Structural and optical properties of diluted magnetic $$\hbox {Ga}_{{1-x}}\hbox {Mn}_{{x}}$$As–AlAs quantum wells grown on high-index GaAs planes

We report on the structural and optical properties of \(\hbox {Ga}_{{1-x}}\hbox {Mn}_{{x}}\hbox {As}\)–AlAs quantum wells (QWs) with \(x = 0.1\%\) grown by molecular beam epitaxy (MBE) on semi-insulating GaAs substrates with orientations (100), (110), (311)B and (411)B. Atomic force microscopy (AFM), X-ray diffraction (XRD) and photoluminescence (PL) techniques were used to investigate these QWs. AFM results have evidenced the formation of Mn-induced islands, which are randomly distributed on the surface. These islands tend to segregate for samples grown on (110) and (411)B planes, while no clear segregation was observed for samples grown on (100) and (311)B orientations. Results show that the PL line width increases with Mn segregation. XRD measurements were used to determine \(2\theta , d\) and cell parameters.     

Thermodynamic Investigation of the Eutectic Mixture of the $$\hbox {LiNO}_{3}$$–$$\hbox {NaNO}_{3}$$NaNO3–$$\hbox {KNO}_{3}$$KNO3–$$\hbox {Ca}(\hbox {NO}_{3})_{2}$$Ca(NO3)2 System

Molten nitrate salt is usually employed as heat transfer or energy storage medium in concentrating solar power systems to improve the overall efficiency of thermoelectric conversion. In the present work, the liquidus curves of the \(\hbox {LiNO}_{3}\)–\(\hbox {NaNO}_{3}\)–\(\hbox {KNO}_{3}\)–\(\hbox {Ca}(\hbox {NO}_{3})_{2}\) system is determined by conformal ionic solution theory according to the solid–liquid equilibrium state of the binary mixture. The calculated eutectic temperature of the mixture is \(93.17\,{^{\circ }}\hbox {C}\), which is close to the experimental value of \(93.22\,{^{\circ }}\hbox {C}\) obtained from differential scanning calorimetry (DSC). Visualization observation experiments reveal that the quaternary eutectic mixture begins to partially melt when the temperature reaches \(50\,{^{\circ }}\hbox {C}\), and the degree of melting increases with temperature. The mixture is completely melted at \(\hbox {130}\,{^{\circ }}\hbox {C}\). The observed changes in the dissolved state at different temperatures correlate well with the DSC heat flow curve fluctuations.     

Synthesis of $$\hbox {Ag}_{2}\hbox {Se}$$–graphene–$$\hbox {TiO}_{2} $$TiO2 nanocomposite and analysis of photocatalytic activity of $$\hbox {CO}_{2}$$CO2 reduction to $$\hbox {CH}_{3}\hbox {OH}$$CH3OH

The present work deals with the development of a new ternary composite, \(\hbox {Ag}_{2}\hbox {Se}\)–\(\hbox {G}\)–\(\hbox {TiO}_{2}\), using ultrasonic techniques as well as X-ray diffraction (XRD), scanning electron microscopy (SEM), high transmission electron microscopy (HTEM), X-ray photoelectron spectroscopy (XPS), Raman spectroscopy and UV–Vis diffuse reflectance spectra (DRS) analyses. The photocatalytic potential of nanocomposites is examined for \(\hbox {CO}_{2}\) reduction to methanol under ultraviolet (UV) and visible light irradiation. \(\hbox {Ag}_{2}\hbox {Se}\)–\(\hbox {TiO}_{2}\) with an optimum loading graphene of 10 wt% exhibited the maximum photoactivity, obtaining a total \(\hbox {CH}_{3}\hbox {OH}\) yield of 3.52 \(\upmu \hbox {mol}\,\hbox {g}^{-1}\,\hbox {h}^{-1}\) after 48 h. This outstanding photoreduction activity is due to the positive synergistic relation between \(\hbox {Ag}_{2}\hbox {Se}\) and graphene components in our heterogeneous system.     

Enhanced infrared transmission characteristics of microwave-sintered $$\hbox {Y}_{2}\hbox {O}_{3}$$–$$\hbox {MgO}$$MgO nanocomposite

Infrared (IR) transparent ceramics are found to have applications in demanding defence and space missions. In this work, \(\hbox {Y}_{2}\hbox {O}_{3}\)–\(\hbox {MgO}\) nanocomposites were synthesised by a modified single-step combustion technique. The characterisation of the as-prepared powder by X-ray diffraction and transmission electron microscopy revealed the presence of cubic phases of ultra-fine nanostructured \(\hbox {Y}_{2}\hbox {O}_{3 }\) and MgO, with an average crystallite size of \({\sim }19 \hbox { nm}\). For the first time the resistive and microwave heatings were effectively coupled for sintering the sample, and it was found that the sintering temperature and soaking time were reduced considerably. The pellets were sintered to 99.2% of the theoretical density at \(1430{^{\circ }}\hbox {C}\) for a soaking duration of 20 min. The well-sintered pellets with an average grain size of \({\sim }200 \hbox { nm}\) showed better transmittance properties relative to pure yttria. The promising percentage transmission of 80% in the UV–visible region and 82% in the mid-IR region shown by \(\hbox {Y}_{2}\hbox {O}_{3}\)–\(\hbox {MgO}\) nanocomposites can be tailored and made cost-effective to fabricate high-quality IR windows for strategic defence and space missions.     

In situ synthesis and properties of self-reinforced $$\hbox {Si}_{3} \hbox {N}_{4}\textendash \hbox {SiO}_{2}\textendash \hbox {Al}_{2} \hbox {O}_{3}\textendash \hbox {Y}_{2}\hbox {O}_{3} \ (\hbox {La}_{2}\hbox {O}_{3}$$) glass–ceramic composites

In-situ-grown \(\upbeta \!\hbox {-Si}_{3}\hbox {N}_{4}\)-reinforced \(\hbox {SiO}_{2}\textendash \hbox {Al}_{2}\hbox {O}_{3}\textendash \hbox {Y}_{2}\hbox {O}_{3}\) \((\hbox {La}_{2}\hbox {O}_{3})\) self-reinforced glass–ceramic composites were obtained without any \(\upbeta \!\hbox {-Si}_{3}\hbox {N}_{4}\) seed crystal. These composites with different compositions were prepared in a nitrogen atmosphere for comparison of phase transformation and mechanical properties. The results showed that \(\hbox {SiO}_{2}\textendash \hbox {Al}_{2}\hbox {O}_{3}\textendash \hbox {Y}_{2}\hbox {O}_{3}\) \((\hbox {La}_{2}\hbox {O}_{3})\) glass can effectively promote \(\upalpha \)- to \(\upbeta \!\hbox {-Si}_{3}\hbox {N}_{4}\) phase transformation. The crystallized \(\hbox {Y}_{2}\hbox {Si}_{2}\hbox {O}_{7}\textendash \hbox {La}_{4.67}\hbox {Si}_{3}\hbox {O}_{13}\) phases with a high melting point significantly benefited the high-temperature mechanical properties of the composites. The \(\hbox {Si}_{3}\hbox {N}_{4}\textendash \hbox {SiO}_{2}\textendash \hbox {Al}_{2} \hbox {O}_{3}\textendash \hbox {Y}_{2}\hbox {O}_{3}\) \((\hbox {La}_{2}\hbox {O}_{3})\) glass–ceramic composites exhibit excellent mechanical properties compared with unreinforced glass–ceramic matrix, which is undoubtedly attributed to the elongated \(\upbeta \!\hbox {-Si}_{3}\hbox {N}_{4}\) grains. These glass–ceramic \(\hbox {Si}_{3}\hbox {N}_{4}\) composites with excellent comprehensive properties might be a promising material for high-temperature applications.     

Cation substitution induced blue-shift of optical band gap in nanocrystalline $$\hbox {Zn}_{(1-x)} \hbox {Ca}_{x}\hbox {O}$$ thin films deposited by sol–gel dip coating technique

Transparent nanocrystalline \(\hbox {Zn}_{(1-x)}\hbox {Ca}_{x}\hbox {O }(0 \le x \le 0.20)\) thin films were deposited on glass substrates by sol–gel dip coating method. The X-ray diffraction (XRD) pattern revealed the polycrystalline nature of the films with hexagonal wurtzite structure and confirmed the non-existence of the secondary phase corresponding to CaO indicating the monophasic nature of the deposited films. The crystallinity of the films deteriorated with higher dopant concentration due to the segregation or separation of dopant ions in grain boundaries. The lattice parameters and the unit cell volume increased to a higher Ca-dopant concentration. This was due to the successful incorporation of \(\hbox {Ca}^{2+}\) ions with larger ionic radius in the host zinc oxide (ZnO) lattice. The optical transmittance spectra of the samples showed transmittances above 60% in the visible spectral range and the absorption edge in the near ultra-violet region got blue-shifted with cation substitution. The estimated optical energy gaps confirmed the band gap widening with increase in Ca-dopant concentration. The calculated values increased from 3.30 eV for undoped ZnO to 3.73 eV for \(\hbox {Zn}_{0.8}\hbox {Ca}_{0.2}\hbox {O}\) thin films giving 13.03% enhancement in the energy gap value due to the electronic perturbation caused by cation substitution as well as deterioration in crystallinity.     

Lattice Dynamical,Elastic and Thermodynamical Properties of III–V Semiconductor AlSb,GaSb and Their Mixed Semiconductor $$\hbox {Ga}_{\mathrm{1-x}}\hbox {Al}_{\mathrm{x}}\hbox {Sb}$$

A proposed eleven-parameter three-body shell model is used to study the lattice dynamical properties such as phonon dispersion relations along high symmetry directions, phonon density of states, variation of specific heat and Debye characteristic temperature with absolute temperature, elastic constants and related properties for III–V semiconductor AlSb, GaSb and their mixed semiconductor \(\hbox {Ga}_{\mathrm{1-x}}\hbox {Al}_{\mathrm{x}}\hbox {Sb}\) having zinc-blende structure. We found an overall good agreement with the available experimental and theoretical results available in the literature.     

Radiative Properties of Ceramic $$\hbox {Al}_{2}\hbox {O}_{3}$$, AlN and $$\hbox {Si}_{3}\hbox {N}_{4}$$Si3N4—II: Modeling

In Part I of this study (Cheng et al. in Int J Thermophys 37: 62, 2016), the reflectance and transmittance of dense ceramic plates were measured at wavelengths from 0.4 \(\upmu \hbox {m}\) to about 20 \(\upmu \hbox {m}\). The samples of \(\hbox {Al}_{2}\hbox {O}_{3}\) and AlN are semitransparent in the wavelength region from 0.4 \(\upmu \hbox {m}\) to about 7 \(\upmu \hbox {m}\), where volume scattering dominates the absorption and scattering behaviors. On the other hand, the \(\hbox {Si}_{3}\hbox {N}_{4}\) plate is opaque in the whole wavelength region. In the mid-infrared region, all samples show phonon vibration bands and surface reflection appears to be strong. The present study focuses on modeling the radiative properties and uses an inverse method to obtain the scattering and absorption coefficients of \(\hbox {Al}_{2}\hbox {O}_{3}\) and AlN in the semitransparent region from the measured directional-hemispherical reflectance and transmittance. The scattering coefficient is also predicted using Mie theory for comparison. The Lorentz oscillator model is applied to fit the reflectance spectra of AlN and \(\hbox {Si}_{3}\hbox {N}_{4}\) from 1.6 \(\upmu \hbox {m}\) to 20 \(\upmu \hbox {m}\) in order to obtain their optical constants. It is found that the phonon modes for \(\hbox {Si}_{3}\hbox {N}_{4}\) are much stronger in the polycrystalline sample studied here than in amorphous films reported previously.     

Liquidus Temperatures and Thermodynamic Properties of the KCl–\mathrm{{KNO}}_{2}, NaCl–\mathrm{{NaNO}}_{2}, and \mathrm{{KNO}}_{2}–\mathrm {NaNO}_{2} Systems

Potassium nitrite is very sensitive to temperature, humidity, and the atmosphere, so few studies have been made in this field for the thermodynamic properties of molten salt with nitrite salt. In this article, the liquidus curves of NaCl– $\mathrm{{NaNO}}_{2}$ NaNO 2 , KCl– $\mathrm{{KNO}}_{2}$ KNO 2 , and $\mathrm {NaNO}_{2}$ NaNO 2 – $\mathrm{{KNO}}_{2}$ KNO 2 are calculated by a simple “hard-sphere” ionic interaction model. The calculated liquidus temperatures show good agreement with experimental values, which implies an ideal mixing enthalpy and entropy for the liquid binary systems. In addition to the phase equilibrium data and experimental thermochemical properties of molten salt systems, the activities of these binary systems are determined by the phase diagrams and the analytical integration of the classical Gibbs–Duhem equation.     

Process optimization of dye-sensitized solar cells using $$\hbox {TiO}_{2}$$–graphene nanocomposites

\(\hbox {TiO}_{2}\)–graphene (TGR) nanocomposites with varying concentrations of graphene from 0 to 1 wt% were prepared by direct mix method. X-ray diffraction (XRD) spectra confirmed the incorporation of graphene in photoanode material, which was further supported by field emission scanning electron microscopy (FESEM) and energy dispersive X-ray (EDX). The UV–visible spectrum of these nanocomposites shifted towards higher wavelength region as compared to pure \(\hbox {TiO}_{2}\) that indicated a reduced band gap and hence, enhanced absorption bandwidth. Significant reduction in electron–hole recombination was confirmed from photoluminescence spectroscopy. These TGR nanocomposite films after tethering with black dye were employed as photoanodes in dye-sensitized solar cells (DSSCs). The efficiency of solar cells at varying concentrations of graphene (in photoandes) was also investigated. TGR 0.25 wt% nanocomposite showed the highest photocurrent density (\(J_{\mathrm{SC}}\)) of \(18.4\,\hbox {mA}\,\hbox {cm}^{-2}\) and efficiency (\(\eta \)) of 4.69%.     

Effect of the method for producing $$\hbox {}$$–$$\hbox {Cr}_{3}\hbox {C}_{2}$$Cr3C2 bulk composites on the structure and properties

Copper–chromium carbide composites containing a carbide phase of 20–30 vol% were obtained with the use of solid- and liquid-phase mechanosyntheses, followed by magnetic pulse compaction (MPC) and spark plasma sintering. The morphology, structural-phase composition, density, hardness and electrical conductivity of the composites were investigated. The structure of composites obtained by MPC represents regions of copper matrix hardened by superfine carbide precipitates surrounded by a layer of chromium carbide. In the composites obtained by spark plasma sintering, the copper matrix hardened by superfine carbide precipitates was divided into areas surrounded by a copper–chromium layer. A composite obtained by the MPC of the powders synthesized using solid-phase mechanosynthesis (MS) (copper, chromium and graphite) had the highest values of Vickers microhardness (4.6 GPa) and Rockwell hardness (HRA 69). The best value of electrical conductivity (36% IACS) was achieved using liquid-phase MS (copper, chromium and xylene) and spark plasma sintering. Liquid-phase MS is the only way to synthesize the powder with a small amount of the carbide phase and without contamination.     

Microwave dielectrics: solid solution,ordering and microwave dielectric properties of $$(1{-}x)\hbox {Ba}(\hbox {Mg}_{1/3}\hbox {Nb}_{2/3})\hbox {O}_{3}{-}x\hbox {Ba(Mg}_{1/8}\hbox {Nb}_{3/4})\hbox {O}_{3}$$ ceramics

The effect of Ba(\(\hbox {Mg}_{1/8}\hbox {Nb}_{3/4})\hbox {O}_{3}\) phase on structure and dielectric properties of \(\hbox {Ba(Mg}_{1/3}\hbox {Nb}_{2/3})\hbox {O}_{3}\) was studied by synthesizing \((1{-}x)\hbox {Ba(Mg}_{1/3}\hbox {Nb}_{2/3})\hbox {O}_{3}{-}x\hbox {Ba}(\hbox {Mg}_{1/8}\hbox {Nb}_{3/4})\hbox {O}_{3}\) (\(x = 0\), 0.005, 0.01 and 0.02) ceramics. Superlattice reflections due to 1:2 ordering appear as low as \(1000^{\circ }\hbox {C}\). \(\hbox {Ba}(\hbox {Mg}_{1/3}\hbox {Nb}_{2/3})\hbox {O}_{3}\) forms solid solution with \(\hbox {Ba}(\hbox {Mg}_{1/8}\hbox {Nb}_{3/4})\hbox {O}_{3}\) for all ‘x’ values studied until \(1350^{\circ }\hbox {C}\). Ordering was confirmed by powder X-ray diffraction pattern, Raman study and HRTEM. Ceramic pucks can be sintered to density \({>}92\%\) of theoretical density. Temperature and frequency-stable dielectric constant and nearly zero dielectric loss (tan \(\delta \)) were observed at low frequencies (20 MHz). The sintered samples exhibit dielectric constant (\(\varepsilon _{\mathrm{r}})\) between 30 and 32, high quality factor between 37000 and 74000 GHz and temperature coefficient of resonant frequency (\(\tau _{\mathrm{f}})\) between 21 and \(24\hbox { ppm }^{\circ }\hbox {C}^{-1}\).     

Electrical and Thermal Characteristics of the Insulator–Metal Transition in Crystalline $$\hbox {V}_{2}\hbox {O}_{5}$$ Films

The electrical and thermal properties with respect to the crystallization in \(\hbox {V}_{2}\hbox {O}_{5}\) thin films were investigated by measuring the resistance at different temperatures and applied voltages. The changes in the crystal structure of the films at different temperatures were also explored using Raman measurements. The thermal diffusivity of the crystalline \(\hbox {V}_{2}\hbox {O}_{5}\) film was measured by the nanosecond thermoreflectance method. The microstructures of amorphous and crystalline \(\hbox {V}_{2}\hbox {O}_{5}\) were observed by SEM and XRD measurements. The temperature-dependent Raman spectra revealed that a structural phase transition does not occur in the crystalline film. The resistance measurements of an amorphous film indicated semiconducting behavior, whereas the resistance of the crystalline film revealed a substantial change near \(250\,{^{\circ }}\hbox {C}\), and Ohmic behavior was observed above \(380\,{^{\circ }}\hbox {C}\). This result was due to the metal–insulator transition induced by lattice distortion in the crystalline film, for which \(T_{\mathrm{c}}\) was \(260\,{^{\circ }}\hbox {C}\). \(T_{\mathrm{c}}\) of the film decreased from 260 \({^{\circ }}\hbox {C}\) to \(230\,{^{\circ }}\hbox {C}\) with increasing applied voltage from 0 V to 10 V. Furthermore, the thermal diffusivity of the crystalline film was \(1.67\times 10^{-7}\,\hbox {m}^{2}\cdot \hbox {s}^{-1}\) according to the nanosecond thermoreflectance measurements.     

Solidification of NaCl–LiF–$$\hbox {CaF}_{2}$$ ternary composites

The purpose of this work is to refine the microstructure of eutectic halides, candidates to polaritonic metamaterials, through the directional solidification of ternary compositions. NaCl–LiF–\(\hbox {CaF}_{2}\) ternary composites have been solidified using Bridgman and micro-pulling-down techniques at pulling rates from 3 to 300 mm/h for the first time. The interparticle spacing is 12% smaller for this composition than for the binary fibrous NaCl–LiF eutectic. Conditions for solidification and growth in order to generate ternary aligned microstructures are discussed. The very small amount of melt remaining in the mixtures until \(580\,^{\circ }\hbox {C}\) is probably the consequence of solid solubility of LiCl in NaCl and the formation of the reciprocal salt pairs, as in NaCl–LiF. However, it does not prevent the solidification of homogenous ternary microstructures.     

Optimization of the liquid–liquid interfacial precipitation method for the synthesis of $$\hbox {C}_{60}$$ nanotubes

Tubular fullerene nanowhiskers called ‘fullerene nanotubes’ are composed of \(\hbox {C}_{60}\) fullerene molecules (\(\hbox {C}_{60}\) NTs) are synthesized at room temperature using the liquid–liquid interfacial precipitation method in the pyridine and isopropyl alcohol (IPA) system. The growth control of fullerene nanotubes is important for their chemical and physical properties as well as for their future applications. In the present study, we investigated the effect of light, water, solvent ratio and temperature on the synthesis of \(\hbox {C}_{60}\) nanotubes. A marked development in the yield of \(\hbox {C}_{60}\) NTs was achieved using dehydrated solvents, a solution with a volume ratio of 1:9 for pyridine: IPA, a growth temperature equal to \(5{^{\circ }}\hbox {C}\) and by illuminating the \(\hbox {C}_{60}\)-pyridine solution with ultraviolet light (wavelength 302 nm) for 102 h. The synthesized fullerene nanotubes were characterized by different analytical techniques including Raman and Fourier transform infrared spectroscopy, optical microscopy, focussed ion beam scanning electron microscopy and transmission electron microscopy.     

Measurement of Out-of-Plane Thermal Conductivity of Epitaxial $$\hbox {YBa}_{2}\hbox {Cu}_{3}\hbox {O}_{7-{\delta }}$$ Thin Films in the Temperature Range from 10 K to 300 K by Photothermal Reflectance

We measured the out-of-plane (c-axis) thermal conductivity of epitaxially grown \(\hbox {YBa}_{2}\hbox {Cu}_{3}\hbox {O}_{7-{\delta }}\) (YBCO) thin films (250 nm, 500 nm and 1000 nm) in the temperature range from 10 K to 300 K using the photothermal reflectance technique. The technique enables us to determine the thermal conductivity perpendicular to a thin film on a substrate by curve fitting analysis of the phase lag between the thermoreflectance signal and modulated heating laser beam in the frequency range from \(10^{2}\,\hbox {Hz}\) to \(10^{6}\,\hbox {Hz}\). The uncertainties of measured thermal conductivity of all samples were estimated to be within \({\pm }9\,\%\) at 300 K, \({\pm }12\,\%\) at 180 K, \({\pm }16\,\%\) at 90 K and \({\pm }20\,\%\) below 50 K. The experimental results show that the thermal conductivity is dependent on the thickness of the thin films across the entire temperature range. We also observed that the thermal conductivity of the present YBCO thin films showed \(T^{1.4}\) to \(T^{1.6}\) glass-like dependence below 50 K, even though the films are crystalline solids. In order to explain the reason for this temperature dependence, we attempted to analyze our results using phonon relaxation times for possible phonon scattering models, including stacking faults, grain boundary and tunneling states scattering models.     

Magnetic measurements,Raman and infrared spectra of metal–ligand complex derived from $$\hbox {CoCl}_{2}\cdot \hbox {6H}_{2}\hbox {O}$$ and 2-benzoyl pyridine

Nanocrystalline complex of \(\hbox {CoCl}_{2}\cdot 6\hbox {H}_{2}\hbox {O}{-}2\)-benzoyl pyridine is prepared by chemical route. Each component of the desired complex is identified by analysing the X-ray diffractograms. Energy-dispersive X-ray analysis (EDX) data confirmed the presence of the desired elements of the sample. Theoretical optimized structure of the complex was derived using ab initio density functional level of theory (DFT) method of calculation. The average nanocrystallite size estimated from the XRD data is \(\sim \)43 nm. Static magnetic property of the complex is studied in the temperature range from 300 K down to 14 K. The estimated magnetic moment of the complex is high when compared to that of the free ion magnetic moment of \(\hbox {Co}^{2+}\) and this is attributed to the less effect of the crystal field acting on the ion in the organic complex due to which orbital moments are not fully quenched. The magnetic property of the complex is also remarkably enhanced compared to that of the diamagnetic 2-benzoyl pyridine which may be suitable for applications in devices. FTIR and Raman spectra of the ligand, 2-benzoyl pyridine and the synthesized complex are recorded at room temperature, which not only confirm the presence of each phase in the complex, but some interesting results are also extracted from the analyses of different Raman active modes of the complex.     

Photoacoustic Spectroscopic Study of Optical Properties of $$\hbox {Cu}_{2}\hbox {GeTe}_{3}$$ in Temperature Range from 80 K to 300 K

We used photoacoustic spectroscopy to investigate the optical properties of \(\hbox {Cu}_{2}\hbox {GeTe}_{3}\). The temperature dependence of the bandgap energy was evaluated from optical absorption spectra obtained in the photon energy range of 0.76 eV to 0.81 eV between 80 K and 300 K. We used the empirical and semi-empirical models of Varshni, Viña, and Pässler to describe the observed bandgap shrinkage in this compound. The Debye temperature and effective phonon temperature of the compound were estimated to be approximately 227.4 K and 151.6 K, respectively. Thus, the temperature dependence of the bandgap is mediated by acoustic phonons.     

Phase Equilibria in the Ternary Reciprocal System K+, Ba2+||Br–, $${\text{MoO}}_{4}^{{2 - }}$$

Inorganic Materials - The ternary reciprocal system K+, Ba2+||Br–, $${\text{MoO}}_{4}^{{2 - }}$$ has been divided into stable simplexes by a thermodynamic method, stable sections have been...