Perovskite Design Program Using Logarithmic Tolerance Factor
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Solution Overview
Problem
The existing methods for designing stable perovskite type crystal structures are time-consuming, especially when dealing with multiple ionic species and finely adjusted solid solutions, due to the vast number of combinations required to achieve a tolerance factor of 1.
Innovation Solution
A design program that uses a computer to determine stable combinations of ions at A and B sites by taking the logarithm of the tolerance factor formula, employing an annealing method with an Ising model or QUBO to perform ground state searches, significantly speeding up the calculation process.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If exhaustive search of all ion combinations is performed to find stable perovskite structures, then the reliability of structure stability is improved, but the calculation time increases significantly
Solution Approach 1:
The patent transforms the tolerance factor calculation by taking the logarithm of the original formula, converting it from a product form to a sum form. This parameter transformation enables efficient computation while maintaining the stability criteria. The logarithmic transformation of the tolerance factor equation allows systematic evaluation of multiple ion combinations without exhaustive search.
Solution Approach 2:
The patent replaces the mechanical exhaustive search process with an information-theoretic approach using information entropy. By calculating information entropy based on ion size ratios and tolerance factors, the system can rapidly identify stable perovskite structures without checking all possible combinations, thus reducing computation time while maintaining reliability.
2Adaptability or versatility
If multiple ionic species are combined to form solid solutions, then the adaptability of material composition is improved, but the device complexity increases due to enormous number of combinations
Solution Approach 1:
The patent applies logarithmic transformation to the tolerance factor formula, converting complex product relationships into additive forms. This parameter change simplifies the evaluation of solid solution systems with multiple ionic species, making it feasible to handle composition flexibility without overwhelming complexity.
Solution Approach 2:
The patent creates a simplified mathematical model that copies the essential features of the complex ion combination problem. By using information entropy and logarithmic transformations, the system creates a reduced representation that captures stability criteria while eliminating the need to explicitly handle all possible ion combinations.
3Manufacturing precision
If tolerance factor calculation uses geometric mean weighted by composition ratio, then the manufacturing precision of solid solutions is improved, but the calculation time increases for finely adjusted compositions
Solution Approach 1:
The patent transforms the tolerance factor calculation by applying logarithms, converting the geometric mean calculation into a linear combination of logarithmic terms. This parameter transformation enables efficient computation even for finely adjusted solid solution compositions, maintaining manufacturing precision while significantly reducing calculation time.
Data Source
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Figure 2A~2B
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AI summary
A computer implemented method for designing a composition of a perovskite type crystal structure having a tolerance factor of 1 is disclosed