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- "

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- "",
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- " ### Predicting the stability of perovskite oxides and halides using a new tolerance factor

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- "

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- "",
- "",
- " ## NOMAD Analytics Toolkit ",
- "

",
- "

",
- " ",
- " created by:",
- " Christopher Bartel^{1} (email),",
- " Christopher Sutton^{2} (email)",
- "

",
- " ",
- " ^{1} University of Colorado Boulder, 3415 Colorado Ave., Boulder, CO, USA

",
- " ^{2} Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, D-14195 Berlin, Germany

",
- " ",
- " [Last updated: October 16, 2017]",
- "

",
- "Back to Analytics Home ",
- "Back to nomad-coe ",
- "

",
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- " is a descriptor that takes as input the chemical composition and outputs a prediction of perovskite stability according to the formula:",
- "",
- "\n ### Predicting the stability of perovskite oxides and halides using a new tolerance factor

\n

\n\n\n ## NOMAD Analytics Toolkit \n

\n

\n \n created by:\n Christopher Bartel^{1} (email),\n Christopher Sutton^{2} (email)\n

\n \n ^{1} University of Colorado Boulder, 3415 Colorado Ave., Boulder, CO, USA

\n ^{2} Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, D-14195 Berlin, Germany

\n \n [Last updated: October 16, 2017]\n

",
- " ",
- " where is the ionic radius of ion, and is the oxidation state of ion, , and indicates stability in the perovskite structure.

",
- " ",
- "

This descriptor was identified by applying the SISSO algorithm developed by R. Ouyang, S. Curtarolo, E. Ahmetick, M. Scheffler, L. Ghiringhelli: Phys. Rev. Materials 2, 083802 (2018) [PDF] {Code} which efficiently identifies from a space of ~3,000,000,000 potential descriptors.

",
- " ",
- " requires the same information as Goldschmidt's famous tolerance factor (noting that is an implict function of ):

",
- " ",
- " While the functional forms are comparable, the accuracies are not. On a set of 576 compounds characterized experimentally at ambient conditions, achieves 92% accuracy in predicting whether the compound will or won't be stable as perovskite compared with 74% using .

",
- " ",
- " is probabilistic, providing not only whether a given composition will crystallize as perovskite but also a probability on this prediction. ",
- " ",
- " Below you can input two cations - and - and one anion - - and the utility will automatically assign oxidation states and radii to each ion (more on this below) and provide the probability that the will form the perovskite structure. is also provided for context.

",
- " ",
- " This result is visualized with respect to the cationic radii to show where in the space of stable and unstable perovskites the given composition sits.

",
- " ",
- " The descriptor also generalizes to double perovskites - compounds with substitutions at the , , or sites. Below you can explore the stability of compounds with 50/50 mixtures of ions on each or all of the sites - i.e., formulas.

",
- " ",
- " More details on the identification and application of are available within the manuscript and associated github repository.",
- "",
- "

\n \n where is the ionic radius of ion, and is the oxidation state of ion, , and indicates stability in the perovskite structure.

\n \n

This descriptor was identified by applying the SISSO algorithm developed by R. Ouyang, S. Curtarolo, E. Ahmetick, M. Scheffler, L. Ghiringhelli: Phys. Rev. Materials 2, 083802 (2018) [PDF] {Code} which efficiently identifies from a space of ~3,000,000,000 potential descriptors.

\n \n requires the same information as Goldschmidt's famous tolerance factor (noting that is an implict function of ):

\n \n While the functional forms are comparable, the accuracies are not. On a set of 576 compounds characterized experimentally at ambient conditions, achieves 92% accuracy in predicting whether the compound will or won't be stable as perovskite compared with 74% using .

\n \n is probabilistic, providing not only whether a given composition will crystallize as perovskite but also a probability on this prediction. \n \n Below you can input two cations - and - and one anion - - and the utility will automatically assign oxidation states and radii to each ion (more on this below) and provide the probability that the will form the perovskite structure. is also provided for context.

\n \n This result is visualized with respect to the cationic radii to show where in the space of stable and unstable perovskites the given composition sits.

\n \n The descriptor also generalizes to double perovskites - compounds with substitutions at the , , or sites. Below you can explore the stability of compounds with 50/50 mixtures of ions on each or all of the sites - i.e., formulas.

\n \n More details on the identification and application of are available within the manuscript and associated github repository.\n\n

", - "Given a new formula, where and are cations and we don't yet know which is and which is , we apply the following scheme:", - "", - "

", - "1) A list of allowed is defined for and based on the set of such that exists within Shannon's data.", - "", - "

2) All pairs of oxidation states that charge-balance are considered, where is typically known

3) In the infrequent case where more than one charge-balanced pair exists, a single solution is chosen based on the electronegativity ratio of the two cations, . If , the pair that minimizes is chosen, otherwise, the pair that maximizes is chosen. ", - "", - "

4) With determined, the radii of each cation if they were to sit on or is generated using Shannon's table.", - "", - "

5) The determination of which cation is larger, and therefore the -site, is made by systematically comparing these radii.", - "", - "This strategy reproduces the assignment of the and cations for 100% of the 313 experimentally labeled perovskites in the set of 576 used to determine . Conveniently, this approach naturally yields which are the inputs to and ." - ], - "hidden": true - }, - "output": { - "state": {}, - "result": { - "type": "BeakerDisplay", - "innertype": "Html", - "object": "\n\n\n and are both functions of the site-specific radii, , yet it is not known

\nGiven a new formula, where and are cations and we don't yet know which is and which is , we apply the following scheme:\n\n

\n1) A list of allowed is defined for and based on the set of such that exists within Shannon's data.\n\n

2) All pairs of oxidation states that charge-balance are considered, where is typically known

3) In the infrequent case where more than one charge-balanced pair exists, a single solution is chosen based on the electronegativity ratio of the two cations, . If , the pair that minimizes is chosen, otherwise, the pair that maximizes is chosen. \n\n

4) With determined, the radii of each cation if they were to sit on or is generated using Shannon's table.\n\n

5) The determination of which cation is larger, and therefore the -site, is made by systematically comparing these radii.\n\nThis strategy reproduces the assignment of the and cations for 100% of the 313 experimentally labeled perovskites in the set of 576 used to determine . Conveniently, this approach naturally yields which are the inputs to and ." - }, - "selectedType": "BeakerDisplay", - "elapsedTime": 0, - "height": 362 - }, - "evaluatorReader": true, - "lineCount": 20 - }, - { - "id": "codesKEWrz", - "type": "code", - "evaluator": "HTML", - "input": { - "body": [ - "", - "", - "", - "", - "", - "", - "", - "", - "

Please allow 10-20 seconds for the utility to run.", - "

Printed output will clear only once the calculation has finished.", - "

For the rapid classification of many candidate formulas, please see the associated github repository." - ], - "hidden": true - }, - "output": { - "state": {}, - "result": { - "type": "BeakerDisplay", - "innertype": "Html", - "object": "\n\n\n\n\n\n\n\n\n

Please allow 10-20 seconds for the utility to run.\n

Printed output will clear only once the calculation has finished.\n

For the rapid classification of many candidate formulas, please see the associated github repository." - }, - "selectedType": "BeakerDisplay", - "elapsedTime": 0, - "height": 87, - "hidden": true - }, - "evaluatorReader": true, - "lineCount": 70, - "initialization": true - }, - { - "id": "codeVUE92J", - "type": "code", - "evaluator": "HTML", - "input": { - "body": [ - "", - "The utility will allow the use of some other cations and anions, but these have not been as thoroughly tested.", - "

", - "", - "