Mg6Ir2H11, a new metal hydride containing saddle-like [IrH4] and square-pyramidal [IrH5] hydrido complexes

Mg₆Ir₂H₁₁ has been synthesised by both hydrogenation of the intermetallic compound Mg₃Ir at 20 bar and 300 °C, and sintering of the elements at 500 °C under 50 bar hydrogen pressure. Neutron powder diffraction on the deuteride indicates a monoclinic structure (space group P2₁/c, Mg₆Ir₂D₁₁: a=10.226(1), b=19.234(2), c=8.3345(9) Å, β=91.00(1)°, T=20 °C) that is closely related to orthorhombic Mg₆Co₂H₁₁. It contains a square-pyramidal [IrH₅]⁴⁻ complex and three saddle-like [IrH₄]⁵⁻ complexes of which one is ordered and two are disordered. Five hydride anions H⁻ are exclusively bonded to magnesium. The compound has a red colour, is presumably non-metallic and decomposes under 3 bar argon at 500 °C into Mg₃Ir, iridium and a previously unreported intermetallic compound of composition Mg₅Ir₂.     

Formation of a tetragonal phase hydride in Ti–Mo–H system

The structural relationship between the hydride phases in Ti–Mo–H solid solution system (Mo content up to 15 at% in the alloy) during dehydrogenation process under annealing has been studied by conventional and in situ X-ray powder diffraction and transmission electron microscopy (TEM) analysis. During dehydrogenation, the saturated hydrides of the Ti–Mo alloys with fcc δ-phase structure transfer into bcc β-phase at higher temperatures. An associated hydrogen concentration reduction for the δ-phase hydride is observed in the process. However, as the hydrogen concentrations decrease to certain values (H/M  1.1–1.7), the unsaturated δ-phase formed at high temperature would become unstable at lower temperature, and transfer into a tetragonal phase (denoted the -phase here). Unlike that of the -phase in Ti–H system, the phase transition does not occur for the saturated δ-phase with hydrogen concentration close to the stoichiometric limit. The hydrogen concentration of this -phase hydride is in between that of the tetragonal γ and -phase in Ti–H system, but more close to the γ-phase. The occurrence region of this -phase expands along with the increase of the Mo content in the alloys. The phase has a lattice similar to that of the -phase in Ti–H system with corresponding fct unit-cell c/a < 1.     

Another unusual phenomenon for Zr7Ni10: structural change in hydrogen solid solution and its conditions

Zr₇Ni₁₀ has three hydrogen occlusion phases, , β and γ, and the following unusual features are known for the phase transitions in the Zr₇Ni₁₀–H₂ system: (1) The intermediate hydride phase (β) appears only during dehydrogenation but not during hydrogenation, and (2) The continuous hydrogen solid solution phase () exhibits a much higher hydrogen solubility during hydrogenation than during dehydrogenation. In order to clarify the mechanism about the difference in the hydrogen solubility of the phase, the relation between the pressure-composition isotherms and corresponding structural change has been examined by a conventional volumetric method and X-ray diffraction. Through the examination, we discovered that the crystal structure of the phase, which undergoes hydrogenation followed by dehydrogenation, is different from that of its pure metal phase, where the crystal structure of the dehydrogenated phase changes from an orthorhombic structure to a tetragonal structure. The conditions causing the structural change were then examined, and it has been found that the phase maintains its original orthorhombic structure as long as it is hydrogenated so as not to absorb enough hydrogen to change it to the hydride with a higher hydrogen content (γ). The phenomenon can be understood as one of the hydrogen-assisted phase transitions such as hydrogen-induced amorphization (HIA) in the sense that the phase transition requires hydrogenation under special conditions.     

Improvement in hydrogen sorption properties of Mg by reactive mechanical grinding with Cr2O3, Al2O3 and CeO2

We tried to improve the hydrogen sorption properties of Mg by mechanical grinding under H₂ (reactive mechanical grinding) with oxides Cr₂O₃, Al₂O₃ and CeO₂. The hydriding rates of Mg are reportedly controlled by the diffusion of hydrogen through a growing Mg hydride layer. The added oxides can help pulverization of Mg during mechanical grinding. A part of Mg is transformed into MgH₂ during reactive mechanical grinding. The Mg+10wt.%Cr₂O₃ powder has the largest transformed fraction 0.215, followed in order by Mg+10wt.%CeO₂ and Mg+10wt.%Al₂O₃. The Mg+10wt.%Cr₂O₃ powder has the largest hydriding rates at the first and fifth hydriding cycle, followed in order by Mg+10wt.%Al₂O₃ and Mg+10wt.%CeO₂. Mg+10wt.%Cr₂O₃ absorbs 5.87wt.% H at 573 K, 11 bar H₂ during 60 min at the first cycle. The Mg+10wt.%Cr₂O₃ powder has the largest dehydriding rates at the first and fifth dehydriding cycle, followed by Mg+10wt.%CeO₂ and Mg+10wt.%Al₂O₃. It desorbs 4.44 wt.% H at 573 K, 0.5 bar H₂ during 60 min at the first cycle. All the samples absorb and desorb less hydrogen at the fifth cycle than at the first cycle. It is considered that this results from the agglomeration of the particles during hydriding–dehydriding cycling. The average particle sizes of the as-milled and cycled powders increase in the order of Mg+10wt.%Cr₂O₃, Mg+10wt.%Al₂O₃ and Mg+10wt.%CeO₂. The quantities of hydrogen absorbed or desorbed for 1 h for the first and fifth cycles decrease in the order of Mg+10wt.%Cr₂O₃, Mg+10wt.%Al₂O₃ and Mg+10wt.%CeO₂. The quantities of absorbed or desorbed hydrogen increase as the average particle sizes decrease. As the particle size decreases, the diffusion distance shortens. This leads to the larger hydriding and dehydriding rates. The Cr₂O₃ in the Mg+10wt.%Cr₂O₃ powder is reduced after hydriding–dehydriding cycling. The much larger chemical affinity of Mg than Cr for oxygen leads to a reduction of Cr₂O₃ after cycling.     

Investigation of reaction between LiNH2 and H2

The reactions for LiNH₂ under a H₂ and an Ar flow were investigated, respectively. The results showed that LiNH₂ can be converted into LiH and NH₃ by reacting with H₂ under a H₂ flow condition, whereas LiNH₂ is converted into Li₂NH and NH₃ by decomposition under an Ar flow. Moreover, the reaction between LiNH₂ and H₂ can be accelerated by mixing LiNH₂ with LiH as well as doping LiNH₂ with TiCl₃. The confirmation of reaction between LiNH₂ and H₂ is helpful for the deeper insight in the systems of Li–N–H and Li–Mg–N–H for hydrogen storage materials.     

The characteristics of Li(CoxNi1 − x)O2 cathode powders formed from the fine-sized Co3O4/NiO precursor powders

Li(Co_xNi_1 − x)O₂ (0 ≤ x ≤ 1) cathode powders were prepared by solid state reaction method using Co₃O₄/NiO precursor powders obtained by spray pyrolysis. The effect of the ratios of cobalt and nickel components on the characteristics of Co₃O₄/NiO precursor and Li(Co_xNi_1 − x)O₂ cathode powders were investigated. The Co₃O₄/NiO precursor powders with the ratios of cobalt and nickel components as 1/0, 0.75/0.25 and 0.5/0.5 had submicron size and regular morphologies. On the other hand, the Co₃O₄/NiO powders with the high contents of nickel component had aggregated morphologies of submicron size primary powders. The fine-sized precursor powders formed the fine-sized LiCoO₂ and Li(Co_0.75Ni_0.25)O₂ cathode powders by solid state reaction with LiOH powders. However, the high contents of the nickel component of the Co₃O₄/NiO precursor powders formed the Li(Co_xNi_1 − x)O₂ (0 ≤ x ≤ 0.5) cathode powders with aggregated morphologies and large sizes. The discharge capacities of the powders increased with increasing the nickel content into the Li(Co_xNi_1 − x)O₂ cathode powders up to 188 mAh/g.     

Interaction of hydrogen with the LaNi4.9In0.1, LaNi4.8In0.2 and LaNi4.8 alloys and their Nd analogues

The single phase nature of the alloys LaNi_4.9In_0.1, LaNi_4.8In_0.2, NdNi_4.9In_0.1, NdNi_4.8In_0.2 of the systems LaNi_5−xIn_x and NdNi_5−xIn_x was confirmed by means of X-ray powder diffractometry. Nonstoichiometric alloys LaNi_4.8 and NdNi_4.8 were prepared and were also found to be good single phase materials. All these alloys crystallize with the same hexagonal structure of the CaCu₅ type (space group P6/mmm) as do their prototypes LaNi₅ and NdNi₅. In order to determine the interaction with hydrogen the alloys were exposed to hydrogen gas and the pressure composition desorption isotherms were measured. It was found that all alloys react readily and reversibly absorb large amounts of up to 6.54 hydrogen atoms per alloy formula unit. Generally the equilibrium pressure and the hydrogen capacity decrease with the decreasing nickel content. Presence of indium in the alloy acts in favour of these trends. Furthermore, the increasing content of indium in the alloy system drastically alters the slope and the pressure of the plateau observed at higher pressure of the two isotherm plateaux of the NdNi₅–hydrogen system. The final result is a merge of both plateaux into a single one for the hydrogen desorption isotherms of NdNi_4.8In_0.2. However, the isotherms of nonstoichiometric NdNi_4.8 still exhibit two separated pressure plateau regions. The thermodynamic parameters of hydride formation, i.e., the entropy change, the enthalpy and the Gibbs free energy of formation have also been extracted for all alloy–hydrogen systems.     

Deactivation of titanium during temperature-induced hydrogen absorption–desorption cycling: I. Effects of water, oxygen and nitrogen traces

The cyclic stability of metallic titanium during absorption–desorption runs in continuous flow system has been studied in the presence of variable level of impurities such as H₂O, O₂ and N₂ in argon and helium flows. Hydrogen absorption–desorption cycles performed in vacuo were reproducible with respect to the absorption rates and uptakes, while absorption–desorption cycles carried out in the flows of carrier gases in the thermoprogrammed mode resulted in the gradual decrease of hydrogen uptakes followed by a shift of absorption maxima from 800 K to 1000 K.

Mass-spectral analysis of the main impurities in a flow of gases revealed that during hydrogen absorption–desorption traces of water, oxygen and nitrogen are consumed by titanium. For the samples subjected to several absorption–desorption cycles in the flow of inert gas XRD revealed the formation of nitrogen-containing titanium compounds, while XPS showed surface enrichment in nitrogen, while oxygen concentration was constant. Nitrogen consumed at higher temperatures during the TPD runs provides better inhibition of hydrogen absorption compared to water and oxygen. Final deactivation state of titanium correlates in general with the overall amount of impurities in the stream.

Although deactivation is controlled mostly by the level of toxic impurities in the feed, certain parameters, i.e., hydrogen absorption/desorption rates are dependent on the nature of neutral media—in contrast to helium, noticeable hydrogen desorption occurs even at room temperature in a flow of pure argon.     

Phase relations and hydrogenation behavior of Sr(Al1−xMgx)2

The phase relations and hydrogenation behavior of Sr(Al_1−xMg_x)₂ alloys were studied. The pseudobinary C36-type Laves phase Sr(Al,Mg)₂ was found as a structural intermediate between the Zintl phase and the C14 Laves phase. The single-phase regions for the Zintl phase, C36 phase and C14 phase, were determined to be x=0–0.10, 0.45–0.68 and 0.80–1, respectively. The Mg-substituted Zintl phase Sr(Al_0.95Mg_0.05)₂ can be hydrogenated to Sr(Al,Mg)₂H₂ at about 473 K. However, the Sr(Al,Mg)₂H₂ directly decomposes into SrH₂ and Sr(Al,Mg)₄ starting at 513 K. When the temperature is 573 K, the C36 Laves phase Sr(Al_0.5Mg_0.5)₂ can be hydrogenated into SrMgH₄ and Al, while the C14 Laves phase Sr(Al_0.1Mg_0.9)₂ is hydrogenated into SrMgH₄, Mg₁₇Al₁₂ and Mg.     

Hydrogen absorption properties of the slurry system composed of liquid C6H6 and F-treated Mg2Ni

The hydrogenation characteristics of the slurry composed of the NH₄F solution treated Mg₂Ni and liquid C₆H₆ were studied. The F-treatment results in a net-shaped MgF₂ surface and higher nickel content in the sub-layer. It is found that the hydride of the NH₄F treated alloy has a much higher activity for the hydrogenation of benzene. The catalytic activity for hydrogenation of the alloy depended strongly on the surface properties of the catalyst. At 483 K and under a hydrogen pressure of 4.0 MPa, the alloy absorbed hydrogen first, transformed into hydride and then the benzene was hydrogenated to cyclohexane with the hydride as the catalyst. The hydrogen absorption capacity of slurry system composed of 20 wt.% treated alloy and benzene reached 6.4 wt.% and the hydrogenation completed in 20 min. Results of X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and scanning electron microscopy (SEM) analysis on the crystal structure, surface composition and surface morphology of the untreated and treated alloy are presented and discussed.     

Influence of the rare earth composition on the properties of Ni–MH electrodes

Lattice parameters, hydrogen absorption properties and electrochemical cycling properties up to 240 cycles have been measured as a function of the Ce content for alloys of composition La_0.82−xCe_xNd_0.15Pr_0.03Ni_3.55Mn_0.4Al_0.3Co_0.75 (0≤x≤0.82). The results show the strong increase of the plateau pressure correlated to the cell volume decrease as a function of x. On the other hand, the hydrogen capacity measured in solid–gas reaction as well as the electrochemical capacity decreases slightly. The results show that both La and Ce have to be present to achieve a good cycle life, the cycling degradation being almost independent of their relative quantities in a broad range of concentrations.     

Structure and hydrogen storage properties of MgH2 catalysed with La2O3

The catalytic effect of the addition of lanthanum oxide (La₂O₃), in the range 0.5–2.0 mol%, on the hydrogen storage properties of MgH₂ prepared by ball milling has been studied. The addition of La₂O₃ reduces the formation during milling of the metastable orthorhombic γ-MgH₂ phase. The desorption rate of samples with 1 and 2 mol% La₂O₃ comes out to be about 0.010 wt% per second at 573 K under an hydrogen pressure of 0.3 bar, better than for sample with 0.5 mol% La₂O₃. The presence of LaH₃ after hydrogenation/dehydrogenation cycles has been observed in all samples. The sample with 1 mol% of La₂O₃ gives a lower hysteresis factor compared with sample with 2 mol%.     

Hydrogen storage properties of melt-spun LaNi4.25Al0.75

Rapidly solidified LaNi_4.25Al_0.75 alloy was prepared by melt spinning and its hydrogen storage properties were examined. The hydrogen storage capacities and the equilibrium pressures of the unannealed melt-spun (UMS) LaNi_4.25Al_0.75 alloy were found to be nearly identical to those of the annealed induction-melt (AIM) alloy. However, the resistance to pulverization was greatly improved and the hysteresis was markedly decreased for the UMS alloy, while its activation became rather difficult.     

Combustion synthesis of TiC–TiB2 composites

An experimental study on formation of TiC–TiB₂ in situ composites with a broad range of compositions was conducted by self-propagating high-temperature synthesis (SHS) using the reactant compacts from different combinations of Ti, B₄C, C, and B powders. Direct reaction of Ti with B₄C at stoichiometry of Ti:B₄C = 3:1 yields a TiB₂-rich composite with TiC:TiB₂ = 1:2. Formation of the products containing 20, 33.3, and 50 mol% of TiB₂ was achieved by the Ti–B₄C–C reactants. In addition, the test specimen composed of Ti, B₄C, and B was employed for the synthesis of a composite with 80 mol% TiB₂. Among three different types of the powder compacts, the boron-containing sample was characterized by the fastest combustion wave and the highest reaction temperature. The lowest combustion temperature and wave velocity were observed in the Ti–B₄C compact. When fine Ni particles were added to the Ti–B₄C reactant, it was found that the propagation rate of the reaction front was increased and the densification of the end product was enhanced significantly. This was attributed to formation of the Ti–Ni eutectic liquid during the reaction. As a result, the relative density of a TiC + 2TiB₂ composite increases from 30 to 86% with the Ni content from 0 to 20 mol%. Based upon the XRD analysis, small amounts of TiNi₃ and TiB were detected in the Ni-reinforced TiC–TiB₂ composites.     

Characterization of NH3 formation in desorption of Li–Mg–N–H storage system

Hydrogen energy may provide the means to an environmentally friendly future. One of the problems related to its application for transportation is “on board” storage. Hydrogen storage in solids has long been recognized as one of the most practical approaches for this. Recently the hydrogen storage system, (Li₃N + 2H₂  LiNH₂ + 2LiH), was introduced by Chen et al. [P. Chen, Z. Xiong, J. Luo, J. Lin, K.L. Tan, Nature 420 (2002) 302–304. [1]]. This type of material has attracted a great attention of the researchers from the metal hydride research community due to its high reversible storage capacity, up to 11.5 wt%. Currently the Li–Mg–N–H system has been shown to be able to deliver 5.2 wt% reversibly at a H₂ pressure of 30 bar and temperature of 200 °C. The accessibility of the capacity beyond 5.2 wt% is being actively explored. One of the issues related to the application of the metal–N–H storage systems is NH₃ formation that takes place simultaneously with H₂ release. NH₃ formation will not only damage the catalyst in a fuel cell, but also accelerate the cyclic instability of the H-storage material since the metal–N–H system turns into a metal–H system after loosing nitrogen and, therefore, it would not function at the temperature and pressure range designed for the metal–N–H system. The accurate determination of the amounts of NH₃ in the H₂ is, therefore, very important and has not been previously reported. Here a novel method to quantify NH₃ in the desorbed H₂, the Draeger Tube, is reported as being suitable for this purpose. The results indicate that the concentration of NH₃ in desorbed H₂ increases with the desorption temperature. For the (2LiNH₂ + MgH₂) system the NH₃ concentration was found to be 180 ppm at 180 °C and 720 ppm at 240 °C.     

Synthesis and optical properties of yttria-doped ZrO2 nanopowders

Yttria-doped zirconia (YDZ) nanopowders were synthesized via a solvothermal route using ethanol as solvent. Evolution of crystal phases for different amount of yttria-doped samples were studied by X-ray diffraction (XRD). Morphology and component of the as-synthesized cubic YDZ were characterized by scanning electron microscopy (SEM) and energy dispersion spectrum (EDS). Defects of the sample were detected using ultraviolet–vis (UV–vis) absorption spectrum and photoluminescence (PL) spectrum. The results indicated that cubic structured nanocrystals can be obtained through doping 4 mol% Y₂O₃ into ZrO₂ lattice. The particles had sphere morphology with an average crystal size of 10 nm and agglomerated into bigger spheres with a diameter of about 120 nm. Mechanism of the agglomeration was also discussed. UV spectra showed two absorption peaks, red shift for both of the adsorption edges was observed. PL spectra with excitation wavelength of 260 and 420 nm revealed six fluorescence peaks which were regarded as various energy levels in the band gap and as the evidence of existence of oxygen vacancies in the as-synthesized sample.     

La–Mg–Ni ternary hydrogen storage alloys with Ce2Ni7-type and Gd2Co7-type structure as negative electrodes for Ni/Mh batteries

Hydrogen strorage alloys with formula La_1.5Mg_0.5Ni₇ were prepared by induction melting followed by different annealing treatments (1073, 1123 and 1173 K) for 24 h. The alloy composition, alloy microstructure and electrochemical properties were investigated, respectively. The results showed that the multi-phase structure of as-cast alloy was converted into a double-phase structure (Gd₂Co₇-type phase and Ce₂Ni₇-type phase) through annealing treatments. Mg atoms were mainly located in Laves unit of Gd₂Co₇-type unit cell and Ce₂Ni₇-type unit cell. The electrochemical capacity of alloy electrodes after annealing treatment could be up to 390 mAh/g. The cyclic stability of alloy electrodes was significantly improved by annealing treatments; After 150 charge/discharge cycles, the capacity retention ratio of alloy annealed at 1173 K was the highest (81.9%). The high rate dischargeability of alloy electrodes was also improved due to annealing treatment.     

LaMg2NiH7, a novel quaternary metal hydride containing tetrahedral [NiH4] complexes and hydride anions

A new ternary compound of composition LaMg₂Ni has been found and investigated with respect to structure and hydrogenation properties. It crystallizes with the orthorhombic MgAl₂Cu type structure (space group Cmcm, a=4.2266(6), b=10.303(1), c=8.360(1) Å; V=364.0(1) ų; Z=4) and absorbs hydrogen near ambient conditions (<200 °C, <8 bar) thereby forming the quaternary metal hydride LaMg₂NiH₇. Neutron powder diffraction on the deuteride revealed a monoclinic distorted metal atom substructure (LaMg₂NiD₇: space group P2₁/c, a=13.9789(7), b=4.7026(2), c=16.0251(8) Å; β=125.240(3)°, V=860.39(8) ų; Z=8) that contains two symmetry independent tetrahedral [NiD₄]⁴⁻ complexes with Ni–D bond lengths in the range 1.49–1.64 Å, and six D⁻anions in tetrahedral metal configuration with bond distances in the ranges 1.82–2.65 Å (Mg) and 2.33–2.59 Å (La). The compound constitutes a link between metallic ‘interstitial’ hydrides and non-metallic ‘complex’ metal hydrides.     

Hydrogen-generating solid-state hydride/hydroxide reactions

Solid-state reactions of ionic hydrides with alkaline hydroxides are shown to produce hydrogen gas and metal oxides. These reactions are analogous to the well-known hydrolysis reactions of ionic hydrides. Both classes of reactions are generally exothermic and are thermodynamically favored; ΔG° < 0 near room temperature. However, solid-state hydride/hydroxide reactant mixtures are kinetically stable at room temperature and can be prepared by mechanical milling without appreciable reaction. Thus, optimally stoichiometric mixtures are possible and nearly theoretical amounts of hydrogen can be generated. Reaction occurs upon heating with H₂ evolution beginning at 50 °C and complete reaction occurring by 200–300 °C. The reaction rate can be enhanced with additives such as TiCl₃. Specifically, we discuss the reactions LiH + LiOH, 2LiH + NaOH, LiBH₄ + 4LiOH, and 3LiBH₄ + 4LiOH·H₂O. The 3LiBH₄ + 4LiOH·H₂O reaction generates approximately 10 wt.% hydrogen with more than 5 wt.% produced at temperatures below 100 °C.     

The effect of sequential and continuous high-energy impact mode on the mechano-chemical synthesis of nanostructured complex hydride Mg2FeH6

The effect of sequential and continuous high-energy impact mode in the magneto-mill Uni-Ball-Mill 5 on the mechano-chemical synthesis of nanostructured ternary complex hydride Mg₂FeH₆ was studied by controlled reactive mechanical alloying (CRMA). In the sequential mode the milling vial was periodically opened under a protective gas and samples of the milled powder were extracted for microstructural examination whereas during continuous CRMA the vial was never opened up to 270 h duration. MgO was detected by XRD in sequentially milled powders while no MgO was detected in the continuously milled powder. The abundance of the nanostructured ternary complex hydride Mg₂FeH₆, produced during sequential milling, and estimated from DSC reached 44 wt.% after 188 h, and afterwards it slightly decreased to 42 wt.% after 210 and 270 h. In contrast, the DSC yield of Mg₂FeH₆ after continuous CRMA for 270 h was 57 wt.%. Much higher yield after continuous milling is attributed to the absence of MgO. This behavior provides strong evidence that MgO is a primary factor suppressing formation of Mg₂FeH₆. The DSC hydrogen desorption onset temperatures are close to 200 °C while the desorption peak temperatures for all powders are below 300 °C and the desorption process is completed within the range 10–20 min. Within the investigated nanograin size range of 5–13 nm, the DSC desorption onset and peak temperatures of β-MgH₂ and Mg₂FeH₆ do not exhibit any trend with nanograin (crystallite) size of hydrides. TPD hydrogen desorption peaks from the powders containing a single ternary complex hydride Mg₂FeH₆, are very narrow, which indicates the presence of small but well-crystallized hydride particles. Their narrowness provides good evidence that the phase composition, bulk hydrogen distribution and hydride particle size distribution are very homogeneous. The overall amount of hydrogen desorbed in TPD from single-hydride Mg₂FeH₆ powders is somewhat higher than that observed in DSC and TGA desorption.

The powder milled sequentially for 270 h and desorbed in a Sieverts-type apparatus at 250 and 290 °C, yielded about a half of the hydrogen content obtained during DSC and TGA tests. No desorption of hydrogen was detected in a Sieverts-type apparatus at 250 and 290 °C after 128 and 70 min, respectively, from the powder continuously milled for 270 h. The latter easily desorbed 3.13 and 2.83 wt.% hydrogen in DSC and TGA tests, respectively.