A Unified Approach to the Thermodynamics and Quantum Scaling Functions of One-Dimensional Strongly Attractive SU(w) Fermi Gases

We present a unified derivation of the pressure equation of states, thermodynamics and scaling functions for the one-dimensional （1D） strongly attractive Fermi gases with SU（w） symmetry. These physical quantities provide a rigorous understanding on a universality class of quantum criticality characterized by the critical exponents z = 2 and correlation length exponent v= 1/2. Such a universality class of quantum criticality can occur when the Fermi sea of one branch of charge bound states starts to fill or becomes gapped at zero temperature. The quantum critical cone can be determined by the double peaks in specific heat, which serve to mark two crossover temperatures fanning out from the critical point. Our method opens to further study on quantum phases and phase transitions in strongly interacting fermions with large SU （ w） and non-SU （ w ） symmetries in one dimension.

Crystal structure,phase transitions,and thermodynamic properties of magnesium metavanadate(MgV_(2)O_(6))

As a promising anode material for magnesium ion rechargeable batteries,magnesium metavanadate(MgV_(2)O_(6))has attracted considerable research interest in recent years.A MgV_(2)O_(6)sample was synthesized via a facile solid-state reaction by multistep-firing stoichiometric mixtures of MgO and V2O5 powder under an air atmosphere.The solid-state phase transition fromα-MgV_(2)O_(6)toβ-MgV_(2)O_(6)occurred at 841 K and the enthalpy change was 4.37±0.04 kJ/mol.The endothermic effect at 1014 K and the enthalpy change was 26.54±0.26 kJ/mol,which is related to the incongruent melting ofβ-MgV_(2)O_(6).In situ XRD was performed to investigate phase transition of the as-prepared MgV_(2)O_(6)at high temperatures.The cell parameters obtained by Rietveld refinement indicated that it crystallizes in a monoclinic system with the C2/m space group,and the lattice parameters of a=9.280 A°,b=3.501 A°,c=6.731 A°,β=111.76°.The solid-state phase transition fromα-MgV_(2)O_(6)toβ-MgV_(2)O_(6)was further studied by thermal kinetics,indicating that this process is controlled first by a fibril-like mechanism and then by a spherulitic-type mechanism with an increasing heating rate.Additionally,the enthalpy change of MgV_(2)O_(6)at high temperatures was measured utilizing the drop calorimetry,heat capacity was calculated and given as:Cp=208.3+0.03583T-4809000T^(−2)(298-923 K)(J mol^(−1)K^(−1)),the high-temperature heat capacity can be used to calculate Gibbs free energy of MgV_(2)O_(6)at high temperatures.

Thermodynamic Functions and Phase Transformation of Metal Nanocrystals

A model to calculate the thermodynamic functions of the pure metal nanocrystals has been developed, with the consideration of the effects of both the interfaces and the crystal in the nano-grain interior. As an example, the enthalpy, entropy and Gibbs free energy, as functions of the excess free volume at interfaces, temperature and grain size, are calculated for the Co nanocrystals. Furthermore, the characteristics of β-Co→α-Co phase transformation are studied, and the transformation temperatures at different levels of grain size, as well as the critical grain sizes at different temperatures, are predicted. The calculation results show that, the nano-grained β-Co （fcc） is thermodynamically stable at temperatures much lower than that for the conventional coarse-grained materials, and may also stably exist at room temperature when the grain size is reduced to be small enough. The present model is verified by comparisons between the experimental findings and the theoretical predictions.

Thermal dehydration kinetic mechanism of Mn_(1.8)Co_(0.1)Mg_(0.1)P_2O_7·2H_2O using Málek's equations and thermodynamic functions determination

Mn1.8Co0.1Mg0.1P2O7·2H2O was synthesized via hydrothermal method and the thermal dehydration product was confirmed to be Mn1.8Co0.1Mg0.1P2O7.The thermogravimetry/differential thermogravimetry/differential thermal analysis,Fourier transform infrared,atomic absorption spectrophotometry,X-ray diffraction and scanning electron microscopy techniques were employed for sample characterization.Non-isothermal kinetics was studied under air atmosphere at four heating rates and the single thermal dehydration process was observed.Iterative Kissinger-Akahira-Sunose equation was used to calculate the apparent activation energy Eαvalues.Dehydration process was confirmed to be a single-step kinetic process with the unique kinetic triplets.Málek’s equations were used to determine the kinetic model f（α）and pre-exponential factor A.？esták-Berggren model was suggested to be the mechanism function for the dehydration process.The best fit led to the kinetic triplets of Eα=（79.97±6.51）k J/mol,ln A=16.83 and f（α）=α^0.520（1-α）^1.255（αis the extent of conversion）.The thermodynamic functions of activation were calculated using activated complex theory together with A value.

Study of Changes in the Thermodynamic Functions in a Magnetic Field

The authors offered the new formula of the thermodynamic functions in a magnetic field. The authors have also found that thermodynamic functions of internal energy dUand free energy dF changes in the magnetic field.

Low Temperature Heat Capacity of Zn Substituted Cobalt Ferrite Nanosphere:The Relation between Magnetic Properties and Microstructure

Co_((1-x))ZnxFe_(2)O_(4)nanospheres(x=0,0.5,0.8)with a unidirectional cubic spinel structure were prepared by a solvothermal method.By using a range of theoretical and empirical models,the experimental heat capacity values were fitted as a function of temperature over a suitable temperature range to explain the possible relationship between the magnetic properties and microstructure of the nanospheres.As a result,at a low temperature(T<10 K),the parameter Bfswdecreases with increasing Zn concentration,implying that the exchange interaction between A and B sites decreases.At a relatively high temperature(T>50 K),the Debye temperature decreases with increasing Zn concentration,which is due to the weakening of the interatomic bonding force after the addition of non-magnetic materials to the Co Fe_(2)O_(4)spinel ferrite.

Low-temperature Heat Capacities and Thermodynamic Properties of Hydrated Sodium Cupric Arsenate [NaCuAsO_4·1.5H_2O(s)]

Low-temperature heat capacities of the solid compound NaCuAsO4·1.5H2O（s）were measured using a precision automated adiabatic calorimeter over a temperature range of T=78 K to T=390 K.A dehydration process occurred in the temperature range of T=368-374 K.The peak temperature of the dehydration was observed to be TD=（371.828±0.146）K by means of the heat-capacity measurement.The molar enthalpy and entropy of the dehydration were ΔDHm=（18.571±0.142）kJ/mol and ΔDSm=（49.946±0.415）J/（K·mol）,respectively.The experimental values of heat capacities for the solid（Ⅰ）and the solid-liquid mixture（Ⅱ）were respectively fitted to two polynomial equations by the least square method.The smoothed values of the molar heat capacities and the fundamental thermodynamic functions of the sample relative to the standard reference temperature 298.15 K were tabulated at an interval of 5 K.

Crystal Structure and Thermodynamic Study of Ephedrine Hydrochloride C_(10)H_(16)NOCl(s)

The crystal structure of ephedrine hydrochloride was determined by means of X-ray crystallography. The crystal system of the compound is monoclinic, and the space group is P21. Unit cell parameters are a=0.7308（6） nm, b=0.6124（5） nm, and c= 1.2618（11） nm; β=90°, β= 102°, and γ =90°; Z=2. Low-temperature heat capacities of the title compound were measured with an improved precision automated adiabatic calorimeter over a temperature range from 77 K to 396 K. A polynomial equation of the heat capacities as a function of temperature in the temperature region was fitted by the least-squares. Based on the fitted polynomial equation, the smoothed heat capacities and thermodynamic functions of the compound relative to the standard reference temperature 298.15 K were calculated and tabulated at the intervals of 5 K.

Low-temperature Heat Capacities and Thermodynamic Properties of Solid State Coordination Compound Zn(nicotinate)_2·H_2O(s)

A novel compound-monohydrated zinc nicotinate was prepared via room temperature solid phase synthesis and ball grinding.FTIR,chemical and elemental analyses and X-ray powder diffraction technique were applied to characterizing the structure and composition of the complex.Low-temperature heat capacities of the solid coordination compound were measured by a precision automated adiabatic calorimeter over a temperature range from 77 to 400 K.A solid-solid phase transition process occurred in a temperature range of 321―342 K inferred according to the heat capacity curve,and the peak temperature,molar enthalpy and entropy of the phase transition of monohydrated zinc nicotinate were determined to be Ttrs=（340.584±0.829） K,ΔtrsHm=（12.682±0.041） kJ/mol and ΔtrsSm=（37.235±0.101） KJ/mol）.The experimental values of the molar heat capacities in the temperature regions of 77―321 K and 342―400 K were,respectively,fitted to two polynomial equations.In addition,the polynomial fitted values of the molar heat capacities and fundamental thermodynamic functions of the sample relative to the standard reference temperature 298.15 K were calculated and tabulated at intervals of 5 K.

Thermodynamic Assessment of DyCl_3-MCl (M=Na, K, Rb, Cs) Systems

Using the CALPHAD （Calculation of Phase Diagram） technique, the DyCl3-MCl （M = Na, K, Rb, Cs） systems were optimized and calculated. The modified quasi-chemical model in the pair approximation for short-range ordering was used to describe the Gibbs energies of the liquid phase in these systems. From the measured phase diagram data and experimental thermodynamic properties, a series of thermodynamic functions were optimized base on an interactive computer-assisted analysis. The optimized parameters and the experimental data were thermodynamically self-consistent. The optimized results were discussed.

Heat Capacities and Thermodynamic Properties of 3-(2,2-Dichloroethenyl)-2,2-dimethylcyclopropanecarboxylic Acid

The heat capacities of 3-（ 2,2-dichloroethenyl）-2,2-dimethylcyclopropanecarboxylic acid （a racemic mixture, molar ratio of cis-/trans-structure is 35/65） in a temperature range from 78 to 389 K were measured with a precise automatic adiabatic calorimeter. The sample was prepared with a purity of 98.75% （ molar fraction）. A solid-liquid fusion phase transition was observed in the experimental temperature range. The melting point, Tm, enthalpy and en- tropy of fusion, △fusHm, △fusSm, of the acid were determined to be （331.48±0.03 ） K, （16.321±0.031） kJ/mol, and （49.24±0.19） J/（ K·mol）, respectively. The thermodynamic functions of the sample, Ht-H298.15, Sr-S298.15 and Gr-G298.15, were reported at a temperature intervals of 5 K. The thermal decomposition of the sample was studied using thermogravimetric（TG） analytic technique, the thermal decomposition starts at ca. 418 K and ends at ca. 544 K, the maximum decomposition rate was obtained at 510 K. The order of reaction, preexponential factor and activation energy are n =0.23, A =7.3 ×10^7 min^-1 , E =70.64 kJ/mol, respectively.

DISSOCIATION EQUILIBRIA OF CRYOLITE IN NaF-AIF_3

The scheme of dissociation of cryolite in NaF-AlF3 melts was proposed. The constants and heats of dissociation for cryolite were evaluated from experimental data. The mole fractions of each kind of ions at 1298K in NaF-AIF3 melts were calculated based upon this scheme. The thermodynamic mixing function for liquid NaF and solid AIF3, and liquidus data of NaF-AlF3 systems were calculated by using the above evaluated parameters. The results obtained are in good agreement with the experimental data.

Low-temperature heat capacities of crystalline Ho(Gly)_(3)Cl_(3)·3H_(2)O from 78 to 348 K

Heat capacities of the rare-earth complex with glycine [Ho(Gly)3Cl3·3H2O] were measured with a high-precision automatic adiabatic calorimeter over the temperature range from 78 to 348 K.In the experimental temperature range,the heat capacities increased in a smooth and continuous manner and no phase transition or thermal anomaly occurred.Therefore,the sample was stable in the above temperature range.The values of experimental heat capacities were fitted to a polynomial equation with least square method and ...

Thermodynamics of hydrogen absorption and desorption in TC21 alloy

In this paper,it was addressed a hydrogen absorbing and desorbing thermodynamics inα+βtype TC21 titanium alloy with high strength and toughness based on thermodynamic experiments and calculation.The relationship between concentration(C),temperature(T),and pressure(P)of TC21 alloy is shown by P-C-T curves during hydrogen absorption and desorption process,which were measured by multistep hydrogenation/dehydrogenation methods from 625 to 750℃.The P-C-T isotherms at a given temperature were separated into three regions.The partial thermodynamic functions of hydrogen reaction were evaluated by a modified form of Sievert’s law and P-CoTrelation of different regions was expressed by the modified Sievert’s law.The results show that the enthalpy of hydrogen reaction in the first and third region relies on hydrogen content.According to Vant’s Hoff law,enthalpy and entropy of hydrogenation platform in TC21 alloys are-53.58 kJ·mol^(-1)and-127.41 J·K·mol^(-1),respectively.Compared with P-C-T curves of hydrogen absorption,that of hydrogen desorption exists hysteresis.

Low-temperature Heat Capacity and Standard Thermodynamic Functions of D-Galactose and Galactitol

The heat capacities of D-galactose and galactitol were measured on a quantum design physical property measurement system（PPMS） over a temperature range of 1.9-300 K, and the experimental data were fitted to a function of T using a series of theoretical and empirical models in appropriate temperature ranges. The fit results were used to calculate thermodynamic function values, C^θp,m, ^T0S0^θm , and △^T0H^θm from 0 K to 300 K. The standard molar heat capacity, entropy and enthalpy values of D-galactose and galactitol at 298.15 K and 0.1 MPa were determined to be C^θp,m=（227.96±2.28） and（239.50±2.40） J·K^-1·mol^-1, S0^θm = （211.22±2.11） and （230.82±2.30） J·K^-1·mol^-1 and μm = （33.95±0.34） and （36.57±0.37） kJ/mol, respectively.

Thermodynamic performance of Dual-Miller cycle(DMC) with polytropic processes based on power output, thermal efficiency and ecological function

This study reports a new model of an air standard Dual-Miller cycle(DMC) with two polytropic processes and heat transfer loss.The two reversible adiabatic processes which could not be realized in practice are replaced with two polytropic processes in order to more accurately reflect the practical working performance. The heat transfer loss is taken into account. The expressions of power output, thermal efficiency, entropy generation rate(EGR) and ecological function are addressed using finite-time thermodynamic theory. Through numerical calculations, the influences of compression ratio, cut-off ratio and polytropic exponent on the performance are thermodynamically analyzed. The model can be simplified to other cycle models under specific conditions, which means the results have an certain universality and may be helpful in the design of practical heat engines. It is shown that the entropy generation minimization does not always lead to the best system performance.

Comparative Effect of an Addition of a Surface Term to Woods-Saxon Potential on Thermodynamics of a Nucleon

In this study, we reveal the difference between Woods-Saxon(WS) and Generalized Symmetric WoodsSaxon(GSWS) potentials in order to describe the physical properties of a nucleon, by means of solving Schr¨odinger equation for the two potentials. The additional term squeezes the WS potential well, which leads an upward shift in the spectrum, resulting in a more realistic picture. The resulting GSWS potential does not merely accommodate extra quasi bound states, but also has modified bound state spectrum. As an application, we apply the formalism to a real problem,an α particle confined in Bohrium-270 nucleus. The thermodynamic functions Helmholtz energy, entropy, internal energy,specific heat of the system are calculated and compared for both wells. The internal energy and the specific heat capacity increase as a result of upward shift in the spectrum. The shift of the Helmholtz free energy is a direct consequence of the shift of the spectrum. The entropy decreases because of a decrement in the number of available states.

Critical assessment of three kinds of activity coefficients of carbon and related mixing thermodynamic functions of Fe-C binary melts based on atom-molecule coexistence theory

Raoultian activity coefficients γ0c of C in infinitely dilute Fe-C binary melts at temperatures of 1833, 1873, 1923, and 1973 K have been determined from the converted mass action concentrations Nc of C in Fe-C binary melts by the developed AMCT-Ni model based on the atom-molecule coexistence theory （AMCT）. The obtained expression of γ0c by the developed AMCT-Ni model has been evaluated to be accurate based on the reported ones from the literature. Meanwhile, three activity coefficients γc,f%,c, andfH,c of C coupled with activity aR,C or a%,c or aH,c have been obtained by the developed AMCT-Ni model and assessed through comparing with the predicted ones by other models from the literature. The first-order activity interaction coefficients ec, ec, and hcc related to γc f%,c, and fH,c are also determined and assessed in comparison with the reported ones from the literature. Furthermore, the integral molar mixing thermodynamic functions such as AmixHm,Fe-C, △mix-Sm,Fe-C, and △mixGm,Fe-C of Fe-C binary melts over a temperature range from 1833 to 1973 K have been determined and evaluated to be valid based on the determined ones from the literature.

LOW-TEMPERATURE HEAT CAPACITY AND THERMODYNAMIC FUNCTIONS OF 2-CHLORO-6-(TRICHLOROMETHYL)PYRIDINE

The heat capacity of 2- chloro- 6- (trichloromethyl)pyridine has heen measured with anadiabatic calorimeter in the range from 13 to 316K. There is no indication of any phasetransition or thermal anomaly in this temperature region for the present compound. Theresults have been compared with those reported in [1] in the overlapping temperaturerange. The experimental heat capacity data have been fitted to a smoothed curve by the aidof the effective frequency distribution method, and the heat capacities below 13K have beenobtained by extrapolating the fitting curve down to 0K. The standard molar thermodynamicfunctions between 0 and 400 K have been derived by combining the present heat capacitymeasurements with the previous ones. The values of C_p^o (T), S^o(T) - S^o(0), [H^o(T) -H^o(0)]/T, and - [G^o(T) - H^o(0)]/T at T = 298.15 K are 189.35, 244.60, 112 .45 and 132.15J·K^(-1)·mol^(-1), respectively.

Low-Temperature Heat Capacities and Thermodynamic Properties of Octahydrated Barium Dihydroxide, Ba（OH）2·8H2O（s）

Low-temperature heat capacities of octahydrated barium dihydroxide, Ba（OH）2·8H2O（s）, were measured by a precision automated adiabatic calorimeter in the temperature range from T=78 to 370 K. An obvious endothermic process took place in the temperature range of 345-356 K. The peak in the heat capacity curve was correspondent to the sum of both the fusion and the first thermal decomposition or dehydration. The experimental molar heat capacifies in the temperature ranges of 78-345 K and 356-369 K were fitted to two polynomials. The peak temperature, molar enthalpy and entropy of the phase change have been determined to be （355.007±0.076） K, （73.506±0.011） kJ·ol^-1 and （207.140±0.074） J·K^-1·mol^-1, respectively, by three series of repeated heat capacity measurements in the temperature region of 298-370 K. The thermodynamic functions, （Hr-H298.15 k ）and （Sr-S298.15k）, of the compound have been calculated by the numerical integral of the two heat-eapacity polynomials. In addition, DSC and TG-DTG techniques were used for the further study of thermal behavior of the compound. The latent heat of the phase change became into a value larger than that of the normal compound because the melfing process of the compound must be accompanied by the thermal decomposition or dehydration of 71-120.