JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY HYDERABAD B.Tech III PROPERTIES OF NANOMATERIALS Previous Question Paper (January/February - 2021 - R16)

The thermal behavior of materials describes how they respond to changes in temperature, characterized primarily by heat capacity, thermal expansion, and thermal conductivity. Heat capacity represents the amount of energy required to raise the temperature of a material, governed by the vibration of atoms within the lattice. At low temperatures, this is described by the Debye model, where heat capacity is proportional to T³, while at higher temperatures, it approaches a constant value according to the Dulong-Petit law.

Thermal expansion occurs due to the asymmetry of the interatomic potential energy well. As temperature increases, the average distance between atoms increases, leading to macroscopic expansion. The coefficient of linear thermal expansion, α, quantifies this change in length per unit temperature change.

Thermal conductivity is the ability of a material to transport heat, primarily through lattice vibrations (phonons) and, in metals, through free electrons. In nanostructured materials, thermal conductivity is often significantly reduced compared to bulk counterparts due to increased phonon scattering at grain boundaries and interfaces, which restricts the mean free path of heat carriers.

Acoustic impedance (Z) is a measure of the opposition a medium presents to the acoustic flow resulting from an acoustic pressure applied to the medium. It is defined as the product of the density of the medium (ρ) and the speed of sound within that medium (v):

When sound waves encounter an interface between two materials with different acoustic impedances, a portion of the wave is reflected, and a portion is transmitted. The reflection coefficient depends on the impedance mismatch; the greater the difference in Z, the higher the reflection at the boundary.

Acoustic radiation refers to the process by which a vibrating surface or source emits sound waves into the surrounding medium. The efficiency of this radiation depends on the coupling between the source and the medium, often described by the radiation impedance. For a small source compared to the wavelength, the radiation is omnidirectional, whereas for larger sources, the radiation becomes highly directional. In nanomaterials, acoustic properties are influenced by the high surface-to-volume ratio, which can alter the effective density and elastic moduli, thereby modifying the impedance characteristics and the efficiency of sound wave propagation and radiation compared to bulk materials.