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Structured Representation of Materials

We present an example of our approach towards defining and storing structured data for materials. The aspects presented herein complement the general introduction.

Example Representation

In the expandable section below, the user can find an example JSON representation of a face-centered cubic Silicon:

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{
    "allOf": [
        {
            "schemaId": "system-bankable-entity", 
            "allOf": [
                {
                    "description": "entity schema", 
                    "allOf": [
                        {
                            "schemaId": "system-timestampable", 
                            "properties": {
                                "createdAt": {
                                    "type": "string", 
                                    "description": "entity creation time"
                                }, 
                                "updatedAt": {
                                    "type": "string", 
                                    "description": "entity last modification time"
                                }
                            }, 
                            "description": "entity timestampable schema", 
                            "title": "timestampable entity schema"
                        }, 
                        {
                            "schemaId": "system-soft-removable", 
                            "properties": {
                                "removedAt": {
                                    "type": "string", 
                                    "description": "Timestamp of the moment when entity was removed"
                                }, 
                                "removed": {
                                    "type": "boolean", 
                                    "description": "Identifies that entity was removed"
                                }
                            }, 
                            "description": "entity removable schema", 
                            "title": "soft removable entity schema"
                        }, 
                        {
                            "schemaId": "system-name", 
                            "properties": {
                                "name": {
                                    "type": "string", 
                                    "description": "entity name"
                                }, 
                                "slug": {
                                    "type": "string", 
                                    "description": "entity slug"
                                }
                            }, 
                            "description": "entity name schema", 
                            "title": "timestampable entity schema"
                        }, 
                        {
                            "schemaId": "system-tags", 
                            "properties": {
                                "tags": {
                                    "items": {
                                        "type": "string"
                                    }, 
                                    "type": "array", 
                                    "description": "entity tags"
                                }
                            }, 
                            "description": "entity tags schema", 
                            "title": "entity tags schema"
                        }
                    ], 
                    "schemaId": "system-entity", 
                    "required": [
                        "_id", 
                        "schemaVersion", 
                        "owner", 
                        "creator"
                    ], 
                    "title": "entity schema", 
                    "properties": {
                        "owner": {
                            "schemaId": "system-entity-reference", 
                            "required": [
                                "_id", 
                                "cls"
                            ], 
                            "properties": {
                                "_id": {
                                    "type": "string", 
                                    "description": "entity identity"
                                }, 
                                "slug": {
                                    "type": "string", 
                                    "description": "entity slug"
                                }, 
                                "cls": {
                                    "type": "string", 
                                    "description": "entity class"
                                }
                            }, 
                            "description": "Subset of the full information about the account who owns the entity.", 
                            "title": "entity reference schema"
                        }, 
                        "schemaVersion": {
                            "type": "string", 
                            "description": "entity's schema version. Used to distinct between different schemas."
                        }, 
                        "_id": {
                            "type": "string", 
                            "description": "entity identity"
                        }, 
                        "description": {
                            "type": "string", 
                            "description": "entity description"
                        }, 
                        "creator": {
                            "schemaId": "system-entity-reference", 
                            "required": [
                                "_id", 
                                "cls"
                            ], 
                            "properties": {
                                "_id": {
                                    "type": "string", 
                                    "description": "entity identity"
                                }, 
                                "slug": {
                                    "type": "string", 
                                    "description": "entity slug"
                                }, 
                                "cls": {
                                    "type": "string", 
                                    "description": "entity class"
                                }
                            }, 
                            "description": "Subset of the full information about the user who created the entity.", 
                            "title": "entity reference schema"
                        }
                    }
                }, 
                {
                    "schemaId": "system-bankable", 
                    "required": [
                        "exabyteId", 
                        "hash"
                    ], 
                    "properties": {
                        "exabyteId": {
                            "type": "string", 
                            "description": "Identity of the corresponding bank entity"
                        }, 
                        "hash": {
                            "type": "string", 
                            "description": "Hash string which is calculated based on the meaningful fields of the entity. Used to identify equal entities."
                        }
                    }, 
                    "description": "bankable schema", 
                    "title": "bankable schema"
                }
            ], 
            "description": "bankable entity schema", 
            "title": "bankable entity schema"
        }
    ], 
    "schemaId": "material", 
    "required": [
        "basis", 
        "lattice"
    ], 
    "title": "material schema", 
    "$schema": "http://json-schema.org/draft-04/schema#", 
    "properties": {
        "icsdId": {
            "type": "integer", 
            "description": "Corresponding ICSD id of the material"
        }, 
        "fileSource": {
            "description": "file source with the information inside", 
            "title": "file source schema", 
            "schemaId": "system-file-source", 
            "required": [
                "extension", 
                "name", 
                "text"
            ], 
            "type": "object", 
            "properties": {
                "text": {
                    "type": "string", 
                    "description": "file content as raw text"
                }, 
                "name": {
                    "type": "string", 
                    "description": "file name without extension"
                }, 
                "extension": {
                    "type": "string", 
                    "description": "file extension"
                }
            }
        }, 
        "basis": {
            "description": "object containing an array of elements and coordinates in the supercell", 
            "title": "basis schema", 
            "schemaId": "properties-directory-structural-basis", 
            "required": [
                "elements", 
                "coordinates"
            ], 
            "type": "object", 
            "properties": {
                "elements": {
                    "schemaId": "properties-directory-structural-basis-atomic-elements", 
                    "properties": {
                        "values": {
                            "items": {
                                "properties": {
                                    "value": {
                                        "type": "string"
                                    }
                                }
                            }, 
                            "schemaId": "core-reusable-atomic-strings", 
                            "allOf": [
                                {
                                    "items": {
                                        "uniqueItems": true, 
                                        "type": "object", 
                                        "properties": {
                                            "id": {
                                                "type": "integer", 
                                                "description": "integer id of this entry"
                                            }
                                        }
                                    }, 
                                    "schemaId": "core-primitive-array-of-ids", 
                                    "type": "array", 
                                    "description": "array of objects containing integer id each", 
                                    "title": "atomic ids"
                                }
                            ], 
                            "title": "atomic vectors schema"
                        }, 
                        "name": {
                            "enum": [
                                "atomic_elements"
                            ]
                        }
                    }, 
                    "description": "elements of atoms by ids, string, unitless", 
                    "title": "atomic elements"
                }, 
                "coordinates": {
                    "schemaId": "properties-directory-structural-basis-atomic-coordinates", 
                    "properties": {
                        "units": {
                            "enum": [
                                "km", 
                                "m", 
                                "pm", 
                                "nm", 
                                "angstrom", 
                                "a.u.", 
                                "bohr", 
                                "fractional", 
                                "crystal", 
                                "cartesian", 
                                "alat"
                            ]
                        }, 
                        "values": {
                            "items": {
                                "properties": {
                                    "value": {
                                        "schemaId": "core-abstract-vector", 
                                        "anyOf": [
                                            {
                                                "title": "array of 3 number elements schema", 
                                                "minItems": 3, 
                                                "items": {
                                                    "type": "number"
                                                }, 
                                                "schemaId": "core-primitive-array-of-3-numbers", 
                                                "maxItems": 3, 
                                                "type": "array"
                                            }, 
                                            {
                                                "title": "array of 3 boolean elements schema", 
                                                "minItems": 3, 
                                                "items": {
                                                    "type": "boolean"
                                                }, 
                                                "schemaId": "core-primitive-array-of-3-booleans", 
                                                "maxItems": 3, 
                                                "type": "array"
                                            }
                                        ], 
                                        "title": "vector schema"
                                    }
                                }
                            }, 
                            "schemaId": "core-reusable-atomic-vectors", 
                            "allOf": [
                                {
                                    "items": {
                                        "uniqueItems": true, 
                                        "type": "object", 
                                        "properties": {
                                            "id": {
                                                "type": "integer", 
                                                "description": "integer id of this entry"
                                            }
                                        }
                                    }, 
                                    "schemaId": "core-primitive-array-of-ids", 
                                    "type": "array", 
                                    "description": "array of objects containing integer id each", 
                                    "title": "atomic ids"
                                }
                            ], 
                            "title": "atomic vectors schema"
                        }, 
                        "name": {
                            "enum": [
                                "atomic_coordinates"
                            ]
                        }
                    }, 
                    "description": "coordinates of atoms by ids, vector, unitless", 
                    "title": "atomic coordinates"
                }
            }
        }, 
        "scaledHash": {
            "type": "string", 
            "description": "Hash string for a scaled structure with lattice vector a set to 1 (eg. for materials under pressure)."
        }, 
        "derivedProperties": {
            "items": {
                "anyOf": [
                    {
                        "schemaId": "properties-directory-structural-volume", 
                        "allOf": [
                            {
                                "schemaId": "core-primitive-scalar", 
                                "required": [
                                    "value"
                                ], 
                                "type": "object", 
                                "properties": {
                                    "value": {
                                        "type": "number"
                                    }
                                }, 
                                "title": "scalar schema"
                            }
                        ], 
                        "properties": {
                            "units": {
                                "enum": [
                                    "angstrom^3"
                                ]
                            }, 
                            "name": {
                                "enum": [
                                    "volume"
                                ]
                            }
                        }, 
                        "title": "volume schema"
                    }, 
                    {
                        "schemaId": "properties-directory-structural-density", 
                        "allOf": [
                            {
                                "schemaId": "core-primitive-scalar", 
                                "required": [
                                    "value"
                                ], 
                                "type": "object", 
                                "properties": {
                                    "value": {
                                        "type": "number"
                                    }
                                }, 
                                "title": "scalar schema"
                            }
                        ], 
                        "properties": {
                            "units": {
                                "enum": [
                                    "g/cm^3"
                                ]
                            }, 
                            "name": {
                                "enum": [
                                    "density"
                                ]
                            }
                        }, 
                        "title": "density schema"
                    }, 
                    {
                        "schemaId": "properties-directory-structural-symmetry", 
                        "properties": {
                            "tolerance": {
                                "properties": {
                                    "units": {
                                        "enum": [
                                            "angstrom"
                                        ]
                                    }
                                }, 
                                "description": "tolerance used for symmetry calculation", 
                                "allOf": [
                                    {
                                        "schemaId": "core-primitive-scalar", 
                                        "required": [
                                            "value"
                                        ], 
                                        "type": "object", 
                                        "properties": {
                                            "value": {
                                                "type": "number"
                                            }
                                        }, 
                                        "title": "scalar schema"
                                    }
                                ]
                            }, 
                            "name": {
                                "enum": [
                                    "symmetry"
                                ]
                            }, 
                            "spaceGroupSymbol": {
                                "type": "string", 
                                "description": "space group symbol in Hermann\u2013Mauguin notation"
                            }
                        }, 
                        "title": "symmetry schema"
                    }, 
                    {
                        "schemaId": "properties-directory-structural-elemental-ratio", 
                        "allOf": [
                            {
                                "schemaId": "core-primitive-scalar", 
                                "required": [
                                    "value"
                                ], 
                                "type": "object", 
                                "properties": {
                                    "value": {
                                        "type": "number"
                                    }
                                }, 
                                "title": "scalar schema"
                            }
                        ], 
                        "properties": {
                            "name": {
                                "enum": [
                                    "elemental_ratio"
                                ]
                            }, 
                            "value": {
                                "max": 1, 
                                "min": 0
                            }, 
                            "element": {
                                "type": "string", 
                                "description": "the element this ratio is for"
                            }
                        }, 
                        "description": "ration of this element in the compound", 
                        "title": "elemental-ratio"
                    }, 
                    {
                        "schemaId": "properties-directory-structural-p-norm", 
                        "allOf": [
                            {
                                "schemaId": "core-primitive-scalar", 
                                "required": [
                                    "value"
                                ], 
                                "type": "object", 
                                "properties": {
                                    "value": {
                                        "type": "number"
                                    }
                                }, 
                                "title": "scalar schema"
                            }
                        ], 
                        "properties": {
                            "name": {
                                "enum": [
                                    "p-norm"
                                ]
                            }, 
                            "degree": {
                                "type": "integer", 
                                "description": "degree of the dimensionality of the norm"
                            }
                        }, 
                        "description": "https://en.wikipedia.org/wiki/Norm_(mathematics)#p-norm", 
                        "title": "p_norm"
                    }
                ]
            }, 
            "schemaId": "properties-directory-derived-properties", 
            "type": "array", 
            "description": "object defining the lattice cell size and shape", 
            "title": "derived properties schema"
        }, 
        "lattice": {
            "oneOf": [
                {
                    "required": [
                        "vectors"
                    ], 
                    "properties": {
                        "vectors": {
                            "schemaId": "properties-directory-structural-lattice-lattice-vectors", 
                            "allOf": [
                                {
                                    "schemaId": "core-abstract-3d-vector-basis", 
                                    "required": [
                                        "a", 
                                        "b", 
                                        "c"
                                    ], 
                                    "type": "object", 
                                    "properties": {
                                        "a": {
                                            "description": "first vector", 
                                            "title": "array of 3 number elements schema", 
                                            "minItems": 3, 
                                            "items": {
                                                "type": "number"
                                            }, 
                                            "schemaId": "core-primitive-array-of-3-numbers", 
                                            "maxItems": 3, 
                                            "type": "array"
                                        }, 
                                        "c": {
                                            "description": "third vector", 
                                            "title": "array of 3 number elements schema", 
                                            "minItems": 3, 
                                            "items": {
                                                "type": "number"
                                            }, 
                                            "schemaId": "core-primitive-array-of-3-numbers", 
                                            "maxItems": 3, 
                                            "type": "array"
                                        }, 
                                        "b": {
                                            "description": "second vector", 
                                            "title": "array of 3 number elements schema", 
                                            "minItems": 3, 
                                            "items": {
                                                "type": "number"
                                            }, 
                                            "schemaId": "core-primitive-array-of-3-numbers", 
                                            "maxItems": 3, 
                                            "type": "array"
                                        }
                                    }, 
                                    "title": "3 dimensional vector basis"
                                }
                            ], 
                            "properties": {
                                "units": {
                                    "enum": [
                                        "km", 
                                        "m", 
                                        "pm", 
                                        "nm", 
                                        "angstrom", 
                                        "a.u.", 
                                        "bohr", 
                                        "fractional", 
                                        "crystal", 
                                        "cartesian", 
                                        "alat"
                                    ]
                                }, 
                                "alat": {
                                    "default": 1.0, 
                                    "type": "number", 
                                    "description": "lattice parameter for fractional coordinates"
                                }
                            }, 
                            "title": "lattice explicit unit"
                        }
                    }
                }, 
                {
                    "required": [
                        "type"
                    ], 
                    "schemaId": "properties-directory-structural-lattice-lattice-bravais", 
                    "allOf": [
                        {
                            "schemaId": "core-primitive-3d-lattice", 
                            "required": [
                                "a", 
                                "b", 
                                "c", 
                                "alpha", 
                                "beta", 
                                "gamma"
                            ], 
                            "type": "object", 
                            "properties": {
                                "a": {
                                    "type": "number", 
                                    "description": "length of the first lattice vector"
                                }, 
                                "c": {
                                    "type": "number", 
                                    "description": "length of the third lattice vector"
                                }, 
                                "b": {
                                    "type": "number", 
                                    "description": "length of the second lattice vector"
                                }, 
                                "beta": {
                                    "type": "number", 
                                    "description": "angle between second and third lattice vector"
                                }, 
                                "alpha": {
                                    "type": "number", 
                                    "description": "angle between first and second lattice vector"
                                }, 
                                "gamma": {
                                    "type": "number", 
                                    "description": "angle between first and third lattice vector"
                                }
                            }, 
                            "title": "3 dimensional lattice schema"
                        }
                    ], 
                    "properties": {
                        "units": {
                            "type": "object", 
                            "properties": {
                                "length": {
                                    "enum": [
                                        "angstrom", 
                                        "bohr"
                                    ], 
                                    "type": "string"
                                }, 
                                "angle": {
                                    "enum": [
                                        "degree", 
                                        "radian"
                                    ], 
                                    "type": "string"
                                }
                            }
                        }, 
                        "type": {
                            "enum": [
                                "CUB", 
                                "BCC", 
                                "FCC", 
                                "TET", 
                                "MCL", 
                                "ORC", 
                                "ORCC", 
                                "ORCF", 
                                "ORCI", 
                                "HEX", 
                                "BCT", 
                                "TRI", 
                                "MCLC", 
                                "RHL"
                            ], 
                            "type": "string", 
                            "description": "Bravais lattice type in short notation"
                        }
                    }, 
                    "title": "lattice implicit schema"
                }
            ], 
            "description": "object defining the lattice cell size and shape", 
            "title": "lattice schema", 
            "schemaId": "properties-directory-structural-lattice", 
            "type": "object", 
            "properties": {
                "name": {
                    "enum": [
                        "lattice"
                    ]
                }
            }
        }, 
        "external": {
            "items": {
                "description": "information about a database source", 
                "title": "database source schema", 
                "schemaId": "system-database-source", 
                "required": [
                    "_id", 
                    "name"
                ], 
                "type": "object", 
                "properties": {
                    "origin": {
                        "type": "string", 
                        "description": "A flag that is true when material is initially imported from a third party * (as opposed to being independently designed from scratch)."
                    }, 
                    "_id": {
                        "type": "string", 
                        "description": "ID string for the materials uploaded from a third party source inside the third party source."
                    }, 
                    "name": {
                        "type": "string", 
                        "description": "Third party source name."
                    }
                }
            }, 
            "type": "array", 
            "description": "information about external sources of this material"
        }, 
        "unitCellFormula": {
            "type": "string", 
            "description": "chemical formula based on the number of atoms of each element in the supercell"
        }, 
        "formula": {
            "type": "string", 
            "description": "reduced chemical formula"
        }
    }
}
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{
    "exabyteId": "RKiswuxHKkF3uvLyA", 
    "hash": "4ac3fa057e3530628eb1295c77110eaa", 
    "name": "Silicon FCC", 
    "creator": {
        "_id": "HtxACY2wX4b2hS8Rv", 
        "slug": "exadmin", 
        "cls": "User"
    }, 
    "scaledHash": "5bd4eb168e3530628eb1295d88221cbb", 
    "derivedProperties": [
        {
            "units": "angstrom^3", 
            "name": "volume", 
            "value": 131.1
        }, 
        {
            "units": "g/cm^3", 
            "name": "density", 
            "value": 2.33
        }, 
        {
            "tolerance": {
                "units": "angstrom", 
                "value": 0.3
            }, 
            "name": "symmetry", 
            "spaceGroupSymbol": "Fd-3m"
        }, 
        {
            "value": 0.71, 
            "name": "p-norm", 
            "degree": 10
        }, 
        {
            "name": "elemental_ratio", 
            "value": 0.71, 
            "element": "Si"
        }
    ], 
    "basis": {
        "units": "crystal", 
        "elements": [
            {
                "id": 1, 
                "value": "Si"
            }, 
            {
                "id": 2, 
                "value": "Si"
            }
        ], 
        "name": "basis", 
        "coordinates": [
            {
                "id": 1, 
                "value": [
                    0.0, 
                    0.0, 
                    0.0
                ]
            }, 
            {
                "id": 2, 
                "value": [
                    0.25, 
                    0.25, 
                    0.25
                ]
            }
        ]
    }, 
    "lattice": {
        "a": 5.0, 
        "c": 5.0, 
        "b": 5.0, 
        "name": "lattice", 
        "beta": 90.0, 
        "alpha": 90.0, 
        "type": "CUB", 
        "gamma": 90.0
    }, 
    "isDefault": false, 
    "updatedAt": "2016-04-04T17:58:42.867Z", 
    "unitCellFormula": "Si2", 
    "owner": {
        "_id": "HtxACY2wX4b2hS8Rv", 
        "slug": "exabyte", 
        "cls": "Account"
    }, 
    "formula": "Si", 
    "schemaVersion": "0.2.0", 
    "_id": "LCthJ6E2QabYCZqf3", 
    "slug": "silicon-fcc", 
    "createdAt": "2016-04-03T05:25:37.430Z"
}

Explanation of Keywords

Keyword Short Description Details
basis Crystal basis with explicit identification per atom The information about the atomic type and coordinates
lattice Crystal lattice in both Bravais and vector notations Crystal lattice parameters - lattice constants and angles. Components of the corresponding lattice vectors are also included.
derivedProperties descriptive properties derived from lattice/basis (only one example shown above) Additional properties of the crystal structure under investigation as explained in the section ensuing the present table.
hash Hash string calculated by the Bank Mapping Function Structure-based hash string for the primitive standard representation of this material, calculated when checking this material against existing entries within the Materials Bank
scaledHash As above, but for the lattice axis scaled to 1.0 (i.e. to identify same structures under different uniform pressure) This hash string is calculated by scaling all the dimensions of the primitive unit cell representation of the material by the a lattice constant

Derived Properties

As seen above, we use the crystal lattice and basis JSON objects as the main identifying properties. Based upon them, we calculate the derivedProperties, that may include such information as:

  • the unit cell volume,
  • density,
  • chemical formula,
  • and a large number of other possibilities.

For every material imported/uploaded to our platform, we pre-calculate a set of such descriptors, and store them inside this "derivedProperties" section. This information can be further used during data analysis or the construction of statistical predictive models.