A VASP-based method for evaluating hydrogen diffusion in TiFe grain boundary alloying
Patent Information
- Application Number
- CN202611136898.4
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-07-29
- Publication Date
- 2026-09-29
AI Technical Summary
[0007]本申请提出了一种基于VASP的TiFe晶界合金化氢扩散评价方法，旨在解决现有评价方法难以排除表面吸附、体扩散及组织缺陷等多因素耦合影响，无法在原子尺度定量评价不同合金元素偏析对TiFe晶界H原子扩散路径、迁移能垒及扩散能力影响的技术问题
（1）本申请通过构建合金元素偏析的TiFe晶界模型，并确定H原子的稳定间隙位置，能够排除表面状态、相组成和体相扩散等因素干扰，实现对特定晶界处H原子扩散行为的独立评价。
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Abstract
Description
Technical Field
[0001] This application belongs to the field of simulation computing, and more specifically, relates to a method for evaluating hydrogen diffusion in TiFe grain boundary alloying based on VASP (Vienna Ab-initioSimulation Package). Background Technology
[0002] TiFe-based hydrogen storage alloys are considered promising solid-state hydrogen storage materials due to their advantages such as high hydrogen storage capacity, low cost, abundant resources, and near-room temperature operation. They can be applied in hydrogen energy storage and transportation, hydrogen compressors, and fuel cell-related hydrogen storage systems. However, traditional TiFe alloys still suffer from difficulties in initial activation, slow hydrogen adsorption / desorption kinetics, and sensitivity to impurity gases, limiting their engineering applications. Existing research has shown that introducing alloying elements such as Co, Cr, Ni, V, and Zn can alter the local crystal structure, electronic structure, and defect states of TiFe alloys, thereby affecting the adsorption, diffusion, and trapping behavior of H atoms.
[0003] In polycrystalline TiFe alloys, grain boundary regions possess high free volume and distortion, making them crucial areas for the rapid diffusion, segregation, and trapping of hydrogen atoms. Segregation of alloying elements at grain boundaries further alters the local electronic structure and atomic environment, significantly impacting the transgrain boundary diffusion capability of hydrogen atoms. Therefore, establishing a method to quantitatively evaluate the influence of different alloying elements on the hydrogen diffusion behavior at TiFe grain boundaries at the atomic scale is of great significance for understanding the hydrogen storage kinetics mechanism of TiFe alloys and guiding alloy composition design.
[0004] While existing experimental methods can characterize the macroscopic hydrogen absorption and desorption kinetics of TiFe alloys, they are difficult to directly distinguish the effects of different alloying elements on the diffusion barrier, diffusion coefficient, and electronic structure of H atoms in specific grain boundary structures.
[0005] The aforementioned technical problems stem from the complex and highly non-uniform local atomic structure of TiFe alloy grain boundaries. After segregation at grain boundaries, alloying elements not only alter the local lattice configuration and electronic structure but also cause synergistic changes in H atom occupancy, diffusion paths, and migration barriers. Existing experimental techniques typically only obtain the overall hydrogen absorption / desorption kinetics or average diffusion performance of the material, failing to directly analyze the cross-grain boundary diffusion process of H atoms. Furthermore, it is difficult to isolate the coupling effects of grain boundary diffusion with surface adsorption, bulk diffusion, crystal defects, and second phases. Therefore, a method for quantitatively evaluating the ability of different alloying elements to regulate H diffusion at TiFe grain boundaries at the atomic scale is currently lacking, thus limiting grain boundary engineering and alloy composition optimization design of TiFe hydrogen storage alloys.
[0006] Therefore, it is necessary to propose a method based on first-principles calculations and CI-NEB path search to systematically evaluate the diffusion capability of H atoms at TiFe grain boundaries after alloy element segregation. Summary of the Invention
[0007] This application proposes a VASP-based evaluation method for hydrogen diffusion in TiFe grain boundary alloying, aiming to solve the technical problem that existing evaluation methods cannot eliminate the coupled influence of multiple factors such as surface adsorption, bulk diffusion, and microstructural defects, and cannot quantitatively evaluate the influence of segregation of different alloying elements on the diffusion path, migration barrier, and diffusion capacity of H atoms in TiFe grain boundaries at the atomic scale.
[0008] This application achieves a quantitative evaluation of the ability of different alloying elements to regulate H diffusion at TiFe grain boundaries by constructing a TiFe grain boundary model, introducing alloying element segregation, determining the stable interstitial positions of H atoms, calculating the H atom diffusion barrier across grain boundaries using the CI-NEB method, and further calculating the diffusion coefficient using the Arrhenius formula.
[0009] This application provides a VASP-based method for evaluating hydrogen diffusion in TiFe grain boundary alloying, comprising the following steps: S1 constructs a TiFe grain boundary model with a clear grain boundary orientation and atomic structure based on the coincident site lattice theory; S2 sets multiple candidate H atom interstitial positions near the grain boundaries of the pure TiFe grain boundary model and the TiFe-X grain boundary model, and performs geometric optimization on each H-containing configuration; Based on the initial and final states of H atoms determined in step S2, S3 inserts several intermediate configurations between them and optimizes them using the CI-NEB method to obtain the lowest energy path for H atoms to migrate across or along grain boundaries. S4 calculates the diffusion coefficient of H atoms and evaluates the control effect of alloying elements.
[0010] Furthermore, the TiFe grain boundary model includes Σ3 (111) grain boundaries and sets a sufficient number of atomic layers along the grain boundary normal to reduce the interaction between adjacent grain boundaries under periodic boundary conditions.
[0011] Furthermore, in step S2, by comparing the total energy of different configurations, the stable interstitial positions of H atoms in the grain boundary region are determined, and two adjacent stable positions are selected as the initial and final states of H atom diffusion.
[0012] Furthermore, in step S3, by comparing the diffusion energy barriers of pure TiFe and different TiFe-X grain boundary models, the promoting or inhibiting effect of alloying elements on H atom diffusion can be determined. The diffusion barrier is the difference between the highest energy in the diffusion path and the initial energy.
[0013] Furthermore, if the diffusion barrier is lowered, it indicates that the alloying element is conducive to the migration of H atoms; if the diffusion barrier is higher, it indicates that it inhibits the diffusion of H atoms or enhances the H trapping effect.
[0014] Furthermore, in step S4, based on the H atom diffusion energy barrier obtained in step S3, the diffusion coefficient of H atoms at different temperatures is calculated in combination with diffusion distance, atomic vibration frequency, Boltzmann constant and thermodynamic temperature.
[0015] Furthermore, based on the transition state theory, the pre-diffusion factor is determined according to the jumping distance, jumping dimension and vibration frequency of H atoms, thereby obtaining the relationship curve of H atom diffusion coefficient with temperature in different TiFe-X grain boundary models.
[0016] Furthermore, the diffusion coefficient of H atoms at different temperatures ν is the atomic vibration frequency. k B Boltzmann's constant, T Thermodynamic temperature D 0 represents the pre-diffusion factor.
[0017] Compared with traditional experimental evaluation methods, this application has the following advantages: (1) By constructing a TiFe grain boundary model of alloy element segregation and determining the stable interstitial position of H atoms, this application can eliminate the interference of factors such as surface state, phase composition and bulk diffusion, and achieve independent evaluation of H atom diffusion behavior at specific grain boundaries.
[0018] (2) This application uses the CI-NEB method to obtain the minimum energy path and diffusion barrier for H atom migration across grain boundaries, and calculates the diffusion coefficient at different temperatures in combination with the Arrhenius relation, thereby quantitatively comparing the promoting or inhibiting effects of different alloying elements on the H atom grain boundary transport capability.
[0019] (3) This application combines charge density and density of states analysis to reveal the mechanism by which alloying elements change the localization degree of H atoms and diffusion barrier from the perspective of electronic structure, thereby quickly screening alloying elements that are conducive to H diffusion or H capture, and providing a theoretical basis for the composition design of TiFe hydrogen storage alloy. Attached Figure Description
[0020] Figure 1 This is a schematic diagram of the atomic model structure of the TiFe alloy ∑3(111)[1-10] grain boundary provided in this application; Figure 2 This application provides the diffusion barrier of H atoms at the Σ3(111)
[110] grain boundary in the TiFe and TiFe–Co systems; Figure 3This is the diffusion coefficient of H atoms at the Σ3(111)
[110] grain boundary in the TiFe and TiFe–Co systems provided in this application; Figure 4 This application provides the diffusion barrier of H atoms at the Σ3(111)
[110] grain boundary in the TiFe and TiFe–Cr systems; Figure 5 This is the diffusion coefficient of H atoms at the Σ3(111)
[110] grain boundary in the TiFe and TiFe–Cr systems provided in this application; Figure 6 This application provides the diffusion barrier of H atoms at the Σ3(111)
[110] grain boundary in the TiFe and TiFe–Ni systems; Figure 7 This is the diffusion coefficient of H atoms at the Σ3(111)
[110] grain boundary in the TiFe and TiFe–Ni systems provided in this application; Figure 8 This application provides the diffusion barrier of H atoms at the Σ3(111)
[110] grain boundary in the TiFe and TiFe–V systems; Figure 9 This is the diffusion coefficient of H atoms at the Σ3(111)
[110] grain boundary in the TiFe and TiFe–V systems provided in this application; Figure 10 This application provides the diffusion barrier of H atoms at the Σ3(111)
[110] grain boundary in the TiFe and TiFe–Zn systems; Figure 11 It is the diffusion coefficient of H atoms at the grain boundary of Σ3(111)
[110] in the TiFe and TiFe–Zn systems provided in this application. Detailed Implementation
[0021] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.
[0022] The core idea of this application is as follows: First, a typical grain boundary model of TiFe alloy is constructed, such as Σ3(111) grain boundary; then, alloying elements such as Co, Cr, Ni, V, and Zn replace Fe sites near the grain boundary to simulate the segregation state of alloying elements at the grain boundary; subsequently, H atoms are arranged near the grain boundary to determine the initial and final stable interstitial positions of H atoms; further, the CI-NEB method is used to calculate the diffusion barrier that H atoms need to overcome during the migration from the initial state to the final state; finally, the diffusion coefficient of H atoms is calculated based on parameters such as diffusion barrier, diffusion distance, and temperature, and the electronic structure mechanism of alloying elements affecting H diffusion is revealed by combining charge density or density of states analysis. This calculation process can be used to screen alloying elements that promote or inhibit H atom diffusion at grain boundaries.
[0023] The method proposed in this application for evaluating the influence of alloying elements on the diffusion ability of H atoms at TiFe grain boundaries based on VASP first-principles calculations specifically includes the following steps: S1 constructs a TiFe grain boundary model for alloy element segregation: A TiFe grain boundary model with a clear grain boundary orientation and atomic structure is constructed based on the coincident site lattice theory, including but not limited to Σ3(111) grain boundaries. Sufficient atomic layers are set along the grain boundary normal to reduce the interaction between adjacent grain boundaries under periodic boundary conditions. After geometric optimization of the grain boundary model, Ti and Fe sites near the grain boundary are replaced by the alloying element X to be evaluated, where X is one or more of Co, Cr, Ni, V, and Zn. The preferred occupancy sites of the alloying element are determined by comparing the formation energies of different replacement models. If necessary, the segregation energy between the grain boundary region and the bulk phase region can be further calculated to determine the tendency of the alloying element to segregate to the grain boundary. This step is used to establish a TiFe-X grain boundary model with a reasonable alloying element occupancy state, avoiding model distortion caused by arbitrary setting of replacement sites, and providing a reliable structural basis for subsequent calculation of stable H atom occupancy and diffusion path.
[0024] S2 determines the stable interstitial positions of the H atoms: Multiple candidate H atom interstitial sites were set near the grain boundaries in both the pure TiFe grain boundary model and the TiFe-X grain boundary model, and the geometry of each H-containing configuration was optimized. By comparing the total energy of different configurations, the stable interstitial sites of H atoms in the grain boundary region were determined, and two adjacent stable sites were selected as the initial and final states of H atom diffusion. Due to the inhomogeneity of atomic arrangement and local chemical environment in the grain boundary region, and the segregation of alloying elements, the stable occupancy of H atoms can also be altered; therefore, it is necessary to screen the candidate sites. This step ensures that both the initial and final states of diffusion are energy-stable structures with practical physical significance, avoiding calculation errors caused by unreasonable selection of diffusion endpoints.
[0025] S3 uses the CI-NEB method to calculate the diffusion barrier of H atoms: Based on the initial and final states of H atoms determined in step S2, several intermediate configurations are inserted between them, and the CI-NEB method is used for optimization to obtain the lowest energy path for H atoms to migrate across or along grain boundaries. The difference between the highest energy in the diffusion path and the initial state energy is defined as the diffusion barrier (Ea). By comparing the diffusion barriers of pure TiFe and different TiFe-X grain boundary models, the promoting or inhibiting effect of alloying elements on H atom diffusion can be determined. If the diffusion barrier (Ea) decreases, it indicates that the alloying element is conducive to H atom migration; if the diffusion barrier (Ea) increases, it indicates that it inhibits H atom diffusion or enhances H trapping. This step can directly obtain the migration path, transition state, and energy barrier of H atoms, which is more accurate than judging diffusion ability solely based on adsorption energy or stable configuration energy.
[0026] S4 calculates the diffusion coefficient of hydrogen atoms and evaluates the effect of alloying elements on their control: Based on the H atom diffusion barrier (Ea) obtained in step S3, combined with the diffusion distance (l), atomic vibration frequency (ν), and Boltzmann constant (…), k B The diffusion coefficient (D) of H atoms at different temperatures was calculated using the Arrhenius relation, given the thermodynamic temperature (T) and the diffusion coefficient (D) of H atoms at different temperatures. E a Let kB and T represent the diffusion barrier, respectively, and kB be the Boltzmann constant and the absolute temperature. B =1.38×10 -23 J.K. -1 According to transition state theory, the expression for the transition rate of atoms in a solid is: In the formula ν The value of represents the vibrational frequency of the atom, and the diffusion coefficient can be expressed as: ;in, l This indicates the diffusion distance of each atom.
[0027] By substituting diffusion distance, diffusion barrier, and vibrational frequency into appropriate formulas, the relationship between diffusion coefficient and temperature under different vacancy concentrations can be derived. Furthermore, based on transition state theory, the pre-diffusion factor can be determined according to the jump distance, jump dimension, and vibrational frequency of H atoms, thereby obtaining the relationship curves of H atom diffusion coefficient versus temperature in different TiFe-X grain boundary models. Since the diffusion barrier is an atomic-scale energy parameter, it is difficult to directly reflect the change in H atom transport rate under actual temperature conditions. This step converts the diffusion barrier into a temperature-dependent diffusion coefficient, enabling quantitative comparison of the effects of different alloying elements within the same temperature range. By comparing the diffusion coefficients of various TiFe-X grain boundary models, the ability of different alloying elements to promote or inhibit H atom grain boundary diffusion can be ranked, providing a quantitative basis for the selection of alloying elements and composition design in TiFe hydrogen storage alloys.
[0028] To further illustrate this application, it is now described in detail below with reference to specific embodiments: Example 1: Evaluation of H atom diffusion capability in a Co segregated TiFe grain boundary model A TiFe-Co grain boundary model was constructed according to the method described in this application to determine the stable initial and final states of H atom diffusion, and the minimum energy migration path of H atoms was calculated using the CI-NEB method. Figure 2 and Figure 3 As shown, in the Σ3(111) grain boundary, the diffusion barrier of H atoms in the undoped TiFe model is 1.260 eV, and the diffusion barrier in the TiFe-Co model is 1.095 eV. Co segregation reduces the diffusion barrier by 0.165 eV and increases the diffusion coefficient accordingly, indicating that Co can reduce the energy barrier that H atoms need to overcome to migrate across the Σ3(111) grain boundary and promote the transport of H atoms in this grain boundary region. In the Σ5(310) grain boundary, the diffusion barrier of H atoms in the TiFe-Co model is 1.149 eV, which is close to that of the undoped TiFe and other element segregation models, indicating that the influence of Co on the H diffusion behavior of this grain boundary is relatively limited, and the migration of H atoms is mainly controlled by the geometry of the Σ5(310) grain boundary.
[0029] This embodiment demonstrates that the present application can quantitatively identify the differences in the role of Co in different grain boundary structures, avoid the mechanism confusion caused by judging the role of Co solely based on macroscopic hydrogen absorption and desorption results, and screen out alloying elements that are beneficial to promoting H transport at TiFe grain boundaries.
[0030] Example 2: Evaluation of H atom diffusion capability in a Cr segregated TiFe grain boundary model A TiFe-Cr grain boundary model was constructed according to the method described in this application, and the diffusion paths, diffusion barriers, and diffusion coefficients of H atoms in different grain boundaries were calculated. Figure 4 and Figure 5 As shown, in the Σ3(111) grain boundary, the H atom diffusion barrier of the TiFe-Cr model is 1.822 eV, which is significantly higher than the 1.260 eV of undoped TiFe, and the corresponding diffusion coefficient is significantly reduced. This result indicates that Cr segregation increases the energy barrier that H atoms need to overcome to migrate across the grain boundary, inhibits H atom diffusion, and may enhance the trapping effect of the grain boundary region on H atoms. In the Σ5(310) grain boundary, the H atom diffusion barrier of the TiFe-Cr model is 1.134 eV, which is close to that of the undoped TiFe and other element segregation models, indicating that H diffusion in this grain boundary is mainly controlled by the grain boundary geometry, and the regulatory effect of Cr is relatively weak.
[0031] This embodiment demonstrates that this application can not only screen alloying elements that promote H diffusion, but also identify alloying elements that may form hydrogen traps and inhibit H transport, thereby achieving a quantitative evaluation of the direction and degree of action of different alloying elements.
[0032] Example 3: Evaluation of H atom diffusion capability in a Ni segregated TiFe grain boundary model A TiFe-Ni grain boundary model was constructed according to the method described in this application to determine the stable diffusion endpoints of H atoms, and the lowest energy diffusion path of H atoms was obtained using the CI-NEB method. Figure 6 and Figure 7 As shown, in the Σ3(111) grain boundary, the H atom diffusion barrier of the TiFe-Ni model is 1.053 eV, lower than the 1.260 eV of undoped TiFe, and the corresponding diffusion coefficient is increased. This result indicates that Ni segregation can reduce the migration barrier of H atoms, which is beneficial to the formation of fast H atom diffusion channels in the Σ3(111) grain boundary region. In the Σ5(310) grain boundary, the H atom diffusion barrier of the TiFe-Ni model is 1.182 eV, which is close to that of the undoped TiFe and other element segregation models, indicating that H atom diffusion in this grain boundary is still mainly affected by the grain boundary geometry.
[0033] This embodiment demonstrates that the present application can quantitatively characterize the promoting effect of alloying elements by diffusion energy barrier and diffusion coefficient, and can further compare the promoting effects of elements such as Ni and Co, providing a basis for screening fast-diffusion alloying elements in TiFe hydrogen storage alloys.
[0034] Example 4: Evaluation of H atom diffusion capability in the V-segregated TiFe grain boundary model A TiFe-V grain boundary model was constructed according to the method described in this application, and the stable occupancy of H atoms, diffusion paths, diffusion barriers, and diffusion coefficients were calculated. Figure 8 and Figure 9 As shown, in the Σ3(111) grain boundary, the H atom diffusion barrier of the TiFe-V model is 2.232 eV, significantly higher than the 1.260 eV of undoped TiFe, and the corresponding diffusion coefficient decreases significantly within the same temperature range. This result indicates that V segregation significantly enhances the localization of H atoms, forming strong H trapping sites in the grain boundary region, thereby inhibiting H atom migration across the grain boundary. In the Σ5(310) grain boundary, the H atom diffusion barrier of the TiFe-V model is 1.161 eV, which is close to that of the undoped TiFe and other element segregation models, indicating that V has little influence on the H diffusion behavior of this grain boundary, and the diffusion process is mainly controlled by the grain boundary structure.
[0035] This embodiment demonstrates that the present application can identify alloying elements that have a strong trapping effect on H atoms, and quantify their degree of suppression through specific diffusion barriers and diffusion coefficients, providing a basis for the design of alloy compositions that need to enhance H trapping or avoid excessive H localization.
[0036] Example 5: Evaluation of H atom diffusion capability in a Zn segregated TiFe grain boundary model A TiFe-Zn grain boundary model was constructed according to the method described in this application, and the diffusion behavior of H atoms in Σ3(111) and Σ5(310) grain boundaries was calculated. Figure 10 and Figure 11 As shown, in the Σ3(111) grain boundary, the H atom diffusion barrier of the TiFe-Zn model is 1.565 eV, which is higher than the 1.260 eV of undoped TiFe, and the corresponding diffusion coefficient is reduced. This result indicates that Zn segregation increases the migration energy barrier of H atoms, which has a certain inhibitory effect on the diffusion of H atoms across the Σ3(111) grain boundary, but its inhibitory effect is lower than that of Cr and V. In the Σ5(310) grain boundary, the H atom diffusion barrier of the TiFe-Zn model is 1.108 eV, which is close to that of the undoped TiFe and other element segregation models, indicating that the H atom diffusion in this grain boundary is mainly controlled by the grain boundary geometry.
[0037] This embodiment demonstrates that the present application can further distinguish the differences in the degree of influence of different inhibitory alloying elements on the diffusion ability of H atoms, and realize the quantitative ranking of the control effect of alloying elements, rather than just making a qualitative judgment of promotion or inhibition.
[0038] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the scope of protection of this application.
Claims
1. A method for evaluating hydrogen diffusion in TiFe grain boundary alloying based on VASP, characterized in that, Includes the following steps: S1 constructs a TiFe grain boundary model with a clear grain boundary orientation and atomic structure based on the coincident site lattice theory; S2 sets multiple candidate H atom interstitial positions near the grain boundaries of the pure TiFe grain boundary model and the TiFe-X grain boundary model, and performs geometric optimization on each H-containing configuration; Based on the initial and final states of H atoms determined in step S2, S3 inserts several intermediate configurations between them and optimizes them using the CI-NEB method to obtain the lowest energy path for H atoms to migrate across or along grain boundaries. S4 calculates the diffusion coefficient of H atoms and evaluates the control effect of alloying elements.
2. The method for evaluating hydrogen diffusion in TiFe grain boundary alloying as described in claim 1, characterized in that, The TiFe grain boundary model includes Σ3 (111) grain boundaries and sets a sufficient number of atomic layers along the grain boundary normal to reduce the interaction between adjacent grain boundaries under periodic boundary conditions.
3. The method for evaluating hydrogen diffusion in TiFe grain boundary alloying as described in claim 1, characterized in that, In step S2, by comparing the total energy of different configurations, the stable interstitial positions of H atoms in the grain boundary region are determined, and two adjacent stable positions are selected as the initial and final states of H atom diffusion.
4. The method for evaluating hydrogen diffusion in TiFe grain boundary alloying as described in claim 1, characterized in that, In step S3, by comparing the diffusion energy barriers of pure TiFe and different TiFe-X grain boundary models, the promoting or inhibiting effect of alloying elements on H atom diffusion can be determined. The diffusion barrier is the difference between the highest energy in the diffusion path and the initial energy.
5. The method for evaluating hydrogen diffusion in TiFe grain boundary alloying as described in claim 4, characterized in that, If the diffusion barrier decreases, it indicates that the alloying element is conducive to the migration of H atoms; if the diffusion barrier increases, it indicates that it inhibits the diffusion of H atoms or enhances the H trapping effect.
6. The method for evaluating hydrogen diffusion in TiFe grain boundary alloying as described in any one of claims 1-5, characterized in that, In step S4, based on the diffusion barrier of H atoms obtained in step S3, the diffusion coefficient of H atoms at different temperatures is calculated in combination with diffusion distance, atomic vibration frequency, Boltzmann constant and thermodynamic temperature.
7. The method for evaluating hydrogen diffusion in TiFe grain boundary alloying as described in claim 6, characterized in that, Based on the transition state theory, the pre-diffusion factor is determined according to the jumping distance, jumping dimension and vibration frequency of H atoms, thereby obtaining the relationship curve of H atom diffusion coefficient with temperature in different TiFe-X grain boundary models.
8. The method for evaluating hydrogen diffusion in TiFe grain boundary alloying as described in claim 6, characterized in that, The diffusion coefficient of H atoms at different temperatures ν is the atomic vibration frequency. k B Boltzmann's constant, T Thermodynamic temperature D 0 represents the pre-diffusion factor.