Central peak

One of the most striking features of the scattered spectrum for either neutrons or light in the vicinity of a phase transition is the appearance of a divergent elastic or quasielastic peak centred near zero frequency shift that lies entirely outside the quasiharmonic soft-mode description of the dynamics (Fleury Lyons, 1983). The first observation of a divergence in scattered intensity is due to Yakovlev et ai, (1956), who observed the phenomenon in the a-fi transition of quartz. The scattered intensity increases dramatically, sometimes by a factor of 10000 near and the maximum value of line width of the diverging feature is itself rather small ( 1 cm ). In Fig. 4.7, typical central peaks are shown for the purpose of illustration. 

It was thought for some time that central peaks were due to impurities, defects and other such extrinsic or intrinsic factors. A number of models and mechanisms based on entropy fluctuations, phonon density fluctuations, dielectric relaxation, molecular 

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By examining the results presented in figure 3, one can notice that the very well marked central peak correspons exactly to the passage of the pick-up coil over the discontinuity, which... 

The Q and ft) dependence of neutron scattering structure factors contains infonnation on the geometry, amplitudes, and time scales of all the motions in which the scatterers participate that are resolved by the instrument. Motions that are slow relative to the time scale of the measurement give rise to a 8-function elastic peak at ft) = 0, whereas diffusive motions lead to quasielastic broadening of the central peak and vibrational motions attenuate the intensity of the spectrum. It is useful to express the structure factors in a form that permits the contributions from vibrational and diffusive motions to be isolated. Assuming that vibrational and diffusive motions are decoupled, we can write the measured structure factor as... 

PRE-TRANSFORMATION LATTICE STRAIN ANISOTROPY AND CENTRAL PEAK SCATTERING... 

High-resolution dilatometric measurements have revealed the appearance of anisotropy in the cubic-phase thermal strain in the precursive temperature region for the soft-mode martensitic transformations in VaSi/ Ni-Al, In-Tl/ and SrTiOa In the case of Ni-Al and SiTiOa, the onset temperatures for the strain anisotropy are close to those at which the appearance of central peak behaviour occurs. 

It is the purpose of this paper to review briefly the thermal strain anisotropy data and to consider the implications for the central peak scattering. 

The observation of the departure from cubic symmetry above Tm co-incident with the appearance of the central peak scattering serves to resolve the conflict between dynamic and lattice strain models. The departure from cubic symmetry may be attributed to a shift in the atomic equilibrium position associated with the soft-mode anharmonicity. In such a picture, the central peak then becomes the precusor to a Bragg reflection for the new structure. 

Such off-zone-centre, soft-mode systems offer the most favourable conditions for a test of the hypothesis that the central peak is a precursor to a Bragg reflection in the transformation phase. Zone-centre softening, such as occurs in NbaSn, results in the central mode scattering emerging from an existing Bragg peak, which ultimately splits in the lower symmetry transformation structure, which presents a problem with resolution. 

B. J. Halperin and C.M. Varma, Defects and the central peak near structural phase... 

J.B. Hastings, S.M. Shapiro, and B.C. Frazer, Central-peak enhancement in hydrogen-reduced SrTiOs, Phys. Rev. Lett. 10 4 (1978). 

A. Zheludev, S.M. Shapiro, and P. Wochner, Phonon anomaly, central peak, and microstructures in Ni2MnGa, Phys. Rev B 51 17 (1995). 

The gaussian distribution is a good example of a case where the mean and standard derivation are good measures of the center of the distribution and its spread about the center . This is indicated by an inspection of Fig. 3-3, which shows that the mean gives the location of the central peak of the density, and the standard deviation is the distance from the mean where the density has fallen to e 112 = 0.607 its peak value. Another indication that the standard deviation is a good measure of spread in this case is that 68% of the probability under the density function is located within one standard deviation of the mean. A similar discussion can be given for the Poisson distribution. The details are left as an exercise. 

Fig. 0.2. (a) The comb spectrum of N2 considered as a quantum rotator. The envelope of the rotational structure of the Q-branch slightly split by the rotovibra-tional interaction is shaded, (b) The depolarized rotovibrational spectrum of N2 at corpuscular density n = 92 amagat, T = 296 K and pressure p = 100 atm. The central peak, reported in a reduced (x30) scale is due to a polarized component [5] (V) experimental (—) best fit. 

Measured at 50.3 MHz in chloroform-rf-referenced to the central peak of the chloroform- triplet (76.9 ppm). eMeasured in chloroform- at 75.5 MHz, referenced to internal Me4Si. 

As mentioned already, the INEPT spectra are typified by the antiphase character of the individual multiplets. The INEPT C-NMR spectrum of 1,2-dibromobutane is shown, along with the normal off-resonance C-NMR spectrum, in Fig. 2.12. Doublets show one peak with positive phase and the other with negative phase. Triplets show the outer two peaks with positive and negative amplitudes and the central peak with a weak positive amplitude. Quartets have the first two peaks with positive amplitudes and the remaining two peaks with negative amplitudes. 

The non-equivalence of the ester protons in the monomethyl- and monophenyl-phosphinic ester function, as in (44, Ch = chalkogen), has been studied. Compounds of type (45) have some interesting stereochemistry. They are prepared from racemic secondary butyl alcohol, and the presence of three signals in the P n.m.r. spectrum confirms that the phosphorus atom is the centre of pseudo-asymmetry. A 1 2 1 triplet is observed which is attributed to the presence of equal amounts of two mesa forms, (45) and (46), which have different values of Sp (outer peaks), and two racemic forms, (47) and (48), which have identical values of 8p (central peak). 

A 13C-NMR spectrum for polyfdimethyl 5-(4-hydroxy butoxy) isophthalate) [146] is shown in Figure 25. The terminal units with the highest mobility (peak 1) is to the left of the spectrum, whereas the least mobile branched units (peak 2) are at the right, whereas the linear units with intermediate mobility (peak 3) are seen as the central peak. 

Fig. 11. Channeling data for the 111 plane (Marwick et al., 1987, 1988), showing data for the nuclear reaction with 2H atoms in the sample and the yield of elastically backscattered 3He ions. The central peak in the 2H scan is important evidence that the 2H atoms occupy bond-center sites. The solid line is a fit to the data, as described in the text.

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