To achieve this aim, the dielectric properties were measured with an open-ended coaxial method to understand the behaviour of the samples under microwave irradiation. The effects of microwave power, duration time and sample mass on the heating rate, and the effects of the stoichiometric amount of graphite on the reduction of ZnO and decomposition of ZnFe2O4 were investigated. The results show that ZnFe2O4 has significantly higher dielectric properties compared to ZnO. Generally, for both samples, the dielectric values at room temperature were quite low, indicating that both ZnO and ZnFe2O4 are poor microwave absorbers. It was found that the temperatures have a more significant effect on the imaginary permittivities than on the real permittivities. The heating rate showed that the sample temperature increased with increase in microwave power and sample mass. Using 700 W of microwave power and two times the stoichiometric amount of graphite, almost complete reduction of ZnO was achieved in 12 min, while ZnFe2O4 completely decomposed to zincite and wustite in 3 min.This paper aims to study the dielectric properties and carbothermic reduction of zinc oxide  and zinc ferrite (franklinite, ZnFe Microwave energy is a new promising technology which can be applied in the processing of primary and secondary raw materials. Microwave energy is a non-ionizing form of electromagnetic radiation with frequencies in the range of 300 MHz to 300 GHz ,2. MicroA growing interest in microwave applications has emerged in recent years. These include microwave-assisted ore grinding, microwave-assisted carbothermic reduction of metal oxides, microwave-assisted drying and anhydration, microwave-assisted mineral leaching, microwave-assisted roasting and smelting of sulfide concentrate, and microwave-assisted waste management ,7.et al. [et al. [Wu et al.  investig [et al.  studied 2O4). A few papers have been published and most of this literature has focused on the study of the reduction behaviour of ZnO and ZnFe2O4 under microwave irradiation. Wang et al. [2O4 by microwave heating. He indicated the decomposition of ZnFe2O4 to ZnO and Fe3O4/FeO phases. Saidi & Azari [2O4 has not been discussed widely in the previous investigations.There is a paucity of information on the microwave heating behaviour of zinc oxide (ZnO) and zinc ferrite  and the dielectric properties 1/2.Complex permittivity The real permittivity  is an important factor which provides an indication of how well a material dissipates stored energy into heat [δd) is expressed asThe loss tangent  and zinc iron oxide . Synthetic graphite  was used as the reducing agent. 4.4.1.2O4) were measured by the Archimedes method using deionized water and a 10.115 cm3 pycnometer . The dielectric properties of the samples were measured with an open-ended coaxial probe method at 2.42 GHz and 1064 MHz frequencies. Details of the procedure are described in the paper [The densities of the samples  made of stainless steel and heated by an electric furnace placed inside the holder cavity. At least two duplicate measurements were carried out for each sample.First, the dielectric characterization of the samples was performed at room temperature (23.5°C) and humidity (45% RH). The effect of temperature on the real and imaginary permittivities of ZnO and ZnFe4.2.Diagrams of the microwave experimental set-up are shown in The microwave absorption ability of samples at different microwave power intensities  and processing times were measured. The temperature of the test sample was measured using a stainless steel-sheathed, K type thermocouple.2 flow rate of 5 ml min−1 was applied. The vapours from the crucible were pulled by the pump and trapped in the collector (The samples were well mixed with synthetic graphite (99.99% purity) at the different stoichiometric amounts. Nitrogen gas was used to maintain the reducing condition inside the microwave oven; an Nollector . A filte4.3.2O4 and graphite were dried at 115°C overnight. Then, ZnO and ZnFe2O4 were well mixed with synthetic graphite (99.99% purity) at different stoichiometric amounts. After the experiments, the sample was weighed, ground and analysed to determine the degree of reduction.ZnO, ZnFemm is the mass of ZnO in metallic form after reduction and m0 is the original mass of ZnO in oxide form [The degree of ZnO reduction was defined as the amount of metal recovered from the corresponding metal oxide and was calculated as follows:ide form .2O4 decomposition with time was calculated with X-ray diffraction (XRD) analyses; the reduced samples were weighed, ground and analysed by XRD to investigate the decomposition of ZnFe2O4.The rate of ZnFe2O4 into elemental zinc may be calculated based on the reduction reactions presented in equations (4.2)–(4.7). It should be noted that the required amount of carbon depends heavily on whether carbon is assumed to react into carbon monoxide (CO) or carbon dioxide (CO2) and whether iron included in ZnFe2O4 is assumed to also be reduced or not. The reduction reactions using different assumptions are presented in equations (4.2)–(4.3) for the reduction of ZnO and in equations (4.4)–(4.7) for the reduction of ZnFe2O4.The stoichiometric amount of carbon required to completely reduce ZnO or ZnFe4.4.2O4. TG gives information about the temperature-dependent mass loss of the sample, while DSC detected the thermal reactions. The DSC–TG was performed using a Netzsch STA409 PC Luxx under N2 atmosphere. Approximately 23.84 mg of sample was placed in a platinum crucible on a pan of the microbalance at a heating rate of 10°C min−1. The temperature range was 20–1400°C.Differential scanning calorimetry (DSC) and thermogravimetry (TG) were used to determine the thermal behaviour of ZnO and ZnFe4.5.2O4 after microwave heating for different times was measured using Rigaku SmartLab 9 kW. The XRD analyses were done using operating conditions with an accelerating voltage of 40 kV and a current of 40 mA with a cobalt tube and a graphite monochromator. The measuring range was from 4° to 90° 2θ using a step size of 0.02° 2θ and a step time of 1 s per step.The phase transformation of ZnFe4.6.2O4 during microwave heating were investigated by combined scanning electron microscopy (SEM)–energy-dispersive X-ray spectroscopy (EDS) using a Zeiss ULTRA plus field emission scanning electron microscope, which was attached to an EDS unit for chemical analysis. To investigate the morphology of the phases, samples were investigated without polishing their surfaces. Small amounts of the samples were dispersed on the sample holder and coated with carbon.The microstructure and microanalyses of phase transformation of ZnFe5.5.1.2O4 as a function of temperature in the absence of any reducing agent was firstly studied. Then, the samples were mixed with two times the stoichiometric amount of carbon required to completely reduce ZnO and ZnFe2O4. (Carbon is assumed to react into carbon monoxide (CO); see §4.3.)The behaviour of ZnO and ZnFe5.1.1.a. The TG–DSC curve did not confirm thermal reaction or mass loss at temperatures below 1200°C (figure 3a). Therefore, we can conclude that there is no phase change. At high temperatures, 1235–1391°C, a deep valley in the DSC plot was due to the sintering of the sample. Figure 5a shows that the ZnO is sintering at high temperature, while the XRD pattern indicated that there is no phase change in the sample.The thermal behaviour of ZnO as a function of temperature is shown in figure 3b, and this can be compared with the results in the absence of any reducing agent (figure 3a). The reduction of ZnO begins at temperature 1025°C; when the temperature reaches 1265°C, almost 100% of Zn is reduced and vaporized [figure 3b). The TG curve shows a mass loss of about 90% due to the complete evaporation of zinc, and graphite gasification (that causes the formation of the CO/CO2 atmosphere), while the remaining mass is attributed to graphite. Figure 5b shows that some graphite is remaining in the crucible after the complete reduction of ZnO.The behaviour of the ZnO under reducing conditions is shown in figure 3aporized   carbon monoxide is produced by Boudouard reactions (reaction (5.3)); (ii) the ZnO is reduced by carbon monoxide to zinc vapour (reaction (5.2)) and (iii) carbon dioxide takes part in the reaction (5.3) again.5.1.2.2O4 in the absence of a reducing agent is shown in figure 4a. TG shows a mass loss of about 2% from 38°C to 456°C. This mass loss is attributed to the evaporation of physically adsorbed water. At high temperature, 1144–1310°C, a deep valley in the DSC plot is due to the sintering of the sample. Figure 5c shows the ZnFe2O4 is sintering at 1216°C, and XRD analysis indicated that there is no phase transformation in the sample. These results indicate that thermal heating has no effect on the decomposition of ZnFe2O4 in the absence of a reducing agent.The thermal behaviour of ZnFe2O4 begins at 925°C [b). The TG curve shows a mass loss of about 50% in the temperature range from 823°C to 1165°C. This mass loss is due to the complete evaporation of zinc from ZnFe2O4 and a reduction of iron oxide to metallic iron. Figure 5d indicates that ZnFe2O4 is completely reduced to metallic iron.Under reducing conditions, the decomposition of the ZnFeat 925°C ,  can be written as follows:2O4 decomposes to ZnO and Fe2O3, as in the reaction (5.5), in the range of 925–968°C. A CO/CO2 atmosphere is produced by reduction processes and the Boudouard mechanism (reactions (5.6) and (5.11)). Gas/solid reactions between carbon monoxide and metal oxide  take place, and the reduction of zinc oxide and iron oxide to zinc and iron metals takes place.ZnFe5.2.2O4 are poor microwave absorbers. The ZnFe2O4 sample has significantly higher dielectric properties compared to ZnO. The change in the dielectric values . From the comparison of the DSC curve, the greater changes in imaginary permittivity  over the temperature range from 100°C to 1100°C at 2423 MHz frequency. There is a slight increase towards the high end of the temperature range.The real (2O4 decreases slightly with an increase in the temperature (300°C) due to removal of free water. The TG curve shows a mass loss of about 2% in this temperature range (a); this mass loss is attributed to the evaporation of physically adsorbed water. After that, there is a small increase in the a.The imaginary ) at a microwave power of 700 W are presented in 5.4.2.2O4 decomposition were interpreted based on the results of the XRD. The concentrations of ZnFe2O4, ZnO, FeO and metallic iron phases were plotted against the processing time. 2O4 with one stoichiometric amount of graphite. Initially, ZnFe2O4 decomposes to the ZnFe2O4, ZnO and FeO phases after 1 min, but grains containing ZnFe2O4 are still present. 2O4 is not attained and traces of franklinite are detected in the sample after 10 min. The wustite content increases with increase in reaction time from 0 to 5 min, but ZnO content decreases from 3 to 5 min. When the reaction time reaches 5 min, no additional reduction of ZnO occurs and the wustite content remains unchanged. At 9 min, no additional reactions occur in the sample. 2O4 phases are still present; this is due to the fact that the amount of carbon is insufficient for the complete decomposition of ZnFe2O4 and removal of the Zn from the sample.The rates of ZnFe2O4 was also reported by other researchers [2O4 at 750°C using carbon monoxide as the reducing agent. Hua et al. [3O4, FeO and zinc vapour at 1000°C. Li et al. [2O4 roasted at 750°C for 1 h decomposed into ZnO and Fe3O4. The results indicated that the rate of ZnFe2O4 decomposition with microwave heating is faster than with conventional heating. The formation of a mixture of FeO and ZnO with microwave instead of Fe2O3/Fe3O4 and ZnO with conventional heating is due to fast microwave reaction and reduction of Fe3O4 into FeO in a short time.The decomposition of ZnFeearchers ,25. Nyirearchers  reportedi et al.  indicate2O4 begins to decompose at 1 min, and the decomposition degree increases with increase in reaction time. A further increase in reaction time (at 5 min) resulted in ZnFe2O4 being consumed with the formation of FeO, metallic iron and ZnO. 2O4 to completely transformed into ZnO and wustite but difficult for reaction under one stoichiometric amount of carbon. The transformation of wustite into metallic iron is promoted as the concentration of FeO decreased compared to the metallic iron content . These results were also observed by Lee et al. [Figure 19c shows the wustite grain formed after 3 min of microwave heating. Spherical metallic iron is observed at the final stage of the reaction (figure 19d).The morphology changes of ZnFee et al. . Figure 2O4 reduced with one stoichiometric amount of graphite at different reaction times are shown in figure 20d), while the wustite peak intensity increases with increase in reaction time.The XRD patterns of the ZnFe6.2O4 by microwave heating have been studied. The following conclusions can be drawn:2O4 at room temperature were quite low. The influence of temperature on the real ((i) The dielectric values of ZnO and ZnFe2O4 is due to the low dielectric values of both samples. The microwave heating rate showed that the sample temperature increased with increase in microwave power and sample mass.(ii) The poor microwave absorption of ZnO and ZnFe(iii) The reduction degree of ZnO is significantly affected by the amount of the reducing agent; with two times the stoichiometric amount of carbon, almost a reduction degree of 99% has been achieved at 12 min using 700 W microwave power.2O4 completely transformed into ZnO and wustite in 3 min. The phase composition of ZnFe2O4 indicated that the ZnFe2O4 decomposed in three stages: reduction of ZnFe2O4 to ZnO and FeO, reduction of ZnO to Zn vapour and reduction of FeO to Fe.(iv) At two times the stoichiometric amount of graphite, ZnFeDielectric properties and carbothermic reduction of ZnO and ZnFe


Although marine aerosols undergo extensive photochemical processing in the troposphere, a molecular level understanding of the elementary steps involved in these complex reaction sequences is still missing. nCln–2(C2HO3)]+, n = 5–11, is studied by a combination of mass spectrometry, laser spectroscopy and ab initio calculations. Glyoxylate acts as a chromophore, absorbing light below 400 nm via two absorption bands centered at about 346 and 231 nm. Cluster fragmentation dominates, which corresponds to internal conversion of the excited state energy into vibrational modes of the electronic ground state and subsequent unimolecular dissociation. Photochemical dissociation pathways in electronically excited states include CO and HCO elimination, leading to [Nan–xCln–x–2HCOO]+ and [NanCln–2COO˙]+ with typical quantum yields in the range of 1–3% and 5–10%, respectively, for n = 5. The latter species contains CO2˙– stabilized by the salt environment. The comparison of different cluster sizes shows that the fragments containing a carbon dioxide radical anion appear in a broad spectral region of 310–380 nm. This suggests that the elusive CO2˙– species may be formed by natural processes in the troposphere. Based on the photochemical cross sections obtained here, the photolysis lifetime of glyoxylate in a dry marine aerosol is estimated as 10 h. Quantum chemical calculations show that dissociation along the C–C bond in glyoxylic acid as well as glyoxylate embedded in the salt cluster occurs after reaching the S1/S0 conical intersection, while this conical intersection is absent in free glyoxylate ions.Although marine aerosols undergo extensive photochemical processing in the troposphere, a molecular level understanding of the elementary steps involved in these complex reaction sequences is still missing. As a defined laboratory model system, the photodissociation of sea salt clusters doped with glyoxylate, [Na The complexity of these processes is a challenge for numerical climate models.λ > 290 nm, the wavelength range of solar radiation that reaches the troposphere.gem-diol form HC(OH)2COO– dominates,gem-diol. Our study using dry HCOCOO– thus represents only the first step towards a comprehensive understanding of glyoxylate photochemistry in this environment.Gas-phase sodium chloride clusters2 and CH2O, with minor contributions of CO and H2.–1.2 formation, from 214 kJ mol–1 to 181 kJ mol–1.et al.2, CO, formic acid, oxalic acid, and tartaric acid.In the gas phase, the major products of glyoxylic acid photodissociation as well as its thermal decomposition are CO2 in aqueous solution in its hydrated form, and the formation of adsorbed oxalate upon near-UV irradiation.2, reported by Ho et al.2, adsorbed formate and methoxy groups, while photodissociation at 350–450 nm leads to CO2, carbonate and formate. All these surface studies are interpreted in terms of photocatalytic activity of the support, while direct photolysis of e.g. the C–C bond in glyoxylate was not considered.Photocatalytic oxidation of glyoxylate adsorbed on quantum-sized ZnO was observed by Hoffmann and co-workers.Here we address the photochemistry of cationic sodium chloride clusters doped with a glyoxylate anion. Photodissociation cross sections are measured, and the photodissociation products are identified by mass spectrometry. Quantum chemical calculations of ground and first excited state provide a molecular level understanding of the observed photodissociation pathways. Comparison of the situation of the ion embedded in the cluster with the bare ion as well as the neutral molecule in the gas phase reveals the influence of the ionic environment.n+1Cln–1(C2HO3)+ are generated by electrospray ionization and transferred to a hexapole collision cell where they are thermalized in collisions with argon at room temperature. After injection into the ICR cell, the ion of interest is mass selected by resonant excitation of unwanted ions.The experimental setup consists of a Bruker Apex Qe Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer interfaced to a tunable optical parametric oscillator (EKSPLA NT342B) as described in detail before.Tunable laser light is allowed into the ICR cell for a defined period of time controlled by a mechanical shutter. Due to the long irradiation times of up to 20 s used in the present study, also very weak photodissociation cross sections can be determined quantitatively. For the calculation of the total photodissociation cross section, also the fragmentation occurring due to black body infrared radiation dissociation (BIRD)I0 represents the intensity of the precursor ion after laser irradiation, Ii the corresponding intensities of fragment i, h Planck's constant, c the speed of light, A the area illuminated by the laser beam, λ the wavelength, p the number of laser pulses, E the energy of a laser pulse, tirr the irradiation time of the precursor ion and kBIRD the rate constant for BIRD. This quantity can be measured independently viaeqn (2) where the precursor ion is stored for different times and exposed to the room temperature blackbody radiation. Since the dissociation due to BIRD follows an exponential law, the fit gives the rate constant kBIRD.σi are calculated viaeqn (3):Ii,i is the intensity of the fragment after irradiation of the precursor ion with UV light and Ii0, the intensity of the fragment contribution due to BIRD.Partial cross sections of the individual fragments kBIRD and the photon flux inside the ICR cell. A peak at Δm/z = 0.17 was present in small amounts in most experiments, which was too close to be ejected without exciting the ion of interest. This peak was assigned, and for stoichiometric reasons its photofragments do not interfere with the major photofragments of the ion of interest, see Fig. S1  was used as solvent. The measurements were performed with a NaCl concentration of 5 mmol L–1 and 1 mmol L–1 glyoxylic acid.All chemicals were purchased from Sigma Aldrich with a purity of at least 98%. Isotopically enriched NanCln+1]– clusters and modified to [Nan+1Cln]+. For each cluster size and for each position of the Cl– ion, we replaced the Cl– ion by the C2HO3– anion and optimized the cluster at the respective level of theory. For n = 5, further isomers with different O–C–C–O dihedral angle were created starting from the respective minima. Several structures were also created by incorporating the ion into the cluster or on its surface. Initial structures for clusters after glyoxylate dissociation were built from the optimized clusters. Cluster optimization was performed at the B3LYP/def2TZVP and B3LYP/6-31+g* level of theory for smaller and larger systems, respectively, with the dispersion correction (D2) as introduced by Grimme.Structure and photochemistry of the clusters were also explored using methods of theoretical chemistry. Initial structures were taken from the Cambridge Cluster Database– ions were present in the cluster ; these states disappear for glyoxylate in the salt environment. The shape of the C2HO3– absorption spectra was modeled using the linearized reflection principle approximation.Excited states of clusters were calculated at the EOM-CCSD level. The TDDFT method with two tested hybrid functionals, BHandHLYP and CAM-B3LYP, predicted artificial charge transfer states when ClDFT and TDDFT calculations were done in the Gaussian software package,535Cl3(C2HO3)]+ cluster was investigated experimentally in the range of 225–400 nm. The measured photodissociation cross section for [Na5Cl3(C2HO3)]+, including the contribution of the individual fragments, is shown in –18 cm2, and a weaker band located at about 320–380 nm with cross sections below 10–19 cm2.The photodissociation spectrum of the +, calculations show that there are several isomers that lie close in energy ]+ isomers are shown in δ, with the isomers with δ ∼ 45° (II–V) absorbing considerably more in the 210–230 nm region. Compared to the spectrum of C2HO3–, the intensity of the 220–240 nm absorption band is predicted to be markedly reduced, and a more structured spectrum can be expected.Electronic transitions of selected ˙+ fragment, a carbon dioxide anion radical embedded in the salt cluster produced in reaction (4), along with the elimination of the formyl radical HCO˙,2 dissociation along reaction (3) is energetically more favorable with 2.43 eV, and might be expected to be a more efficient reaction channel in the ground state. This fragment, however, is not observed over the studied wavelength range. We note that the situation is similar for the photochemistry of the isolated glyoxylate anion, where the dissociation into CO2˙– and HCO˙ is 0.75 eV higher in energy than the dissociation into CO2 and HCO–, see reactions (1) and (2) in The final proof for excited state photochemistry is provided by the + cluster, the CASSCF calculations predict that the energy provided by the excitation into the S1 state suffices to directly reach this intersection. After funneling into the electronic ground state in the vicinity of the conical intersection, the glyoxylate anion might further dissociate, be formed again in a vibrationally hot ground electronic state, or the dissociating HCO˙ radical may react with CO2˙– and transfer a hydrogen atom to form formate HCO2– and CO. The barrier for such an H atom transfer in the ground state is calculated to be 1.93 eV and 2.75 eV for C2HO3– and NaC2HO3, respectively, at the B3LYP+D2/def2TZVP level of theory. Both values are significantly smaller than the initial excitation energy, thus formate formation is energetically accessible. Due to the momentum gained along the dissociation coordinate, the main channel can be expected to be HOCO˙ and Na+·CO2˙– formation for glyoxylic acid and Na(C2HO3), respectively. With the significantly larger number of degrees of freedom in Na5Cl3(C2HO3)+, however, the probability for energy redistribution increases, and internal conversion reaching the original structure may prevail, followed by statistical dissociation from the electronic ground state. This would explain the dominance of the stoichiometric fragments NaxClx–2(C2HO3)+ and NaxClx–1+. It may be noted that this photochemical reaction pathway does not require a photocatalyst, as implied in earlier studies of adsorbed glyoxylate.This picture changes dramatically when glyoxylate is protonated to form glyoxylic acid  or when 2˙– is only a few microseconds, because the free radical anion is metastable.2˙–, and it has been observed in liquid water,2 clusters2˙– as an intermediate in a future electrochemical utilization of carbon dioxide,The most intriguing fragmentation channel is the dissociation of glyoxylate into the reactive HCO˙ radical and a carbon dioxide radical anion stabilized by the ionic environment of the salt cluster.2˙– fragment was found not only in the deeper UV in the wavelength range of 225–244 nm with no relevance for tropospheric chemical reactions (the corresponding light is completely absorbed in the stratosphere). The fragment was also measured in the actinic region of 310–370 nm, i.e. at wavelengths that reach the ground and thus are able to induce photochemical reactions in the troposphere.It is important to note that the CO5Cl3]˙+ fragment formed via reaction (13) is observed in the deeper UV up to 243 nm. Its formation requires a charge transfer reaction from glyoxylate to the positive charge centers, i.e. one or more sodium ions. This charge transfer followed by release and decomposition of the C2HO3˙ radical is calculated to be 5.04 eV endothermic. The C2HO3˙ radical is unstable and is predicted to dissociate into CO2 and CHO˙. This reaction may also proceed in two steps, i.e. CHO˙ dissociation followed by charge transfer with concomitant loss of CO2 from the intermediate Na5Cl3CO2+ cluster.The [Na5Cl3(C2HO3)]+ ion might be extrapolated to sea salt aerosols, we repeated the experiment with clusters containing up to 11 sodium ions. All studied clusters exhibit the α-cleavage of the glyoxylate as a photodissociation channel, resulting in a sodium chloride cluster containing CO2˙–. n = 5–9 and the very small cross sections of the corresponding CO2˙– fragment down to 10–21 cm–2. The carbon dioxide anion fragments appear roughly in the wavelength range of 310–370 nm, which corresponds to 4.00–3.35 eV, in agreement with theoretically calculated energies that predict nearly constant dissociation energy of 3.2–3.5 eV in the investigated cluster size range, see reactions (14)–(19) in n = 5, the quantum yield lies typically in the range of 5–10%. The clusters with n = 6, 11 also show quantum yields up to 5.6% while the values for n = 7–10 are between 1–3% ]+ experiment with the global tilt spectrumThe measured photodissociation cross sections are used to estimate the photochemical lifetime of glyoxylate on the surface of sea-salt aerosols. Solar irradiance data was taken from terrestrial reference spectra for photovoltaic performance evaluation.x or [NaxClx–1(C2HO3)]. A genuinely photochemical product is the carbon dioxide radical anion CO2˙– embedded in the salt environment. This radical is produced by photolysis of the C–C bond of glyoxylate, accompanied by the release of a neutral HCO˙ radical. The salt environment stabilizes CO2˙–. The radical anion was observed in the 300–400 nm wavelength range for all cluster sizes [NanCln–2(C2HO3)]+, n = 5–11, suggesting that it is formed as a transient species in the troposphere. The photochemical lifetime calculated with typical solar irradiation data is in the range of 10 h, which renders the photodissociation of glyoxylate a potentially relevant reaction in the photochemical aging of sea-salt aerosols. Excited state calculations reveal that C–C bond cleavage takes places by surpassing a relatively small barrier along the excited state reaction coordinate and reaching the S1/S0 conical intersection. In the isolated glyoxylate anion in the gas phase, the S0 and S1 states are well separated, which prevents non-radiative relaxation to the electronic ground state. The electronic structure of gaseous neutral glyoxylic acid, however, is very similar to glyoxylate interacting with the salt environment. Repeating the calculations with NaC2HO3 reveals that the interaction of the deprotonated acid functional group with a single sodium ion is sufficient to restore the photochemical behavior of neutral glyoxylic acid.We investigated photodissociation of salt clusters doped with glyoxylate in the wavelength range of 225–400 nm. Internal conversion of the excitation energy results in loss of stoichiometric cluster fragments [NaCl]There are no conflicts to declare.Supplementary informationClick here for additional data file.


The data presented here are related to the research article entitled “Expression, purification, and preliminary characterization of human presenilin-2" E. coli strain C43 (DE3) was extracted by detergent solubilisation. The sample isolation efficiency by detergents and the protein identification by mass spectrometry and western blot are described.Human Presenilin-2 is the catalytic subunit of γ-secretase and a possible calcium leakage channel  This data article describes the near and far UV circular dichroism measurements and the data deconvolution in terms of secondary structure at 4 and 98 °C. Also, a refolding spectrum is presented.The raw CD spectra used for deconvolution of the helix and stand segments and average length are deposited into Protein Circular Dichroism Data Bank with PCDDBid: CD0005962000 (4 °C far UV), CD0005963000 (98 °C far UV), CD0005964000 (back to 4 °C far UV) and CD0005965000 (4 °C near UV CD). Specifications TableValue of the data•Data on solubilization efficiencies of membrane proteins are rare. Benchmarking the different effects of detergents from various classes on solubilization of membrane proteins provides relevant data for sample preparation and extends the existing knowledgebase of membrane protein solubilization.•Sample characterization by MS and western blot is required for comparison of biophysical data obtained from samples.•Near and far UV CD data of PS2 characterize the state of the protein and will allow for comparison with data of activated PS2 to elucidate changes in secondary and tertiary structure relevant for the acquisition of enzymatic functionality.•The presented CD data show that PS2 does not unfold upon heating but changes its structure from mainly α-helix to β-strand by irreversible transition.1Presenilins are the catalytic subunits of γ-secretase which produces the neuro-toxic Aβ peptides relevant for Alzheimer Disease E.coli membrane. The sample identity is shown by MS and western blot. The secondary structure of PS2 is obtained from far UV CD data and the tertiary structure fingerprint by near UV CD. The CD data after re-cooling to 4 °C allow assessing the reversibility of structural transitions.This data contains the table of the solubilization efficiency of 13 detergents from 3 classes with various chain length and charge properties in extracting hisPS2 from The identified peptides are shown in bold red. Transmembrane segment are in bold blue and underlined.22.1Cell lysis and membrane preparation is similar as described in 2.2Chromatographically isolated trimeric full length hisPS2 2.3−1 cm−1 by Expasy ProtParam The concentration of hisPS2 in CD buffer  FC14) were determined by absorbance at 280 nm using the calculated extinction coefficient of 76780 MCD spectra were measured using an Aviv CD-425 spectrometer from 260 to 185 nm for far UV and 350 to 250 nm for near UV


The article describes data concerning the separation performances of polymeric hollow-fiber membranes.2 post-combustion capture: rigorous analysis and simulation of a single stage gas permeation process”  2 separation degree.The data were obtained using a model for simulating gas separation, described in the research article entitled “Interplay of inlet temperature and humidity on energy penalty for CO Specifications TableValue of the data•The data describe the separation performances and the specific energy requirement of a single-stage membrane unit; hence they can be used in future works to compare simulation results of different membrane system models.•2 capture from exhaust flue gases; hence these data can be used to support the study of more complex membrane separation systems, such as those based on dual-stage configuration.The data contain key information regarding the performances of a single-stage membrane system operating the CO•2 capture system based on a single-stage membrane configuration.The data can be used by other researchers for a preliminary assessment of energy penalty inflicted to power plants integrating a post-combustion CO•2 capture reuse applications.The data are valuable for other studies concerning the conceptual design of single-stage membrane systems for CO12 capture membrane system. Data consist of molar fractions of permeate stream, membrane area and specific energy requirement of membrane system. Data were obtained by varying the CO2 separation degree from 0 to 100% and the feed pressure from 4 bar to 10 bar.Data shared in this article concern the validation of a model for evaluating the performances of a post-combustion CO2With the aim to validate a model for simulating the gas separation in polymeric hollow-fiber membrane modules 2 separation degree and the feed pressure. It is noted that the trend of simulated data varying the CO2 separation degree fits very well with the literature data. For instance, setting a feed pressure of 10 bar and increasing the CO2 separation degree from 20% to 100%, 2 molar fraction reduces from around 70% to 30% and N2 molar fraction increases from around 20% to 60%. Almost the same values are observed in 2 and N2 molar fractions attain the same values (≈45%) for a CO2 separation degree of around 90%. The good agreement is also confirmed at a lower feed pressure (4 bar), where both models show that CO2 and N2 molar fractions pass from 50% to 25% and from 40% to less than 70% respectively, for a corresponding increase of CO2 separation degree up to 95% (p to 95% c and d.2 for a CO2 separation degree of 90%.2 separation, assuming feed pressures values of 4 bar and 10 bar. Specific energy requirement exhibits an exponential decreasing trend in both models; values evaluated by the model proposed are comparable or slightly lower than that in 2 separation degree of 90%, specific energy requirement for a feed pressure of 4 bar states at less than 150 kWh/tonne CO2 separated in both models; increasing feed pressure to 10 bar, specific energy states at less than 250 kWh/tonne in Finally,


These tables have now been updated. To reflect the updated Table S7, the number of significantly differentially expressed genes between embryonic time points has also been updated in Figure S4A, as shown below.In Table S1, the subheadings of the mean and standard deviation columns were mislabeled as EPI and PE throughout the spreadsheet, even where the data presented were derived from other lineages. The correct column headings appear in the updated Table S1.In Table S5, we accidently inverted the prefixes “E5” and “E5_prelin” in labels of columns containing mean expression and standard deviation in the three sections with the subheadings “E5_prelinvsE5_EPI”, “E5_prelinvsE5_PE” and “E5_prelinvsE5_TE.” In addition, in sections comparing E5 vs E6 and E6 vs E7 cells in Table S5, we presented the data by lineage first and then time . However, the labels of these columns appeared as time first and then lineage , resulting in a mismatch between the label and the data columns. These have now been corrected.None of these changes, which appear in the article online, affect the conclusions of the article. We sincerely regret these mistakes and apologize for any confusion that may have arisen.


TC of 5.3 K. Structure refinements indicate that the consecutive phase transitions are correlated to the changes in the Bi–Te bond and bond angle as function of pressures. The Hall Effect measurements reveal an intimate relationship between superconductivity and the unusual change in carrier density that points to possible unconventional superconductivity.Strong spin orbital interaction (SOI) can induce unique quantum phenomena such as topological insulators, the Rashba effect, or p-wave superconductivity. Combining these three quantum phenomena into a single compound has important scientific implications. Here we report experimental observations of consecutive quantum phase transitions from a Rashba type topological trivial phase to topological insulator state then further proceeding to superconductivity in a SOI compound BiTeI tuned via pressures. The electrical resistivity measurement with V shape change signals the transition from a Rashba type topological trivial to a topological insulator phase at 2 GPa, which is caused by an energy gap close then reopen with band inverse. Superconducting transition appears at 8 GPa with a critical temperature  Studies on the systems of strong spin orbital interactions (SOI), which play important roles in forming novel quantum states, intensively grown12345679372Te32Te32Se3Rashba polar semiconductor BiTeI hosts the largest known spin split band from its bulk polar atomic configurationThis paper reports on the discovery of superconductivity in BiTeI induced by pressure that borders the transition from a Rashba type topological trivial state to a topological insulator state. Structure evolutions, including local structure distortion at high pressures, are investigated by Raman spectroscopy in conjunction with high pressure synchrotron X-ray diffraction.P3m1 with lattice parameters of a = 4.3392 Å and c = 6.854 Å1010TC(onset) of 5.3 K, where the value of TC is defined using the methodTC(onset) value decreased to 4.5 K at 14 GPa with a rate dTC/dP = −0.14 K/GPa and then reached approximately 4.1 K with a non-linear decrease as shown in The ambient phase of BiTeI crystallizes into a non-centrosymmetric layered structure of the trigonal space group PC) of ~2 GPa where the gap closes in the Rashba phase. Upon crossing the PC, the inversion and opening up of the Bi 6pz orbital and Te/I-5pz orbitals leads to the semiconducting behavior as shown in PC as shown in ac magnetic susceptibility measurement that results in transition with TC at ~5 K that is similar to the conductivity measurements as shown in H perpendicular to the ab plane of the BiTeI single crystal. TC decreases with the applied magnetic field H. The change in TC with H is shown in HC2(0) = −0.691TC × [dHC2(T)/ dT]|T = Tc, the upper critical field Hc2 was estimated to be 2.9 T and 2.8 T at 14 GPa and 26 GPa, respectively, for the magnetic H perpendicular to ab plane, which are comparable to those of Bi2Te32Te3H perpendicular to the ab plane of the sample up to 5 T at a fixed temperature (30 K) for each given pressure. The samples show n type carrier features in all pressure temperature ranges as shown in The superconductivity nature in the BiTeI single crystal was validated by the High pressure synchrotron X-ray diffraction of BiTeI was conducted  to trace1 + 2E1(1) vibrational mode is gradually suppressed and disappears at ~4 GPa at ambient phase, which has relevance with the electronic topological transition, although no sufficient theoretical evidence proves this condition; (ii) A1(2) and E(2) vibrational modes blue shift up to ~7.5 GPa, and a new mode M1 at ~136 cm−1 appeared above ~8.9 GPa, which should be the signatures for the first structure transition; (iii) all the three modes become softened above ~15.8 GPa, whereas a new mode M2 appeared at ~163 cm−1 that can be associated with the further high pressure induced structure transition.Raman spectroscopy was conducted to obtain insights into the local structure evolution at high pressure levels . The symP3m1 (denoted as α BiTeI) ambient phase to the orthorhombic Pnma (denoted as β BiTeI) high pressure phase. The second structure transition should be at 15.8 GPa to 17.2 GPa from the orthorhombic Pnma high pressure phase to the tetragonal P4/nmm (denoted as γ BiTeI) high pressure phase13The high pressure synchrotron X-ray diffraction and high pressure Raman spectroscopy experiments jointly indicate that the first pressure induced structure transition should be at 7.5 GPa to 8.9 GPa from the hexagonal TC(a) and carrier densities (b) as function of pressures. BiTeI is of n type carriers with a carrier density of 3.62 × 1019 cm−3 at ambient pressure as measured from the Hall coefficient similar to that in21 cm−3 at 10 GPa as indicated in TC(onset) decreases with the further pressure increase to 32 GPa.+ layer and I− anions; however, Bi-I contacts are considered to be ionicThe previous structureTo understand the structural related origin of transport properties, we plotted the bond length of Bi-Te and Bi-I, the bond angle of Te~Bi~Te obtained from the Rietvield Refinements based on our experiments in PC. The decrease in the Bi-I bond length with pressure to 2 GPa indicates an enhanced band width, which results into a gradual narrowing and closing of the band gap. The increase in these structural parameters with pressure to 8 GPa in turn leads to the gradual reopening of the band gap above 2 GPa. Signatures of V shape change of resistivity from transport measurements shown in + ladders, where Bi-Te has weak Bi−Te covalent bonds surrounded by I− ions+ ladders along the b-axis and suppresses the band gap. The above structure distortion can contribute to less semiconductive behavior and properly coincides with the resistivity decrease in this phase as shown in TC decreases dramatically, whereas the carrier density maintains almost no change in the pressure range from 11 GPa to 20 GPa. This condition is inconsistent with conventional superconductivity, where TC generally changes as function of carrier densityN(EF) can be balanced to control TCas stated by BCS theory or the McMillan electron-phonon coupling formalismB0 and lattice volume V0 in phases α and β are comparable as shown in β can preserve a similar lattice property with phase α. Considering that superconductivity emerged at the border across the topological phases α to β, this condition implies that the superconductivity in this pressure range should result from a topological precursorThe BiTeI structure in phase β (high pressure phase 1) consists of positively charged (BiTe)TC in this phase initially decreases when the bond length of the Bi-Te atoms decreases. TC then increases slightly when the bond lengths of Bi-Te and Bi-I, as well as the Te~Bi~Te bond angle, remain almost non change. These observations indicate that the TC variation correlates with the structure evolution at pressures. B0 in phase γ is much larger than that in phase β, whereas the refined V0 is much smaller than that of phase β, which indicates that the phase γ structure differs from that of phase β. The ac magnetic susceptibility measurement shows that the superconducting volume fraction increases with applied pressure, which signifies that the superconductivity transforms from the surface states at the border range in phases α to β to bulk nature in phase γ.The bond length of the Bi-Te atoms in phase γ (high pressure phase 2) decreases, whereas the Bi-I bond length remains almost constant. The electronic band structure shows that BiTeI in this phase is metallicIn summary, we successfully observed pressure induced consecutive transitions for a SOI compound from a Rashba-type topological trivial phase to a topological insulator followed by a classical quantum condensation . The evolutions properly correlate with the bonding parameter changes of the structures. The observed superconductivity from the topological precursor phase points to a possible unconventional nature.−4 Pa and heated to 660 °C for 24 h, followed by slow cooling at a rate of 12 °C/h to 100 °C before quenching to room temperature.The BiTeI single crystals are grown utilizing the Bridgeman method. The Te powder, Bi, and I reagents are mixed together at a proper stoichiometric ratio. The mixtures are then grounded thoroughly in an agate mortar to ensure homogeneity. The mixtures are sealed in an evacuated quartz tube under 10The electronic transport properties of BiTeI at a low pressure range (<2 GPa) are measured through four probe electrical conductivity methods in a Piston Cylinder cell made of CuBe alloy. A piece of the BiTeI single crystal with a dimension of 2 mm * 1 mm * 0.15 mm was loaded into a Teflon-made vessel with Daphne oil loaded as the pressure transmitting medium. A manganese copper wire was placed near the sample as a pressure marker. The cell was placed inside a Maglab system with an automatic temperature control model. A semiconductor thermometer was mounted on the surface of the cell to monitor the temperature. The electronic transport properties of BiTeI with pressure higher than 2 GPa are measured through four probe electrical conductivity methods in a diamond anvil cell (DAC) made of CuBe alloy. The diamond culet is 300 μm in diameter. The Au wires with a diameter of 18 μm are used as electrodes. A T301 stainless steel gasket was compressed from a thickness of 250 μm to 40 μm, and then a hole at 150 μm in diameter was drilled. The cubic BN applied as an insulating layer was pressed into this hole. A small center hole at 100 μm in diameter was further drilled to serve as the sample chamber, where NaCl fine powder serves as a pressure transmitting medium and a piece of BiTeI single crystal with dimensions of 90 μm * 90 μm * 20 μm was loaded. A piece of ruby was loaded simultaneously as a pressure marker. The DAC was placed inside a Maglab system with automatic temperature control. A thermometer was mounted near the diamond to monitor the temperature. The high pressure Hall coefficients are measured utilizing the Van der Paul method.−1 in a DAC. Silicon oil was applied as the pressure medium. The diamond culet is 300 μm in diameter. The T301 stainless steel gasket was compressed from 250 μm to 40 μm, and a center hole at 140 μm in diameter was drilled. A small piece of ruby was placed aside the specimen to measure pressure.The high pressure Raman experiments are conducted on single crystal BiTeI with dimensions of 60 μm * 60 μm * 20 μm with Renishaw Raman Spectroscopy with a laser wavelength of 532 nm and spectral resolution ~1 cmθ versus intensity data utilizing the Fit2D software package24High pressure synchrotron X-ray diffraction experiments are performed at 16 BMD, HPCAT of the Argonne National Laboratory with a wavelength of 0.4246 Å in a symmetric DAC with a culet at 300 μm in diameter. The T301 steel gasket was pre-indented from 300 μm to ~40 μm, and a center hole at 150 μm in diameter was drilled. The hole was compressed to 120 μm with neon loaded as a nearly hydrostatic pressure transmitting medium. Ruby balls are placed near the sample as pressure markers. The X-ray diffraction patterns are collected with a MAR 3450 image plate detector. The obtained 2D image plate patterns are converted to 1D 2How to cite this article: Jin, M.L. et al. Superconductivity Bordering Rashba Type Topological Transition. Sci. Rep.7, 39699; doi: 10.1038/srep39699 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.


The oxidation mechanism of sulfides is the key issue during the sulphide–metallurgy process. In this study, the phase transformation and element migration were clearly demonstrated by in–situ laboratory–based X–ray diffraction (XRD) and energy–dispersive X–ray spectroscopy (EDS), respectively. The reaction sequence and a four–step oxidation mechanism were proposed and identified. The elemental distribution demonstrated that at a low temperature, the Fe atoms diffused outward and the Ni/Cu atoms migrated toward the inner core, whereas the opposite diffusion processes were observed at a higher temperature. Importantly, the unique visual presentation of the oxidation behaviour provided by the combination of in–situ XRD and EDS might be useful for optimising the process parameters to improve the Ni/Cu extraction efficiency during Ni–Cu sulphide metallurgy. Magmatic–sulphide deposits host ~40% of the global Ni resources and supply ~60% of the Ni in the world market. With the unceasing mining and consumption of the rich ore resources, the extensive exploitation and utilization of low–grade nickel sulphide ores are becoming important problems for the sustainability of nickel production.Since the first super–large magmatic Ni–Cu–platinum–group elements (PGE) deposit  was discovered in 1883, several super–large Ni–Cu–PGE deposits rich in sulphides have been mined , Noril’sk Ni–Cu–PGE and Pechenga Ni–Cu–PGE deposits (Russia), Voisey’s Bay Ni–Cu–Co deposit (Canada))6. The oxidation behaviour of sulphide ores, which is of principal and vital importance in the sulphide–extraction metallurgy process, is complex and highly dependent on the sulphides phases in the minerals. Pentlandite (expressed as Pn) and chalcopyrite (expressed as Ccp), which are the common minerals used in pyrometallurgical nickel and copper production, respectively, have been theoretically and experimentally investigated during the oxidative–roasting process by many researchers for decades16. A detailed review of the oxidation mechanisms of Pn and Ccp is presented in Fig. As a traditional pyrometallurgy method, the flash smelting–converter–grinding–floatation–anode electrolysis process requires a high nickel concentrate and is tedious and complicated. From the 1960s to the 1990s, an oxidation–sulphation roasting process followed by leaching was proposed and investigated to treat low–grade Ni–Cu sulphide oreset al.8. Recently, researchers studied the isothermal oxidation behaviour of synthetic Pn in depth and proposed a novel stepwise phase–transformation mechanism14. As shown in Fig. xSy, FeyNi1–yS, Ni3S2, NiS) and finally oxidised into Fe2O3, NiO, and NixFe2+xO4. For the past few years, researchers have tended to investigate the oxidation behaviour of Pn taken nickel concentrate as a raw material19.Early on, the various oxidative reactions of natural Pn were deduced and summarised via thermogravimetric (TG)/mass spectroscopy (MS) analysis, differential thermal analysis (DTA), and X–ray diffraction (XRD) analysis by Dunn 23. Prasad et al.17 suggested that it was extremely important and necessary for copper extraction to concentrate on the oxidative–roasting procedure of Ccp. Various reactions occurring in the oxidation of Ccp were summarised in early studies and are briefly presented in Fig. 25. As shown in this figure, the first stage is the oxidation of Ccp into Cu2S (or Cu5FeS4) and FeS. This is followed by the formation of metal sulphates and finally the decomposition of the sulphates of iron and copper into oxides . A. Baba et al.23 conducted a detailed review of the role of Ccp in the pyrometallurgical and hydrometallurgical processes of copper, and suggested that low–grade complex sulphide ores have attracted attention because of the recent decline in deposits of high–grade ores.As the most exploited mineral for the extraction metallurgy of copper, Ccp has been extensively studied theoretically and experimentally26 have investigated the preferential oxidation of Fe and S during the roasting process using energy–dispersive X–ray spectroscopy (EDS), reporting that the Ni or Cu tends to diffuse into the centre while Fe migrates outward to the oxide rim layer.Another interesting and important problem that occurs during the oxidative roasting of polymetallic sulphides is the elemental distribution of the ore grains. Many researchers34. In this study, the oxidation behaviour of a Ni–Cu sulphide ore was investigated in detail during the roasting process using in–situ laboratory–based XRD and EDS in tandem.Given the aforementioned findings, the oxidation mechanism of the sulphide mineral, which is a long– and well–studied problem, has been investigated in detail using traditional analysis and characterization methods, such as TG, DTA, MS, XRD and EDS. Because of the complexity of the Ni–Cu sulphide ore and the weakness of traditional characterization methods, some of the oxidation mechanisms proposed by early researchers should be further examined. However, thorough studies on the oxidative mechanism of polymetallic sulphide minerals have rarely been reported. The in–situ XRD method, which has recently been used to investigate the mechanism of the metallurgical process, is growing in popularity4.5Fe4.5S8–CuFeS2–SO2–O2 system at 450 to 900 °C in air (p(O2) = 0.21 atm) was developed using the Factsage software package35. As shown in Fig. 2(SO4)3, CuSO4, and NiSO4) together with Fe2O3. As the temperature increases, the predominance areas shift toward the formation of oxides.To investigate the thermodynamics of the Ni–Cu sulphide mineral system, a phase–stability diagram for the Ni2(SO4)3, CuSO4, and NiSO4, respectively; and finally decomposed at higher temperatures.The TG and differential TG (DTG) curves for different heating rates in Fig. 7S8)) slowly decreased, but as the temperature increased, the peak intensity of pyrite (FeS2) increased, which indicates that Pn, Ccp, and pyrrhotite slowly decomposed36. When the temperature reached 350 °C or higher, the sulphides oxidised rapidly and disappeared round 400, 450 and 500 °C for Pn, Pyrrhotite and Ccp respectively, and the initial oxidative products were metal sulphates (Fe2(SO4)3, CuSO4) and NiS. In the range of 350 to 650 °C, the peak intensity of Fe2O3 gradually increased, reaching its maximum at 650 °C. As the temperature increased from 500 to 700 °C, the NiS phase gradually decreased and was eventually eliminated; however, the spinel and NiO phases exhibited a different behaviour. As the temperature increased from 650 to 900 °C, the spinel and NiO phases increased, while the Fe2O3 phase tended to decrease. As shown in Figs 2(SO4)3 phase appeared at 400 °C and disappeared at ~650 °C 3 phase at 400 °C and then gradually disappeared with the appearance and increase of the CuO.CuSO4 phase at 700–800 °C. Finally, the CuO.CuSO4 phase disappeared at 850 °C  fixed model. According to the patterns shown in Fig. 8. Then, both the Pn and Ccp disappeared rapidly at ~425 °C, as shown in Fig. 2O3 above 425 °C, as shown in Fig. Initial oxidative stage: At the beginning, the sulphide–mineral sample hardly changed as the temperature increased. However, there may have been subtle variations in the peak intensities for Pn and Ccp, as shown in Fig. 2(SO4)3 and CuSO4) were formed almost instantaneously around 425 °C and increased gradually with the increase of the oxidation temperature. Figure 2(SO4)3 phases gradually transformed into iron oxide (Fe2O3) and iron oxide sulphate (Fe2O3.5Fe2(SO4)3) in the temperature range of 500 to 700 °C. Then, the iron oxide sulphate (Fe2O3.5Fe2(SO4)3) decomposed into Fe2O3 and disappeared at ~750 °C.Sulphation stage: As shown in Figs 4 was rapidly generated around 425 °C and remained stable below ~600 °C. CuO.CuSO4, which was detected in the range of 650 to 750 °C, was the decomposition product of CuSO4  increased rapidly around 500 °C and reached its maximum value when the temperature increased to ~750 °C. In addition, as shown in Fig. 2O3 diffraction peak profile occurred during the heating and cooling processes, which might be the results of the growth of Fe2O3 crystal. As shown in Fig. 2O3 firstly increased at the heating stage, remained constant at the temperature range from 600 °C to 700 °C, and increased at temperature up to 800 °C, then remained unchanged until the cooling stage. The spinel phase was initially generated around 750 °C, as shown in Fig. 2O3 was reduced as the temperature increased. As shown in Fig. Spinel–formation stage: As demonstrated in Fig. Cooling stage: The phase components of the sample remained constant in the cooling stage, as shown in Fig. 2(SO4)3 outer layer, the intermediate thin band of the NiS phase, and the inner core of Pn or 9Sx8– (Pn’). However, for the Ccp particles .The elemental distribution of the cross–section of the particles was studied by EDS, as discussed in this section. The SEM and EDS analysis of Pn and Ccp grains at different temperatures are shown in Figs les Fig. , the out2) diffusing outward collided with the O2 undergoing inward diffusion at the rim of the Fe2O3 layer. As shown in Figs 2(SO4)3 outer rims were then formed at both the Pn and Ccp grains. Simultaneously, the inward diffusion of O2 resulted in Ni– and Cu–enriched cores of Pn and Ccp, respectively. The Cu–enriched core further sulphated into CuSO4, whereas the Ni–S enriched core remained stable at 550 °C. This phenomenon is consistent with the sulphate–leaching experiments 3 layers into Fe2O3 at 650 °C  in the Pn grain 22. Recently, researchers used the ab–initio density functional theory to investigate and explain the preferential oxidation of Fe at the Pn and Ccp surface37. And, based on the characterization presented in the present study, this preferential oxidation may have resulted from the chemical–affinity of metals  for oxygen and sulphur38. While the Fe was preferentially oxidized into Fe–O phase on the surface of Pn or Ccp crystal structure, the concentration of Fe–S declined sharply, resulting in the outward migration of Fe atoms. Then the Ni/Cu atoms diffused into the inner core and formed Ni–S or Cu–S phase.Considering the aforementioned results, the reaction sequence of the Ni–Cu sulphide ore during the roasting in air was deduced, as summarised in Table 2O3 remained at the interlayer between the outer Fe2(SO4)3 layer and the inner core  at this stage. A large amount of SO2 gas, which was produced by the oxidation of Fe in the interlayer, diffused outward, possibly reacted with O2 to form SO3, and then transformed the previously formed Fe2O3 layer into the outer Fe2(SO4)3 layer. At this stage, the domain reaction was the sulphation of Fe and Cu, and the NiS in the inner core remained stable.As the temperature increased from 450 to 550 °C, Fe and S were continuously preferentially oxidized over Ni and Cu, but the Fe4 was formed at the internal layer between the NiS core and the Fe2O3 outer rim at this stage, owing to the small amount of SO2 concentrate produced by the decomposition of Fe2(SO4)3 and CuSO4. A small part of the CuSO4 decomposed and formed a CuO.CuSO4 rim, yet most of the CuSO4 remained stable in the inner core. Hence, this stage was suitable for the sulphation roasting of nickel concentrate, which simultaneously leached Ni and Cu in water and separated Fe from the Ni–Cu sulphide mineral.The sulphation of Ni occurred at a higher temperature (approximately 650–750 °C), and a small amount of NiSO4, CuSO4, and NiSO4 and the formation of the spinel phase . The Ni and Cu tended to react with the Fe2O3 to form a stable spinel phase. The high chemical stability of the spinel phase may lead to the formation of chemical potential at the reactive interface, then may have caused the outward diffusion of Cu/Ni and the inward diffusion of Fe at a higher temperature43. Moreover, the CuxFex3−Oy4− was diffusely distributed in the grain, while the NixFex3−Oy4− was just an internal rim with the inner core of NiO. And it may be due to the difference in cation diffusion rates between Ni and Cu during the roasting process.The final stage involved the decomposition of CuO.CuSOIn conclusion, the oxidation behaviour of a Ni–Cu sulphide ore, which is closely related to the sulphide–extraction metallurgy process, was thoroughly investigated by in–situ laboratory–based XRD and EDS. A four–step oxidation mechanism, including the preferential oxidation of Fe and S, metal sulphation, the decomposition of sulphates, and the formation of a spinel phase, was proposed according to phase–diagram analysis, TG–DTG analysis, the sulphate–leaching process, and in–situ XRD patterns. The reaction sequence that occurred during the oxidation of the Ni–Cu sulphide ore was summarised. In addition, the EDS elemental distribution demonstrated that the Fe atoms diffused outward and the Ni/Cu atoms migrated toward the inner core during the first three stages, whereas these diffusion processes were opposite at the final stage, possibly because of chemical–affinity of metals  for oxygen and sulphur and the high chemical stability of the spinel phase, respectively. A unique visual characterization of the oxidation mechanism in the Ni–Cu sulphide ore roasting process was performed by a combination of in–situ XRD and EDS. This mechanism may be conducive to an alternative metallurgy process for the Ni–Cu sulphide ore.47. The Rietveld refinement of the diffraction pattern resulted in good–quality fits with a goodness of fit (Gof) of nearly 2, as shown in Fig. A Ni–Cu sulphide ore sample, which was a product of flotation and originated from Jinchuan Group Ltd., China, was investigated. The powder sample was dried at 100 °C for 24 h and passed over vibrating sieves to obtain an extremely fine powder with a diameter of less than 74 um. XRD analysis indicated that the sample was composed of Pn, magnetite, Ccp, pyrrhotite, lizardite, pyrite, and quartz. XRD quantitative phase analysis (QPA) was performed using the Rietveld refinement method with the TOPAS softwareTG analysis was performed to evaluate the oxidation behaviour of Ni–Cu sulphide ore powder samples using a TG analyser (NETZSCH STA 449 F3 Jupiter) at different heating rates  in air. 2 g of the Ni–Cu sulphide ore powder sample was put into a crucible (30 mm × 70 mm) and then the crucible was placed in a muffle furnace, which was heated to a target temperature  at a rate of 5 °C/min and maintained for 30 min. The calcines were then leached in 150 mL of water at 80 °C for 2 h to evaluate the amount of sulphate species formed during the oxidative–roasting process. After filtration, the filtrate was analysed by ICP–AES.In–situ laboratory–based XRD experiments were performed using a laboratory X–ray powder diffractometer . An Anton Paar XRK 900 reactor chamber with a Macor sample holder, which was designed for the in–situ XRD investigation of solid–state and solid–gas reactions at temperatures ranging from 25 to 900 °C, was fitted to the diffractometer. The powder sample rested upon a ceramic sieve (pore size of 0.2 mm), so that reactive gas could penetrate the sample and sample holder. XRK 900 was connected to a TCU 750 temperature–control unit. The heating procedure and measuring parameters were set using the control software of the X–ray diffractometer. The in–situ XRD experiments focused on the oxidative–roasting process of the Ni–Cu sulphide ore sample under a 40 mL/min flow of air steam.47, allowing phase abundances to be quantified.For the full–pattern scanning model of the in–situ XRD, the sample was heated from 25 to 900 °C at 5 °C/min. XRD patterns were collected at different temperatures (every 50 °C from 100 to 900 °C °C) under the isothermal condition. To ensure that the reactions approach chemical equilibrium, a delay of 30 min was set for the data collections. The patterns were recorded in the 2θ range of 20 to 65° with a step size of 0.02° and a counting time of 1 s per step. The diffraction patterns were analysed by Rietveld refinement using TOPAS softwareFor the PSD fixed model of the in–situ XRD, the detector was set at a fixed angle to enable the simultaneous detection of a certain 2θ range of the diffraction–pattern data. The sample was roasted from 25 to 900 °C at 5 °C/min and cooled to room temperature at −10 °C/min. A certain 2θ angle  was set as the starting angle to collect the characteristic diffraction–pattern data instantaneously throughout the heating and cooling process. The opening slit of the detector was set as 2.8° , allowing us to obtain diffraction patterns over the maximum 2θ range. The diffraction data were collected with a counting time of 2 min for each point, yielding temperature resolutions of 10 and 20 °C during the heating and cooling, respectively.The Ni–Cu sulphide ore sample was evenly sprinkled on four corundum crucibles, forming ultrathin layers of mineral particles at the bottom of each crucible. The four resulting samples were roasted in a muffle furnace in the ambient atmosphere from 25 °C to 450, 550, 650, and 750 °C, respectively, at a heating rate of 5 °C/min. When the given temperature was reached, the samples were removed from the furnace and immediately quenched in liquid nitrogen. The cooling oxidative–powder samples were mounted in epoxy resin. Then, the cured epoxy samples were ground with metallographic abrasive paper and polished on a diamond pad with an oil–based 0.3–µm diamond suspension as the polishing media. Finally, the polished samples were coated with Pt and then characterised using a scanning electron microscope  complemented by an energy–dispersive X–ray detector (Oxford Inca X–Max).Supplementary Information


The goal of this paper was to evaluate the possibility of bi-component T1ρ and T2 relaxation mapping of human skeletal muscle at 3 T in clinically feasible scan times. T1ρ- and T2-weighted images of calf muscle were acquired using a modified 3D-SPGR sequence on a standard 3 T clinical MRI scanner. The mono- and biexponential models were fitted pixel-wise to the series of T1ρ and T2 weighted images. The biexponential decay of T1ρ and T2 relaxations was detected in ~30% and ~40% of the pixels across all volunteers, respectively. Monoexponential and bi-exponential short and long T1ρ relaxation times were estimated to be 26.9 ms, 4.6 ms (fraction 22%) and 33.2 ms (fraction: 78%), respectively. Similarly, the mono- and bi-exponential short and long T2 relaxation times were 24.7 ms, 4.2 ms (fraction 15%) and 30.4 ms (fraction 85%) respectively. The experiments had good repeatability with RMSCV < 15% and ICC > 60%. This approach could potentially be used in exercise intervention studies or in studies of inflammatory myopathies or muscle fibrosis, permitting greater sensitivity and specificity via measurement of different water compartments and their fractions. The change of muscle fiber type affects the muscle relaxation times4. As the disease progresses, the water content of the muscle will increase, leading to a lengthening of the relaxation time4. Hence, monitoring relaxation times such as T2 and T1ρ as noninvasive biomarkers may provide valuable information on the disease progression. Monoexponential measurement of T1ρ and T2 was investigated for disease monitoring9 and the elevated T1ρ and T2 due to a disease or an injury have been shown in several studies12. Recently, Iijima et al.10 showed the increase of T2 relaxation time in rotator cuff muscles with the extent of the tear. Moreover, Maillard et al.7 proposed using T2 relaxation as a quantitative measure of muscle inflammation. In another study, Hatakenaka et al.13 showed the effect aging on T2 relaxation time. However, as shown by Hazlewood et al.14 different fractions of non- (or slowly) exchanging water exists in the muscle tissues. Hence; a multiexponential model may better present the relaxation time components in the muscle. Saab et al. reported the multiexponential behavior of T2 relaxation in skeletal muscle. More recently, Araujo et al.2 proposed a method to measure the short T2 component in skeletal muscle (SKM) in the presence of fat using a UTE sequence. Moreover, the biexponential behavior of T1ρ relaxation has been observed in rat muscle15.Skeletal muscle is a very heterogeneous tissue, which composed of different types of muscle fiber. In most cases, the muscular disease affects the properties of the muscle fibers and as a result, changes their relaxation times. For example, in muscle fibrosis, the damaged striated skeletal muscle is replaced mainly by excessive collagenin vivo. The purpose of this work is to evaluate the in-vivo feasibility of biexponential analysis of T1ρ and T2 relaxation times of human calf muscle using 3T MRI in clinically feasible scan times.To the best of our knowledge, the biexponential measurement of T1ρ and T2 has yet to be reported in-vivo T1ρ and T2 experiments was 65 ± 11 and 76 ± 13, respectively; hence about [12–16%] (T1ρ) and [9–14%] (T2) estimation error was expected for in-vivo estimation of short relaxation time, and about [5–10%] error is expected in estimating the long relaxation time as well as the short and long fractions. The number of time points (TSL or TE) also affects the estimation. As shown in Fig. TSL/TE points were selected for the in-vivo experiment. As shown Fig. As shown in Fig. 16 in the model. Moreover, the biexponential fit has smaller residuals than the monoexponential fit which confirm that it can better represent the relaxation decay.Figure Figure Figure in-vivo, bi-component T1ρ and T2 analysis of calf muscle. Five ROIs were defined in the muscle and T1ρ, and T2 relaxation times were measured in each ROI. The calf muscle chemical composition consists of intra- (~25%) and extracellular water (~75%), contractile proteins  and other components . The short components are thought to be related to the tightly bound macromolecular  and intracellular water compartments; while the long relaxation component corresponds mainly to the loosely bound water (extracellular/vascular). The results showed that biexponential fitting might better present and distinguish the different relaxation times in the muscle due to different water compartments. The estimated monoexponential relaxations were comparable to the other studies13. The monoexponential estimated T1ρ was higher than T2. To the best of our knowledge this comparison has not been reported for the calf muscle, however, our results trend are in agreement with other tissues such as articular cartilages20 in which T1ρ > T2.In this paper, we presented a 3T MRI technique for 22. Saab et al.21 reported the in vivo multi-component T2 relaxations in flexor digitorum profundus muscle while Cole et al.22 measured the T2 relaxation in rat muscle. These three components have been related to the hydration shell of macromolecules, intracellular water, and extracellular water, respectively23. In a study performed by Araujo et al.24 the existence of the biexponential relaxation behavior  has been confirmed for T2 relaxation time using a localized 2D-ISIS-CPMG sequence. However, no short component has been detected due to long TE’s used in the sequence24. In contrast, our method can measure a short component and provide 3D volumetric maps. Recently, Araujo et al.2 proposed a UTE sequence to measure the short T2 components. Only the short component was measured due to the short TEs used in this study. The total acquisition time to acquire one scan with 7 TE values was 7 min, 49 s. They measured T2 in only one thick (6 mm) slice while we acquired 3D volumetric scans. However, our method cannot detect very short T2 due to using TE of 3.78 ms in the readout.The existence of three relaxation components was shown in previous studies using Carr-Purcell-Meiboom-Gill (CPMG) sequenceDue to the SAR limitation in the T1ρ experiment, the longest TE/TSL in our study was 55 ms. Hence; our long component is close to the third component, and our short component is close to the first component calculated in Saab study. Moreover, the smaller slice thickness (2 ms) in our study in comparison with Saab study (10 mm) leads to lower partial volume effect (PVE).ρ measurement of muscle has only been done on animals. For example, a biexponential analysis of T1ρ in rat muscles was reported by Yuan et al.15. The mono, short and long T1ρ were measured as (~30–33 ms), (~9–11 ms) and (~37–41 ms), respectively. The short and long fractions were (~12–20%) and (~80–88%). 25 temporal points from TSL = 1 ms to 60 ms were acquired in this study at the cost of increasing the total acquisition time to ~30 minutes15. Our T1ρ estimations using 10 TSLs acquired in 15 minutes scans are in good agreement with this study. The difference is probably due to the higher temporal resolution in Yuan study.To the best of our knowledge, biexponential T1The selection of TR can affect the T1ρ and T2 estimation due to the T1 relaxation. We evaluated this effect using Bloch simulation. Our simulation showed that there is ~5% difference between the T1ρ or T2 estimation error with TR = 1500 ms and TR = 5000 ms. Considering the longer acquisition time of TR = 5000 ms, we considered this error as negligible.26.The fatty infiltration of muscular occurring in some cases such as atrophy and muscular dystrophy does not affect the relaxation time since the fat signal was suppressed in the scans by exciting only the water with a binomial RF excitation pulseshort < Tlong can produce some bias. We chose this condition based on the suggestion in Juras study27.Our study has some limitations. The biexponential condition of 4Tρ imaging is very sensitive to B0 and B1 inhomogeneities. To compensate this effect, as described in our previous studies26, we used spin-lock phase alteration and a refocusing pulse for B1 and B0 compensation, respectively. In addition, the manual shimming was performed to further correct the field inhomogeneities. Our results showed a homogenous B0 (ΔB0 < ±5 Hz) and B1 changes less than ±50 Hz across ROIs. However, the compensation techniques used in this study may not be successful for scanning large volumes such as gluteus muscle or covering inhomogeneous regions such as arms and dorsal muscles. Moreover, the binomial RF excitation pulse is not robust in the presence of large inhomogeneities, and hence, the fatty infiltration may affect the estimation. Further studies in the large volumes muscles and, in the presence of fatty infiltration are warranted to evaluate the performance of our method.Field inhomogeneities also affected the estimation since the spin-locking in T10 may affect the T1ρ and T2 values. The spins decay monoexponentially when the tissue’s orientation to B0 is about 55°28, though T1ρ is relatively less sensitive than T2 to this effect29.The magic angle effect related to dipolar interactions of fiber orientation with respect to BFinally, we expect an elevation in relaxation components due to a muscular disease such as muscle fibrosis. However, only a small number of asymptomatic participants were scanned in this study and further validation in patients with fibrosis is warranted.in vivo measurement of bi-exponential T1ρ and T2 relaxation of human calf muscle in clinically feasible scan times. Our method could potentially be used in intervention exercise studies or in studies of inflammatory myopathies or muscle fibrosis, permitting greater sensitivity and specificity via measurement of different water compartments and their fractions.In conclusion, in this study, we showed the feasibility of M exponential terms with different fractions (ai) and relaxation time constants (Ti):S(t) is the MRI signal intensity at time t (TSL in T1ρ and TE in T2 imaging), S0 is initial value, ai is the fraction of ith exponential term with the assumption of N is the additive noise. Assuming S0 = 1, to express biexponential decay (M = 2), the equation can be written as:Ts and Tl are long and short relaxing components, respectively. The long  and short (as) fractions can be expressed in percentage as Fl = 100 × al⁄ and Fs = 100 × as⁄ , respectively. To estimate the relaxation time constants and their fractions, the MR signal must be acquired at several time points. Under given signal to noise ratio (SNR), the smaller number of points is desired to minimize the scan time. To determine the adequate range and number of points for successful estimation, Mont Carlo simulation30 was performed for 1000 random noise trail with normal distribution N. The SNR was defined as SNR = 1/σ. The estimation errors were calculated for each noise trail as:ya and ye are the actual and estimated values, respectively. The average of errors in 1000 trial was reported in percentage as the Monte Carlo simulation result.The signal decay during the spin-lock duration (TSL) or echo time (TE) can be defined as the summation of 2) and four male participants (age: 30 ± 3 years and BMI: 24 ± 2) with no signs of muscle pains or history of lower leg muscle injuries were recruited for this study. Additionally, follow-up scans were acquired from three participants two weeks after their first scan. 3D T1ρ and T2-weighted MR scans were taken on a 3T whole-body clinical MRI scanner  with a 15-channel Tx/Rx knee coil . 3D-Cartesian turbo-flash (TFL) sequence was used after T1ρ or T2 preparation module as readout followed by a delay for T1 restoration. The sequence timing diagram is shown in Fig. 2, matrix size 256 × 128 × 64, slice thickness = 2 ms, GRAPPA31 acceleration factor (AF) = 3. The spin-lock frequency (FSL) of 500 Hz was used in T1ρ preparation module.The study was approved by the institutional review board (IRB). All methods were performed in accordance with the relevant guidelines and regulations, and all of the participants signed a written informed consent prior to MRI scanning. Four females . The mono- and biexponential models were applied pixel by pixel over five consecutive slices for each volunteer in the five ROIs . Wilcoxon rank sum test was applied to compare T1ρ and T2 relaxation components as well as gender difference. T1ρ and T2 relaxation components were also compared in different ROIs using the Kruskal-Wallis test.The repeatability studies were performed on three participants by repeating the scans after two weeks. The coefficient of variation (CV) for each participant was calculated asMoreover, the intra-class correlation (ICC) was calculated as:The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.


Separating electronic distortions from intrinsic deformations within the low temperature superstructure of magnetite provides new insights into the charge and trimeron orders. Ellipsoidal analysis can be useful for exploring local structure in many materials such as coordination complexes and frameworks, organometallics and organic molecules.The idea of the coordination polyhedron is essential to understanding chemical structure. Simple polyhedra in crystalline compounds are often deformed due to structural complexity or electronic instabilities so distortion analysis methods are useful. Here we demonstrate that analysis of the minimum bounding ellipsoid of a coordination polyhedron provides a general method for studying distortion, yielding parameters that are sensitive to various orders in metal oxide examples. Ellipsoidal analysis leads to discovery of a general switching of polyhedral distortions at symmetry-disallowed transitions in perovskites that may evidence underlying coordination bistability, and reveals a weak off-centre ‘ Simple polyhedra in crystalline compounds are often deformed, so methods for analysing their distortions are useful. Here, the authors demonstrate that analysis of the minimum bounding ellipsoid of a coordination polyhedron provides a general method for studying distortion. Continuous symmetry and shape distortion approaches provide some simplifications by parameterizing distortions as a numerical deviation from an idealized polyhedron, and by describing distorted structures in terms of similarity to more ideal polyhedral shapes1234d such as Δ=σ2(d)/<d2> (where variance σ2(d)=<d2>–<d>2 and <> denotes an average) are not sensitive to angular distortions, while angular variance functions ignore distance variations67Symmetry group analysis provides a rigorous approach for quantifying distortions of coordination polyhedra but large numbers of modes are often present, for example, an MXR1≥R2≥R3. Their mean <R> is related to the polyhedron size and their variance σ2(R) or s.d. σ(R)=✓σ2(R) quantifies polyhedral distortion. Ellipsoid shape is represented by the parameter S=R3/R2−R2/R1 which has range −1≤S≤1 where oblate  and prolate  ellipsoids respectively have S<0 and S>0, and a sphere has S=0. This method allows the magnitude of distortions of different symmetry to be compared directly, as shown in 93 formatesA simple and general method for analysing distortions of polyhedra that takes account of shape irrespective of coordination number and geometry is to use an ellipsoidal approximation. Vertices of high symmetry polyhedra lie on the surface of a sphere. Deformations of the polyhedra transform the enclosing sphere into an ellipsoid and in this study we calculate the minimum bounding ellipsoid (MBE) of a given coordination polyhedron, which is the ellipsoid of smallest volume that encompasses all atoms, as described in ‘Methods' section. The MBE can be calculated for any polyhedron, irrespective of coordination number and geometry. All geometric information for the polyhedron is reduced to the properties of the MBE, plus the displacement vector of the central atom relative to the ellipsoid centre for complexes lacking inversion symmetry. The principal ellipsoid radii are ordered Taking published crystal structures of metal oxides as examples, we demonstrate below that ellipsoidal analysis based on fitting the MBE provides new insights into phase transitions in perovskites, and complex distortions and electronic orders in iron oxides. Our approach has the advantages of providing sensitivity to both distance and angle distortions and of enabling straightforward comparison of coordination polyhedra of any size and symmetry with many fewer parameters than full symmetry mode analysis.3, magnetics and spintronics, for example, Lax1−SrxMnO3, and photovoltaics, for example, (CH3NH3)PbI3  as the order parameter for transitions between these phases.Perovskites are an important class of materials with diverse uses including ferroelectrics, for example, BaTiObI3 ref. . The ide3 has one of the simplest and most studied perovskite transitions, between low temperature rhombohedral (space group R3c) and high temperature cubic (m) structures at Tc=820 K. The R3c structure is formed by introduction of a single tilt with loss of some symmetry operations of the cubic phase and the transition is continuous (second order)1612 and AlO6 polyhedra in LaAlO3 using published structural dataR3c regime. Thermal variations of the ellipsoid radii and their average <R> and s.d. σ(R) are shown in LaAlO6 octahedra deforms the LaO12 polyhedron and σ(R)La is found to reproduce the temperature variation of the AlO6 tilt angle φ, which is proportional to t½ in the critical region approaching Tc (where t is the reduced temperature t=(Tc−T)/Tc) as shown in σ(R) values for the Al ellipsoid are an order of magnitude smaller but they provide a sensitive measure of AlO6 octahedral strain. This is predicted to vary with φ2 and hence show a ∼t1 critical variation6 octahedra in LaAlO3, through σ(R)La and σ(R)Al, respectively.Tilting of AlOm structure are possible through successive tilting transitions, many investigated perovskites show symmetry-disallowed transitions. These have no group-subgroup relation between structures and hence are necessarily first order. Symmetry-disallowed transitions are relatively common in oxide perovskites, as shown in Although several branches of continuous symmetry descent from the cubic 3 perovskites where good quality structural data are available over multiple temperatures proximate to phase transitions. We use the ellipsoid shape parameter which has range −1≤S≤1, where negative and positive values respectively correspond to oblate and prolate distortions of S=0 spherical coordination. Symmetry-disallowed transitions between perovskite tilt superstructures are discovered to always change the sign of the shape parameter (s(S)=+ or −) for at least one of the two coordination ellipsoids  all display the m transition described above for LaAlO3  in the Imma structure to oblate (S<0) in the R3c regime, as shown in 3 perovskites having this Imma→3) or a Pnma→3, LaCrO3 and LaGaO3) symmetry-disallowed transition also display a sign change in at least one of the two ellipsoids as shown in Orthorhombic-rhombohedral transitions are observed in many perovskites. RAlOlO3 Fig. . At loweImma→I4/mcm transitions in BaPbO3 and BaTbO3 and the Pnma→I4/mcm transition in CaTiO3 all show a change of s(S)B from positive to negative  changes. This material forms a series of ferroelectric phases where changes in the polarization defined by off-centre Ti displacement directions [111]→[110]→[100]→[000] (non-polar) gives rise to the R3m→Amm2→P4mm→m sequence of phase transitions19216 octahedron are less explored. Shape parameters SBa and STi calculated from published structural data23R3m→Amm2→P4mm transitions in The famous perovskite BaTiO3. The prevalence of sign changes suggests that there is a general bistability to the coordination polyhedra in tilted perovskite superstructures. In the simplest ellipsoidal approximation the distortions can be either prolate or oblate, and if these two states are of similar energy then changes of temperature or other tuning variables such as pressure or composition can lead to changes between them. Prolate and oblate distortions are generally accommodated by different tilt systems, resulting in frequent observation of symmetry-disallowed transitions in perovskites. The switching may be enhanced by electronic instabilities such as weak crystal field effects for Ce3+ and Pr3+ in RAlO3 or the second order Jahn–Teller instability of Ti4+ in BaTiO3.The sign changes in ellipsoidal shape parameter at symmetry-disallowed perovskite phase transitions provide an important structural insight that has not been previously reported, even for much-studied materials like BaTiO2+ and 401 Fe3+ sites have coordination numbers between 4 and 6. Results are shown in Ellipsoidal analysis provides a useful approximation for comparing the distortions and shapes of polyhedra with different coordination numbers and geometries through data-mining of crystallographic databases such as Inorganic Crystal Structure Database (ICSD) or Cambridge Structural Database (CSD) refs , 26. Theσ(R) versus mean radius <R> plot in n coordinations. The distributions for FeO4 tetrahedra and FeO6 octahedra both have many points near σ(R)=0, reflecting their high ideal symmetries, and are clustered around <R>≈d where d is an average Fe–O distance for each coordination. Ideal values based on standard ionic radii for the predominant high spin Fe3+ state in tetrahedral and octahedral geometries are d=1.89 and 2.05 Å, respectively. Five-coordinate polyhedra are rarer and have less regular geometries, as evidenced by the bulk of the distribution lying between σ(R)≈0.1 and 0.3 Å. Highly anisotropic polyhedra have <R> values far from d and large values of σ(R). Ellipsoids describing FeO4 square planes have principal axes R1≈R2≈d and R3≈0 so <R>≈(2/3)d and σ(R)≈(✓2/3)d. The points at σ(R)>0.8 Å show this coordination, with a cluster of flat square planes at <R>≈1.3 Å and a more distorted variant at <R>=1.8 Å.The plot of ellipsoid s.d. σ(R) versus ellipsoid shape S in S varies from near -1 for square planar complexes in the oblate distortion limit through many distorted and regular tetrahedra and octahedra at S≈−0.2 to 0.3. The V-shaped appearance of the distribution results from the most symmetric ellipsoid shapes imposing lower limits on σ(R); oblate coordinations (S<0) have σ(R)=−(✓2/3)R2S while prolate ellipsoids (S>0) have σ(R)=(✓2/3)R2S/(1-S). These limits are shown on the plot together with the line for geometrically scalene  ellipsoids, which have S=0 but are non-spherical with R3/R2=R2/R1 but R1≠R2≠R3. This distortion is seen to be rather rare compared with oblate and prolate coordinations.The plot of 3O4, where proposed Fe2+/Fe3+ charge order below the Verwey transition at 125 K has been controversial for many decades27282930313233342+/Fe3+ charge order and Fe2+ orbital order over 16 independent B-site FeO6 octahedra2+ sites to B-site neighbours further revealed weak direct Fe–Fe bonding effects that give rise to linear Fe3 units known as trimerons. Comparison of ellipsoidal parameter distributions for the 16 FeO6 octahedra in magnetite, which are constrained through connectivity and cooperative electronic distortions, against the large unconstrained set of six-coordinate iron oxide polyhedra from the above analysis of literature structures in Analysis of the coordination environment is important when subtle electronic features such as charge or orbital orders are present. A famous example is the iron oxide spinel magnetite, Feσ(R) versus mean ellipsoid radius <R> plot for the literature FeO6 polyhedra in R> histograms  to observe variations from N=0 to N>100) for Fe2+ and Fe3+ according to their ideal Fe–O distances based on ionic radii which are d=2.18 and 2.05 Å. However, the corresponding plot for magnetite (3+ and largest Fe2+ states having comparably large σ(R) values. This reflects the highly correlated nature of the distortions in magnetite, as each octahedron shares edges with six neighbours leading to an increase in σ(R) with increasing deviation in <R> from the overall structural average. However, instead of meeting with a symmetric V-shape, there is a significant excess in σ(R) for the Fe2+ line relative to that for the Fe3+ line where the two distributions meet at <R>=2.06 Å . This excess distortion provides direct evidence for the intrinsic Jahn–Teller distortion of octahedra containing triply-degenerate, high spin 3d6 Fe2+ whereas 3d5 Fe3+ is non-degenerate. The 0.03 Å magnitude of the excess in σ(R) is equivalent to a tetragonal compression where four coplanar Fe–O bonds expand by 0.02 Å and the other pair contract by 0.04 Å. Hence the ellipsoidal σ(R) versus <R> plot is valuable as it enables the single-ion electronic distortion due to Jahn–Teller instability for Fe2+ states to be separated from the correlated deformations of the octahedra due to their high connectivity in the magnetite structure. This is not easily done when using simpler measures of distortion such as the Δ parameter.The s.d. agnetite  has a V-D of the Fe atom displacement relative to the ellipsoid centre are plotted against mean ellipsoid radius <R> in R>≈2.0 Å (close to the average Fe–O distance for the predominant Fe3+ state) showing that many near-regular FeO6 polyhedra have off-centre instabilities.  Octahedra at a crystallographic inversion centre have D=0 but there is a striking difference between the D>0 distributions for Fe2+ and Fe3+ states. Fe2+ displacements fall off with increasing D values up to a maximum value of 0.19 Å, whereas Fe3+ displacements range up to D=0.30 Å with a peak in the distribution at D≈0.15 Å. This disparity is greater than might be expected from crystal field effects (as σ(R) distributions for Fe2+ and Fe3+ in d5 effect' for the half-filled d-shell of Fe3+, similar to the much stronger d0 effect that gives rise to substantial off-centre displacements (second order Jahn–Teller distortions) for cations such as Ti4+ in BaTiO3 above. d0 distortions have previously been analysed by continuous shape measures3+ in trigonal bipyramidal coordinationd5 configuration.Magnitudes D with <R> are observed for both Fe2+ and Fe3+ states in low temperature magnetite in D≈0.04 Å for Fe3+ ions where the two distributions meet at <R>=2.06 Å. Previous structural analysis showed that these Fe3+ displacements are associated with trimeron formation333+ ions move towards the spatially ordered lobes of t2g orbitals of adjacent Fe2+ states resulting in weak Fe–Fe bonds. However, in light of the general analysis of Fe displacements revealed in d5 effect' may also enhance the Fe3+ displacements and hence assist trimeron formation in magnetite.Linear variations of σ(R) versus ellipsoid shape S for literature FeO6 polyhedra in σ(R) corresponding to symmetric ellipsoid shapes as described above, and many polyhedra lie close to the oblate (S<0) or prolate (S>0) limits reflecting their high crystallographic symmetries. The corresponding plot for magnetite in 6 octahedra fall close to three lines parallel to the symmetric ellipsoid limits. The spinel lattice imposes a prolate trigonal distortion on the unique FeO6 octahedron in the high temperature cubic structure  versus S plot provides an elegant separation of the single-ion electronic distortion, which is tetragonal and oblate, from the trigonal prolate deformations that are intrinsic to the distorted spinel lattice, with the two effects behaving as additive vectors parallel to the ellipsoid limits.The V-shaped distribution in the plot of s.d. The above results demonstrate the utility of ellipsoidal analysis of coordination polyhedra. Our ellipsoidal approximation based on fitting the MBE has the advantages of providing sensitivity to both distance and angle distortions and of enabling straightforward comparison of coordination polyhedra of any size and symmetry with many fewer parameters than full symmetry mode analysis. Although the derived ellipsoidal parameters are not predicated on any particular type of distortion being present, they are shown to be highly sensitive to the orders of interest in the metal oxide examples presented.d5 effect' for Fe3+ ions that may be exploited in multiferroics. Ellipsoidal plots for the magnetite superstructure have enabled local electronic distortions to be separated from correlated lattice deformations, providing new representations of the complex electronic order for future analysis.Ellipsoidal analysis provides a convenient parameterization of octahedral tilts and strains in perovskites and has led to discovery of a general switching of polyhedral distortions at symmetry-disallowed transitions that may evidence underlying coordination bistability. This method is also useful for comparing large numbers of structures from crystallographic databases, here providing evidence for a weak off-centre ‘Coordination polyhedra are ubiquitous to chemical structure so ellipsoidal analysis is likely to prove an equally useful tool for probing coordination complexes and frameworks, organometallics and organic molecules, and could even be applied to larger scale packings of molecules or nanoparticles.D of the central atom. The principal ellipsoid radii are ordered R1≥R2≥R3. Their mean <R> is related to the polyhedron size and their variance σ2(R) or s.d. σ(R)=✓σ2(R) quantifies distortion. S=R3/R2 – R2/R1 describes ellipsoid shape. Values of <R>, σ(R) and S enable straightforward analysis and comparison of coordination polyhedra of any size and symmetry.The MBE for a given coordination polyhedron is calculated using a Khachiyan minimization algorithmR3 is set to zero. The algorithm can be accessed directly or operated via simple graphical or command-line interfaces which allows direct input of CIF files, with optional control over parameters such as which atoms are coordinating, the maximum radius to use for coordination searching, and the fit tolerance. A number of other routines have also been implemented for data analysis within the PIEFACE package including output of ellipsoid parameters to a number of formats and interactive visualization of the resulting ellipsoids.The MBE fitting algorithm is implemented within the PIEFACE  software package which uses Python 2.7. PIEFACE fits an ellipsoid to a set of points in Cartesian coordinates to within a supplied tolerance; if the points are coplanar then Structural data were taken from published crystal structures. Where possible, structures obtained from neutron diffraction refinement were used to ensure accurate oxygen positions in the presence of heavy atoms. In the perovskite phase transition examples, variable temperature data were extracted from a single study wherever possible to avoid problems of systematic offsets between different experiments. For analysis of Fe oxide materials, polyhedra with Fe-coordinating atoms other than oxygen were rejected, as were mixed-cation sites with Fe occupations below 80%. Only ambient pressure and temperature structures were used.https://github.com/jcumby/PIEFACE.Version 1.0.0 of PIEFACE used in this study is archived at doi:10.5281/zenodo.198370. Code updates are available at 3 shown in All structural data used for ellipsoid fitting were taken from published crystal structures in the ICSD (version 2015.2)How to cite this article: Cumby, J. & Attfield, J. P. Ellipsoidal analysis of coordination polyhedra. Nat. Commun.8, 14235 doi: 10.1038/ncomms14235 (2017).Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.Supplementary Figures, Supplementary Tables, Supplementary Notes and Supplementary References