## Ray Diffraction

X-ray diffraction (XRD) is one of the most commonly used spectroscopic techniques which ultizes the diffraction of a light through the crystalline lattice serving as a diffraction grating. When X-ray radiation passes through matter, the radiation interacts with the electrons in the atoms, resulting in scattering of the radiation. If the atoms are organized in planes (i.e., the matter is crystalline) and the distances between the atoms are of the same magnitude as the wavelength of the X-rays, constructive and destructive interference will occur. This results in diffraction where X-rays are emitted at characteristic angles based on the spaces between the atoms organized in crystalline structures called planes. Most crystals can have many sets of planes passed through their atoms. Each set of planes has a specific interplanar distance and gives rise to a characteristic angle of diffracted X-rays. The relationship between wavelength, atomic spacing d, and angle 6 is described geometrically by the Bragg equation as nA = 2d sin 6. If the wavelengh A is known depending on the type of X-ray tube used and the angle 6 is measured with a camera or diffractometer, then the inter-planar distance can be calculated from the Bragg equation. n is an integer and represents the order of reflection, as in the case of light diffracted from an optical grating. But whereas diffraction from an optical grating takes place essentially at a single plane, X-rays penetrate through many planes of atoms and diffraction takes within a certain volume of the crystal, which acts as a kind of three-dimensional diffraction grating. A set of d-spaces obtained from a single compound represents the set of planes that can be passed through the atoms and can be used for comparison with sets of d-spaces obtained from standard compounds.

There are many X-ray diffractometers made by different companies with different radiations, among which CuKa or CoKa radiation is the most common one. As an example, a Rigaku D/Max-rA rotation target diffractometer is normally equipped with a graphite crystal monochromater for calibration. XRD can be used for analysis of the formation of the phases and their structures, not only for bulk materials but also for nanoparticles and nanocapsules. Since X-rays penetrate through many planes of atoms, XRD usually gives the information of a comparatively large (or macroscopic) amount of the materials, namely, that of the whole system. Detailed structural information, like space group, characteristic interplanar spacings, lattice parameters, atomic site coordinate, atomic occupation, etc., can be derived for the phases in the materials. It is easier to detect a bulk material with a single phase, or better a single crystal, for a quanta-tive characterization.

Due to advances in XRD technology, XRD data can be analyzed quantatively for the relative amount of different phases in a bulk material, when the diffraction factors of each kind of atom or phase in the material are known. However, it is hard to derive the relative amount of different phases and to obtain detailed structural information on the nanocapsules from XRD observation. The difficulties are mainly due to the fact that too many XRD peaks of different phases mix each other and that the different mechanisms and/or factors for the contribution to the XRD peak strengths come from the nanoparticles, the bulk materials, and the interfaces/surfaces. The average grain sizes of the materials can be deduced from Scherrer's method of XRD, in which slow scans are performed around the properly selected reflections and each scan is corrected for Ka spectral and instrument broadening by a computer implementation of Stokes's procedure.

Fig. 10 shows the XRD spectrum of Fe(B) nanocapsules showing diffraction peaks associated with the existence of a-Fe [a-Fe(B) solid solution], FeB, y-Fe, and Fe3B phases in the cores [122]. There are some weak peaks corresponding to the Fe3O4 [and/or Fe3O4(B)] phase. Almost all diffraction peaks in the XRD spectrum of the nanocapsules come

| Fc(li) Nanocapsules

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