Studying Some of Physical Properties of a Lead Doping Titanium Dioxide TiO₂: Pb with Different Ratios

X-ray Diffraction Test

The XRD pattern show the participation of all the undoped and Pb doped TiO2 powders with the peaks corresponding to the crystalline levels (110), (012), (040), (111), (211), (123), (112), (220). Preferred orientation is (110) in all undoped and Pb doped samples, while the peaks corresponding to levels (210), (213), (160), (203) disappear or shift in The similar sample whose percentage of lead equals 0.9 g, while the corresponding peak of the level (220) disappears or shifts in the similar sample whose percentage of lead equals 0.7 g. It was also noted with different doping ratios that there is an absence of some peaks corresponding to pure titanium dioxide and the appearance of new peaks due to lead impurity (Figure 2).

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We calculated the relative intensity of the pure and lead-dominated TiO2 powders. The distance values between crystal planes were calculated using the following Bragg’s law [29]:

2d sin = n θ λ (1)

Where d is the distance between crystal planes in angstroms (A°) and θ is Braggs’s angle in radians (rad) and ë is the wavelength of the x-rays ( ë = 1.78897 A°) and we calculated the crystallite size from Scherrer’s quation [30]:

cos k D λ β θ = (2)

where D is the crystal size in nanometer (nm).

K is Scherrer’s constant, so for a cubic crystal system it takes the value 0.94, and for a non-cubic crystal system it takes the value 0.89 and therefore the value we use is the last value [31].

λ is the wavelength of x-rays measured in angstrom (A°). β is the full width at half maximum intensity (FWHM) measured in radians.

θ is the Braggs’s angle, also measured in radians.

The dislocation density ä is defined as the length of the dislocation lines per unit volume and is calculated from the following equation [32]:

1

2 D δ = (3)

The lattice constants a (A°), b (A°) and c (A°) a for the tetragonal crystal system of the anatase, rutile and orthorhombic crystal system of the brookite phase were determined from the equations (4) and (5), respectively [18] & [33]:

2 2 2

2 2 2 2 1 h k l d a b c = + + (5)

where a = b ≠ c; for anmatase and rutile phases just .

where d is the distance between two successive one angstroms of crystal planes in angstroms (A°) and (hkl) are the Miller indices. The grid constants a (A°), b (A°) and c (A°) a given in Tables 1, 2, 3 were also calculated, which match well with the JCPDS data. were also calculated, for brookite,( a = 5.455 A°, b = 9.18 A°, c = 142 A°), and for rutile (a = b = 4.593 A°, c = 2.959A°), and for anatase (a= b = 3.785 A°, c = 9.513 A°), and for lead Pb(a= b=3.265 A° , c = 5.387 A°) . The change in peak intensity is mainly due to the replacement of Ti+4 ions by Pb+4 ions in the TiO2 lattice. We also computed initial cell size from relation [34]:

V = a . b . c (6)

where a , b , c are the crystal lattice constants given in Tables 2-6.

This process leads to the movement of Pb+4 ions into the substitution sites. It was observed that the increase in the doping ratio increases the size of the primary cell, the size of the crystal, the relative intensity, and the density of the dislocation decreases, and this is consistent with the researchers [26] and [35]. We observed from Tables 2, 3 & 4 that 0.2g lead-doped TiO2 is the closest value to the undoped sample.

Lattice Constants for Phases Phases Cell Size V(A°)3 a(A°) b(A°) c(A°)

Lattice Constants for Phases Phases Cell Size V(A°)3 a (A°) b (A°) c (A°)

The preferred orientation along the plane (211) for all samples, as the reason for the peak corresponding to the previous plane is due to the presence of crystals from the rutile phase, regardless of the percentage of doping. And we note that brookite crystallizes in the direction (012) for all the pure and lead-doped samples. As for the lead – doped sample by x=0.9g, it crystallizes in the direction (121) and anatase crystallizes in the direction (200) for all samples except the lead - doped sample by x = 0.9g as it crystallizes according to the direction (220) and lead crystallizes according to the direction (100) for all samples except for the sample with a doping ratio of x = 0.9g, it crystallizes according to the direction (110) and the reason is that those samples maintained their direction up to the dopance ratio x = 0.9g is that at that ratio there was the largest increase in crystal size and the largest increase in cell size, and this explains that this alloy is likely to cancel some of the grain boundary when the grains coalesce to form crystals of larger size, as well as canceling the defects that exist after the occurrence of The process of natural growth of crystals and rearrangement of crystal grains , as the grains take enough energy for the natural growth of crystals and arrangement within that lattice, as these limits were impeding the movement of electrons and canceling some of them, the electrical conductivity in the metallic material increases due to diminished for electrical resistance [25].

Sample 2θ β (deg) (hkl) d(A°) Rel. Int. (%)

D (nm) D (nm)

(deg) Lattice Constants for Phases Phases Cell Size V(A°)3 a (A°) b (A°) c (A°)

δ 1015 Line/ m2

We also note that with the increase in the ratios of doping, new peaks appeared for the three phases and for lead, and most of the peaks were for the brookite phase among the three phases, which increased with the increase in the ratios of doping. (2θ) with an increase in the doping ratio and the explanation for this displacement is due to the small ionic radius of titanium (0.745 Ao) compared to the ionic radius of lead impurity (11.950 Ao). An ionic diameter greater than 0.8 Ao leads to a decrease in the crystal size of TiO2 due to a decrease in the distance between the crystalline levels (d) and then an increase in the diffraction angle, and thus the displacement of the characteristic peaks towards the right in the diffraction pattern because it has an inverse relation according to Bragg’s law [29] as stated in Pauling’s principle [36, 37, 38].

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Figure 3 shows that the average crystal size of the 0.2g lead-doped sample is closer to that of the pure sample, However, the decrease in the average crystal size increase of 0.7g compared to the other similar samples and may be due to the linear increase in the average size The crystal starting from the pure compound and passing through each of the doping ratios with 0.5g and 0.2g lead indicates that the impurities effectively prevent the growth of the granules by forming dissimilar boundary regions and because of the increase in the doping ratio that causes the increase in the crystal size and this agrees with the researcher [8] It is known that the increase in the particle sizes reduces the stress in the grain boundaries resulting from the crushing process. These boundaries are suitable locations for the sites of defects and crystal impurities that lead to the enhancement of the electrical resistance and thus the electrical conductivity will increase [12] and Since the phases have no difference in chemical composition between them, while there is a change in the atomic arrangement and crystal orientation across the phase boundaries, the surfaces that separate them are not similar in energy and composition to the grain boundaries with a small inclination angle , It is possible that the presence of crystal defects in the dopant sample with a percentage of 0.7g is the reason for the change of the linear increase, as we noticed a decrease in the crystal size at it (57.379), where we note in Table 4. The decrease in the size of the grains in both brookite and rutile except for anatase [11]. The crystal size of the three phases together falls within the range [57.379- 85.370 nm], distributed over anatase [62.565-118.236 nm], brookite [40.303-94.310 nm] and rutile [35.080-99.233 nm] and this is consistent with the researcher Fouzia A and Bensaha R [26].

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Figure 4: The crystal lattice constants a (AO), c (AO) in the anatase phase (A), (B), respectively, for the compound of pure and lead-doped titanium dioxide in different ratios (x = 0.2 - 0.5 - 0.7 - 0.9 g), the brookite (C) and (D) phase, respectively, for the compound of pure and lead - doped titanium dioxide in different ratios (x = 0.0 - 0.2 - 0.5 - 0.7 - 0.9 g), the rutile (E) and (F) phase, respectively, for the compound of pure titanium dioxide doped with lead in different proportions (x = 0.2 - 0.5 - 0.7 - 0.9 g).

It is possible that the increase in one of the crystal lattice constants a, b or c is due to the increase in vacanses, the stretching of the crystal lattice and the increase in the size of the primary cell and vice versa [39] (Figure 4). The expansion of the z-axis and this expansion in the basal plane is due to an increase in crystal vacancies and vice versa for rutile in which the constant c has decreased. Its decrease in anatase at the first rate of doping while maintaining a constant value until the last percentage of doping due to the contraction of each of the x and y axes and a decrease in the possibility of voids resulting from the occurrence of fualt stacking during the process of natural crystal growth of the material according to this level of the crystal structure of the material and the occurrence of shrinkage of the quaternary crystal lattice, and the increase in the lattice constants is due to the increase in the distance between the crystal levels, and this agrees with the researcher Yu J, et al. [5].

Then we calculated the Theoretical density of the X-ray diffraction spectrum for pure and dopant samples using the equation (7) [40] (Table 7):

Z M = N V ρ (7)

wt X-ray a

X-ray ρ : The theoretical density of the X-ray diffraction spectrum for powders is g/cm3. Where Z: The number of atoms per unit cell, which is 2 in the rutile phase, 8 in the brookite phase, and 4 in the anatase phase. Mwt: The molar mass is g/mol, which is 79.866 g/mol for the three phases of TiO2. Na: Avogadro’s number 6.023 x 1023 mol-1. V: The initial cell size given in Tables (2-6) whose unit is (A°)3.

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We note that the theoretical density X-ray ñ decreased with the increase of the dopance due to the increase in the cell size with the increase in the dopance from the inverse relationship between the two parameters [40] (Figure 5), because the cell size decreased by the same value for all ratios compared to pure rutile by increasing the dopant ratio, the lattice coefficients and the theoretical density, which we note that there is no change in it, remain constant until certain dot ratios. The change in the stability of the previous parameters [25].

The number of material atoms can also be calculated using the relation (8) [41] (Table 8):

ρ (8) X-ray a wt n = N M

n: the number of atoms of a substance in a unit volume of atom/cm3. Na: Avogadro’s number 6.02 x 1023 mol-1 .

X-ray ρ : The theoretical density of the X-ray diffraction spectrum for powders is g/cm3. Mwt: The molar mass is g/mol, which is 79.866 g/mol for the three phases of TiO2.

We note the increase in the number of substance atoms per unit volume with an increase in the percentage of doping, but this increase slightly decreased at the doping percentage with lead g 0.9, and this is related to the previous changes that occurred in the theoretical density of the X-ray diffraction spectrum for powders due to the direct proportionality between these two parameters.

By calculating n, we can calculate the average distance between atoms in nanometer unit, for materials in which the number of atoms per unit volume is within n = 6 x1022 atom/ cm3 by substituting in the equation (9) [14] (Table 9):

L = (n)1/3 (9)

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We notice the linear increase in the distance between the atoms in the two samples of pure and lead-doped titanium dioxide with a ratio of 0.2 g, then this increase was fixed at the dopance ratio of 0.5 g , while at the ratio of 0.7 g it took a decrease to reach the dopance ratio of 0.9 g. And with the decreasing distance between the atoms and their approach to the constants of the crystal lattice, the dissolution of the intermittent energy levels occurs and energy bands are formed, the width of which decreases as we go deeper inward towards the nucleus (Figure 6). The permissible energy bands separate, with forbidden bands Eg that cannot be occupied by electrons , and thus the interaction between them increases and the height and width of the voltage barrier between atoms decreases, as the decrease in height leads to the fall of the final atomic level above the voltage barrier, which makes the electron free to That level, as these electrons match perfectly with all atoms of the substance, forming a so-called electronic gas, which facilitates the passage of internal electrons (other than valence electrons) through the barriers that separate neighboring atoms and their movement within the crystal itself and the ability of electrons to meet . In our study, we take into consideration that the atoms are composed of spheres with a net positive charge resulting from the nucleus (Ti+4 and Pb+4) in addition to the electrons of the inner core of the atom, since the potential energy is closely related to the distance between the atoms. We note that at 0.9 g of doping of lead, the potential energy and bonding forces between the atoms are the largest compared to the other doping ratios due to the decrease in the distance between the atoms at this ratio of doping. When the atoms get close to each other, the orbitals overlap and the valence electrons begin to rearrange themselves until they reach to a more stable arrangement, and during this rearrangement, different types of bonds are formed between the atoms and this rearrangement causes an increase in the cohesion of the atoms and the formation of the solid state.