Geometric characterization of continuously defective elastic crystals

We show how some differential geometric structures associated with a concept of a homogeneous space appear naturally in a kinematic model of continuously distributed defects in an elastic crystal solid and discuss how one can use them to describe the defectiveness of such a continuum.

Elastic organic crystals with ultralong phosphorescence for flexible anti-counterfeiting

Ultralong organic phosphorescence (UOP) crystals have attracted increased attention due to the distinct photophysical property of a long-lived lifetime. However, organic crystals are generally brittle, leading to a serious problem for their application in flexible technology. Herein, we report three types of elastic organic crystals (EOCs) with ultralong phosphorescence via introducing halogen atoms (Cl, Br, I) into π-conjugated phosphorescent molecules. Especially, the crystal containing iodine atoms displayed both excellent elasticity (ε = 3.01%) and high phosphorescent efficiency (ΦPh = 19.1%) owing to the strong halogen bonds. Taking advantage of its highly efficient UOP and excellent elasticity, we successfully used a DCz4I crystal for anti-counterfeiting application. These findings may provide guidance for the development of elastic crystals with afterglow and expand the scope of potential applications on flexible materials.

Crystal Period Vectors under External Stress in Statistical Physics

For crystals under external stress and temperature, a general equation to determine their period vectors (cell edge vectors) was derived based on the principles of statistical physics. This equation applies to both classical systems and quantum systems. It is consistent and can be combined with the previously derived one in the Newtonian dynamics. The existing theory for crystals under external pressure is covered as a special case. The new equation is also the mechanical equilibrium condition and the equation of state for crystals under external stress and temperature. It should be helpful in studying piezoelectric and piezomagnetic materials, since the period vectors change with external stress. For linear elastic crystals, it is the microscopic and temperature-dependent form of the generalized Hooke's law, therefore, it can be used to calculate the corresponding elastic constants, for given temperatures.

Crystal Period Vectors under External Stress in Statistical Physics

For crystal periodic structure prediction, a new and concise approach based on the principles of statistical physics was employed to derive a new form of the equation to determine their period vectors (cell edge vectors), under general external stress. Then the new form is applicable to both classical physics and quantum physics. It also turned out to be the equation of state and the mechanical equilibrium condition for crystals under external stress and temperature. It should be helpful in piezoelectric and piezomagnetic studies, as the period vectors were changed by the external stress. For linear elastic crystals, it is actually also the microscopic but temperature-dependent form of the generalized Hooke's law, then can be used to calculate the corresponding elastic constants of the law, for given temperatures.

Crystal Period Vectors under External Stress in Statistical Physics

For crystal periodic structure prediction, a new and concise approach based on the principles of statistical physics was employed to derive a new form of the equation to determine their period vectors (cell edge vectors), under general external stress. Then the new form is applicable to both classical physics and quantum physics. It also turned out to be the equation of state and the specific explicit equilibrium condition for crystals under external stress and temperature. It should be helpful in piezoelectric and piezomagnetic studies, as the period vectors were changed by the external stress. For linear elastic crystals, it is actually also the microscopic but temperature-dependent form of the generalized Hooke's law, then can be used to calculate the corresponding elastic constants of the law, for given temperatures.

Crystal Period Vectors under External Stress in Statistical Physics

For crystal periodic structure prediction, a new and concise approach based on the principles of statistical physics was employed to derive a new form of the equation to determine their period vectors (cell edge vectors), under general external stress. Then the new form is applicable to both classical physics and quantum physics. It also turned out to be the equation of state and the specific explicit equilibrium condition for crystals under external stress and temperature. It should be helpful in piezoelectric and piezomagnetic studies, as the period vectors were changed by the external stress. For linear elastic crystals, it is actually also the microscopic but temperature-dependent form of the generalized Hooke's law, then can be used to calculate the corresponding elastic constants of the law, for given temperatures.

Crystal Period Vectors under External Stress in Statistical Physics

For crystal periodic structure prediction, a new and concise approach based on the principles of statistical physics was employed to derive a new form of the equation to determine their period vectors (cell edge vectors), under general external stress. Then the new form is applicable to both classical physics and quantum physics. It also turned out to be the equation of state and the specific explicit equilibrium condition for crystals under external stress and temperature. It should be helpful in piezoelectric and piezomagnetic studies, as the period vectors were changed by the external stress. For linear elastic crystals, it is actually also the microscopic but temperature-dependent form of the generalized Hooke's law, then can be used to calculate the corresponding elastic constants of the law, for given temperatures.