Researchers devised a theoretical method to predict variations of the lattice structure in response to external disturbances

February 12, 2021

*Image by Pexels from Pixabay*

In a new study, researchers from the Indian Institute of Technology Bombay (IIT Bombay) have devised a theoretical method to predict variations of the lattice structure in response to external disturbances. This study, published in the journal *npj Computational Materials*, was partially funded by the IIT Bombay-Industrial Research and Consultancy Centre, the Ministry of Human Resource and Development (now Ministry of Education), Department of Atomic Energy, and the Department of Science and Technology, Government of India. For more than five decades, scientists have bombarded solids like silicon with X-ray or electrons beams and observed how this beam interacts with its lattice. “The response of the solid to the beam leaves specific imprints on the outgoing beam, revealing the atomic vibrations in the lattice,” says Prof Dipanshu Bansal, another author of the study. An innovative mathematical technique first invented by Joseph Fourier, called ‘Fourier analysis’, helps them in studying the small structures of the lattice in both space and time.

In the current study, the researchers carried out mathematical calculations and demonstrated that one could use a similar technique to study solids subject to a temporary, external disturbance. They used an extended version of Fourier’s method along with the laws of quantum physics. Additionally, they used the fundamental idea that time flows in one direction. These led them to calculate a mathematical quantity which determines how the lattice structure reacts to the external disturbance. Using this mathematical quantity, also called the „response functionâ€ź, the researchers predicted how solids would behave in time, down to a few femtoseconds, and space, down to fractions of a nanometre. Then, they calculated the response function from images available from experiments conducted over the last decade with lasers. This quantity, the researchers of the current study demonstrated, exactly matches the theoretical response function. Their calculation shows for the first time that there is no need to carry out the sophisticated experiments to study the dynamics of solids. The researchers assert that their method is applicable for solids in different environments like in a magnetic field, under external pressure, or high temperature.

*(Source: Indian institute of Technology Bombay news release) *

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