Synthesis and properties of the Co7Se8−xSx and Ni7Se8−xSx solid solutions

We report the synthesis and elementary properties of the Co₇Se_8−xS_x (x=0-8) and Ni₇Se_8−xS_x (x=0-7) solid solutions. Both systems form a NiAs-type structure with metal vacancies. In general, the lattice parameters decrease with increasing x, but in the Ni₇Se_8−xS_x system c increases on going from x=5 to 7. Magnetic susceptibility measurements show that all samples exhibit temperature-independent paramagnetism from 25-250 K. Samples within the Co₇Se_8−xS_x system, as well as Ni₇Se₈ and Ni₇SeS₇, were found to be poor metals with resistivities of ∼0.20 and ∼0.06 mΩ cm at 300 K, respectively. The Sommerfeld constant (γ) was determined from specific heat measurements to be ∼13 mJ/mol_CoK² and ∼7 mJ/mol_NiK² for Co₇Se_8−xS_x and Ni₇Se_8−xS_x, respectively.     

Microstructure and electrical-optical properties of cesium tungsten oxides synthesized by solvothermal reaction followed by ammonia annealing

Cesium tungsten oxides (Cs_xWO₃) were synthesized by solvothermal reactions using ethanol and 57.1 vol% ethanol aqueous solution at 200 °C for 12 h, and the effects of post annealing in ammonia atmosphere on the microstructure and electrical-optical properties were investigated. Agglomerated particles consisting of disk-like nanoparticles and nanorods of Cs_xWO₃ were formed in the pure ethanol and ethanol aqueous solutions, respectively. The samples retained the original morphology and crystallinity after annealing in ammonia atmosphere up to 500 °C, while a small amount of nitrogen ion were incorporated in the lattice. The as-prepared Cs_xWO₃ sample showed excellent near infrared (NIR) light shielding ability as well as high transparency in the visible light region. The electrical resistivity of the pressed pellets of the powders prepared in pure ethanol and 57.1 vol% ethanol aqueous solution greatly decreased after ammonia annealing at 500 °C, i.e., from 734 to 31.5 and 231 to 3.58 Ω cm, respectively.     

Crystal structure, thermal expansion and conductivity of anisotropic La1−xSrxGa1−2xMg2xO3−y (x=0.05, 0.1) single crystals

Crystal structure and anisotropy of the thermal expansion of single crystals of La_1−xSr_xGa_1−2xMg_2xO_3−y (x=0.05 and 0.1) were measured in the temperature range 300-1270 K. High-resolution X-ray powder diffraction data obtained by synchrotron experiments have been used to determine the crystal structure and thermal expansion. The room temperature structure of the crystal with x=0.05 was found to be orthorhombic (Imma, Z=4, a=7.79423(3) Å, b=5.49896(2) Å, c=5.53806(2) Å), whereas the symmetry of the x=0.1 crystal is monoclinic (I2/a, Z=4, a=7.82129(5) Å, b=5.54361(3) Å, c=5.51654(4) Å, β=90.040(1)°). The conductivity in two orthogonal directions of the crystals has been studied. Both, the conductivity and the structural data indicate three phase transitions in La_0.95Sr_0.05Ga_0.9Mg_0.1O_2.92 at 520-570 K (Imma-I2/a), 770 K (I2/a-R3c) and at 870 K (R3c-R-3c), respectively. Two transitions at 770 K (I2/a-R3c) and in the range 870-970 K (R3c-R-3c) occur in La_0.9Sr_0.1Ga_0.8Mg_0.2O_2.85.     

Structure and phase composition of nanocrystalline Ce1−xLuxO2−y

The microstructure and phase stability of nanocrystalline mixed oxide Lu_xCe_1−xO_2−y (x=0-1) are described. Nano-sized (3-4 nm) oxide particles were prepared by the reverse microemulsion method. Morphological and structural changes upon heat treatment in an oxidizing atmosphere were studied by transmission electron microscopy (TEM), X-ray diffraction (XRD), Raman and Yb³⁺ emission spectroscopy, the latter ion being present as an impurity in the Lu₂O₃ starting material. Up to 950 °C, the samples were single phase, with structure changing smoothly with Lu content from fluorite type (F) to bixbyite type (C). For the samples heated at 1100 °C phase separation into coexisting F- and C-type structures was observed for 0.35<x<0.7. It was also found that addition of Lu strongly hinders the crystallite growth of ceria during heat treatment at 800 and 950 °C.     

Enzyme mimics of spinel-type CoxNi1−xFe2O4 magnetic nanomaterial for eletroctrocatalytic oxidation of hydrogen peroxide

A series of spinel-type Co_xNi_1−xFe₂O₄ (x = 0, 0.2, 0.4, 0.5, 0.6, 0.8, 1.0) magnetic nanomaterials were solvothermally synthesized as enzyme mimics for the eletroctrocatalytic oxidation of H₂O₂. X-ray diffraction and scanning electron microscope were employed to characterize the composition, structure and morphology of the material. The electrochemical properties of spinel-type Co_xNi_1−xFe₂O₄ with different (Co/Ni) molar ratio toward H₂O₂ oxidation were investigated, and the results demonstrated that Co_0.5Ni_0.5Fe₂O₄ modified carbon paste electrode (Co_0.5Ni_0.5Fe₂O₄/CPE) possessed the best electrocatalytic activity for H₂O₂ oxidation. Under optimum conditions, the calibration curve for H₂O₂ determination on Co_0.5Ni_0.5Fe₂O₄/CPE was linear in a wide range of 1.0 × 10⁻⁸–1.0 × 10⁻³ M with low detection limit of 3.0 × 10⁻⁹ M (S/N = 3). The proposed Co_0.5Ni_0.5Fe₂O₄/CPE was also applied to the determination of H₂O₂ in commercial toothpastes with satisfactory results, indicating that Co_xNi_1−xFe₂O₄ is a promising hydrogen peroxidase mimics for the detection of H₂O₂.     

Sol-gel synthesized semiconducting LaCo0.8Fe0.2O3-based powder for thick film NH3 gas sensor

Perovskite type LaCo_xFe_1−xO₃ nanoparticles was synthesized by a sol-gel citrate method. The structural, electrical and sensing characteristics of the LaCo_xFe_1−xO₃ system were investigated. The structural characteristics were performed by using X-ray diffraction (XRD) and transmission electron microscopy (TEM) to examine the phase and morphology of the resultant powder. The XRD pattern shows nanocrystalline solid solution of LaCo_xFe_1−xO₃ with perovskite phase. Electrical properties of synthesized nanoparticles are studied by DC conductivity measurement. The sensor shows high response towards ammonia gas in spite of other reducing gases when x = 0.8. The effect of 0.3 wt.% Pd-doped LaCo_0.8Fe_0.2O₃ on the response and a recovery time was also addressed.     

H2S sensing properties of nanocrystalline Sr2FeO.6NiO.4MoO6 thick film prepared by sol-gel citrate method

Nanocrystalline Sr₂FeMoO₆ (SFMO) belonging to the group of double perovskite oxides, was prepared by the sol-gel citrate method. The structural and microstructural characterization has been carried out with the help of X-ray diffraction (XRD) and transmission electron microscopy (TEM), respectively. XRD of Sr₂Fe_1−xNi_xMoO₆ (SFNMO) shows the formation of solid solution with average grain size of about 40 nm. A comparative study of gas sensing behaviour of Sr₂FeMoO₆ and Sr₂Fe_1−xNi_xMoO₆ with reducing gases like hydrogen sulfide (H₂S), liquid petroleum gas (LPG), hydrogen (H₂), ethanol (C₂H₅OH) and carbon monoxide (CO) were also discussed. The sensitivity is calculated by measuring the change the resistance of the sensor material in the presence of gas. Among the different composition of x (x = 0.2, 0.3, 0.4, 0.5), Sr₂Fe_0.6Ni_0.4MoO₆ (x = 0.4) shows better response to H₂S gas at 260 °C. Incorporation of palladium (Pd) improves the gas response, selectivity, response time and reduced the operating temperature from 260 to 220 °C for H₂S gas.     

Thermoelectric properties of polycrystalline La1−xSrxCoO3

Thermoelectric properties of polycrystalline La_1−xSr_xCoO₃, where Sr²⁺ is substituted in La³⁺ site in perovskite-type LaCoO₃, have been investigated. Sr-doping increases the electrical conductivity (σ) of La_1−xSr_xCoO₃, and also decreases the Seebeck coefficient (S) for 0.01?x?0.40. A Hall coefficient measurement reveals that the increase in electrical conductivity arises from increases in both carrier concentration and the Hall mobility. The decrease in the Seebeck coefficient is caused by a decrease in carrier effective mass as well as increase in carrier concentration. The highest power factor (σS²) is 3.7×10⁻⁴ W m⁻¹ K⁻² at 250 K for x=0.10. The thermal conductivity (κ) is about 2 W m⁻¹ K⁻¹ at 300 K for 0?x?0.04, and increases for x?0.05 because of an increase in heat transport by conductive carrier. The thermoelectric properties of La_1−xSr_xCoO₃ are improved by Sr-doping, and the figure of merit (Z=σS² κ⁻¹) reaches 1.6×10⁻⁴ K⁻¹ for x=0.06 at 300 K (ZT=0.048). For heavily Sr-doped samples, the thermoelectric properties diminish mainly because of the decrease in the Seebeck coefficient and the increase in thermal conductivity.     

The La0.95Ni0.6Fe0.4O3-CeO2 system: Phase equilibria, crystal structure of components and transport properties

Phase equilibria, crystal structure, and transport properties in the (100−x) La_0.95Ni_0.6Fe_0.4O₃-xCeO₂ (LNFCx) system (x=2-75 mol%) were studied in air. Evolution of phase compositions and crystal structure of components was observed. The LNFCx (2≤x≤10) are three-phase and comprise the perovskite phase with rhombohedral symmetry (R3?c), the modified ceria with fluorite structure (Fm3?m), and NiO as a secondary phase. These multiphase compositions exhibit metallic-like conductivity above 300 °C. Their conductivity gradually decreases from 395.6 to 260.6 S/cm, whereas the activation energy remains the same (E_a=0.04-0.05 eV), implying the decrease in the concentration of charge carriers. Phase compositions in the LNFCx (25≤x≤75) are more complicated. A change from semiconducting to metallic-like conductivity behavior was observed in LNFC25 at about 550 °C. The conductivity of LNFCx (25≤x≤75) could be explained in terms of a modified simple mixture model.     

An X-ray diffraction, magnetic susceptibility and spectroscopic studies of Yb2−xCrxO3

Polycrystalline samples with general formula Yb_2−xCr_xO₃ (0<x<0.03), obtained by sol-gel method and analyzed by X-ray diffraction, formed solid solutions over all the mentioned range. Cr showed a maximum solubility of 2.8 mol% in Yb₂O₃ sesquioxide at 1000 °C. A preferential substitution of Cr³⁺ ions over two cationic sites, 8b and 24d in the space group Ia-3 was found. The lattice parameters a are found to vary linearly (10.4402(4) Å <a<10.4372(1) Å) with the composition x. The two independent atoms Yb/Cr have octahedral coordination; however, the degrees of distortion of their coordination polyhedron are different. Replacing Yb³⁺ by Cr³⁺ introduces slight changes in the atomic coordinates leading to an increase of the mean cation-anion distances. The ability of Raman spectroscopy to detect changes in local coordination is utilized. A pseudo-tetrahedral coordination for the Cr³⁺ in the 24d site was found. Magnetic susceptibility measurements of all samples were done in a temperature range of 2-50 K. For T<37 K, the inverse paramagnetic susceptibilities depend linearly on temperature. However, in the high-temperature region, for T>37 K, the inverse paramagnetic susceptibilities are non-linear versus temperature. This deviation from the Curie-Weiss behaviour was discussed.     

Synthesis, structure and physical properties of GdCu4Al and GdCu4Ga

Two non-stoichiometric Gd compounds, GdCu_5−xTr_x (Tr=Al, Ga) have been synthesized from the corresponding elements by high temperature reactions in sealed tantalum containers. They crystallize in the hexagonal CaCu₅-type (Pearson's symbol hP6, space group P6/mmm, No. 191) with lattice parameters determined from single-crystal X-ray diffraction at room temperature as follows: a=5.0831(10) Å; c=4.156(2) Å for GdCu_3.98(4)Al_1.02(4), and a=5.1025(10) Å; c=4.155(2) Å for GdCu_3.9(1)Ga_1.1(1), respectively. Structure refinements from single crystal X-ray diffraction data reveal that substitution of Cu for Al or Ga takes place preferably on one of the two transition metal sites with site symmetry mmm (3g). Both compounds order antiferromagnetically below ∼40 K and ∼36 K, respectively, as determined from temperature dependent dc-magnetization, resistivity and heat-capacity measurements.     

Structural and magnetic properties of high-pressure/high-temperature synthesized (Sr1-xRx)CoO3 (R=Y and Ho) perovskites

Polycrystalline perovskite cobalt oxides Sr_1-xR_xCoO₃ (R=Y and Ho; 0?x?1) were prepared by high-pressure/high-temperature technique. X-ray powder patterns of the Y-system indicated cubic perovskite form for 0?x?0.5, and orthorhombic perovskite form for x=0.8 and 1.0, while coexisting of the two phases for x=0.6. The cubic perovskite samples had metallic electric resistivities while the orthorhombic ones with semiconducting or insulating nature. The parent compound SrCoO₃ showed a ferromagnetic transition at 266 K. With the Y substitution, the transition temperature increased slightly to ∼275 K at x=0.1, then decreased rapidly to ∼60 K for x=0.6. The YCoO₃ (x=1) sample showed non-magnetic behavior. The Ho-substituted system showed quite similar structural, transport and magnetic properties to those of the Y-system.     

Structure and conductivity of strontium-doped cerium orthovanadates Ce1−xSrxVO4 (0≤x≤0.175)

A-site substituted cerium orthovanadates, Ce_1−xSr_xVO₄, were synthesised by solid-state reactions. It was found that the solid solution limit in Ce_1−xSr_xVO₄ is at x=0.175. The crystal structure was analysed by X-ray diffraction and it exhibits a tetragonal zircon structure of space group I4₁/amd (1 4 1) with a=7.3670 (3) and c=6.4894 (1) Å for Ce_0.825Sr_0.175VO₄. The UV-vis absorption spectra indicated that the compounds have band gaps at room temperature in the range 4.5-4.6 eV. Conductivity measurements were performed for the first time up to the strontium solid solution limit in air and in dry 5% H₂/Ar with conductivity values at 600 °C ranging from 0.3 to 30 mS cm⁻¹ in air to 30-45 mS cm⁻¹ in reduced atmosphere. Sample Ce_0.825Sr_0.175VO₄ is redox stable at a temperature below 600 °C although the conductivity is not high enough to be used as an electrode for solid oxide fuel cells.     

Mechanosynthesis of nanopowders of the proton-conducting electrolyte material Ba(Zr, Y)O3−δ

The formation of perovskite nanopowders of the common proton-conducting, electrolyte material Ba(Zr_1−xY_x)O_3−δ is demonstrated by room temperature mechanosynthesis for the compositional range x=0, 0.058 and 0.148. This is achieved with a planetary ball mill at 650 rpm in zirconia vials, starting from BaO₂ with ZrO₂, (ZrO₂)_0.97(Y₂O₃)_0.03 or (ZrO₂)_0.92(Y₂O₃)_0.08 precursors, respectively. Powder X-ray diffraction (XRD) reveals the formation of the perovskite phase in the early stages of milling with phase purity being achieved after milling times of 240 min for composition x=0.058 whereas 420 min is necessary for composition x=0.148. In contrast, traces of ZrO₂ are apparent in composition x=0 even after milling times of 420 min. The use of BaCO₃ as precursor does not allow the formation of the perovskite phase for any composition. The perovskite crystallites are spherical in shape with an average size determined from XRD of ca. 30 nm in agreement with transmission electron microscopy observations. FTIR spectra demonstrate that contamination levels of BaCO₃ in the mechanosynthesized powders are very low. The spherical shape and nanoscale of the crystallites allow densification levels that are highly competitive when compared to BaZrO₃-based materials formed by alternative synthesis techniques documented in the literature.     

The solid state reaction between lanthanum oxide and strontium carbonate

The reaction between lanthanum oxide and strontium carbonate was studied non-isothermally between 350 and 1150 °C at different heating rates, intermediates and the final solid product were characterized by X-ray diffractometry (XRD). The reaction proceeds through formation of lanthanum oxycarbonate La₂O(CO₃)₂, lanthanum dioxycarbonate La₂O₂CO₃, and non-stoichiometric strontium lanthanum oxide La₂SrO_x (x = 4 + δ). La₄SrO₇ was found to be the final product which begins to form at ∼700 °C. Li⁺ doping enhances the formation of the final product as well as commencement of the reactions at lower temperatures.     

On phase equilibria and crystal structures in the systems Ce-Pd-B and Yb-Pd-B. Physical properties of R2Pd13.6B5 (R=Yb, Lu)

Phase equilibria and crystal structures of ternary compounds were determined in the systems Ce-Pd-B and Yb-Pd-B at 850 °C in the concentration ranges up to 45 and 33 at% of Ce and Yb, respectively, employing X-ray single crystal and powder diffraction. Phase relations in the Ce-Pd-B system at 850 °C are governed by formation of extended homogeneity fields, τ₂-CePd₈B_2−x (0.10<x<0.48); τ₃-Ce₃Pd_25−xB_8−y (1.06<x<1.87; 2.20<y<0.05), and CePd₃B_x (0<x<0.65) the latter arising from binary CePd₃. Crystallographic parameters for the new structure type τ₂-CePd₈B_2−x (space group C2/c, a=1.78104(4) nm, b=1.03723(3) nm, c=1.16314(3), β=118.515(1)° for x=0.46) were established from X-ray single crystal diffraction. The crystal structures of τ₂-CePd₈B_2−x and τ₃-Ce₃Pd_25−xB_3−y are connected in a crystallographic group-subgroup relationship. Due to the lack of suitable single crystals, the novel structure of τ₁-Ce₆Pd_47−xB₆ (x=0.2, C2/m space group, a=1.03594(2) nm, b=1.80782(3) nm, c=1.01997(2) nm, β=108.321(1)°) was determined from Rietveld refinement of X-ray powder diffraction data applying the structural model obtained from single crystals of homologous La₆Pd_47−xB₆ (x=0.19) (X-ray single crystal diffraction, new structure type, space group C2/m, a=1.03988(2) nm, b=1.81941(5) nm, c=1.02418(2) nm, β=108.168(1)°).The Yb-Pd-B system is characterized by one ternary compound, τ₁-Yb₂Pd₁₄B₅, forming equilibria with extended solution YbPd₃B_x, YbB₆, Pd₅B₂ and Pd₃B. The crystal structures of both Yb₂Pd₁₄B₅ and isotypic Lu₂Pd₁₄B₅ were determined from X-ray Rietveld refinements and found to be closely related to the Y₂Pd₁₄B₅-type (I4₁/amd). The crystal structure of binary Yb₅Pd_2−x (Mn₅C₂-type) was confirmed from X-ray single crystal data and a slight defect on the Pd site (x=0.06) was established.The three structures τ₁-Ce₆Pd_47−xB₆, τ₂-CePd₈B_2−x and τ₃-Ce₃Pd_25−xB_8−y are related and can be considered as the packings of fragments observed in Nd₂Fe₁₄B structure with different stacking of common structural blocks.Physical properties for Yb₂Pd_13.6B₅ (temperature dependent specific heat, electrical resistivity and magnetization) yielded a predominantly Yb-4f¹³ electronic configuration, presumably related with a magnetic instability below 2 K. Kondo interaction and crystalline electric field effects control the paramagnetic temperature domain.     

Copper nanoparticles entrapped in SWCNT-PPy nanocomposite on Pt electrode as NOx electrochemical sensor

A highly sensitive NO_x sensor was designed and developed by electrochemical incorporation of copper nanoparticles (CuNP) on single-walled carbon nanotubes (SWCNT)-polypyrrole (PPy) nanocomposite modified Pt electrode. The modified electrodes were characterized by scanning electron microscopy and energy dispersive X-ray analysis. Further, the electrochemical behavior of the CuNP-SWCNT-PPy-Pt electrode was investigated by cyclic voltammetry. It exhibited the characteristic CuNP reversible redox peaks at −0.15 V and −0.3 V vs. Ag/AgCl respectively. The electrocatalytic activity of the CuNP-SWCNT-PPy-Pt electrode towards NO_x is four-fold than the CuNP-PPy-Pt electrode. These results clearly revealed that the SWCNT-PPy nanocomposite facilitated the electron transfer from CuNP to Pt electrode and provided an electrochemical approach for the determination of NO_x. A linear dependence (r² = 0.9946) on the NO_x concentrations ranging from 0.7 to 2000 μM, with a sensitivity of 0.22 ± 0.002 μA μM⁻¹ cm⁻² and detection limit of 0.7 μM was observed for the CuNP-SWCNT-PPy-Pt electrode. In addition, the sensor exhibited good reproducibility and retained stability over a period of one month.     

Thermoelectric properties of p-type pseudo-binary (Ag0.365Sb0.558Te)x-(Bi0.5Sb1.5Te3)1−x (x=0-1.0) alloys prepared by spark plasma sintering

In this paper, pseudo-binary (Ag_0.365Sb_0.558Te)_x-(Bi_0.5Sb_1.5Te₃)_1−x (x=0-1.0) alloys were prepared using spark plasma sintering technique, and the composition-dependent thermoelectric properties were evaluated. Electrical conductivities range from 7.9×10⁴ to 15.6×10⁴ Ω⁻¹ m⁻¹ at temperatures of 507 and 318 K, respectively, being about 3.0 and 8.5 times those of Bi_0.5Sb_1.5Te₃ alloy at the corresponding temperatures. The optimal dimensionless figure of merit (ZT) of the sample with molar fraction x=0.025 reaches 1.1 at 478 K, whereas that of the ternary Bi_0.5Sb_1.5Te₃ alloy is 0.58 near room temperature. The results also reveal that a direct introduction of Ag_0.365Sb_0.558Te in the Bi-Sb-Te system is much more effective to the property improvement than naturally precipitated Ag_0.365Sb_0.558Te in the Ag-doped Ag-Bi-Sb-Te system.     

Fluorinated transition alumina with Al2−x/3O3−xFx compositions: Thermal, chemical, structural and morphological investigations

Fluorinated transition aluminas (Al_2−x/3O_3−xF_x) with hexagonal platelet shape were synthesized via decomposition of α-AlF₃ under air; they are thermally stable up to 1000 °C and exhibit at 1150 °C a weight loss with volume reduction caused by fluorine departure corresponding to a phase transition toward corundum alumina. The different characterizations performed in this study are structural (XRD), chemical (TGA-MS and microprobe analysis) and morphological (SEM, TEM and dilatometry). The evidence provided from this study is consistent with the formation of an Al-O-F phase as an intermediate compound in the pyrohydrolysis of an aluminium trifluoride phase to α-Al₂O₃.     

Phase relations in a barium-rich high-temperature region (25-45 mol% CuO, 900-1100 °C) of the BaO-CuOx system

The phase relations have been studied in the BaO-CuO_x system in the range of 25.0-45.0 mol% CuO at 900-1100 °C at P(O₂)=21 kPa (air) by visual polythermal analysis (VPA), powder X-ray diffraction (XRD), electron diffraction (ED) with simultaneous energy-dispersive X-ray (EDX) elemental analysis in a transmission electron microscope (TEM), and iodometric chemical analysis. The discrete deviations 2.02 (101:50), 2.04 (102:50), 2.10 (105:50) of Ba/Cu (Ba:Cu) composition from the stoichiometric ratio 2:1 have been found for the known Ba₂CuO_3+δ oxides in the subsolidus region 900-970 °C. Unit cell parameters of the 101:50 orthorhombic oxide, 102:50 tetragonal one, 105:50 orthorhombic one are, respectively, a=4.049, b=3.899, c=13.034 Å; a=3.985, c=12.968 Å; a=4.087, b=3.897 and c=12.950 Å. ED patterns of the 101:50, 102:50, 105:50 oxides show characteristic supercell reflections with the respective vector 1/60[5 4 0], ≈2/11〈1 1 0〉 and 1/6[2 0 0]. Oxides of the 2:1, 7:4, 5:3 and 23:20 compositions have been found in the crystallization region 970-1050 °C. Unit cell parameters of the 2:1 orthorhombic oxide are a=4.095, b=3.795, c=13.165 Å. Interplanar spacings and X-ray characteristic peak intensities of the 7:4, 5:3 and 23:20 oxides are given. Oxides 2:1 and 7:4 melt pseudocongruently at 1020 and 1005 °C, oxides 5:3 and 23:20 melt incongruently at 995 and 980 °C, respectively. A diagram of the phase relations in the studied region of the BaO-CuO_x system has been constructed, whose structure is considered as the total projection of phase states of the system existing for different x.