Difference between revisions of "Battery Explorer Manual"

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The battery diffusion data shown in the Materials Project differs from other data in that it is computed with classical approaches rather than first-principles approaches. In particular, the accuracy of these methods are lower than Density Functional Theory calculations, and in general they are used to make qualitative rather than quantitative predictions. We review the important concepts for understanding the diffusion data in this section.
 
The battery diffusion data shown in the Materials Project differs from other data in that it is computed with classical approaches rather than first-principles approaches. In particular, the accuracy of these methods are lower than Density Functional Theory calculations, and in general they are used to make qualitative rather than quantitative predictions. We review the important concepts for understanding the diffusion data in this section.
  
 +
 +
==Classical bond valence method==
 +
 +
Empirical relationships between bond length ''R''<sub>A-X</sub> and the so-called ''bond valence'' ''s''<sub>A-X</sub>= exp[(''R''<sub>0</sub>-''R''<sub>A-X</sub>)/b] are widely used in crystal chemistry to identify plausible equilibrium sites for an atom in a structure as sites, where the ''bond valence sum'' V(A) of A from interactions with all its surrounding counterions X matches its oxidation state.[[#_edn1|[i]]]
 +
 +
A few years ago, we introduced a systematic adjustment of the bond valence parameter ''b'' to bond softness.[[#_edn2|[ii]]] Together with the inclusion of the weak interactions beyond the first coordination shell, this makes it possible to extend the application range of the bond valence method to assess also non-equilibrium sites more adequately and therefrom to predict pathways for mobile ions in models of local structures as regions in a structure model where the bond valence sum V(A) deviates only marginally from the ''ideal valence'' V<sub>id</sub>(A) (i.e., its oxidation state). To enhance chemical plausibility of such ''bond valence mismatch landscapes'' |ΔV(A)| penalty functions have been introduced that (i) discriminate against sites, where a matching V(A) is achieved by strongly asymmetric coordinations and (ii) exclude sites close to other immobile cation types.
 +
 +
The determination of the empirical bond valence parameters ''R<sub>0</sub>'' and ''b'' is based on fits to large sets of experimental reference structures. Thus it may be expected that their application to ab initio structure models (with typically slightly larger unit cell volumes) causes a somewhat reduced accuracy of the approach. 
 +
 +
==Bond valence site energy calculation==
 +
A natural way to combine the bond valence approach with penalty functions for repulsions between the mobile and immobile cation types is to use Coulomb repulsion, but then the bond valence mismatch term also has to be expressed in energy units. In reference [2] we discuss in detail an effective way to translate the squared bond valence (sum) mismatches into approximate a Morse-type bond valence site energy for the mobile ion.  The approach automatically includes bond asymmetry penalties (for details and a table of the employed parameters see reference Adams & Rao ).
 +
In brief, the bond valence site energy E(Li) for a cation Li at a given position is calculated from the position of its N anion neighbours Xj (j = 1,…,N) and P immobile cations is calculated as
 +
,
 +
 +
where
 +
- is the distance between the central Li+ cation and the neighbouring anion Xj
 +
-   and  are the tabulated bond valence parameters for the interaction between a Li cation and anions of type Xj.
 +
-   is the bond valence for the equilibrium bond distance  which itself is estimated from the bond valence parameters, the tabulated preferred coordination number NC and the absolute softnesses σ of the respective ions using the empirical formula
 +
 +
- The bond dissociation energy  is estimated from
 +
                             
 +
with nLi, nXj representing the principal quantum numbers of Li+ and the anion Xj; Vid(Xj) the absolute value of the nominal charge of anion Xj (Vid(Xj) =1). Note that a slightly different formula for calculating the dissociation energy applies to transition metal cations.
 +
- the screened Coulomb repulsion between Li and an the P surrounding immobile cations M¬i (i=1,…,P) is
 +
 +
using fractional charges, where the systematic assignment of context sensitive fractional charges again involves the  inverse square root of the principal quantum number as a scaling factor  (for details see [2]). The screening factor ρLi-Mi is assumed to equal the sum of the covalent radii of the two ions involved times a scaling factor f that depends on the average absolute cation electronegativity and the average cation charge in the compound. Typical values of f in ternary and quaternary lithium oxides fall into the range 0.74±0.04 and thereby ρ is of the order of 2 Å.
 +
 +
These calculations are repeated for a dense grid of points covering the unit cell (grid size ca. 0.1 Å) and pathways of low activation are identified as regions in the structure for which E(Li) assumes low values. It should be noted that the inclusion of weak interactions to counter-ions beyond the first coordination shell is indispensable for such a modeling ion transport to avoid artifacts when an ion moves across the border of its coordination shell. To limit computation-nal effort the well-converging E(Li) calculation can be cut off at a distance of 5 – 8 Å depending on the atom size and bond softness.
 +
 +
As the parameters vary with the oxidation state of all atoms involved and atomic positions are slightly different, it is expected that transport pathways and especially the activation energies will differ between lithiated and delithiated forms of the cathode material. In the initial release only data for the delithiated phase of the redox couple are shown.
  
  

Revision as of 18:16, 20 August 2012

Introduction

The Battery Explorer is a customized tool to search the Materials Project database for Li-ion battery materials satisfying various critical criteria such as voltage, capacity, stability and energy density.

Currently, this app contains approximately 50 lithium intercalation compounds. However, new compounds are being continuously added to the database, including many new structural predictions.

Using the Li-ion Battery Explorer

The Li-ion battery explorer is highly customized to make it easy for battery scientists to find the materials that they are interested in quickly. Useful defaults have been set for the voltage range, minimum gravimetric and minimum volumetric capacity. In fact, simply clicking Search in the Battery Explorer without changing any of the fields already brings up many interesting battery compounds. However, if you have a particular chemistry in mind, judicious use of the form fields will help you find the material you want efficiently. Here's a summary of the various fields and how they can be used:

  1. Elements - Use this field (alternatively, you can click the mini-periodic table to specify the elements) to limit the search for compounds containing only those elements present in the battery materials. F
  2. No. of Elements (inc Li) - Use this field to limit the search to battery compounds containing a total number of elements.
  3. Formula - The formula field should be used as an alternative to specifying the elements and number of elements. In fact, typing in the formula field will automatically fill up the element and no. of elements fields with appropriate parameters. The formula field can be used to restrict the search to compounds satisfying a particular chemical formula.
  4. Voltage Range - Use this slider to set the voltage range you want to search in.
  5. Min. Grav. Capacity - Use this slider to set the minimum gravimetric capacity for the search.
  6. Min. Vol. Capacity - Use this slider to set the minimum volumetric capacity for the search.

Advanced options

  1. Excluded elements - Use this field to exclude certain elements from the search. For example, if you want to exclude certain expensive or toxic elements.
  2. Materials Id - Use this field to search for a battery material containing a material with a particular Materials Id within the delithiation range.
  3. Battery Id - Use this field to search for a battery material with the corresponding battery id.
  4. Max. Volt. Step - Use this slider to limit the search to battery materials having a voltage step less than the specified number.
  5. Max. Vol. Change - Use this slider to limit the search to battery materials having a volume change upon lithiation/delithiation smaller than the specified percentage.
  6. Max. energy above hull - Use this slider to limit how unstable the lithiated or delithiated battery material can be.

The Search Result Table

The search result table presents the results from your search. You can add or hide fields from the result table by clicking the Show/Hide Button.

We have provided additional tools to aid you in analyzing the results. For example, you can select a few battery compounds by clicking the checkbox on the rightmost column of the table, and then click the "voltage profile" button to show all the voltage profiles in one easy plot for comparison. You can also compare any two materials for structural similarity. Finally, you can click on the BattId of any material to go to the Battery Material page, which provides detailed information about a battery material, including an assessment of oxidative stability, a Jmol view of the molecule, etc.

Viewing Details of a battery compound

You can click the blue links in any of the search results to see a detailed summary of that battery compound. Each details page is dedicated to one structural framework, e.g. Mn2O4 spinel, and provides information on *all* lithiation levels into this structural framework.

The details view has many components:

Voltage curve

The voltage curve graph displays the calculated equilibrium voltage versus state of charge. If voltage criteria were specified in the query, the line might be segmented into different colors. The green portion of the curve matches the query, whereas the the blue portion of the curve does not.

O2 evolution curve

One concern for cathode design is resistance to O2 release, as O2 release from the cathode can lead to thermal runaway. The O2 evolution diagram determines the equilibrium chemical potentials at which O2 release can be expected, and the amount of O2 released[1][2]. One way to read this chart is to look at the chemical potential at which O2 release begins (the first x-value for which the y-axis is greater than zero). Compounds for which O2 release begins at more negative muO2 are more stable with respect to O2 release. Note that the O2 release chart is specific to one lithiation level of the set of compounds forming the cathode system. There is a drop-down that allows you to choose the lithiation level (e.g. fully delithiated, fully lithiated). The muO2 needed for release can be referenced against common binary systems to get an idea of stability to O2 release:

Muoscale.gif

A muO2 of zero is roughly calibrated to atmospheric conditions.

Overall materials properties

The overall materials properties display aggregate or average properties over all lithiation levels of a given structural framework. Note that some lithiation levels presented in this section may be outside the desired range of voltage, stability, or safety. More details are given in the 'Voltage pair properties' section.

Voltage pair properties

This table displays calculated data for each voltage step along the voltage profile.

Diffusion data

The battery diffusion data shown in the Materials Project differs from other data in that it is computed with classical approaches rather than first-principles approaches. In particular, the accuracy of these methods are lower than Density Functional Theory calculations, and in general they are used to make qualitative rather than quantitative predictions. We review the important concepts for understanding the diffusion data in this section.


Classical bond valence method

Empirical relationships between bond length RA-X and the so-called bond valence sA-X= exp[(R0-RA-X)/b] are widely used in crystal chemistry to identify plausible equilibrium sites for an atom in a structure as sites, where the bond valence sum V(A) of A from interactions with all its surrounding counterions X matches its oxidation state.[i]

A few years ago, we introduced a systematic adjustment of the bond valence parameter b to bond softness.[ii] Together with the inclusion of the weak interactions beyond the first coordination shell, this makes it possible to extend the application range of the bond valence method to assess also non-equilibrium sites more adequately and therefrom to predict pathways for mobile ions in models of local structures as regions in a structure model where the bond valence sum V(A) deviates only marginally from the ideal valence Vid(A) (i.e., its oxidation state). To enhance chemical plausibility of such bond valence mismatch landscapes |ΔV(A)| penalty functions have been introduced that (i) discriminate against sites, where a matching V(A) is achieved by strongly asymmetric coordinations and (ii) exclude sites close to other immobile cation types.

The determination of the empirical bond valence parameters R0 and b is based on fits to large sets of experimental reference structures. Thus it may be expected that their application to ab initio structure models (with typically slightly larger unit cell volumes) causes a somewhat reduced accuracy of the approach. 

Bond valence site energy calculation

A natural way to combine the bond valence approach with penalty functions for repulsions between the mobile and immobile cation types is to use Coulomb repulsion, but then the bond valence mismatch term also has to be expressed in energy units. In reference [2] we discuss in detail an effective way to translate the squared bond valence (sum) mismatches into approximate a Morse-type bond valence site energy for the mobile ion. The approach automatically includes bond asymmetry penalties (for details and a table of the employed parameters see reference Adams & Rao ). In brief, the bond valence site energy E(Li) for a cation Li at a given position is calculated from the position of its N anion neighbours Xj (j = 1,…,N) and P immobile cations is calculated as

,

where - is the distance between the central Li+ cation and the neighbouring anion Xj - and are the tabulated bond valence parameters for the interaction between a Li cation and anions of type Xj. - is the bond valence for the equilibrium bond distance which itself is estimated from the bond valence parameters, the tabulated preferred coordination number NC and the absolute softnesses σ of the respective ions using the empirical formula

- The bond dissociation energy is estimated from

with nLi, nXj representing the principal quantum numbers of Li+ and the anion Xj; Vid(Xj) the absolute value of the nominal charge of anion Xj (Vid(Xj) =1). Note that a slightly different formula for calculating the dissociation energy applies to transition metal cations. - the screened Coulomb repulsion between Li and an the P surrounding immobile cations M¬i (i=1,…,P) is

using fractional charges, where the systematic assignment of context sensitive fractional charges again involves the inverse square root of the principal quantum number as a scaling factor (for details see [2]). The screening factor ρLi-Mi is assumed to equal the sum of the covalent radii of the two ions involved times a scaling factor f that depends on the average absolute cation electronegativity and the average cation charge in the compound. Typical values of f in ternary and quaternary lithium oxides fall into the range 0.74±0.04 and thereby ρ is of the order of 2 Å.

These calculations are repeated for a dense grid of points covering the unit cell (grid size ca. 0.1 Å) and pathways of low activation are identified as regions in the structure for which E(Li) assumes low values. It should be noted that the inclusion of weak interactions to counter-ions beyond the first coordination shell is indispensable for such a modeling ion transport to avoid artifacts when an ion moves across the border of its coordination shell. To limit computation-nal effort the well-converging E(Li) calculation can be cut off at a distance of 5 – 8 Å depending on the atom size and bond softness.

As the parameters vary with the oxidation state of all atoms involved and atomic positions are slightly different, it is expected that transport pathways and especially the activation energies will differ between lithiated and delithiated forms of the cathode material. In the initial release only data for the delithiated phase of the redox couple are shown.


References

  1. S. P. Ong, L. Wang, B. Kang, G. Ceder., The Li-Fe-P-O2 Phase Diagram from First Principles Calculations, Chemistry of Materials, vol. 20, Mar. 2008, pp. 1798-1807.
  2. S.P. Ong, A. Jain, G. Hautier, B. Kang, and G. Ceder, Thermal stabilities of delithiated olivine MPO4 (M=Fe, Mn) cathodes investigated using first principles calculations, Electrochemistry Communications, vol. 12, 2010, pp. 427-430.

Authors

  1. Shyue Ping Ong
  2. Anubhav Jain