Phonon wings

Fig. 8. Luminescence spectra at T=10K of [Rh(thpy)2bpy]+ (upper trace) and of [Ir(thpy)2bpy] + (lower trace) doped into [Rh(ppy)2bpy] PF6. The inserts show the expanded origin region of the spectra. pws and pwa label the Stokes or Antistokes phonon wings, respectively, which accompany the origin line and the vibrational sidebands. The arrows mark two vibrations in the lr3+ spectrum without a counterpart in the spectrum of the corresponding Rh3 complex...

Distinct differences for the various matrices are observed with regard to the coupling of Pt(2-thpy)2 to lattice modes (phonons). These occur in the spectra as resolved phonon satellites and/or as umesolved phonon wings. Such satellites accompany all electronic transitions and also satelhtes of vibrational fundamentals. For example, in Tables 1,5, and 7 (shown later) energies of lattice mode satellites are given for n-octane. 

A striking feature in the vibronic structure of the low temperature emission spectrum of ruthenocene is a repetitive pattern of clusters of bands. The pattern consists of the main peak and three side-peaks which are separated from the main peak by about 47 cm , 65 cm , and 112 cm . The first two side peaks are often not well resolved. The separation between the bands within a cluster is less than the energy of any normal mode. A possible explanation for the side-peaks could be phonon wings on the main 333 cm progression. However, the spectra obtained from organic glasses contain the same repetitive pattern. Thus the structure must arise from molecular normal modes and not from crystal lattice modes. 

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... 

That intensity arising from the vth internal transition but not remaining at (Oo is the intensity in the phonon wing, 5 w. 

Table 2.7 The weights of the phonon wing orders, n, calculated for the antisymmetric stretching mode of the [FHF] ion, at a g of 7 A". ...

Substituting the molecular mass for the reduced mass and a (= 0.0128 A2) for implies a putative Einstein fi equency of about 34 cm. For the purpose of this exercise the one phonon lattice mode spectrum will be represented by a single, sharp transition line at this energy. (This is mathematically convenient but unrealistic, see Chapter 5.) The phonon wings appear to higher fi-equencies of the band origin, as a series of lines spaced at 34 cm intervals, see Table 2.8. 

As the value of Q continues to increase the centre of the Gaussian envelope moves out to higher frequencies and its width expands. The envelope s central intensity maximum decreases dramatically and the total intensity falls, since the Debye-Waller factor is smaller. Eventually the envelope will broaden and weaken to such an extent that it disappears into the experimental background. This simple picture nicely summarises the effects of phonon wings but it will be considerably modified by the introduction of more realistic treatments of the external vibrations of molecular crystals, see Chapter 5. However, the model remains sufficiently robust to provide an introduction to the effects of molecular recoil. 

Whenever the external vibrations produee large anisotropic displacement parameter values for the scattering atoms it will exaggerate the impact of any given value of Q. The phonon wing envelope will move to even higher frequencies and the response will broaden. Only two characteristics of a sample bear on its anisotropic displacement parameter (with samples at low temperatures), the effective molecular mass, Hef[, and the Einstein frequency, see ( 2.6.2.1). The lighter the... 

As an exercise the reader may wish to recalculate the distribution of phonon wing intensities for the earlier example of the bifluoride ( 2.6.4) at a value of 20 A. The results of such a calculation are shown in Fig. 2.7, where the individual components are enveloped in a broad Gaussian. The envelope is centred at, E r =153 cm away from the band origin, at 1370 cm, and it has a width (FWHH) zl = 180 cm. We proceed to calculate both the /Weff and from these parameters using Eqs. (2.77) and (2.78)... 

The characteristic frequency, previously determined ( 2.6.4) as 34 cm is here found to be 38 cm, whilst the calculated effective mass of the bifluoride is 44 amu, close to the molecular mass of 39 amu. The two calculations are clearly self-consistent, as they must be since the phonon wings are simply the start of the molecular recoil in the lattice. However, the extreme naivety of the Einstein model is not usually successful at modelling the lattice dynamics of even simple systems. 

The modem methods of treating INS spectra obtained on powders were introduced and the simple example of the bifluoride ion was treated in detail. The most important band shaping processes were introduced and a Ml treatment of phonon wings was given. With this as a foundation we may proceed in the following chapter to apply the theory to some more realistic yet still straightforward examples. 

Phonon wings were introduced in the context of their impact on the internal vibrational spectrum of molecules but the librational mode is an external mode, it is itself a phonon. However, this is only a question of classification and semantics. The phonon wing treatment is simply one approach to calculating the intensities of combination bands. It is the method of choice when detailed information on the external mode atomic displacements is absent. We now proceed to apply the phonon wing treatment of 2.6.3, from which we shall obtain the value of the mean square displacement of the ammonium ion due to the translational vibrations of the lattice, own (which is but one of the contributions to the full ext.)... 

If the phonon wing model is reasonable the value obtained will be realistic. In preparation for this we calculate the relevant Q values ( 2.3) for this spectrometer at the librational transition, Eq. (5.5). 

The value at the centre of the first order phonon wing, with an energy of 505 cm is different, 23.9 A. The intensities of the zero phonon band and the first order phonon wing are found by integrating the observed spectrum across the individual transitions. In this case from 310 to 380 cm for the librational mode s band origin intensity. So, and from... 

The Eq. (5.10) applies to the total intensity from the vibration and band origin intensities, S2 S = 0.352, must be corrected for any intensity loss, due to phonon wing effects. We extracted a value for a, above, and can use this directly ... 

The internal modes can be seen in Fig. 5.2(b) above 1200 cm. This region of the spectrum is very rich and again there are too many features to be explained by the two fundamentals alone. The external mean square displacement value is so big that most of the intensity arising from the internal vibrations is actually found in the phonon wings ( 2.6.5). Here the full wing is operative and includes translational and librational contributions. Indeed few of the sharp features present in this part of the spectrum are due to zero phonon transitions of the fundamentals. This is but a slightly more severe case of the analysis that will be covered in detail for benzene and we end our analysis of the pure ammonium bromide salt here. 

However, other ammonium halides enable us to explore the spectral impact of the most extreme phonon wing effects, molecular recoil. 

The INS spectrum of the (NH4)o,5Ko.5l mixed salt is compared with that of pure NH4I in Fig. 5.3. The sharp phonon wing features seen in the INS of NH4I have been washed out into a broad smooth band. A schematic diagram of how different systems respond under recoil is given in Fig. 5.4. The intensity appears as a broadened feature at higher energy transfer ( 2.6.5) and in this case the broad band is centred at 2130... 

Fig. 5.5 Comparison of the observed, lower trace, and the calculated, upper trace, INS spectra of benzene. This represents the beginning of the analysis process using the scaled (xO.95) positions of the bands and a naive, isotropic phonon wing.

However, the strength of the external modes has been seriously underestimated, the internal mode band origins are too strong and the phonon wings too weak. The external mode contribution parameter is adjusted by eye so that the observed and calculated distribution of intensities more closely resembles one another in the internal mode region. Most of the sharp peaks observed in the INS correspond to... 

Subsequently both curves decrease in intensity at high Q, due to the Debye-Waller factor and from Eq. (5.25) a = 0.0247 A (= 2/81). Because of this unusual sample the determination of a is imclouded by concerns over the impact of phonon wings ( 5.3.3). 

It is stressed that spectral contamination of transition intensities is a common feature of INS data at all energy transfers and on all types of instrument. It arises from the spectral congestion typical of molecules (even those as simple as benzene) and the effects of phonon wings. The effects of congestion can be exacerbated on direct geometry spectrometers if their energy resolution is not good. 

The impact of phonon wings on the spectra observed on direct geometry spectrometers can be as taxing as their effects on indirect geometry spectrometers at the same Q values. The spectrum of Rb2[PtH6]... 

Fig. 5.14 The development of a phonon wing shown simplified for the V30 mode of adamantane.

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