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Table of Contents

Table of ContentsLi-ion diffusion in LiFePO4 for battery applications

Import LiFePO4 bulk structureNew functionality in QuantumATK 2017:

Optimize LiFePO4 lattice parametersCreate the Li 1 − x 1−xFePO4 structures

Create initial and final structures for diffusion along B directionCreate initial and final structures for diffusion along C direction

Optimize initial and final configurationsCreate initial NEB trajectoriesOptimize Li diffusion path

Analyze the results

Calculate the reaction rates using harmonic transition state theoryReferences

Downloads & LinksDownloads & Links

PDF version Tutorial Synopsis Basic QuantumATK Tutorial ATK Reference Manual Calculat ing react ion rates using harmonic t ransit ion state theory Pt diffusion on Pt surfaces using NEB calculat ions

Docs » Tutorials » Bat teries and energy storage » Li- ion diffusion in LiFePO for bat tery applicat ions

Li- ion dif fusion in LiFePOLi- ion dif fusion in LiFePO for battery applicat ions for battery applicat ionsVersion:Version: 2016.3

LiFePO is among the typical rechargeable Li- ion bat tery cathode materials with high energy density andlow cost , while also being environmentally friendly [IF14][YW15]. In this tutorial you will use ATK-DFT toest imate the Li- ion diffusion rates along different crystallographic direct ions in LiFePO .

In part icular, you will:

Import the LiFePO bulk st ructure.Opt imize the LiFePO lat t ice parameters.Create the Li

FePO st ructures.Opt imize the init ial and f inal configurat ions.Create init ial NEB t rajectories (IDPP interpolat ion).Opt imize the Li diffusion path.Calculate the react ion rates using harmonic t ransit ion state theory (HTST).

Im por t LiFePOIm por t LiFePO bu lk st ruct ure bu lk st ruct ure

The LiFePO st ructure can be imported from the Cryst allography Open Dat abaseCryst allography Open Dat abase plugin inQuantumATK.

1. Click the BuilderBuilder.2. Open the From Plugin ‣ Crystallography Open Database.3. Select Li, Fe, P, O as elements and click the T o result sT o result s but ton.4. Choose Lithium Iron Phosphate(V), Simple Orthorhombic(Pnma).5. Click Add t o st ashAdd t o st ash but ton.

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It will be automat ically loaded in the BuilderBuilder stash.

N e w f unc t i o nal i t y i n Quant umAT K 2017 :N e w f unc t i o nal i t y i n Quant umAT K 2017 :

From the Quant umAT K 2017Quant umAT K 2017 version, crystal st ructures such as LiFePO can be imported by theQuantumATK Dat abasesDat abases tool as follows: Click the Dat aBasesDat aBases. See CODCOD (Crystallography OpenDatabase) and Mat erials ProjectMat erials Project . Both are possible to get the LiFePO st ructure. In the COD case, selectLi, Fe, P, O as elements and click the SearchSearch but ton.

You can also use the Mat erials ProjectMat erials Project database. Choose the Materials Project . Select elements or typeLiFePO4. Select one and click the importimport but ton, it will be automat ically loaded in the LabFloorLabFloor in thesame way as the COD. In this case, you can get more calculat ion informat ion including the st ructure fromthe Material Project database.

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For more opt ions, see also Import XYZ, CIF, CAR, VASP files in QuantumATK tutorial.

Opt im ize LiFePOOpt im ize LiFePO lat t ice param et ers lat t ice param et ers

You can import the LiFePO st ructure to the BuilderBuilder to have a deeper look into the st ructure.

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In order to bet ter compare with the results of reference [YJ13] you can use the Bulk Tools ‣ SwapAxes tool to swap C< - >AC<- >A and Z< - >XZ<- >X. However, by doing so, the configurat ion will lose the informat ionabout the symmetry type, in this case Simple orthorhombic. Use the Bulk Tools ‣ Lat t ice Parameterstool to set the Lat t ice type to Simple orthorhombic.

In order to opt imize the lat t ice parameters, send the LiFePO st ructure from the St ashSt ash to the Script erScript erto set up a new DFT calculat ion as follows:

1. Add the New Calculat orNew Calculat or block and modify the following parameters:SGGA-PBE exchange correlat ion potent ial7x5x3 k-point sampling

(We will use the the default FHI pseudopotent ials and DZP basis set ).

2. Add an Opt imiz eGeomet ryOpt imiz eGeomet ry block and modify:Max forces 0.02 eV/ÅMax st ress 0.1 GPaRemove check from Const rain cellConst rain cell to allow for cell opt imizat ionCheck Save t raject orySave t raject ory and specify the f ile LiFePo4_opt.nc

3. Change default output f ile name to LiFePo4_opt.nc

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4. Finally, send the script to the JobManagerJobManager and run the calculat ion.

It takes about 30 minutes on 8 cores. After f inishing the job, open the opt imized BulkConfigurat ion withobject ID glD002 with the BuilderBuilder. Check the new opt imized lat t ice parameters which agree to within 0.1percent with the experimental data.

Creat e t he LiCreat e t he LiFePOFePO st ruct ures st ruct ures

In this tutorial you will study the diffusion of one Li atom for a Li-deficient st ructure such as LiFePO . In part icular, you will remove one of the four Li atoms from the bulk configurat ion. Note that the

diffusion energy barriers depend on the Li concentrat ion [OSW+04].

In the next sect ion you will set up the calculat ion for the diffusion of a Li atom along two differentdirect ions. You thus need to create init ial configurat ions and f inal configurat ions for the same Li atomdiffusing along the B and C direct ions.

Cre at e i ni t i al and f i nal st ruc t ure s f o r di f f usi o n al o ng B di re c t i o nCre at e i ni t i al and f i nal st ruc t ure s f o r di f f usi o n al o ng B di re c t i o n

1. Right -click on the configurat ion on the St ashSt ash and make three copies such that you have 4 ident icalconfigurat ions. We will make init ial and f inal st ructures for the B and C direct ions.

2. From the f irst configurat ion, delete one Li atom as in the f igure below. This will be your init ial st ructurefor the B direct ion NEB calculat ions and you can rename it init ial_B.

3. Double click the second configurat ion to make it act ive. Next rename it f inal_B. Select the same Liatom you just deleted from the init ial configurat ion and open the Periodic T ablePeriodic T able tool. Click onGoldGold (Au) element to change the Li atom to Gold.

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You are applying this t rick to be able to move the Li atom into a specif ic posit ion. In this case,the posit ion of the Li vacancy defined by the Gold atom. There are indeed several otherworkarounds to build this f inal configurat ion, e.g. by copying the coordinates of the original Liatom you removed. You are welcome to use here the procedure that you f ind more relevant andintuit ive for you.

4. Select Li atom number 7 (the one next to the Gold atom along the B direct ion) and use the MoveMovetool to move it on top of the Gold atom. Be sure that the Snap opt ion is enabled.

5. Use the Fuse opt ion to remove the Gold atom and your f inal st ructure is now ready.6. Finally, check the Li atom number 6 in the init ial_B and f inal_B configurat ions. Li atom number 6 should

be moved in the B direct ion.

Cre at e i ni t i al and f i nal st ruc t ure s f o r di f f usi o n al o ng C di re c t i o nCre at e i ni t i al and f i nal st ruc t ure s f o r di f f usi o n al o ng C di re c t i o n

Follow the same procedure as above to create the configurat ion along the C direct ion. The init ial st ructurefor the C direct ion is the same as the int ial_B st ructure. Rename it init ial_C. In this case, the f inal st ructuremoves Li atom number 4 to the removed Li posit ion (subst ituted Gold) in the inital_C st ructure. Renamethe f inal st ructure, f inal_C.

Opt im ize in it ial and f inal conf igurat ionsOpt im ize in it ial and f inal conf igurat ions

Send each st ructure, init ial_B, f inal_B, init ial_C and f inal_C, to the Script erScript er and set up a geometryopt imizat ion calculat ion with the same parameters as for the LiFePO st ructure. However, in this case youwill not opt imize the lat t ice parameters. Check the Constrain cell opt ion as indicated below.

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Moreover, in this case you can use the unpolarized GGA.PBE funct ional. This will allow you to run yourcalculat ion much faster. Here you can download the four input scripts: init ial_B.py, f inal_B.py, init ial_C.py and f inal_C.py.

Creat e in it ial NEB t raject or iesCreat e in it ial NEB t raject or ies

The tutorial Pt diffusion on Pt surfaces using NEB calculat ions will teach you how to set up the NEB object .Here we will highlight only the main steps.

1. When the opt imizat ion of the end points are done you will f ind the opt imized configurat ions loaded inthe LabFloorLabFloor with object ID equal to glD002. Drag and drop these BulkConfigurat ion objects direct lyinto the BuilderBuilder.

2. In the BuilderBuilder open the Builders ‣ Nudged Elast ic Band plugin and drag and drop from the St ashSt ash theinit ial and f inal configurat ions corresponding to the diffusion of a Li atom along the B direct ion,initial_B.nc and final_B.nc configurat ions.

3. Select the Image Dependent Pair Potent ial interpolat ion method and use 9 images including the endpoints.

4. Create the init ial Li diffusion path along C direct ion with the initial_C.nc and final_C.nc

configurat ions. Use 9 images with 0.8 Å maximum distance including the end points .

Opt im ize Li d if fusion pat hOpt im ize Li d if fusion pat h

You are now ready to set up and opt imize the Li diffusion path in LiFePO .

1. Send the two NEB objects from the St ashSt ash to the Script erScript er.2. Add and set up a New Calculat orNew Calculat or with the same set t ings as for the calculators of the end points.3. Add a Opt imiz eGeomet ryOpt imiz eGeomet ry block and be sure to select the Climbing Image Method.4. Finally, run the two NEB calculat ions neb_B.py and neb_C.py.

Note that as described in the Pt diffusion on Pt surfaces using NEB calculat ions, you can run thiscalculat ion in parallel over many MPI processes. In part icular, a NEB run is parallelized over the internalimages. AT KAT K will t ry to detect the best parallelizat ion st rategy and it will write a small report at thebeginning of your log f ile.

In this example, you will immediately see that a load balance problem has been detected. However, 2 out16 cores will be idle, so it is a rather small loss of eff iciency, not “great ly reduced” as it says in the log f ilebelow. It takes about 2 hours in 16 processes. You can also change the number of MPI processes you areusing to achieve the best performance.

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+------------------------------------------------------------------------------+| NEB image level parallelism enabled. |+------------------------------------------------------------------------------+| Total number of interior images: 7 || Total number of processes: 16 || Processes per image: 2 || Images calculated in parallel: 8 || || Process group # 0 will calculate images: 1 || Process group # 1 will calculate images: 2 || Process group # 2 will calculate images: 3 || Process group # 3 will calculate images: 4 || Process group # 4 will calculate images: 5 || Process group # 5 will calculate images: 6 || Process group # 6 will calculate images: 7 || Process group # 7 will be idle! || WARNING: Load balance problem detected. || The number of interior images calculated in parallel is not a || divisor of the number of interior images. This will greatly || reduce parallel performance. Either modify the parameter || "processes_per_image" or the number of MPI processes. || || With 2 processes_per_image ideal performance will be obtained || by using 14 MPI processes.

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You can speed up the opt imizat ion by f irst running a simple NEB calculat ion with a high force tolerance,e.g. 0.08 eV/Å, and without using the Climbing Image Method. This will in general be a faster calculat iongiving you a rough est imate of the energy barrier and the diffusion path. After this step, you can set upa more precise NEB run and also use the climbing method to f inalize your results.

Anal yze t he re sul t sAnal yze t he re sul t s

Once the calculat ion is properly converged you will f ind the opt imized NudgedElast icBand object loaded inthe LabFloorLabFloor

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Always remember to check the log f ile at the end of your simulat ion. In part icular, check thatconvergence is achieved:

+------------------------------------------------------------------------------+| NEB Optimization using the LBFGS optimizer |+------------------------------------------------------------------------------+| Iteration Step Length Max. Force Max. Energy Image Max. Energy |+------------------------------------------------------------------------------+| 0 0.000e+00 1.473e+00 4 0.925917 || 1 4.825e-02 1.362e+00 4 0.794101 |...| 23 1.220e-02 2.772e-01 4 0.405770 || 24 3.731e-03 4.938e-02 4 0.404796 |+------------------------------------------------------------------------------+| NEB optimization converged after 24 steps. |+------------------------------------------------------------------------------+

In the two f igures below, the opt imized Li diffusion process for the Li atom moving along the B and C

direct ions are illust rated by using the Movie T oolMovie T ool plugin.

While the Li atom can more easily move along the B direct ion with 0.39 eV energy barrier, you found a highenergy barrier, 2.3 eV for the Li atom moving along the C direct ion. The results are in agreement withreference [OSW+04].

Calcu lat e t he react ion rat es using harm onic t ransit ionCalcu lat e t he react ion rat es using harm onic t ransit ionst at e t heoryst at e t heory

For detailed informat ion about how react ion rates are calculated and the theory behind the harmonict ransit ion state theory please refer to the Calculat ing react ion rates using harmonic t ransit ion state

theory.

To set up the analysis:

1. Open the Script erScript er.2. Double click on Analysis f rom f ileAnalysis f rom f ile and select the neb_B.nc configurat ion with object ID glD001.3. Add the HT ST EventHT ST Event analysis and set the prefactor to 1e+13 1/s.

4. Run the analysis which will only take a minute. Here is the input script . HTST_analysis.py

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The t ime required for an HTSTEvent analysis st rongly depends on whether or not the prefactor isassumed or calculated. If you need to calculate the prefactor, it can take a long t ime, depending on themethod and system. Therefore, it is usually a very good approximat ion to assume the prefactor forsolid state react ions like bulk diffusion.

In order to visualize the results from the HT ST Event sHT ST Event s analysis, select the corresponding object from theLabFloorLabFloor and select the HTST Rates plugin on the right hand side.

Here, you can calculate the forward and reverse react ion rates for your diffusion mechanism. In this caseyou will f ind these two values to be very close to each other because the init ial and f inal states areessent ially equivalent .

Here, you can also set the opt ions for an Arrhenius plot :

The table below summarized the results found in this tutorial.

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Table 3 Table: energy barriers (eV) andreaction rates (s ) calculated at 300 K for Li

diffusion in LiFePO along the B and C directions.¶

Direct ion Barrier k

B 0.39 2.6 x 10

C 2.30 1.9 x 10

ReferencesReferences

[IF14] M. Saiful Islam and Craig A. J. Fisher. Lithium and sodium battery cathode materials: computat ionalinsights into voltage, diffusion and nanostructural propert ies. Chem. Soc. Rev., 43(1):185, 2014.doi:10.1039/C3CS60199D.

[OSW+04] (1, 2) Chuying Ouyang, Siqi Shi, Zhaoxiang Wang, Xuejie Huang, and Liquan Chen. First -principles studyof li ion diffusion in lifepo 4. Physical Review B, 2004. doi:10.1103/PhysRevB.69.104303.

[YW15] William Davidson Richards Yan Wang. Design principles for solid-state lithium superionic conductors.Nature Materials, 14(10):1026, 2015. doi:10.1038/nmat4369.

[YJ13] Dhamodaran Santhanagopalan Yuri Janssen. Reciprocal salt f lux growth of lifepo 4 single crystals withcontrolled defect concentrat ions. Chemistry of Materials, 25(22):4574, 2013. doi:10.1021/cm4027682.

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