Atomic-scale strain mapping has become increasingly vital for investigating deformation mechanisms and the governing principles of solid materials.This is due to the significant impact of atomic-scale strain on the ph...Atomic-scale strain mapping has become increasingly vital for investigating deformation mechanisms and the governing principles of solid materials.This is due to the significant impact of atomic-scale strain on the physical,chemical,and mechanical properties of nanomaterials that comprise functional devices such as nanoelectronics,communication devices,electromechanical systems,and sensors.The advent of advanced electron microscopes has enabled the acquisition of high-magnification images with atomic resolution,providing an exceptional platform for measuring the atomic-scale strain of solid materials.However,accurate and unified strain mapping methods and standards for evaluating atomic-scale strain distribution remain scarce.Consequently,a unified strain mapping framework is proposed for atomic-scale strain measurement.Utilizing finite deformation analysis and the least-squares mathematical method,two types of atomic-scale strain field mapping methods have been developed,including the phase analysis-based methods(PAD and PAS)and the peak matching-based strain mapping method(PMS)for high-resolution scanning transmission electron microscope images.The prototypical 2D materials,graphene and molybdenum disulfide,serve as the subjects for the strain field mapping research,conducted through both simulation and experimentation.Upon comparing the theoretical strain mapping results of single-layer graphene and molybdenum disulfide with and without defects,it is demonstrated that the proposed strain mapping methods,particularly the PMS method,can accurately describe the large deformation surrounding a significant strain gradient.展开更多
Certain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the...Certain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the strain tensor.Virial stress is widely accepted as the stress measurement in molecular dynamics(MD).However,its conjugate strain is not yet identified.An atomic logarithmic strain is proposed and numerically verified as the conjugate strain of virial stress at 0 K temperature.The strain energy is calculated by virial stress and the proposed atomic logarithmic strain equals to the interatomic potential energy density.This conclusion is numerically verified with(1)Coulomb-Buckingham potential,Lenard-Jones potential,or arbitrary nonlinear pair potential and(2)randomly generated atomic configurations and deformation gradients.Examples are given in determining the stress–strain relation for magnesium oxide with MD simulation.The result shows that the atomic logarithmic strain is identical to engineer-ing strain when deformation is small.展开更多
基金support from the National Natural Science Foundation of China through Grants 12172190,11872035,11632010,and 12302236。
文摘Atomic-scale strain mapping has become increasingly vital for investigating deformation mechanisms and the governing principles of solid materials.This is due to the significant impact of atomic-scale strain on the physical,chemical,and mechanical properties of nanomaterials that comprise functional devices such as nanoelectronics,communication devices,electromechanical systems,and sensors.The advent of advanced electron microscopes has enabled the acquisition of high-magnification images with atomic resolution,providing an exceptional platform for measuring the atomic-scale strain of solid materials.However,accurate and unified strain mapping methods and standards for evaluating atomic-scale strain distribution remain scarce.Consequently,a unified strain mapping framework is proposed for atomic-scale strain measurement.Utilizing finite deformation analysis and the least-squares mathematical method,two types of atomic-scale strain field mapping methods have been developed,including the phase analysis-based methods(PAD and PAS)and the peak matching-based strain mapping method(PMS)for high-resolution scanning transmission electron microscope images.The prototypical 2D materials,graphene and molybdenum disulfide,serve as the subjects for the strain field mapping research,conducted through both simulation and experimentation.Upon comparing the theoretical strain mapping results of single-layer graphene and molybdenum disulfide with and without defects,it is demonstrated that the proposed strain mapping methods,particularly the PMS method,can accurately describe the large deformation surrounding a significant strain gradient.
文摘Certain stress tensor and strain tensor form a conjugate pair if there exists a scalar valued strain energy function such that the stress tensor is equal to the derivative of strain energy function with respect to the strain tensor.Virial stress is widely accepted as the stress measurement in molecular dynamics(MD).However,its conjugate strain is not yet identified.An atomic logarithmic strain is proposed and numerically verified as the conjugate strain of virial stress at 0 K temperature.The strain energy is calculated by virial stress and the proposed atomic logarithmic strain equals to the interatomic potential energy density.This conclusion is numerically verified with(1)Coulomb-Buckingham potential,Lenard-Jones potential,or arbitrary nonlinear pair potential and(2)randomly generated atomic configurations and deformation gradients.Examples are given in determining the stress–strain relation for magnesium oxide with MD simulation.The result shows that the atomic logarithmic strain is identical to engineer-ing strain when deformation is small.
