X-ray Thermodiffraction Research Articles

On the polymorphism of La2SiMoO8: New metastable high temperature forms and NTE (negative thermal expansion) phase transitions

Following a previous study on scheelite LT-La2SiMoO8, a new high temperature polymorph was discovered after metastabilization down to room temperature (HT). An attempt at structural determination by neutron diffraction led to large atomic displacement parameters of the Mo cation and/or of some of its oxygen neighbors, suggesting structural instability. It was confirmed by thermal analysis and X-ray thermodiffraction, showing the existence of a phase transition at 440 ​°C between two very close polymorphs, probably mixed in the HT sample. The structural derivation of the two HT forms from the baryte-type BaSO4 structure was identified, with alternating [LaMoO4]+ and [LaSiO4]- layers. The differentiation between these two forms most likely comes from a slightly different arrangement of their respective [LaMoO4] layers. The anisotropic thermal expansion is accompanied by a volume contraction of −0.56% between the two HT forms, and a much larger one (−5.3%) at higher temperatures when the LT form stabilizes.

Thin-Film Stabilization of a Ferroelectric Orthorhombic α-Pr2WO6 Polymorph

An orthorhombic α-Pr2WO6 (PrWO) polymorph with a = 16.57(5) Å, b = 5.52(5) Å, and c = 8.73(1) Å, isostructural to α-La2WO6 and α-Nd2WO6, has been stabilized in the form of thin film by pulsed laser deposition on (001)-oriented SrTiO3 substrates. Combining X-ray diffraction pole-figure measurements and transmission electron microscopy (TEM) analysis, the c-axis films gave evidence of the orientations [100]PrWO || [110]STO and [010]PrWO || [110]STO in the plane. Advanced φ-scans and reciprocal space mapping characterizations confirm the existence of the orthorhombic (Pm21n) structure in the film in place to the tetragonal one as also suggested. X-ray thermodiffraction measurements highlight the stability of this polymorph in thin film up to 900 °C at least. Optical measurements performed by spectroscopic ellipsometry reveal that the band gap in such 36 nm thick films (as confirmed by both X-ray reflectivity and TEM measurements) is 2.5 eV. Besides, the local piezoelectric hysteresis loops recorded by using the spectroscopic tool of piezoresponse force microscopy attest to the robustness of the piezoelectricity and ferroelectricity in these α-Pr2WO6 films. This study demonstrates the existence of a new lead-free ferroelectric material in the series of α-Ln2WO6 (lanthanide) tungstates, which can be considered as a promising candidate for applications in both nanoelectromechanical and energy-harvesting systems as well as for integrating optics.

X-ray Thermo-Diffraction Study of the Aluminum-Based Multicomponent Alloy Al58Zn28Si8Mg6.

Newly designed multicomponent light alloys are giving rise to non-conventional microstructures that need to be thoroughly studied before determining their potential applications. In this study, the novel Al58Zn28Si8Mg6 alloy, previously studied with CALPHAD methods, was cast and heat-treated under several conditions. An analysis of the phase evolution was carried out with in situ X-ray diffraction supported by differential scanning calorimetry and electron microscopy. A total of eight phases were identified in the alloy in the temperature range from 30 to 380 °C: α-Al, α’-Al, Zn, Si, Mg2Si, MgZn2, Mg2Zn11, and SrZn13. Several thermal transitions below 360 °C were determined, and the natural precipitation of the Zn phase was confirmed after nine months. The study showed that the thermal history can strongly affect the presence of the MgZn2 and Mg2Zn11 phases. The combination of X-ray thermo-diffraction with CALPHAD methods, differential scanning calorimetry, and electron microscopy offered us a satisfactory understanding of the alloy behavior at different temperatures.

Revisiting the Decomposition Process of Tetrahydrate Co(II) Acetate: A Sample’s Journey through Temperature

Cobalt oxides, CoO and Co3O4, were obtained from Co (II) acetate tetrahydrate. The thermal decomposition pathway of the starting product was followed by combining thermogravimetric analysis and in situ X-ray thermodiffraction. Under a nitrogen atmosphere, cobalt monoxide with Zn-blende and rocksalt polymorphs could be obtained almost as single phases at 330 and 400 °C, respectively. In addition to these oxides, a Co (II) oxyacetate, Co3O(CH3COO)4, was stabilized as an intermediate phase. Under an air atmosphere, Co3O4 (spinel structure type) was obtained as the only final product. The involved phases in this thermal decomposition process were characterized with scanning and transmission electron microscopy (SEM and TEM, respectively).

LaNi0.6Co0.4−xFexO3−δ as Air-Side Contact Material for La0.3Ca0.7Fe0.7Cr0.3O3−δ Reversible Solid Oxide Fuel Cell Electrodes

The goal of the current work was to identify an air-side-optimized contact material for La0.3Ca0.7Fe0.7Cr0.3O3−δ (LCFCr) electrodes and a Crofer22APU interconnect for use in reversible solid oxide fuel cells (RSOFCs). LaNi0.6Co0.4−xFexO3 (x = 0–0.3) perovskite-type oxides were investigated in this work. The partial substitution of Co by Fe decreased the thermal expansion coefficient values (TEC) closer to the values of the LCFCr and Crofer 22 APU interconnects. The oxides were synthesized using the glycine–nitrate method and were characterized using X-ray thermodiffraction and 4-probe DC electrical conductivity measurements. Based on the materials characterization results from the Fe-doped oxides investigated here, the LaNi0.6Co0.2Fe0.2O3−δ composition was selected as a good candidate for the contact material, as it exhibited an acceptable electrical conductivity value of 395 S·cm−1 at 800 °C in air and a TEC value of 14.98 × 10−6 K−1 (RT-900 °C).

Synthesis and Characterization of High Temperature Properties of YBa2Cu3O6+δ Superconductor as Potential Cathode for Intermediate Temperature Solid Oxide Fuel Cells

YBa2Cu3O6+δ (YBC) oxygen deficient perovskite was synthesized by an auto-combustion method and was studied as potential cathode for Intermediate Temperature Solid Oxide Fuel Cell (IT-SOFC). Synchrotron X-ray thermodiffraction in air shows a phase transition from orthorhombic Pmmm to tetragonal P4/mmm space groups at ~ 425 °C. The chemical compatibility with Ce0.9Gd0.1O1.95 (GDC) electrolyte was investigated in air where certain reactivity was observed above 800 °C. However, the main phase is Ba(Ce1-xYx)O3, a good ionic conductor. The catalytic performance in air was obtained by electrochemical impedance spectroscopy (EIS) measurements on YBC/GDC/YBC symmetrical cells. The area specific resistance (ASR) values change from 13.66 to 0.14 Ω cm2 between 500 and 800 °C, with activation energy (Ea) of 0.41 eV. The results suggest potential applications of YBC as IT-SOFC cathode.

CRYSTALLINE FORMS OF BETULIN: POLYMORPHISM OR PSEUDOPOLYMORPHISM?

By recrystallization with different solvents as well as decomposition of betulin ethanol solvate at room temperature a new crystalline form of the biologically active compound betulin, namely hemihydrate of betulin, is obtained. By single crystal X-ray diffraction data the crystal structure of hemihydrate of betulin is determined. By powder X-ray thermodiffraction and differential scanning calorimetry it is found that when hemihydrate of betulin is heated to melting, Н2О molecules are removed and solid-phase transformations occur, which are related to the formation of an intermediate crystalline form and an orthorhombic modification of betulin.

TG, DTA and X-ray thermodiffraction study of wall paintings from the fifteenth century

In this work, it is reported that thermal analysis techniques such as TG, DTA and X-ray thermodiffraction, performed in air or nitrogen atmosphere, are very useful for evaluating and characterizing the pigments and the supports used for the manufacture of wall paintings from the San Isidoro del Campo Monastery (fifteenth century) in which different scenes from the life of San Jeronimo are represented. The use of thermal techniques has allowed for collecting information on the technology and raw materials used in the manufacture of these wall paintings. The composition of the different colours forming the wall paintings is the following: blue by azurite, green by atacamite, red by iron oxide (hematite), cinnabar and ochre by iron oxyhydroxides (goethite), black by carbon and white by calcite. In all the colours, calcite and quartz were also identified. The paintings were performed by using the fresco technique. The support mortars are constituted of calcite, quartz and straw.

Kinetic Analysis of the Thermal Decomposition of Iron(III) Phosphates: Fe(NH3)2PO4 and Fe(ND3)2PO4.

The hydrothermal synthesis and both the chemical and structural characterization of a diamin iron phosphate are reported. A new synthetic route, by using n-butylammonium dihydrogen phosphate as a precursor, leads to the largest crystals described thus far for this compound. Its crystal structure is determined from single-crystal X-ray diffraction data. It crystallizes in the orthorhombic system (Pnma space group, a = 10.1116(2) Å, b = 6.3652(1) Å, c = 7.5691(1) Å, Z = 4) at room temperature and, below 220 K, changes towards the monoclinic system P21/n, space group. The in situ powder X-ray thermo-diffraction monitoring for the compound, between room temperature and 1100 K, is also included. Thermal analysis shows that the solid is stable up to ca. 440 K. The kinetic analysis of thermal decomposition (hydrogenated and deuterated forms) is performed by using the isoconversional methods of Vyazovkin and a modified version of Friedman. Similar values for the kinetic parameters are achieved by both methods and they are checked by comparing experimental and calculated conversion curves.

Encapsulation of β-alanine model amino-acid in zirconium(IV) metal organic frameworks: Defect engineering to improve host guest interactions

Metal-Organic Frameworks (MOFs) are porous coordination networks assembled through metal complexes with organic linkers. Due to their chemical versatility, these materials are being investigated for various applications including gas storage and separation, biomedicine and catalysis. The aim of this work is the encapsulation of the model β-alanine amino-acid in the nanostructured zirconium-based MOF (UiO-66) which contains the ligand H2BDC (1,4-benzenedicaboxylic acid). Additionally, ligand functionalization (by using H2doBDC (2,5-dihydroxy-1,4-benzenedicarboxylic acid) and defect engineering have been carried out to produce UiO-66 derivatives, in order to modify the host-guest interactions, and hence study their influence on the β-alanine loading capacity and release kinetics. The as-obtained materials have been characterized by X-ray diffraction (XRD), X-ray thermo diffraction (TDX), infrared (IR) spectroscopy, thermogravimetric analysis-differential scanning calorimetry (TG-DSC) and elemental analysis (EA). Morphology of nanoscale MOFs has been explored by transition electron microscopy (TEM). Adsorption isotherms have been constructed, and the concentration of β-alanine in the post-adsorption solution (supernatant) has been quantified by high performance liquid chromatography coupled with mass spectroscopy (HPLC-MS) and EA. Adsorption capacity values indicate that the presence of hydroxyl groups at the organic linker H2doBDC enhances the host-guess affinity between the framework and the adsorbate β-alanine. The influence of defect engineering, on the adsorption however, is not that obvious. On the other hand, desorption experiments show similar behaviour for H2doBDC-based derivatives. An adsorption mechanism has been proposed consisting of a combination of host-guest interaction at low concentrations, and covalent anchoring/ligand displacement by β-alanine at the inorganic clusters.

Thermal Expansion of Mg3B2O6 Borate

The thermal expansion of magnesium borate (Mg3B2O6) is studied by the method of X-ray thermodiffraction in the temperature range 25–1100°C. The coefficients of thermal expansion are calculated as follows: αa = 13.0(5), αb = 8.5(5), αc = 8.0(5), αV = 30(1) × 10–6°С−1 at 25°C; and αa = 20.0(5), αb = 13.0(5), αc = 13.0(5), αV = 46(1) × 10–6°С−1 at 1100°С. The direction of the maximal thermal expansion (αa) is perpendicular to the preferred orientation of the BO3 triangles.

Synthesis by Thermal Decomposition of Two Iron Hydroxyfluorides: Structural Effects of Li Insertion

The synthesis and the electrochemical properties of iron hydroxyfluorides with an open structure, prepared from the thermal decomposition of Fe2+Fe3+F5(H2O)2 and Fe2+Fe23+F8(H2O)2 under ambient air, are reported. The combination of thermogravimetric analyses, X-ray thermodiffraction (XRD), and infrared spectroscopy has evidenced two unstable lacunar oxyfluorides that transform rapidly into hydroxyfluorides under ambient air. Their formulations and structural features have been determined from powder XRD, Mössbauer spectrometry, and pair distribution function, leading to Fe3+F2.5(OH)0.5 with the pyrochlore network and to Fe3+F2.66(OH)0.34 with the hexagonal tungsten bronze (HTB) structure. The electrochemistry of these hydroxyfluorides indicates excellent and similar capacities with a significant decrease after the first cycle to reach sustained values of ∼110 mAh g–1 upon cycling. In situ XRD measurements reveal that the pyrochlore network undergoes amorphization (xLi+ > 0.5) while the HTB phase transforms into the ReO3-type phase (xLi+ > 0.33).

Phase transition study in strongly correlated VO2 based sensing systems

Intermediate phase monoclinic M2 was observed by inducing in situ X-ray thermo diffraction on VO2 (M) nanoplatelets. The solid-solid phase transition occurs at around 65°C assisted with the percolative transition metal-insulator. The existence of an intermediate crystalline phase with room temperature insulator phase and high temperature metallic phase across MIT in VO2 could be of relevance to understand structural contributions to the phase transition dynamics. In addition, pellet of VO2 nanostructures have shown to present good sensing properties to various alcohols vapors at room temperature and good selectivity of methanol with 5.54% sensitivity and limit detection below 5ppm, compared to isopropanol 3.2% and acetone 2.4% respectively.

Series of Hydrated Heterometallic Uranyl-Cobalt(II) Coordination Polymers with Aromatic Polycarboxylate Ligands: Formation of U═O-Co Bonding upon Dehydration Process.

Five new heterometallic UO22+-Co2+ coordination polymers have been obtained by hydrothermal reactions of uranyl nitrate and metallic cobalt with aromatic polycarboxylic acids. Single-crystal X-ray diffraction reveals the formation of four 3D frameworks with the mellitate (noted mel) ligand and one 2D network with the isophthalate (noted iso) ligand. The compounds [(UO2(H2O))2Co(H2O)4(mel)]·4H2O (1), [UO2Co(H2O)4(H2mel)]·2H2O (2), and [(UO2(H2O))2Co(H2O)4(mel)] (4) consist of 3D frameworks built up from the connection of mellitate ligands and mononuclear metallic centers. These three compounds exhibit two types of geometry for the uranyl cation: pentagonal bipyramidal environment for 1 and 4, and hexagonal bipyramidal environment for 2. Using the mellitate ligand, the uranyl dinuclear unit is isolated in the compound [(UO2)2(OH)2(Co(H2O)4)2(mel)]·2H2O (3). Due to their 2D framework and the presence of uncoordinated cobalt(II) cations, the compound [(UO2)(iso)3][Co(H2O)6]·3(H2O) (5) is drastically different than the previous one. The thermal behavior of compounds 1, 2, and 3 has been studied by thermogravimetric analysis, X-ray thermodiffraction, and in situ infrared. By heating, the dehydration of compounds 1 and 2 promotes two structural transitions (1 → 1' and 2 → 2'). The crystal structures of [(UO2(H2O))2Co(H2O)2(mel)] (1') and [(UO2)Co(H2mel)] (2') were determined by single-crystal X-ray diffraction; each of them presents a heterometallic interaction between uranyl bond and the Co(II) center. Due to the rarely reported coordination environment for the cobalt center in compound 2' (square pyramidal configuration), the magnetic properties and EPR characterizations of the compounds 2 and 2' were also investigated.

Effect of the synthesis temperature on the dimensionality of hybrid fluorozincates

Abstract A series of new hybrid fluorozincates incorporating 5-aminotetrazole (Hamtetraz) is obtained from a same starting mixture of ZnF2, HF solution and Hamtetraz in acetronitrile at different synthesis temperatures. The structures, determined by single crystal X-ray diffraction, exhibit various networks with dimensionalities that increase as a function of the synthesis temperature. At 120 °C, two phases, ZnF2(H2O)(Hamtetraz) (1) and ZnF2(Hamtetraz)2 (2), coexist and display 1D infinite chains. ∞[ZnN2F2O] chains are built up from ZnN2F3(H2O) octahedra linked by opposite fluorine corners in 1, while ∞[ZnN2F2] chains of edge sharing ZnN2F4 octahedra are found in 2. At 130 °C, dense layers appear in Zn3F5(H2O)2(amtetraz) (3); they result from the condensation of ∞[ZnF3N2] and ∞[ZnF2NO] chains by fluorine corners to form a neutral 2D network. At 140 °C, [NH4]·(Zn4F5(amtetraz)4)·3H2O (4) presents an anionic 3D network containing small cavities in which water molecules and ammonium cations are inserted. The thermal behavior of the coordination polymers 3 and 4 is studied by TGA analysis and X-ray thermodiffraction; an intermediate phase is observed during the decomposition of 4.

Characterization of tobelite formed from kaolinite under hydrothermal conditions (200 °C)

The aim of this paper is the characterization of pure tobelite synthesized in the system (NH4)2O-Al2O3-SiO2-H2O, which is a first, indispensable step for accurately interpreting the data obtained in more complex chemical systems. Tobelite has been synthesized at hydrothermal conditions (200±3°C), using a solid:solution ratio (in weight)=1:15, and reaction times from 1 to 90days and has been characterized by X-ray diffraction; infrared and Raman spectroscopy; differential thermal analysis and thermogravimetry; and transmission-analytical electron microscopy. The average chemical composition of tobelite formed after 90days run time, determined by combining the analytical electron microscopy data with nitrogen determination in the solid products of the reaction by elemental analysis, was [NH4Al1.98(Si3.07Al0.93)O10(OH)2]. The refinement of the X-ray diffraction patterns indicated that the 1M polytype predominates, and the determined cell-parameters were: a=5.219 (0.004) Å; b=9.021 (0.007) Å; c=10.556 (0.009) Å; β=101.41° (0.08); V=487.23 (0.69) Å3. The infrared spectra indicated the presence of two υ4 bands (at 1403 and 1435cm−1), which can be related to the presence of two main tobelite populations with mean particle sizes of 400×60 and 2000×200Å. The thermal study by means of differential thermal analysis and thermogravimetry, combined with X-ray thermodiffraction suggested that the mechanisms of NH4 loss were different in the two differently-sized tobelite populations: the thinner particles showed a low thermal stability (between 380° and 440°C) and the NH4 loss was coupled with dehydroxylation, leading directly to the decrease of the tobelite content. Loss of NH4 from the thicker particles occurred between 440° and 500°C, causing a gradual contraction of the basal spacing, which was followed by dehydroxylation. There were no previous data of Raman spectroscopy of tobelite and this study presents its most characteristic features.

In situ Synchrotron X-ray Thermodiffraction of Boranes

Boranes of low molecular weight are crystalline materials that have been much investigated over the past decade in the field of chemical hydrogen storage. In the present work, six of them have been selected to be studied by in situ synchrotron X-ray thermodiffraction. The selected boranes are ammonia borane NH3BH3 (AB), hydrazine borane N2H4BH3 (HB), hydrazine bisborane N2H4(BH3)2 (HBB), lithium LiN2H3BH3 (LiHB) and sodium NaN2H3BH3 (NaHB) hydrazinidoboranes, and sodium triborane NaB3H8 (STB). They are first investigated separately over a wide range of temperature (80–300 K), and subsequently compared. Differences in crystal structures, the existence of phase transition, evolutions of unit cell parameters and volumes, and variation of coefficients of thermal expansion can be observed. With respect to AB, HB and HBB, the differences are mainly explained in terms of molecule size, conformation and motion (degree of freedom) of the chemical groups (NH3, N2H4, BH3). With respect to LiHB, NaHB and STB, the differences are explained by a stabilization effect favored by the alkali cations via M···H interactions with four to five borane anions. The main results are presented and discussed herein.

Evidence of New Fluorinated Coordination Compounds in the Composition Space Diagram of FeF3/ZnF2–Hamtetraz-HFaq System

The exploration of the composition space diagram of the FeF3/ZnF2–Hamtetraz-HFaq system (Hamtetraz = 5-aminotetrazole) by solvothermal synthesis at 160 °C for 72 h in dimethylformamide (DMF) has evidenced five new hybrid fluorides (1–5); the structures are characterized from single crystal X-ray diffraction data. [Hdma]·(ZnFeIII(H2O)4F6) (1) and [Hdma]·[Hgua]2·(FeIIIF6) (2) contain anionic inorganic chains (1) or isolated octahedra (2) weakly hydrogen bonded (Class I hybrids) to dimethylammonium (Hdma) and/or guanidinium (Hgua) cations which are produced from the tetrazole ligand and solvent decomposition. [Hdma]2·[Hgua]·[NH4]·[ZnFeIIIF5(amtetraz)2]2 (3), [Hdma]2·[Zn1.6FeII0.4FeIIIF6(amtetraz)3] (4), and [Hdma]·[Zn4F5(amtetraz)4] (5) are considered as Class II hybrids in which the (amtetraz)− anions are strongly linked to divalent metal cations via N–M bonds. In 3, ∞{[NH4]·[ZnFeIIIF5(amtetraz)2]2} layers are separated by [Hdma]+ and [Hgua]+ cations. 4 and 5 exhibit three-dimensional (3D) hybrid networks that contain small cavities where [Hdma]+ cations are inserted. A porous 3D metal–organic framework intermediate is evidenced from the thermogravimetric analysis and X-ray thermodiffraction of 5.

Metal–organic frameworks assembled from lanthanide and 2,5-pyridinedicaboxylate with cubane-like [Ln4(OH)4] building units

Lanthanide–organic frameworks based on 2,5-pyridinedicaboxylate (25p) ligand, formulated as [Yb4(OH)4(25p)4(H2O)3]·H2O (25pYb), [Y4(OH)4(25p)4(H2O)3]·H2O (25pY-1) and [Y6(OH)8(25p)5(H2O)2] (25pY-2), have been obtained as single phases under hydrothermal conditions. 25pYb and 25pY-1 are isostructural, and crystallize in the triclinic space group, P-1, with a=8.6075(5)Å, b=14.8478(7)Å, c=15.9164(9)Å, α=86.277(4)°, β=80.196(5)°, γ=81.785(4)°, and a=8.7166(6)Å, b=14.966(1)Å, c=15.966(1)Å, α=86.260(6)°, β=80.036(6)°, γ=81.599(6)°, respectively. 25pY-2 crystallizes in the monoclinic space group, P21/c, with a=24.9117(17)Å, b=13.7340(8)Å, c=14.3385(10)Å, β=100.551(7)°. 25pYb and 25pY-2 have been structurally characterized by single-crystal X-ray diffraction. The 25pYb structure is based on tetranuclear cubane-like [Yb4(OH)4]8+ clusters, which are interconnected to eight neighbouring clusters through teen surrounding 25p ligands leading to neutral 3D framework, while the structure of 25pY-2 is based on two independent cuban-like [Y4(OH)4]8+ clusters, which are joined together through Y1 cation leading to the formation of hexanuclear [Y6(OH)8]10+ clusters, which in turn are joined via Y2 cation resulting in infinite inorganic chain extending along c-axis, and each chain is interconnected to six adjacent chains through 25p ligands leading finally to 3D framework. The luminescence properties of Eu3+ and Tb3+ doped 25pY-1 and 25pY-2 compounds have also been investigated. All materials has been characterized by powder X-ray diffraction, thermal analyses (TG–SDTA–MS), FTIR spectroscopy, C–H–N elemental analysis, scanning electron microscopy (SEM-EDX), and powder X-ray thermodiffraction.

New iron tetrazolate frameworks: synthesis, temperature effect, thermal behaviour, Mössbauer and magnetic studies.

The exploration of the FeF3/FeF2-Hamtetraz-HF system in dimethylformamide by solvothermal synthesis evidences two isostructural 3D hybrid fluoroferrates. They are prepared from the same starting mixture at two different synthesis temperatures: 120 °C for [Hdma]·(Fe4(II)Fe(III)F8(H2O)2(amtetraz)4) () and 140 °C for [Hdma]1.5·(Fe4.5(II)Fe0.5(III)F7(H2O)(HCOO)(amtetraz)4) (). Both compounds are characterized by single crystal X-ray diffraction, X-ray thermodiffraction, TGA analysis, Mössbauer spectrometry and SQUID magnetometry. They crystallize in the monoclinic system and are built from two distinct chains connected by aminotetrazolate anions. The first chain ∞(Fe(II)FN4) is common to and and can be found in numerous fluorides. In the second chain ∞(Fe3X12) (X = F, N, O), iron cations adopt both valence states Fe(ii)/Fe(iii). The hydrolysis of DMF implies the formation of a [Hdma](+) cation and a (HCOO)(-) anion. The presence of Fe(3+) in both phases is evidenced by (57)Fe Mössbauer spectrometry. The magnetic properties are studied and two transitions from a paramagnetic regime to a long range ordered state below 30 K and 5 K are identified.