Thermodynamic Criteria Research Articles

Revisiting Stability Criteria in Ball‐Milled High‐Entropy Alloys: Do Hume–Rothery and Thermodynamic Rules Equally Apply?

Stability descriptors for the formation of solid solutions can be divided into two categories: inspired by Hume–Rothery rules (HRR) and derived from thermodynamic approaches. Herein, HRRs are extended from binary to high‐entropy alloys (HEAs) focusing on compositions prepared by ball milling. Parameters describing stability criteria are interrelated and implicitly account for the microstrains’ storage energy, more determinant than entropy increase in stabilization of HEAs and more effective in bcc structures than close‐packed ones (fcc and hcp). An effective temperature, Teff, is defined as the ratio between increase in metallic bonding energy of solid solutions with respect to segregated pure constituents and configurational entropy. This versatile parameter is used as a threshold for stabilization of HEAs at equilibrium and out of equilibrium. When Teff is below room temperature, HEA would be stable at equilibrium. When Teff is below melting temperature, HEA would be obtained by rapid quenching. Limitations related to electronegativity differences remain valid in mechanically alloyed solid solutions. However, ball milling broadens the allowed differences in atomic size to form HEA. Moreover, thermodynamic criteria can be surpassed in these systems, allowing the formation of single‐phase solid solutions beyond the compositional range predicted by those criteria.

Designing an Efficient Singlet Fission Material with B-N Substitution in Pyrene: A Model Exact Study.

The electronic structure of boron (B)-nitrogen (N)-substituted pyrene molecules is the center of attraction in designing an efficient intermolecular singlet fission (x-SF) material. Thermodynamic energy criteria required for x-SF are obtained by captodative substitution with B and N in pristine pyrene to increase the lowest singlet-triplet energy gap. We computed low-lying excited states of BN-embedded pyrene molecules by exactly solving the Pariser-Parr-Pople (PPP) model Hamiltonian and compared these results with the TDDFT and EOM-CCSD values. Exact diagonalization of the PPP model Hamiltonian suggests that pristine pyrene, which is endothermic for x-SF, becomes isoergic with certain (BN)2 substitution. The low-lying excited state energies calculated using the model Hamiltonian match very well with experimental values over EOM-CCSD and TDDFT. Moreover, the low value of the spin-orbit coupling constant calculated for BN-substituted pyrene strengthens its applicability as an SF material.

Enhanced heat transfer technology for solar air heaters

Abstract Solar air heaters (SAHs) exhibited low thermal performance due to air thermal properties. To optimize the convective heat transfer between air and the absorber plate, researchers designed plenty of enhanced structures based on experimental and numerical analysis. This article reviewed the improvement methods of SAHs and emphasized the crucial role of thermodynamic models and evaluation criteria. Current research focuses on improving the convective heat transfer coefficient. In terms of enhanced structures, using flow deflectors, flow disruptors, corrugated absorber plates, and porous media improved collection efficiency. This result showed these enhanced structures could effectively further the performance of SAHs and provide new ways for sustainable energy utilization.

The structural, electronic, optical and photocatalytic properties of two-dimensional ZrIN monolayer: A first-principles study

This study presents a comprehensive investigation of the structural stability, electronic and optical properties of two-dimensional ZrIN using first-principles calculations. The stability of two-dimensional (2D) ZrIN was confirmed through investigation of thermodynamic, mechanical, dynamic and thermal criteria. The ZrIN monolayer is predicted to be an indirect bandgap semiconductor with a gap value of 2.28 eV. Notably, it exhibits significant transmittance in the violet region of the visible spectrum. Furthermore, the photocatalytic attributes of 2D ZrIN are examined under varying pH conditions (0 and 7) by assessing band edge positions. The efficacy of ZrIN in electrocatalytic water decomposition is confirmed through simulations of the oxygen evolution reaction (OER) and hydrogen evolution reaction (HER). The influence of mechanical strain on the band structure and photocatalytic performance is also investigated. It is observed that compressive strain restricts the photocatalytic operational range of the ZrIN monolayer, while tensile strain broadens this range. Nevertheless, excessive tensile strain leads to a reduction in the effective catalytic operational region. These results offer valuable insights into the potential applications of 2D ZrIN in optoelectronics and catalysis.

Basics of the reaction kinetics on metallic alloys.

Kinetics of heterogeneous catalytic reactions are often complicated by various factors, and from the perspective of statistical physics the development of the corresponding models is frequently challenging especially in the case of practically important alloy catalysts. To extend the basics in this area, I use a generic kinetic model of N_{2} formation inthe NO reaction with such species as CO or H_{2}. The focus is onthe reaction on the surface of a bimetallic alloy with low integral fraction of one of the metals so that the alloy is formed only at the surface. The main goal is to illustrate the specifics of the reaction kinetics and to clarify the accuracy of various approximations which are often inevitable for the analysis of such systems. The key results are as follows. (i) In the baseline one-metal case with the Langmuir-type equations, the model predicts the existence of the optimal adsorbate binding energy corresponding to the maximal reaction rate. (ii) With suitable substitution of the symbols, the equations employed for a uniform surface [item (i)] can be used for the mean-field description of reaction on the surface of a random alloy. In particular, the maximum in the dependence of the reaction rate on the binding energy is converted to the maximum with respect to the alloy composition. (iii) The reaction kinetics on the random-alloy surface have been described exactly. The corresponding maximum in the reaction rate is lower and somewhat smeared compared to that predicted in the mean-field approximation for an alloy or for the optimal monometallic catalyst. (iv) The reaction kinetics have been scrutinized also in the case of two-dimensional (2D) segregation of metal atoms at the surface in the limits of slow and rapid adsorbate diffusion between the spots. The kinetics are shown to be qualitatively different in these limits and also compared to the random-alloy case. (v) The thermodynamic criteria for 2D segregation of metal atoms at the surface have been derived as well.

Self-consistent sharp interface theory of active condensate dynamics

Biomolecular condensates help organize the cell cytoplasm and nucleoplasm into spatial compartments with different chemical compositions. A key feature of such compositional patterning is the local enrichment of enzymatically active biomolecules which, after transient binding via molecular interactions, catalyze reactions among their substrates. Thereby, biomolecular condensates provide a spatial template for nonuniform concentration profiles of substrates. In turn, the concentration profiles of substrates, and their molecular interactions with enzymes, drive enzyme fluxes which can enable novel nonequilibrium dynamics. To analyze this generic class of systems, with a current focus on self-propelled droplet motion, we here develop a self-consistent sharp interface theory. In our theory, we diverge from the usual bottom-up approach, which involves calculating the dynamics of concentration profiles based on a given chemical potential gradient. Instead, reminiscent of control theory, we take the reverse approach by deriving the chemical potential profile and enzyme fluxes required to maintain a desired condensate form and dynamics. The chemical potential profile and currents of enzymes come with a corresponding power dissipation rate, which allows us to derive a thermodynamic consistency criterion for the passive part of the system (here, reciprocal enzyme-enzyme interactions). As a first-use case of our theory, we study the role of reciprocal interactions, where the transport of substrates due to reactions and diffusion is, in part, compensated by redistribution due to molecular interactions. More generally, our theory applies to mass-conserved active matter systems with moving phase boundaries. Published by the American Physical Society 2024

A new equilibrium temperature inflow profile for modelling the non-isothermal atmospheric boundary layer in CFD simulation

The atmospheric boundary layer (ABL) flow in urban morphologies, ranging from micro-scale to local-scale, will become non-isothermal due to the combined effects of solar radiation, wall heat transfer, the urban heat island, and anthropogenic heat, resulting in a mutually coupled urban thermal and wind environment. An appropriate temperature inflow profile is the key prerequisite for Computational Fluid Dynamics (CFD) simulations of the non-isothermal ABL flow and the urban thermal and wind environment, as it must coincide with actual thermal characteristics while being compatible with CFD. Based on the equilibrium ABL model, a new equilibrium temperature inflow profile compatible with the energy equation, the standard gradient diffusion hypothesis, and the turbulence model is derived, which is proportional to the turbulent kinetic energy inflow profile, with the ratio further determined by the wall heat flux, demonstrating that turbulent thermal diffusion is strongly related to turbulent characteristics and atmospheric stability. To address the scaled effect, its full expression is provided based on thermodynamic similarity criteria. Using a numerical model of empty domain based on the SST k-ω model, the horizontal homogeneity of the equilibrium thermal and wind field modeled by the new set of inflow profiles is verified. Taking the flow around a single square building model as an example, its applicability in simulating the urban thermal and wind environment around buildings has been numerically validated, where the comparison of numerical and test results reveals tolerable errors overall.

Effect of sputtering power and substrate bias on microstructure, mechanical properties and corrosion behavior of CoCrFeMnNi high entropy alloy thin films deposited by magnetron sputtering method

The CoCrFeMnNi high entropy alloy thin films with crystalline (solid solution) structure or amorphous state were fabricated by magnetron sputtering process at different target powers and different substrate bias. Effects of the target power and substrate bias on the characteristics of the CoCrFeMnNi thin films such as microstructures, morphology and surface topography, as well as mechanical properties and corrosion behavior were studied. Phase prediction was calculated by using thermodynamic and kinetic criteria under various deposition conditions. The enthalpy, entropy, δ and Ω parameters, and electronegativity differences influenced the solid solution stability of thin films. These parameters led to the formation of solid solutions with crystalline or amorphous structures under specific limits, which corresponded to the practical XRD and TEM analysis results. Using a substrate bias in the deposition of CoCrFeMnNi thin film changed the amorphous structure to a crystalline (solid solution (BCC + FCC)) at higher target powers (200 and 300 W). On the other hand, the film structure was entirely amorphous at all sputtering target powers without the substrate bias. The mechanical properties, such as hardness, Young's modulus, film strength, and fracture toughness of CoCrFeMnNi thin film, can be enhanced by using the substrate bias and increasing the sputtering power. The potentiodynamic polarization test in 3.5 wt% NaCl aqueous solution indicated that the deposition of CoCrFeMnNi thin films at different sputtering powers and without substrate bias could increase the corrosion resistance of 304 stainless steel substrate. Using the substrate bias of −100 V in the fabrication of CoCrFeMnNi thin film decreased the corrosion current density and increased its polarization resistance.

Nb2C and Nb2CO2 MXenes as Anodes in Li-Ion Batteries: A Comparative Study by First-Principles Calculations.

The new generation of Li-ion batteries is based on integrating 2D materials into the electrodes to increase the energy density while reducing the charging time and size. The two-dimensional transition metal carbide or nitride (MXene) materials offer ideal electronic properties, such as metallic behavior, low energy barriers for Li-ion diffusion, and structural stability. This study focuses on Nb2C and Nb2CO2 MXenes, which have shown promising Li-storage capacity, especially the oxidized phase. By using density functional theory (DFT) and thermodynamic criteria, we studied the Li intercalation process in both MXenes. The results show that the Li intercalation process in the oxidized phase is more stable. Also, the Li diffusion barriers are 35 and 250 meV for the bare and oxidized phase, due to the strong interaction between Li ions and O functional groups. Nb2C and Nb2CO2 MXenes deliver a maximum gravimetric theoretical capacity of 275 and 233.26 mA h/g, respectively, with a stable performance.

Ab initio investigation of electronic structure and magnetic transformation during the bcc to hcp transition in Fe induced by pressure

The pressure-induced structural transition from a body-centered cubic (bcc) to a hexagonal close-packed (hcp) crystal in Fe is studied through ab initio electronic structure calculations, combining with the thermodynamic and kinetic phase-transition methods. According to the energy-volume relationship and thermodynamic criterion, the reasonable phase transition pressure is calculated to be about 13.88 GPa. The SSNEB method is employed to examine kinetic structural and barrier changes along bcc-hcp transition under various pressures. The transformation path involves the deformation of (110)bcc into the tightly packed (0001)hcp, accompanied by the relative slip of (110)bcc along the [1̅10]bcc direction, leading to the formation of the hcp structure. Our results indicate a reduction in the transition barrier of bcc-hcp with increasing pressure. Under the thermodynamic phase transition pressure, the bcc-hcp phase transition barrier is still as high as 140 meV, implying that pure hydrostatic pressure is not a sufficient condition to drive the phase transition. In addition, different from the continuous change of volume, the magnetism of the structure undergoes a magnetic mutation at the transition state, and the phase transition process involves complex magnetic transitions.

Hydrodynamics and instabilities of relativistic superfluids at finite superflow

We study the linear response of relativistic superfluids with a non-zero superfluid velocity. For sufficiently large superflow, an instability develops via the crossing of a pole of the retarded Green’s functions to the upper half complex frequency plane. We show that this is caused by a local thermodynamic instability, i.e. when an eigenvalue of the static susceptibility matrix (the second derivatives of the free energy) diverges and changes sign. The onset of the instability occurs when ∂ζ(nsζ) = 0, with ζ the norm of the superfluid velocity and ns the superfluid density. The Landau instability for non-relativistic superfluids such as Helium 4 also coincides with the non-relativistic version of this criterion. We then turn to gauge/gravity duality and show that this thermodynamic instability criterion applies equally well to strongly-coupled superfluids. In passing, we compute holographically a number of transport coefficients parametrizing deviations out-of-equilibrium in the hydrodynamic regime and demonstrate that the gapless quasinormal modes of the dual planar black hole match those predicted by superfluid hydrodynamics.

Swirl flow stability: thermodynamic analysis and experiments

The current paper presents a theoretical analysis of swirl flow stability, both inside a tube (vortex tube) and in a free annular swirl flow. The starting concept is the study of the evolution of velocity and temperature fluctuations. Methods of non-equilibrium thermodynamics are used to describe the magnitude of fluctuations and their properties. The important role of the total enthalpy follows from a variational analysis. Moreover, the thermodynamic criterion of the stability is formulated using the total enthalpy, and compared with experiments, numerical results and classical Rayleigh theory support its applicability. It was shown that the solid body vortex is at the margin of stability, which is experimentally observed. Analogously, the potential vortex is by the thermodynamic criterion stable; however, by the Rayleigh criteria it is on the onset of stability. The classical Taylor experiment of flow between two rotating cylinders is analysed from the point of view of this criterion. These results are underlined by swirl tube experiments at the Institute of Aerospace Thermodynamics at Stuttgart University and the annular nozzle experiments performed in the Institute of Thermomechanics CAS in Prague. Both independent experiments confirm the transformation of the initial annular vortex into a stable potential-type vortex. The results of this theory can also be used to explain the exceptional stability of tropical cyclones.

The propagation behavior of reaction wave for Ni/Al clad particle composites under shock loading.

Prior studies indicate that the reaction wave can propagate from the impact surface, but the possibility and the influencing factors of the reaction wave formation are still unclear. This work investigates the propagation behavior of the shock-induced reaction wave for Ni/Al clad particle composites with varying stoichiometry (from 0.5 to 0.75 of the Ni mole fraction) through molecular dynamics simulations. It is found that the solid-state reaction processes with or without wave propagation strongly depend on the conjunction of stoichiometry and shock intensity. Within the cases of wave propagation, the calculated propagation velocity (in the range of 135-170m/s) increases linearly or exponentially with the Ni mole fraction. Furthermore, the thermodynamic criteria for the reaction wave formation, including Al melting at the collision surface and higher temperature gradient, are established by analysis of the shock-induced high-entropy layer. In addition, microstructural characterization reveals the intrinsic mechanisms of the propagation of the reaction wave and the formation of additional reaction wave, namely, the dissolution of Ni into Al and the coalescence of reaction zones. Apart from the propagation behavior, the initial stoichiometry influences the crystallization-dissolution of B2-NiAl during reaction processes, notably through an exponential growth relationship between maximum crystallinity and the Ni mole fraction. These findings may provide a physical basis for improving traditional reaction rate models to break through phenomenological understanding.

Ba2MgXO6 (X = S, Se), Chalcogenide‐Based Double Perovskite Materials for Green Optoelectronics and Thermoelectric Applications

Chalcogenide‐based double perovskite materials have recently attracted attention of researchers because of their excellent properties and eco‐friendly nature. These compounds have proven to comprise better oxidation resistance, high‐temperature stability, and lower processing cost. In this report, the first‐principles study on chalcogenides double perovskites Ba2MgXO6 (X = S, Se) is described. It is shown that these perovskites can be synthesized, as they satisfy the structural, dynamical, and thermodynamical stability criteria. It is revealed that these double perovskites are inherently semiconductors in nature with low bandgap values, 0.33 eV for Ba2MgSO6 and 0.66 eV for Ba2MgSeO6 along Γ symmetry point. The absorption coefficient ≈105 cm−1 and the reflectivity below 12% in visible region are calculated. Therefore, the Ba2MgXO6 for solar cell applications is recommended. Also, on the basis of calculated larger values of figure of merit, these perovskites are proposed for thermoelectric applications at high temperatures.

Origin of shear induced ‘catching bonds’ on half Heusler thermoelectric compounds XFeSb (X = Nb, Ta) and SnNiY (Y = Ti, Zr, Hf)

Half Heusler materials exhibit excellent thermoelectric and mechanical properties, rendering them potential candidates for advanced thermoelectric devices. Currently, the developments on interrelated devices are impeded by their inherent brittleness and limited ductility. Nevertheless, it exists the potential ductility on half Heusler materials with face-centered cubic sub-lattices through the expectation of the occurrence of shear-induced ‘catching bonds’ which can result in excellent ductility on other face-centered cubic materials. This work focuses on half Heusler thermoelectric materials XFeSb (X = Nb, Ta) and SnNiY (Y = Ti, Zr, Hf), the shear deformation failure processes are deeply investigated through the first principle calculations. Shear-induced ‘catching bonds’ are found on XFeSb (X = Nb, Ta) along the (111)/<-1-12> slip system, which releases the internal stress and exactly resulting in the potential ductility. According to the thermodynamic criterion based on generalized stacking fault energy, the essence of shear-induced ‘catching bonds’ are interpreted as the (111)/<-110> slips formed by several 1/3(111)/<-1-12> partial dislocations motions. During the (111)/<-1-12> shear on SnNiY (Y = Ti, Zr, Hf), the structural integrity is maintained without inducing ‘catching bonds’. Different deformation processes occurring in the identical crystal structure are elucidated through the energy explanation, revealing that shear-induced ‘catching bonds’ originate from the crystal plane cleavage on the (111) plane. The present works offer significant advantages for the assessment and comprehension of shear-induced ‘catching bonds’ in other materials and facilitate the development of XFeSb (X = Nb, Ta)-based thermoelectric devices with excellent ductility.

A hybrid solar-driven vacuum thermionic generator and looped multi-stage thermoacoustically driven cryocooler system: Exergy- and emergy-based analysis and optimization

Significant high-quality heat is wasted in the vacuum thermionic generator (VTIG), which can be efficiently utilized as a prime mover of a bottoming system for cogeneration applications. For this purpose, a new environmental-friendly hybrid system composed of a heliostat solar field, VTIG, and looped multi-stage thermoacoustically driven cryocooler (LMTC) is established, in which the high-temperature heat source of the solar receiver runs the VTIG to generate power, and the LMTC recovers the waste heat of the VTIG to produce a cooling load. Thermodynamic, economic, and environmental analyses of the system are carried out based on exergy and emergy concepts. Moreover, a parametric study is performed to assess the effect of design parameters on the system's thermodynamic, economic, and environmental criteria. Finally, the multi-criteria salp swarm optimization algorithm and decision-making procedures are conducted to improve the exergetic performance and decrease the system's cost and monetary emergy rates along with the environmental impact and ecological emergy rate. Findings depict that at the reliable, optimal operation of the system, the exergetic efficiency can reach 29.36% with a maximum power of 17.2 MW and cooling load of 0.260 MW. The system's cost and monetary emergy rate can be reduced to 0.059 $/s and 5.94 × 1010 seJ/s, with 10.6% and 10% reductions, respectively. Moreover, the environmental impact and ecological emergy rates decline by 6% and 7.4%, respectively. The theoretical findings may offer guidance for the optimum designing and practical running of such a solar solid-state cogeneration system.

A novel TLFD-GA algorithm for multi-objectives optimization of ORC power plants with the effect of pressure drop considered

This research introduces a novel TLFD-GA algorithm for the three-level criteria optimization of organic Rankine cycle (ORC) power plants. It replaces the non-dominated sorting of NSGA-II with three-level fuzzy decision to simultaneously optimize environmental, thermodynamic, and techno-economic criteria. The algorithm provides direct optimization results without needing additional decision-making methods. Furthermore, the impact of pressure drop in plate heat exchangers is investigated, revealing a proportional relationship between pressure drop and the increment of evaporation pressure. A parametric study on 24 basic and recuperative trans-critical geothermal ORC systems indicates that compensating for pressure drop leads to a 5% decrease in thermodynamic performance, a 20% decrease in techno-economic performance, and a 20–60% increase in heat transfer area per net output power. After TLFD-GA optimization, the saving to investment ratio improves by an average of 4.5% across scenarios. R1270 stands out with a remarkable ratio of 3.13 and 4.32 in medium and high-temperature geothermal reservoirs. Moreover, the proposed TLFD-GA optimization algorithm has demonstrated its superiority in terms of superb convergence and stability when compared to NSGA-II, which suggests its prospective application in the low-carbon and green energy fields.

Thermodynamic Stability Is a Poor Indicator of Cocrystallization in Models of Organic Molecules.

Cocrystallizing a given molecule with another can be useful for adjusting the physical properties of molecules in the solid state. However, most combinations of molecules do not readily cocrystallize but form either one-component crystals or amorphous solids. Computational methods of crystal structure prediction can, in principle, identify the thermodynamically stable cocrystal and thus predict if molecules will cocrystallize or not. However, the pronounced polymorphism and tendency of many organic molecules to form disordered solids suggest that kinetic factors can play an important role in cocrystallization. The question remains: if a binary system of molecules has a thermodynamically stable cocrystal, will it indeed cocrystallize? To address this question, we simulate the crystallization of more than 2600 distinct pairs of chiral model molecules of similar size in 2D and calculate accurate crystal energy landscapes for all of them. Our analysis shows that thermodynamic criteria alone are unreliable in the prediction of cocrystallization. While the vast majority of cocrystals that form in our simulations are thermodynamically favorable, most coformer systems that have a thermodynamically stable cocrystal do not cocrystallize. We furthermore show that cocrystallization rates increase 3-fold when coformers are used that do not form well-ordered single-component crystals. Our results suggest that kinetic factors of cocrystallization are decisive in many cases.

Development of Thermodynamic Criteria for Determining the Composition of Duplex Stainless Steels with High Corrosion Resistance.

One of the most popular methods for ranking duplex stainless steels (DSSs) and predicting their corrosion properties is the calculation of the pitting resistance equivalent number (PREN). However, since DSSs are two-phase materials with a significant fraction of secondary phases and precipitates, the application of the PREN can be highly limited. This article attempted to use a new approach to describe the corrosion resistance of these steels. The corrosion resistance of two DSSs of the same class was investigated. Under identical solution heat treatments in the temperature range of 1050-1200 °C, the crevice corrosion resistance of one steel increased, while that of the other decreased. It was demonstrated that the amounts of austenite and ferrite changed similarly in these steels, and the different corrosion resistances were associated with the behaviors of secondary phases: niobium carbonitride and chromium nitride. SEM-EDS analysis was conducted to analyze the redistribution of elements between phases in both cases, showing good agreement with the thermodynamic modeling results. The PREN was calculated for each phase depending on the treatment temperature, and a method for calculating the effective PREN (PRENeff), accounting for phase balance and secondary phases, was proposed. It was shown that this indicator described corrosion properties better than the classical PREN calculated for the average steel composition. This study demonstrated how the calculation of critical temperatures (the temperature of equal amounts of ferrite and austenite, the temperature of the beginning of chromium nitride formation, and the temperature of the beginning of σ-phase formation) could describe the corrosion resistance of DSSs. Maximum possible deviations from these temperatures were defined, allowing the attainment of the required corrosion properties for the steels. Based on the conducted research, an approach for selecting new compositions of DSSs was proposed.

Recognition of supercritical CO2 liquid-like and gas-like molecules based on deep neural network

So far, it is still controversial about how to divide the liquid-like and gas-like states boundary and Widom delta, since the deviation of boundaries determined by different thermodynamic criteria increases significantly when away from the critical point. For this reason, a superior method that does not rely on thermodynamic criteria to define the boundary line between liquid-like and gas-like states needs to be proposed urgently and the recent extensive use of deep neural networks in molecular dynamics simulation provides a feasible choice. The present work attempts to determine a novel phase state boundary and Widom delta of supercritical CO2 from extracting the microstructure features of subcritical vapor and liquid states in equilibrium by deep neural network coupled with molecular dynamics simulation. In addition, visualization of simulated systems containing distinct liquid-like molecule ratio πLL of supercritical CO2 is also presented as well as the radial distribution function at different states. The results show that the novel boundary is located in the middle of the Widom lines constructed by multiple thermodynamic criteria. The lower boundary T- of the novel Widom delta agrees well with the theoretical boundary constructed by pseudo-boiling theory when it is close to the critical point but starts to deviate when it is far away from the critical point, while the upper boundary T+ of that is opposite. More importantly, the novel boundary and Widom delta constructed have no pressure upper limit compared to those constructed by thermodynamic criteria, only depending on πLL, which means that the novel boundary and Widom delta can extend to the supercritical deep region. Further, the visualization and radial distribution function of simulated systems of supercritical CO2 at different states provide the persistence of a liquid-like and a gas-like transition. The work conducted here can present novel microscopic insight into supercritical phase transition and provide another available alternative to define the Widom line.