High-throughput method to predict bulk properties of inorganic materials
Methods for representing crystal structure of inorganic materials in matrix form, and for quantitative comparison of multiple inorganic materials, can be employed to identify candidate materials with high potential to possess a desired property. Such methods can include conversion of an atomic coordinate set to a coordinate set for an anion only lattice, anion substitution, and unit cell re-scaling. Such methods can further include simulation of x-ray diffraction data for modified anion-only lattices, and generation of n×2 matrices from the simulated diffraction data. Quantitative structural similarity values can be derived from the n×2 matrices. The quantitative structural similarity values can be useful for structural categorization, as well as prediction of functional properties.
1. A method for selecting an inorganic material having a desired property, the method comprising:
selecting:
a standard inorganic material known to have the desired property; and
a plurality of candidate inorganic materials that may have the desired property;
obtaining a set of atomic coordinates for the standard-inorganic material and each of the plurality of candidate inorganic materials, each set of atomic coordinates comprising:
a cation lattice, comprising a cation identity and set of cation coordinates; and
an anion lattice, comprising an anion identity and set of anion coordinates;
removing the cation lattice from each set of atomic coordinates, to produce an anion-only lattice, each anion-only lattice defining an anionic unit cell, each anionic unit cell having volume per anion;
replacing the anion identity in each of the anion-only lattices with an identity of a designated monoatomic anion, to ensure that all of the anion-only lattices have the same anion identity;
re-scaling each anionic unit cell to a selected volume, to ensure that all anionic unit cells have the same volume per anion, to produce a modified anion-only lattices from each anion-only lattice;
generating a simulated x-ray diffraction pattern for each modified anion-only lattice;
generating, using the simulated x-ray diffraction pattern, a matrix for each anion-only lattice, each matrix comprising a series of diffraction angles, {x i }, and a series of corresponding, simulated diffraction intensities, {y i }, each series having indices, i, where x i is the same for all n×2 matrices at each index;
generating, for each of the plurality of candidate inorganic materials, a numerical value, S, defining structural similarity between the standard inorganic material and the respective candidate inorganic material, by performing a calculation:
S=E [( Y−μ Y ( Y′−μ Y′ )]/σ Y σ Y′
wherein S, ranging from zero to one, is the numerical value defining structural similarity; Y is a vector defining the series {y i } for the matrix corresponding to the standard inorganic material; Y′ is a vector defining the series {y i ′} for the matrix corresponding to the respective candidate inorganic material, μ Y is the mean of Y; μ Y′ is the mean of Y′; σ Y is the standard deviation of Y; σ Y′ is the standard deviation of Y′; and
E is an operation to obtain the expectation value over all indices; and
selecting the candidate inorganic material having a desired value of S.
2. The method of claim 1 , wherein rescaling the unit cell comprises an isotropic expansion/swelling of the lattice according to the formula:
a′/a 0 =b′/b 0 =c′/c 0 =( N×V 0 /V ) 1/3
wherein a′, b′, and c′ are the lattice parameters after rescaling; a o , b o , c o are the lattice parameters before rescaling, N is the number of anions in the unit cell, V is the volume of the unit cell, and V o is the normalized volume of anions.
3. A method for performing a quantitative comparison of inorganic crystal structures, the method comprising:
selecting at least two inorganic materials to be compared;
obtaining a set of atomic coordinates for each of the at least two inorganic materials, each set of atomic coordinates comprising:
a cation lattice, comprising a cation identity and set of cation coordinates; and
an anion lattice, comprising an anion identity and set of anion coordinates;
removing the cation lattice from each set of atomic coordinates, to produce an anion-only lattice, each anion-only lattice defining an anionic unit cell, each anionic unit cell having a volume per anion;
replacing the anion identity in each of the anion-only lattices with an identity of a designated monoatomic anion, to ensure that all of the anion-only lattices have the same anion identity;
re-scaling each anionic unit cell to a selected volume, to ensure that all anionic unit cells have the same volume per anion, to produce a modified anion-only lattices from each anion-only lattice;
generating a simulated x-ray diffraction pattern for each modified anion-only lattice;
generating, using the simulated x-ray diffraction pattern, a matrix for each anion-only lattice, each matrix comprising a series of diffraction angles, {x i }, and a series of corresponding, simulated diffraction intensities, {y i }, each series having indices, i, where x i is the same for all n×2 matrices at each index;
generating, for each of the plurality of candidate inorganic materials, a numerical value, S, defining structural similarity between the standard inorganic material and the respective candidate inorganic material, by performing a calculation:
S=E [( Y−μ Y )( Y′−μ Y′ )]/σ Y σ Y′
wherein S, ranging from zero to one, is the numerical value defining structural similarity; Y is a vector defining the series {y i } for the matrix corresponding to the standard inorganic material; Y′ is a vector defining the series {y i ′} for the matrix corresponding to the respective candidate inorganic material, μ Y is the mean of Y; μ Y′ is the mean of Y′; σ Y is the standard deviation of Y; σ Y′ is the standard deviation of Y′; and E is an operation to obtain the expectation value over all indices.
4. The method according to claim 3 , wherein rescaling the unit cell coordinates for each reciprocal crystal lattice structure comprises an isotropic expansion/swelling of the lattice according to a formula:
a′/a 0 =b′/b 0 =c′/c 0 =( N×V 0 /V ) 1/3
wherein a′, b′, and c′ are the lattice parameters after rescaling; a o , b o , c o are the lattice parameters before rescaling, N is the number of anions in the unit cell, V is the volume of the unit cell, and V o is the normalized volume of anions.
5. A method for representing a crystal structure of an inorganic material in an n×2 matrix, the method comprising:
obtaining a set of atomic coordinates for the inorganic material, the set of atomic coordinates comprising:
a cation lattice, comprising a cation identity and set of cation coordinates; and
an anion lattice, comprising an anion identity and set of anion coordinates;
removing the cation lattice from the set of atomic coordinates, to produce an anion-only lattice, the anion-only lattice defining an anionic unit cell, the anionic unit cell having a volume per anion;
generating a simulated x-ray diffraction pattern for the anion-only lattice;
generating the n×2 matrix, using the simulated x-ray diffraction pattern, the n×2 matrix comprising a series of diffraction angles, {x i }, and a series of corresponding, simulated diffraction intensities, {y i }.
6. The method as recited in claim 5 , further comprising:
replacing the anion identity in the anion-only lattice with an identity of a designated monoatomic anion.
7. The method as recited in claim 6 , further comprising:
re-scaling the anionic unit cell to a selected volume.