Role of phonons on phase stabilization of RE2Si2O7 over wide temperature range (RE = Yb,Gd)

Thermodynamic phase stabilities of α, β, γ and δ polymorphs of RE₂Si₂O₇ (RE = Yb, Gd), promising candidates for environmental barrier coating systems of gas turbine engines in next generations, were investigated using harmonic and quasi-harmonic lattice dynamics in conjunction with ab initio calculations. By quantifying their Gibbs free energies with dynamics of atoms taken into account, we showed the phase stability of β-Yb₂Si₂O₇ up to melting temperature under an ideal condition, and also under thermal stresses, ensuring the reliability of β-Yb₂Si₂O₇ in environmental barrier coating systems. It was also found that the difference of anharmonic phonons in these polymorphs, which was measured as mode Grüneisen parameters, significantly changed their phonon free energies and invoked the formation of δ-Gd₂Si₂O₇ at high temperature. These results enable a quantitative comprehension of the phase transformation of RE₂Si₂O₇ and future discussions of other factors which may affect the phase stability such as lattice defects.     

Phase stability and thermal conductivity of RE2O3 (RE=La,Nd, Gd,Yb) and Yb2O3 co-doped Y2O3 stabilized ZrO2 ceramics

Y₂O₃ stabilized ZrO₂ (YSZ) has been considered as the material of choice for thermal barrier coatings (TBCs), but it becomes unstable at high temperatures and its thermal conductivity needs to be further reduced. In this study, 1 mol% RE₂O₃ (RE=La, Nd, Gd, Yb) and 1 mol% Yb₂O₃ co-doped YSZ (1RE1Yb–YSZ) were fabricated to obtain improved phase stability and reduced thermal conductivity. For 1RE1Yb–YSZ ceramics, the phase stability of metastable tetragonal (t′) phase increased with decreasing RE³⁺ size, mainly attributable to the reduced driving force for t′ phase partitioning. The thermal conductivity of 1RE1Yb–YSZ was lower than that of YSZ, with the value decreasing with the increase of the RE³⁺ size mainly due to the increased elastic field in the lattice, but 1La1Yb–YSZ exhibited undesirably high thermal conductivity. By considering the comprehensive properties, 1Gd1Yb–YSZ ceramic could be a good potential material for TBC applications.     

M2(Si,Al)4(N,C)7 (M = La,Y,Ca) carbonitrides: II. The crystal structure of Ca0.8Y1.2Si4N6.8C0.2

A new (Ca,Y)Si₄(N,C)₇ phase has been characterised lying between the two end-members Y₂Si₄N₆C and CaYSi₄N₇. This phase is similar to BaYbSi₄N₇, which is made up of a network of [N(SiN₃)₄] structural units linked together in a three-dimensional network, with the large cations located in the interstices, but (Ca,Y)Si₄(N,C)₇ is a disordered variant, with nitrogen atoms partially occupying two sets of equivalent sites related by the combined operations of rotation and tilt. The crystal of (Ca,Y)Si₄(N,C)₇ used for structure determination contained Ca and Y in the atomic ratio 2:3, the excess positive charge in the cation sites being balanced by the partial replacement of nitrogen by carbon in the central non-metal site of the [N(SiN₃)₄] unit. Powder diffraction data are listed for Ca_0.8Y_1.2Si₄N_6.8C_0.2, which is hexagonal with a=5.9874(4), c=9.7849(8) Å at ambient temperature. The crystal structure has been determined from single crystal data; Z=2; S.G. P6₃mc (no. 186); R_int=0.0274, R1=0.0384, wR2=0.0993 for all data.     

Potential red-emitting NaGd(MO4)2:R (M=W,Mo, R=Eu,Sm, Bi) phosphors for white light emitting diodes applications

NaGd(MO₄)₂:R (M=W, Mo, R=Eu³⁺, Sm³⁺, Bi³⁺) phosphors were synthesized by solid-state reaction. The structure and photoluminescence properties of the samples were characterized using X-ray powder diffraction and fluorescence spectrophotometry. The ⁵D₀→⁷F₂ transition of Eu³⁺, which led to a red emission of the phosphors, was dominantly observed in the photoluminescence spectra. The doped Bi³⁺ and Sm³⁺ efficiently sensitized the emission of Eu³⁺ and effectively extended and strengthened the absorption of near-UV light with wavelengths ranging from 395 to 405 nm. In addition, energy transfers from Bi³⁺ to Eu³⁺ and from Sm³⁺ to Eu³⁺ occurred. The chromaticity coordinates of the obtained phosphors were close to the standard values of the National Television Standard Committee (x=0.670, y=0.330). The results suggest that NaGd(WO₄)_2−y(MoO₄)_y:Eu³⁺, Sm³⁺, Bi³⁺ is an efficient red-emitting phosphor for light-emitting diode applications.     

Effect of TiO2 and Ta2O5 co-doping on phase stability,fracture toughness,and sintering behavior of ZrO2 stabilized by 10mol%(Y0.4Gd0.3Yb0.3)2O3

The effect of TiO₂ and Ta₂O₅ co-doping on the phase structure, fracture toughness, and sintering behavior of 10mol%(Y_0.4Gd_0.3Yb_0.3)₂O₃-stabilized zirconia was investigated using X-ray diffraction, scanning electron microscopy, microindentation, and pressureless sintering. The results showed that 10mol%(Y_0.4Gd_0.3Yb_0.3)₂O₃–ZrO₂ had a single cubic phase structure, and an increase in the Ta₂O₅ (≥6 mol%) and TiO₂ doping concentrations resulted in a simultaneous increase in the content and stability of the tetragonal phase. The fracture toughness of TiO₂ and Ta₂O₅ co-doping 10mol%(Y_0.4Gd_0.3Yb_0.3)₂O₃–ZrO₂ decreased with an increase in the Ta₂O₅ content. On the other hand, the TiO₂ content had no significant effect on the fracture toughness of 10mol%(Y_0.4Gd_0.3Yb_0.3)₂O₃–ZrO₂. The sintering resistance of the specimens increased with an increasing in the Ta₂O₅ content; however, an increase in the TiO₂ content accelerated the densification of the specimens. When the Ta₂O₅ content was 10 mol% and the TiO₂ content was in the range of 4–8 mol%, a single non-transformable tetragonal phase structure with fracture toughness similar to that of 6–8 wt% Y₂O₃ stabilized ZrO₂ and excellent anti-sintering properties could be obtained. This structure can be explored as a thermal barrier coating material for high-temperature applications.     

Effects of ionic radius on phase evolution in Ln-Al co-doped Ca1-xLnxZrTi2-xAlxO7 (Ln = La,Nd, Gd,Ho, Yb) solid solutions

Zirconolite ceramic has been considered as a promising matrix to dispose high-level radioactive waste due to its excellent performance in immobilizing radionuclides. In this work, a series of zirconate solid solutions with stoichiometric Ca_1-xLn_xZrTi_2-xAl_xO₇ (Ln = La, Nd, Gd, Ho, Yb; x?=?0.1–1) were systematically studied to investigate the radius effect on their phase evolution. Powder X-ray diffraction (XRD) and scanning electron microscopy with energy dispersive X-Ray spectrometry (SEM-EDX) were used to characterize the products. XRD and SEM results show that complete solid solutions of Ln and Al in zirconolite phase for Ca_1-xLn_xZrTi_2-xAl_xO₇ cannot found. In the Ca_1-xLa_xZrTi_2-xAl_xO₇ ceramics, single zirconolite phase cannot form, instead of multiple phases, such as zirconolite-2M, zirconia, perovskite and LaTi₂Al₉O₁₉. In the Nd-Al co-doping ceramics, nearly single zirconolite-2M and zirconolite-3O were found at x?≤?0.6 and 0.8?≤?x?≤?0.9, respectively. The miscibility gap between zirconolite-2M and 3O was found at x?=?0.7. Single zirconolite-2M formed in the Gd-Al, Ho-Al and Yb-Al co-doped ceramics can only be detected in a compositional range of 0.1?≤?x?≤?0.8. Higher incorporation contents in these three series can form an additional phase cubic zirconia which is usually a ceramic waste form for radionuclides. Based on the XRD data, lattice parameters of zirconolite-2M and zirconolite-3O were calculated by Pawley refinement method. The evolution of lattice parameters of zirconolite-2M shows great difference between different lanthanide ions, indicating different substitution mechanisms in the Ln-Al co-doped zirconolite-2M.     

Phase stability and thermophysical properties of CeO2-Re2O3 (ReEu,Gd, Dy,Y, Er,Yb) co-stabilised zirconia

A series of 16 mol% CeO₂-2 mol% Re₂O₃ co-stabilised zirconia (ZrO₂) (16Ce4ReSZ, ReEu, Gd, Dy, Y, Er, Yb) ceramic materials were synthesised using a chemical coprecipitation– high-temperature roasting method. Their phase structure, high-temperature phase stability, mechanical properties, thermal conductivity and coefficient of thermal expansion (CTE) were investigated. The results show that the ZrO₂ tetragonal phase co-stabilised by CeO₂ and Re³⁺ with a smaller radius has better stability. The 16Ce4ReSZ (ReDy, Y, Er, Yb) materials have high fracture toughnesses, low thermal conductivities, and high CTE values. As the radius of the Re³⁺ ions decreases, the lattice energy increased, while the lattice distortion decreases, the CTE decreases slightly and the thermal conductivity of the material increases slightly. Owing to the high phase stability of 16Ce4YbSZ, its mechanical properties are best after 100 h of sintering at 1400 °C.     

Influence of Yb3+ ion incorporation in the structure of Yttrium Divanadate(V) on the properties of a new ceramic solid solution Y8-yYbyV2O17

New substitutional, limited solid solution of the formula Y_8-yYb_yV₂O₁₇ where 0 < y ≤ 2.0 was synthesized by the high-temperature reaction in the air from mixtures of α-Y₈V₂O₁₇ with Yb₈V₂O₁₇. The new Y_8-yYb_yV₂O₁₇ were characterized by powder XRD, DTA–TGA, IR, UV–vis-DRS and SEM methods. The structure, thermal stability, unit cell volume, band gap energies as well as the position of the IR absorption bands in the spectrum of Y_8-yYb_yV₂O₁₇ were determined. The solid solution was established to have the same structure as β-Y₈V₂O₁₇ and it was found that with increasing concentration of Yb³⁺ ions in its crystal lattice the volume of its unit cell decreases along with its energy gap decreasing to 2.4 eV (for y = 2.0), while the IR absorption bands are shifted towards higher wavenumbers. The morphologies of the high temperature polymorph of Y₈V₂O₁₇ and solid solution were analyzed.     

M2(Si,Al)4(N,C)7 (M=La,Y,Ca) carbonitrides: I. Synthesis and structural characterisation by XRD and NMR

A series of new nitrides and carbonitrides has been identified with crystal structures similar to those of the hexagonal quaternary nitrides of the type (Ba,Sr,Eu)YbSi₄N₇. The large divalent cations in these structures can be replaced by trivalent cations such as Ln and/or Y, if valency balance is preserved by the simultaneous substitution of carbon for nitrogen in the unique [4]-coordinated anion site. This has been demonstrated by carbon-13 magic-angle spinning NMR spectra which for the yttrium member of this series shows a peak at 36.7 ppm corresponding to carbon atoms occupying the central non-metal atom site in the characteristic [C(NSi₃)₄] structural unit. The resulting compounds have compositions of the types La₂Si₄N₆C, Y₂Si₄N₆C or (La,Y)₂Si₄N₆C; the crystal structure of a related mixed (Ca,Y) derivative of composition (Ca,Y)₂Si₄(N,C)₇ is reported in Part II of this series. When the two large cations are different, the hexagonal symmetry characteristic of the (Ba,Sr,Eu)YbSi₄N₇ compounds is maintained; when both cations are the same, lower symmetries are observed. The powder diffraction pattern of La₂Si₄N₆C indexes on an orthorhombic unit cell with a=6.0360(7), b=10.1246(9), c=10.5664(11) Å and the crystal structure has been determined. An alternative way of achieving valency balance without incorporation of carbon is to replace some of the silicon by aluminium; related derivatives of the type M₂Si₃AlN₇, where M=La, Y or mixed La,Y have been prepared and their unit cell dimensions are reported.     

Corrosion of RE2Si2O7 (RE=Y,Yb, and Lu) environmental barrier coating materials by molten calcium-magnesium-alumino-silicate glass at high temperatures

With the increased demand for high operating temperature of gas turbine engines, corrosion by molten calcium-magnesium-alumino-silicate (CMAS) exhibits a significant challenge to the development of durable environmental barrier coatings (EBCs). EBC candidates, γ-Y₂Si₂O₇, β-Yb₂Si₂O₇, and β-Lu₂Si₂O₇ were explored on their corrosion resistance to CMAS melts at 1300 °C and 1500 °C for 50 h. Interaction and degradation mechanisms were investigated and the corrosion behaviors showed different trends at high temperatures. At 1300 °C, RE₂Si₂O₇ dissolves into CMAS melts and apatite phases reprecipitate forming a thick recession layer. However, when the temperature increases to 1500 °C, CMAS melts vigorously penetrate through the grain boundary of RE₂Si₂O₇ and ‘blister’ cracks form throughout the samples. The reduced grain boundary stability at 1500 °C promotes the penetration of CMAS melts in RE₂Si₂O₇. Grain boundary engineering is critically demanded to optimize CMAS corrosion at high temperatures.     

Directionally solidified Al2O3-ME3Al5O12 (ME: Y,Er and Yb) eutectic coatings for thermophotovoltaic systems

Selective emitters for thermophotovoltaic systems consisting of directionally solidified Al₂O₃-ME₃Al₅O₁₂ (ME: Y, Er and Yb) eutectic coatings on Al₂O₃ substrates were produced and characterizated. Coatings were deposited by dip-coating on cylindrical substrates. After sintering, a continuous-wave CO₂ laser was used to produce the surface resolidification. The optimization of the processing parameters yielded dense eutectic coatings with good adhesion to the substrate and with 90–200 µm in thickness. All coatings were free of voids and showed a eutectic microstructure consisting of a three dimensional interpenetrated network of Al₂O₃ and ME₃Al₅O₁₂. The mechanical properties of the coatings (hardness and fracture toughness) were evaluated by indentation techniques. Thermal emission was studied by heating the rods with a CO₂ laser at temperatures between 1000 and 1400 °C. Selective emission was observed in Er³⁺ and Yb³⁺ based coatings and attributed to the electronic transitions of the rare earth ions. Er³⁺-coatings showed the best emission properties as selective emitters for thermophotovoltaic converters.     

Effect of multi-component rare-earth doping on maintaining structure stability of RE2Zr2O7 (RE = La,Sm, Gd,Y, Yb) coatings under thermal cycling

Inspired by the high entropy effects of high-entropy components, a novel high-entropy rare-earth zirconate (La_1/5Gd_1/5Y_1/5Sm_1/5Yb_1/5)₂Zr₂O₇ (HEC-LZ) was designed and successfully synthesized in this work. In addition, two binary rare-earth doped zirconates (RE-LZ), (La_1/3Sm_1/3Yb_1/3)₂Zr₂O₇ (LSYZ) and (La_1/3Gd_1/3Y_1/3)₂Zr₂O₇ (LGYZ), were proposed using the same rare-earth elements for comparison. The thermal barrier coatings with LZ-based ceramic top layer were prepared by spray granulation, solid-phase synthesis and atmospheric plasma spraying techniques. The as-synthesized LZ-based ceramics are all dominated by the pyrochlore phase. Under 1000 °C, the thermal cycling performances of the three coatings were studied. The microstructure evolution and crack expansion during the failure process were investigated in detail. The strengthening mechanism and the cause of coating spallation are proposed in combination with mechanical properties and thermal matching analysis. The results showed that compared with the undoped LZ coating, the thermal shock life of LGYZ coating, LSYZ coating and HEC-LZ coating is improved by nearly 46%, 27% and 57%, respectively. Due to the characteristics of high randomness, HEC-LZ ceramic has a large lattice distortion than RE-LZ ceramics, resulting in a higher coefficient of thermal expansion and fracture toughness, which contributes to maintaining the structure stability of coatings under thermal stress.     

Structural characterization of (Sm,Tb)PO4 solid solutions and pressure-induced phase transitions

Sm_1-xTb_xPO₄ solid solutions were synthesized and extensively characterized by powder X-ray diffraction, vibrational spectroscopy, and X-ray absorption spectroscopy. At ambient conditions solid solutions up to x?=?0.75 crystallize in the monazite structure, whereas TbPO₄ is isostructural to xenotime. For x?=?0.8 a mixture of both polymorphs was obtained. Moreover, a phase with anhydrite structure was observed coexisting with xenotime, which was formed due to mechanical stress. Selected solid solutions were investigated at pressures up to ～40?GPa using in situ high pressure synchrotron X-ray diffraction and in situ high pressure Raman spectroscopy. SmPO₄ and Sm_0.5Tb_0.5PO₄ monazites are (meta)stable up to the highest pressures studied here. TbPO₄ xenotime was found to transform into the monazite structure at a pressure of about 10?GPa. The transformation of Sm_0.2Tb_0.8PO₄ xenotime into the monazite polymorph commences already at about 3?GPa. This study describes the reversibility of the pressure-induced (Sm,Tb)PO₄ xenotime-monazite transformation.     

The influence of Gd doping on thermophysical properties,elasticity modulus and phase stability of garnet-type (Y1-xGdx)3Al5O12 ceramics

In this work, Gd³⁺ was selected to partially substitute the Y³⁺ in yttrium aluminum garnet (YAG) in order to improve the thermophysical properties of YAG. A series of (Y_1-xGd_x)₃Al₅O₁₂ (x = 0, 0.1, 0.2, 0.3, 0.4) ceramics were synthesized through chemical co-precipitation route. The microstructure, thermophysical properties and elasticity modulus of (Y_1-xGd_x)₃Al₅O₁₂ were investigated. The (Y_1-xGd_x)₃Al₅O₁₂ ceramics was comprised of single garnet-type Y₃Al₅O₁₂ phase. The thermal conductivities of (Y_1-xGd_x)₃Al₅O₁₂ bulk samples decreased with increasing doping concentration to 0.2, but increased with furthering increasing the concentration to 0.4. The thermal conductivity of (Y_0.8Gd_0.2)₃Al₅O₁₂ was 1.51 W m⁻¹ K⁻¹ at 1200 °C. The average thermal expansion coefficient of (Y_0.8Gd_0.2)₃Al₅O₁₂ was slightly larger than that of Y₃Al₅O₁₂. (Y_0.8Gd_0.2)₃Al₅O₁₂ bulk sample exhibited the lowest elasticity modulus among the investigated (Y_1-xGd_x)₃Al₅O₁₂. In addition, (Y_0.8Gd_0.2)₃Al₅O₁₂ ceramic remained good phase stability from room temperature to 1600 °C.     

Influence of Yb3+ doping on phase stability and thermophysical properties of (Y1-xYbx)3Al5O12 under high temperature

In this work, Yb³⁺ was selected to replace the Y³⁺ in yttrium aluminum garnet (YAG) in order to reduce its thermal conductivity under high temperature. A series of (Y_1-xYb_x)₃Al₅O₁₂ (x=0, 0.1, 0.2, 0.3, 0.4) ceramics were prepared by solid-state reaction at 1600 °C for 10 h. The microstructure, thermophysical properties and phase stability under high temperature were investigated. The results showed that all the Yb doped (Y_1-xYb_x)₃Al₅O₁₂ ceramics were comprised of a single garnet-type Y₃Al₅O₁₂ phase. The thermal conductivities of (Y_1-xYb_x)₃Al₅O₁₂ ceramics firstly decreased and subsequently increased with Yb ions concentration rising from room temperature to 1200 °C. (Y_0.7Yb_0.3)₃Al₅O₁₂ had the lowest thermal conductivity among investigated specimens, which was about 1.62 W m⁻¹ K⁻¹ at 1000 °C, around 30% lower than that of pure YAG (2.3 W m⁻¹ K⁻¹, 1000 °C). Yb had almost no effect on the coefficients of thermal expansion (CTEs) of (Y_1-xYb_x)₃Al₅O₁₂ ceramics and the CTE was approximate 10.7×10⁻⁶ K⁻¹ at 1200 °C. In addition, (Y_0.7Yb_0.3)₃Al₅O₁₂ ceramic remained good phase stability when heating from room temperature to 1450 °C.     

Synthesis,crystal structure,optical and adsorption properties of BaAl2O4: Eu2+, Eu2+/ L3+ (L = Dy,Er, Sm,Gd, Nd,and Pr) phosphors

In this work, the BaAl2O4: Eu²⁺, Eu²⁺/L³⁺ (L= Dy, Er, Sm, Gd, Nd, and Pr) phosphors were synthesized via a facile solid-state reaction method using LiCl as a flux material at 1100 °C. The structural properties, microstructure, adsorption and photoluminescence characteristics of products were evaluated by X-ray diffraction (XRD), field-emission scanning electron microscopy (FE-SEM), transmission electron microscopy (TEM), Uv–vis adsorption and photoluminescence (PL) analyses. The observation of XRD patterns showed that even 10% LiCl is not able to produce any impurity phase in BaAl₂O₄: Eu²⁺ crystal structure, although the microstructure morphology is considerably affected. The particle size of BaAl₂O₄: Eu²⁺ phosphors was about 220 nm while the use of LiCl flux resulted in a remarkable decrease of this parameter to about 120 nm. Furthermore, the PL patterns disclosed that Eu²⁺ ions have occupied one type of Ba²⁺ sites while larger quantities of lanthanides (L³⁺) occupied the second type of Ba²⁺ sites. The strongest photoluminescence emission intensity at the wavelength of 495 nm was achieved when 5 wt% LiCl was added to BaAl₂O₄: Eu²⁺. Also, the absorption analysis revealed that the addition of flux enriches the adsorption of Congo red (CR) dye on the phosphor powders. The use of 5 wt% flux material led to noticeable improvement of CR adsorption capacity from 38.53 to 48.3 mg g⁻¹.     

Temperature-Dependent Viscosity of SiREAl-Based Glasses as a Function of N:O and RE:Al Ratios (RE = La, Gd, Y, and Lu)

Tailoring glass compositions can raise the viscosity of SiREAl oxynitride glasses. In the present study, viscosity data are obtained by determining the compressive creep response of bulk glasses in air. The findings reveal that increasing both the nitrogen-to-oxygen and the yttrium-to-aluminum ratios of the glasses shifts the glass viscosity to higher temperatures. In addition, the substitution of progressively smaller rare earths in the glass composition results in a further increase in the glass viscosity. These effects have important implications in the creep resistance of silicon nitride ceramics where the amorphous intergranular films are a major factor in creep resistance.     

Sintering,thermal expansion,and thermal transport properties of A4Ta2O9 (A= Ca,Mg) tantalates

Searching for new oxides with low thermal conductivity and high thermal expansion coefficients (TECs) as thermal barrier coatings (TBCs) is vital for the development of highly efficient gas turbines and aeroengines. We report the densification sintering, high TECs, and low thermal conductivity of A₄Ta₂O₉ (A = Ca, Mg) tantalates. The best sintering temperature of dense A₄Ta₂O₉ ceramics was determined via an optical contact angle tester, and samples with a relative density of 99.8% were synthesized via spark plasma sintering (SPS). The hardness (9–10 GPa), Young's modulus (172.7–211.8 GPa) and fracture toughness (1.5–1.6 MPa m^1/2) of the A₄Ta₂O₉ ceramics are primarily affected by the bonding strength. Furthermore, we studied the thermal transport properties of A₄Ta₂O₉. The low thermal conductivity (1.78–1.93 W m^?1 K^?1 at 900 °C), extraordinary phase stability, and high TECs (11.4–11.8 × 10^?6 K^?1 at 1200 °C) of A₄Ta₂O₉ ceramics make them candidate TBCs with high operating temperatures.     

Experimental phase relations between MgO-saturated magnesium-aluminate spinel (MgAl2O4) and CuOx-rich liquid

Experimental phase equilibrium data for the Cu-O-Al₂O₃-MgO system is required to improve the performance of MgAl₂O₄-containing refractories and slagging in non-ferrous smelting. In this work, the phase relations of MgAl₂O₄ in the Cu-O-Al₂O₃-MgO system were studied experimentally in air within a temperature range of 1100–1400 °C using the equilibration and quenching method. The chemical compositions of the phases in the quenched samples were determined using electron probe microanalysis (EPMA). Less than 1 wt% of Al₂O₃ or MgO were found in the oxide liquid phase, whereas the solid MgAl₂O₄ and MgO phases contained up to 23 wt% and 30 wt% of ‘Cu₂O’, respectively. Discrepancies between these results and the corresponding calculated values generated by the MTDATA 6.0 software and Mtox database Version 8.2 ranged from 3 wt% to 19 wt%. The results of this work indicate that the MgAl₂O₄ spinel is chemically stable in the presence of a CuO_x-rich liquid under the conditions studied.