Neutron diffraction, scattering

Neutron diffraction/scattering can also probe SRO and low-lying excited states called spin waves, but this discussion lies again outside the scope of this article. 

The reason that neutron diffraction is so much more effective than x-ray diffraction as a means for locating hydrogen atoms can be seen in the atomic scattering amplitudes given in Table 9-II (taken from reference 94, except for the neutron diffraction scattering factor for deuterons). 

Single crystal neutron diffraction is in many ways a complementary technique to X-ray diffraction. In neutron diffraction scattering by the atomic nuclei rather than the electron density gives rise to diffraction. However, neutrons have a spin and polarisation of the neutron beam can be used to undertake diffraction experiments to map the distribution of unpaired electrons (the spin density) in a crystal. 

Figure 2 depicts schematically the geometry and the spin-charge order for an in-plane stripe as derived from low-energy neutron diffraction/scattering in a typical hole-doped cuprate... 

Neutron diffraction scattering with isotope substitution (NDIS) is considered today the only means by which we can extract direct information about the site-site pair correlation functions of liquids and amorphous materials [143-146]. What makes this approach possible is the justifiable assumption that light (H2O) and deuterated D2O) water exhibit the same structural features [147], and allow the extraction of... 

Electron scattering /diffraction techniques Neutron diffraction / scattering Optical microscopy... 

In a sense, a superconductor is an insulator that has been doped (contains random defects in the metal oxide lattice). Some of the defects observed via neutron diffraction experiments include metal site substitutions or vacancies, and oxygen vacancies or interstituals (atomic locations between normal atom positions). Neutron diffraction experiments have been an indispensable tool for probing the presence of vacancies, substitutions, or interstituals because of the approximately equal scattering power of all atoms. 

B. N. Brockhouse (McMaster University) and C. G. Schull (Massachusetts Institute of Technology) pioneering contributions to neutron scattering techniques for studies of condensed matter (namely neutron spectroscopy and neutron diffraction techniques, respectively). 

Neutron diffraction is one of the most widely used techniques for the study of liquid structure. In the experiment, neutrons are elastically scattered off the nuclei in the sample and are detected at different scattering angles, typically 3° to 40°, for the purpose of measuring intermolecular structure whilst minimizing inelasticity corrections. The resultant scattering profile is then analyzed to provide structural information. 

X-ray diffraction has been used for the study both of simple molten salts and of binary mixtures thereof, as well as for liquid crystalline materials. The scattering process is similar to that described above for neutron diffraction, with the exception that the scattering of the photons arises from the electron density and not the nuclei. The X-ray scattering factor therefore increases with atomic number and the scattering pattern is dominated by the heavy atoms in the sample. Unlike in neutron diffraction, hydrogen (for example) scatters very wealdy and its position cannot be determined with any great accuracy. 

Beryllium(II) is the smallest metal ion, r = 27 pm (2), and as a consequence forms predominantly tetrahedral complexes. Solution NMR (nuclear magnetic resonance) (59-61) and x-ray diffraction studies (62) show [Be(H20)4]2+ to be the solvated species in water. In the solid state, x-ray diffraction studies show [Be(H20)4]2+ to be tetrahedral (63), as do neutron diffraction (64), infrared, and Raman scattering spectroscopic studies (65). Beryllium(II) is the only tetrahedral metal ion for which a significant quantity of both solvent-exchange and ligand-substitution data are available, and accordingly it occupies a... 

Why, then, is the magnetisation density used The answer is that the magnetisation density is important for certain approximations which are usually made in analysing neutron scattering experiments. In the standard polarised neutron diffraction (PND) experiment [5], only one parameter is measured - the so-called flipping ratio . It is impossible to determine a vector quantity like the magnetisation density from a single number, unless some assumptions are made. The assumptions usually made are ... 

Also known for some time is a phase transition at low temperature (111K), observed in studies with various methods (NQR, elasticity measurement by ultrasound, Raman spectrometry) 112 temperature-dependent neutron diffraction showed the phase transition to be caused by an antiphase rotation of adjacent anions around the threefold axis ([111] in the cubic cell) and to lower the symmetry from cubic to rhombohedral (Ric). As shown by inelastic neutron scattering, this phase transition is driven by a low-frequency rotatory soft mode (0.288 THz 9.61 cm / 298 K) 113 a more recent NQR study revealed a small hysteresis and hence first-order character of this transition.114 This rhombohedral structure is adopted by Rb2Hg(CN)4 already at room temperature (rav(Hg—C) 218.6, rav(C—N) 114.0 pm for two independent cyano groups), and the analogous phase transition to the cubic structure occurs at 398 K.115... 

The model reference density pref is a good approximation to the dominant part of p appearing very close to the nuclei, and so Ap(r) will be very small everywhere and is assumed to be experimental noise. If the peaks in p are located, then the nuclear positions are known and the structure is resolved. Because they have no core, hydrogen atoms produce only very small maxima, and thus their positions are difficult to locate with any accuracy. If it is important to locate their positions accurately, this can be done by neutron diffraction. Neutrons are scattered by nuclei rather than electrons, and so the positions of the nuclei are obtained directly. Neutron diffraction is particularly important for the accurate determination of the positions of hydrogen atoms. 

Although X-ray and neutron diffraction and scattering methods give only approximate estimates of hydration numbers they can provide precise measures of ion-water distances in solution. In calcium chloride and bromide solutions of various concentrations, Ca-0 distances of between 2.40 and 2.44 A have been reported (167,168,171,172) Ca-0 — 2.26A was claimed in an early X-ray investigation of molar calcium nitrate solution (167,186). EXAFS and LAXS studies showed a broad and asymmetric distribution of Ca-0 distances centered on a mean value of 2.46 A (174). 

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