**3.1.2. Powder neutron diffraction**

**c.** Solubility data based on chemical extraction methods, e.g. neutral ammonium citrate

The most important techniques used for the identification and characterization of phosphate minerals include methods for identification of phase composition, chemical composition, structure, surface properties, etc. A few often applied methods are introduced in this chap‐

The diffraction of a beam of X-rays by a crystalline material is the process of beam scattering1 by electrons associated with atoms in the crystal and of the interference of these scattered Xrays because of the periodic arrangement of atoms in the crystal and its symmetry.2

diffraction analysis (XRD) is used for the determination of mineralogical composition and quantitative X-ray diffraction analysis (Rietveld method) for the refinements of structure of

have the wave properties and diffract from a periodic atomic array by VON LAUE [12] and his students in 1912–1913, the analytical application of *X*-ray diffraction has developed slowly over the next 20 years. Most of the earliness efforts were aimed at the solution of crystal structures of common phases. DEBYE and SHEERER (1916) and HULL (1917) suggested that powder diffraction patterns could be used for the identification of quantification of crystalline compounds. However, because most of the early developments were directed toward solving single-crystal structures, it was really the middle 1930s when the powder diffraction method began to attract the follower with the publication of the procedure of HANAWALT and RINN and the database of patterns by HANAWALT, RINN and FREVEL (1938). With the conversion of data sets into the first set of the Powder Diffraction File in 1941, the phase identification applica‐ tions expanded, and the modern counter diffractometer was developed by PARRISH, HAMACH‐

The phase identification was one of the first applications to grow to useful level. Other major applications of diffraction analysis include following phase changes under nonambient conditions and atmospheres. The first diffraction experiments were actually done on single crystals. The method is primarily directed toward determining the crystal periodicity and symmetry and solving the arrangement of atoms in the material because this information is

<sup>1</sup> Scattering is the process where the beam of radiation or particles is deviated from its initial trajectory by the inhomo‐

Other kinds of radiation commonly used for diffraction analysis are neutrons (**Section 3.1.2**) and electrons (**Chapter**

<sup>3</sup> Wilhelm Conrad Röentgen (1845–1923) was the rector of the University of Würzburg [8]. The first X-ray photography

X-ray

[8],[10],[11] in 1895 and the proof that *X*-rays

**d.** PO4/CO3 ratio as a measure of carbonate substitution in phosphate minerals

**e.** Surface area and pore size distribution indicating the potential reactivity

112 Apatites and their Synthetic Analogues - Synthesis, Structure, Properties and Applications

apatite from measured data using specialized software [3],[4],[5],[6].

Following the discovery of *X*-rays by RÖENTGEN3

solubility (NAC, **Section 3.4.3**)

**3.1.1. X-ray diffraction analysis**

ER and LOWITZSCH [5].

was published in 1896 [9].

2

**3.1.10**).

geneity in the medium which it transverses [7].

ter [1],[2].

Neutron powder diffraction (PND) or elastic neutron scattering enables to determine nucle‐ ar and magnetic structure of solids. Most of the information on the nature of ordered magnet‐ ic phases or magnetic structures comes from neutron diffraction experiments. Neutrons have no electric charge and interact with the nuclei rather than with the charge distribution of atoms in matter. They have the wavelength in the range of interatomic distances. They have magnetic moment and interact with the magnetic moment of atoms in matter. The mass of neutrons is similar to that of atomic nuclei; hence, they have energy and momentum similar to those of atoms in solid and fluid materials [13],[14]. The first neutron diffraction experiments were performed in 1945 by EO WOLLAN in the graphite reactor at Oak Ridge National Laboratory, USA [15].

Neutron scattering (NS) results from the interactions with atomic nuclei, i.e. overscattering lengths (distances) of the order of 10−15 m (1 fm).4 Although scattering amplitude decreases greatly with the scattering vector (it is inverse to the scattering length), there are insignifi‐ cant variations of scattering amplitude in the same range of scattering vector for neutrons. Consequently, powder diffraction with neutrons can resolve very fine structural and textur‐ al details of complex atomic structures. Moreover, the weak interaction of neutrons with matter results in very low attenuation offering a unique advantage for nondestructive, in situ work and bulk analysis (for polycrystalline materials, no crushing is required to obtain the pat‐ terns) [14].

Neutron diffraction was used to determine atomic arrangement in material. Inelastic neu‐ tron scattering measures the vibrations of atoms and small-angle neutron scattering5 (SANS) is used to study larger structures such as polymers and colloids. The technique of surface reflection (reflectometry) was used to study layered materials. The technique of SANS provides the information about the size, shape and domain orientations; conformational changes and/or flexibility; and molecular associations is solution. For the structural studies, the elastic scattering effects, where there is no energy exchange between the radiation and atoms, are exploited [7],[14],[16].

Neutron powder diffraction is a method often used for the structure refinement of apatite or apatite type compounds from measured data using specialized software [17],[18],[19],[20],

<sup>4</sup> The interaction with electrons during X-ray analysis takes place over the distances of 10−10 m (1 Å) [14].

<sup>5</sup> Small angle scattering (SAS) of X-rays is abbreviated as SAXS [7].

[21],[22],[23],[24] and the effect of substitutions in the apatite structure [25]. Neutron diffrac‐ tion data enable to explain the oxygen over-stoichiometry in the structure of La9.67(SiO4)6O2.5 apatite [17]. Since neutrons make possible the accurate determination of the thermal factors and provide the visualization of the diffusion paths in ionic conductors, powder neutron diffraction is also used for the characterization of solid oxide fuel cell materials [26]. This method is also used to investigate apatite in hard tissues where it provides the evidence about the deficiency of hydroxyl ion in bone apatites [27] and reconfirms that the inorganic por‐ tion is basically a hydroxylapatite-like material [27],[28].
