Method for high-precision quantification of soil phase change critical temperature based on nucleation and pre-melting principles

Abstract

The invention discloses a method for high-precision quantification of soil phase change critical temperature based on nucleation and pre-melting principles. The method comprises the following steps: step 1, determining a phase change Gibbs free energy equation and an ice water chemical potential equation; 2, determining a Gibbs free energy equation of the freezing process; 3, determining a freezing nucleation temperature equation; 4, determining a pre-melting process Gibbs free energy equation; and 5, determining a pre-melting initial temperature equation. According to the classic nucleation principle and the interface pre-melting principle, the method capable of quantifying the soil temperature with high precision is determined, the freezing nucleation temperature and the pre-melting starting temperature are determined, and the application range is wide. According to the quantitative method, the actual condition of soil freeze-thaw cycle is considered, each parameter is clear in physical significance and easy to obtain, and theoretical support can be provided for related research of unsaturated saline soil freeze-thaw phase change.

Description

Technical Field

[0001] The invention relates to a method for quantifying the critical temperature of soil phase change, and in particular to a method for quantifying the critical temperature of soil phase change with high precision based on the nucleation and pre-melting principles. Background Art

[0002] With the advancement of global warming and strategies such as the development of Arctic shipping routes, the number of projects in cold regions is increasing, and a large number of roads, bridges, houses and infrastructure construction are being carried out in frozen soil areas. However, due to its special freezing and thawing characteristics, frozen soil often causes engineering diseases such as frost heave and thaw settlement, which seriously threaten the stability of infrastructure. During the freezing and thawing process, the redistribution of water, solutes and heat in the soil will change the soil structure. In saline soil areas, the crystallization and dissolution effects of salt will further aggravate the problems of frost heave and salt expansion, leading to uneven settlement and instability of the foundation. The melting of frozen soil will also release a large amount of greenhouse gases stored in the soil, thereby exacerbating global warming and forming a positive feedback effect of climate change. At the same time, the dynamic process of freezing and thawing changes the regional hydrological cycle, affecting the temporal and spatial distribution of water resources and the function of the ecosystem.

[0003] During the freezing and thawing process, the phase transition temperature is a key characteristic quantity that describes the effect of the solid-liquid phase transition of water molecules in the soil on the supercooling phenomenon and hysteresis mechanism. Existing studies have mostly focused on the macroscopic characteristics and environmental responses of frozen soils, lacking in-depth discussions on microscopic mechanisms such as nucleation behavior during freezing, crystal growth, and water transformation during melting. Currently, the theoretical methods commonly used to predict the phase transition characteristics of saline soil during freezing and thawing include: classical nucleation theory, pre-melting theory, soil water potential theory, and thermodynamic Gibbs free energy theory. With the increasing requirements for numerical simulation accuracy in engineering applications, it is urgent to propose a physical model that can accurately quantify the critical temperature of phase transition of saline soil.

[0004] The present invention aims to accurately quantify the critical temperature of phase change of saline soil. Specifically, the present invention will determine a method that can quantify the critical temperature of soil phase change with high precision based on the principle of heterogeneous nucleation and the principle of interface pre-melting. The present invention will help to reveal the freezing mechanism of saline soil and provide a theoretical basis for the numerical simulation of saline soil engineering in cold regions. Summary of the invention

[0005] In order to solve the above problems, the present invention discloses a method for high-precision quantification of the critical temperature of soil phase change based on the nucleation and pre-melting principles. Compared with other measurement methods, the method of the present invention is simple to calculate, and the physical meaning of each parameter is clear and easy to obtain.

[0006] The objective of the present invention is achieved through the following technical solutions:

[0007] A method for quantifying the critical temperature of soil phase change with high precision based on the nucleation and pre-melting principle comprises the following steps:

[0008] Step 1, determine the phase transition Gibbs free energy equation and ice-water chemical potential equation;

[0009] The step 1 comprises the following sub-steps:

[0010] a. During the freeze-thaw cycle, when the system changes state, the thermodynamic quantity Gibbs free energy will change, which can be used to determine whether the system has undergone a phase change. The total Gibbs free energy is expressed as the sum of the changes in the energy of each component.

[0011] ΔG total =ΔG 1 +ΔG 2 +...+ΔG i +...+ΔG n (1)

[0012] In the formula, ΔG total is the total Gibbs free energy change, ΔG i ,i=1,...,n is the change of energy of each component.

[0013] b. At the same temperature and pressure, the thermodynamic driving force for spontaneous phase change is represented by the difference Δμ between the chemical potential of water molecules (liquid phase) and the chemical potential of ice molecules (solid phase):

[0014] Δμ=μ w (p w ,a w ,T)-μ i (p i ,T) (2)

[0015] In the formula, μ w (p w ,a w ,T),μ i (p i , T) represent the chemical potentials in deionized water and ice crystals, respectively.

[0016] c. Determine the chemical potential equation. Set the freezing point of deionized water as the analytical standard state [T 0 (273.13K), P 0 (101.013 kPa)], the water chemical potential can be expressed as:

[0017]

[0018] Where V w is the molar volume of liquid water, is the chemical potential of deionized water in standard state.

[0019] d. Ice chemical potential is expressed as:

[0020]

[0021] Where V i is the molar volume of the ice nucleus, The chemical potentials of ice crystals and water in the standard state are equal.

[0022] e. In the phase change process of freeze-thaw cycle, the melting latent heat affects the energy exchange, temperature change of frozen soil, mechanical behavior of soil and water migration. The melting latent heat is introduced to determine the phase change temperature equation:

[0023] ΔH f =T 0 (S i -S w ) (5)

[0024] In the formula, ΔH f is the latent heat of phase change of water molecules. Under standard conditions, the melting latent heat of ice is about 6.01 kJ / mol; S i , S w are the entropies of ice and liquid water, respectively. The molecular freedom of liquid substances is greater than that of solid substances. S i -S w Is a negative value.

[0025] Step 2, determine the Gibbs free energy equation of the freezing process;

[0026] The step 2 includes the following sub-steps:

[0027] a. Considering the influencing factors of soil storage environment such as solute concentration and capillary effect of soil pores, the heterogeneous nucleation theory is modified. In the initial stage of nucleation (when the amount of ice formed is very small), the changes in gravity field and external pressure can be ignored. During the nucleation process, the change in the total free energy of the system ΔG total-1 It is divided into the following five parts: surface energy ΔG surface , volume free energy ΔG volume , Coulomb field energy ΔG electric , solute concentration contribution to energy ΔG solute , and the adsorption effect of the pores ΔG capillary .

[0028] ΔG total-1 =ΔG surface +ΔG volume +ΔG electric +ΔG solute +ΔG capillary (6)

[0029] b. Determine the surface energy equation. During the nucleation process, a liquid-solid interface is formed, and the surface energy barrier must be overcome to achieve freezing.

[0030] ΔG surface =4πr 2 σ iw (7}

[0031] Where r is the radius of the crystal core, σ iw is the surface tension of the ice-water interface.

[0032] c. Calculate the surface tension of ice-water interface using Hardy model:

[0033] σ iw [J.m -2 ]=2.91·10 -2 +(TT 0 )·0.18·10 -3 (8)

[0034] Where, T 0 is 0 degrees Celsius and T is the actual temperature.

[0035] d. Determine the volume free energy equation. The volume free energy ΔG during the transformation of water into ice volume Changes in freezing latent heat ΔG v-1 and nucleation ΔG v-2 The free energy change caused. When a crystal nucleus forms in liquid water, the order of the local system increases with an increase in free energy (transition state); after stable nucleation, the ice crystal growth releases free energy. During the freezing process, heat is released when water changes from liquid to solid:

[0036]

[0037] In the formula, ρ i is the density of ice; r is the radius of the crystal core; L f is the latent heat of freezing.

[0038] e. Considering that the free energy of the crystal nucleus molecules will change after the solution molecules generate the crystal nucleus, the relationship between the solution partial pressure and the ice pressure is introduced. For the solution-ice crystal system, using Raoult's law, we get:

[0039]

[0040] In the formula, e li is the stable vapor pressure ratio of solution and ice crystals at the same temperature and pressure; a w is water activity; e i It indicates the stable vapor pressure ratio of water and ice crystals at the same temperature and pressure.

[0041] f. Calculate the stable vapor pressure ratio e i :

[0042]

[0043] g. Change in free energy caused by nucleation:

[0044]

[0045] In the formula, k B is the Boltzmann constant, k B ≈1.380649×10 -23 J / K;v i is the average lattice volume occupied by ice molecules, calculated using the Zobrist equation: Among them, T r =(TT 0 ) / T 0 , N A is Avogadro's constant, r is the nucleus radius, ρ i is the density of ice, which can be calculated by the HRPruppacher & J.D.Klett equation i =0.9167g / cm 3 , the molecular mass of water is M w =18.015 g / mol.

[0046] h. Determine the volume free energy equation.

[0047]

[0048] i. Determine the free energy equation caused by the Coulomb field. In soil pore solutions containing solutes or other charged substances, charged molecules or ions will change the molecular arrangement at the interface, causing energy changes in the nucleation process and affecting the nucleation temperature. Assume that the particles are point charges, the amount of charge in the system is the same, and only consider the interaction between a single particle and its own electric field. The free energy change caused by the Coulomb field energy is ΔG electric It can be calculated as follows:

[0049]

[0050] Where q is the charge of the ion, q = 1.602 × 10 -19 C;∈ is the dielectric constant; r is the crystal nucleus radius.

[0051] j. Determine the solution free energy equation. Solutes (such as salts, minerals, or other chemicals) dissolved in water interfere with the formation of hydrogen bonds between water molecules, reducing the free energy of freezing, thereby changing the freezing characteristics of water and lowering the freezing point of water. Therefore, the change in solution free energy during nucleation, ΔG solute It can be expressed as:

[0052]

[0053] k. In the early stage of freezing, supercooling is usually closely related to capillary water in the soil macropores, which results in the critical nucleation radius of the solution being much smaller than the radius of the pores. Compared with liquid water, adsorbed water molecules have low degrees of freedom and are not prone to large-scale phase changes. Before and after nucleation, the binding effect of soil particles on pore water contributes little to energy, and the adsorption effect of the pores ΔG capillary Item can be ignored.

[0054] 1. Combining formulas (13)-(15), the total Gibbs free energy expression of the freezing process is obtained:

[0055]

[0056] Step 3, determine the freezing nucleation temperature equation;

[0057] The step 3 includes the following sub-steps:

[0058] a. The change of system free energy changes with the formation of crystal nuclei. The minimum size of the crystal nucleus that can grow stably is the critical radius corresponding to the minimum value of the system free energy change. According to the thermodynamic conditions of the critical nucleation state Combined with formula (16), the numerical solution of the critical nucleation radius is accurately obtained:

[0059]

[0060] b. Critical nucleation amount n * It is expressed as:

[0061]

[0062] c. Critical nucleation work ΔG * It is expressed as:

[0063]

[0064] d. The amount of substance that introduces water into the pore unit n l , through the pore equivalent radius r c Build l With S r The relationship is as follows:

[0065]

[0066] e. The average chemical potential barrier that needs to be crossed to form a stable critical nucleus for:

[0067]

[0068] f. When the ice-water two-phase is in the critical nucleation state, the phase change driving force (the difference in chemical potential between the two phases) is equal to the average nucleation barrier:

[0069]

[0070] g. Combine formula (22) with (2)-(5) to obtain the equilibrium equation:

[0071]

[0072] h. When the reference state of the solution is normal pressure, it is assumed that the phase pressure of the solution remains unchanged before and after freezing, that is, P w =P 0 When ice melts into water, entropy increases, Simplified to:

[0073]

[0074] i. Determine the freezing nucleation temperature equation. Introduce the Young–Laplace equation The initial freezing temperature equation of the saline soil-water system Combining formula (24), the freezing nucleation temperature equation can be obtained:

[0075]

[0076] Where, T 0 is the freezing temperature of pure water (273.15K); R is the universal gas constant (8.314 N·m / mol·K); r is the radius of the ice nucleus; r c is the radius of curvature; S r is the pore saturation; V i is the molar volume of the ice nucleus, V i * =19.63cm 3 / mol; ΔS m is the entropy difference between ice and water, ΔS m =1.2MPa / K.

[0077] Step 4, determine the Gibbs free energy equation of the pre-melting process;

[0078] The step 4 includes the following sub-steps:

[0079] a. Determine the total Gibbs free energy equation for the melting process. In the process of frozen soil melting, the mechanism of grain boundary pre-melting and solid-liquid interface pre-melting is considered. The chemical potential term of solid, liquid, impurity, mixing entropy term and effective interface free energy term are introduced to obtain the total Gibbs free energy equation:

[0080] ΔG total-2 =ΔG solid +ΔG liquid +ΔGimpurities +ΔG mix +ΔG interface (26)

[0082] In the formula, ΔG solid , ΔG liquid , ΔG impurities are the free energy terms of solid, liquid and impurity respectively; ΔG mix is the mixing entropy term of impurities at low impurity concentration; ΔG interface (d) is the total effective interfacial free energy.

[0083] b. Determine the total Gibbs free energy equation per unit area of ​​the system. The premelting phenomenon is the appearance of two different and immiscible quasi-liquid layers on the ice surface. The present invention assumes a three-layer plane premelting model: the first layer is ice crystals, the second layer is a pre-melted quasi-liquid layer with a thickness of d, and the third layer is the substrate. When the interface is premelted, the substrate is composed of porous medium materials; when the grain boundary is premelted, it is composed of ice. The Gibbs free energy per unit area of ​​the system ΔG total-2 :

[0084] ΔG total-2 =μ s n s +μ l n l +μ i n i +ΔG mix +ΔG interface (d) (27)

[0085] In the formula, μ s , μ l , μ i are the chemical potential terms of solid, liquid and impurity respectively; n s 、n l 、n i are the molar numbers per unit area of ​​solid, liquid and impurity respectively. mix Calculations were performed to consider the effect of solid-liquid interactions on entropy. The original expression for mixing entropy is ΔS mix =-nR(x A lnx A +x B lnx B ), and because x B <<1, then

[0086] c. Determine the effective interface energy equation per unit area. Including the dispersion force F disp (d) Electrostatic force F at the interface elec (d), and the hydrogen bond energy F H-Bond(d). The expression is as follows:

[0087] ΔG interface (d) = F disp (d)+F elec (d)+F H-Bond (d) (28)

[0088] d. Determine the dispersion force equation. At the solid-liquid interface, the dispersion force is mainly generated by the instantaneous electric dipole interaction between molecules and the dipole interaction of neighboring molecules, and its influence on the molecular behavior at the nanoscale or microscopic interface cannot be ignored. Dispersion force F disp (d) The expression is as follows:

[0089]

[0090] In the formula, A H is the Hamaker constant, which represents the interaction between the particle surface and the liquid due to the short-range van der Waals force. For a symmetric system, when the grain boundary melts, A H is positive, the dispersion force is attractive dispersion force, in soil application A H =6·10 - 20 J; d is the thickness of the pre-melted layer.

[0091] e. Determine the charge electrostatic force equation. In a system containing solutes or charged particles, the charge distribution at the interface will produce electrostatic interactions. During the pre-thaw process of frozen soil, the distribution of interfacial charge and the electric field strength will affect the phase change behavior of ice or water and change the physical and chemical properties of the interface. The charge electrostatic force F at the interface elec (d) is expressed as follows:

[0092]

[0093] In the formula, q s is the surface charge density; e is the electron charge, e = 1.602×10 -19 C;∈ 0 is the vacuum dielectric constant, ∈ 0 =8.854×10 -12 F / m; ∈ is the relative dielectric constant of the solvent. The relative dielectric constant of water is about 80 at room temperature; κ -1 is the Debye length of monovalent ions, and the unit of K is 1 / m.

[0094] f. Determine the Debye length, which describes the characteristic attenuation of the ionic field near a charged surface due to screening by counterions.

[0095]

[0096] Where N Ais Avogadro's constant (6.022×10 23 mol -1 );k B is the Boltzmann constant (1.380649×10 -23 J / K).

[0097] g. Determine the hydrogen bonding energy equation. Water molecules in ice form a hexagonal lattice structure through hydrogen bonds. During the melting process of frozen soil, the ice lattice structure is destroyed at the ice-water interface, and the hydrogen bonds are partially broken, resulting in a weakening of the attraction between molecules. A certain amount of energy needs to be absorbed to overcome these interaction forces, and the free energy changes significantly, affecting the pre-melting starting temperature. Assuming that the ratio of broken hydrogen bonds is x, the total hydrogen bonding energy can be expressed as follows:

[0098] F H-Bond (d) = 4xn l ·E H-Bond =11.304n l (32)

[0099] In the formula, E H-Bond is the hydrogen bond energy, which is 18.84 kJ / mol, and the corresponding hydrogen bond length is 276 pm. During the melting process of ice, about 15-20% of the hydrogen bonds will break, reducing about 0.5-1 hydrogen bonds, so x15% is taken; under the plane pre-melting assumption, n l =ρ l d.

[0100] h. Considering the curvature of the ice-water interface in the actual soil-water storage environment, assuming that the ice crystal is spherical with a radius of r, the corrected total Gibbs free energy is expressed as follows:

[0101]

[0102] Where N s ,N l ,N i are the molar numbers of solid, liquid and impurities in the whole system respectively, and γ is the ice-water interface free energy.

[0103] Step 5, determining the pre-melting starting temperature equation;

[0104] The step 5 comprises the following sub-steps:

[0105] a. When pre-melting occurs, the solid and liquid phases in the system exchange substances and obtain the thermodynamic equilibrium condition:

[0106]

[0107] b. Determine the chemical potential equilibrium equation. According to formula (34), we get:

[0108]

[0109] c. Introducing latent heat of fusion as a key thermodynamic parameter, The chemical potential differential balance is obtained:

[0110]

[0111] Where r is the radius of curvature of the ice-water interface, ρ s is the molar density of ice crystals, satisfying T m The equilibrium melting temperature.

[0112] d. Solve for the radius of curvature:

[0113]

[0114] e. Combining formulas (33)-(36), we get the relationship between the melting characteristic value:

[0115]

[0116] f. Solving formula (38) yields the expression for supercooling:

[0117]

[0118] g. According to equation (39), the pre-melting starting temperature can be obtained:

[0119]

[0120] Beneficial effects of the present invention:

[0121] The present invention determines a method that can quantify the critical temperature of soil phase change with high precision based on the classical nucleation principle and the interface pre-melting principle, and obtains the freezing nucleation temperature and pre-melting starting temperature of saline soil, which has a wide range of applications. The quantification method takes into account the actual situation of soil freeze-thaw phase change, and the physical meaning of each parameter is clear and easy to obtain. In addition to the above-mentioned purposes, features and advantages, the present invention has other purposes, features and advantages. The present invention will be further described in detail with reference to the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0122] Figure 1 It is a schematic diagram of the process of the method for quantifying the critical temperature of soil phase change with high precision in the present invention.

[0123] Figure 2 Schematic diagram of the soil water nucleation process in the present invention.

[0124] Figure 3 It is a schematic diagram of the plane pre-melting model in the present invention.

[0125] Figure 4 It is a schematic diagram of the spherical ice crystal pre-melting model in the present invention.

[0126] Figure 5 This is a prediction effect and analysis diagram of the method of the present invention.

[0127] Specific implementation instructions

[0128] Step 1, determine the phase transition Gibbs free energy equation and ice-water chemical potential equation;

[0129] The step 1 includes the following sub-steps:

[0130] a. During the freeze-thaw cycle, when the system changes state, the thermodynamic quantity Gibbs free energy will change, which can be used to determine whether the system has undergone a phase change. The total Gibbs free energy is expressed as the sum of the changes in the energy of each component.

[0131] ΔG total =ΔG 1 +ΔG 2 +...+ΔG i +...+ΔG n (1)

[0132] In the formula, ΔG total is the total Gibbs free energy change, ΔG i ,i=1,...,n is the change of energy of each component.

[0133] b. At the same temperature and pressure, the thermodynamic driving force for spontaneous phase change is represented by the difference Δμ between the chemical potential of water molecules (liquid phase) and the chemical potential of ice molecules (solid phase):

[0134] Δμ=μ w (p w ,a w ,T)-μ i (p i ,T) (2)

[0135] In the formula, μ w (p w ,a w ,T),μ i (p i , T) represent the chemical potentials in deionized water and ice crystals, respectively.

[0136] c. Determine the chemical potential equation. Set the freezing point of deionized water as the analytical standard state [T 0 (273.13K), P 0 (101.013 kPa)], the water chemical potential can be expressed as:

[0137]

[0138] Where V w is the molar volume of liquid water, is the chemical potential of deionized water in standard state.

[0139] d. Ice chemical potential is expressed as:

[0140]

[0141] Where V i is the molar volume of the ice nucleus, The chemical potentials of ice crystals and water in the standard state are equal.

[0142] e. In the phase change process of freeze-thaw cycle, the melting latent heat affects the energy exchange, temperature change of frozen soil, mechanical behavior of soil and water migration. The melting latent heat is introduced to determine the phase change temperature equation:

[0143] ΔH f =T 0 (S i -S w ) (5)

[0144] In the formula, ΔH f is the latent heat of phase change of water molecules. Under standard conditions, the melting latent heat of ice is about 6.01 kJ / mol; S i , S w are the entropies of ice and liquid water, respectively. The molecular freedom of liquid substances is greater than that of solid substances. S i -S w Is a negative value.

[0145] Step 2, determine the Gibbs free energy equation of the freezing process;

[0146] The step 2 includes the following sub-steps:

[0147] a. Considering the influencing factors of soil storage environment such as solute concentration and capillary effect of soil pores, the heterogeneous nucleation theory is modified. In the initial stage of nucleation (when the amount of ice formed is very small), the changes in gravity field and external pressure can be ignored. During the nucleation process, the change in the total free energy of the system ΔG total-1 It is divided into the following five parts: surface energy ΔG surface , volume free energy ΔG volume , Coulomb field energy ΔG electric , solute concentration contribution to energy ΔG solute , and the adsorption effect of the pores ΔG capillary .

[0148] ΔG total-1 =ΔG surface +ΔG volume +Δg electric+ΔG solute +ΔG capillary (6)

[0149] b. Determine the surface energy equation. During the nucleation process, a liquid-solid interface is formed, and the surface energy barrier must be overcome to achieve freezing.

[0150] ΔG surface =4πr 2 σ iw (7)

[0151] Where r is the radius of the crystal core, σ iw is the surface tension of the ice-water interface.

[0152] c. Calculate the surface tension of ice-water interface using Hardy model:

[0153] σ iw [J.m -2 ]=2.91·10 -2 +(TT 0 )·0.18·10 -3 (8)

[0154] Where, T 0 is 0 degrees Celsius and T is the actual temperature.

[0155] d. Determine the volume free energy equation. The volume free energy ΔG during the transformation of water into ice volume Changes in freezing latent heat ΔG v-1 and nucleation ΔG v-2 The free energy change caused. When a crystal nucleus forms in liquid water, the order of the local system increases with an increase in free energy (transition state); after stable nucleation, the ice crystal growth releases free energy. During the freezing process, heat is released when water changes from liquid to solid:

[0156]

[0157] In the formula, ρ i is the density of ice; r is the radius of the crystal core; L f is the latent heat of freezing.

[0158] e. Considering that the free energy of the crystal nucleus molecules will change after the solution molecules generate the crystal nucleus, the relationship between the solution partial pressure and the ice pressure is introduced. For the solution-ice crystal system, using Raoult's law, we get:

[0159]

[0160] In the formula, e li is the stable vapor pressure ratio of solution and ice crystals at the same temperature and pressure; a w is water activity; ei It indicates the stable vapor pressure ratio of water and ice crystals at the same temperature and pressure.

[0161] f. Calculate the stable vapor pressure ratio e i :

[0162]

[0163] g. Change in free energy caused by nucleation:

[0164]

[0165] In the formula, k B is the Boltzmann constant, k B ≈1.380649×10 -23 J / K;v i is the average lattice volume occupied by ice molecules, calculated using the Zobrist equation: Among them, T r =(TT 0 ) / T 0 , N A is Avogadro's constant, r is the nucleus radius, ρ i is the density of ice, which can be calculated by the HRPruppacher & J.D.Klett equation i =0.9167g / cm 3 , the molecular mass of water is M w =18.015 g / mol.

[0166] h. Determine the volume free energy equation.

[0167]

[0168] i. Determine the free energy equation caused by the Coulomb field. In soil pore solutions containing solutes or other charged substances, charged molecules or ions will change the molecular arrangement at the interface, causing energy changes in the nucleation process and affecting the nucleation temperature. Assume that the particles are point charges, the amount of charge in the system is the same, and only consider the interaction between a single particle and its own electric field. The free energy change caused by the Coulomb field energy is ΔG electric It can be calculated as follows:

[0169]

[0170] Where q is the charge of the ion, q = 1.602 × 10 -19 C;∈ is the dielectric constant; r is the crystal nucleus radius.

[0171] j. Determine the solution free energy equation. Solutes (such as salts, minerals, or other chemicals) dissolved in water interfere with the formation of hydrogen bonds between water molecules, reducing the free energy of freezing, thereby changing the freezing characteristics of water and lowering the freezing point of water. Therefore, the change in solution free energy during nucleation, ΔG solute It can be expressed as:

[0172]

[0173] k. In the early stage of freezing, supercooling is usually closely related to capillary water in the soil macropores, which results in the critical nucleation radius of the solution being much smaller than the radius of the pores. Compared with liquid water, adsorbed water molecules have low degrees of freedom and are not prone to large-scale phase changes. Before and after nucleation, the binding effect of soil particles on pore water contributes little to energy, and the adsorption effect of the pores ΔG capillary Item can be ignored.

[0174] 1. Combining formulas (13)-(15), the total Gibbs free energy expression of the freezing process is obtained:

[0175]

[0176] Step 3, determine the freezing nucleation temperature equation;

[0177] The step 3 includes the following sub-steps:

[0178] a. The change of system free energy changes with the formation of crystal nuclei. The minimum size of the crystal nucleus that can grow stably is the critical radius corresponding to the minimum value of the system free energy change. According to the thermodynamic conditions of the critical nucleation state Combined with formula (16), the numerical solution of the critical nucleation radius is accurately obtained:

[0179]

[0180] b. Critical nucleation amount n * It is expressed as:

[0181]

[0182] c. Critical nucleation work ΔG * It is expressed as:

[0183]

[0184] d. The amount of substance that introduces water into the pore unit n l , through the pore equivalent radius r c Build l With S r The relationship is as follows:

[0185]

[0186] e. The average chemical potential barrier that needs to be crossed to form a stable critical nucleus for:

[0187]

[0188] f. When the ice-water two-phase is in the critical nucleation state, the phase change driving force (the difference in chemical potential between the two phases) is equal to the average nucleation barrier:

[0189]

[0190] g. Combine formula (22) with (2)-(5) to obtain the equilibrium equation:

[0191]

[0192] h. When the reference state of the solution is normal pressure, it is assumed that the phase pressure of the solution remains unchanged before and after freezing, that is, P w =P 0 When ice melts into water, entropy increases, Simplified to:

[0193]

[0194] i. Determine the freezing nucleation temperature equation. Introduce the Young–Laplace equation The initial freezing temperature equation of the saline soil-water system Combining formula (24), the freezing nucleation temperature equation can be obtained:

[0195]

[0196] Where, T 0 is the freezing temperature of pure water (273.15K); R is the universal gas constant (8.314 N·m / mol·K); r is the radius of the ice nucleus; r c is the radius of curvature; S r is the pore saturation; V i is the molar volume of the ice nucleus, V i * =19.63cm 3 / mol; ΔS m is the entropy difference between ice and water, ΔS m =1.2MPa / K.

[0197] Step 4, determine the Gibbs free energy equation of the pre-melting process;

[0198] The step 4 includes the following sub-steps:

[0199] a. Determine the total Gibbs free energy equation for the melting process. In the process of frozen soil melting, the mechanism of grain boundary pre-melting and solid-liquid interface pre-melting is considered. The chemical potential term of solid, liquid, impurity, mixing entropy term and effective interface free energy term are introduced to obtain the total Gibbs free energy equation:

[0200] ΔG total-2 =ΔG solid +ΔG liquid +ΔG impurities +ΔG mix +ΔG interface (26)

[0202] In the formula, ΔG solid , ΔG liquid , ΔG impurities are the free energy terms of solid, liquid and impurity respectively; ΔG mix is the mixing entropy term of impurities at low impurity concentration; ΔG interface (d) is the total effective interfacial free energy.

[0203] b. Determine the total Gibbs free energy equation per unit area of ​​the system. The premelting phenomenon is the appearance of two different and immiscible quasi-liquid layers on the ice surface. The present invention assumes a three-layer plane premelting model: the first layer is ice crystals, the second layer is a pre-melted quasi-liquid layer with a thickness of d, and the third layer is the substrate. When the interface is premelted, the substrate is composed of porous medium materials; when the grain boundary is premelted, it is composed of ice. The Gibbs free energy per unit area of ​​the system ΔG total-2 :

[0204] ΔG total-2 =μ s n s +μ l n l +μ i n i +ΔG mix +ΔG interface (d)(27)

[0205] In the formula, μ s , μ l , μ i are the chemical potential terms of solid, liquid and impurity respectively; n s 、n l 、n i are the molar numbers per unit area of ​​solid, liquid and impurity respectively. mix Calculations were performed to consider the effect of solid-liquid interactions on entropy. The original expression for mixing entropy is ΔS mix =-nR(x A lnx A +x B lnx B), and because x B <<1, then

[0206] c. Determine the effective interface energy equation per unit area. Including the dispersion force F disp (d) Electrostatic force F at the interface elec (d), and the hydrogen bond energy F H-Bond (d). The expression is as follows:

[0207] ΔG interface (d) = F disp (d)+F elec (d)+F H-Bond (d) (28)

[0208] d. Determine the dispersion force equation. At the solid-liquid interface, the dispersion force is mainly generated by the instantaneous electric dipole interaction between molecules and the dipole interaction of neighboring molecules, and its influence on the molecular behavior at the nanoscale or microscopic interface cannot be ignored. Dispersion force F disp (d) The expression is as follows:

[0209]

[0210] In the formula, A H is the Hamaker constant, which represents the interaction between the particle surface and the liquid due to the short-range van der Waals force. For a symmetric system, when the grain boundary melts, A H is positive, the dispersion force is attractive dispersion force, in soil application A H =6·10 - 20 J; d is the thickness of the pre-melted layer.

[0211] e. Determine the charge electrostatic force equation. In a system containing solutes or charged particles, the charge distribution at the interface will produce electrostatic interactions. During the pre-thaw process of frozen soil, the distribution of interfacial charge and the electric field strength will affect the phase change behavior of ice or water and change the physical and chemical properties of the interface. The charge electrostatic force F at the interface elec (d) is expressed as follows:

[0212]

[0213] In the formula, q s is the surface charge density; e is the electron charge, e = 1.602×10 -19 C;∈ 0 is the vacuum dielectric constant, ∈ 0 =8.854×10 -12 F / m; ∈ is the relative dielectric constant of the solvent. The relative dielectric constant of water is about 80 at room temperature; κ -1is the Debye length of a monovalent ion, and the unit of κ is 1 / m.

[0214] f. Determine the Debye length, which describes the characteristic attenuation of the ionic field near a charged surface due to screening by counterions.

[0215]

[0216] Where N A is Avogadro's constant (6.022×10 23 mol -1 );k B is the Boltzmann constant (1.380649×10 -23 J / K).

[0217] g. Determine the hydrogen bonding energy equation. Water molecules in ice form a hexagonal lattice structure through hydrogen bonds. During the melting process of frozen soil, the ice lattice structure is destroyed at the ice-water interface, and the hydrogen bonds are partially broken, resulting in a weakening of the attraction between molecules. A certain amount of energy needs to be absorbed to overcome these interaction forces, and the free energy changes significantly, affecting the pre-melting starting temperature. Assuming that the ratio of broken hydrogen bonds is x, the total hydrogen bonding energy can be expressed as follows:

[0218] F H-Bond (d) = 4xn l ·E H-Bond =11.304n l (32)

[0219] In the formula, E H-Bond is the hydrogen bond energy, which is 18.84 kJ / mol, and the corresponding hydrogen bond length is 276 pm. During the melting process of ice, about 15-20% of the hydrogen bonds will break, reducing about 0.5-1 hydrogen bonds, so x15% is taken; under the plane pre-melting assumption, n l =ρ l d.

[0220] h. Considering the curvature of the ice-water interface in the actual soil-water storage environment, assuming that the ice crystal is spherical with a radius of r, the corrected total Gibbs free energy is expressed as follows:

[0221]

[0222] Where N s ,N l ,N i are the molar numbers of solid, liquid and impurities in the whole system respectively, and γ is the ice-water interface free energy.

[0223] Step 5, determining the pre-melting starting temperature equation;

[0224] The step 5 comprises the following sub-steps:

[0225] a. When pre-melting occurs, the solid and liquid phases in the system exchange substances and obtain the thermodynamic equilibrium condition:

[0226]

[0227] b. Determine the chemical potential equilibrium equation. According to formula (34), we get:

[0228]

[0229] c. Introducing latent heat of fusion as a key thermodynamic parameter, The chemical potential differential balance is obtained:

[0230]

[0231] Where r is the radius of curvature of the ice-water interface, ρ s is the molar density of ice crystals, satisfying T m The equilibrium melting temperature.

[0232] d. Solve for the radius of curvature:

[0233]

[0234] e. Combining formulas (33)-(36), we get the relationship between the melting characteristic value:

[0235]

[0236] f. Solving formula (38) yields the expression for supercooling:

[0237]

[0238] g. According to equation (39), the pre-melting starting temperature can be obtained:

[0239]

[0240] Verification of the quantification method for freeze-thaw temperature of unsaturated saline soil:

[0241] The present invention selects the root mean square error RMSE, the mean percentage error MPAE and the determination coefficient R 2 The actual prediction effect was tested. Three unsaturated saline soils with different water content and salt content: sandy soil, silty soil and silty clay were taken for freezing / heating bath test. The quantitative method of the present invention was evaluated through the freeze-thaw cycle temperature monitoring curve data of different water content, salt content and soil types.

[0242]

[0243] In the formula, θ m(i) is the measured value, is the average value of the measured value, θ p(i) The calculation results of the above measurement parameters are shown in Table 3.

[0244] Table 1 provides the basic physical properties of the three soils

[0245]

[0246] Table 2 Salt and water content of three kinds of soil

[0247]

[0248] Table 3 provides the model prediction error analysis

[0249]

[0250] The coefficient of determination R of the model of the present invention 2 The freezing nucleation temperature (T) of sand, silt and silty clay is shown in Figure 2. sc ) and pre-melting starting temperature (T bt ) are compared with the theoretical simulation results and experimental measurements.

[0251] like Figure 1 As shown, the main flow chart of the method for high-precision quantification of critical temperature of soil phase change based on nucleation and pre-melting principles of the present invention.

[0252] like Figure 2 As shown, the schematic diagram of soil water nucleation during the freezing process of the present invention is that in the initial stage of nucleation (extremely small amount of ice formed), the changes in the gravity field and external pressure can be ignored.

[0253] like Figure 3 As shown, a three-layer plane pre-melting model is assumed in the melting process of the present invention: the first layer is ice crystals, the second layer is a pre-melted quasi-liquid layer with a thickness of d, and the third layer is the substrate. When the interface is pre-melted, the substrate is composed of porous medium materials; when the grain boundary is pre-melted, it is composed of ice.

[0254] like Figure 4 As shown, in the melting process described in the present invention, it is assumed that the ice crystals are spherical with a radius r, and the total Gibbs free energy is corrected.

[0255] like Figure 5As shown in (a)-(c), most of the measured points fall within the ±0.5% error line of the model prediction value, indicating that the model prediction results are reliable. The high temperature values ​​in the figure correspond to high water activity and low mass salinity. It can be found that under high water activity conditions, the difference between the theoretical prediction and the experimental results is small, indicating that the model has good accuracy in predicting temperature under high water activity.

[0256] like Figure 5 As shown in (d), the average absolute error (AE) ± standard error (SE) of the model prediction results shows that the absolute error of this part of the data is always lower than 1.1K, showing a good prediction effect. This proves that the model of the present invention can be applied to sodium chloride saline soils of different soil types and salt contents, and shows a good prediction effect.

[0257] In summary, the soil phase change critical temperature quantification method obtained by the present invention can effectively predict the soil phase change critical temperature for unsaturated saline soils with different salt contents and different soil types. It is feasible to apply the soil phase change critical temperature quantification method of the present invention to obtain the actual soil phase change critical temperature.

Claims

1. A method for quantifying the critical temperature of soil phase change with high precision based on the principle of nucleation and pre-melting, characterized in that: For the following steps: Step 1, determine the phase transition Gibbs free energy equation and ice-water chemical potential equation; Step 2, determine the Gibbs free energy equation of the freezing process; Step 3, determine the freezing nucleation temperature equation; Step 4, determine the Gibbs free energy equation of the pre-melting process; Step 5: Determine the pre-melting starting temperature equation.

2. The method for quantifying the critical temperature of soil phase change with high precision based on the nucleation and pre-melting principle according to claim 1 is characterized by: The step 1 comprises: a. During the freeze-thaw cycle, when the system changes state, the thermodynamic quantity Gibbs free energy will change, which can be used to determine whether the system has undergone a phase change. The total Gibbs free energy is expressed as the sum of the changes in the energy of each component. ΔG total =ΔG1+ΔG2+...+ΔG i +...+ΔG n (1) In the formula, ΔG total is the total Gibbs free energy change, ΔG i ,i=1,...,n is the change of energy of each component. b. At the same temperature and pressure, the thermodynamic driving force for spontaneous phase change is represented by the difference Δμ between the chemical potential of water molecules (liquid phase) and the chemical potential of ice molecules (solid phase): Dm=m w (p w ,a w ,T)-m i (p i ,T) (2) In the formula, μ w (p w ,a w ,T),μ i (p i , T) represent the chemical potentials in deionized water and ice crystals, respectively. c. Determine the chemical potential equation. Set the freezing point of deionized water to the analytical standard state [T0 (273.13K), P0 (101.013kPa)], and the water chemical potential can be expressed as: Where V w is the molar volume of liquid water, is the chemical potential of deionized water in standard state. d. Ice chemical potential is expressed as: Where V i is the molar volume of the ice nucleus, The chemical potentials of ice crystals and water in the standard state are equal. e. In the phase change process of freeze-thaw cycle, the melting latent heat affects the energy exchange, temperature change of frozen soil, mechanical behavior of soil and water migration. The melting latent heat is introduced to determine the phase change temperature equation: ΔH f =T0(S i -S w ) (5) In the formula, ΔH f is the latent heat of phase change of water molecules. Under standard conditions, the melting latent heat of ice is about 6.01 kJ / mol; S i , S w are the entropies of ice and liquid water, respectively. The molecular freedom of liquid substances is greater than that of solid substances. S i -S w Is a negative value.

3. The method for quantifying the critical temperature of soil phase change with high precision based on the nucleation and pre-melting principle according to claim 1 is characterized by: The step 2 comprises: a. Considering the influencing factors of soil storage environment such as solute concentration and capillary effect of soil pores, the heterogeneous nucleation theory is modified. In the initial stage of nucleation (when the amount of ice formed is very small), the changes in gravity field and external pressure can be ignored. During the nucleation process, the change in the total free energy of the system ΔG total-1 It is divided into the following five parts: surface energy ΔG surface , volume free energy ΔG volume , Coulomb field energy ΔG electric , solute concentration contribution to energy ΔG solute , and the adsorption effect of the pores ΔG capillary . ΔG total-1 =ΔG surface +ΔG volume +ΔG electric +ΔG solute +ΔG capillary (6) b. Determine the surface energy equation. During the nucleation process, a liquid-solid interface is formed, and the surface energy barrier must be overcome to achieve freezing. ΔG surface =4πr 2 s iw (7) In the formula, r is the radius of the crystal core, σ iw is the surface tension of the ice-water interface. c. Calculate the surface tension of ice-water interface by Hardy model: σ iw [J·m -2 ]=2.91·10 -2 +(T-T0)·0.18·10 -3 (8) Where T0 is 0 degrees Celsius and T is the actual temperature. d. Determine the volume free energy equation. The volume free energy ΔG during the transformation of water into ice volume Changes in freezing latent heat ΔG v-1 and nucleation ΔG v-2 The free energy change caused. When a crystal nucleus forms in liquid water, the order of the local system increases with an increase in free energy (transition state); after stable nucleation, the ice crystal growth releases free energy. During the freezing process, heat is released when water changes from liquid to solid: In the formula, ρ i is the density of ice; r is the radius of the crystal core; L f is the latent heat of freezing. e. Considering that the free energy of the crystal nucleus molecules will change after the solution molecules generate the crystal nucleus, the relationship between the solution partial pressure and the ice pressure is introduced. For the solution-ice crystal system, using Raoult's law, we get: In the formula, e li is the stable vapor pressure ratio of solution and ice crystal at the same temperature and pressure; a w is water activity; e i It indicates the stable vapor pressure ratio of water and ice crystals at the same temperature and pressure. f. Calculate the stable vapor pressure ratio e i : g. Change in free energy caused by nucleation: In the formula, k B is the Boltzmann constant, k B ≈1.380649×10 -23 J / K;v i is the average lattice volume occupied by ice molecules, calculated using the Zobrist equation: Among them, T r =(T-T0) / T0,N A is Avogadro's constant, r is the nucleus radius, ρ i is the density of ice, which can be calculated by the HRPruppacher & J.D.Klett equation i =0.9167g / cm 3 , the molecular mass of water is M w =18.015 g / mol. h. Determine the volume free energy equation. i. Determine the free energy equation caused by the Coulomb field. In soil pore solutions containing solutes or other charged substances, charged molecules or ions will change the molecular arrangement at the interface, causing energy changes in the nucleation process and affecting the nucleation temperature. Assume that the particles are point charges, the amount of charge in the system is the same, and only consider the interaction between a single particle and its own electric field. The free energy change caused by the Coulomb field energy is ΔG electric It can be calculated as follows: Where q is the charge of the ion, q = 1.602 × 10 -19 C;∈ is the dielectric constant; r is the crystal nucleus radius. j. Determine the solution free energy equation. Solutes (such as salts, minerals, or other chemicals) dissolved in water interfere with the formation of hydrogen bonds between water molecules, reducing the free energy of freezing, thereby changing the freezing characteristics of water and lowering the freezing point of water. Therefore, the change in solution free energy during nucleation, ΔG solute It can be expressed as: k. In the early stage of freezing, supercooling is usually closely related to capillary water in the soil macropores, which results in the critical nucleation radius of the solution being much smaller than the radius of the pores. Compared with liquid water, adsorbed water molecules have low degrees of freedom and are not prone to large-scale phase changes. Before and after nucleation, the binding effect of soil particles on pore water contributes little to energy, and the adsorption effect of the pores ΔG capillary Item can be ignored.

1. Combining formulas (13)-(15), the total Gibbs free energy expression of the freezing process is obtained:

4. The method for quantifying soil phase change temperature with high precision based on the nucleation and pre-melting principle according to claim 1 is characterized by: The step 3 comprises: a. The change of system free energy changes with the formation of crystal nuclei. The minimum size of the crystal nucleus that can grow stably is the critical radius corresponding to the minimum value of the system free energy change. According to the thermodynamic conditions of the critical nucleation state Combined with formula (16), the numerical solution of the critical nucleation radius is accurately obtained: b. Critical nucleation amount n * It is expressed as: c. Critical nucleation work ΔG * It is expressed as: d. The amount of substance that introduces water into the pore unit n l , through the pore equivalent radius r c Build l With S r The relationship is as follows: e. The average chemical potential barrier that needs to be crossed to form a stable critical nucleus for: f. When the ice-water two-phase is in the critical nucleation state, the phase change driving force (the difference in chemical potential between the two phases) is equal to the average nucleation barrier: g. Combine formula (22) with (2)-(5) to obtain the equilibrium equation: h. When the reference state of the solution is normal pressure, it is assumed that the phase pressure of the solution remains unchanged before and after freezing, that is, P w =P0. When ice melts into water, entropy increases, Equation (23) is simplified to: i. Determine the freezing nucleation temperature equation. Introduce the Young–Laplace equation The initial freezing temperature equation of the saline soil-water system Combining formula (24), the freezing nucleation temperature equation can be obtained: Where T0 is the freezing temperature of pure water (273.15K); R is the universal gas constant (8.314 N·m / mol·K); r is the radius of the ice nucleus; c is the radius of curvature; S r is the pore saturation; V i is the molar volume of the ice nucleus, V i * =19.63cm 3 / mol; ΔS m is the entropy difference between ice and water, ΔS m =1.2MPa / K.

5. The method for quantifying the critical temperature of soil phase change with high precision based on the nucleation and pre-melting principle according to claim 1 is characterized by: The step 4 comprises: a. Determine the total Gibbs free energy equation for the melting process. In the process of frozen soil melting, the mechanism of grain boundary pre-melting and solid-liquid interface pre-melting is considered. The chemical potential term of solid, liquid, impurity, mixing entropy term and effective interface free energy term are introduced to obtain the total Gibbs free energy equation: ΔG total-2 =ΔG solid +ΔG liquid +ΔG impurities +ΔG mix +ΔG interface (26) In the formula, ΔG solid , ΔG liquid , ΔG impurities are the free energy terms of solid, liquid and impurity respectively; ΔG mix is the mixing entropy term of impurities at low impurity concentration; ΔG interface (d) is the total effective interfacial free energy. b. Determine the total Gibbs free energy equation per unit area of ​​the system. The premelting phenomenon is the appearance of two different and immiscible quasi-liquid layers on the ice surface. The present invention assumes a three-layer plane premelting model: the first layer is ice crystals, the second layer is a pre-melted quasi-liquid layer with a thickness of d, and the third layer is the substrate. When the interface is premelted, the substrate is composed of porous medium materials; when the grain boundary is premelted, it is composed of ice. The Gibbs free energy per unit area of ​​the system ΔG total-2 : ΔG total-2 =μ s n s +m l n l +m i n i +ΔG mix +ΔG interface (d)(27) In the formula, μ s , μ l , μ i are the chemical potential terms of solid, liquid and impurity respectively; n s 、n l 、n i are the molar numbers per unit area of ​​solid, liquid and impurity respectively. mix Calculations were performed to consider the effect of solid-liquid interactions on entropy. The original expression for mixing entropy is ΔS mix =-nR(x A lnx A +x B lnx B ), and because x B <<1, then c. Determine the effective interface energy equation per unit area. Including the dispersion force F disp (d) Electrostatic force F at the interface elec (d), and the hydrogen bond energy FH -Bond (d). The expression is as follows: ΔG interface (d)=F disp (d)+F elec (d)+F H-Bond (d) (28) d. Determine the dispersion force equation. At the solid-liquid interface, the dispersion force is mainly generated by the instantaneous electric dipole interaction between molecules and the dipole interaction of neighboring molecules, and its influence on the molecular behavior at the nanoscale or microscopic interface cannot be ignored. Dispersion force F disp (d) The expression is as follows: In the formula, A H is the Hamaker constant, which represents the interaction between the particle surface and the liquid due to the short-range van der Waals force. For a symmetric system, when the grain boundary melts, A H is positive, the dispersion force is attractive dispersion force, in soil applications A H =6·10 -20 J; d is the thickness of the pre-melted layer. e. Determine the charge electrostatic force equation. In a system containing solutes or charged particles, the charge distribution at the interface will produce electrostatic interactions. During the pre-thaw process of frozen soil, the distribution of interfacial charge and the electric field strength will affect the phase change behavior of ice or water and change the physical and chemical properties of the interface. The charge electrostatic force F at the interface elec (d) is expressed as follows: In the formula, q s is the surface charge density; e is the electron charge, e = 1.602×10 -19 C;∈0 is the dielectric constant of vacuum,∈0=8.854×10 -12 F / m; ∈ is the relative dielectric constant of the solvent. The relative dielectric constant of water is about 80 at room temperature; κ -1 is the Debye length of a monovalent ion, and the unit of κ is 1 / m. f. Determine the Debye length, which describes the characteristic attenuation of the ionic field near a charged surface due to screening by counterions. Where N A is Avogadro's constant (6.022×10 23 mol -1 );k B is the Boltzmann constant (1.380649×10 -23 J / K). g. Determine the hydrogen bonding energy equation. Water molecules in ice form a hexagonal lattice structure through hydrogen bonds. During the melting process of frozen soil, the ice lattice structure is destroyed at the ice-water interface, and the hydrogen bonds are partially broken, resulting in a weakening of the attraction between molecules. A certain amount of energy needs to be absorbed to overcome these interaction forces, and the free energy changes significantly, affecting the pre-melting starting temperature. Assuming that the ratio of broken hydrogen bonds is x, the total hydrogen bonding energy can be expressed as follows: F H-Bond (d)=4xn l ·E H-Bond =11.304n l (32) In the formula, E H-Bond is the hydrogen bond energy, which is 18.84 kJ / mol, and the corresponding hydrogen bond length is 276 pm. During the melting process of ice, about 15-20% of the hydrogen bonds will break, reducing about 0.5-1 hydrogen bonds, so x15% is taken; under the plane pre-melting assumption, n l =ρ l d. h. Considering the curvature of the ice-water interface in the actual soil-water storage environment, assuming that the ice crystal is spherical with a radius of r, the corrected total Gibbs free energy is expressed as follows: Where N s ,N l ,N i are the molar numbers of solid, liquid and impurities in the whole system respectively, and γ is the ice-water interface free energy.

6. The method for quantifying the critical temperature of soil phase change with high precision based on the nucleation and pre-melting principle according to claim 1 is characterized by: The step 5 comprises: a. When pre-melting occurs, the solid and liquid phases in the system exchange substances and obtain the thermodynamic equilibrium condition: b. Determine the chemical potential equilibrium equation. According to formula (34), we get: c. Introducing latent heat of fusion as a key thermodynamic parameter, The chemical potential differential balance is obtained: Where r is the radius of curvature of the ice-water interface, ρ s is the molar density of ice crystals, satisfying T m The equilibrium melting temperature. d. Solve for the radius of curvature: e. Combining formulas (33)-(36), we get the relationship between the melting characteristic value: f. Solving formula (38) yields the expression for supercooling: g. According to equation (39), the pre-melting starting temperature can be obtained:

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