Localized Soft Vibrational Modes and Coherent Structural Phase Transformations in Rutile TiO<sub>2</sub> Nanoparticles under Negative Pressure.
basic_science · Level V
Where this comes from
- Record sourced from PubMed, PMID 35797495.
- Also identified by DOI 10.1021/acs.nanolett.2c01939 and PMC identifier 9335867.
- Licence recorded as CC BY.
- The licence permits redistribution, so the abstract is shown in full and the full text is available from the publisher.
Abstract
We study the effect of size on the vibrational modes and frequencies of nanoparticles, by applying a newly developed, robust, and efficient first-principles-based method that we present in outline. We focus on rutile TiO<sub>2</sub>, a technologically important material whose bulk exhibits a softening of a transverse acoustic mode close to <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mrow><mo>(</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>2</mn></mrow></mfrac><mo>,</mo><mfrac><mrow><mn>1</mn></mrow><mrow><mn>4</mn></mrow></mfrac><mo>)</mo></mrow></math>, which becomes unstable with the application of negative pressure. We demonstrate that, under these conditions, nanoparticles above a critical size exhibit unstable localized modes and we calculate their characteristic localization length and decomposition with respect to bulk phonons. We propose that such localized soft modes could initiate coherent structural phase transformations in small nanoparticles above a critical size.