A CALPHAD method for predicting PCT curves of hydrogen storage alloys

Abstract

This invention belongs to the technical field of prediction of hydrogen storage alloy materials, and in particular discloses a CALPHAD method for predicting the PCT curve of hydrogen storage alloys. The method comprises establishing a thermodynamic description of a sublattice model to obtain the chemical free energy volume density of the alloy system; obtaining the elastic strain energy of the alloy system; obtaining the total free energy of the system, solving the rate of decrease of the total free energy of the system, and constructing a free energy dissipation term; establishing a kinetic equation with phase fraction and composition as variables; solving the kinetic equation, plotting the PCT curve, and analyzing it. Compared with existing technologies, this invention establishes an innovative model with high precision. Compared with other computational simulation methods, it has higher prediction accuracy and reliability, reduces trial and error costs, and accelerates the design and optimization of hydrogen storage alloy materials. It can play an important role in the design and optimization of hydrogen storage alloy materials.

Description

Technical Field

[0001] The present invention relates to the technical field of prediction of hydrogen storage alloy materials, in particular to a CALPHAD method for predicting PCT curves of hydrogen storage alloys. Background Art

[0002] Hydrogen storage alloys are important materials for storing and releasing hydrogen, and their hydrogen absorption and desorption properties are key factors in evaluating their application performance. The PCT curve, which shows how hydrogen pressure (Pressure), temperature (Temperature), and hydrogen concentration (Composition) affect the absorption and desorption properties of hydrogen storage alloys, is a key parameter in evaluating the performance of hydrogen storage alloys. Therefore, predicting the PCT curve of hydrogen storage alloys has important research value and application prospects.

[0003] At present, the methods for predicting the PCT curve of hydrogen storage alloys mainly include experimental measurement, computational simulation and machine learning. Experimental measurement is currently the most direct and accurate method for determining the PCT curve, but the experimental cycle is long, the cost is high, and the operation is difficult, so it has certain limitations in the research and application of hydrogen storage alloy materials. Computational simulation refers to the use of computers to simulate the hydrogen absorption and desorption process of hydrogen storage alloy materials, and predict their PCT curves based on the thermodynamic properties and reaction kinetic characteristics of the materials. The computational simulation method can shorten the experimental cycle, save costs, and reduce the experimental difficulty, but it requires detailed modeling and simulation of the thermodynamic and reaction kinetic models of hydrogen storage alloy materials. The machine learning method refers to the use of statistical and machine learning algorithms to process and analyze large amounts of experimental data to predict the PCT curve of hydrogen storage alloy materials. The machine learning method can shorten the prediction cycle, but it requires a large amount of experimental data to train the model, and the prediction accuracy and reliability of the model may be limited by the data quality and model complexity.

[0004] While these methods have, to a certain extent, addressed the PCT curve prediction problem for hydrogen storage alloys, they still suffer from several deficiencies in practical application, such as low accuracy, large data volumes, and difficulty in model establishment. The CALPHAD (Computational Thermodynamics and Phase Diagram) method is a method for alloy thermodynamic calculations and material simulation. It predicts material properties and behavior by establishing phase diagrams and thermodynamic models.

[0005] The present invention provides a method for predicting the PCT curve of hydrogen storage alloys based on the CALPHAD method, establishes an innovative model for fine modeling, and has higher prediction accuracy and reliability than other computational simulation methods, reduces trial and error costs, accelerates the design and optimization of hydrogen storage alloy materials, and can play an important role in the design and optimization of hydrogen storage alloy materials. Summary of the Invention

[0006] The present invention provides a CALPHAD method for predicting the PCT curve of hydrogen storage alloys. Based on thermodynamic calculations and phase diagram analysis, this method models and calculates the composition and thermodynamic parameters of hydrogen storage alloy materials to predict their hydrogen absorption and desorption properties and PCT curves. Specifically, the method includes the following steps:

[0007] Step 1: According to the CALPHAD method, the thermodynamic parameters of the hydrogen storage alloy are obtained to establish the thermodynamic description of the sub-lattice model of the solid solution phase, precipitation phase and gas phase, and the chemical free energy volume density of the alloy system is obtained;

[0008] Step 2: Combined with the atomic-scale elastic isotropic strain energy theory, the elastic strain energy of the alloy system is obtained;

[0009] Step 3: Obtain the total free energy of the system by superposing the chemical free energy volume density and elastic strain energy of the alloy system, and calculate the rate of decrease of the total free energy of the system; at the same time, construct the free energy dissipation term;

[0010] Step 4: Establish a kinetic equation with phase fraction and composition as variables, and solve the derivative of the phase fraction with respect to time and the derivative of the mole fraction of hydrogen atoms in the phase with respect to time;

[0011] Step 5: Set appropriate physical parameters of the hydrogen storage alloy and input parameters of the simulation system, solve the kinetic equation, draw the PCT curve based on the solved data, and analyze the thermodynamic hysteresis evolution law of the PCT curve of the cyclic adsorption / desorption of hydrogen in the hydrogen storage alloy.

[0012] Furthermore, the specific steps of step 1 are:

[0013] Step 1.1, obtain the thermodynamic parameters of the hydrogen storage alloy according to the CALPHAD method, and then establish a sublattice model of the complex phase structure;

[0014] Step 1.2: Establish the bulk free energy volume density of the Nd-H alloy.

[0015] Furthermore, the free energy volume density of the alloy body established in step 1.2 is as follows:

[0016]

[0017] Among them, φ Dhcp is the phase fraction of the solid solution phase Dhcp, φ γ is the phase fraction of the precipitated phase γ, φ G is the G phase fraction of the gas phase; and f G (T, P) are the chemical free energy molar densities of Nd1(H, Va)2, which are the solid solution phase Dhcp, the precipitation phase γ and the gas phase G, respectively. V m is the molar volume.

[0018] Furthermore, the chemical free energy molar density of the solid solution phase Dhcp is for:

[0019]

[0020] Chemical free energy molar density of precipitated phase γ for:

[0021]

[0022] Chemical free energy molar density f of the gas phase G G (T,P) is:

[0023]

[0024] Where Nd represents metal atom, H represents hydrogen atom, and T is temperature. are the occupancy rates of hydrogen atoms and holes in the Dhcp phase and the γ phase, respectively. The thermodynamic model of the Dhcp phase and the γ phase is Nd1(H,Va)2, where the Nd element occupies the position of lattice 1, and the H element and the hole Va occupy the position of lattice 2. The atomic occupancy rate and the concentration mole fraction in the Dhcp phase and the γ phase are coupled to obtain: and are the formation enthalpies of NdH2 and NdVa2 in the Dhcp phase and γ phase, respectively, is the formation enthalpy of H2 in the Gas phase.

[0025] Furthermore, based on the stacking fault theory, a stress-strain model of structural phase transition is established, and the elastic strain energy molar density expression of the alloy system is as follows:

[0026]

[0027] in is the parameter related to the molar density of elastic strain energy, V m is the molar volume, G S is the shear modulus, σ is Poisson's ratio, is the dependence of the crystal lattice parameters on the concentration, is the average mole fraction of solute hydrogen atoms between the Dhcp phase and the γ phase, where and are the mole fractions of hydrogen atoms in the γ phase and the Dhcp phase, respectively, and ω is the volume fraction of the γ phase.

[0028] Furthermore, in step 3, the total free energy F of the system is obtained by superimposing the chemical free energy and elastic strain energy of the alloy system:

[0029]

[0030] Where r represents the volume integral, represents the total free energy of the Dhcp phase, represents the total free energy of the γ phase, Metal atom M=Nd; λ H and λ M They are the component conservation constraints and The Lagrange multiplier of λ0 is the phase fraction constraint φ Dhcp +φ γ +φ G =1 Lagrange multiplier.

[0031] In step 3, according to the principle of maximum entropy production, it is necessary to calculate the rate of decrease of the total free energy of the system

[0032]

[0033] in

[0034] and

[0035] Furthermore, the free energy dissipation term Q in step 3 is:

[0036]

[0037] in It is the phase fraction mobility of Dhcp phase, γ phase and G phase; and are the solute atomic mobility in the Dhcp phase and γ phase, respectively.

[0038] Furthermore, the specific steps of step 4 are:

[0039] Step 4.1: Establish the kinetic equation with phase fraction and composition as variables;

[0040] Step 4.2: Use phase constraints and composition conservation conditions to solve the kinetic equations with phase fraction and composition as variables.

[0041] Furthermore, the kinetic equation in step 4.1 with phase fraction and composition as variables is:

[0042]

[0043]

[0044]

[0045]

[0046]

[0047] in, are the time derivatives of the phase fractions of the solution phase Dhcp, the precipitated phase γ and the gas phase G, and are the time derivatives of the mole fractions of hydrogen atoms in the precipitated γ phase and the solid solution Dhcp phase, respectively;

[0048] Furthermore, the phase constraint in step 4.2 is: Dhcp +φ γ +φ G =1; the composition conservation condition is:

[0049] Solving the kinetic equations yields and for:

[0050]

[0051]

[0052]

[0053]

[0054]

[0055] Where, They are the mobility of phase transition Dhcp→γ, the mobility of γ→G, and the mobility of G→Dhcp, and [x H ] Dhcp,γ 、[x H ] G,Dhcp 、[x H ] γ,G They are the differences between the two phase components Dhcp / γ, γ / G, and G / Dhcp, respectively. and in It is the difference between the self-consumption energy of the Dhcp / γ phase divided by the difference between the components of the Dhcp / γ phase. It is the difference between the self-consumption energy of the G / Dhcp phases divided by the difference between the components of the G / Dhcp phases.

[0056] The advantages of the CALPHAD method provided by the present invention are:

[0057] (1) High prediction accuracy: Thermodynamic calculations based on the CALPHAD method can accurately describe the thermodynamic characteristics of hydrogen storage alloy materials, thereby improving prediction accuracy and reliability.

[0058] (2) Small amount of data: Compared with machine learning methods, the CALPHAD method requires a smaller amount of experimental data and can make predictions quickly.

[0059] (3) Simple model establishment: Compared with traditional computational simulation methods, the model establishment of the CALPHAD method is relatively simple and does not require complex modeling and simulation. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] Figure 1 Flowchart of the present invention. DETAILED DESCRIPTION

[0061] The present invention is further described below with reference to the accompanying drawings and specific embodiments. Taking Nd-H alloy as an example, a CALPHAD method for predicting the PCT curve of hydrogen storage alloys is provided. The method includes the following:

[0062] Step 1: The thermodynamic parameters of the hydrogen storage alloy are obtained according to the CALPHAD method to establish a thermodynamic description of the sublattice model of the solid solution phase Dhcp, the precipitated phase γ and the gas phase G, and further obtain the chemical free energy volume density of the alloy system;

[0063] 1.1 The thermodynamic parameters of hydrogen storage alloys are obtained according to the CALPHAD method. The sublattice model M1(H,Va)2 of the complex phase structure is established based on the thermodynamic parameters of the alloy, where Va represents the hole, and its thermodynamic description is performed. and f G (Y, P) is the chemical free energy molar density of the solution phase α, the precipitated phase β and the gas phase G

[0064] The composition of Nd-H system hydrogen storage alloys and the CALPHAD thermodynamic database are collected and processed through experimental determination or literature research. The CALPHAD method is used to establish a thermodynamic model of hydrogen storage alloys, predict the phase diagram and phase equilibrium information of hydrogen storage alloys, and then describe the thermodynamic characteristics of their hydrogen absorption and desorption transformation process.

[0065] 1.2 The free energy volume density of Nd-H alloy is established as follows:

[0066]

[0067] in, for Phase fraction or order parameter of the phase is the chemical free energy molar density of the Nd1(H,Va)2 solid solution phase Dhcp, is the chemical free energy molar density of Nd1(H,Va)2 precipitation phase γ, f G (T,P) is the chemical free energy molar density of Nd1(H,Va)2 gas phase G, V m is the molar volume, expressed as follows:

[0068] Chemical free energy molar density of solid solution phase Dhcp for:

[0069]

[0070] Chemical free energy molar density of precipitated phase γ for:

[0071]

[0072] Chemical free energy molar density f of the gas phase G G (T,P) is:

[0073]

[0074] Where Nd represents metal atom, H represents hydrogen atom, and T is temperature. are the occupancy rates of hydrogen atoms and holes in the Dhcp phase and the γ phase, respectively. The thermodynamic model of the Dhcp phase and the γ phase is Nd1(H,Va)2, where the Nd element occupies the position of lattice 1, and the H element and the hole Va occupy the position of lattice 2. By coupling the atomic occupancy rate and the concentration mole fraction in the Dhcp phase and the γ phase, we can get: and are the formation enthalpies of NdH2 and NdVa2 in the Dhcp phase and γ phase, respectively, is the formation enthalpy of H2 in the Gas phase. The expression is shown in Table 1 in the CALPHAD thermodynamic database.

[0075] Table 1 CALPHAD thermodynamic database for Nd-H alloy system

[0076]

[0077]

[0078]

[0079] In the table, T is the thermodynamic temperature, P is the pressure, is the free energy of single phase φ in pure component i, and is the free energy of single phase φ in the terminal component (compound form composed of different sublattice components), and is the interaction parameter between components (n can be 0, 1, or 2 to represent the order of the interaction parameter), and are the Curie temperature parameter and average atomic moment of the terminal component CN in the Fcc phase, respectively.

[0080] Step 2: Combined with the atomic-scale elastic isotropic strain energy theory, the elastic strain energy of the alloy system is obtained; based on the stacking fault theory, a stress-strain model of structural phase transition is established. The molar density expression of the elastic strain energy of the alloy system is as follows:

[0081]

[0082] in, is the parameter related to the molar density of elastic strain energy, V m is the molar volume, G S is the shear modulus, σ is Poisson's ratio, is the dependence of the crystal lattice parameters on the concentration, is the average mole fraction of solute hydrogen atoms between the Dhcp phase and the γ phase, where and are the mole fractions of hydrogen atoms in the γ phase and the Dhcp phase, respectively, and ω is the volume fraction of the γ phase.

[0083] Step 3: Obtain the total free energy of the system by superposing the chemical free energy volume density and elastic strain energy of the alloy system, solve the rate of decrease of the total free energy of the system, and construct the free energy dissipation term.

[0084] The total free energy F of the system is obtained by superposing the chemical free energy and elastic strain energy of the alloy system:

[0085]

[0086] Where r represents the volume integral, represents the total free energy of the Dhcp phase, represents the total free energy of the γ phase, is the mole fraction of hydrogen in the gas phase, Metal atom M=Nd. Note that elastic energy only exists in the solid phase. H and λ M They are the component conservation constraints and The Lagrange multiplier of λ0 is the phase fraction constraint φ Dhcp +φγ +φ G =1 Lagrange multiplier.

[0087] In step 3, according to the principle of maximum entropy production, it is necessary to calculate the rate of decrease of the total free energy of the system

[0088]

[0089] in

[0090] and

[0091] Because there are two dissipation mechanisms of the total Gibbs free energy, namely phase change and solute diffusion, the total Gibbs free energy dissipation term Q can be expressed according to the thermodynamic equilibrium condition:

[0092]

[0093] in It is the phase fraction mobility of Dhcp phase, γ phase and G phase; and are the solute atomic mobility in the Dhcp phase and γ phase, respectively.

[0094] Step 4: Based on the principle of maximum entropy production, a kinetic equation with phase fraction and composition as variables is established and the time derivatives of the phase fractions of the solid solution phase Dhcp, the precipitate phase γ, and the gas phase G, as well as the time derivatives of the mole fractions of hydrogen atoms in the precipitate phase γ and the solid solution phase Dhcp, are solved.

[0095] Step 4.1, according to the principle of maximum entropy generation, right and Perform variational calculus to establish kinetic equations with phase fraction and composition as variables;

[0096]

[0097]

[0098]

[0099]

[0100]

[0101] in are the time derivatives of the phase fractions of the solution phase Dhcp, the precipitated phase γ and the gas phase G, and are the time derivatives of the mole fractions of hydrogen atoms in the precipitated γ phase and the solid solution Dhcp phase, respectively;

[0102] Step 4.2, using the phase constraint and composition conservation conditions to solve the kinetic equation with phase fraction and composition as variables, we get:

[0103] According to the phase constraint φ Dhcp +φ γ +φ G =1, get;

[0104]

[0105]

[0106]

[0107] in

[0108]

[0109]

[0110]

[0111] They are the mobility of phase transition Dhcp→γ, the mobility of γ→G, and the mobility of G→Dhcp; Δf Dhcp ,γ , Δf γ,G , Δf G,Dhcp are the driving forces for phase transitions Dhcp→γ, γ→G, and G→Dhcp, respectively; and [x H ] Dhcp,γ 、[x H ] G,Dhcp 、[x H ] γ,G They are the differences between the two phase components Dhcp / γ, γ / G, and G / Dhcp, respectively. and in It is the difference between the self-consumption energy of the Dhcp / γ phase divided by the difference between the components of the Dhcp / γ phase. It is the difference between the self-consumption energy of the G / Dhcp phases divided by the difference between the components of the G / Dhcp phases.

[0112] Will and Substitute the composition conservation condition into the expression The Lagrange multiplier λ can be solved H -λ M The expression is:

[0113]

[0114] where the multiplier λ H -λ M For about A linear function of .

[0115] Further, we have and

[0116]

[0117]

[0118]

[0119]

[0120]

[0121] In step 4, the nucleation of Dhcp phase: In the system where γ / G phases coexist, if (Assuming φ Dhcp >0), it can be considered that Dhcp begins to nucleate, and φ Dhcp =1×10 -6 Substitute into the dynamic equation and solve;

[0122] In step 4, the disappearance of the Dhcp phase: if φ Dhcp =0, resulting in and At this point, the model completely degenerates into a γ / G two-phase transition, and the kinetic equation can be simplified to:

[0123]

[0124]

[0125]

[0126] in,

[0127] Step 5: Set appropriate physical parameters of the hydrogen storage alloy and input parameters of the simulation system, solve the kinetic equation, draw the PCT curve based on the solved data, and analyze the thermodynamic hysteresis evolution law of the PCT curve of the cyclic adsorption / desorption of hydrogen in the hydrogen storage alloy.

[0128] In step 5, appropriate physical parameters of the hydrogen storage alloy and input parameters of the simulation system are set to solve the kinetic equations. To plot the PCT curve, a constant temperature, T0, is first set. At the initial simulation moment, the system pressure is P0. At time t, the pressure is gradually increased to Pt or set according to experimental requirements. By solving the kinetic equations related to phase fraction and composition, the phase fraction and composition of each phase at each time t are obtained. Based on these solved data, a PCT curve is plotted, and the thermodynamic hysteresis evolution of the PCT curve for the cyclic adsorption / desorption of hydrogen in the hydrogen storage alloy is analyzed.

[0129] The CALPHAD method provided by the present invention can be applied to the following fields

[0130] 1. Design and optimization of hydrogen storage alloy materials: By predicting the PCT curves of different hydrogen storage alloy materials, their hydrogen storage performance can be evaluated and compared, providing important reference and guidance for material design and optimization.

[0131] 2. Performance evaluation of hydrogen storage materials: By predicting the PCT curve of hydrogen storage alloy materials, their hydrogen storage performance can be evaluated, thereby providing guidance for the application of hydrogen storage materials.

[0132] 3. Application research of hydrogen storage materials: By predicting the PCT curve of hydrogen storage alloy materials, we can study their application in hydrogen storage equipment and provide support and guidance for the development of hydrogen storage technology.

Claims

1. A CALPHAD method for predicting PCT curves of hydrogen storage alloys, characterized in that: The specific steps are as follows: Step 1: According to the CALPHAD method, the thermodynamic parameters of the hydrogen storage alloy are obtained to establish the thermodynamic description of the sub-lattice model of the solid solution phase, precipitation phase and gas phase, and the chemical free energy volume density of the alloy system is obtained; Step 2: Combined with the atomic-scale elastic isotropic strain energy theory, the elastic strain energy of the alloy system is obtained; In step 2, based on the stacking fault theory, a stress-strain model of structural phase transition is established. The elastic strain energy molar density expression of the alloy system is as follows: in is the parameter related to the molar density of elastic strain energy, V m is the molar volume, G S is the shear modulus, σ is Poisson's ratio, is the dependence of the crystal lattice parameters on the concentration, is the average mole fraction of solute hydrogen atoms between the Dhcp phase and the γ phase, where and are the mole fractions of hydrogen atoms in the γ phase and the Dhcp phase, respectively, and ω is the volume fraction of the γ phase; Step 3: Obtain the total free energy of the system by superposing the chemical free energy volume density and elastic strain energy of the alloy system, and calculate the rate of decrease of the total free energy of the system; at the same time, construct the free energy dissipation term; Step 4: Establish a kinetic equation with phase fraction and composition as variables, and solve the derivative of the phase fraction with respect to time and the derivative of the mole fraction of hydrogen atoms in the phase with respect to time; Step 4: Step 4.1: Establish the kinetic equation with phase fraction and composition as variables; The kinetic equation in step 4.1 with phase fraction and composition as variables is: in, are the time derivatives of the phase fractions of the solution phase Dhcp, the precipitated phase γ and the gas phase G, and are the time derivatives of the mole fractions of hydrogen atoms in the precipitated γ phase and the solid solution Dhcp phase, respectively; Step 4.2: Use phase constraints and composition conservation conditions to solve the kinetic equations with phase fraction and composition as variables; The phase constraint in step 4.2 is: Dhcp +φ γ +φ G =1; the composition conservation condition is: Solving the kinetic equations yields and for: Where, They are the mobility of phase transition Dhcp→γ, the mobility of γ→G, and the mobility of G→Dhcp, and are the differences between the two phase components Dhcp / γ, γ / G, and G / Dhcp, respectively; and in It is the difference between the self-consumption energy of the Dhcp / γ phase divided by the difference between the components of the Dhcp / γ phase. It is the difference between the self-consumption energy of the G / Dhcp phase and the difference between the components of the G / Dhcp phase; Step 5: Set appropriate physical parameters of the hydrogen storage alloy and input parameters of the simulation system, solve the kinetic equation, draw the PCT curve based on the solved data, and analyze the thermodynamic hysteresis evolution law of the PCT curve of the cyclic adsorption / desorption of hydrogen in the hydrogen storage alloy.

2. The CALPHAD method for predicting the PCT curve of hydrogen storage alloys according to claim 1, characterized in that: The specific steps of step 1 are: Step 1.1, obtain the thermodynamic parameters of the hydrogen storage alloy according to the CALPHAD method, and then establish a sublattice model of the complex phase structure; Step 1.2: Establish the bulk free energy volume density of the Nd-H alloy.

3. The CALPHAD method for predicting the PCT curve of hydrogen storage alloys according to claim 2, characterized in that: The free energy volume density of the alloy established in step 1.2 is as follows: Among them, φ Dhcp is the phase fraction of the solid solution phase Dhcp, φ γ is the phase fraction of the precipitated phase γ, φ G is the G phase fraction of the gas phase; and f G (T, P) are the chemical free energy molar densities of Nd1(H, Va)2, which are the solid solution phase Dhcp, the precipitation phase γ and the gas phase G, respectively. V m is the molar volume.

4. The CALPHAD method for predicting the PCT curve of hydrogen storage alloys according to claim 3, characterized in that: Chemical free energy molar density of solid solution phase Dhcp for: Chemical free energy molar density of precipitated phase γ for: Chemical free energy molar density f of the gas phase G G (T,P) is: Where Nd represents metal atom, H represents hydrogen atom, and T is temperature. are the occupancy rates of hydrogen atoms and holes in the Dhcp phase and the γ phase, respectively. The thermodynamic model of the Dhcp phase and the γ phase is Nd1(H,Va)2, where the Nd element occupies the position of lattice 1, and the H element and the hole Va occupy the position of lattice 2. The atomic occupancy rate and the concentration mole fraction in the Dhcp phase and the γ phase are coupled to obtain: and are the formation enthalpies of NdH2 and NdVa2 in the Dhcp phase and γ phase, respectively, is the formation enthalpy of H2 in the Gas phase.

5. The CALPHAD method for predicting the PCT curve of hydrogen storage alloys according to claim 1, characterized in that: In step 3, the total free energy F of the system is obtained by superimposing the chemical free energy and elastic strain energy of the alloy system: Where r represents the volume integral, represents the total free energy of the Dhcp phase, represents the total free energy of the γ phase, Metal atom M = Nd; λ H and λ M They are the component conservation constraints and Lagrange multiplier of ;λ0 is the phase fraction constraint φ Dhcp +φ γ +φ G =1 Lagrange multiplier; In step 3, according to the principle of maximum entropy production, it is necessary to calculate the rate of decrease of the total free energy of the system in and 6. The CALPHAD method for predicting the PCT curve of hydrogen storage alloys according to claim 1, characterized in that: The free energy dissipation term Q in step 3 is: in It is the phase fraction mobility of Dhcp phase, γ phase and G phase; and are the solute atomic mobility in the Dhcp phase and γ phase, respectively.

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