The effect of alumina addition on the electrical conductivity of Gd-doped ceria

Acceptor doped-ceria is a possible electrolyte material for the IT-SOFC (intermediate temperature solid oxide fuel cell) due to its high oxygen-ion conductivity. However, its use has been limited by its mechanical weakness and the appearance of electronic conductivity in reducing condition. In this study, alumina was selected as an additive in the doped-ceria to see if it increases the oxygen-ion conductivity and mechanical strength. Effects of alumina addition in doped ceria were studied as a function of alumina content and acceptor (Gd) content. The electrical conductivity of (Ce_1−x Gd _x O_2−δ)_1−y + (Al₂O₃) _y (x = 0–0.35, y = 0–0.10) was measured by using impedance spectroscopy. The grain conductivity of Ce_0.8Gd_0.2O_2-δ (GDC20) with 5 mol% alumina increased ∼3 times from that of GDC20 at 300^∘C. The grain conductivity was even ∼2 times higher than that of Ce_0.9Gd_0.1O_2−δ (GDC10) at 300^∘C. The electrical conductivity of GDC20 without alumina addition, measured at 500^∘C in air, rapidly decreased after exposure to reducing condition (Po₂∼10⁻²² atm) at 800^∘C. However, the decrease was much slower in GDC20 with alumina addition, indicating the improved mechanical strength. Among the examined compositions, (Ce_0.75Gd_0.25 O_2-δ)_0.95 + (Al₂O₃)_0.05 (GDC25A5) showed the highest conductivity at most temperatures.     

Nano-sized Pr<Subscript>0.8</Subscript>Sr<Subscript>0.2</Subscript>Co<Subscript>1-x</Subscript>Fe<Subscript>x</Subscript>O<Subscript>3</Subscript> powders prepared by single-step combustion synthesis for solid oxide fuel cell cathodes

Different sets of perovskite-type oxides of general formula Pr_0.8Sr_0.2Co_1-xFe_xO_3-δ (x = 0.0, 0.2, 0.5, 0.8 and 1.0) were successfully prepared by low-cost single-step combustion synthesis at low temperatures based on the auto-ignition reaction of a nitrate solution in the presence of citric acid. Thermogravimetric and differential thermal analysis was carried out on nitrate-citrate precursors to determine the perovskite-phase formation process. The results revealed that the nitrate-citrate precursor exhibited self-propagating combustion behavior. Pr_0.8Sr_0.2Co_1-xFe_xO_3-δ powders showed an orthorhombic single-phase, with their unit cell volume increasing as a function of the Fe content (x). Scanning electron microscopy observations showed that the prepared powders were nanocrystalline. The Pr_0.8Sr_0.2Co_1-xFe_xO_3-δ powders were characterized as fuel cell electrodes on Ce_0.8Sm_0.2O_2-δ pellets in symmetrical cells, and the electrochemical properties of the electrode/electrolyte interfaces were investigated using electrochemical impedance spectroscopy (EIS) as a function of the temperature, Fe content (x) and oxygen partial pressure.     

Oxygen Permeation Properties of Ceria-Ferrite-Based Composites

The oxygen flux density of Ce_0.8Gd_0.2O_1.9–x vol% MnFe₂O₄ (CGO-xMFO) composite-type ceramics membranes has been investigated. The samples and reforming catalysts were prepared by the Pechini process. For the CGO-xMFO composites, oxygen permeation was observed even at x = 3 vol%, presumably due to the presence of grain boundary phases. For CGO-15MFO, the n-type electronic conductivity was found to be dominant at 900C or higher. The thickness dependence of jO₂ revealed that surface exchange kinetics was significantly involved in the case of the membrane thickness of L < 0.5 mm. The highest oxygen flux density of 10 molcm^–2s^–1 was achieved for CGO-15MFO with the 10 mass% Ni-Pr:CeO₂ catalyst (L = 0.25 mm) at 1000C and a flow rate of 270 sccm.     

Praseodymium-cerium oxide thin film cathodes: Study of oxygen reduction reaction kinetics

Praseodymium-Cerium Oxide (Pr_xCe_1-xO_2−δ; PCO), a potential three way catalyst oxygen storage material and solid oxide fuel cell (SOFC) cathode, exhibits surprisingly high levels of oxygen nonstoichiometry, even under oxidizing (e.g. air) conditions, resulting in mixed ionic electronic conductivity (MIEC). In this study we examine the redox kinetics of dense PCO thin films using impedance spectroscopy, for x = 0.01, 0.10 and 0.20, over the temperature range of 550 to 670°C, and the oxygen partial pressure range of 10⁻⁴ to 1 atm O₂. The electrode impedance was observed to be independent of electrode thickness and inversely proportional to electrode area, pointing to surface exchange rather than bulk diffusion limited kinetics. The large electrode capacitance (10⁻²F) was found to be consistent with an expected large electrochemically induced change in stoichiometry for x = 0.1 and x = 0.2 PCO. The PCO films showed surprisingly rapid oxygen exchange kinetics, comparable to other high performance SOFC cathode materials, from which values for the surface exchange coefficient, k ^q , were calculated. This study confirms the suitability of PCO as a model MIEC cathode material compatible with both zirconia and ceria based solid oxide electrolytes.     

Effects of strontium gallate additions on sintering behavior of gadolinia-doped ceria

The densification behavior and grain growth of Ce_0.8Gd_0.2O_1.9 ceramics were investigated with the strontium gallate concentration ranging from 0 to 5 mol%. Both the sintered density and grain size were found to increase rapidly up to 0.5 mol% Sr₂Ga₂O₅, and then to decrease with further addition. Dense Ce_0.8Gd_0.2O_1.9 ceramics with 97% of the theoretical density could be obtained for 0.5 mol% Sr₂Ga₂O₅-added specimen sintered at 1250^∘C for 5 h, whereas pure Ce_0.8Gd_0.2O_1.9 ceramics needed to be sintered at 1550^∘C in order to obtain an equivalent theoretical density. The addition of Sr₂Ga₂O₅ was found to promote the sintering properties of Gd₂O₃-doped CeO₂.     

Nonstoichiometry and Defect Chemistry in Praseodymium-Cerium Oxide

Praseodymium cerium oxide (Pr_xCe_{1 – x}O_{2 –} ) is a mixed ionic-electronic conductor with high levels of nonstoichiometry under oxidizing conditions resulting from reduction of Pr^{4 +} to Pr^{3 +}. Coulometric titration measurements performed on (Pr_xCe_{1 – x}O_{2 –} ) with x = 0.2 are generally consistent with those derived from electrical conductivity measurements. Nevertheless, a somewhat larger degree of nonstoichiometry measured via coulometric titration implies that non-charged defect species may be significant in the system.     

Defects and transport in Gd-doped BaPrO3

The electrical conductivity of BaPr_1−x Gd_xO_3−δ has been characterized by means of the four-point van der Pauw technique at 200–1100 °C as a function of pO₂ and pH₂O. The contributions from ionic charge carriers were investigated by the EMF of concentration cells and the H⁺/D⁺ isotope effect on the total conductivity. BaPr_1−x Gd _x O_3−δ is predominately a p-type electronic conductor under oxidizing conditions, while ionic conduction is barely measurable. Gd(III) substituted for Pr(IV) is charge compensated mainly by electron holes, with protons and oxygen vacancies contributing significantly but as minority defects only at low temperatures (wet conditions) and at high temperatures, respectively. The conductivity behaviour has been modelled under these assumptions to extract thermodynamic parameters for the defect reactions at play. The practical use of this material is limited by its poor chemical stability.     

Microwave dielectric properties of Ca[(Li1/3Nb2/3)1−x Tix]O3−δ ceramics with glass

The effect of the addition of glass on the densification, low temperature sintering, and microwave dielectric properties of the Ca[(Li_1/3Nb_2/3)_1−x Ti_x]O_3−δ(CLNT) was investigated. Addition of glass (B₂O₃-ZnO-SiO₂-PbO system) improved the densification and reduced the sintering temperature from 1150^∘C to 900^∘C of Ca[(Li_1/3Nb_2/3)_1−x -Ti_x]O_3−δ microwave dielectric ceramics. As increasing glass contents from 10 wt% to 15 wt%, the dielectric constants (ε_r) and bulk density were increased. The quality factor (Q⋅f₀), however, was decreased slightly. The temperature coefficients of the resonant frequency (τ_f) shifted positive value as increasing glass contents over Ti content is 0.2 mol. The dielectric properties of Ca[(Li_1/3Nb_2/3)_0.75Ti_0.25]O_3−δ with 10 wt% glass sintered at 900^∘C for 3 h were ε_r = 40 Q·f₀ = 11500 GHz, τ_f = 8, ppm/°C. The relationship between the microstructure and dielectric properties of ceramics was studied by X-ray diffraction (XRD), and scanning electron microscope (SEM).     

Characterization of Pr- and Sm-Doped Ce0.8Gd0.2O2 − δ

Ce_0.8Gd_{0.2 – y}Pr_yO_{2 –} (y = 0–0.05) and Ce_0.8Gd_{0.2 – y}Sm_yO_{2 –} (y = 0–0.05) SOFC electrolyte materials were prepared using a reverse-strike co-precipitation method. The resulting powders were characterized using X-ray diffraction, Raman spectroscopy and electrochemical methods. XRD confirmed a single fluorite phase for all compositions. Increased Pr and Sm dopant level was found to cause a shift in the peak positions to slightly higher d-spacings with respect to pure CeO₂. The experimental lattice parameter was calculated using the peak positions determined from the XRD patterns. Raman spectra, for all dopant levels, showed two distinctive band features, namely a band at ca. 460 cm^{– 1} and a broader, weaker band at ca. 570 cm^{– 1}. As the proportion of praseodymia dopant is increased, the oxygen vacancy band shifts to a slightly lower wavenumber and decreases in relative intensity to the F_2g band. However, an anomaly occurs at the 1% dopant level; the oxygen vacancy band having a very low relative intensity. The conductivity was determined using AC—impedance spectroscopy, and it was found that for praseodymia, a maximum is observed at y = 0.015, while for samaria the maximum is observed at y = 0.01. It is also observed that the ionic conductivity for the samaria doped samples are lower than those of the praseodymia doped samples.     

Study of bulk and grain-boundary conductivity of Ln<Subscript>2+x</Subscript>Hf<Subscript>2−x</Subscript>O<Subscript>7−δ</Subscript> (Ln = Sm-Gd; x = 0, 0.096) pyrochlores

The electrical conductivity of new solid electrolytes Eu_2.096Hf_1.904O_6.952 and Gd₂Hf₂O₇ have been compared with those for different pyrochlores including titanates and zirconates Ln_2+xМ_2−xO_7−δ (Ln = Sm-Lu; M = Ti, Zr; x = 0−0.81). Impedance spectroscopy data demonstrate that Eu_2.096Hf_1.904O_6.952 and Gd₂Hf₂O₇ synthesized from mechanically activated oxides have high ionic conductivity, comparable to that of their zirconate analogues. The bulk and grain-boundary components of conductivity in Sm_2.096Hf_1.904O_6.952 (Т_synth = 1600oС), Eu_2.096Hf_1.904O_6.952 and Gd₂Hf₂O₇ (Т_synth = 1670oС) have been determined. The highest bulk conductivity is offered by the disordered pyrochlores prepared at 1600oC and 1670oC: ~1.5 × 10⁻⁴ S/cm for Sm_2.096Hf_1.904O_6.952, 5 × 10⁻³ S/cm for Eu_2.096Hf_1.904O_6.952 and 3 × 10⁻³ S/cm for Gd₂Hf₂O₇ at 780oС, respectively. The conductivity of the fluorite-like phases at the phase boundaries of the Ln_2+xМ_2−xO_7−δ (Ln = Eu, Gd; M = Zr, Hf; x ~ 0.286) solid solutions, as well as that of the high-temperature fluorite-like phases Ln_2+xМ_2−xO_7−δ (Ln = Eu, Gd; M = Zr, Hf; x = 0−0.286), is lower than the conductivity of the disordered pyrochlores Ln_2+xМ_2−xO_7−δ (Ln = Eu, Gd; M = Zr, Hf; x = 0−0.096).     

Control of Microwave Dielectric Properties in the System BaO ⋅ Nd<Subscript>2</Subscript>O<Subscript>3</Subscript> ⋅ 4TiO<Subscript>2</Subscript>—BaO ⋅ Al<Subscript>2</Subscript>O<Subscript>3</Subscript> ⋅ 4TiO<Subscript>2</Subscript>

BaO ⋅ Nd₂O₃ ⋅ 4TiO₂—based ceramics were prepared by the mixed oxide route. Specimens were sintered at temperatures in the range 1200–1450^∘C. Microstructures were investigated by scanning electron microscopy (SEM) and transmission electron microscopy (TEM); microwave dielectric properties were determined at 3 GHz by the Hakki and Coleman method. Product densities were at least 95% theoretical. The addition of up to 1 wt% Al₂O₃ to the starting mixtures reduced the sintering temperatures by at least 100^∘C. Incorporation of small levels of Al into the structure (initially Ti sites) led to an increase in Q × f values, from 6200 to 7000 GHz, a decrease in relative permittivity (ε_r) from 88 to 78, and moved the temperature coefficient of resonant frequency (τ_f) towards zero. The addition of 0.5 wt% Al₂O₃ with 8 wt% Bi₂O₃ improved densification, increased both ε_r (to 88) and Q× f (to 8000 GHz) and moved τ_f closer to zero. Ceramics in the system (1 − x)BaO ⋅ Nd₂O₃ ⋅ 4TiO₂ + xBaO ⋅ Al₂O₃ ⋅ 4TiO₂ exhibited very limited solid solubility. The end member BaO ⋅ Al₂O₃ ⋅ 4TiO₂ was tetragonal in structure with the following dielectric properties: ε_r = 35; Q× f = 5000 GHz; τ_f = −15ppm/^∘C. Microstructures of the mixed Nd-Al compositions contained two distinct phases, Nd-rich needle-like grains and large Al-rich, lath-shaped grains. Products with near zero τ_f were achieved at compositions of approximately 0.14BaO ⋅ Nd₂O₃ ⋅ 4TiO₂ + 0.86BaO ⋅ Al₂O₃ ⋅ 4TiO₂, where Q× f = 8200 GHz and ε_r = 71.     

Preparation and electrochemical properties of La<Subscript>1.0</Subscript>Sr<Subscript>1.0</Subscript>FeO<Subscript>4+δ</Subscript> as cathode material for intermediate temperature solid oxide fuel cells

Cathodic material La_1.0Sr_1.0FeO_4+δ for an intermediate temperature solid oxide fuel cell (IT-SOFC) was prepared via the glycine-nitrate process and characterized by X-ray diffraction (XRD), Fourier-transform infrared spectroscopy (FTIR), scanning electron microscopy (SEM). XRD results showed that no reaction occurred between the La_1.0Sr_1.0FeO_4+δ electrode and Sm_0.2Ce_0.8O_1.9 (SDC) electrolyte at 1000 °C. SEM results showed that the electrode formed good contact with the SDC electrolyte after sintering at 1000 °C for 2 h. The electrochemical properties of La_1.0Sr_1.0FeO_4+δ were measured using electrochemical impedance spectroscopy (EIS) and steady state polarization measurement. At 700 °C, the polarization resistance was about 3.90 Ωcm², and the lowest polarization overpotential was 57 mV at a current density of 55 mA cm⁻².     

Preparation of lithium-ion polymer battery using LiNi1/3Co1/3Mn1/3O2 as a cathode material and its electrochemical properties

In this work, LiNi_1/3Mn_1/3Co_1/3O₂ powders were synthesized from co-precipitated spherical metal hydroxide. In the voltage range of 2.8–4.2, 2.8–4.4, and 2.8–4.6 V, the discharge capacities of LiNi_1/3Mn_1/3Co_1/3O₂ electrode were 163, 177, and 193 mAh⋅g⁻¹, respectively. A gel polymer electrolyte (GPE) was also prepared using polyoxyalkylene glycol acrylate (POAGA) as a macromonomer. LiNi_1/3Mn_1/3Co_1/3O₂/GPE/graphite cells were prepared and their electrochemical properties were evaluated at various current densities and temperatures. The ionic conductivity of the GPE was more than 6.2 × 10⁻³ S⋅cm⁻¹ at room temperature. POAGA-based cells were showed good electrochemical performances such as rate capability, low-temperature performance, and cycleability.     

Effect of Ca co-dopant on the electrical conductivity of Gd-doped ceria

Co-doped ceria of Ce_0.8Gd_0.2?x Ca _x O_2-δ (x?=?0?0.2), were prepared by oxalate co-precipitation method. Their structures and conductivities were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), X-ray photoelectron spectroscopy (XPS) and AC impedance spectroscopy (IS). All the electrolytes were found to be single phase with cubic fluorite structure. SEM cross-section image showed relatively uniform grains with distinct and clean grain boundaries. The chemical states of the surface of the prepared samples were analyzed by XPS. Though Gd and Ca were present in their characteristic chemical state, Ce was found in single Ce⁴⁺ state or in mixed Ce⁴⁺ and Ce³⁺ states. IS measurements indicated that the conductivities for Ce_0.8Gd_0.2–x Ca _x O_2-δ pellets increased with increasing the sintering temperature. Moreover, co-doping with appropriate ratio of gadolinium and calcium was found to effectively enhance the conductivity in comparison to the singly doped ceria. The isothermal conductivity plots showed that sample Ce_0.8Gd_0.1Ca_0.1O_2-δ had the maximum conductivity with minimum activation energy (σ _700°C?=?0.0742?S/cm, Ea?=?0.58?eV), which is much higher compared to the conductivity exhibited by most of the reported codoped ceria compositions.     

Flame spray synthesis and characterisation of stabilised ZrO2 and CeO2 electrolyte nanopowders for SOFC applications at intermediate temperatures

Zirconia (Y_0.16Zr_0.84O₂, Sc_0.2Zr_0.8O₂ and Sc_0.2Ce_0.01Zr_0.79O₂) and ceria (Gd_0.2Ce_0.8O₂) based electrolyte materials are synthesised at production rates up to 260 g h^?1 by a liquid-fed one-step flame spray synthesis from water-based solutions, or cost-effective rare earth nitrates with a high water content. It was found that this one-step synthesis, based on an acetylene-supported flame is able to produce phase pure and highly crystalline, nanoscale electrolyte materials. The as-synthesised powders show a cubic lattice structure independent of production rates. Specific surface areas of the powders were adjusted between 20 and 60 m² g^?2, where the latter is an upper limit for the further processing of the powders in terms of screen printing. The influence of process parameters on morphology, particle size, composition, crystallinity, lattice parameter, shrinkage behaviour and coefficient of thermal expansion of the as-synthesised powders were systematically investigated by transmission electron microscopy (TEM), nitrogen adsorption (BET), X-ray diffraction (XRD) and dilatometry. Electrochemical impedance spectroscopy (EIS) was applied at temperatures between 300 °C and 900 °C and confirmed the high quality and the competitive electrochemical behaviour of the produced powders.     

The electronic conductivity of Ba0.5Sr0.5CoxFe1?xO3?δ (BSCF: x?=?0?～?1.0) under different oxygen partial pressures

The electronic conductivity of sintered BSCF ceramics (Ba_0.5Sr_0.5Co _x Fe_1−x O_3−δ, 0 ≤  x  ≤ 1) was measured as a function of temperature up to 1273 K in air. The conductivity of BSC is thermally activated over 298–1273 K with an activation energy of 0.21 eV. The conductivity of BSF and BSCF (0.2 ≤  x  ≤ 0.8) is thermally activated below ∼673 K with activation energies of 0.21 eV–0.40 eV. Above 673 K, the formation of oxygen vacancies results in a decrease in p-type carrier concentration and a decrease in electronic conductivity. Ba_0.5Sr_0.5Co_0.8Fe_0.2O_3−δ (BSCF5582) was also measured under 10⁻⁵ atm ≤ pO₂ ≤ 1 atm. Below ∼673 K, the electronic conductivity of BSCF 5582 shows no dependence on pO₂. Above 673 K, the conductivity of BSCF5582 increases with increasing pO₂ for pO₂ ≥ 0.01 (p-type conduction) and decreases slightly with increasing pO₂ for pO₂  ≤ 0.01 atm. The activation energy for conduction above ∼673 K and at pO₂ ≥ 0.1 is ∼0.07 eV. Above ∼823K and at pO₂ ≥ 0.01 atm, the activation energy for conduction is ∼0.2 eV.     

Effects of Mn-doping on TSDC and degradation of BaTiO3

The effects of Mn-doping on TSDC (Thermally Stimulated Depolarization Current) and electrical degradation of BaTiO₃ have been investigated. TSDCs of un-doped BaTiO₃ and Ba(Ti_1−x Mn_x)O_3−δ exhibited the three sharp TSDC peaks around phase transition temperatures. TSDC of Ba(Ti_0.995Mg_0.005)O_2.995 increased gradually from 50^∘C and this anomalous depolarization current kept going up well above the Curie temperature (∼130^∘C). TSDCs of un-doped BaTiO₃ and Ba(Ti_0.995Mn_0.005)O_3−δ decreased in the temperature range above the Curie point, whereas a slight increase in TSDC was confirmed at the specimen of Ba(Ti_0.99Mn_0.01)O_3−δ. TSDCs of Ba(Ti_0.995−y Mg_0.005Mn_y)O_3−δ (y = 0.005, 0.01) were lower than that of Ba(Ti_0.995Mg_0.005)O_2.995.     

Control of 0.2CaTiO3-0.8Li0.5Nd0.5TiO3 microwave dielectric ceramics by additions of Bi2Ti2O7

Ceramics of 0.2CaTiO₃-0.8Li_0.5Nd_0.5TiO₃) have been prepared by the mixed oxide route using additions of Bi₂O₃-2TiO₂ (up to 15 wt%). Powders were calcined 1100^∘C; cylindrical specimens were fired at temperatures in the range 1250–1325^∘C. Sintered products were typically 95% dense. The microstructures were dominated by angular grains 1–2 μm in size. With increasing levels of Bi₂O₃-2TiO₂ additions, needle and lath shaped second phases developed. For Bi₂Ti₂O₇ additions up to 5 wt%, the relative permittivity increased from 95 to 131, the product of dielectric Q value and measurement frequency increased from 2150 to 2450 GHz and the temperature coefficient of resonant frequency (τ _f ) increased from −28pp/^∘C to +22pp/^∘C. A product with temperature stable τ _f could be obtained at ∼2 wt% Bi₂Ti₂O₇ additions. For high levels of additives, there is minimal change in relative permittivity, the Qxf values degrade and τ _f becomes increasingly negative.     

Synthesis and sintering properties of (La0.8Ca0.2−x Sr x )CrO3 perovskite materials for SOFC interconnect

Synthesis and sintering properties of the (La_0.8Ca_0.2−x Sr _x )CrO₃ samples doped by two alkaline earth metals in comparison to the doped only by one alkaline earth metal were evaluated by phase analysis, sintering properties, thermal expansion behaviors, and electrical conductivity. The sintered (La_0.8Ca_0.2−x Sr _x )CrO₃ (x = 0, 0.05, and 0.1) and (La_0.8Ca_0.2−x Sr _x )CrO₃ (x = 0.2) were found to have orthorhombic and rhombohedral symmetries, respectively. Relative density of the (La_0.8Sr_0.2)CrO₃ sample sintered at 1500^∘C for 5 h was lower than that of the (La_0.8Ca_0.2−x Sr _x )CrO₃ (x = 0, 0.05, and 0.1) sample. TECs of the (La_0.8Ca_0.2−x Sr _x )CrO₃ (x = 0, 0.05, 0.1, and 0.2) in air were 11 × 10⁻⁶/^∘C, 11.2 × 10⁻⁶/^∘C, 11.2 × 10⁻⁶/^∘C, and 11.3 × 10⁻⁶/^∘C, respectively. The electric conductivity of the (La_0.8Ca_0.2−x Sr _x )CrO₃ sample was determined.     

On the Poisson ratio and XRD determination of strain in thin films of Ce0.8Gd0.2O1.9

XRD measurement of the room temperature in-plane and out-of-plane d-spacings of the (422) diffraction peak of 11 thin film samples of fluorite Ce_0.8Gd_0.2O_1.9 demonstrates that the zz and xx (=yy) components of the strain tensor for this material are not related via a constant, i.e. the Poisson ratio, as is the case for elastic materials. Rather, these strains are independent. We attribute this behavior to the inelastic character of Ce_0.8Gd_0.2O_1.9 deriving from the chemical strain effect, i.e. the lability of point defect-containing complexes under stress. Chemical strain is dependent on the thermal and mechanical history of the film, and above 200 °C, is no longer observed, being transformed into elastic strain and stress. This transformation may compromise the mechanical stability of Ce_0.8Gd_0.2O_1.9 containing devices, which must operate over a broad temperature range. Measurements analogous to those described here can assist in predicting the magnitude of such an effect.