THE SCIENCE AND APPLICATIONS OF ACOUSTICS - H. H. Arnold ...

454 16. Ultrasonicson each and every cycle (Gaitan and Crum, 1992; Gaitan et al., 1992). This is theSBSL-type of sonoluminescence.Sonochemistry deals with high-energy chemical reactions that occur duringultrasonic irradiation of liquids. The chemical effects of ultrasound do not resultfrom direct molecular interactions but occur principally from the effects ofacoustic cavitation. Cavitation provides the means of concentrating the diffuseenergy of sound, with bubble collapse producing intense, local heating and highpressures that are extremely transient. Among the clouds of cavitating bubbles,the highly localized hot spots have temperatures of roughly 5000 ◦ K, pressuresexceeding 2000 atm, and heating and cooling rates greater than 10 7 K/s. Ultrasonicscan serve as useful chemical tool, as its chemical effects are diverse andit can provide dramatic improvements in both stoichiometric and catalytic reactions.In a number of cases, ultrasonic irradiation can increase reactivity by amillion-fold.The chemical effects can be categorized into three areas: (a) homogeneoussonochemistry of liquids, (b) heterogeneous sonochemistry of liquid–liquid orliquid–solid systems, and (c) sonocatalysis (which constitutes an overlap of thefirst two categories). Chemical reactions have generally not been observed in theultrasonic irradiation of solids and solid–gas systems.16.4 PhononsIn quantum mechanics, energy states are considered to occur only at discrete levelsor eigenstates, not at any arbitrary values. In the analytical treatment of crystallinesolids, the concept of phonons, often referred to as a “quantitized sound waves,”is used to represent the effects of a transition between the eigenstates of a systemof coupled quantum mechanical oscillators. Phonons generally apply to discretestrictly linear systems, while “classical” sound waves derive from continuous,intrinsically nonlinear systems within the limits of small amplitudes. Althoughphonons can occur in all states of matter, they are most easily discerned in crystallinesolids.In 1819, Dulong and Petit discovered the first evidence for phonons in solidswhen they observed that the specific heat of a solid is twice that of the correspondinggas. This finding suggested the fact that solids have a way of storingpotential energy, in addition to the kinetic energy that is so apparent in gases.Einstein first postulated an acoustic theory of the specific heat of solids by assumingthat the kinetic energy and potential energy arose from atoms oscillatingabout the equilibrium positions in the crystalline lattices. Applying the Planckquantum theory, Einstein related the energy to the frequency but he had made thesimplifying assumption that each atom oscillated independently of the other, so hisformula for the specific heat was therefore incorrect. Peter Debye in 1912 correctlyinferred that these atomic oscillators are coupled, and later Max Born, Theodorevon Kármán, and Moses Blackman refined the theory to the extent of matching theexperimental results of the temperature dependence of the specific heat of solids.