Temperature Dependence Of Conductivity Research Articles

Investigation of diabatic imparity involving asymmetric convection in two-dimensional longitudinal fins using lattice Boltzmann solver

This manuscript investigates the effect of diabatic imparity on two-dimensional (2-D) transient fins having naturally obtained non-linear variation of temperature-dependent conductivity. The diabatic imparity arises due to asymmetrical convection coefficient on the surfaces, implemented using different Biot numbers on each respective surface of the fin, which resembles pragmatic industrial applications. The transient solution of 2-D fin has been obtained using a Lattice Boltzmann (LB) solver, firstly, the suitability of 2-D LB formulation is established with the validity of the existing results, and subsequently extending the LB formulation for the present study. The numerical solution is determined under the two types of step-changing boundary conditions at the fin root having (i) heat flow and (ii) temperature. Results have been plotted graphically, and these include instantaneous isotherms, equilibrium isotherms, and threshold iso-temporal lines. Reported results facilitate the fin designer to examine the effect of diabatic imparity on the attainment of steady-state and occurrence of transverse temperature gradient on 2-D transient fin. The reported results provided are pertinent to the pragmatic application and are seldom reported in the literature. The outcomes of the present investigation are eminently informative to practising engineers and will serve as design monograms.

The influence of the volume concentration of hydrogen on the fine structure of the IR absorption spectra and conductivity features in congruent LiTaO3 crystals

A new method for changing the volume concentration of hydrogen in congruent LiTaO3 (lithium tantalate, LT) crystals has been studied. It has been established that pre-treatment of the sample in adipic acid significantly increases the volumetric concentration of hydrogen in the sample during subsequent annealing in a humid atmosphere at a relatively low annealing temperature. First of all, this preserves the LT single crystal in a single-domain state. In contrast to known methods for increasing the volumetric concentration of hydrogen, the proposed method affects the absorption coefficient of the sample in the optical range less than for a congruent LiNbO3 crystal. It has been shown that the type of IR absorption spectrum of OH− groups and the defect structure of the LT crystal significantly depend on the volume concentration of hydrogen in the sample. The study also analyzed the reasons for this effect. The temperature dependences of the electrical conductivity of LT samples with different hydrogen concentrations have been studied. It has been shown that the type of electronic conductivity of LT samples changes when the concentration of OH groups in the crystal increases significantly.

Nanoparticles hybridization in bidirectional flowing of Prandtl–Eyring material with temperature-dependent conductivity: A numerical approach

Due to the vast applications of nanofluids in hybrid cooling processes and their role in improving heat transfer in thermal systems, an attempt has been made to investigate the consequence of temperature-dependent thermal conductivity in the bidirectional flowing of Prandtl–Eyring (PE) hybrid nanomaterial. Zirconium dioxide (ZrO2) and copper (Cu) nanoparticles have been dispersed into an engine oil (EO) to create an effective hybrid nanomaterial. Viscous dissipation, magnetization, linear thermal radiation, and Ohmic heating mechanisms also influence the dynamics of the hybrid nanomaterial. The governing equations have been parameterized by using similarity transformations and the thermophysical properties of nanoparticles. Keller–Box simulations for the modeled problem have been conducted using an in-house code developed in MATHEMATICA. Convergence analysis has been presented and robust validation of the results has been performed to certify the accuracy of the numerical inspection. Post-processing of the results has been carried out by plotting temperature and velocity curves. Drag coefficient and Nusselt number have been formulated and analyzed in tabular forms. The rate of heat transfer is developed with the hybridization of ZrO2 and Cu nanoparticles into the base liquid, while drag forces are enhanced when utilizing PE material as the base liquid.

Thermal diffusivity of inclined magnetized Cross fluid with temperature dependent thermal conductivity: Spectral Relaxation scheme

Understanding and controlling the thermal transport phenomena are crucial in numerous applications. The current research emphasizes thermal diffusivity of an inclined magnetized Cross fluid with temperature-dependent thermal conductivity with a computational iterative spectral relaxation scheme. Cross mathematical model is employed to characterizes non-Newtonian behavior and to uncover viscoelastic properties of fluid. Flow is incorporated under temperature thermal influence and external inclined magnetic strength is considered for thermal variations. Various prominent factors, including cross index, magnetic field, inclination angle, temperature-dependent thermal conductivity are analyzed on the fluid's thermal diffusivity. The flow governing PDEs are converted into system of ODEs by using suitable transformation. Spectral relaxation computation scheme is then used for controlling the new set equations. SRM algorithm controlling subsystems is built through MATLAB. Numerical results are illustrated by MATLAB graphs. Physical quantities such as Sherwood numbers, Nusselt and skin friction coefficient are visually taken place through statistical graphs with two cases of imposed magnetic field. The results of this investigation shed light on how non-Newtonian fluids behave when exposed to temperature changes and magnetic fields and useful in understanding and leverage these effects for specific applications.

Phase transitions of choline dihydrogen phosphate: A vibrational spectroscopy and periodic DFT study.

Choline dihydrogen phosphate, [Chol][H2PO4], is a proton-conducting ionic plastic crystal exhibiting a complicated sequence of phase transitions. Here, we address the argument in the literature around the thermal properties of [Chol][H2PO4] using Raman and infrared microspectroscopy. The known structure of the low-temperature crystal, which contains the anti-conformer of [Chol]+ and hydrogen-bonded dimers of anions, was used to do periodic density functional theory calculations of the vibrational frequencies. Raman spectra indicate that the solid-solid transition at 20 °C is linked to a conformational change to the gauche [Chol] conformer with a concurrent local rearrangement of the anions. The distinct bands of lattice modes in the low-frequency range of the Raman spectra vanish at the 20 °C transition. Given the ease with which metastable crystals can be produced, Raman mappings demonstrate that a sample of [Chol][H2PO4] at ambient temperature can contain a combination of anti- and gauche conformers. Heating to 120 °C causes continuous changes in the local environment of anions rather than melting as suggested by a recent calorimetric investigation of [Chol][H2PO4]. The monotonic change in vibrational spectra is consistent with earlier observations of a very small entropy of fusion and no abrupt jump in the temperature dependence of ionic conductivity along the phase transitions of [Chol][H2PO4].

CONDUCTIVITY OF HAFNIUM OXIDE LMS OBTAINED BY ELECTRON BEAM SPUTTERING

Films of hafnium oxide HfOx with a thickness of about 40 nm were obtained by electron beam sputtering at di erent oxygen ow rates in the chamber. The electrophysical properties of lms in air and vacuum were studied. It is shown that the temperature dependences of lm conductivity, measured in vacuum inthe temperature range from 20 to 180 ◦C, have an activation character with an activation energy of 0.82 ±0.02 eV. It has been suggested that charge transfer in the resulting lms is determined by the activation of electrons into the conduction band from the donor level associated with oxygen vacancies. It was found that the conductivity of lms in air changes greatly with varying oxygen ow, while in vacuum the conductivity is practically independent of the oxygen ow. This indicates signi cant di erences in the surface properties of lms obtained at di erent oxygen ows in the chamber during the deposition process.

Thermal Conductivity of MgSiO3‐H2O System Determined by Machine Learning Potentials

AbstractThermal conductivity plays a pivotal role in understanding the dynamics and evolution of Earth's interior. The Earth's lower mantle is dominated by MgSiO3 polymorphs which may incorporate trace amounts of water. However, the thermal conductivity of MgSiO3‐H2O binary system remains poorly understood. Here, we calculate the thermal conductivity of water‐free and water‐bearing bridgmanite, post‐perovskite, and MgSiO3 melt, using a combination of Green‐Kubo method with molecular dynamics simulations based on a machine learning potential of ab initio quality. The thermal conductivities of water‐free bridgmanite and post‐perovskite overall agree well with previous theoretical and experimental studies. The presence of water mildly reduces the thermal conductivity of the host minerals, significantly weakens the temperature dependence of the thermal conductivity, and reduces the thermal anisotropy of post‐perovskite. Overall, water reduces the thermal conductivity difference between bridgmanite and post‐perovskite, and thus may attenuate lateral heterogeneities of the core‐mantle boundary heat flux.

An investigation into the thermal rectification in one-dimensional asymmetric systems

The thermal rectification phenomenon in a one-dimensional asymmetric system of two thin films with different temperature-dependent thermal conductivities is studied. Based on the traditional thermal diffusion equation, the optimization condition for maximizing the thermal rectification ratio is re-examined; a new sufficient condition is found that the interface temperatures in the forward and reverse heat transfer directions should be equal, regardless of how the thermal conductivities depend on temperature. In other words, the thermal rectification ratio is maximized when the temperature dependence of the thermal conductivity over the entire operating temperature range is fully exploited. This sufficient condition can be used to find out the optimal geometric parameters of nanostructures which determine the effective thermal conductivity. An illustration of an asymmetric system composed of monolayer graphene sheet (GS) and graphene nanomesh (GNM) is presented. This study is beneficial to the development of thermal devices such as thermal resistors, thermal diodes, and thermal logic circuits.

Quantum Nature of Charge Transport in Inkjet-Printed Graphene Revealed in High Magnetic Fields up to 60T.

Inkjet-printing of graphene, iGr, provides an alternative route for the fabrication of highly conductive and flexible graphene films for use in devices. However, the contribution of quantum phenomena associated with 2D single layer graphene, SLG, to the charge transport in iGr is yet to be explored. Here, the first magneto-transport study of iGr in high magnetic fields up to 60 T is presented. The observed quantum phenomena, such as weak localization and negative magnetoresistance, are strongly affected by the thickness of the iGr film and can be explained by a combination of intra- and inter-flake classical and quantum charge transport. The quantum nature of carrier transport in iGr is revealed using temperature, electric field, and magnetic field dependences of the iGr conductivity. These results are relevant for the exploitation of inkjet deposition of graphene, which is of particular interest for additive manufacturing and 3D printing of flexible and wearable electronics. It is shown that printed nanostructures enable ensemble averaging of quantum interference phenomena within a single device, thereby facilitating comparison between experiment and underlying statistical models of electron transport.

Thermal and thermoelectric properties of potassium-doped Pr0.6Sr0.4-xKxMnO3 (x = 0.05 and x = 0.1)

The temperature dependence of thermal conductivity and thermopower was studied for a series of monovalent doped Pr0.6Sr0.4-xKxMnO3 (with x = 0.05 and x = 0.1). The influence of the external magnetic field up to 2 T was investigated with a focus on the vicinity of the ferromagnetic–paramagnetic transition. The analysis of κ(T) data suggests that thermal transport is governed by phonon scattering processes, as both the electronic and magnon contribution to total thermal conductivity is well below 1%. The temperature behavior corresponds to typical curves observed in other manganites, both in shape and value. Thermopower investigation S(T) showed a negative value in all studied temperatures, and for further analysis was divided into ferromagnetic and paramagnetic regions. In the first one, the experimental data followed a standard empirical equation S0+S3/2T3/2+S4T4, bringing information about the prevailing electron–magnon scattering processes. For the latter one, the polaron hopping model was used.

Slow magnetic relaxation and proton conduction in a highly hydrogen-bonded dinuclear holmium(III) complex

Multifunctional magnetic-electrical materials are highly interesting, such as proton-conductive lanthanide single-ion magnets (SIMs). Herein, we reported the synthesis, crystal structure, magnetic and electrical properties of a bifunctional binuclear holmium(III) complex, [Ho2(H2dobdc)(H2O)14]·(H2dobdc)2·8H2O (Ho2, H4dobdc = 2,5-dioxodo-1,4-benzenedicarboxylate), which was constructed by a hydroxy‑functionalizd dicarboxybenzene and holmium(III) ions. Interestingly, single-crystal X-ray diffraction analysis reveals a highly hydrogen-bonded supramolecular structure and highly oxygenated site were formed within the complex. Magnetic measurements indicate the complex exhibits filed-induced slow magnetic relaxation property. Additionally, the impedance spectroscopy measurements show the complex also exhibits humidity- and temperature-dependent proton conduction behaviour via the Grotthus mechanism. These results support a proton-conductive holmium(III) single-ion magnet of Ho2. This work not only provides the first bifunctional HoIII complexes showing slow magnetic relaxation and proton-conducting behaviour but also a supramolecular way for advanced magnetic-electrical systems linking slow magnetic relaxation with unique proton conducting behaviour exploiting a possible cooperative behaviour.

Thermoelectric properties of sintered Ba2AgSi3 crystals and search for impurities to control conductivity type by first-principles calculation

In this study, the basic properties of Ba2AgSi3 were investigated in detail from both experimental and computational viewpoints. Polycrystalline Ba2AgSi3 formed by an arc-melting apparatus under an argon atmosphere was ground into powders, and then powder samples were sintered using the spark plasma sintering method. Both n-type and p-type samples were obtained. This may be due to a slight deviation from the stoichiometric composition. The energy bandgap of Ba2AgSi3 was measured to be around 0.17 eV from the temperature dependence of electrical conductivity and was in agreement with that by first-principles calculations. Sintered samples exhibited a high Seebeck coefficient of −273 μV K−1 and a high power factor of 0.38 mW m−1 K−2 at 307 K for n-type samples. They were 217 μV K−1 and 0.23 mW m−1 K−2, respectively, at 320 K for p-type samples. The electronic structures of impurity-doped Ba2AgSi3 were also discussed using first-principles calculations to investigate the insertion site of impurity atoms. The calculations suggest that the substitution of B (P) at any Si site shifts the Fermi level and transforms it into p-type (n-type) semiconductors. On the other hand, substitution of Ba or Ag sites with B or P is unlikely to occur in terms of formation energy.

Elaboration of La (Sr/Na) Mn (Ti) O3 ceramic, structural, and morphological investigations, and contribution of direct and indirect interactions on transport properties

The charge carrier's dynamics of La0.7(Sr5/6Na1/6)0.3Mn0.7Ti0.3O3 (LSNMTO) ceramic is conducted using the temperature and frequency dependences of the electrical conductivity and their scaling formalisms. The structural study indicates that LSNMTO crystallizes in a rhombohedral R3‾c perovskite structure with no detectible secondary phases. A phase transition from the high-temperature metallic behavior to the low-temperature semiconductor nature is observed from the electrical conductivity curve at TS-M = 415 K. Further, it is observed that the cation-anion-cation and the cation-cation interactions are present in the material, and play important role in governing the electrical behaviors of LSNMTO. From 200 K to 415 K, the Non-adiabatic Small Polaron Hopping is the predominant conduction process, although the Mott-Variable Range Hopping mechanism governs the conductivity at low temperatures. In the intermediate temperature range, the dynamic of the charge carriers is explained using the Shklovskii Efros model. The frequency-activated conductivity obeyed the universal laws (double-Jonscher and Jonscher laws). At high frequencies, the dispersion of the conductivity spectra is attributed to the presence of hopping and tunneling conduction processes. The Time-Temperature Superposition Principle (TTSP) is obeyed over a large temperature range from 160 K to 350 K. Below 160 K, the deviation from the TTSP is attributed to the coexistence of hopping and tunneling conduction mechanisms. Deviations from the Summerfield scaling and shifts of the isotherms to higher values on decreasing the temperature are due to the local structural disorder in LSNMTO. Therefore, the structural particularities of LSNMTO can result in diverse conduction pathways giving an increase to the deviations from the Summerfield scaling. The studied ceramic exhibits a very motivating maximum negative temperature coefficient of resistance NTCR = −13.36% which is significantly elevated as compared to previously investigated compounds.

Peristaltic transport of nanofluid with temperature dependent thermal conductivity: A numerical study

Peristaltic flow of nanofluid with temperature-dependent thermal conductivity is investigated. Variation of effective thermal conductivity of nanofluids with temperature is addressed. Mathematical modeling of momentum and energy equation is considered in a symmetric channel. Viscous dissipation, Ohmic heating, and mixed convection are accounted. Applied magnetic field and convective boundary conditions are imposed. Dimensionless expressions are simplified under long wavelength approximation. The relevant problems are solved by numerical technique. Velocity, temperature, pressure, and heat transfer characteristics are studied graphically. Heat transfer rate rapidly increases by increasing the concentration of nanomaterial. Therefore, nanomaterial is used for the cooling process in engineering and biomedical devices.

Effect of La, Zr Doping on the Structural and Electrical Conduction Behaviour of BiFeO<sub>3</sub>-BaTiO<sub>3</sub> Ceramics

<p>This study presents a comprehensive investigation of the crystal structure and DC conduction mechanism of [(Ba<sub>0.7-x</sub> La<sub>x</sub>) Bi<sub>0.3</sub>][(Ti<sub>0.5</sub> Zr<sub>0.2</sub>) Fe<sub>0.3</sub>]O<sub>3</sub> with x = 0.00, 0.01, 0.03, 0.05 employing X-ray diffraction (XRD) and electrical conductivity measurements. Various compositions were synthesized through the solid-state ceramic route. XRD was used to investigate phase formation. Analysis of XRD data suggested a structural transition from cubic to tetragonal for x ≥ 0.01. The average crystallite size first increases for x = 0.01 and then decreases for x ≥ 0.03. The temperature-dependent electrical conductivity measurements were investigated over a wide temperature range which revealed distinct conductivity mechanisms governing the material's transport properties. The activation energy (E<sub>a</sub>) has been estimated from temperature-dependent DC conductivity. Overall, this study provides valuable insights into the correlation between crystal structure and electrical properties in [(Ba<sub>0.7-x</sub> La<sub>x</sub>) Bi<sub>0.3</sub>][(Ti<sub>0.5</sub> Zr<sub>0.2</sub>) Fe<sub>0.3</sub>]O<sub>3</sub>, offering significant implications for its potential applications in electronic and optoelectronic devices requiring tailored conductivity characteristics.</p>

Effects of Pd atom vibration in the Sr–Te octahedral interstitial space in Zintl compound SrPdTe on lattice anharmonicity and thermoelectric properties

Based on first-principles calculations, the current study deeply explores the thermoelectric properties of the Zintl compound SrPdTe. We found that the anharmonic vibration of Pd atoms plays an important role in the quartic anharmonic effect and the temperature dependence of the thermal conductivity. In the crystalline structure, Sr atoms form octahedra with eight surrounding Te atoms, while Pd atoms are located in the gaps between the octahedra. This structure makes the strong atomic mean square displacement of Pd atoms the main factor leading to the ultralow thermal conductivity. The study also reveals the effects of phonon frequency renormalization and four-phonon scattering on heat transfer performance. Even considering the spin–orbit coupling effect, multiple secondary valence band tops maintain the power factor of the material at high temperatures, providing a potential opportunity for achieving excellent thermoelectric performance.

Studies of the Properties of New Electrospun Based on PVA-PEG Polymer Systems Electrolytes for Energy Storage Devices

Solid polymer electrolytes (SPEs) have been considerably investigated due to various electrochemical device applications. Most of the SPEs comprise polymer as a host material to provide strength and good mechanical stability and salt that transfers charge carriers to cause conductivity. Nanocomposite solid polymer electrolyte membranes based on poly(vinyl alcohol) (PVA)-poly(ethylene glycol) (PEG) blend complexed with LiClO4 and nanofillers Al2O3 at different weight percent ratios have been obtained by using electrospinning method. The conductivity and structural properties of the different systems have been characterized by using various experimental approaches such as X-ray diffraction (XRD) and Fourier transform infrared FTIR spectroscopy. The ionic conductivity of the systems has been measured by using an LCR meter in a temperature ranging from 298 to 353 K. Maximum ionic conductivity of 1.58 × 10-4 S cm-1 at room temperature has been observed for the system of PVA-PEG-LiClO4-Al2O3 (50-25-15-10) with 15 wt% weight percent of LiClO4 salt in PVA-PEG blend matrix. The ac conductivity report indicates that the ionic conductivity of the PVA-PEG-LiClO4-Al2O3 complex is influenced by the concentration of LiClO4. The effect of temperature on the ionic conductivity of polymer electrolyte complexes has been estimated by changing the temperature ranging from 298 to 353 K. However, the conductivity of the nanofiber polymer electrolyte systems increases with the rise of temperature, and the maximum conductivity of 1.58 × 10-2 S cm-1 has been recorded at 353 K. The temperature-dependent conductivity follows the Arrhenius behavior.

Effectiveness of Maxwell velocity and smoluchowski thermal slip constraints in presence of non-uniform heat source

Magnetohydrodynamic flow of nanomaterial by a stretched boundary is addressed. Entropy generation is examined. Variable fluid characteristics are considered. Buongiorno thermal enhancement model in presence of Darcy-Forchheimer expression is addressed. Nonlinear thermal radiation, non-uniform heat source and dissipation are considered in thermal expression. Slip conditions in chemically reactive flow are addressed. Here Maxwell slip velocity and Smoluchowski slip temperature are under consideration. Impact of Arrhenius activation energy is deliberated. Optimal homotopy analysis approach (OHAM) is utilized for construction of convergent solutions. Graphical description for liquid motion, entropy rate, concentration and temperature are examined. Higher magnetic variable has reverse effect on entropy rate and velocity. Higher temperature and entropy rate are seen for radiation parameter. Higher temperature dependent conductivity parameter has opposite effect on liquid motion and entropy rate. Liquid flow has same impact for both porosity and velocity slip parameters. Larger thermal slip variable lead to decrease thermal distribution while reverse impact holds for heat source. Concentration has opposite trend through both random and thermophoresis parameters. An enhancement in thermal distribution and entropy rate are seen through variable thermal conductivity. An intensification in entropy rate has been noticed through concentration dependent conductivity variable. The considered configuration has relevance for detecting cooling towers, polymer extrusion, spinning of filaments, cable coating and metallurgical processes.

Numerical simulation of heat transfer during meat ball cooking and microbial food safety enhancement.

This study was conducted to apply the finite volume method (FVM) to solve the partial differential equation (PDE) governing the heat transfer process during meat cooking with convective surface conditions. For a one-dimensional, round-shaped food, such as meat balls, the domain may be divided into shells of equal thickness, with energy balance established for each adjacent shell using in the finite difference scheme (FDS) to construct a set of finite difference equations, which were then solved simultaneously using the FORTRAN language and the IVPAG subroutine of the International Mathematics and Statistics Library. The FDS is flexible for temperature-dependent physical properties of foods, such as thermal conductivity (k), specific heat (Cp ), thermal diffusivity (α), and boundary conditions, for example, surface heat transfer coefficient (h), to predict the dynamic temperature profiles in beef and chicken meat balls cooked in an oven. Once the FVM model was established and validated, it was used to simulate the dynamic temperature profiles during cooking, which were then used in combination with the general method to evaluate the thermal lethality of Shiga toxin-producing Escherichia coli and Salmonella spp. using D and z values in ground meats during cooking. The method can be applied to design cooking processes that effectively inactivate foodborne pathogens while maintaining the quality of cooked meats and evaluate the adequacy of a cooking process. PRACTICAL APPLICATION: The temperature dependences of thermal conductivity (k) and thermal diffusivity (α) of raw ground beef and ground chicken meats were measured. These thermal properties were then used in numerical simulation to predict the dynamic heating temperature profile and thermal lethality of ground beef and chicken meat balls. The numerical simulation method may be used to optimize and evaluate thermal processes and ensure the inactivation of pathogens in meat products during cooking.

STRUCTURAL AND ELECTRICAL PROPERTIES OF MONOCRYSTALLINE Ag7+xGexP1-xS6 (x = 0.75; 0.5) SOLID SOLUTIONS

Compounds of the argyrodite structure are considered to be promising functional materials due to their peculiarities. The functional parameters of these compounds are provided by the peculiarities of the crystal structure, namely the simultaneous coexistence of a mobile cationic sublattice within a rigid anionic framework. Such a crystal structure motif determines the formation of wide regions of solid solutions based on argyrodites and makes it possible to increase the values of the functional parameters of these phases within the homogeneity regions. This work presents the results of the study of the structural and electrical properties of Ag7+xGexP1-xS6 (x = 0.75; 0.5) solid solutions with an argyridite structure. Single-crystal samples of solid solutions of Ag7.75Ge0.75P0.25S6 and Ag7.5Ge0.5P0.5S6 were obtained by the method of directional crystallization from the melt in vacuum-sealed quartz ampoules. It was found that the solid solutions of Ag7+xGexP1-xS6 (x = 0.75; 0.5) crystallize in orthorhombic crystal system: SG Pna21, with lattice parameters: a = 15.093 Å, b = 7.462 Å, c = 10.571 Å (Ag7.75Ge0.75P0.25S6) and a = 15.023 Å, b = 7.450 Å, c = 10.545 Å (Ag7.5Ge0.5P0.5S6). The frequency and temperature dependence of the total electrical conductivity was studied by impedance spectroscopy. The total electrical conductivity of the investigated single crystals is Ag7.75Ge0.75P0.25S6 5.43×10–3 S/cm (0.199 eV) and Ag7.5Ge0.5P0.5S6 2.22×10–2 S/cm (0.152 eV) at a temperature of 25 °C.
 Keywords: argyrodites; single crystals; electrical conductivity; phase analysis.