Size-dependent thermal stresses in the core—shell nanoparticles

Abstract

The thermal stress in a magnetic core—shell nanoparticle during a thermal process is an important parameter to be known and controlled in the magnetization process of the core—shell system. In this paper we analyze the stress that appears in a core—shell nanoparticle subjected to a cooling process. The external surface temperature of the system, considered in equilibrium at room temperature, is instantly reduced to a target temperature. The thermal evolution of the system in time and the induced stress are studied using an analytical model based on a time-dependent heat conduction equation and a differential displacement equation in the formalism of elastic displacements. The source of internal stress is the difference in contraction between core and shell materials due to the temperature change. The thermal stress decreases in time and is minimized when the system reaches the thermal equilibrium. The radial and azimuthal stress components depend on system geometry, material properties, and initial and final temperatures. The magnitude of the stress changes the magnetic state of the core—shell system. For some materials, the values of the thermal stresses are larger than their specific elastic limits and the materials begin to deform plastically in the cooling process. The presence of the induced anisotropy due to the plastic deformation modifies the magnetic domain structure and the magnetic behavior of the system.

Internal Thermal Stress-Driven Phase Transformation in Van der Waals Layered Materials

“…14 Experimental observations of phase transformation at final temperatures below 70 °C strongly indicate the presence of additional geometric factors (G) that elevate the internal thermal stress; thus, thermal stress can be described as σ = GEΔαΔT. 10,15 The extracted geometric factor (G = 7.1) is a reasonable value as confirmed by stress simulations (discussed in Figure 3c).…”

“…The maximum internal stress reaches ∼0.3 GPa (Figure c, orange dotted line), which is far below the external pressure required for phase transformation from RP to BP (black dashed line) . Experimental observations of phase transformation at final temperatures below 70 °C strongly indicate the presence of additional geometric factors ( G ) that elevate the internal thermal stress; thus, thermal stress can be described as σ = GE ΔαΔ T . , The extracted geometric factor ( G = 7.1) is a reasonable value as confirmed by stress simulations (discussed in Figure c).…”

“…A mantle material is selected that melts at high temperatures, whereas the core material remains solid, fully encapsulated by the molten mantle in the crucible (Figure a and Figure S1). Upon cooling, internal thermal stress (σ) is generated at the interface in the mantle–core heterostructure: where E mantle is Young’s modulus of the mantle, Δα is α mantle – α core , and α mantle and α core are respectively the thermal expansion coefficient of the mantle and core. T i and T f are respectively the initial and final temperature during the cooling process.…”

“…A mantle material is selected that melts at high temperatures, whereas the core material remains solid, fully encapsulated by the molten mantle in the crucible (Figure 1a and Figure S1). Upon cooling, internal thermal stress (σ) is generated at the interface in the mantle−core heterostructure: 10 (1…”

Dimension effects on the dielectric properties of fine BaTiO 3 ceramics

“…The performances of BaTiO 3 ceramics can be changed and improved through the addition of different dopants in order to meet the special application. However, it is very easy to result in coreshell structured grains after sintering, [1][2][3][4][5] due to the solid solution of dopants in the grain boundary and diffusion of dopants to the interior of the grain. Grain growth could be inhibited due to the drag effect caused by the dopant atoms distributing on the outer layer of the grain.…”