Neutron diffraction materials

L. H. Schwartz and J. B. Cohen. Diffraction from Materials. Springer-Verlag, Berlin, 1987. A recent text that includes X-ray, neutron, and electron diffiaction, but emphasizes XRD in materials science. A good introduction and highly recommended. 

Like X-ray and electron diffraction, neutron diffraction is a technique used primarily to characterize crystalline materials (defined here as materials possessing long-range order). The basic equation describing a diffraction experiment is the Bra equation ... 

Fitch AN, Cole M (1991) The stmcture of KU02P04.3D20 refined from neutron and synchrotron-radiation powder diffraction data. Material Res 6ull 26 407-414 Fitch AN, Fender 6EF (1983) The stmcture of deuterated ammonium uranyl phosphate trihydrate, ND4U02P04(D20)3by powder neutron diffraction. Acta Crystallogr C39 162-166 Flachsbart 1 (1963) Zur Kristallstruktur von Phosphoferrit (Fe, Mn)3(P04)2(H20)3. Z Kristallogr 118 327-331... 

Instrumentation. The experimental setup is similar to that employed for in situ X-ray diffraction. The material under investigation is pressed into a thin sheet and mounted together with suitable counter and reference electrodes into a silica cell. In order to decrease the large incoherent scattering contributions from protons in aqueous electrolyte solutions, deuterated solutions are used. In a typical study, the reaction mechanism of Ni(OH)2 (employed in nickel accumulators) was studied with neutron powder diffraction NPD [46]. A direct and continuous structural transformation of both the y- and jS-NiOOH phases into j8-Ni(OH)2 was observed during reduction with no direct relationship or discontinuity related to the transition from the first discharge electrode potential to the second one, which was located about 0.4 V lower. 

Physics chemistry geology X-ray diffraction electron diffraction neutron diffraction materials science crystallography mechanical engineering physical chemistry quantum mechanics organic chemistry molecular biology fiber diffraction mineralogy metallurgy differential equations partial differential equations Fourier analysis optics spectroscopy. 

Today, a variety of ph3 ical methods are used to investigate the structural features of electrode materials X-ray diffraction, neutron diffraction, XANES spectroscopy, NMR, ESR, Raman spectroscopy, and so on. The presence of transition metal ions (Co, Ni, Mn, V, Fe) in majority of the cathode materials stimulates their study by means of electron spin resonance (ESR) technique as well. The ESR is the sensitive method to study the details of local electronic and crystal structure and allows determining the valence state of magnetic ions in a crystal structure. 

The important structural information for amorphous materials is usually derived (as in crystalline counterparts) from X-ray diffraction, neutron diffraction, or electron diffraction or a combination of these methods. 

See also Inelastic Neutron Scattering, Applications Inelastic Neutron Scattering, Instrumentation Inorganic Compounds and Minerals Studied Using X-Ray Diffraction Materials Science Applications of X-Ray Diffraction Neutron Diffraction, Theory Powder X-Ray Diffraction, Applications Structure Refinement (Solid State Diffraction). 

Keywords In situ Neutron Powder Diffraction, Cathode materials. Solid Oxide Fuel Cell, Ruddlesden-Popper Oxides, Thermal analysis... 

The specific surface area of a solid is one of the first things that must be determined if any detailed physical chemical interpretation of its behavior as an adsorbent is to be possible. Such a determination can be made through adsorption studies themselves, and this aspect is taken up in the next chapter there are a number of other methods, however, that are summarized in the following material. Space does not permit a full discussion, and, in particular, the methods that really amount to a particle or pore size determination, such as optical and electron microscopy, x-ray or neutron diffraction, and permeability studies are largely omitted. 

We have thus far discussed the diffraction patterns produced by x-rays, neutrons and electrons incident on materials of various kinds. The experimentally interesting problem is, of course, the inverse one given an observed diffraction pattern, what can we infer about the stmctirre of the object that produced it Diffraction patterns depend on the Fourier transfonn of a density distribution, but computing the inverse Fourier transfomi in order to detemiine the density distribution is difficult for two reasons. First, as can be seen from equation (B 1.8.1), the Fourier transfonn is... 

A variety of experimental techniques have been employed to research the material of this chapter, many of which we shall not even mention. For example, pressure as well as temperature has been used as an experimental variable to study volume effects. Dielectric constants, indices of refraction, and nuclear magnetic resonsance (NMR) spectra are used, as well as mechanical relaxations, to monitor the onset of the glassy state. X-ray, electron, and neutron diffraction are used to elucidate structure along with electron microscopy. It would take us too far afield to trace all these different techniques and the results obtained from each, so we restrict ourselves to discussing only a few types of experimental data. Our failure to mention all sources of data does not imply that these other techniques have not been employed to good advantage in the study of the topics contained herein. 

Vitreous siUca is considered the model glass-forming material and as a result has been the subject of a large number of x-ray, neutron, and electron diffraction studies (12—16). These iavestigations provide a detailed picture of the short-range stmcture ia vitreous siUca, but questioas about the longer-range stmcture remain. 

Alternatives to XRD include transmission electron microscopy (TEM) and diffraction, Low-Energy and Reflection High-Energy Electron Diffraction (LEED and RHEED), extended X-ray Absorption Fine Structure (EXAFS), and neutron diffraction. LEED and RHEED are limited to surfaces and do not probe the bulk of thin films. The elemental sensitivity in neutron diffraction is quite different from XRD, but neutron sources are much weaker than X-ray sources. Neutrons are, however, sensitive to magnetic moments. If adequately large specimens are available, neutron diffraction is a good alternative for low-Z materials and for materials where the magnetic structure is of interest. 

Here Pyj is the structure factor for the (hkl) diffiaction peak and is related to the atomic arrangements in the material. Specifically, Fjjj is the Fourier transform of the positions of the atoms in one unit cell. Each atom is weighted by its form factor, which is equal to its atomic number Z for small 26, but which decreases as 2d increases. Thus, XRD is more sensitive to high-Z materials, and for low-Z materials, neutron or electron diffraction may be more suitable. The faaor e (called the Debye-Waller factor) accounts for the reduction in intensity due to the disorder in the crystal, and the diffracting volume V depends on p and on the film thickness. For epitaxial thin films and films with preferred orientations, the integrated intensity depends on the orientation of the specimen. 

The classical approach for determining the structures of crystalline materials is through diflfiaction methods, i.e.. X-ray, neutron-beam, and electron-beam techniques. Difiiaction data can be analyzed to yield the spatial arrangement of all the atoms in the crystal lattice. EXAFS provides a different approach to the analysis of atomic structure, based not on the diffraction of X rays by an array of atoms but rather upon the absorption of X rays by individual atoms in such an array. Herein lie the capabilities and limitations of EXAFS. 

Since the recognition in 1936 of the wave nature of neutrons and the subsequent demonstration of the diffraction of neutrons by a crystalline material, the development of neutron diffraction as a useful analytical tool has been inevitable. The initial growth period of this field was slow due to the unavailability of neutron sources (nuclear reactors) and the low neutron flux available at existing reactors. Within the last decade, however, increases in the number and type of neutron sources, increased flux, and improved detection schemes have placed this technique firmly in the mainstream of materials analysis. 

As with other diffraction techniques (X-ray and electron), neutron diffraction is a nondestructive technique that can be used to determine the positions of atoms in crystalline materials. Other uses are phase identification and quantitation, residual stress measurements, and average particle-size estimations for crystalline materials. Since neutrons possess a magnetic moment, neutron diffraction is sensitive to the ordering of magnetically active atoms. It differs from many site-specific analyses, such as nuclear magnetic resonance, vibrational, and X-ray absorption spectroscopies, in that neutron diffraction provides detailed structural information averaged over thousands of A. It will be seen that the major differences between neutron diffraction and other diffiaction techniques, namely the extraordinarily... 

Another major difference between the use of X rays and neutrons used as solid state probes is the difference in their penetration depths. This is illustrated by the thickness of materials required to reduce the intensity of a beam by 50%. For an aluminum absorber and wavelengths of about 1.5 A (a common laboratory X-ray wavelength), the figures are 0.02 mm for X rays and 55 mm for neutrons. An obvious consequence of the difference in absorbance is the depth of analysis of bulk materials. X-ray diffraction analysis of materials thicker than 20—50 pm will yield results that are severely surface weighted unless special conditions are employed, whereas internal characteristics of physically large pieces are routinely probed with neutrons. The greater penetration of neutrons also allows one to use thick ancillary devices, such as furnaces or pressure cells, without seriously affecting the quality of diffraction data. Thick-walled devices will absorb most of the X-ray flux, while neutron fluxes hardly will be affected. For this reason, neutron diffraction is better suited than X-ray diffraction for in-situ studies. 

Some of the techniques included apply more broadly than just to surfaces, interfaces, or thin films for example X-Ray Diffraction and Infrared Spectroscopy, which have been used for half a century in bulk solid and liquid analysis, respectively. They are included here because they have by now been developed to also apply to surfaces. A few techniques that are applied almost entirely to bulk materials (e.g.. Neutron Diffraction) are included because they give complementary information to other methods or because they are referred to significantly in the 10 materials volumes in the Series. Some techniques were left out because they were considered to be too restricted to specific applications or materials. 

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