Thermal conductivity of yttria-stabilized zirconia thin films grown by plasma-enhanced atomic layer deposition

Zirconia doped with yttrium, widely known as yttria-stabilized zirconia (YSZ), has found recent applications in advanced electronic and energy devices, particularly when deposited in thin film form by atomic layer deposition (ALD). Although ample studies reported the thermal conductivity of YSZ films and coatings, these data were typically limited to Y₂O₃ concentrations around 8 mol% and thicknesses greater than 1 μm, which were primarily targeted for thermal barrier coating applications. Here, we present the first experimental report of the thermal conductivity of YSZ thin films (∼50 nm), deposited by plasma-enhanced ALD (PEALD), with variable Y₂O₃ content (0–36.9 mol%). Time-domain thermoreflectance measures the effective thermal conductivity of the film and its interfaces, independently confirmed with frequency-domain thermoreflectance. The effective thermal conductivity decreases from 1.85 to 1.22 W m⁻¹ K⁻¹ with increasing Y₂O₃ doping concentration from 0 to 7.7 mol%, predominantly due to increased phonon scattering by oxygen vacancies, and exhibits relatively weak concentration dependence above 7.7 mol%. The effective thermal conductivities of our PEALD YSZ films are higher by ∼15%–128% than those reported previously for thermal ALD YSZ films with similar composition. We attribute this to the relatively larger grain sizes (∼23–27 nm) of our films.     

The influence of hafnium removal on the microstructure and properties of 8YSZ ceramics

The effects of hafnium removal on the sinterability, phase composition, and microstructural, mechanical, and electrical properties of 8YSZ (8 mol% yttrium stabilized zirconia) were investigated using SEM, XRD, Raman spectroscopy, EBSD, three-point bending, Vickers indentation, and impedance spectroscopy. The 8YSZ and 8YSZ₀ (8 mol% yttrium-stabilized hafnium-free zirconia) ceramics were prepared via dry pressing and atmospheric sintering, respectively. The overall mechanical properties of the 8YSZ₀ ceramic were poor. However, at a sintering temperature of 1450°C, the relative density of 8YSZ and 8YSZ₀ ceramics was almost identical. 8YSZ₀ had a slightly smaller grain size and activation energy, and its electrical properties were slightly better than those of the 8YSZ ceramics. The presence of tetragonal secondary phases in the cubic structure of 8YSZ ceramics inhibited crack propagation and led to an increase in the mechanical properties and a decrease in the ion conductivity. In terms of the crystal structure, the increase in the cubic phase lattice parameters and tetragonal phase c/a values of the 8YSZ₀ ceramics was attributed to the larger Zr⁴⁺radius, reduced local lattice distortion, and increased matrix oxygen vacancy concentration and cubic phase content. The EBSD analysis results indicated that there was no significant difference in grain orientation between the two types of ceramics, but the content of 8YSZ ceramics in large angle grain boundaries was slightly higher, especially in special grain boundaries Σ3 and Σ9. Therefore, this material can be used as a solid-state electrolyte candidate.     

High Yttria–Zirconia and Yttria Ceramics for Petrochemical Reverse‐Flow Reactor Applications

Reverse‐flow reactors achieve the desired hydropyrolysis reaction of natural gas and other hydrocarbon feeds at very high temperatures of up to 2000°C, which enables the production of many high‐value chemicals. To identify refractory ceramic materials suitable for constructing key components of the reactor, the full range of solid solutions between zirconia and yttria having 18 to 100 mol% yttria have been tested in a laboratory reactor. Conventional yttria‐stabilized zirconia (YSZ) materials having 8 mol% Y₂O₃ appear to accommodate reactor thermal severity, but are prone to a new form of corrosion termed ceramic dusting that is observed when pyrolysis and oxidation cycles are alternated under reverse‐flow conditions. Yttria and high yttria–zirconia ceramics having ~80 mol% or more yttria suppress ceramic dusting corrosion in steam‐free pyrolysis environments. The addition of low levels of steam of ~5% to the pyrolysis gas stream increases the stability of YSZ materials substantially, so that the stability threshold is closer to 40 mol% Y₂O₃ in the yttria–zirconia system. The two approaches can be combined to optimize reactor performance. Key experimental results are presented and discussed taking into account the thermodynamic phase stability of the different phases.     

Experimental investigation of Al2O3/8YSZ and CeO2/8YSZ plasma sprayed thermal barrier coating on diesel engine

In this research work, aluminium oxide/yttria stabilized zirconia (20%Al₂O₃/80%8YSZ) and ceria/yttria stabilized zirconia (20%CeO₂/80%8YSZ) were coated through atmospheric plasma spray technique (APS) as thermal barrier coating (TBC) over CoNiCrAlY bond coat on aluminium alloy (Al-13%Si) substrate piston crown material and their thermal cycling behavior were studied experimentally. Thermal cycle test of both samples were conducted at 800?°C. Microstructural, phase and elemental analysis of the TBC coatings were experimentally investigated. The performance, combustion and emission characteristics of Al₂O₃/8YSZ, CeO₂/8YSZ TBC coated and uncoated standard diesel engine were experimentally investigated. The test results revealed that CeO₂/8YSZ based TBC has an excellent thermal cycling behavior in comparison to the Al₂O₃/8YSZ based TBC. The spallation of the Al₂O₃/8YSZ TBC occurred mainly due to the formation of thermally grown oxide (TGO), and growth of residual stresses at top coating and bond coating interface. The experimental results also revealed that the increase of brake thermal efficiency and reduction of specific fuel consumption for both TBC coated engine. Further reduction of HC, CO and smoke and increase of NOx emission were recorded for both TBC coated engine compared to the standard diesel engine.     

Highly-stable,nondegradable M2A-reinforced YSZ ceramic composites prepared by SPS

Magnesia-rich spinel (M₂A)-reinforced yttria-stabilized zirconia (YSZ) ceramic composites have been fabricated by SPS using m-ZrO₂, Y₂O₃, and waste-derived M₂A powders. The results showed that m-ZrO₂ in M₂A-free YSZ0 specimen is partially stabilized upon temperature rising into tetragonal phase whereas YSZ10-50 composites containing 10-50 wt% M₂A demonstrated variant behavior where their m-ZrO₂ is stabilized into a cubic form. YSZ10-50 composites SPSed at 1400°C for 30 minutes revealed greater than 99% relative density, 10-13 GPa Vickers hardness, 3.5-5 MPa m^0.5 fracture toughness and less than 0.5% apparent porosity. Aging hydration test for five hours soaking at 134°C and water vapor pressure of 2 bar, resulted in a conversion of ~2.8% of t-ZrO₂ to m-ZrO₂ for M₂A-free YSZ0 composite but it does not affect the YSZ10-50 composites. The outcomes indicate that M₂A has significantly improved both the densification and stabilization behavior of m-ZrO₂ through facilitating the diffusion of Y³⁺, Mg²⁺, and Al³⁺ ions inside zirconia lattice structure. In this regard, this study opens the door wide for producing fully stabilized c-ZrO₂ ceramics that could be potentially utilized as industrial ceramics for a broad scope of structural applications of high temperature, high-stress and corrosive environmental conditions.     

Phase stability,thermo-physical properties and thermal cycling behavior of plasma-sprayed CTZ,CTZ/YSZ thermal barrier coatings

ZrO₂ co-stabilized by CeO₂ and TiO₂ with stable, nontransformable tetragonal phase has attracted much attention as a potential material for thermal barrier coatings (TBCs) applied at temperatures >?1200?°C. In this study, ZrO₂ co-stabilized by 15?mol% CeO₂ and 5?mol% TiO₂ (CTZ) and CTZ/YSZ (zirconia stabilized by 7.4?wt% Y₂O₃) double-ceramic-layer TBCs were respectively deposited by atmospheric plasma spraying. The microstructures, phase stability and thermo-physical properties of the CTZ coating were examined using scanning electron microscopy (SEM), X-ray diffraction (XRD), thermogravimetric-differential scanning calorimeter (TG-DSC), laser pulses and dilatometry. Results showed that the CTZ coating with single tetragonal phase was more stable than the YSZ coating during isothermal heat-treatment at 1300?°C. The CTZ coating had a lower thermal conductivity than that of YSZ coating, decreasing from 0.89?W?m^?1 K^?1 to 0.76?W?m^?1 K^?1 with increasing temperature from room temperature to 1000?°C. The thermal expansion coefficients were in the range of 8.98?×?10^?6 K^?1 – 9.88 ×10^?6 K^?1. Samples were also thermally cycled at 1000?°C and 1100?°C. Failure of the TBCs was mainly a result of the thermal expansion mismatch between CTZ coating and superallloy substrate, the severe coating sintering and the reduction-oxidation of cerium oxide. The thermal durability of the TBCs at 1000?°C can be effectively enhanced by using a YSZ buffer layer, while the thermal cycling life of CTZ/YSZ double-ceramic-layer TBCs at 1100?°C was still unsatisfying. The thermal shock resistance of the CTZ coating should be improved; otherwise the promising properties of CTZ could not be transferred to a well-functioning coating.     

Determinations of Ce solid solution mechanism and limit thermal conductivity of YTaO4 ceramics

x mol% CeO₂-YTaO₄ (x = 0, 3, 6, 9, 12) ceramics have been synthesized by the spark plasma sintering (SPS) technique. We focus on the changes in lattice distortion, bonding length, thermal conductivity, thermal expansion, and phase stability of the prepared samples. XRD, Raman, and XPS are used to determine the chemical valence and solid solution mechanism of Ce in the lattice of YTaO₄, while its effects on thermal/mechanical properties are elucidated from microstructures. Y³⁺ is substituted via Ce³⁺, and all samples maintain a monoclinic phase. The limit thermal conductivity (1.2 W?m^?1?K^?1, 900 °C) is realized in 9 mol% CeO₂-YTaO₄, and the thermal expansion coefficients are increased to 10.2 × 10^?6 K^?1 at 1200 °C. Furthermore, the exceptional phase stability and mechanical properties of all samples indicate that they can provide good thermal insulation at high temperatures, and have higher working temperatures than the current YSZ thermal barrier coatings.     

Thermal stability and sintering behavior of plasma sprayed nanostructured 7YSZ, 15YSZ and 5.5SYSZ coatings at elevated temperatures

Nanostructured scandia, yttria doped zirconia (5.5SYSZ), 7 wt% yttria stabilized zirconia (7YSZ) and 15YSZ thermal barrier coatings (TBCs) were produced by plasma spraying on nickel-based superalloy substrates with NiCrAlY as the bond coat. The thermal stability and sintering behavior of the three as-sprayed TBCs at 1480 °C were investigated. The results indicated that the thermal stability of SYSZ and TBCs was longer than the 7YSZ TBCs due to higher amount of tetragonal phase. Furthermore, the results demonstrated that the nanostructured 7YSZ coating exhibits higher sintering resistance than 5.5SYSZ TBC.     

Thermal stability of plasma-sprayed La2Ce2O7/YSZ composite coating

A composite coating composed of La₂Ce₂O₂ (LCO) and yttria-stabilized zirconia (YSZ) in a weight ratio of 1:1 was deposited by the plasma spraying using a blended YSZ and LCO powders, and the stability of the LCO/YSZ interface exposed to a high temperature was investigated. The LCO/YSZ deposits were exposed at 1300 °C for different durations. The microstructure evolution at the LCO/YSZ interface was investigated by quasi-in-situ scanning electron microscopy assisted by X-ray energy-dispersive spectrum analyses and X-ray diffraction measurements. At an exposure temperature of 1300 °C, the grain morphology of LCO splats in contact with YSZ splats changed from columnar grains to quasi-axial grains with interface healing, and some grains tended to disappear during the thermal exposure. The results indicate that the phases in LCO–YSZ composite coating are not stable at 1300 °C. The element La in the LCO splat diffused towards the adjacent YSZ splat during the exposure, generating the reaction product layers composed of La₂Zr₂O₇ between the LCO and YSZ splats. After exposed for 200 h, the composite coating consisted of a mixture of mainly La₂Zr₂O₇ and CeO₂ and a minor amount of YSZ, accounting for the unusual decrease in the thermal conductivity at the late stage of exposure.     

Development of stabilized zirconia–alkali salts dual membranes for carbon dioxide capture

Molten Na₂CO₃–K₂CO₃ (NKC, 56–44 mol%) eutectic compositions were vacuum-impregnated, at the eutectic temperature, into two porous ZrO₂:8.6 mol% MgO (magnesium-partially stabilized zirconia, MgPSZ) and ZrO₂:8 mol% Y₂O₂ (yttria-fully stabilized zirconia, 8YSZ) ceramics. Thermogravimetric analyses were performed in mixtures of that composition with MgPSZ and 8YSZ ceramic powders. Before impregnation, porosity was achieved in the two compounds by addition and thermal removal of 30 vol.% NKC. To ascertain the carbonates had filled up through the ceramic body, both sides of the parallel and fracture surfaces of the disk-shaped impregnated compositions were observed in a scanning electron microscope and analyzed by energy-dispersive X-ray spectroscopy. The electrical conductivity of the two ceramics, before and after impregnation, was evaluated by electrochemical impedance spectroscopy in the 5 Hz–13 MHz frequency range from approximately 530 to 740°C. The permeation of the carbonate ions through the membranes via the eutectic composition was assessed by the threshold temperatures of the onset of the carbonate ion percolation. The objectives were to prepare dual-phase membranes for the separation of carbon dioxide and for the development of carbon dioxide sensors.     

Development of Ce‐PSZ‐/Y‐PSZ‐Toughened Alumina Inserts for High‐Speed Machining Steel

The nanocomposite CeO₂/Y₂O₃ partially stabilized zirconia (Ce‐PSZ/Y‐PSZ)‐toughened alumina was prepared by wet chemical simultaneous coprecipitation process. The thermal stability of phases and morphology of powders were characterized by TG‐DTA, FTIR, and FESEM. The microstructure, stabilization of phases and compositional analysis with different mol% CeO₂/Y₂O₃‐doped zirconia in alumina are characterized by FESEM, XRD, and EDAX spectra. Significant improvement in fracture toughness and flexural strength has been observed in 10 vol% of partially stabilized zirconia (2.5 mol% Y₂O₃ in ZrO₂/9 mol% CeO₂ in ZrO₂)‐toughened alumina, which is suitable for high‐speed machining applications.     

Effect of CeO2 doping on high temperature oxidation resistance of YSZ TBCs

In the present work, YSZ TBCs and 10 wt% CeO₂-doped YSZ thermal barrier coatings (CeYSZ TBCs) were prepared via atmospheric plasma spraying(APS) respectively, whereupon high temperature oxidation experiment was carried out at 1100 °C to compare the high temperature oxidation behavior and mechanism of the two TBCs. The results showed that the doping of CeO₂ reduced the porosity of YSZ TBCs by 23%, resulting in smaller oxidation weight gain and lower TGO growth rates for CeYSZ TBCs. Besides, the TGO generated in CeYSZ TBCs was obviously thinner and there were fewer defects inside it. For YSZ TBCs, as the oxidation process proceeded, Al, Cr, Co and Ni elements in the bonding coating were oxidized successively to form loose and porous spinel type oxides (CS), which was apt to cause the spalling failure of TBCs. While, the Al₂O₃ layer of the TGO generated in CeYSZ TBCs ruptured later than that in YSZ TBCs, which delayed the oxidation of Cr, Co, and Ni elements and the formation of CS accordingly. Therefore, CeO₂ doping can effectively improve the high temperature oxidation resistance of YSZ TBCs.     

Effects of manganese oxide addition and reductive atmosphere annealing on the phase stability and microstructure of yttria stabilized zirconia

The effects of Mn₃O₄ addition and reductive atmosphere (N₂:H₂ = 97:3) annealing on the microstructure and phase stability of yttria stabilized zirconia (YSZ) ceramics during sintering at 1500 °C for 3 h in air and subsequent annealing in a reductive atmosphere were investigated. Mn₃O₄ added 6 mol% YSZ (6YSZ) and 10 mol% YSZ (10YSZ) ceramics were prepared via the conventional solid-state reaction processes. The X-ray diffraction results showed that a single cubic phase of ZrO₂ was obtained in 1 mol% Mn₃O₄ added 6YSZ ceramic at a sintering temperature of 1500 °C for 3 h. A trace amount of monoclinic ZrO₂ phases were observed for 1 mol% Mn₃O₄ added 6YSZ ceramics after annealing at 1300 °C for 60 cycles in a reductive atmosphere by transmission electron microscopy. Furthermore, a single cubic ZrO₂ phase existed stably as Mn₃O₄ added 10YSZ ceramics was annealed at 1300 °C for 60 cycles in reductive atmosphere.     

Low–thermal–conductivity and high–toughness CeO2–Gd2O3 co–stabilized zirconia ceramic for potential thermal barrier coating applications

Yttria partially stabilized zirconia (～4.0?mol% Y₂O₃–ZrO₂, 4YSZ) has been widely employed as thermal barrier coatings (TBCs) to protect the high–temperature components of gas–turbine engines. The phase stability problem existing in the conventional 4YSZ has limited it to application below 1200?°C. Here we report an excellent zirconia system co–doped with 16?mol% CeO₂ and 4?mol% Gd₂O₃ (16Ce–4Gd) presenting nontransformable feature up to 1500?°C, in which no detrimental monoclinic (m) ZrO₂ phase formed on partitioning. It also exhibits a high fracture toughness of ～46?J m^?2 and shows high sintering resistance. Besides, the thermal conductivity and thermal expansion coefficient of 16Ce–4Gd are more competent for TBCs applications as compared to the 4YSZ. The combination of properties suggests that the 16Ce–4Gd system could be of potential use as a thermal barrier coating at 1500?°C.     

Structure and properties of Al2O3-bonded porous fibrous YSZ ceramics fabricated by aqueous gel-casting

To meet requirements for high porosity and high strength, novel aqueous gel-casting process has been successfully developed to fabricate Al₂O₃-bonded porous fibrous YSZ ceramics with ρ-Al₂O₃ and YSZ fibers as raw materials. Microstructure, phase composition, apparent porosity, bulk density, thermal conductivity, and compressive strength of fabricated porous ceramics were investigated, and effects of fiber content on properties were discussed. According to results, bird nest 3D mesh with interlaced YSZ fibers and Al₂O₃ binder was formed, ensuring the ability to obtain high performance, lightweight ceramics. An increase in the number of YSZ fibers led to more complex interlaced arrangement of fibers and denser network structure of porous ceramics at retaining their stability. Furthermore, their apparent porosity and bulk density increased, whereas thermal conductivity and compressive strength decreased with increasing the fiber content. In particular, comparatively high porosity (71.1–72.7%), low thermal conductivity (0.209–0.503 W/mK), and relatively high compressive strength (3.45–4.24 MPa) were obtained for as-prepared porous ceramics, making them promising for applications in filters, thermal insulation materials, and separation membranes.     

Effect of Ga2O3 on Sintering and Phase Stability of Sc2O3‐Doped Tetragonal Zirconia Prepared via Aqueous Solution Route

The effects of the presence of Ga₂O₃ on low‐temperature sintering and the phase stability of 4, 5, and 6 mol% Sc₂O₃‐doped tetragonal zirconia ceramics (4ScSZ, 5ScSZ, and 6ScSZ, respectively) were investigated. A series of zirconia sintered bodies with compositions (ZrO₂)_0.99?x(Sc₂O₃)_x(Ga₂O₃)_0.01, x = 0.04, 0.05, and 0.06 was fabricated by sintering at 1000°C to 1500°C for 1 h using fine powders that were prepared via the combination of homogeneous precipitation method and hydrolysis technique using monoclinic zirconia sols synthesized through the forced hydrolysis of an aqueous solution of zirconium oxychloride at 100°C for 168 h. The presence of 1 mol% Ga₂O₃ was effective in reducing sintering temperature necessary to fabricate dense bodies and enabled to obtain dense sintered bodies via sintering at 1100°C for 1 h. The phase stability, that is, low‐temperature degradation behavior of the resultant zirconia ceramics was determined under hydrothermal condition. The zirconia ceramics codoped with 1 mol% Ga₂O₃ and 6 mol% Sc₂O₃ (1Ga6ScZ) fabricated via sintering at 1300°C for 1 h showed high phase stability without the appearance of monoclinic zirconia phase, that is the tetragonal‐to‐monoclinic phase transformation was not observed in the 1Ga6ScZ after treatment under hydrothermal condition at 150°C for 30 h.     

A novel way to fabricate highly porous fibrous YSZ ceramics with improved thermal and mechanical properties

Inspired by nest structure, highly porous fibrous yttria-stabilized zirconia (YSZ) ceramics were fabricated through tert-butyl alcohol (TBA)-based gel-casting process and pressureless sintering by using YSZ fibers as raw material and adding K₂SO₄ as removable sintering aid. Different sintering temperature and soaking time were investigated to achieve optimal thermal and mechanical properties. The results show that all specimens consist of crystallized t-YSZ phase. Fibers interconnect with good interfacial bonding on junctions. Under higher sintering temperature, porosity drops gradually while compressive strength increases significantly. With prolonged soaking time, there is no obvious change in porosity and compressive strength increases gradually. All specimens have uniformly distributed pores with average size of 30.2 μm and show good structural stability at high temperature. Ultra-low thermal conductivity is achieved and ductile fracture mode with high elongation makes it more applicable in high-temperature thermal insulating applications.     

Brazing YSZ ceramics by a novel SiO2 nanoparticles modified Ag filler

Yttria-stabilized zirconia (YSZ) ceramics are soundly brazed in air using a novel amorphous SiO₂ nanoparticles (NPs) modified Ag filler. Scanning electron microscopy, transmission electron microscopy and X-ray diffraction are employed to characterize the interfacial microstructure of YSZ joints. A uniform amorphous SiO₂ layer is observed on the YSZ substrate surface. Micro-sized SiO₂ clusters are dispersed in the Ag braze matrix, which forms the brazing seam. The content of SiO₂ NPs and the brazing temperature exert significant effects on the formation of YSZ joints. The maximum shear strength of YSZ joints reaches 47 MPa under the optimized brazing conditions (Ag–2SiO₂, 1050 °C/30 min, 2 MPa load pressure).     

Layered YSZ/SCSZ/YSZ Electrolytes for Intermediate Temperature SOFC Part I: Design and Manufacturing

(Sc₂O₃)_0.1(CeO₂)_0.01(ZrO₂)_0.89 (SCSZ) ceramic electrolyte has superior ionic conductivity in the intermediate temperature range (700–800 °C), but it does not exhibit good phase and chemical stability in comparison with 8 mol% Y₂O₃–ZrO₂ (YSZ). To maintain high ionic conductivity and improve the stability in the whole electrolyte, layered structures with YSZ outer layers and SCSZ inner layers were designed. Because of a mismatch of coefficients of thermal expansion and Young's moduli of SCSZ and YSZ phases, upon cooling of the electrolytes after sintering, thermal residual stresses will arise, leading to a possible strengthening of the layered composite and, therefore, an increase in the reliability of the electrolyte. Laminated electrolytes with three, four, and six layers design were manufactured using tape‐casting, lamination, and sintering techniques. After sintering, while the thickness of YSZ outer layers remained constant at ∼30 μm, the thickness of the SCSZ inner layer varied from ∼30 μm for a Y–SC–Y three‐layered electrolyte, ∼60 μm for a Y–2SC–Y four‐layered electrolyte, and ∼120 μm for a Y–4SC–Y six‐layered electrolyte. The microstructure, crystal structure, impurities present, and the density of the sintered electrolytes were characterized by scanning and transmission electron microscopy, X‐ray and neutron diffraction, secondary ion mass spectroscopy, and water immersion techniques.     

Effect of spontaneous polarization of tourmaline on the grain growth behavior of 3YSZ powder

This paper introduces a new method for adjusting the particle size of ZrO₂ powder through the electric field effect of tourmaline. The 3 mol% yttria-stabilized ZrO₂ (3YSZ) powder was prepared by using ZrOCl₂∙8H₂O, YCl₃∙6H₂O, NaOH, and nano-tourmaline powder as raw materials through direct precipitation. The powder was characterized with thermogravimetric-differential scanning calorimeter, X-ray diffraction, Brunauere-Emmette-Teller, Fourier transform infrared, scanning electron microscope, and transmission electron microscope, and the mechanism of tourmaline in the process of powder preparation was also discussed. Findings demonstrate that the electric field generated by spontaneous polarization of tourmaline can control the size of ZrO₂ crystal grains, improve the dispersibility of the powder, and promote the stability of ZrO₂ in the tetragonal phase. When the electric intensity of tourmaline is 9.02 × 10⁶ V/m, and the addition amount is 2.5 vol%, tourmaline/3YSZ powders are mainly tetragonal phase, and the grain size is the smallest, with an average crystallite size of 19 nm. Then the mechanical properties of tourmaline/3YSZ ceramics were tested. Compared with 3YSZ ceramics without tourmaline, the flexural strength and fracture toughness were improved by 39.5% and 35.8%.