Inelastic neutron scattering spectroscopy INSS

The description of this method lies outside the scope of this chapter (see Ref. 8). It has only recently been applied to polymers, but has already yielded a figure for the modulus transverse to the chain direction i, as mentioned below.  

3 EXPERIMENTAL VALUES FOR THE MODULUS , ALONG THE CHAIN—THE CRYSTALLINE REGION 

The results are shown on the left hand side of Table 2 (taken from Ref. 8), alongside the calculated values which will be discussed separately. Two of the measured values were obtained from low frequency Raman spectra, and one from INSS (in this case deuterated high density polyethylene was used). Otherwise all the results were obtained by the X-ray method. The same data is shown graphically on the left hand side of Fig. 2. 

It will be seen that the measured elastic modulus parallel to the chain axis varies from 358 x 10 N m for polyethylene, to 41 x 10 N m for polyvinyl tert. butyl ether—a factor of about 90 times. In contrast to this, as will be discussed below, the elastic modulus perpendicular to the chain is found to be about 3 x 10 N m with a range of only 3 times. 

EXPERIMENTAL AND CALCULATED VALUES FOR ELASTIC MODULI ALONG THE CHAIN- j, 

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D.J. Jones J. Roziere (1993). Solid State Ionics, 61, 13-22. Complementarity of optical and incoherent inelastic neutron scattering spectroscopies in the study of proton conducting materials. 

It is difficult to determine the 5 parameters A, B, C, N and E in the Eqs. 5-8 in a unique i/ay because all contribute to -In K°° at high temperatures. To reduce the number of free parameters we assume N = 1 for octahedral site occupancy and select a value of C similar to those obtained by inelastic neutron scattering spectroscopy. In the case of D and T the Einstein temperature Cq and Cj were obtained by scaling C with the inverse of the square root of the hydrogen mass. The results are listed in Table II and plotted as solid lines in the Figs. 2 and 3. One sees that Eqs. 5-7 give a very good description of the -In C values. 

As we shall discuss below, it is also more straightforward to calculate the relative intensity of vibrational modes observed by inelastic neutron scattering than in electron-energy-loss and optical spectroscopies. The relative intensity of the modes, as well as their frequency, can then be used to identify the atomic displacement pattern or eigenvector of the mode. We shall also see through examples of model calculations how the relative intensity of surface vibratory modes is sensitive to the orientation of the adsorbed molecule and the strength and location of its bond to the surface. 

The shifts in vibrational frequencies between the LS and HS species are responsible for the major parts of the entropy changes AS in spin transitions [13]. This has been repeatedly confirmed by infrared [13-15], Raman [14-17], and inelastic neutron scattering spectroscopies [18]. Since the observed entropy change 13.8 J K-1 mol-1 [12] in the present compound is not explained adequately solely by the entropy of the spin multiplicity (R ln(5/3) = 4.25 J K-1 mol-1). However, we cannot assign the extra entropy change to a vibrational origin, since the Raman spectra of the two phases differ only in intensities. 

Vibrational spectroscopy with neutrons is a spectroscopic technique in which the neutron is used to probe the dynamics of atoms and molecules in solids. In this introductory chapter we provide a descriptive account of the discovery and properties of the neutron, the development of neutron scattering, how inelastic neutron scattering spectroscopy compares with infrared and Raman spectroscopy and the benefits of using the neutron as a spectroscopic probe. 

Phonon wings are probably the most important band shaping processes in inelastic neutron scattering spectroscopy and this theme is developed in later chapters. The intensity arising from the vth internal transition and remaining at the band origin, coq, is termed the zero-phonon-band intensity, often found in the literature as Sq. From Eq. (2.62), for R = 0... 

J. Tomkinson G.J. Kearley (1989). J. Chem. Phys., 91, 5164-5169. Phonon wings in inelastic neutron scattering spectroscopy the harmonic approximation. 

J. Eckert, J.M. Nicol, J. Howard F.R. Trouw (1996). J. Phys. Chem., 100, 10646-10651. Adsorption of hydrogen in Ca-exchanged Na-A zeolites probed by inelastic neutron scattering spectroscopy. 

J. Tomkinson, I.J. Braid, J. Howard T.C. Waddington (1982). Chem. Phys., 64, 151-157. Hydrogen-bonding in potassium hydrogen maleate and some simple derivatives studied by inelastic neutron-scattering spectroscopy. 

Also discussed in that section was the information obtained by Zhuravlev, who used mainly classic methods, such as differential thermogravimetry combined with mass spectroscopy and deuterium-exchange. A novel and modern approach for the study of silica surfaces is based on the combined use of computational chemistry and inelastic neutron scattering spectroscopy (43, 44). 

In the RSb manifest crystal-field effects have been observed. They were among the first compounds to be investigated (Liithi et al. 1973b, Mullen et al. 1974). The RSb compounds are well characterized substances with rather small electrical conductivities (Hulliger 1979). The crystal-field splittings have been determined by inelastic neutron scattering spectroscopy (Birgeneau et al. 1973). Therefore, crystal-field effects in the elastic constants have been measured and interpreted quantitatively. 

The organization of this chapter is the following. After definition of some physical constants to be kept in mind and an abstract presentation of infrared and Raman spectroscopy, inelastic neutron scattering spectroscopy is featured in Section 2. In Section 3, the long lasting problem of force-field calculation is enlightened by comparison of calculated and observed INS profiles. By direct comparison, unrealistic dynamical models can be eliminated quite safely. 

Vibrational spectroscopy provides detailed infonnation on both structure and dynamics of molecular species. Infrared (IR) and Raman spectroscopy are the most connnonly used methods, and will be covered in detail in this chapter. There exist other methods to obtain vibrational spectra, but those are somewhat more specialized and used less often. They are discussed in other chapters, and include inelastic neutron scattering (INS), helium atom scattering, electron energy loss spectroscopy (EELS), photoelectron spectroscopy, among others. 

At T < tunneling occurs not only in irreversible chemical reactions, but also in spectroscopic splittings. Tunneling eliminates degeneracy and gives rise to tunneling multiplets, which can be detected with various spectroscopic techniques, from inelastic neutron scattering to optical and microwave spectroscopy. The most illustrative examples of this sort are the inversion of the... 

Kearley, G. J., Pressman, H. A. Slade, R. C. T. (1986). The geometry of the HjOJ ion in dodecatungstophosphoric acid hexahydrate, (HjOJ)j (PWjjOfo), studied by inelastic neutron scattering vibrational spectroscopy. Journal of the Chemical Society Chemical Communications, 1801-2. 

Supplementary to other vibrational spectroscopies, inelastic neutron scattering (INS) spectroscopy is a very useful technique for studying organic molecules as it is extremely sensitive to the vibrations of hydrogen atoms. INS spectroscopy has been used to analyze the molecular dynamics of the energetic compound ANTA 5 <2005CPL(403)329>. 

Vibrations in molecules or in solid lattices are excited by the absorption of photons (infrared spectroscopy), or by the scattering of photons (Raman spectroscopy), electrons (electron energy loss spectroscopy) or neutrons (inelastic neutron scattering). If the vibration is excited by the interaction of the bond with a wave... 

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