Cathode Materials Design Lab
Contents
- 1 Introduction
- 2 User Manual : Lobby
- 3 User Manual : Working Studio
- 3.1 How to create the cathode material
- 3.2 How to Analyze Cathode Material
- 3.3 How to create the surface model of cathode material
- 3.4 Infromatics
- 4 Technical Information
- 5 Contact
- 6 Connection to Other Documents
Introduction
Status bar
Both lobby and working-studio pages in the lab have common status bar on the top. It contains the buttons for lobby and working studio . It also shows the present user ID (e-mail address) and the present project name in bold with login time (In this example, krlee@kist.re.kr in project "3rd year demo" (20-15-09-15 10:59:01)
). On the right corner of the status bar are the help button to see this document and the job status button that shows the present status of on-going jobs in this lab.
How to use the module
User Manual : Lobby
When you first come the the cathode materials design lab, you are in lobby. This is the default setting of the lab.
You can go to working studio anytime by clicking the working studio button in the status bar.
You can come to lobby anytime by clicking the lobby button in the status bar.
Lobby has two sections:
- Visualization Window to show the atomic structure of Cathode or the final configuration of the job.
- Results Table to list the Cathode you have worked in the present project.
Visualization Window
On the left of the lobby is the visualization window that shows the atomic structure or final configuration of the job. Cathode structure (final configuration of the job) is displayed depending on your selection in the Results table (Job table). Color of atom in this visualization is based on the CPK coloring convention. However, slight modification is applied for better distinction. See color of atom page for the color list.
Number of mouse action can be used to change the visualization.
- Scrolling the center wheel to zoom in & zoom out
- Drag with left button to change the viewing angle
- Drag with right button to move the image
You can take the snapshot of the image of the visualization window by using the camera button on the right upper corner, . As you click the camera button, new window with the sanpshot opens. Every snapshot appears in separate windows so that the user can compare the images. The snapshot image can be stored as a file that can be used later for the user's purpose. In order to save the image, place the cursor on the snapshot image then right click to invoke the menu of Chrome browser.
Results Table
All jobs you and your colleagues have done are listed on the Results Table. Data is generated when the user executes calculation in the working studio.
- Owner : Name of the user
- U/R/A : It shows whether the job is 'unrelaxed' or 'relaxed' status. If you execute advance calculation for analysis, it will be turn into 'advanced' status.
- Job Name : Name of the job
- : This button is to delete the cathode job
The results data can be filtered by many factors. To filter the data, click the title of the list that you want to filter with. Then the filtering box will be shown. choose the condition and type the value. Click the Apply
to apply. Multiple filters can be applied in once. See the example below.
To send the works from Results Table to Working Studio, just click the checkbox of the works and move on to Working Studio.
User Manual : Working Studio
Working studio in the Cathode section consists of 6 sub parts
In the Working studio, you can design and simulate the cathode material as your choice
- Crystal builder : Generating the crystal structure of cathode material
- Visualization : Showing the atomic structure of crystal structure made in Crystal builder
- High Throughput Calculation : Calculating the stoichiometric chemical formula from the atomic structure
- Results : Showing the calculated results
- Analysis : Simulating the cathode material through the various method
- Informatics: Enumerating the information of cathode material
How to create the cathode material
In Cathode section, you can build the crystal structure and simulate the the crystal structure to analyze the cathode material
Build the crystal structure of cathode material
To create the cathode material, first click the button on the Lobby page
- In the Working studio page,you can design cathode material
- In the working studio page, you can create crystal structure of cathode
- On the crystal builder window, you can enter specific crystal information of cathode material you want to simulate
- LiCoO2 is the one of the typical cathode material. LiCoO2 is R-3m, O3 type structure and has being used as cathode material. you also load the CIF information to build the cathode material. The atomic information of LiCoO2 is entered in crystal_builder window and then click the
Generate
button
- And then, Working studio show the atomic information and cell information of LiCoO2
- In the middle of the working studio page, there is a visualization window that show the atomic structure you built right before
- Visualization window provide the atomic structure viewer. Color of atom is based on the CPK coloring convention, with slight modification for better distinction. See color of atom page for the color list.
- If you click the button, you will see the plane of the crystal structure perpendicular to x,y,z axis and brief cell information
- In the working studio page, there are High Throughput Calculation window
- If you just use the crystal structure entering the input on the crystal builder window, click the
Enumerate
button
- Then, possible stoichiometric composition come out
- You can save the structure by entering the Job name box and then you also calculate by clicking the
Calculate
button
- After clicking the
Calculate
button, results come out on the Result window
Doping from the crystal structure
To dope the initial atom to the other atoms, you should first create the crystal structure as like before Build crystal structure section
- From the LiCoO2 crystal structure, there are each atom on the Visualization window. You can click the atom(Selected atom) you want to dope to the other atom(Target element) and then the selected atom automatically come out beside Selected atoms(s). You can also select more than one atom
- After that, you can enter doping atom in the Target element(s) box and then click the
Enumerate
button. (X is for empty space)
- Then, possible stoichiometric composition come out
- You can save the structure by entering the Job name box and then you also calculate by clicking the
Calculate
button
- After clicking the
Calculation
button, results with initial stoichiometric composition and doped stoichiometric composition come out on the Result window
How to Analyze Cathode Material
To Analyze the Cathode Material, you should first complete Design Cathode Materials process and should first simulate
- There are Analysis window on the Working studio page
- You can simulate Relaxation,Diffusion,Voltage,Free Energy,Phase and Density of States from the crystal structure already created
Relaxation
To Relax the crystal structure, you should first calculate the structure like before Design Cathode Materials section
- On the Analysis window, click the button and then click the
확 인
. Then Relaxation process will progress
- After the Relaxation, then Results window change the status from Unrelaxed to Relaxed
Diffusion by NEB
To Diffuse the crystal structure, you should first calculate the structure like before Design Cathode Materials section
- You can confirm the relaxed cathode information, which are Material name, diffusion path and caculation status
- Then you can select the atom that you want to move by clicking
select
and then clicking the atom
- Then you can select the atom which is destination by clicking
select
and then clicking the atom's destination - After that, you shoud click the
Simulate
to caculate Diffusion by NEB
- After the calculation end, the energy barrier and diffusion path is shown on the window
Potential
To calculate Potential, you should first relax the structure like before Relaxation section
- On the Analysis window, click the button and then you can confirm the Potential figure on the Delithiation Potential window
Free energy
To calculate Free energy, you should first relax the structure like before Relaxation section
- On the Analysis window, click the button and then you can confirm the Free energy figure on the Free Energy window
Diffusivity of Li by molecular dynamics (MD) simulation
To compute diffusivity of Li ion in cathode materials, one should first calculate the structure as in the Design Cathode Materials section.
- Mean square displacement: The mobility of atoms can be described by the mean square displacement (MSD).
- Diffusivity: The diffusivity (or diffusion coefficient) D, can be determined from the MSD by the Einstine relation.
- On the Analysis window, click the button and then input temperature (K) and time (ps) for molecular dynamics (MD) simulation.
- The mean square displacement (MSD) is computed for a half MD simulation time (see 4.3). A simulation time greater than 100 ps is recommended for the computation of MSD.
- Click the simulate button to start the molecular dynamics simulation. The sample is automatically duplicated along the x, y and z axis to reach a box size greater than 24 Å (the minimum size for the present simulation technique). The number of atoms in those samples is 1,000~2,000, and the computing would take 2~3 days for a simulation time of 200 ps.
- When the MD simulation is completed, the jobs are listed in a table. Click the job to plot the MSD curve in the graph, and Drag your mouse to the region you want to compute diffusivity by the slope.
Phase field
By clicking the phase field button , new window for phase field model opens.
User interface
User interface of phase field model divided into two window, input status window and result window.
Input status window
- Material properties obtained from DFT data.
- Process : Selection of discharge and charge process.
- Geometry : The structure modeling for job. Cubic, Cylinder, Sphere, Polyhedron, and Hexagonal plate structures are available. A user could apply porosity for each structure.
- Porosity : User could select even and uneven distribution of pores. Selectable porosities are 0, 10, 20, 30, 40, and 50 %.
- C-rate : Charge rate, charge or discharge rate equal to the capacity of a battery in one hour. When high c-rate condition set, discharge process ended in short time.
- Time : The time user wants for the job. When discharge process is finished, job could end even the set time is not reached.
< Geometry model detail >
Cylinder : Select radius and length
Polyhedron : Select circumscribed sphere radius
Hexagonal plate : Select length
Phase field model input example
Process: Charge
Geometry: Sphere with 250 nm radius, 30% porosity, evenly distributed
Charge/discharge rate: 2 c-rate
1. Select charge process
2. Select sphere with 250 nm radius
3. Select evenly distributed, 30% porosity
4. Select 2 c-rate
5. Enter job name and click simulation button
Result window
By clicking left top button of the result window, user could change result window into [Li fraction], [Phase distribution],[Temperature] and [2d plot]
[Li fraction], [Phase distribution] and [Temperature]
On the left of the result window is the visualization window that shows the Li-ion fraction or phase distribution or temperature of the job.
On the right of the result window, 2 dimensional slice plane visualized. Position and direction of slice plane could be changed by button xy, yz, zx and scroll bar.
Number of mouse action can be used to change the visualization.
- Scrolling the center wheel to zoom in & zoom out
- Drag with left button to change the viewing angle
- Drag with right button to move the image
Three buttons on the left lower corner, will align the image from +x, +y and +z directions, respectively.
[2d plot]
The result window shows graph of Li fraction and phase distribution of simulated job.
The graph calculated from adding all data from [Li fraction], [Phase distribution], [Temperature] tab and divided by cathode volume.
Specific capacity showed in the bottom of interface calculated from Li fraction at expected time for designed c-rate.
For example, in 4-crate condition, shows specific capacity of cathode at 900 sec(3600sec/4).
<Phase field model output example>
1. Process: Charge, Geometry: Sphere, 30% porosity, evenly distributed, Charge/discharge rate: 2 c-rate
[figure][figure][figure][figure]
2. Process: Charge, Geometry: Sphere, 10% porosity, unevenly distributed, Charge/discharge rate: 4 c-rate
[figure][figure][figure][figure]
3. Process: Discharge, Geometry: cube, Charge/discharge rate: 4 c-rate
[figure][figure][figure][figure]
Density of States
To calculate Density of States, you should first relax the structure like before Relaxation section
- On the Density of states window, therer are Atoms to draw : with check circles where you can select whether to see density of states of all atoms or specific atom
- Then, you also can choice specific orbitals among integrated states in the Orbitals to draw : with check boxes
- First, if you check the ⊙ All such as , Density of States window will show the integrated energy states of all atoms.
- Next, you can choice integrated states or specific states by clicking the states you wnat to see below the Orbitals to draw :
- After these step, click the
Draw
- Integrated Density of States of all atoms
- Slected orbital's Density of States of all atoms
- Combined with all state and each orbital state can be calculted all together about all atoms
- As mentioned above, Density of States of speicif atom can be simulated by clicking the specific atom on the visualization window and then the name of selected atom come out next to the ⊙ Atom , as like
- Integrated Density of States of specific atoms
- Slected specific Density of States of all atoms
- Slected orbital's Density of States of specific atoms
- Combined with all state and each orbital state can be calculted all together about specific atoms
How to create the surface model of cathode material
Build the surface model of cathode material
In the Crystal builder , you can control vacuum setting to create the surface model of cathode material
- After design the cathode material in crystal builder, you can set the surface information
- First, you can select the surface directions ( x, y, z directions )
- And then, you can also select the vacuum layer
- If you enter the vacuum layer and click the
Generate
button, surface model of your cathode material will be created
Analyze the surface model
- After creating surface model, you can analyze this model as like the bulk mode described in above documentation sections( 3.1 & 3.2 )
- To analyze the surface model, just follow the same process described in the documentation 3.2 and then you can check the calculated results(NEB, Potential, Free energy ...) for your surface cathode model
How to build the carbon coating surface model of cathode material
- After creating surface model, you could coating carbons on the your surface model
- In the Crystal builder , you can control carbon coating(c coating) thickness to create the carbon coated surface model of cathode material
To coating carbon on your surface model, just enter the coating thickness of your choice and click Apply
button
- To simulate the coating simulation, enter the target temperature and simulation time
Next,click AIMD Relax check box and enter the AIMD name for AIMD simulation
And also, motion of AIMD model could be check by click the Explore
button in the Crystal builder window
In the AIMD Explorer window, select AIMD name and click the Animate
button
Infromatics
To conform the information on the cathode material that you made through before process, you click the button And then you can check the information
Technical Information
Density Functional Theory Simulation
Density Functional theory (DFT) Simulation is carried out to predict phase behaviors, structural stability, electrochemical voltage and electronic structures for redox reaction and to design a new cathode. (Click this link for details of DFT scripts)
Delithiation simulation
Delithiation simulation of cathodes is the most significant calculations to predict electrochemical voltage behaviors, structural stability associated with phase variations and redox behaviors of transition metals. Most cathode materials in lithium ion battery originally contain lithium ion as the same experiments. Therefore, a user firstly have to model lithiated cathode structures except for specialized cathodes that should electrochemically insert lithium ion into the structures. With generated lithiated cathodes, a user can extract lithium ion with all possible Li-vacancy configuration at the specific content of lithium ion from a fully lithiated structure to a fully delithiated structure.
Analysis
Relaxation
To find optimized structures with thermodynamically stable phases, relaxation should be performed. Initial atomic coordinates and lattice parameters are initial guess, which means that those information would not be ground states. Therefore, relaxation process should be conducted to reach ground states with given calculation conditions by users.
From the relaxation, you can obtain various parameters such as specific atomic coordinates and configurations, lattice parameters, cell volume.
Mixing enthalpy
From the perspective of thermodynamics, the mixing enthalpy calculated by Li/vacancy configurations indicates relatively structural stability of the different configurations at each Li concentrations as follows:
[math]\Delta H_{mixing}= E_{Li_{1-x}TMO_{2}}-xE_{LiTMO_{2}}-(1-x)E_{TMO_{2}} [/math]
, where [math]E_{Li_{1-x}TMO_{2}}[/math] is the total energy of a specific Li-vacancy configuration at a mole fraction [math]x[/math], [math]E_{LiTMO_{2}}[/math] is the total energy of fully lithiated structure and [math]E_{TMO_{2}}[/math] is the total energy of fully delithiated structure. The configurational mixing enthalpy is crucially important to analyze the phases (e.g., two or one phase), electrochemical voltage behaviors and cycleability. Using configurational mixing enthalpy, users can obtain thermodynamically stable phase at targeting Li concentrations with specific atomic configurations. See the related reference as below.
- J.-M. Lim, D. Kim, Y.-G. Lim, M.-S. Park, Y.-J. Kim, M. Cho, K. Cho, "The origins and mechanism of phase transformation in bulk Li2MnO3: first-principles calculations and experimental studies", J. Mater. Chem. A, 2015.
- D. Kim, J.-M. Lim, M.-S. Park, K. Cho, M. Cho, "Phase Separation and d Electronic Orbitals on Cyclic Degradation in Li-Mn-O Compounds: First-Principles Multiscale Modeling and Experimental Observations", ACS Appl. Mater. Interfaces, 2016.
Voltage
In electrochemical system, calculations of voltage are very important process because voltage is directly related to energy density of electrode. The equilibrium voltage, denoted as the open circuit voltage (OCV), between the anode (e.g., negative electrode) and cathode (e.g., positive electrode) is calculated by the difference of Li chemical potential between the anode and cathode as follows:
[math]V=-\frac{\mu_{Li}-\mu_{Li}}{nF}[/math]
, where F is the Faraday constant and n is the number of Li mol involving in redox reaction and [math]\mu_{Li}[/math] refers to the Li chemical potential in cathodes and [math]\mu_{Li}[/math] indicates the Li chemical potential as Li metal in anodes. Even though it is difficult to calculate the chemical potential of Li in cathode materials as a function of Li concentration, the average delithiation potential, , can be easily obtained from the total system energies calculated using DFT.
, where is the two Li ions intercalation limits, refers the change of Gibbs free energy according to the delithiation process. The variation of the Gibbs free energy, ,can be approximated by the change of the internal energy()at 0 K. A very small change in volume () and the thermal energy term (File:Thermal.jpg) almost do not affect the free energy.
See the related reference as below.
- M. K. Aydinol, A. F. Kohan, G. Ceder, K. Cho, J. Joannopoulos "Ab initio study of lithium intercalation in metal oxides and metal dichalcogenides", Phys. Rev. B, 1997.
Diffusion by NEB
From the perspective of kinetics, the migration barrier of Li ion is significant factor to power density related to C-rate in Li ion battery system. The barrier can be varied as a function of Li concentration and is calculated by NEB (Nudged Elastic Band) presenting a method to find saddle points and minimized energy pathway between reactants and products. For the calculation, a number of predicted intermediate images along the reaction path are required to work. Also, the migration barrier of transition metals directly correlated with phase transformations in cathodes is calculated by NEB method. The transition metal barrier can be different as a function of Li concentration and affected by doping other elements. See the related reference as below.
- J.-M. Lim, D. Kim, M.-S. Park, M. Cho, K. Cho, "Underlying mechanisms of the synergistic role of Li2MnO3 and LiNi1/3Co1/3Mn1/3O2 in high-Mn, Li-rich oxides", Phys. Chem. Chem. Phys., 2016.
Density of states
In solid-state and condensed matter physics, the density of states (DOS) of a system describes the number of states per interval of energy at each energy level that are available to be occupied. In Li-ion battery system, electronic behaviors of general redox from transition metals in oxides are major driving force during the lithiation/delithiation, that is, DOS to investigate electronic structures and behaviors should be understood to design cathode materials. The DOSis actually derived from the difference of the integrated DOS between two energy states.
, whereis the difference between two energy states, andrefers the integrated DOS expressed as the following. .
This method indicates the total number of electrons in the whole energy range or in the specific range of calculated system by users. See the related reference as below.
- D. Kim, J.-M. Lim, Y.-G. Lim, J.-S. Yu, M.-S. Park, M. Cho, K. Cho, "Design of Nickel-rich Layered Oxides Using d Electronic Donor for Redox Reactions", Chem. Mater., 2015.
- J.-M. Lim, D. Kim, Y.-G. Lim, M.-S. Park, Y.-J. Kim, M. Cho, K. Cho, "Mechanism of Oxygen Vacancy on Impeded Phase Transformation and Electrochemical Activation in Inactive Li2MnO3", ChemElectroChem, 2016.
- Y.-G. Lim, D. Kim, J.-M. Lim, J.-S. Kim, J.-S. Yu, Y.-J. Kim, D. Byun, M. Cho, K. Cho, M.-S. Park, J. Mater. Chem. A, 2015.
Molecular dynamics simulation
To investigate dynamic properties in atomic scale, the molecular dynamics (MD) simulation technique can be employed. An interatomic potential model is required to perform MD simulations and the potential should be able to cover the metal oxide systems for the application of cathode materials. (Click this link for details of MD script)
- Interatomic potential model: ‘2NN MEAM + Qeq’ potential: See the references for details.
- E. Lee, K.-R. Lee, M. I. Baskes, and B.-J. Lee, ‘A modified Embedded-Atom method interatomic potential for ionic systems: 2NNMAM+Qeq’, Physical Review B 93, 144110 (2016)
- Materials systems that can be covered by the MD simulation
- Li-Mn-O
- Li-Co-O
- Li-Ni-O
Phase field
Phase Field Modeling(PFM) simulation could simulate discharge and charge process about microstructures. With PFM simulation, it is possible to enhance efficiency of cathode by comparing capacity of various shape of structures.
Cahn-hilliard equation is used for PFM simulation. [math]\mu[/math] represents chemical potential and is composed by derivative of chemical energy [math]f(c)[/math] and interface energy [math]0.5h\left\vert \nabla c\ \right\vert^2[/math].
[math]\frac{\partial c}{\partial t}=\nabla \ \cdot [D \nabla \ \mu], \mu=f'(c)-h \nabla^2 \ c [/math]
<Discretization>
Semi-implicit Fourier spectral method applied to increase space resolution & calculation speed.
[math]\frac{\partial c}{\partial t}=A \nabla^2 \ c + f(c) , f(c)=\nabla \ \cdot [D \nabla \ \mu]- A \nabla^2 \ c [/math]
Additionally, 2-SBDF (second order semi-implicit backward differentiation) applied to increase time integration stability.
[math]\frac{3}{2}c^{n+1}-2c^n+\frac{1}{2}c^{n-1}=\Delta t(\nabla \ ^2 c^{n+1})+2Q^n-Q^{n+1}[/math]
[math]Q^n=\Delta t[\nabla \ \cdot (D\nabla \ \mu^n)-A\nabla^2 \ c^n][/math]
The equation above are effectively calculated with the Fourier transform.
[math]\hat c^{n+1}=\frac{4\hat c^n-\hat c^{n-1}+4\hat Q^n-2 \hat Q^{n-1}}{3+2\Delta t k^2}[/math]
[math]\hat Q^n=\Delta t [i \mathbf{K} \cdot \left \{ D_n (i \mathbf{K} \hat \mu^n)_r \right \}_k +k^2 \hat c ^n] [/math]
Vector [math] \mathbf{K} [/math] denotes the wave vector in Fourier space, and [math] k^2=k^2_1+k^2_2+k^2_3. [/math]
The subscript [math] r [/math] denotes the inverse Fourier transform.
<Normalization>
The governing equation is normalized with the characteristic time and length are set to be [math] t_c = 0.5 s [/math] and [math] l_c = 5.0 nm [/math], respectively.
Boundary condition
The boundary condition for Cahn-Hilliard equation is that the flux([math]\mathbf{J}[/math]) on the particle surface is related to the discharge/charge current density [math]i_{loc}[/math] as
[math]\mathbf{J}\cdot\mathbf{n}=i_{loc}/F[/math]
[math]F[/math] is Faraday constant.
Joule heat
[math]\dot{q}=i_{loc}\eta[/math]
1) [math]i_{loc}[/math] (local current density)
2) [math]\eta[/math] (overpotential)
[math]F[/math] : Faraday constant (96485 C/mol)
[math]k_0[/math] : Surface electrochemical reaction-rate constant
[math]c[/math] : Surface Li-ion concentration
[math]c_{max}[/math] : Maximum Li-ion concentration
[math]\beta[/math] : Anodic transfer coefficient (=0.5)
[math]R[/math] : Ideal gas constant (=8.314 J/mol/K)
[math]T[/math] : Temperature (K)
heat equation
[math]\rho[/math] : Density
[math]c_p[/math] : Specific heat capacity
[math]\kappa[/math] : Thermal conductivity
Contact
Prof. Dongchoul Kim, Sogang University (Tel: +82-2-705-8643)