**3.2.1. Identification of the specimen**

Some techniques mentioned above will be demonstrated on the specimen of apatite sample (**Fig. 14**(**a**)) from Sljudjanka, Bajkal. The translucent specimen with glassy luster is greenish blue colored and brittle as can be seen from large amount of smoothly curving conchoidal fractures on the surface (please see also **Fig.** 20). When scratched by a single crystal of corundum (**Fig. 14**(**b**)), the sample shows white colored scratch. Since the sample surface can be also scratched by feldspar (**Fig. 14**(**c**)) but not by fluorite, the hardness in the Mohs scale17 is equal to 5, i.e. corresponds to apatite.

<sup>15</sup> The flow of fluids through porous materials is of great importance in the fields of industrial chemistry, oil technology, and agriculture. In general, it may be stated that the principal interest is in the transport through reactive materials [147].

<sup>16</sup> Experimental techniques for the measurement of relative permeability can be divided to steady- (1) and unsteady-state (displacement) methods (2). The steady-state method was developed by HASSLER (1944). Semipermeable membranes are provided at each end which keeps the fluids separated, except inside the core where the fluids flow simultaneously. The pressure is measured in each phase through semipermeable barriers, and the pressure differences between the phases are maintained constant throughout the medium so as to eliminate the capillary end effect as well as to ensure a uniform saturation along the core. The saturation can be altered by applying capillary pressures across the nonwetting phase ports and wetting phase semipermeable membranes [146].

<sup>17</sup> The Mohs scale of mineral hardness is graduated as follows: talc (1), gypsum (2), calcite (3), fluorite (4), apatite (5), orthoclase (6), quartz (7), topaz (8), corundum (9), and diamond (10). Apatite should be also scratched by steel knife (up to 5.5) and glass (up to 6).

**Fig. 14.** Specimen of apatite from Sljudjanka, Bajkal (a) shows white color of scratch (b). The sample can be also scratched by minerals with hardness ≥6 (feldspar and higher) on the Mohs scale (c).

The microhardness of apatite sample was then determined by Vickers microhardness test.18 **Fig. 15** shows the replica of diamond pyramid base19 on the surface after the indentation of sample. The average hardness of sample was determined to be 552 (±30) HV 0.05/10. The formation of radial cracks on the corners indicates brittle material [157]. According to the mineral hardness conversion charts, the measured value is in good agreement with the tabular value of apatite (535 HV [158]).

Moreover, the sample does not show any luminescence when elucidated by long UV light (**Fig. 16**(**a**)). The specific gravity of the specimen was assessed by hydrostatic weighting (b) and pycnometric technique (c) to be 3.18 and 3.16 ± 0.20 g·cm−3, respectively. These values are in a good agreement with average density of apatite (3.19 g·cm−3, **Chapter 1**). All properties of investigated specimen mentioned above identify it as apatite, but the exact kind of apatite mineral and its chemical composition must still be determined yet.

**Fig. 15.** The Vickers microhardness test with the load of 0.05 kgf for the time of 10 s and the correlation of results with the Mohs scale.

<sup>18</sup> Hardness tester LECO AMH 43. The method is also known as the Vickers pyramid number (HV) or the diamond pyramid hardness (DPH).

<sup>19</sup> Diamond pyramid with apical angle of 136°.

**Fig. 16.** The specimen of apatite under UV light (compared with the fragment of red luminescence of alumina).

The sample was next treated to fine powder via milling in stain-less steal laboratory vibra‐ tion mill. The apatite mineral was then determined by *X*-ray diffraction analysis (**Fig. 17**), midinfrared spectroscopy (**Fig. 18**) and EBDS (**Fig. 23**) as fluorapatite (Ca5(PO4)3F, ref. [159]) with small amount (1%) of accessory mineral calcite20 (CaCO3). Since the crystallographic parame‐ ters of identified hexagonal apatite are *a* = 9.3917, *c* = 6.8826 Å and *Z* = 2, it is possible to calculate the axial ratio (**Eq. 11**), the volume of cell (**Eq. 12**) and the density (**Eq. 13**) as follows:

$$a\text{:c} = 1 \text{:} 0.7328 \tag{11}$$

$$W = a^2 \ c \ \sin(60) = 9.3917^2 \ 6.8826 \ \sin(60) = \\$25.74 \ \stackrel{\circ}{A} \tag{12}$$

$$\begin{aligned} \rho\_{\text{calculated}} &= \int \rho\_{\text{quine}} \, \mathbf{Z} \left\langle \begin{array}{c} N\_A \\ N\_A \end{array} \right\rangle = 504.3 \, \text{l} \times 2 \, \text{l} \\ \mathbf{j} &= 3.19 \text{ g} \cdot \text{cm}^3 \end{aligned} \right\vert \, 525.74 \frac{6.025 \times 10^{23}}{1 \cdot 10^{24}} \tag{13}$$

where *M* is the molecular weight of fluorapatite (**Table 7** in **Chapter 1**) and *N*<sup>A</sup> is the Avogadro constant. The reconstruction of the cell of investigated apatite specimen is shown in **Fig. 24**.

#### **3.2.2. X-ray diffraction analysis**

**Fig. 14.** Specimen of apatite from Sljudjanka, Bajkal (a) shows white color of scratch (b). The sample can be also

The microhardness of apatite sample was then determined by Vickers microhardness test.18

sample. The average hardness of sample was determined to be 552 (±30) HV 0.05/10. The formation of radial cracks on the corners indicates brittle material [157]. According to the mineral hardness conversion charts, the measured value is in good agreement with the tabular

Moreover, the sample does not show any luminescence when elucidated by long UV light (**Fig. 16**(**a**)). The specific gravity of the specimen was assessed by hydrostatic weighting (b) and pycnometric technique (c) to be 3.18 and 3.16 ± 0.20 g·cm−3, respectively. These values are in a good agreement with average density of apatite (3.19 g·cm−3, **Chapter 1**). All properties of investigated specimen mentioned above identify it as apatite, but the exact kind of apatite

**Fig. 15.** The Vickers microhardness test with the load of 0.05 kgf for the time of 10 s and the correlation of results with

<sup>18</sup> Hardness tester LECO AMH 43. The method is also known as the Vickers pyramid number (HV) or the diamond

on the surface after the indentation of

scratched by minerals with hardness ≥6 (feldspar and higher) on the Mohs scale (c).

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

mineral and its chemical composition must still be determined yet.

**Fig. 15** shows the replica of diamond pyramid base19

value of apatite (535 HV [158]).

the Mohs scale.

pyramid hardness (DPH).

<sup>19</sup> Diamond pyramid with apical angle of 136°.

Powder X-ray diffraction analysis of the apatite specimen (**Fig. 17**) identified it as fluorapa‐ tite. According to quantitativeRietveld analysis, the sample contains 99% offluorapatite. There is also small amount (1%) of calcite21 that occurs on the surface of apatite specimen. Since the fluorapatite specimen (**Fig. 14**) is single crystal (**Section 3.2.6**), the crystal faces cannot be recognized, i.e. the crystal habit is anhedral (refer to **Footnote 2** in **Chapter 2**). Nevertheless, XRD pattern shows that the most intensive diffraction possesses the Miller index (211), which corresponds to the Miller-Bravais indices (21–31), i.e. dihexagonal dipyramid (**Chapter 1**).

<sup>20</sup> Since it is present as "free carbonate," the sample cannot be considered as carbonate-fluorapatite (**Section 2.6** and **4.6.1**). 21 As the results of thermal analysis revealed (**Section 3.2.4**), the Rietveld analysis slightly overestimates the content of free carbonate in the sample.

There is also basal pinacoid {1000}, first-order {10–10} and second-order {11–20} hexagonal prism and dihexagonal prism {21–30}.

**Fig. 17.** X-ray diffraction analysis of investigated specimen of apatite.

It is obvious that fluorapatite belongs to the hexagonal-dipyramidal crystal system, but the estimation of crystal habit of corresponding euhedral crystals from these results is highly speculative due to possible combination of pinacoid (*c*), first-order (m) and second-order hexagonal prisms (a) and first-order (*p*) and second-order dipyramids (*s*) with dihexagonal dipyramid (*v*) faces in the single crystal.

#### **3.2.3. Infrared and Raman spectroscopy**

Infrared (mid-FT-IR22) and Raman spectrum of fluorapatite is shown in **Fig. 18**(**a**) and (**b**), respectively. The most expressive infrared bands are attributed to fundamental frequencies of tetrahedral phosphate ion [PO4] 3−. The structure of apatite leads to the reduction of ion symmetry from *T*<sup>d</sup> (four fundamental frequencies with IR inactive *ν*<sup>1</sup> mode) to *C*s, where *ν*<sup>1</sup> mode becomes IR active [128],[160],[161],[162],[163]:


<sup>22</sup> Baseline corrected spectrum measured by KBr technique.

<sup>23</sup> Abbreviation used for the expression of intensity and width of peak in the spectrum: very weak (*vw*), weak (*w*), middle (*m*), strong (*s*) and very strong (*vs*), shoulder (*sh*), broad (*b*), very broad (*vb*), and sharp (*sp*). Spectral bands related to impurities are abbreviated as *imp* [162].


There is also basal pinacoid {1000}, first-order {10–10} and second-order {11–20} hexagonal

It is obvious that fluorapatite belongs to the hexagonal-dipyramidal crystal system, but the estimation of crystal habit of corresponding euhedral crystals from these results is highly speculative due to possible combination of pinacoid (*c*), first-order (m) and second-order hexagonal prisms (a) and first-order (*p*) and second-order dipyramids (*s*) with dihexagonal

respectively. The most expressive infrared bands are attributed to fundamental frequencies of

symmetry from *T*<sup>d</sup> (four fundamental frequencies with IR inactive *ν*<sup>1</sup> mode) to *C*s, where *ν*<sup>1</sup>

23 Abbreviation used for the expression of intensity and width of peak in the spectrum: very weak (*vw*), weak (*w*), middle (*m*), strong (*s*) and very strong (*vs*), shoulder (*sh*), broad (*b*), very broad (*vb*), and sharp (*sp*). Spectral bands related to

) and Raman spectrum of fluorapatite is shown in **Fig. 18**(**a**) and (**b**),

3−. The structure of apatite leads to the reduction of ion

) band that is related to symmetric stretching of

prism and dihexagonal prism {21–30}.

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

**Fig. 17.** X-ray diffraction analysis of investigated specimen of apatite.

mode becomes IR active [128],[160],[161],[162],[163]:

dipyramid (*v*) faces in the single crystal.

**3.2.3. Infrared and Raman spectroscopy**

**1.** The *ν*1(PO4) mode is very weak (*vw*<sup>23</sup>

22 Baseline corrected spectrum measured by KBr technique.

tetrahedral phosphate ion [PO4]

Infrared (mid-FT-IR22

phosphate ion.

**2.** Bending: *ν*2 mode (*vw*).

impurities are abbreviated as *imp* [162].

**Fig. 18.** Infrared (a) and Raman (b) spectrum of investigated specimen of fluorapatite.

The crystallinity of natural and synthetic apatite samples is often determined from the broadening of *ν*4(PO4) infrared absorption bands [160]. The assignment of bands in infrared and Raman spectrum of fluorapatite is listed in **Table** 2.



**Table 2.** The interpretation of infrared and Raman bands in the spectrum of stoichiometric fluorapatite [164].

Factor group analysis of the hexagonal P63/M space group fluorapatite structure (*Z* = 2) yields an irreducible representation for optically active vibration of [165]:

$$\Gamma = 12\ \ A\_{\rm g} \left( R \right) + 7\ A\_{\rm u} \left( \text{IR} \right) + 8E\_{\rm lg} \left( R \right) + 11E\_{\rm u} \left( \text{IR} \right) + 13E\_{2g} \left( R \right) \tag{14}$$

where IR and R denote infrared and Raman activity, respectively. The influence of pressure on the infrared and Raman spectra of fluorapatite was investigated by WILLAMS and KNITTLE [165]. Fluorapatite remains stable under pressures of at least 25 GPa at 300 K. Local environ‐ ment of phosphate groups in fluorapatite becomes progressively less distorted from tetrahe‐ dral symmetry under the compression, as manifested by progressively smaller site-group.

The Davydov (factor group) splitting also decreases under the compression. This decrease is consistent with nondipole effects playing a primary role in the Davydov splitting of apatite; indeed, the magnitude of the Davydov splitting appears to be modulated by increases of the site symmetry of phosphate group under the compression [165].

The spectrum **Fig. 18**(**a**) shows weak peak located in the domain of OH stretching modes (from 3500 to 3600 cm−1) at the wave number of 3535 cm−1. This band belongs to the OH stretching mode in the hydrogen bond F…OH…(F) [166]. According to FREUND and KNOBEL [167], the band at ~744 cm−1 belongs to the vibration of OH…F bond. According to KNUBO‐ VETS [168], the bands in the range from 745 to 720 cm−1 in apatite spectra could also be attrib‐ uted to symmetric valence oscillations of the P-O-P bridge bonds, formed by the condensation of the PO4 3− tetrahedron. The presence of calcite causes that antisymmetric stretching mode (*ν*3) of planar CO3 2− ion appears in the infrared spectrum of investigated sample [169].
