Longitudinal collective oscillation

As an example, let us consider liquid water (Fig. 8). The highest oscillator strength, fx = 0.43, corresponds to the transition ha>x = 13.5 eV. The peak the energy-loss function Im [-l/e(w)] has around 21 eV is of plasmon nature, that is, corresponds to longitudinal collective oscillations... 

Collective oscillation of electron gas in metal is known as plasmon. Generally, plasmon refers to the longitudinally collective oscillation of electron gas with respect to the crystal lattice. Plasmon can be crudely categorized as bulk, surface, and particle (Mie) plasmons. The bulk plasmon denotes a collective excitation of the electron gas in the bulk of the metal, which propagates as a longitudinal charge density fluctuation at a resonance frequency ( pj) as mentioned in Equation 13.1. 

For most of the metals, the energy corresponding to cOpj is observed in the order of 10-15 eV. But due to the longitudinal nature of bulk plasmon, excitation with visible light is not possible. In case of surface plasmon (SP), two directions are observed for the mobility of electrons, along the plane parallel to surface which is high (quasi free electrons) and perpendicular to the surface which is limited due to the surface of the metal. So the collective oscillation at the surface is less pronounced than that of the bulk. The relation between bulk and SP is defined by Equation 13.2. 

A collective oscillation of carriers with a plasma resonance is obtained whenever E =0 and (dei/dci ) , =0 >0. We notice that at 300K E in fig. 12 has three zero crossings, whore those at 1.75 and 0.0053 eV fulfill the conditions for a longitudinal oscillation of free carriers. The transition at about 0.1 eV with (dei/dcu) =o <0 indicates a transverse excitation and is due to the d-f interband transition. 

Valence electrons also can be excited by interacting with the electron beam to produce a collective, longitudinal charge density oscillation called a plasmon. Plas-mons can exist only in solids and liquids, and not in gases because they require electronic states with a strong overlap between atoms. Even insulators can exhibit... 

Since micro-gravimetry with the EQCM lacks specificity only the difference of cation and anion fluxes can be obtained by microgravimetry and therefore an independent measurement of specific ions is needed. Scanning electrochemical microscopy (SECM) coupled with a quartz crystal microbalance with independent potential control of the tip and substrate has been recently done by Cliffel and Bard [28]. In this experiment generation at the substrate (EQCM crystaj) working electrode and collection at the tip of an ultramicroelectrode (UNE) that was approached perpendicular to the EQCM crystal was employed with measurement of A/. Hillier and Ward [8] had previously used a scanning microelectrode to map the mass sensitivity across the surface of the QCM crystal. Reflection of longitudinal waves at the UME tip limits these experiments due to oscillations. 

Plasmons consist of layers of electrons in a metal that oscillate collectively at the plasma frequency. The electrons interact with the ion cores causing them to oscillate at their longitudinal frequency >l. 

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