Researchers at the Jawaharlal Nehru Centre for Advanced Scientific Research, (JNCASR), an autonomous institution under the Department of Science & Technology, have introduced a novel quantitative measure of mechanical flexibility for crystals.

The measure can be used to screen materials databases to identify next-generation flexible materials, said the team.

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They carried out an in-depth analysis of the mechanisms underlying the flexibility of crystals of Metal-organic frameworks (MOFs) — a large class of crystalline materials that possess the remarkable ability to absorb gasses, such as carbon dioxide, and store them as well as act as filters for crude oil purification.

The team attributed the flexibility to large structural rearrangements associated with soft and hard vibrations within a crystal that strongly couple to strain fields.

The analysis opens doors to innovative materials with diverse applications in various industries, said the researchers.

MOFs derive their ability from the presence of nanopores, enhancing their surface areas that, in turn, make them adept at absorbing and storing gases. However, limited stability and mechanical weakness have hindered their broader applications, which was addressed by the new measure.

The new findings, published in the journal Physical Review B, present groundbreaking insights into the origin of mechanical flexibility. Flexibility in crystals has, historically, been assessed in terms of a parameter called elastic modulus — a measure of a material’s resistance to strain-induced deformation, but, on the contrary, the study “proposes a unique theoretical measure based on the fractional release of elastic stress or strain energy through internal structural rearrangements under symmetry constraints”.

Using theoretical calculations, the team examined the flexibility of four different systems with varying elastic stiffness and chemistries. The results showed that “flexibility arises from large structural rearrangements associated with soft and hard vibrations within a crystal that strongly couples to strain fields”.

The newfound measure of flexibility is also poised to revolutionise materials science, especially in the context of MOFs. “This theoretical framework enables the screening of thousands of materials in databases, providing a cost-effective and efficient way to identify potential candidates for experimental testing. The design of ultra-flexible crystals becomes more achievable, offering a practical solution to the challenges posed by traditional experimental methods,” said Professor Umesh V. Waghmare from the Theoretical Sciences Unit at JNCASR.

The potential applications of this research extend beyond the realm of physics, opening doors to innovative materials with diverse applications in various industries, the team said.