Exponential Temperature Research Articles

Tracking Eruption Column Thermal Evolution and Source Unsteadiness in Ground‐Based Thermal Imagery Using Spectral‐Clustering

AbstractVolcanic eruption columns typically have unsteady source conditions, where mass and heat fluxes from the vent evolve or fluctuate on time scales from seconds to hours. However, integral plume models routinely assume source conditions that are statistically stationary, and the degree to which source unsteadiness influences the mechanics of column rise and air entrainment has not been established with quantitative predictions. We address this knowledge gap by examining eruptions with varying unsteady character at Sabancaya Volcano, Peru. Using a novel tracking algorithm based on spectral clustering, we track the spatiotemporal evolution of coherent turbulent structures in columns using ground‐based, thermal infrared imagery. For turbulent structures tracked in time and space, we calculate the power law decay exponent of excess temperature with height. In general, the starting pulses of transient events are characterized by power law exponents matching theoretical predictions for an instantaneous point release of buoyancy (i.e., a thermal), which evolve with sustained emissions to values consistent with steady plumes. Our results support previous findings from field evidence and laboratory experiments that entrainment and gravitational stability in unsteady volcanic columns are inadequately captured by time‐averaging or constant entrainment coefficients. We propose a quantitative definition for column source unsteadiness which captures the timing and magnitude of source fluctuations on time scales that influence entrainment mechanics, and which provisionally predicts our observed differences in power law behavior. We argue for systematic experimental and numerical studies of the relationship between source unsteadiness and entrainment to implement unsteady entrainment parameterizations for integral plume models.

Investigation on laminar burning velocity measurements of premixed Ethane-Air mixture at higher pressure and temperature conditions

The externally heated diverging channel (EHDC) method was utilized to evaluate the laminar burning velocity (LBV) of premixed ethane-air flames at higher mixture temperature (350-620 K) and pressure (1-5 atm) conditions over different mixture strengths (ϕ = 0.7-1.3). The maximum LBV was noted at ϕ = 1.1 for all pressure and temperature conditions. The inverted parabolic behavior of the temperature exponent was obtained with the minima at ϕ = 1.1. The pressure exponent (β) exhibits a parabolic variation with its maxima at ϕ = 1.0. The current results are further analyzed and compared with the literature measurements, and the comprehensive kinetic model predictions of USC mech II, San Diego mech, and Aramco mech 1.3. The present LBV measurements match well with the kinetic model predictions of Aramco mech 1.3 at most of the mixture and pressure conditions. The present results propose the variation of pressure exponent (β) as a function of temperature ratio, and temperature exponent (α) as a function of pressure ratio for different mixture conditions (ϕ). A revised power-law correlation for α and β variations is also recommended as, Su=Su0Tu/Tu0∝0+∝11-Pu/Pu0)Pu/Pu0β0+β11-Tu/Tu0. The sensitivity analysis indicates the maximum decrement in the positive sensitivity for the chain branching reaction HCO + M ↔ H + CO + M (R30) across all the stated mixture conditions, owing to an increment in the third body effects along with pressure and temperature. The reaction pathway analysis reveals a maximum net reduction in the elemental flux (∼56 %) for the reaction between the species carbon monoxide (CO) and carbon dioxide (CO2) through different reactions, due to a rise in pressure and temperature.

Unsteady magnetized flow of micropolar fluid with prescribed thermal conditions subject to different geometries

Due to realistic implementations of heat transfer flows, this study communicates with the two cases of the prescribed thermal process. A comparative analysis of the time-dependent flow of a micropolar fluid between two problems of linear stretching sheet and exponential stretching sheet is demonstrated. In the context of the linear stretching sheet, the investigation covers situations involving prescribed surface temperature (PST) and prescribed heat flux (PHF). Likewise, for the exponential stretching sheet, the study examines cases of prescribed exponential order temperature (PEST) and prescribed exponential order heat flux (PEHF). For both problems, the two cases of the thermal process are examined for heat transfer analysis considering joule heating and nonlinear thermal radiation. The two-dimensional flow in the presence of a variable magnetic field is explored for both the linear and exponential stretching sheet problems. Graphical representations are employed to provide a comparative illustration of flow properties concerning relevant parameters for both cases. From the graphical and tabular analysis, we deduce that an exponential stretching sheet provides more consequential results as compared to a linear stretching sheet. Furthermore, the material parameter demonstrates an increase in the velocity field for both of the considered sheets.

Physical and electrical properties of Sm2O3 doped Boro-Zinc-Vanadate glasses

Sm2O3 doped boro-zinc-vanadate glass systems were synthesised by following the melt quenching method. XRD patterns indicated largely non-crystalline nature with few nano-crystallites. Room temperature density was measured. Molar volume and various polaron parameters were estimated. Density and molar volume are found to vary non-linearly with samarium concentration. Conductivity has been measured by two probe technique for temperature range 303K - 573K. High temperature conductivity obeyed the small polaron hopping (SPH) theory. Activation energy for conduction in the temperature regime of small polaron theory is found to vary from 0.249 eV to 0.368 eV non-linearly with Sm2O3 concentration. The conductivity data at low temperature deviated has been looked into using Mott’s VRH model and the density of states at Fermi level were determined. Shimakawa’s multiphonon tunnelling model has also been applied to the low temperature conductivity and found linearity between logarithmic conductivity, ln(σ) and logarithmic temperature ln(T) as predicted by the model. The temperature exponent values obtained from Shimakawa’s model fit are found to be in good agreement with literature. Therefore, it is concluded that at low temperature, carrier multiphonon tunnelling is the charge transport mechanism in the present glasses.

Experimental measurements of laminar burning velocity of premixed propane-air flames at higher pressure and temperature conditions

This paper presents laminar burning velocity (LBV) measurements of premixed propane-air flames simultaneously at higher mixture pressure (1-5 atm) and temperature (350-630 K) conditions over mixture conditions (ϕ = 0.7-1.3) utilizing the externally heated diverging channel (EHDC) method. The maximum LBV was observed at ϕ = 1.1 for all pressure and temperature conditions. The non-monotonic behavior of the temperature exponents was noted with the minima at ϕ = 1.1. The pressure exponent (β) variation was observed to be parabolic with the maxima at ϕ = 1.0. The current measurements are then compared with the literature results, and the detailed kinetic model predictions of Qin mech, San Diego mech, and USC mech II. The present LBV measurements are in a better match with the mechanism predictions of San Diego mech at the majority of mixture and pressure conditions. The current measurement suggests the variation of temperature exponent (α) as a function of pressure ratio, and pressure exponent (β) as a function of temperature ratio for different mixture conditions (ϕ). A revised power-law correlation for α and β variations is also suggested as, Su=Su0TuTu0∝0+∝11-PuPu0PuPu0β0+β11-TuTu0. The sensitivity analysis reveals a significant increase (≈ 45%) in negative sensitivity for the chain termination reaction H + CH3 (+M) ↔ CH4 (+M) (R56), with a rise in pressure and temperature at all mixture conditions. The reaction pathway analysis indicates a maximum increment in elemental flux (≈ 305 %) in the formation of ethane (C2H6) from its predecessor methyl radical (CH3), due to enhanced pressure and temperature conditions.

Feasibility of the EDICAM camera for runaway electron detection in JT-60SA disruptions

The visible camera system EDICAM (Event Detection Intelligent Camera), recently installed on JT-60SA, is simulated to assess whether it can be used for measuring synchrotron radiation from relativistic runaway electrons. In this simulation, the SOFT synthetic synchrotron diagnostic framework is used to compute the synthetic synchrotron camera images from a JT-60SA-like disruption modelled with the DREAM disruption simulation code. In the studied scenario, a large amount of argon is added to the plasma, and a disruption is simulated by starting a prescribed exponential temperature drop and finishing with further cooling provided by the argon in a self-consistent simulation of the current quench. The background plasma evolution is calculated by DREAM self-consistently with the fast electron population, which is modelled kinetically. The resulting runaway electron distribution function along with the parameters of the EDICAM visible camera system are used as an input to the SOFT framework to assess the feasibility of the camera for runaway electron detection. We find that the runaway electron beam formed in the disruption can produce synchrotron radiation observable by the EDICAM system, thus enabling the use of the EDICAM for the characterization of runaway electron beams.

Effect of ammonia addition on laminar burning velocity of CH4/H2 premixed flames at high pressure and temperature conditions

Global emissions of nearly 30% stem from fossil fuel combustion for long-distance transportation vehicles. Therefore, investigations on newer alternatives for clean and green fuels is desired in pursuance of net-zero carbon emissions by 2050. Given this contemplation, the current study aims at studying the effect of ammonia addition, a carbon-free fuel, on laminar burning velocity of CH4/H2 fuel blends at high-pressure and high-temperature conditions utilizing the high-pressure diverging-channel method. The NH3 varies from 0% to 30% in the CH4/H2 fuel blend by volume. With regard to adiabatic flame temperature, this NH3/CH4/H2 mixture is comparable to pure CH4-air mixtures, but with a reduction in carbon emissions of about 26.6%. The research involves conducting measurements at high temperatures between 300 K and 750 K, pressures between 1 atm and 5 atm, and equivalence ratios between ϕ = 0.7 and 1.4. When the pressure is 5 atm, the obtained burning velocities of NH3/CH4/H2 blends are analogous to that of CH4-air mixtures. The temperature exponent, α, does not change when the NH3 fraction or pressure changes, but at high temperatures there is a slight shift in the pressure exponent, β. The experimental results suggest that the Okafor and Li kinetic models align well with the measurements made in the current work up to 5 atm, while the Reduced GRI Mech 3.0 mechanism overestimates the burning velocity values. Additionally, an increase in NH3 fraction and pressure results in a decrease in burning velocity and NO formation due to the presence of NHi (i = 0–2) radicals. Overall, this study convincingly demonstrates the viability of NH3/CH4/H2-air mixtures as a practical alternative to reduce carbon emissions.

The influence of line mixing on the j and k dependencies of halfwidths and temperature exponents in N2-broadening coefficients of CH3F spectral lines

The N2-broadening halfwidths of CH3F in the ν5 and ν6 perpendicular bands have been calculated, along with their temperature exponents. These calculations utilize a modified and refined version of the Robert-Bonamy formalism, developed by the current authors within a semi-classical line shape framework. Extensive comparisons between the predicted halfwidths from the model and experimental measurements at 296 K and 183 K are presented. Our latest model accurately predicts the dependencies of the halfwidths on both the j and k quantum numbers. Furthermore, by extending our calculations to two additional temperatures, namely 240 K and 350 K, the temperature exponent N is determined for various sub-branches. The dependencies of N on j and k are analyzed, and theoretical explanations are provided to elucidate the predicted behaviors of N.

Laminar burning velocity measurements of C1-C4 alkane-air mixtures at elevated mixture temperatures

This study presents, the measurements of the laminar burning velocity (LBV) for C1-C4 alkane fuels with air at higher mixture temperatures, using an externally heated diverging channel (EHDC) method. The experimental results are shown for mixture conditions ranging from ϕ = 0.7 to 1.3, with a mixture temperature of 350–660 K at ambient pressure conditions. The temperature exponent (α) is obtained using the power-law correlation to explain the influence of LBV variation with the mixture temperature at different mixture equivalence ratios, ϕ. The maximum value of mixture burning velocity is recorded for marginally rich mixture conditions, (ϕ = 1.1) at different temperatures. The lowest value of temperature exponent (α) is observed at ϕ = 1.1. The data obtained from the current measurements are then compared with the literature results, and mechanism predictions are made using the kinetic models of USC Mech II, FFCM-1, Aramco Mech 2.0, Qin Mech, San Diego Mech, GRI Mech 3.0, and LLNL. The normalized sensitivity analysis for these straight chain C1-C4 alkane fuels reveals that the decomposition of formyl radical in reaction R163: HCO + M ↔ H + CO + M, which exhibits further major root of H atom, leading to enhancement of the LBV of these fuels at elevated mixture temperature conditions.

Statistical and entropy optimization modeling for radiative hybrid nanofluid flow with Hall effect over exponential stretching/shrinking plate

Scientists have become intrigued by the capacity of two solid components to dissolve in a conventional fluid to enhance the thermal efficiency of novel hybrid nanofluids. The Bejan number and entropy formation of three-dimensional hybrid Al2O3 − Cu/H2O nanoparticles flowing via a stretching/shrinking bidirectional exponential plate are investigated in this research while taking into account thermal radiation and the Hall Effect. In the heat equation, the Joule heating and Cattaneo-Christov heat flux model are contemplated. Through using proper similarity transformations, equations involving momentum and heat transfer are simplified into ordinary differential equations. The Homotopy analysis approach is used to solve these equations using the computer software MATHEMATICA. By resolving the flow limitations on temperature and velocity, the entropy production is computed. Using graphical demonstration, the impact of various parameters such as suction/injection parameter, Brinkman number, magnetic parameter, stretching/shrinking parameter, temperature ratio parameter on flow, thermal relaxation parameter, temperature exponent parameter, Hall effect parameter, on velocity, temperature, entropy production, and Bejan number has been thoroughly discussed. The local Nusselt number and skin friction can also be identified for practical reasons for various approximations of physical parameters. The outcomes specify that the tangential velocity and redial velocity decrease for greater values of injection and suction parameters. The temperature profile falls for larger values of the suction parameter and rises for greater values of the thermal relaxation parameter and injection parameter. Entropy production develops when the magnetic parameter is improved. Bejan number was reduced in response to rising magnetic parameter values.

An analytical solution for heat and mass transfer in falling film absorption with arbitrary thermal boundary conditions

Absorption, the process of capturing the absorptive component in the volume of the absorbent, is essential for various industrial applications. Several analytical solutions exist for falling film absorbers, which is the most common absorber used in industrial applications. However, in existing models, the temperature of the heat transfer fluid has been assumed to be constant, while the design of falling film absorbers for absorption heat pumps requires an analytical model accounting for the variation in the heat transfer fluid temperature changes. This study presents a new and comprehensive analytical solution for non-volatile absorbents using the Laplace transform method, where an arbitrary heat flux is applied to the heat exchanger wall in contact with the heat transfer fluid. For the first time, this study provides analytical solutions for various wall boundary conditions, including arbitrary heat flux, isothermal, as well as mean, linear, and exponential temperature variation of the heat transfer fluid. The present model is validated with experimental data available in the literature with a relative difference of 11% for several absorber configurations. Considering a case study of an absorber with a length of 1 m, it is shown that assuming an average temperature for the heat transfer fluid overestimates the optimal length of the absorber and results in up to 3 times the absorption rate at the outlet region of the absorber compared to a linear and an exponential temperature estimation.

Effect of rare earth dopant on the ac conductivity and dielectric study of GeSbSe chalcogenides glasses

Chalcogenides glasses Ge17Sb8Se75-xErx with composition x = 0, 0.4, 0.8, 1.0 have been synthesized by conventional melt quenching technique and its dielectric and ac conductivity studies have been carried out in the temperature and frequency range 300–334 K and 5 kHz–20 kHz, respectively. Dielectric constant dependence on temperature and frequency was established for orientation polarization in the system. Dielectric loss variations with temperature and frequency were described by the conduction loss as well as single polaron hopping of charge carriers (Elliot and Shimakawa theory) for chalcogenides glasses. Correlated barrier hopping (CBH) model is used to interpret relation between temperature and frequency exponent. It was observed that with increase in frequency, both dielectric constant and dielectric loss decreases and increases with the increase in temperatures. The compositional variation in the dielectric parameters and conduction mechanism has also been explored.

Entropy generation in viscous flow due to generalized exponential wall velocity and temperature

The study of entropy generation in convective transport processes is of current interest. For the better understanding of this phenomenon it is preferred to investigate it for those flows which admit an exact solution. This is the reason that majority of the published literature, concerning entropy generation analysis, has been done for the self-similar flows. Particular to the stretching sheet flows, which do also have important applications in industry, entropy production analysis is of particular importance. In this regard a two dimensional boundary layer flow due to an exponentially stretching wall (following generalized exponential form) has been considered in this study for the analysis of entropy generation. The stretching wall velocity and the wall temperature function have so properly been chosen that an similarity solution is possible. The modeled, equations are converted to ordinary differential equations by employing appropriate similarity transformations. These equations are solved numerically by using bvp-4c implemented in Matlab. To implement this method, differential equations are converted to set of first order equations and are solved. The problem has been analyzed for the heat transfer phenomenon and the entropy generation. The dimensionless form of entropy generation number requires m ≡ n for a similarity solution to exist. The enhancement is observed in the Nusselt number by enhancing the values of m, n, and Pr. Eventually, the entropy generation at the wall is maximum for increasing values of and However, for such a large values of of and the entropy profile reduces rapidly in the boundary layer thus avoiding a farther speed of entropy in the boundary layer. It is also noticed that to minimize the entropy generation across the boundary layer and also to get an enhanced rate of heat transfer some higher values of and must be chosen.

Dynamics of Heat Transfer in Magneto-Micropolar Fluids Flow Past a Vertically Expanding Sheet Featuring Prescribed Wall Temperature (PWT)

This study assesses the motion and the dynamics of heat propagation in magneto-micropolar fluid along a sheet which vertically stretches on a two-dimensional plane in a porous material. The heat distribution is developed and evaluated under the condition of the prescribed wall temperature, constant magnetic field, thermal radiation, variable heat source and viscous dissipation. The main equations are re-formulated from partial to ordinary derivatives using similarity tools and consequently solved numerically by shooting and the Runge-Kutta Fehlberg approach. The parameters of interest are presented graphically to demonstrate their reactions on the velocity profiles, thermal field and heat transfer mechanism of the problem. The outcomes of the current investigation reveal that the heat transfer appreciates in the presence of higher Prandtl number, temperature exponent term and material parameter but decreases as the magnetic field term soars.Besides, the heat boundary structure expands and heat spread occurs as the thermal radiation, magnetic field and Eckert number terms escalates but a reverse trend is encountered as the Prandtl number, material micropolar term, Grashof number and heat exponent terms grows in magnitude. Under some limiting scenarios, the obtained data strongly correspond to the published studies in the open literature.

How do silicate weathering rates in shales respond to climate and erosion?

Mineral weathering, a major control on long term atmospheric CO2, can be limited by processes such as reaction kinetics, supply of fresh mineral, or water throughput in the weathering zone. In these cases, weathering fluxes increase with temperature, erosion, and runoff, respectively, and we refer to the regimes as kinetically limited (KL), erosive transport limited (ETL), and runoff limited (RL). Larger watersheds can exhibit mixtures of these behaviors in a transition regime (TR). To understand these weathering regimes, we focused on the lithology (shale) that is one of the most widespread lithologies exposed on continents globally. We identified and analyzed 142 shale watersheds across the United States, spanning a diverse range of climatic (mean annual temperature (MAT): 3–17 °C; mean annual precipitation (MAP): 220–1975 mm yr−1; potential evapotranspiration (PET): 908–2059 mm yr−1), topographic (mean catchment elevation: 78–2346 m; mean catchment slope: 0.4–28°), and hydrologic (annual runoff (q): 0.002–1.3 m yr−1) conditions. For these sites, we calculated silica fluxes (i.e., FSiO2) using SiO2 concentrations and river discharge measurements. We observed that when the humidity index (HI; MAP/PET) is <0.55, FSiO2 increases with MAP and q; however, when HI > 0.55 FSiO2, does not increase with MAP nor q. We posit that sites with HI < 0.55 are RL. The river chemistry for the RL sites is consistent with equilibrium between smectite and kaolinite. Fitting the data for sites with HI > 0.55 to an exponential temperature dependence, we find that the sensitivity of weathering to temperature is consistent with an apparent activation energy, Ea, of 56 ± 8 kJ mol−1. If sites with HI > 0.55 but average slopes <10°are removed, the value increases to 92 ± 10 kJ mol−1. This value is consistent with the Ea measured experimentally for the dissolution of the common shale clay, chlorite. To extrapolate from our measurements, we use geospatial-based definitions to classify HUC12 watersheds across the United States. This reveals that 48%, 37%, 9%, and 7% of US shale watersheds are RL, ETL, TR, and KL, respectively. Globally, we estimate that silicates weathering in shales consume 2.6 × 1012 mol CO2 yr−1, which is 22% of the total CO2 sequestered by silicate weathering.

Local Non-Similar Solution for Non-Isothermal Electroconductive Radiative Stretching Boundary Layer Heat Transfer with Aligned Magnetic Field

Continuous two-dimensional boundary layer heat transfer in an electroconductive Newtonian fluid from a stretching surface that is biased by a magnetic field aligned with thermal radiation is the subject of this study. The effects of magnetic induction are induced because the Reynolds number is not small. The sheet is traveling with a temperature and velocity that are inversely related to how far away from the steady edge it is from the plane in which it is traveling. We also imposed external velocity u=uex=Dxp in the boundary. The necessary major equations are made dimensionless by the local non-similarity transformation and become a system of non-linear ordinary differential equations after being transformed from non-linear partial differential equations. The subsequent numerical solution of the arisen non-dimensional boundary value problem utilizes a sixth-order Runge–Kutta integration scheme and Nachtsheim–Swigert shooting iterative technique. A good correlation is seen when the solutions are compared to previously published results from the literature. Through the use of graphical representation, the physical impacts of the fluid parameters on speed, induced magnetic field, and temperature distribution are carried out. Furthermore, the distributions for skin friction coefficient and local Nusselt number are also studied for different scenarios. The skin friction coefficient and local Nusselt number are observed to increase with greater values of the temperature exponent parameter and velocity exponent parameter. However, as heat radiation increases, the local Nusselt number decreases even though temperatures are noticeably higher. The study finds applications in magnetic polymer fabrication systems.

Magnetohydrodynamics tangent hyperbolic nanofluid flow over an exponentially stretching sheet: Numerical investigation

This article gives a numerical study of tangent hyperbolic nanofluid flow across an exponentially stretched sheet by considering two heat transfer situations: prescribed exponential order surface temperature (PEST) and prescribed exponential order heat flux (PEHF). Tangent hyperbolic nanofluid is being used extensively in the cooling of electronic components, which generate a lot of heat during operation. The improved thermal conductivity of tangent hyperbolic nanofluids can help to dissipate the heat more effectively, reducing the risk of overheating and component failure. A mathematical model of the problem is based on conservation laws of momentum, mass, and energy. The governing system of nonlinear PDEs is transformed into a system of nonlinear ODEs using appropriate similarity transformations. MATLAB's bvp4c tool was utilised to address the converted system of modelled equations. The drag coefficient, heat transfer, and mass transfer rate values are tabulated. It is observed that both the magnetic parameter (M) and Weissenberg number (We) causes to reduce the boundary layer. It is also noticed that increasing the Brownian motion parameter (Nb) and the thermophoresis parameter (Nt) leads the temperature θ(η) and concentration profile g(η) to increase for both cases of heat transfer i.e., PEST and PEHF.

Combined effects of surface sharpness and transverse curvature on thermal transport in separating flow region

Heat transfer analysis in a retarded laminar boundary layer over bodies of revolution with a variable radius subject to retarded surface temperature is presented. This study focuses to develop numerical data for local Nusselt number N ux under the influence of retarded free stream velocity and decreasing surface temperature along with body contour and surface transverse curvature. With the use of such retarded velocities and body contour the similarity of flow phenomenon does not sustain, and the problem becomes non-similar in nature which has been solved using an efficient numerical scheme, commonly known as Keller-Box. The effects of pertinent parameters such as exponent of free stream velocity m, exponent of surface temperature q, body contour n, and surface transverse curvature k on temperature profile, rate of heat transfer at the surface, and energy thickness of thermal boundary layer are presented through various graphs and tables. The rate of heat transfer and the energy thickness of the thermal boundary layer are observed to decrease with increasing levels of retardation. Furthermore, the rate of heat transfer decreases as the body contour parameter increases, whereas the surface transverse curvature parameter exhibits the opposite trend.

Two types of superconducting pairs in stripe-ordered La2−xBaxCuO4 (x=1/8) : Evidence from resistivity measurements

Recent angle-resolved $c$-axis resistivity measurements of the stripe-ordered ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Ba}}_{x}{\mathrm{CuO}}_{4}$ (LBCO) with $x=1/8$ revealed an unexpected dependence on the direction of the in-plane magnetic field. We argue that these and other available data for the $c$-axis transport point to the existence of superconducting pairs of two different types in the $x=1/8$ LBCO below the stripe ordering temperature. The pairs of one type carry finite momentum and are confined to the Cu-O planes; the pairs of other type (probably the conventional $d$ wave with zero momentum) propagate along narrow conducting channels traversing the sample in the $c$-axis direction. The evidence for this comes from the observed exponential temperature dependence of the $c$-axis resistivity ${\ensuremath{\rho}}_{c}(T)$ which we attribute to the thermally excited slips of the superconducting phase and flux flows. We present a simple theory to fit the observed $\ensuremath{\pi}/2$-periodic dependence of ${\ensuremath{\rho}}_{c}$ on the direction of the in-plane magnetic field and the other data.

Resistive-like Behavior of Ferroelectric p–n Bilayer Structures Based on Epitaxial Pb(Zr0.2Ti0.8)O3 Thin Films

The p–n junctions are the building blocks of nowadays electronic devices. The n- or p-type conductivity is obtained in classic semiconductors, like Si, by doping with atoms acting as donors or acceptors, respectively. Doping was used in ferroelectrics to influence the transition temperature, magnitude of some physical properties, but not necessarily conduction type. Therefore, comprehensive studies to obtain true ferroelectric p–n junctions by controlled doping are missing. Recently, it has been shown that Pb(Zr0.2Ti0.8)O3 films doped with ≈1% atomic Nb (n-type doping) or Fe (p-type doping) have different orientations of polarization in the as-grown state. Knowing that polarization orientation depends on doping type, the next step is to build ferroelectric p–n homojunctions and to study their properties in relation to ferroelectric polarization. p–n and n–p structures were grown for this purpose by successive deposition of Nb-doped and Fe-doped Pb(Zr,Ti)O3 layers with different thicknesses. We find that these p–n homojunctions are ferroelectric, but the magnitude of the polarization and coercive field, as well as the dominant polarization orientation in the as-grown state, depend on the conduction type of the first grown layer. The I–V characteristics are quasi-linear, although the interfaces with the electrodes behaves as Schottky contacts. The resistance extracted from the I–V characteristics displays an exponential dependence on temperature, with an activation energy in the range of 0.14–0.17 eV. These results are explained assuming that the total current in the junction is the total of electron and hole injections at the electrode interfaces. It is shown that for relatively low doping concentrations, the current density contains a dominant term with a linear voltage dependence and an exponential temperature dependence, as observed experimentally, and a secondary (correction) term that is dependent on the free carrier density and can induce non-linear voltage dependence when this density is significant.