Prerpints.org logo
Preprint
Article

The Crystal Structure of Pb10(PO4)6O Revisited: The Evidence of Superstructure

Altmetrics

Downloads

142

Views

48

Comments

0

A peer-reviewed article of this preprint also exists.

supplementary.zip (155.91KB )

This version is not peer-reviewed

Submitted:

09 August 2023

Posted:

10 August 2023

You are already at the latest version

Alerts
Abstract
The crystal structure of Pb10(PO4)6O, the proposed matrix for the potential room-temperature superconductor LK-99, Pb10-xCux(PO4)6O (x = 0.9-1.0), has been reinvestigated by single-crystal X-ray diffraction using crystals prepared by Merker and Wondratschek (The crystal structure is trigonal, P, a = 9.8109(6), c = 14.8403(12) Å, V = 1237.06(15), R1 = 0.0413 using 3456 unique observed reflections. The crystal structure of Pb10(PO4)6O is a superstructure with regard to the ‘standard’ P63/m apatite structure type. The doubling of the c parameter is induced by the ordering of ‘additional’ O’ atoms within the structure channels running parallel to the c axis and centered at (00z). The O’ atoms form short bonds to the Pb1 atoms, resulting in splitting the Pb1 site into two, Pb1A and Pb1B. The structural distortions are further transmitted to the Pb phosphate framework formed by four Pb2 sites and PO4 groups. The structure data previously reported by Krivovichev and Burns (Z. Kristallogr. 2003, 218, 357-365) may either correspond to the Pb10(PO4)6Ox(OH)2-x (x ~ 0.4) member of the Pb10(PO4)6O - Pb10(PO4)6(OH)2 solid solution series, or to the high-temperature polymorph of Pb10(PO4)6O (with the phase with doubled c parameter being the low-temperature polymorph).
Keywords: 
Subject: Physical Sciences  -   Condensed Matter Physics

1. Introduction

In the series of recent preprints, S. Lee and co-authors [1,2,3] reported on the discovery of room-temperature superconductor LK-99 with the chemical formula Pb10-xCux(PO4)6O (x = 0.9-1.0). The authors claimed that the superconducting properties of the material (Tc = 400 K) are proved by the measurements of its resistivity, current, magnetic field, and the Meissner effect. Lee et al. point out that ‘the superconductivity of LK-99 originates from minute structural distortion by a slight volume shrinkage (0.48%) … caused by Cu2+ substitution of Pb2+(2) ions in the insulating network of Pb(2)-phosphate’ [1]. The stress caused by the substitution ‘…transfers to Pb(1) of the cylindrical column resulting in distortion of the cylindrical column interface, which creates superconducting quantum wells (SQWs) in the interface’ [1]. The claims by Lee et al. [1,2,3] are currently under hot debates and detailed scrutiny by the international scientific community [4,5,6,7,8]. The density functional theory (DFT) studies on LK-99 have been performed by a number of groups [9,10,11,12,13], showing the interesting electronic features of LK-99, which itself raises important issues about its unique physical and structural properties. The structure models constructed for the DFT studies are based upon the available crystallographic data for Pb10(PO4)6O reported by Krivovichev and Burns [14] or the data on Pb10(PO4)6(OH)2 [15,16]. Both sets of data correspond to the high-symmetry apatite structure type with the P63/m space group and the cell of a ~ 9.85 and c ~ 7.43 Å [17]. The proper understanding of the crystal structure of the matrix material Pb10(PO4)6O is of outmost importance for the elucidation of the mechanisms that generate superconductivity of LK-99.
The aim of the present paper is to re-consider the crystal structure of Pb10(PO4)6O in order to provide insight into its atomic nature and the character of structural distortions induced by its crystal-chemical modification. First, we provide some background information on Pb10(PO4)6O, including historical notes and personal experience. Second, we present a new structure model of Pb10(PO4)6O, based upon the experimental crystal-structure analysis. The crystal chemical analysis of the new model reveals its basic differences from the models assumed in the DFT modelling. Finally, we provide discussion of the possible mechanisms of the Pb-Cu substitution in LK-99 based upon the available crystal chemical information.

2. Background Information

‘Oxypyromorphite’ Pb10(PO4)6O has been known at least for more than 70 years. Rooksby [18] obtained it through crystallization of glass with respective chemical composition and provided the unit cell parameters a = 9.75 and c = 7.23 Å. The first detailed study of the synthesis and X-ray diffraction data of Pb10(PO4)6O were due to Merker and Wondratschek [19], who prepared the compound by crystallization from melt formed by mixing PbO and NH4H2PO4 as initial reagents. The melting temperature of Pb10(PO4)6O was estimated as 967 oC (see Figure 3 in [19]) and the compound was reported as being melting incongruently [20]. Merker and Wondratschek [19] reported for the ‘oxypyromorphite’ a hexagonal unit cell with a = 9.84 and c = 14.86 Å, i.e., the superstructure of apatite with the doubled c parameter. They pointed out that the differences between these parameters and the parameters reported by Rooksby [18] can be due to the possible mixed character of the sample studied by the latter (‘Da es sehr viele Bleiverbindungen mit Apatit-Struktur und ahnlichen Gitterkonstanten gibt, die zudem weitgehend Mischkristalle bilden können, halten wir es nicht fur ausgeschlossen, das irgendeine andere dieser Verbindungen vorlag’ [19]). Merker and Wondratschek [19] assigned the doubling of the c parameter of their Pb10(PO4)6O to the ordering of ‘additional’ (not bonded to P) O atoms in the structure channels. Ito [21] suggested that the true formula of ‘oxypyromorphite’ can be written as Pb2+9Pb4+(PO4)6O2, in order to be in accord with the general formula of apatite-type compounds given as A5(TO4)3X. However, this hypothesis was declined by Merker et al. [20], who demonstrated the validity of the Pb2+10(PO4)6O composition.
In their study of the crystal structures lead oxide phosphates, Krivovichev and Burns [14] prepared and, for the first time, structurally characterized ‘oxypyromorphite’. The crystals of Pb10(PO4)6O have been obtained by heating the mixture of 0.446 g PbO and 0.058 g NH4H2PO4 to 950 oC in platinum crucibles, followed by cooling to 50 oC over 150 hours. The majority of the resulting reaction products consisted of elongated transparent crystals of Pb4O(PO4) with a small quantity of isometric hexagonal crystals of Pb10(PO4)6O. The single-crystal X-ray diffraction structure analysis [14] demonstrated that the latter compound crystallizes in the P63/m space group with a = 9.8650(3) and c = 7.4306 Å. The structure model obtained is hereinafter denoted as Pb10(PO4)6O-KB (after Krivovichev and Burns [14]).
After publication of the paper [14] in 2003, the author of this article had received an email message from Prof. Hans Wondratschek (1925-2014), who pointed out to the observation of Merker and Wondratschek [19] of the doubling of the c parameter of Pb10(PO4)6O relative to the ‘standard’ apatite structure. Prof. Wondratschek also indicated the possibility that the phase studied by Krivovichev and Burns [14] could be, in fact, Pb5(PO4)3(OH), the conclusion that cannot be verified now due to the unavailability of the sample. After the suggestion of the re-study of the crystals of Pb10(PO4)6O using modern X-ray diffraction equipment, Prof. Wondratschek mailed to us the crystals prepared in 1968 by Prof. Günther Engel (University of Aalen, Germany). In addition, in 2006, Prof. Engel sent us additional samples for the further studies, which appeared to be structurally identical to those sent by Prof. Wondratschek. In this paper, the crystal structure model for Pb10(PO4)6O prepared by Wondratschek and Engel (hereinafter denoted as Pb10(PO4)6O-WE).

3. Materials and Methods

The crystals of Pb10(PO4)6O-WE used in this study have been obtained from Prof. Wondratschek and Prof. Engel as described above.
The single-crystal structure X-ray diffraction data have first been obtained by means of a STOE IPDS II X-ray diffractometer equipped with Image Plate area detector and operated at 50 kV and 40 mA. More than a hemisphere of three-dimensional data was collected using monochromatic MoKα X-radiation, with frame widths of 2° in ω, and with a 5 min count for each frame. The analysis of the reciprocal space revealed the presence of the reflections that correspond to the doubling of the c unit-cell parameter, well in agreement with the observations by Merker and Wondratschek [19] (Figure 1). The unit-cell parameters (a = 9.832(1) and c = 14.913(3) Å) were refined using least-squares techniques. The intensity data were integrated and corrected for Lorentz, polarization, and background effects using the STOE X-Red program. However, the attempts to solve and refine the crystal structure generally failed with the R1 factor being always higher than 0.10.
In order to obtain better data, the crystal of Pb10(PO4)6O-WE was transferred to the Bruker Smart Apex II diffractometer at the Department of Crystallography, St. Petersburg State University, Russia. More than a hemisphere of X-ray diffraction data with the frame widths of 0.5º in ω, and with 60 s spent counting for each frame were collected at room temperature using MoKα radiation. The indexing of the obtained reflections indicated the doubling of the c parameter, in agreement with the observations by Merker and Wondratschek [19] and the Stoe IPDS II data. The data were integrated and corrected for absorption using the Bruker programs APEX and XPREP. The observed systematic absences were inconsistent with the presence of the 63 screw axis characteristic for the ‘standard’ P63/m space group typical for many apatite-type compounds. The subsequent attempts were undertaken to solve the crystal structure in the subgroups of P63/m, from which the only P 3 ¯ model provide more or less reasonable structure model with R1 > 0.12. The twinning model was introduced using the [100/010/00 1 ¯ ] matrix, which allowed the R1 index to drop to ~0.05. The refinement resulted in the 0.503:0.497 ratio of the two twin components related to each other through the (001) mirror plane. The crystal structure was refined to R1 = 0.0413 using 3456 unique observed reflections (Table 1). The SHELX program package was used for all structural calculations [22]. The final model included all atomic positional parameters, refinable weighting scheme of the structure factors and anisotropic-displacement parameters (ADPs) for all atoms. Anisotropic refinement of few O atoms resulted in physically unrealistic displacement parameters. In order to obtain physically reasonable model, the ADPs of the O atoms that are equivalent relative to the c/2 pseudo-translation were restrained to be equal. The final atomic coordinates, site occupation factors, bond-valence sums, and isotropic displacement parameters are given in Table 2, selected interatomic distances are listed in Table 3. The bond-valence sums for Pb and O atoms have been calculated using Pb-O bond-valence parameters from [23] and [24]; the P-O bond-valence parameters from [24] have been used to calculate the P BVSs. The CIF file and the list of observed and calculated structure factors are given as a Supplementary Information to this paper.

4. Results

Since Pb10(PO4)6O-WE is superstructure with regard to the ‘standard’ P63/m apatite structure type, it is reasonable to describe the structure peculiarities through the comparison of Pb10(PO4)6O-WE (P 3 ¯ , double c parameter) with Pb10(PO4)6O-KB (P63/m, single c parameter). Both crystal structures are depicted in Figure 2 in projections along the c axes. In order to make the structure comparison easier, the atom sites in Pb10(PO4)6O-WE have been numbered to be in maximal correspondence with the site numbering in Pb10(PO4)6O-KB.
The transition between the KB and WE structure types can be described as consisting of two steps. First, the P63/m space group changes to its maximal non-isomorphic space group P 3 ¯ with index 2. The transition is translationengleiche, that is, does not change the unit cell dimensions and is denoted as ‘t2’ [25]. In the second step, the c parameter is doubled [(a, b, c) → (a, b, 2c)] without space-group change, i.e., the transition is klassengleiche and is denoted as ‘k2’ (the space group P 3 ¯ (a, b, 2c) is a subgroup of index 2 of the space group P 3 ¯ (a, b, c)). Thus, the total transition from the KB and WE structure types can be described as a following sequence:
P63/m (a, b, c) → t2 → P 3 ¯ (a, b, c) → k2 → P 3 ¯ (a, b, 2c),
where the intermediate P 3 ¯ (a, b, c) structure type is a hypothetical transitional structure. The relations between the Wyckoff sites occupied by Pb, P, and O atoms in the KB, transitional, and WE structure types are shown in Figure 3. In order to distinguish between the O atoms of the PO4 groups and the ‘additional’ O atoms not bonded to P, the latter are denoted as O’. Note that the occupancies of the O’ sites in the P63/m (a, b, c) and P 3 ¯ (a, b, c) structure types are equal to 0.25, whereas it is equal to 0.5 for the P 3 ¯ (a, b, 2c) structure type (Table 2).
The diagram shown in Figure 3 indicates that, as a result of the imaginary Pb10(PO4)6O-KB → Pb10(PO4)6O-WE transition, the Pb1 site (6h) in the former is splitted into two 6g sites, Pb1A and Pb1B, in the latter. In the same manner, the Pb2 site (4f) is splitted into four 2d sites, Pb2A, Pb2B, Pb2C, and Pb2D. The coordination environments of Pb atoms within the coordination sphere of 3.2 Å as well as coordination of the O’ atoms in the crystal structures of KB and WE are shown in Figure 4. It can be seen that the coordination of the Pb2 sites in the two structures are topologically identical and correspond to tricapped trigonal prisms. In contrast, the coordination of the Pb1 sites changes drastically. In Pb10(PO4)6O-KB, the Pb1 site centers the basis of the Pb1O6 pentagonal pyramid complemented by two Pb-O’ bonds with the occupancy of the O’ sites of 0.25. In Pb10(PO4)6O-WE, there are two Pb1 sites. The Pb1A site forms the Pb1AO6 pentagonal pyramid with no additional Pb-O’ bonds and thus displays a typical coordination of Pb2+ cations with stereochemically active 6s2 lone electron pairs [26]. The coordination of the Pb1B site is again the Pb1BO6 pentagonal pyramid, but complemented by two Pb-O’ (Pb1B–O5A and Pb1B-O5B) bonds and one longer Pb1B-O3A bond of 3.175 Å. Taking into account that Pb1A and Pb1B sites are connected by the c/2 pseudo-translation, the doubling of the c parameter in Pb10(PO4)6O-WE is obviously due the ordering of the O’ atoms in the structure channels centered by the [001] direction at (00z), which is in agreement with the prediction by Merker and Wondratschek [19].
The coordination of the O’ sites in the two structures deserves special attention, especially in the light of the following discussion on the relations between the KB and WE phases (see section 4.2). In Pb10(PO4)6O-KB, the O4 sites are arranged on the 63 screw axis into columns with the O’-O’ separations of 1.721 and 1.944 Å. Each O4 site is coordinated by three Pb1 atoms with the O4-Pb1 distance of 2.582 Å and the Pb1-O4-Pb1 angles of ca. 109.5o. The O4 atom is at the top of a trigonal pyramid with its basis formed by three Pb1 atoms. The bond-valence sum for the O4 atoms is 0.85 v.u., which is much lower than the expected value of 2.0 v.u. However, it should be taken into account that this coordination is averaged, since the site-occupation factor (s.o.f.) for the O4 site is 0.25.
In Pb10(PO4)6O-WE, there are two O’ sites, O5A and O5B, with s.o.f.s equal to 0.55 and 0.45, respectively. The O5A site forms three O5A-Pb1B bonds of 2.324 Å with the Pb1B-O5A-Pb1B angles of 111.8o. The O5B site is coordinated by three Pb1B atoms as well with the O5B-Pb1B bond lengths of 2.240 Å and the Pb1B-O5B-Pb1B angles of 118.4o, which means that the O5B(Pb1B)3 configuration is very close to a planar triangle centered by the O5B site. Thus, the O’ sites in Pb10(PO4)6O-WE are bonded much more tightly than those in Pb10(PO4)6O-KB. The bond-valence sums for the O5A and O5B sites are 1.55 and 1.87 v.u., respectively. The O’-Pb bond lengths in Pb10(PO4)6O-WE are in the ranges typical for the Pb oxysalt compounds with ‘additional’ O atoms [26].

5. Discussion

5.1. Symmetry considerations

The imaginary Pb10(PO4)6O-KB → Pb10(PO4)6O-WE transition is associated with the removal of the m mirror plane running in KB through the Pb1, O1 and O3 atoms at z = ¼. Figure 5 shows projections of the columns of Pb1On coordination polyhedra in both structures. In the crystal structure of Pb10(PO4)6O-KB, the O’ (O4) atoms are arranged regularly along the c axis and the m plane is conserved. In Pb10(PO4)6O-WE, the O’ atoms are in more ordered configuration, which results in the splitting of Pb1 site into two sites, Pb1A not bonded to O’, and Pb1B bonded to O’. The reasons for the disappearance of the m plane in WE are especially clearly seen from the comparison of the Pb1B-O3A and Pb1B-O2B bonds that are related by the mirror plane in the parent structure of KB. In the crystal structure of WE, the Pb1B-O3A and Pb1B-O2B bond lengths are 2.453 and 2.769 Å, respectively, with the difference larger than 0.3 Å.
The absence of the m plane in WE can also be illustrated by considering the column of tricapped Pb2O9 prisms in both structures (Figure 6). Again, the symmetry breaking can be illustrated by the comparison of the Pb2D-O1A and Pb2C-O1A bond lengths (2.428 and 2.617 Å, respectively), which differ by ~0.2 Å. The level of distortion of the substructure of the Pb2 polyhedra in the structure of WE is lower than that for the Pb1 substructure, which is reasonable, taking into account that Pb1A and Pb1B atoms are in the channels occupied by O’ atoms. Thus, the ordering of the O’ atoms in the structure channels results in the distortions of the coordination environments of the Pb1 atoms, which is transmitted to the Pb phosphate substructure formed by Pb2 atoms.

5.2. The relations between KB and WE

The relations between Pb10(PO4)6O-KB and Pb10(PO4)6O-WE is the crucial problem for the understanding of the crystal structure of Pb10(PO4)6O and its Cu-substituted derivatives. There are two possible solutions to this question: (i) Pb10(PO4)6O-KB is in fact Pb10(PO4)6(OH)2; (ii) Pb10(PO4)6O-KB and Pb10(PO4)6O-WE are two polymorphs of Pb10(PO4)6O separated by the order-disorder phase transition. We consider the two possibilities separately.
Table 4 provides unit-cell parameters reported in the literature for ‘oxypyromorphite’ Pb10(PO4)6O, hydroxypyromorphite Pb10(PO4)6(OH)2, and their Cu-substituted varieties, along with some details of the coordination of O’ atoms (O2- or (OH)- anions).
First, we note that the V/Z value for Pb10(PO4)6O-WE (618.5 Å3) is smaller than that for LK-99 (623.2 Å3), which means that incorporation of Cu2+ into Pb10(PO4)6O does not result in the volume shrinkage (S. Lee et al. [3] based their conclusion on the V/Z value for Pb10(PO4)6O-KB, which is, indeed, higher than that for LK-99).
Second, it can be clearly seen that, in terms of the unit-cell parameters, Pb10(PO4)6O-KB is most closely related to Pb10(PO4)6(OH)2 as reported by Brueckner et al. [15] and Kim et al. [16] (the results by Barinova et al. [27] are obviously for another Pb phosphate apatite, most propably Pb5(PO4)3F). The O’ coordination in Pb10(PO4)6O-KB is almost identical to the coordination of OH group in Pb10(PO4)6(OH)2 as reported by Kim et al. [16] from neutron diffraction studies.
The free refinement of the X-ray diffraction data used by Krivovichev and Burns [14] indicated the occupancy of the O4 site equal to 0.40, whereas 0.25 and 0.50 are expected for O2- and (OH)- anions, respectively. Therefore, it is quite likely that the crystal studied in [14] was in fact an intermediate member of the Pb10(PO4)6O - Pb10(PO4)6(OH)2 solid solution, that is, the compound Pb10(PO4)6Ox(OH)2-x with x ~ 0.4. However, taking into account that Pb10(PO4)6O-KB was prepared by heating the mixture of PbO and NH4H2PO4 to 950 oC, the scenario of its formation should involve incorporation of H2O either from air or from the traces of NH4H2PO4.
Another possibility is that Pb10(PO4)6O-KB and Pb10(PO4)6O-WE are two polymorphs of Pb10(PO4)6O separated by order-disorder phase transition. To check this hypothesis, one should investigate behavior of the crystal structure of Pb10(PO4)6O-WE (which is supposed to be a more ordered low-temperature modification) under high-temperature conditions.

5.3. Structural complexity

The information-based structural complexity parameters of the Pb10(PO4)6O-KB and Pb10(PO4)6O-WE structure types as well as of the intermediate hypothetic structure type with the space group P 3 ¯ (a, b, c) have been calculated using the following equations [29,30]:
I G = − ∑ i = 1 k p i log 2 p i ( bit / atom ) ,
I G , total = − v ∑ i = 1 k p i log 2 p i ( bit / cell ) ,
where k is the number of different crystallographic orbits (Wyckoff sites) in the structure and pi is the random choice probability for an atom from the ith crystallographic orbit, that is:
pi = mi/v,
where mi is a multiplicity of a crystallographic orbit (i.e., the number of atoms of a specific Wyckoff site in the reduced unit cell) and v is the total number of atoms in the reduced unit cell.
The v/IG/IG,total parameters for the three structure types under consideration are given on the right side of Figure 3. The symmetry breaking in the sequence of transitions P63/m (a, b, c) → t2 → P 3 ¯ (a, b, c) → k2 → P 3 ¯ (a, b, 2c) corresponds to the gradual increase of structural complexity, both in terms of information amounts per atom and per reduced unit cell. If Pb10(PO4)6O-KB and Pb10(PO4)6O-WE are polymorphs, the relation of their complexities corresponds to the general observation that high-temperature polymorphs are simpler than their low-temperature counterparts.

5.4. On the mechanism of the Pb-Cu substitution in ‘oxypyromorphite’

The incorporation of Cu2+ into the crystal structure of Pb10(PO4)6O (‘oxypyromorphite’) was claimed to be crucial for the superconductivity of LK-99. The current DFT calculations are based upon the assumption that Cu2+ is accommodated into the Pb2 site of the P63/m structure [9,10,11,12,13]. Such an accommodation should be accompanied by considerable local disorder as observed in some complex Pb-Cu oxides [31,32,33]. The disorder is due to the different electronic structure of Pb2+ and Cu2+ cations. The Pb2+ cation possesses a 6s2 lone electron pair, which may be stereochemically active in the presence of strong Lewis bases [26]. In contrast, Cu2+ cations in oxygen environments experience the Jahn-Teller distortion with characteristic planar-square coordination complemented by longer Cu-O bonds [34,35,36]. In some cases, the Cu-Pb substitution results in the splitting of the cation site into separate sites, as it was observed, e.g., for prewittite, KPb1.5ZnCu6(SeO3)2O2Cl10 [37], where the disordered Cu2+ and Pb2+ cations are separated by 1.04 Å, each having its specific coordination environment. The coordination of Cu2+ ions in LK-99 should deserve special attention, especially in the case if the unusual superconducting properties of this material are confirmed.
Ben Moussa et al. [28] studied the incorporation of Cu2+ ions into the crystal structure of hydroxypyromorphite and obtained the series of phases with the general composition Pb10-xCux(PO4)6(OH)2 with x = 2, 4, 6. The unit-cell parameters for these phases are given in Table 4. The incorporation of Cu into Pb10(PO4)6(OH)2 results in the general shrinkage of the unit cell with the c parameter being the most sensitive to the value of x.

6. Conclusions

In conclusion, we reported the crystal structure of Pb10(PO4)6O with doubled c unit-cell parameter and the space group P 3 ¯ . The symmetry breaking relative to the ‘standard’ apatite P63/m space group is the result of ordering of ‘additional’ O’ atoms in the structure channels running along the c axis and centered at (00z). Our results show that the crystal structure of LK-99 may appear to be more complex than it is assumed in the recent DFT calculations, which should be taken into account in further studies of this material.

Supplementary Materials

The following supporting information can be downloaded at: CIF and structure factors file for Pb10(PO4)6O-WE.

Funding

This research was funded by the Russian Science Foundation, grant 19-17-00038.

Data Availability Statement

The structural data for Pb10(PO4)6O-WE are available upon request..

Acknowledgments

This paper is dedicated to the memory of Professor Hans Wondratschek (1925-2014), an extraordinary crystallographer and great man, for his outstanding contributions to the crystal chemistry of apatite-type minerals and inorganic compounds.

Conflicts of Interest

The author declares no conflict of interest.

References

  1. Lee, S.; Kim, J.; Im, S.; An S., M.; Kwon, Y.-W.; Ho, A. Consideration for the Development of Room-Temperature Ambient-Pressure Superconductor (LK-99). J. Korean Crystal Growth Crystal Technol. 2023, 33, 61–70. [Google Scholar]
  2. Lee, S.; Kim, J.; Kim, H.-T.; Im, S.; An, S.; Auh, K.H. Superconductor Pb10-xCux(PO₄)₆O Showing Levitation at Room Temperature and Atmospheric Pressure and Mechanism. arXiv:2307. 1203. [Google Scholar]
  3. Lee, S.; Kim, J.-H.; Kwon, Y.-W. The First Room-Temperature Ambient-Pressure Superconductor. arXiv:2307. 1200. [Google Scholar] [CrossRef]
  4. Hou, Q.; Wei, W.; Zhou, X.; Sun, Y.; Shi, Z. Observation of Zero Resistance above 100 K in Pb10-xCux(PO₄)₆O. arXiv:2308. 0119. [Google Scholar] [CrossRef]
  5. Kurleto, R.; Lany, S.; Pashov, D.; Acharya, S.; Schilfgaarde, M. van; Dessau, D.S. Pb-Apatite Framework as a Generator of Novel Flat-Band CuO Based Physics, Including Possible Room Temperature Superconductivity. arXiv:2308. 0069. [Google Scholar] [CrossRef]
  6. Liu, L.; Meng, Z.; Wang, X.; Chen, H.; Duan, Z.; Zhou, X.; Yan, H.; Qin, P.; Liu, Z. Semiconducting Transport in Pb10-xCux(PO₄)₆O Sintered from Pb₂SO₅ and Cu₃P. arXiv:2307. 1680. [Google Scholar] [CrossRef]
  7. Abramian, P.; Kuzanyan, A.; Nikoghosyan, V.; Teknowijoyo, S.; Gulian, A. Some Remarks on Possible Superconductivity of Composition Pb₉CuP₆O25. arXiv:2308. 0172. [Google Scholar] [CrossRef]
  8. Wu, H.; Yang, L.; Xiao, B.; Chang, H. Successful Growth and Room Temperature Ambient-Pressure Magnetic Levitation of LK-99. arXiv:2308. 0151. [Google Scholar] [CrossRef]
  9. Si, L.; Held, K. Electronic Structure of the Putative Room-Temperature Superconductor Pb₉Cu(PO₄)₆O. arXiv:2308. 0067. [Google Scholar] [CrossRef]
  10. Lai, J.; Li, J.; Liu, P.; Sun, Y.; Chen, X.-Q. First-Principles Study on the Electronic Structure of Pb10−xCux(PO4)6O (x = 0, 1). J. Mater. Sci. Technol. 2023. [Google Scholar] [CrossRef]
  11. Tavakol, O.; Scaffidi, T. Minimal Model for the Flat Bands in Copper-Substituted Lead Phosphate Apatite. arXiv:2308. 0131. [Google Scholar] [CrossRef]
  12. Griffin, S.M. Origin of Correlated Isolated Flat Bands in Copper-Substituted Lead Phosphate Apatite. arXiv:2307. 1689. [Google Scholar] [CrossRef]
  13. Cabezas-Escares, J.; Barrera, N.F.; Cardenas, C.; Munoz, F. Theoretical Insight on the LK-99 Material. arXiv:2308. 0113. [Google Scholar] [CrossRef]
  14. Krivovichev, S.V.; Burns, P.C. Crystal Chemistry of Lead Oxide Phosphates: Crystal Structures of Pb4O(PO4)2, Pb8O5(PO4)2 and Pb10(PO4)6O. Z. Kristallogr. 2003, 218, 357–365. [Google Scholar] [CrossRef]
  15. Brückner, S.; Lusvardi, G.; Menabue, L.; Saladini, M. Crystal Structure of Lead Hydroxyapatite from Powder X-Ray Diffraction Data. Inorganica Chimica Acta 1995, 236, 209–212. [Google Scholar] [CrossRef]
  16. Kim, Jean Y. ; Hunter, Brett A.; Fenton, R.R.; Kennedy, B.J. Neutron Powder Diffraction Study of Lead Hydroxyapatite. Aust. J. Chem. 1998, 50, 1061–1066. [Google Scholar]
  17. White, T.J.; ZhiLi, D. Structural Derivation and Crystal Chemistry of Apatites. Acta Crystallogr. 2003, B59, 1–16. [Google Scholar] [CrossRef]
  18. Rooksby, H.P. Identification by X-Ray Diffraction of Crystalline Inclusions in Glass. Analyst 1952, 77, 759–765. [Google Scholar] [CrossRef]
  19. Merker, L.; Wondratschek, H. Der Oxypromorphit Pb10(PO4)6O und der Ausschnitt Pb4P2O9—Pb3(PO4)2 des Systems PbO—P2O5. Z. Anorg. Allg. Chem. 1960, 306, 25–29. [Google Scholar] [CrossRef]
  20. Merker, L.; Engel, G.; Wondratschek, H.; Ito, J. Lead Ions and Empty Halide Sites in Apatites. Amer. Miner. 1970, 55, 1435–1437. [Google Scholar]
  21. Ito, J. Silicate Apatites and Oxyapatites. Amer. Miner. 1968, 53, 890–907. [Google Scholar]
  22. Sheldrick, G.M. Crystal Structure Refinement with SHELXL. Acta Crystallogr. 2015, C71, 3–8. [Google Scholar] [CrossRef]
  23. Krivovichev, S.V.; Brown, I.D. Are the Compressive Effects of Encapsulation an Artifact of the Bond Valence Parameters? Z. Kristallogr. 2001, 216, 245–247. [Google Scholar] [CrossRef]
  24. Gagné, O.C.; Hawthorne, F.C. Comprehensive Derivation of Bond-Valence Parameters for Ion Pairs Involving Oxygen. Acta Crystallogr. 2015, B71, 562–578. [Google Scholar] [CrossRef]
  25. Müller, U. Symmetry Relationships between Crystal Structures: Applications of Crystallographic Group Theory in Crystal Chemistry; Oxford University Press, 2013; ISBN 978-0-19-966995-0.
  26. Siidra, O.I.; Krivovichev, S.V.; Filatov, S.K. Minerals and Synthetic Pb(II) Compounds with Oxocentered Tetrahedra: Review and Classification. Z. Kristallogr. 2008, 223, 114–125. [Google Scholar] [CrossRef]
  27. Barinova, A.; Bonin, M.; Pushcharovskii, D.; Rastsvetaeva, R.; Schenk, K.; Dimitrova, O. Crystal Structure of Synthetic Hydroxylpyromorphite Pb5(PO4)3(OH). Crystallogr. Rep. 1998, 43, 189–192. [Google Scholar]
  28. Ben Moussa, S.; Bachoua, H.; Brigui, N.; Badraoui, B. Synthèse, caractérisation et étude structurale des hydroxyapatites à base de plomb Pb10-xMx(PO4)6(OH)2 (M = Zn, Cu). J. Mater. Environ. Sci. 2016, 7, 4754–4766. [Google Scholar]
  29. Krivovichev, S.V. Structural Complexity of Minerals: Information Storage and Processing in the Mineral World. Miner. Mag. 2013, 77, 275–326. [Google Scholar] [CrossRef]
  30. Krivovichev, S., V.; Krivovichev, V.G.; Hazen, R.M.; Aksenov, S.M.; Avdontceva, M.S.; Banaru, A.M.; Gorelova, L.A.; Ismagilova, R.M.; Kornyakov, I., V.; Kuporev, I., V.; et al. Structural and Chemical Complexity of Minerals: An Update. Miner. Mag. 2022, 86, 183–204. [Google Scholar] [CrossRef]
  31. Liu, R.S.; Hu, S.F.; Chen, D.H.; Shy, D.S.; Jefferson, D.A. Crystal Structure of the (Pb,Hg)Sr2(Ca,Y)Cu2O7-δ Superconductor. Physica C: Superconductivity 1994, 222, 13–18. [Google Scholar] [CrossRef]
  32. Wada, T.; Ichinose, A.; Izumi, F.; Nara, A.; Yamauchi, H.; Hajime-Asano; Tanaka, S. Neutron Powder Diffraction Study of the Pb-Based Copper Oxide Containing Thick Fluorite Blocks: (Pb,Cu)Sr2(Ho,Ce)3Cu2O11+z. Physica C: Superconductivity 1991, 179, 455–460. [Google Scholar] [CrossRef]
  33. Ishigaki, T.; Tokiwa-Yamamoto, A.; Izumi, F.; Kamiyama, T.; Asano, H.; Syono, Y. Structural Changes of PbBaSr(Y0.8Ca0.2)Cu3O7+z on Oxygen Introduction into Block Layers. Physica C: Superconductivity 1994, 231, 357–366. [Google Scholar] [CrossRef]
  34. Jahn, H.A.; Teller, E. Stability of polyatomic molecules in degenerate electronic states. Proc. R. Soc. Ser. A 1937, 161, 220–235. [Google Scholar]
  35. Hathaway, B.J. A new look at the stereochemistry and electronic properties of complexes of the copper(II) ion. In Complex Chemistry. Structure and Bonding; Emsley, J., Ernst, R.D., Hathaway, B.J., Warren, K.D., Eds.; Springer: Berlin/Heidelberg, Germany, 1984; Volume 57, pp. 55–118. [Google Scholar]
  36. Burns, P.C.; Hawthorne, F.C. Static and dynamic Jahn-Teller effects in Cu2+ oxysalt minerals. Can. Mineral. 1996, 34, 1089–1105. [Google Scholar]
  37. Shuvalov, R.R.; Vergasova, L.P.; Semenova, T.F.; Filatov, S.K.; Krivovichev, S.V.; Siidra, O.I.; Rudashevsky, N.S. Prewittite, KPb1.5Cu6Zn(SeO3)2O2Cl10, a New Mineral from Tolbachik Fumaroles, Kamchatka Peninsula, Russia: Description and Crystal Structure. Amer. Miner. 2013, 98, 463–469. [Google Scholar] [CrossRef]
Preprints 82010 g001
Figure 1. Reconstructed sections of reciprocal diffraction space for Pb10(PO4)6O-WE obtained using STOE IPDS II X-ray diffractometer: (a) section perpendicular to [ 1 ¯ 1 ¯ 0 ] ; (b) section perpendicular to [100]; (c) the (hk3) section. The reflections doubling the c parameter with respect to the ‘standard’ apatite structure are indicated by red arrows and red indices.
Figure 1. Reconstructed sections of reciprocal diffraction space for Pb10(PO4)6O-WE obtained using STOE IPDS II X-ray diffractometer: (a) section perpendicular to [ 1 ¯ 1 ¯ 0 ] ; (b) section perpendicular to [100]; (c) the (hk3) section. The reflections doubling the c parameter with respect to the ‘standard’ apatite structure are indicated by red arrows and red indices.
Preprints 82010 g001
Preprints 82010 g002
Figure 2. The crystal structures of Pb10(PO4)6O-KB (a) and Pb10(PO4)6O-WE (b) in projections along the c axes. The Pb-O bonds shorter and longer than 2.5 Å are shown as solid and dashed lines, respectively.
Figure 2. The crystal structures of Pb10(PO4)6O-KB (a) and Pb10(PO4)6O-WE (b) in projections along the c axes. The Pb-O bonds shorter and longer than 2.5 Å are shown as solid and dashed lines, respectively.
Preprints 82010 g002
Preprints 82010 g003
Figure 3. Relations between the Wyckoff sites in the P63/m (a, b, c) (Pb10(PO4)6O-KB, P 3 ¯ (a, b, c) (hypothetical structure type) and P 3 ¯ (a, b, 2c) Pb10(PO4)6O-WE. The complexity parameters for the three structure types are given on the right side of the Figure.
Figure 3. Relations between the Wyckoff sites in the P63/m (a, b, c) (Pb10(PO4)6O-KB, P 3 ¯ (a, b, c) (hypothetical structure type) and P 3 ¯ (a, b, 2c) Pb10(PO4)6O-WE. The complexity parameters for the three structure types are given on the right side of the Figure.
Preprints 82010 g003
Preprints 82010 g004
Figure 4. Coordination polyhedra of Pb and O’ sites in the crystal structures of Pb10(PO4)6O-KB (a) and Pb10(PO4)6O-WE (b). The Pb-O bonds shorter and longer than 2.5 Å are shown as solid and dashed lines, respectively.
Figure 4. Coordination polyhedra of Pb and O’ sites in the crystal structures of Pb10(PO4)6O-KB (a) and Pb10(PO4)6O-WE (b). The Pb-O bonds shorter and longer than 2.5 Å are shown as solid and dashed lines, respectively.
Preprints 82010 g004
Preprints 82010 g005
Figure 5. The chain of the Pb1On coordination polyhedra in Pb10(PO4)6O-KB (a) and Pb10(PO4)6O-WE (b). The Pb-O bonds shorter and longer than 2.5 Å are shown as solid and dashed lines, respectively.
Figure 5. The chain of the Pb1On coordination polyhedra in Pb10(PO4)6O-KB (a) and Pb10(PO4)6O-WE (b). The Pb-O bonds shorter and longer than 2.5 Å are shown as solid and dashed lines, respectively.
Preprints 82010 g005
Preprints 82010 g006
Figure 6. The chains of the Pb3O9 tricapped trigonal prisms in Pb10(PO4)6O-KB (a) and Pb10(PO4)6O-WE (b). The Pb-O bonds shorter and longer than 2.5 Å are shown as solid and dashed lines, respectively.
Figure 6. The chains of the Pb3O9 tricapped trigonal prisms in Pb10(PO4)6O-KB (a) and Pb10(PO4)6O-WE (b). The Pb-O bonds shorter and longer than 2.5 Å are shown as solid and dashed lines, respectively.
Preprints 82010 g006
Table 1. Crystal data and structure refinement parameters for the Pb10(PO4)6O-WE.
Table 1. Crystal data and structure refinement parameters for the Pb10(PO4)6O-WE.
Temperature/K 293(2)
Crystal system trigonal
Space group P 3 ¯
a/Å 9.8109(6)
c/Å 14.8403(12)
Volume/Å3 1237.06(15)
Z 2
Dcalc, g/cm3 7.135
μ/mm-1 68.270
F(000) 2220
Crystal size/mm3 0.06 × 0.05 × 0.01
Radiation MoKα (λ = 0.71073)
2Θ range for data collection/° 5.50 to 69.06
Index ranges -6 ≤ h ≤ 15, -15 ≤ k ≤ 11, -23 ≤ l ≤ 22
Reflections collected 11777
Independent reflections 3456 [Rint = 0.0885, Rsigma = 0.0955]
Data/restraints/parameters 3456/0/105
Goodness-of-fit on F2 0.866
Final R indices [I ≥ 2σ(I)] R1 = 0.0413, wR2 = 0.0749
Final R indices [all data] R1 = 0.0544, wR2 = 0.0771
Largest diff. peak/hole / e Å-3 4.010/-4.537
Table 2. Atomic coordinates, bond-valence sums (BVS, v.u. = valence units) and isotropic displacement parameters (10-4 Å2) for Pb10(PO4)6O-WE.
Table 2. Atomic coordinates, bond-valence sums (BVS, v.u. = valence units) and isotropic displacement parameters (10-4 Å2) for Pb10(PO4)6O-WE.
Site BVS* BVS** x/a y/b z/c Uiso
Pb1A 1.90 1.98 0.25369(5) -0.00015(5) -0.12920(4) 0.01239(10)
Pb1B 1.93 1.97 -0.00445(6) 0.22423(5) 0.37576(6) 0.02123(12)
Pb2A 2.05 2.06 1/3 2/3 0.00402(8) 0.0123(3)
Pb2B 2.07 2.07 1/3 2/3 0.25395(7) 0.0132(3)
Pb2C 2.04 2.06 1/3 2/3 0.49982(8) 0.0187(3)
Pb2D 2.05 2.07 1/3 2/3 -0.25587(7) 0.0125(3)
P1A 4.94 4.94 0.3740(3) 0.4021(3) 0.3698(3) 0.0078(5)
P1B 4.90 4.90 0.0230(3) -0.3765(3) -0.1215(3) 0.0084(5)
O1A 1.99 2.00 -0.1578(9) -0.4786(9) -0.1223(9) 0.0131(11)
O1B 2.00 2.02 0.4953(10) 0.3468(9) 0.3692(9) 0.0131(11)
O2A 1.90 1.90 0.0807(14) -0.2676(14) -0.2034(6) 0.0121(19)
O2B 1.99 1.99 0.2777(14) 0.3560(13) 0.2826(6) 0.0121(19)
O3A 1.94 1.93 0.2533(14) 0.3211(14) 0.4471(6) 0.021(2)
O3B 1.85 1.85 0.0869(16) -0.2716(17) -0.0366(6) 0.021(2)
O4A 2.11 2.15 0.0949(9) -0.4866(10) -0.1233(9) 0.0166(12)
O4B 2.06 2.07 0.4563(10) 0.5820(10) 0.3809(9) 0.0166(12)
O5A*** 1.43 1.55 0 0 0.330(3) 0.031(7)
O5B**** 1.70 1.87 0 0 0.395(3) 0.031(7)
* calculated using bond-valence parameters for Pb-O from [23]. * calculated using bond-valence parameters for Pb-O from [24]. *** s.o.f. = 0.55(4). **** s.o.f. = 0.45(4).
Table 3. Selected interatomic distances (Å) for the crystal structure of Pb10(PO4)6O-WE.
Table 3. Selected interatomic distances (Å) for the crystal structure of Pb10(PO4)6O-WE.
Pb1A-O4A 2.234(8) Pb2A-O1A 2.505(11) 3x
Pb1A-O2B 2.451(10) Pb2A-O4A 2.791(11) 3x
Pb1A-O2A 2.554(12) Pb2A-O3B 2.835(13) 3x
Pb1A-O3B 2.638(10) <Pb2A-O> 2.710
Pb1A-O3B 2.703(13)
Pb1A-O1A 2.801(8) Pb2B-O4B 2.588(11) 3x
<Pb1A-O> 2.564 Pb2B-O1A 2.647(11) 3x
Pb2B-O2B 2.847(11) 3x
Pb1B-O5B 2.240(6) <Pb2B-O> 2.694
Pb1B-O5A 2.325(14)
Pb1B-O3A 2.453(12) Pb2C-O4B 2.503(11) 3x
Pb1B-O4B 2.731(8) Pb2C-O1B 2.616(11) 3x
Pb1B-O3A 2.749(10) Pb2C-O3A 3.172(12) 3x
Pb1B-O2A 2.757(10) <Pb2C-O> 2.764
Pb1B-O2B 2.769(12)
Pb1B-O1B 3.057(8) Pb2D-O1B 2.428(11) 3x
Pb1B-O3A 3.175(12) Pb2D-O4A 2.843(11) 3x
<Pb1B-O> 2.695 Pb2D-O2A 2.961(11) 3x
<Pb2D-O> 2.744
P1A-O2B 1.532(11) P1B-O2A 1.527(11)
P1A-O1B 1.536(9) P1B-O1A 1.541(8)
P1A-O4B 1.539(9) P1B-O3B 1.548(12)
P1A-O3A 1.552(12) P1B-O4A 1.558(9)
<P1A-O> 1.540 <P1B-O> 1.544
Table 4. Unit-cell parameters and coordination of O’ atoms in Pb10(PO4)6O, Pb10(PO4)6(OH)2, and their Cu-substituted varieties.
Table 4. Unit-cell parameters and coordination of O’ atoms in Pb10(PO4)6O, Pb10(PO4)6(OH)2, and their Cu-substituted varieties.
Phase a, Å c, Å V/Z, Å3 O’ coordination O’-Pb, Å Ref.
Pb10(PO4)6O-WE 9.84 14.86 623.0 - - 19
Pb10(PO4)6O-WE 9.811 14.840 618.5 trigonal 2.240/2.325 3x this work
Pb10(PO4)6O-KB 9.865 7.431 626.3 trigonal 2.582 3x 14
Pb10(PO4)6(OH)2 9.866 7.426 626.0 trigonal 2.896 3x 15
Pb10(PO4)6(OH)2 9.883 7.441 629.4 trigonal 2.588 3x 16
Pb10(PO4)6(OH)2 9.774 7.291 603.2 octahedral 2.926 6x 27
Pb10(PO4)6(OH)2 9.871 7.427 626.7 - - 28
LK-99 9.843 7.428 623.2 - - 3
Pb8Cu2(PO4)6(OH)2 9.870 7.398 624.1 - - 28
Pb6Cu4(PO4)6(OH)2 9.868 7.392 623.4 - - 28
Pb4Cu6(PO4)6(OH)2 9.866 7.383 622.3 - - 28
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.
Prerpints.org logo

Preprints.org is a free preprint server supported by MDPI in Basel, Switzerland.

facebook logotwitter logolinkedin logo
MDPI Initiatives
Important Links
Subscribe

Disclaimer

Terms of Use

Privacy Policy

© 2024 MDPI (Basel, Switzerland) unless otherwise stated