49][50]. Optimum inhomogeneity considers pairing in the CuO 2 layer that may be enhanced by an optimal inhomogeneity distribution of oxygen sites and/or by a clustering of vacancies rich and vacancies poor regions [51,52].
Recently, bulk superconductivity with T c > 70 K was discovered in a new layered cuprate Ba 2 CuO 4−y (nominal content y~0.8) [53][54][55]. It is synthesized at 18 GPa and 1000 • C in a highly oxidizing atmosphere. It should be noted that this material is very hygroscopic and cannot be prepared at lower pressures. Surprisingly, the exhibited T c is more than 30 K higher than for doped La 2 CuO 4 and superconducting volume fraction reaches as high as 30%. This evidence for bulk superconductivity was also confirmed by the muon spin rotation (µSR) showing approximately 40% superfluid density and the specific heat measurements. X-ray diffraction showed La 2−x Sr x CuO 4 -like structure (I4/mmm) and the Rietveld refinement yields the lattice parameters of the compound with a = 4.003 Å and c = 12.94 Å at room temperature, respectively.
Moreover, it was demonstrated that this new cuprate has some peculiar features making it different from "conventional" cuprate superconductors: (a) the apical oxygen distance is significantly shorter than that known for all other cuprates so far; (b) superconductivity occurs at very high hole doping. It should be considered as strongly overdoped state in comparison to the optimal value of p~0.14-0.15 for the previously known "conventional" high T c cuprates; (c) its structure contains numerous oxygen vacancies, presumably located in Cu-O plane. Moreover, Cu-O in-plane distances are 2.00 Å and longer than apical ones (1.86 Å), i.e., the defect octahedron is very compressed [56][57][58]. It is shown by X-ray absorption measurement that in the compressed octahedron, the 3dz 2 -r 2 orbital should be lifted above the 3dx 2 -y 2 orbital resulting in significant 3D nature in addition to the conventional 3dx 2 -y 2 orbital [59]. Based on these data, it was suggested that Ba 2 CuO 4-y is a member of a different branch of high-T c cuprate materials [60,61]. Another example of cuprate synthesized at high-pressure is Cu 0.75 Mo 0.25 Sr 2 YCu 2 O 7.54 , it has crystal structure similar to YBCO123 phase and exhibited T c at~87 K being strongly overdoped (nominal content p~0.46) [62,63].
It can be concluded that further increase of high pressure may result in the discovery not only of higher members of known superconducting series, but also some new superconducting materials with high T c and possibly new original superconductivity mechanisms.

Cuprates with Edge-Shared CuO 4 Units in Sr-Cu-O and Ca-Cu-O Systems: Spin-Ladder and Infinite-Chain Composite Structures
Numerous cuprates contain edge-shared (CuO 2 ) square-planar units. An interesting example is the series of so-called spin-ladder cuprates. They belong to the homologous series Sr n−1 Cu n+1 O 2n (n = 1, 2) [64]. These compounds can only be synthesized under high pressures. It should be underlined that at normal pressure the stable compounds in SrO-CuO system are SrCuO 2 [35], Sr 2 CuO 3 [65] and Sr 14 Cu 24 O 41 [66,67]. SrCuO 2 crystal structure is quasi-one-dimensional (1D). It contains Cu 2+ in square-planar coordination, CuO 2 fragments are only edge-shared forming ribbon-like chains. The Sr 2 CuO 3 crystal structure is heavily oxygen deficient and, therefore, Cu is in square-planar coordination and CuO 2 units are corner-shared. Sr 14 Cu 24 O 41 has a composite crystal structure which consists of two incommensurate sublattices, first contains (Cu 2 O 3 ) ladders and second contains Cu-O 1D edge-shared chains similar to SrCuO 2 ( Figure 5). Therefore, it contains spin-ladder fragment as in 80 K superconductor YBa 2 Cu 4 O 8 [68,69].
Molecules 2021, 26, x FOR PEER REVIEW 8 of 2 longer than apical ones (1.86 Å), i.e., the defect octahedron is very compressed [56][57][58]. I is shown by X-ray absorption measurement that in the compressed octahedron, the 3dz 2 r 2 orbital should be lifted above the 3dx 2 -y 2 orbital resulting in significant 3D nature in addition to the conventional 3dx 2 -y 2 orbital [59]. Based on these data, it was suggested tha Ba2CuO4-y is a member of a different branch of high-Tc cuprate materials [60,61]. Anothe example of cuprate synthesized at high-pressure is Cu0.75Mo0.25Sr2YCu2O7.54, it has crysta structure similar to YBCO123 phase and exhibited Tc at ~ 87 K being strongly overdoped (nominal content p ~ 0.46) [62,63]. It can be concluded that further increase of high pressure may result in the discovery not only of higher members of known superconducting series, but also some new super conducting materials with high Tc and possibly new original superconductivity mecha nisms.

Cuprates with Edge-Shared CuO4 Units in Sr-Cu-O and Ca-Cu-O Systems: Spinladder and Infinite-chain Composite Structures
Numerous cuprates contain edge-shared (CuO2) square-planar units. An interesting example is the series of so-called spin-ladder cuprates. They belong to the homologou series Srn−1Cun+1O2n (n = 1, 2) [64]. These compounds can only be synthesized under high pressures. It should be underlined that at normal pressure the stable compounds in SrO CuO system are SrCuO2 [35], Sr2CuO3 [65] and Sr14Cu24O41 [66,67]. SrCuO2 crystal structur is quasi-one-dimensional (1D). It contains Cu 2+ in square-planar coordination, CuO2 frag ments are only edge-shared forming ribbon-like chains. The Sr2CuO3 crystal structure i heavily oxygen deficient and, therefore, Cu is in square-planar coordination and CuO units are corner-shared. Sr14Cu24O41 has a composite crystal structure which consists o two incommensurate sublattices, first contains (Cu2O3) ladders and second contains Cu O 1D edge-shared chains similar to SrCuO2 ( Figure 5). Therefore, it contains spin-ladde fragment as in 80 K superconductor YBa2Cu4O8 [68,69]. Members of the spin-ladder homologous series Srn−1Cun+1O2n (n = 3, 5), Sr2Cu4O6 and Sr4Cu6O10, are stabilized by high-pressure because they have elevated crystallographi These first and second series members with n = 3 and n = 5 were synthesized in bulk form at 6 GPa and 1200 • C, the next member with n = 7 was not obtained yet, although it seems that it could be obtained at higher pressures [71]. Refinement of Sr 4 Cu 6 O 10 crystal structure using neutron powder diffraction data confirmed the 3-leg model (see Figure 6). The Cu-O planes consist of square planar CuO 2 units which are linked by both edge-and corner-sharing, corner-sharing chains of CuO 2 squares form the legs of the ladder, running in the a-direction. These ladders are connected by edge-sharing forming double chains. density in comparison with normal pressure phase Sr14Cu24O41 (5.51 g/cm 3 , 5 4.68 g/cm 3 ), respectively.
These first and second series members with n = 3 and n = 5 were synthe form at 6 GPa and 1200 °C, the next member with n = 7 was not obtained ye seems that it could be obtained at higher pressures [71]. Refinement of Sr4 structure using neutron powder diffraction data confirmed the 3-leg model The Cu-O planes consist of square planar CuO2 units which are linked by b corner-sharing, corner-sharing chains of CuO2 squares form the legs of the lad in the a-direction. These ladders are connected by edge-sharing forming dou Single crystals of Sr4Cu6O10 slightly doped by Ca (ca. 4%) were grown argon-gas-pressure technique with an Ar partial gas pressure of 1.82 GPa in Canthal furnace [72]. Crystal structure determination using single crystal X-r data confirmed the 3-leg model.
Cuprates with ladder structures are of particular interest as so-calle compounds. There are theoretical predictions of superconductivity or cha wave properties for properly doped spin-ladder materials with an even nu [73,74]. However, up to now, bulk superconductivity was never observed i cuprates. All attempts to induce superconductivity by appropriate electron a ing (by La 3+ , Nd 3+ , Na + and K + ) in Sr2Cu4O6 and Sr4Cu6O10 failed to give any po Superconductivity in Ca-doped Sr14Cu24O41 was reported, but never confirm the bulk state [75]. AFM transition was observed in the non-doped phase be it was attributed to the spin orientation predominantly perpendicular to chains [76]. Therefore, it is still an open question whether is possible to indu ductivity by the appropriate doping in the parent spin-ladder compound edge-shared CuO2 units even if Cu has the appropriate oxidation state There is a considerable theoretical interest in one-dimensional 1D Hei 1/2 systems because they exhibit a number of properties that are entirely d quantum-mechanical behavior and have no analogues in three-dimensiona particular, it has been shown that the Heisenberg S51/2 chain represents system characterized by a macroscopic number of conservation laws [77].
Some 1D cuprates showed unusual behavior at low temperatures, pa research efforts were focused on interesting quantum magnetic phenome oxygen chains with integer spins. It should be mentioned the spin-Peierls CuGeO3 [78] and the Haldane-gap appearance in Heisenberg chains with [79]. Single crystals of Sr 4 Cu 6 O 10 slightly doped by Ca (ca. 4%) were grown using a high argon-gas-pressure technique with an Ar partial gas pressure of 1.82 GPa in a three-zone Canthal furnace [72]. Crystal structure determination using single crystal X-ray diffraction data confirmed the 3-leg model.
Cuprates with ladder structures are of particular interest as so-called spin-ladder compounds. There are theoretical predictions of superconductivity or charge-density-wave properties for properly doped spin-ladder materials with an even number of legs [73,74]. However, up to now, bulk superconductivity was never observed in spin-ladder cuprates. All attempts to induce superconductivity by appropriate electron and hole-doping (by La 3+ , Nd 3+ , Na + and K + ) in Sr 2 Cu 4 O 6 and Sr 4 Cu 6 O 10 failed to give any positive results. Superconductivity in Ca-doped Sr 14 Cu 24 O 41 was reported, but never confirmed, at least in the bulk state [75]. AFM transition was observed in the non-doped phase below 60 K and it was attributed to the spin orientation predominantly perpendicular to the 1D CuO 2 chains [76]. Therefore, it is still an open question whether is possible to induce superconductivity by the appropriate doping in the parent spin-ladder compounds containing edge-shared CuO 2 units even if Cu has the appropriate oxidation state There is a considerable theoretical interest in one-dimensional 1D Heisenberg spin-1/2 systems because they exhibit a number of properties that are entirely dominated by quantum-mechanical behavior and have no analogues in three-dimensional systems. In particular, it has been shown that the Heisenberg S51/2 chain represents an integrable system characterized by a macroscopic number of conservation laws [77].
Some 1D cuprates showed unusual behavior at low temperatures, particularly the research efforts were focused on interesting quantum magnetic phenomena in copperoxygen chains with integer spins. It should be mentioned the spin-Peierls transition in CuGeO 3 [78] and the Haldane-gap appearance in Heisenberg chains with integer spins [79].
Thermal conductivities of normal pressure 1D spin-chain compounds SrCuO 2 and Sr 2 CuO 3 were studied in detail [80,81]. Although the crystal structures of the two compounds are different in the sense that the former contains linear and the latter consists of zigzag Cu-O chains, the thermal conductivity of both materials is remarkably similar. In particular, the heat transport in the directions perpendicular to the chains is dominated by phonons, but along the chain direction and at high temperatures there is a substantial excess contribution related to the transport of energy by spinons. The phonon thermal conductivity is analyzed employing a Debye-type approximation. The main sources of phonon scattering are phonons at high temperatures and lattice defects, presumably dislocations, at low temperatures. The spin-phonon interaction is not seen in the phonon heat transport, most likely because it is masked by other scattering processes.
As was noticed, high isostatic pressure in belt-type apparatus and cubic anvils leads to stabilization of phases with elevated crystallographic densities, but in the case of high partial oxygen pressure of 0.2 GPa in a double chamber gas system, Sr 0.73 CuO 2 was obtained at the temperature range 950-1180 • C, single phase polycrystalline samples and single crystals were obtained [82]. Its cation and oxygen stoichiometry was confirmed by energy dispersive X-ray (EDX) analysis and volumetric determination method [83]. Its incommensurate composite crystal structure belongs to the NaCuO 2 structural type and consists of two sublattices, associated with Sr 2+ cations and (CuO 2 ) n− edge-shared square-planar units, respectively. First sublattice has an orthorhombic C-centered subcell with a = 3.78 Å, b = 6.82 Å, c = 5.51 Å and second has an orthorhombic F-centered subcell with a = 2.72 Å, b = 6.82 Å, c = 11.02 Å. Therefore, there is a mismatch between them resulting in incommensurate modulations along the a-axis (Figure 7).
Molecules 2021, 26, x FOR PEER REVIEW by phonons, but along the chain direction and at high temperatures there is a su excess contribution related to the transport of energy by spinons. The phonon conductivity is analyzed employing a Debye-type approximation. The main so phonon scattering are phonons at high temperatures and lattice defects, presum locations, at low temperatures. The spin-phonon interaction is not seen in the pho transport, most likely because it is masked by other scattering processes.
As was noticed, high isostatic pressure in belt-type apparatus and cubic anv to stabilization of phases with elevated crystallographic densities, but in the cas partial oxygen pressure of 0.2 GPa in a double chamber gas system, Sr0.73CuO2 tained at the temperature range 950-1180 °C, single phase polycrystalline sam single crystals were obtained [82]. Its cation and oxygen stoichiometry was confi energy dispersive X-ray (EDX) analysis and volumetric determination method incommensurate composite crystal structure belongs to the NaCuO2 structural consists of two sublattices, associated with Sr 2+ cations and (CuO2) n− edge-shared planar units, respectively. First sublattice has an orthorhombic C-centered subce = 3.78 Å, b = 6.82 Å, c = 5.51 Å and second has an orthorhombic F-centered subce = 2.72 Å, b = 6.82 Å, c = 11.02 Å. Therefore, there is a mismatch between them res incommensurate modulations along the a-axis (Figure 7).  Ca 0.83 CuO 2 has similar composite incommensurate structure. It was obtained as nearly single-phase polycrystalline sample from precursors of Ca 2 CuO 3 and CuO heated at 1020 • C for 36 h and oxygen partial pressure of 0.174 GPa. The oxygen stoichiometry of Ca 0.83 CuO 2 was confirmed by volumetric titration. Single crystals were grown by using a BaCuO 2 + CuO flux [84]. It was shown that Ca-containing phase has an incommensurate composite crystal structure similar to Sr 0.73 CuO 2 . However, some peculiarities were manifested. It contains Cu in oxidation state +2.34 that is well below +2.54 revealed for Sr-containing phase. Recently, it was reported Ca 0.83 CuO 2 synthesis at ambient pressure using very effective soft chemistry sol-gel technique in flowing oxygen at 700 • C [85].
The powder diffraction data were collected using synchrotron radiation with λ = 0.685 Å. Then the crystal structure was refined using the Jana 2006 software package adopted for composite structure refinement [87].
It is important to note that the CuO 4 square-planar units were significantly distorted due to propagation of a tilted wave along the ribbons. Cu-O distances are between 1.85 Å and 2.05 Å with an average value 1.93 Å. Taking into account the mixed Cu oxidation state, the possibility of periodic charge-ordering phenomena along the Cu-O chains is envisaged.
Magnetic properties of Sr 0.73 CuO 2 and Ca 0.83 CuO 2 were studied in details by DC magnetic susceptabilities, EPR, specific heat and elastic neutron scattering on polycrystalline samples, and magnetic torque measurements on single crystals [84,88,89]. It was reported that in Sr 0.73 CuO 2 and Ca 0.83 CuO 2 , in contrast to Sr 14 Cu 24 O 41 , long-range 3D AF magnetic order occurs below T N~1 2 K and~10 K, respectively (Figures 8 and 9). At higher temperatures, Sr 0.73 CuO 2 , Ca 0.83 CuO 2 and Sr 14 Cu 24 O 41 showed similar magnetic properties: CuO 2 chains in both compounds are diluted highly magnetically by holes which render the CuO 2 unit nonmagnetic.

Importance of High-pressure for Synthesis of New Oxide Superconductors and Future Prospects
It is particularly important to underline the crucial role of high pressure in the synthesis of layered cuprates. It is briefly summarized in Table 1. Table 1. Series of cuprates containing structural flat fragments: high-pressure (HP) synthesis and superconductivity.

General Formula
HP for Synthesis Superconductivity A Ba-containing composite phase was reported as well, its formula was expressed as Ba 2 Cu 3 O 5+d and the crystal structure was briefly described [90]. It has an incommensurable modulated structure probably similar to Sr 0.73 CuO 2 and Ca 0.83 CuO 2 , but the structure details and physical properties still need to be carefully investigated.

Importance of High-Pressure for Synthesis of New Oxide Superconductors and Future Prospects
It is particularly important to underline the crucial role of high pressure in the synthesis of layered cuprates. It is briefly summarized in Table 1. In general, solid-state synthesis in most cases can only be performed at high temperatures. That may be a negative factor, in two cases: preparation of low-temperature structural forms and stabilization of metastable materials [91,92]. These problems can be solved by using high pressure, especially if the final product has a smaller volume, negative value of ∆V (and, therefore, higher crystallographic density) that the precursors mixture. Indeed, CaCuO 2 with "infinite-layer" structure has slightly higher density than the mixture of precursors Ca 2 CuO 3 + CuO, the difference is about 10%, that's why this metastable compound is strongly stabilized by high-pressure. Another example is the low-temperature superconductor (T c = 2 K) KOs 2 O 6 with partially A-deficient cubic pyrochlore-like structure that at 3 GPa and 900 • C transforms into a triclinic structure with higher density [93,94].
It is well known that high-pressure application increases the chemical reactivity of precursors and accelerates the kinetics of solid-state reactions. This is particularly important for the synthesis of higher members of homologous series, because usually the kinetics of these reactions are very slow and occur via formation of lower series members as intermediary products. Moreover, high pressure suppresses the decomposition of thermally unstable precursors. These three important factors, negative ∆V value, increase of precursors thermal stability and acceleration of kinetics of solid-state reactions open large space for synthesis of novel materials. The example can be stabilization of C-containing layered cuprates and synthesis of corresponding homologous series C(Sr 2−x Ca x ) 2 (Ca,Ln) n−1 Cu n O 2n+2 (n = 1-4; Ln = rare-earth cations) and similar B-containing series at high pressures. Their crystal structures contain triangular oxycarbonate (CO 3 ) 2− and oxyborate (BO 3 ) 3− fragments alternate with perovskite-like blocks along the c-axis [95][96][97][98][99][100][101][102]. The first members, CSr 2 CuO 5 (but not CCa 2 CuO 5 ) and RBaCuO 2 BO 3 (R = La-Eu), were obtained at ambient pressure. They have weak tetragonal superstructure with a s = a √ 2, c s = 2a, due to an ordering of triangular oxycarbonate (CO 3 ) 2and oxyborate (BO 3 ) 3− structural fragments with alternating orientation and for that reason it is not detectable from X-ray diffraction data. Structural peculiarities of NdBaCuO 2 BO 3 were revealed from neutron powder diffraction data ( Figure 10). It should be noted that the boron atom has an almost ideal triangle coordination with a B-O average distance of~1.38 Å and it is considerably longer that corresponding C-O average distance equal to~1.27 Å [95].
C and B-contained 1201 crystal structures are similar, but the space group of NdBaCuO 2 BO 3 is non-centrosymmetric P4bm due to an ordering of Nd 3+ and Ba 2+ cations that was deduced from TEM data.
Moreover, a (Cu,N,C)Sr 2 Ca n−1 Cu n O y series with more complicated composition was reported. Its four members (n = 3-6) were synthesized in a belt-type apparatus at 6 GPa and 1350 • C for 1-6 h [103]. It is interesting that only some discreet members (n = 2, 5) were obtained in nitrogen-free systems, and even the small amount of N-doping strongly stabilizes the series.
Incorporation of nitrate to the crystal structures of (Cu,N,C)Sr 2 Ca n−1 Cu n O y was confirmed by EELS [104]. It is very interesting that the two different superstructures were observed simultaneously in the case of n = 3, 2a × b × 2c and 4a × b × 2c. For the next member (n = 4) only the first type of superstructure was revealed and no evidence of superstructure was found for the members with n = 5 and 6.
The two first members of this series were synthesized at slightly lower pressure and temperature, 5.5 GPa and 1270 • C [105]. Contrary to non-superconducting CSr 2 CuO 5 and its Ca-substituted analog, the sample with nominal initial composition C 0.8 N 0.2 Sr 2 CuO 5.3 exhibited bulk superconductivity with T c = 33 K, however the doping mechanism is still remains unclear. If we consider the presence of pentavalent nitrogen in nitrate (NO 3 ) − form, it is logical to expect electron doping. However, two known families of cuprate superconductors with electron as a hole carrier are SrCuO 2 with infinite-layer structure doped by rare-earth trivalent cation (La-Eu) and R 2 CuO 4 (R = Nd-Gd) doped by Ce 4+ , so-called T'-phase [106][107][108]. Typical Cu-O in-plane distance is 1.97-1.98 Å. Both contain Cu in a square-planar coordination. In CSr 2 CuO 5 crystal structure copper is in squarepyramidal coordination, Cu-O in-plane distance is much shorter and below 1.95 Å, so the scenario of electron-doped superconductivity seems very improbable in this case.  However, the principal question is to how define an efficient working tool that will provide a reliable prediction of new compounds with high Tc. Combinatorial solid-state chemistry is proved to be an efficient way to search for new superconducting compounds, but the related problem of identification of diamagnetic phases in polyphasic samples is not easily solved. In [110], samples were synthesized by solid state reactions in a system of randomly mixed starting components (Ca, Sr, Ba, La, Y, Pb, Bi, Tl, and Cu oxides). They showed an onset of diamagnetic transition above 115 K in bulk measurements. Imaging of this diamagnetic response in ceramic samples by scanning SQUID microscopy (SSM) revealed local superconducting areas with sizes down to as small as the spatial resolution of a few micrometers. In addition, locally formed superconducting phases were extracted from polyphasic samples by magnetic separation. The analysis of single grains (d < 80 mm) by X-ray diffraction, elemental analysis, and SQUID measurements allowed to identity Tl2Ca3Ba2Cu4O12, TlCaBaSrCu2O7−δ, BaPb0.5Bi0.25Tl0.25O3−δ, TlBa2Ca2Cu3O9, Tl2Ba2CaCu2O8, and YBa2Cu3O7 well-known superconducting phases with high Tc.
In another publication, the authors introduced two different approaches such as the high-pressure, high-temperature method and ceramic combinatorial chemistry and reported their application to several typical examples [111]. The authors demonstrated that a single sample synthesis concept based on multielement ceramic mixtures can produce a variety of local products. This concept should include local probe analyses and separation techniques to identify compounds of interest. The authors presented the results obtained by applying the new concept to random mixtures of Ca, Sr, Ba, La, Zr, Pb, Tl, Y, Bi, and All reported members of the (Cu,N,C)Sr 2 Ca n−1 Cu n O y series exhibited superconducting transitions with T c = 33, 91, 90, 113, 65 and 52 K, for the members with n = 1, 2, 3, 4, 5 and 6, respectively. It should be pointed out that (Cu,N,C)-1212-Sr phase has a typical 4a × b × 2c superstructure the same as (Cu,C)-1212-Sr originating from Cu-C-C-C-type ordering in the (Cu,C)-plane. However, X-ray single crystal studies of CCa 2 CuO 5 and CSr 1.9 Ca 1.1 Cu 2 O 7 did not reveal any additional reflexes corresponding to the above-mentioned superstructures [109]. It would be interesting to grow and study N-doped single crystals and to perform a neutron powder diffraction study to investigate in detail of light atoms coordination and interatomic distances.
It can conclude that the application of high-pressure, indeed, has a large potential for the realization of different compounds of various structure types, some of which can be only stabilized under high-pressure conditions. However, the principal question is to how define an efficient working tool that will provide a reliable prediction of new compounds with high T c . Combinatorial solid-state chemistry is proved to be an efficient way to search for new superconducting compounds, but the related problem of identification of diamagnetic phases in polyphasic samples is not easily solved. In [110], samples were synthesized by solid state reactions in a system of randomly mixed starting components (Ca, Sr, Ba, La, Y, Pb, Bi, Tl, and Cu oxides). They showed an onset of diamagnetic transition above 115 K in bulk measurements. Imaging of this diamagnetic response in ceramic samples by scanning SQUID microscopy (SSM) revealed local superconducting areas with sizes down to as small as the spatial resolution of a few micrometers. In addition, locally formed superconducting phases were extracted from polyphasic samples by magnetic separation. The analysis of single grains (d < 80 mm) by X-ray diffraction, elemental analysis, and SQUID measurements allowed to identity Tl 2 Ca 3 Ba 2 Cu 4 O 12 , TlCaBaSrCu 2 O 7−δ , BaPb 0.5 Bi 0.25 Tl 0.25 O 3−δ , TlBa 2 Ca 2 Cu 3 O 9 , Tl 2 Ba 2 CaCu 2 O 8 , and YBa 2 Cu 3 O 7 well-known superconducting phases with high T c .
In another publication, the authors introduced two different approaches such as the high-pressure, high-temperature method and ceramic combinatorial chemistry and reported their application to several typical examples [111]. The authors demonstrated that a single sample synthesis concept based on multielement ceramic mixtures can produce a variety of local products. This concept should include local probe analyses and separation techniques to identify compounds of interest. The authors presented the results obtained by applying the new concept to random mixtures of Ca, Sr, Ba, La, Zr, Pb, Tl, Y, Bi, and Cu oxides reacted at different conditions. By adding Zr but removing Tl, Y, and Bi, the bulk state superconductivity got enhanced up to about 122 K.
Another very promising way includes a methodology for crystal structure prediction that is based on the evolutionary algorithm USPEX and the machine-learning interatomic potentials actively learning on-the-fly [112]. It allows for an automated construction of an interatomic interaction model from scratch, replacing the expensive density functional theory (DFT) and giving a speedup of several orders of magnitude. This methodology was successfully tested on prediction of crystal structures of carbon, high-pressure phases of sodium, and boron allotropes, including those that have more than 100 atoms in the primitive cell.
Based on this algorithm, two high-T c hydride superconductors ThH 9 (T c = 149 K) and ThH 10 (T c = 159-161 K) were predicted and synthesized at 170-175 GPa [113,114]. It is important to note that ThH 10 with cubic fcc structure has very wide interval of stability from 85 to 185 GPa.
Moreover, a new non-empirical method for the prediction of material(s) among all possible combinations of all elements has been reported recently [115]. It was stated that this method possesses the best combination of target properties because it combines a new coevolutionary approach with the carefully restructured "Mendelevian" chemical space, energy filtering, and Pareto optimization to ensure that the predicted materials have optimal properties and a high chance to be synthesizable. The approach was supported by the first calculations, in particular, it was found that diamond (and its polytypes, including lonsdaleite) are the hardest possible materials and that bcc-Fe has the highest zerotemperature magnetization among all possible compounds. There is no doubt that these two methodologies are very promising in the search for new superconducting materials.

Conclusions
Synthesis, crystal structures and magnetic properties of several families of layered cuprates were discussed. These materials are superconductors or related phases. It is underlined that high-pressure is the most important tool and its application opens large prospects for design and synthesis of new superconducting materials, particularly when used together with combinatorial solid state chemistry and advanced methodologies for prediction of new phases with high-T c .
Funding: The research receive no external funding.