Reply to 'Experimental measurement of assembly indices are required to determine the threshold for life'.

We clarify misunderstandings of Walker et al. (Walker 2024 21, 20240367 (doi:10.1098/rsif.

Molecular assembly indices of mineral heteropolyanions: some abiotic molecules are as complex as large biomolecules.

Molecular assembly indices, which measure the number of unique sequential steps theoretically required to construct a three-dimensional molecule from its constituent atomic bonds, have been proposed as potential biosignatures. A central hypothesis of assembly theory is that any molecule with an assembly index ≥15 found in significant local concentrations represents an unambiguous sign of life. We show that abiotic molecule-like heteropolyanions, which assemble in aqueous solution as precursors to some mineral crystals, range in molecular assembly indices from 2 for HCO or Si(OH) groups to as large as 21 for the most complex known molecule-like subunits in the rare minerals ewingite and ilmajokite.

The AM-4 Family of Layered Titanosilicates: Single-Crystal-to-Single-Crystal Transformation, Synthesis and Ionic Conductivity.

Flexible crystal() structures, which exhibit() single-crystal()-to-single-crystal() (SCSC) transformations(), are attracting attention() in many applied aspects: magnetic() switches, catalysis, ferroelectrics and sorption. Acid treatment() for titanosilicate material() AM-4 and natural() compounds with the same structures led to SCSC transformation() by loss() Na, Li and Zn cations with large structural() changes (20% of the unit()-cell() volume()). The conservation() of crystallinity through complex() transformation() is possible due() to the formation() of a strong hydrogen bonding() system().

One of Nature's Puzzles Is Assembled: Analog of the Earth's Most Complex Mineral, Ewingite, Synthesized in a Laboratory.

Through the combination of low-temperature hydrothermal synthesis and room-temperature evaporation, a synthetic phase similar in composition and crystal structure to the Earth's most complex mineral, ewingite, was obtained. The crystal structures of both natural and synthetic compounds are based on supertetrahedral uranyl-carbonate nanoclusters that are arranged according to the cubic body-centered lattice principle. The structure and composition of the uranyl carbonate nanocluster were refined using the data on synthetic material.

The role of local heteropolyhedral substitutions in the stoichiometry, topological characteristics and ion-migration paths in the eudialyte-related structures: a quantitative analysis.

Topological analysis of the heteropolyhedral MT framework (where M and T are octahedral and tetrahedral cations, respectively) in the eudialyte-type structure and its derivatives was performed based on a natural tiling analysis of the 3D cation. To analyze the migration paths of sodium cations in these structures, the Voronoi method was used. The parental eudialyte-type MT framework is formed by isolated ZO octahedra, six-membered [M(1)O] rings of edge-sharing M(1)O octahedra, and two kinds of rings of tetrahedra, [SiO] and [SiO].

Polymorphism, polytypism and modular aspect of compounds with the general formula AM(TO) (A = Na, Rb, Cs, Ca; M = Mg, Mn, Fe, Cu; T = S, P): order-disorder, topological description and DFT calculations.

The crystal structure of NaMn(SO) [unit-cell parameters a = 14.8307 (18), b = 9.9107 (18), c = 8.

Global earth mineral inventory: A data legacy.

Minerals contain important clues to understanding the complex geologic history of Earth and other planetary bodies. Therefore, geologists have been collecting mineral samples and compiling data about these samples for centuries. These data have been used to better understand the movement of continental plates, the oxidation of Earth's atmosphere and the water regime of ancient martian landscapes.

Expanding the Averievite Family, ()CuO(O) ( = P, V; = K, Rb, Cs, Cu; = Cl, Br): Synthesis and Single-Crystal X-ray Diffraction Study.

Averievite-type compounds with the general formula ()[CuO(O)], where = alkali metal, = halogen and = P, V, have been synthesized by crystallization from gases and structurally characterized for six different compositions: ( = Cs; = Cl; = P), ( = Cs; = Cl; = V), ( = Rb; = Cl; = P), ( = K; = Br; = P), ( = K; = Cl; = P) and ( = Cu; = Cl; = V). The crystal structures of the compounds are based upon the same structural unit, the layer consisting of a kagome lattice of Cu ions and are composed from corner-sharing (OCu) anion-centered tetrahedra. Each tetrahedron shares common corners with three neighboring tetrahedra, forming hexagonal rings, linked into the two-dimensional [OCu] sheets parallel to (001).

Embedding parallelohedra into primitive cubic networks and structural automata description.

The main goal of the paper is to contribute to the agenda of developing an algorithmic model for crystallization and measuring the complexity of crystals by constructing embeddings of 3D parallelohedra into a primitive cubic network (pcu net). It is proved that any parallelohedron P as well as tiling by P, except the rhombic dodecahedron, can be embedded into the 3D pcu net. It is proved that for the rhombic dodecahedron embedding into the 3D pcu net does not exist; however, embedding into the 4D pcu net exists.

Polyoxometalate clusters in minerals: review and complexity analysis.

Most research on polyoxometalates (POMs) has been devoted to synthetic compounds. However, recent mineralogical discoveries of POMs in mineral structures demonstrate their importance in geochemical systems. In total, 15 different types of POM nanoscale-size clusters in minerals are described herein, which occur in 42 different mineral species.

RbCaCu(PO)O, a novel oxophosphate with a shchurovskyite-type topology: synthesis, structure, magnetic properties and crystal chemistry of rubidium copper phosphates.

Single crystals of RbCaCu(PO)O were synthesized by a hydrothermal method in the multicomponent system CuCl-Ca(OH)-RbCl-BO-RbPO. The synthesis was carried out in the temperature range from 690 to 700 K and at the general pressure of 480-500 atm [1 atm = 101.325 kPa] from the mixture in the molar ratio 2CuO:CaO:RbO:BO:PO.

High-temperature Fe oxidation coupled with redistribution of framework cations in lobanovite, KNa(FeMgNa)Ti(SiO)O(OH) - the first titanosilicate case.

The high-temperature (HT) behaviour of lobanovite, KNa(FeMgNa)Ti(SiO)O(OH), was studied using in situ powder X-ray diffraction in the temperature range 25-1000°C and ex situ single-crystal X-ray diffraction of 17 crystals quenched from different temperatures. HT iron oxidation associated with dehydroxylation starts at 450°C, similar to other ferrous-hydroxy-rich heterophyllosilicates such as astrophyllite and bafertisite. A prominent feature of lobanovite HT crystal chemistry is the redistribution of Fe and Mg+Mn cations over the M(2), M(3), M(4) sites of the octahedral (O) layer that accompanies iron oxidation and dehydroxylation.

Producing highly complicated materials. Nature does it better.

Through the years, mineralogical studies have produced a tremendous amount of data on the atomic arrangement and mineral properties. Quite often, structural analysis has led to elucidate the role played by minor components, giving interesting insights into the physico-chemical conditions of mineral crystallization and allowing the description of unpredictable structures that represented a body of knowledge critical for assessing their technological potentialities. Using such a rich database, containing many basic acquisitions, further steps became appropriate and possible, into the directions of more advanced knowledge frontiers.

The Fedorov-Groth law revisited: complexity analysis using mineralogical data.

The Fedorov-Groth law points out that, on average, chemical simplicity corresponds to higher symmetry, and chemically complex compounds usually have lower symmetry than chemically simple compounds. Using mineralogical data, it is demonstrated that the Fedorov-Groth law is valid and statistically meaningful, when chemical complexity is expressed as the amount of Shannon chemical information per atom and the degree of symmetry as the order of the point group of a mineral.

Polyoxometalate chemistry at volcanoes: discovery of a novel class of polyoxocuprate nanoclusters in fumarolic minerals.

Polyoxometalate (POM) chemistry is an important avenue of comprehensive chemical research, due to the broad chemical, topological and structural variations of multinuclear polyoxoanions that result in advanced functionality of their derivatives. The majority of compounds in the polyoxometalate kingdom are synthesized under laboratory conditions. However, Nature has its own labs with the conditions often unconceivable to the mankind.

Extraordinary structural complexity of ilmajokite: a multilevel hierarchical framework structure of natural origin.

The crystal structure of ilmajokite, a rare Na-K-Ba-Ce-titanosilicate from the Khibiny mountains, Kola peninsula, Russia, has been solved using single-crystal X-ray diffraction data. The crystal structure is based on a 3D titanosilicate framework consisting of trigonal prismatic titanosilicate (TPTS) clusters centered by Ce in [9]-coordination. Four adjacent TPTS clusters are linked into four-membered rings within the (010) plane and connected ribbons parallel to 101.

Chemically Induced Polytypic Phase Transitions in the Mg[(UO)(O)(HO)](HO) ( = S, Se) System.

Chemically induced polytypic phase transitions have been observed during experimental investigations of crystallization in the mixed uranyl sulfate-selenate Mg[(UO)(O)(HO)](HO) ( = S, Se) system. Three different structure types form in the system, depending upon the Se:S ratio in the initial aqueous solution. The phases with the Se/(Se + S) ratios (in mol %) in the ranges 0-9, 16-47, and 58-100 crystallize in the space groups 2, 2, and 2/, respectively.

High pressure phase transitions of paracelsian BaAlSiO.

Three new polymorphs of aluminosilicate paracelsian, BaAlSiO, have been discovered using synchrotron-based in situ high-pressure single crystal X-ray diffraction. The first isosymmetric phase transition (from paracelsian-I to paracelsian-II) occurs between 3 and 6 GPa. The phase transition is associated with the formation of pentacoordinated Al and Si ions, which occurs in a stepwise fashion by sequential formation of Al-O and Si-O bonds additional to those in AlO and SiO tetrahedra, respectively.

Penta- and hexa-coordinated beryllium and phosphorus in high-pressure modifications of CaBePO.

Beryllium oxides have been extensively studied due to their unique chemical properties and important technological applications. Typically, in inorganic compounds beryllium is tetrahedrally coordinated by oxygen atoms. Herein based on results of in situ single crystal X-ray diffraction studies and ab initio calculations we report on the high-pressure behavior of CaBePO, to the best of our knowledge the first compound showing a step-wise transition of Be coordination from tetrahedral (4) to octahedral (6) through trigonal bipyramidal (5).

Functionality in metal-organic framework minerals: proton conductivity, stability and potential for polymorphism.

Rare metal-organic framework (MOF) minerals stepanovite and zhemchuzhnikovite can exhibit properties comparable to known oxalate MOF proton conductors, including high proton conductivity over a range of relative humidities at 25 °C, and retention of the framework structure upon thermal dehydration. They also have high thermodynamic stability, with a pronounced stabilizing effect of substituting aluminium for iron, illustrating a simple design to access stable, highly proton-conductive MOFs without using complex organic ligands.

On the origin of crystallinity: a lower bound for the regularity radius of Delone sets.

The mathematical conditions for the origin of long-range order or crystallinity in ideal crystals are one of the very fundamental problems of modern crystallography. It is widely believed that the (global) regularity of crystals is a consequence of `local order', in particular the repetition of local fragments, but the exact mathematical theory of this phenomenon is poorly known. In particular, most mathematical models for quasicrystals, for example Penrose tiling, have repetitive local fragments, but are not (globally) regular.

ℇ-RbCuCl, a new polymorph of rubidium copper trichloride: synthesis, structure and structural complexity.

A novel polymorph of RbCuCl (rubidium copper trichloride), denoted ℇ-RbCuCl, has been prepared by chemical vapour transport (CVT) from a mixture of CuO, CuCl, SeO and RbCl. The new polymorph crystallizes in the orthorhombic space group C222. The crystal structure is based on an octahedral framework of the 4H perovskite type.

A closer look into close packing: pentacoordinated silicon in a high-pressure polymorph of danburite.

Due to their high technological and geological relevance, silicates are one of the most studied classes of inorganic compounds. Under ambient conditions, the silicon in silicates is almost exclusively coordinated by four oxygen atoms, while high-pressure treatment normally results in an increase in the coordination from four- to sixfold. Reported here is a high-pressure single-crystal X-ray diffraction study of danburite, CaBSiO, the first compound showing a step-wise transition of Si coordination from tetrahedral to octahedral through a trigonal bipyramid.

The first lead cobalt phosphite, PbCo(HPO).

Single crystals of a new lead cobalt phosphite, PbCo(HPO), have been synthesized using mild hydrothermal techniques and characterized by X-ray diffraction analysis, SQUID magnetic measurements, IR spectroscopy, UV/vis spectroscopy, thermogravimetric analysis, and scanning electron microscopy. PbCo(HPO) crystallizes in the non-centrosymmetric (NCS) R3m space group, a = 5.3145(15) Å, c = 25.

Xenon in Rigid Oxide Frameworks: Structure, Bonding and Explosive Properties of Layered Perovskite KXeO.

The tendency of high-valence xenon to form consolidated oxide structures is herein supported by the study of KXeO, the first example of a layered xenon perovskite. Xenon seems to be the only nontransition element that can adopt single-cation oxide perovskite frameworks. At the same time, peculiarities of electronic structure of xenon impose specific features on the bonding within a perovskite structure.