Spectroscopic Properties of Pb 2+ -Doped BaF 2 Crystals

: Various concentrations of PbF 2 -doped BaF 2 crystals were grown by the Bridgman method using a shaped graphite heater. The room temperature optical absorption spectra showed two UV absorption bands (labeled A and D), characteristic of the Pb 2+ ions. The structure of the bands was analyzed using the Gaussian multi-peak ﬁtting. The distribution of the Pb 2+ ions along the crystals and the effective segregation coefﬁcient were studied using the optical absorption method. The obtained effective segregation coefﬁcient was >1. The Pb 2+ ions were not uniformly distributed along the samples. High intensity emission bands were observed in the near UV domain and the visible region.


Introduction
The alkaline earth fluorides MeF 2 (Me = Ca, Sr, Ba) were used as lens and optical windows from the VUV to the IR domain as laser host materials and scintillators, etc. [1][2][3][4][5][6].The fastest scintillator for elementary particle and γ-ray detection with a decay time of 600 ps at 220 nm was made from BaF 2 crystals.It was attempted to eliminate the unwanted slow emission at 310 nm by doping the crystals with various ions.The influence of La, Nd, Ce, Eu, Gd, Tm, and Pr dopants on the slow component suppression was studied by Woody et al. [1].BaF 2 crystals that were exposed to radiations due to various dopants showed the formation of color centers that gave rise to unwanted optical absorption bands; radiation hardness may also have been affected [2].The alkali halide crystals doped with ns 2 electronic configuration ions, such as Tl + , In + , Sn 2+ , Bi 3+ , and Pb 2+ , were studied for their optical properties [7][8][9][10].The properties of these ions in other hosts were investigated by [11][12][13][14][15][16][17][18][19][20].The ns 2 electronic configuration ions had similar optical behavior in different matrices; in general, four absorption bands in the UV domain were induced.Among the ions with the ns 2 electronic configuration, the Pb 2+ ion optical properties in the BaF 2 crystal has been less studied.Bohum et al. [21] studied the absorption spectra in the VUV domain of CaF 2 crystals doped with Pb and oxygen.They observed a doublet in the 200-210 nm domain.The 206 nm peak was attributed to O 2− -V F − pairs and that at 202 nm to lead centers; the peak at 166 nm was unidentified; the 155 nm peak was assigned to the Pb centers; the 145 nm band was ascribed to excitons.The low PbF 2 concentration (~10 16 ions cm −3 ) doped CaF 2 crystals were investigated by Arkhangelskaya et al. [22] in the VUV domain.The observed bands were denoted by A) the doublet at 215.9 nm and 202.4 nm, B) the peak at 165.3 nm, and C) the triplet at 157.9, 154.5, and 152.1 nm.A broad emission band, with maximum intensity at 222 nm, was obtained by excitations in all the absorption bands.Fockele et al. [23] investigated the emission of the X-ray-irradiated Pbdoped CaF 2 , SrF 2 , and BaF 2 crystals.Intense infrared emission was observed.Laser action of the Pb + (1) center was expected.The absorption spectra of the unirradiated samples were not discussed.The optical absorption (in the VUV domain, 124-225 nm) and the emission of Pb 2+ and Bi 3+ centers in different alkaline earth fluorides were reported by Oboth et al. [24].Using the same notations as in the reference [22], the observed peaks were 204.8 and 201.1 nm (the A band), 164.6 nm (the B band), 154 nm (the C band), and 127.8 nm (the D band).Excitation in the A band (204 nm) gave rise to emissions at 217 nm.For excitation in the C band, emissions at 175.4 nm and 217 nm were detected.The influence of the Pb 2+ ion concentration on the spectroscopic properties of the PbF 2 -doped CaF 2 crystals was studied by Nicoara et al. [25].Four absorption bands in the UV domain that peaked at 195 nm, 206 nm, 243 nm, and 306 nm (labeled D, C, B, A) were observed.Characteristic for these broad bands was their structure; two or three components formed the absorption band.As the Pb 2+ ion concentration increased, the intensity of the peaks increased.High intensity emission bands in the near UV domain at 322 nm and 341 nm were observed.The luminescence properties of ions with an ns 2 electronic configuration in different hosts were investigated [14,[16][17][18][26][27][28].The luminescence of Pb 2+ depended strongly on the host lattice and was quite diverse.Intense emission in the near UV and the visible domain was characteristic.The distribution of the dopant in crystals is an important subject because this can influence the physical properties of the crystals used for different devices.The effective segregation coefficient, k eff , gives information about the dopant distribution along the crystals.Baldochi et al. [29] measured the distribution coefficient of Pb 2+ ions in BaLiF 3 by X-ray fluorescence analysis.The estimated distribution coefficient of three crystals grown from 0.1 to 1 mol% PbF 2 -doped BaLiF 3 was 0.05.This means that the dopant had a tendency to be away from the growing interface, resulting in a small incorporation of Pb in the ingot.Abe et al. [30] studied the Tm 3+ ion distribution along the BaF 2 :10% TmF 3 crystal using the electron probe microanalysis (EPMA) method.The estimated k eff for Tm 3+ ions was 0.6.This meant that, in the central part of the ingot, the concentration of the Tm 3+ ions was less than at the edge parts.The Yb 3+ and Yb 2+ ion distribution along the YbF 3 -doped BaF 2 crystals was investigated by Stef et al. [31].To estimate the effective segregation coefficient of both ions, the optical absorption method was used.As the YbF 3 concentration in BaF 2 increased, the difference in the Yb ion concentration between the bottom and the top of the crystal was higher.The calculated effective segregation coefficients of Yb 3+ ranged from 0.7 to 0.84 and of Yb 2+ ions from 0.66 to 0.82, depending on the YbF 3 concentration.The Er 3+ ion distribution along ErF 3 -doped BaF 2 crystals was analyzed by Nicoara et al. [32].For concentrations < 0.15 mol% ErF 3 , the C 3v type ions were distributed approximately uniformly; the estimated segregation coefficient was around 0.9.The Pb 2+ ion distribution in CaF 2 crystals was studied by [33].The dopant distribution showed an oscillatory behavior along the crystals.The obtained effective segregation coefficient increased as the dopant concentration increased.For 0.5 and 1 mol% PbF 2 , the k eff was <1 (0.85, respectively 0.92); for concentration > 1 mol% PbF 2, the segregation coefficient was >1, (1.002 and 1.15).
The goal of this work was to investigate the influence of Pb 2+ ion concentration on the spectroscopic properties-the optical absorption and the emission-of PbF 2 -doped BaF 2 crystals.The distribution of the Pb 2+ ions along the crystals and the effective segregation coefficient were also determined.The spectroscopic properties of Pb 2+ ions in a BaF 2 host and their distribution along the crystals have not previously been reported.

Materials and Methods
The conventional Stockbarger-Bridgman technique was used in order to obtain the low concentration (0.05, 0.1, 0.25 and 0.5 mol%) PbF 2 -doped BaF 2 crystals.As starting materials, BaF 2 optical UV-VIS windows, provided by Crystran Ltd., Poole, UK, and suprapure grade (Merck) PbF 2 were used.Four PbF 2 -doped BaF 2 crystals were obtained, with the following amount of PbF 2 added in the starting crushed optical windows: 0.01, 0.1, 0.25, and 0.5 mol% PbF 2 .The crystals were grown in our crystal research laboratory using our Bridgman setup [34].The crystallization process took place in the desired temperature distribution in a shaped graphite furnace [34].The temperature distribution along the heater before the growth process is shown in Figure 1a.A typical temperature distribution during the Crystals 2023, 13, 659 3 of 15 growth process, measured at the bottom of the crucible using an S-type thermocouple, is shown in Figure 1a.In the first hour of the growth process, the temperature gradient was G 2 = 17 • C/cm.The temperature gradient measured before the growth process was G 1 = 14 • C/cm.The used electrical powers (P) are also indicated in the figure.The crystals were obtained in a vacuum (~10 −1 Pa), using a spectral pure graphite crucible, with a pulling rate of 4 mm/h.After the growth process was finished (~14-15 h), the crystal was cooled at room temperature over a period of 10 h.A thin floating graphite lid was put on the powder charge in the crucible along with a screwed cap in order to prevent the evaporation of the PbF 2 .Transparent colorless crystals ~5 cm in length and ~10 mm in diameter were obtained, with a good cleavage plane (111) (Figure 1b).In order to study the spectroscopic properties, the crystals were cleaved from the bottom to the top in 10-17 slices with a thickness of ~2 mm (Figure 1c).

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along the heater before the growth process is shown in Figure 1a.A typical temperature distribution during the growth process, measured at the bottom of the crucible using an S-type thermocouple, is shown in Figure 1a.In the first hour of the growth process, the temperature gradient was G2 = 17 °C/cm.The temperature gradient measured before the growth process was G1 = 14 °C/cm.The used electrical powers (P) are also indicated in the figure.The crystals were obtained in a vacuum (~10 −1 Pa), using a spectral pure graphite crucible, with a pulling rate of 4 mm/h.After the growth process was finished (~14-15 h), the crystal was cooled at room temperature over a period of 10 h.A thin floating graphite lid was put on the powder charge in the crucible along with a screwed cap in order to prevent the evaporation of the PbF2.Transparent colorless crystals ~5 cm in length and ~10 mm in diameter were obtained, with a good cleavage plane (111) (Figure 1b).In order to study the spectroscopic properties, the crystals were cleaved from the bottom to the top in 10-17 slices with a thickness of ~2 mm (Figure 1c).To check the crystals' quality, the dislocation density on the cleavage plane was studied using the chemical etching method.This method consisted of immersing the fresh cleaved sample in 2N HCl at 60 °C for 2 min.Small pits developed at the emergence points of the dislocations.The etch pits had hexagonal shapes (Figure 2).The obtained values of ~10 4 disl/cm 2 (Table 1) for the dislocation density meant these crystals were good quality.The optical absorption spectra, at room temperature, of every slice and every crystal, were recorded in the 190-1000 nm range using a Shimadzu 1650 PC spectrophotometer.We used the automatic correction of the instrument for baseline correction; this also took into account the effect of setup noise and light scattering due to the undesired particles in the sample.The room temperature luminescence spectra in the UV-VIS domain were recorded using a LS55 Perkin Elmer fluorescence spectrometer.To check the crystals' quality, the dislocation density on the cleavage plane was studied using the chemical etching method.This method consisted of immersing the fresh cleaved sample in 2N HCl at 60 • C for 2 min.Small pits developed at the emergence points of the dislocations.The etch pits had hexagonal shapes (Figure 2).The obtained values of ~10 4 disl/cm 2 (Table 1) for the dislocation density meant these crystals were good quality.The optical absorption spectra, at room temperature, of every slice and every crystal, were recorded in the 190-1000 nm range using a Shimadzu 1650 PC spectrophotometer.We used the automatic correction of the instrument for baseline correction; this also took into account the effect of setup noise and light scattering due to the undesired particles in the sample.The room temperature luminescence spectra in the UV-VIS domain were recorded using a LS55 Perkin Elmer fluorescence spectrometer.

Results
The alkaline earth fluoride MeF2 (Me = Ca, Sr, Ba) crystallized in the well-known fluorite structure.To better understand how the different dopants were incorporated in the lattice, the fluorite lattice could be regarded as a simple cubic lattice of F − ions, in which every other body center position was occupied by a Me 2+ ion.When impurities (dopants) were introduced into the lattice, they usually replaced the Me 2+ ions.If the dopant had the same valence as the Me 2+ ion, no charge compensation process was needed.This was the case for the PbF2 dopant.

Optical Absorption Spectra
In order to identify the optical transitions of Pb 2+ ion-doped BaF2 crystals, we compared the optical absorption spectra of the PbF2-doped CaF2 [33] with our doped BaF2 crystals (Figure 3a).The three absorption bands observed for the Pb 2+ ion-doped BaF2 crystals are labeled A, D and E. The absorption bands, corresponding with the transitions from the 1 S0 ground state to the excited states of the Pb 2+ ions are marked in Figure 3a for both hosts: BaF2 and CaF2 ( 3 P0, 3 P1, 3 P2 levels and the singlet 1 P1 are shown in Figure 3b).Compared with the absorption spectrum of Pb 2+ :CaF2, in the case of the Pb 2+ :BaF2 crystals, the C band was missing and the A and D bands moved towards the shorter wavelengths.The unidentified E band was observed in both type of crystals.The A absorption band denoted by Oboth et al. [24] corresponded with our D band.The optical absorption bands were assigned to electronic transitions: A ( 1 S0-3 P1, spin orbit allowed), B ( 1 S0-3 P2 vibrationally allowed), and C ( 1 S0-1 P1 dipole allowed).

Results
The alkaline earth fluoride MeF 2 (Me = Ca, Sr, Ba) crystallized in the well-known fluorite structure.To better understand how the different dopants were incorporated in the lattice, the fluorite lattice could be regarded as a simple cubic lattice of F − ions, in which every other body center position was occupied by a Me 2+ ion.When impurities (dopants) were introduced into the lattice, they usually replaced the Me 2+ ions.If the dopant had the same valence as the Me 2+ ion, no charge compensation process was needed.This was the case for the PbF 2 dopant.

Optical Absorption Spectra
In order to identify the optical transitions of Pb 2+ ion-doped BaF 2 crystals, we compared the optical absorption spectra of the PbF 2 -doped CaF 2 [33] with our doped BaF 2 crystals (Figure 3a).The three absorption bands observed for the Pb 2+ ion-doped BaF 2 crystals are labeled A, D and E. The absorption bands, corresponding with the transitions from the 1 S 0 ground state to the excited states of the Pb 2+ ions are marked in Figure 3a for both hosts: BaF 2 and CaF 2 ( 3 P 0 , 3 P 1, 3 P 2 levels and the singlet 1 P 1 are shown in Figure 3b).Compared with the absorption spectrum of Pb 2+ :CaF 2 , in the case of the Pb 2+ :BaF 2 crystals, the C band was missing and the A and D bands moved towards the shorter wavelengths.The unidentified E band was observed in both type of crystals.The A absorption band denoted by Oboth et al. [24] corresponded with our D band.The optical absorption bands were assigned to electronic transitions: A ( 1 S 0 -3 P 1 , spin orbit allowed), B ( 1 S 0 -3 P 2 vibrationally allowed), and C ( 1 S 0 -1 P 1 dipole allowed).
The optical absorption spectra of various concentrations of the Pb 2+ : BaF 2 crystals revealed three absorption bands: A, D, and E (Figure 4a).The intensity of the E band varied with the PbF 2 concentration.For a concentration > 0.05 mol% PbF 2, this band overlapped with the components of the D band, resulting in a broad absorption band, denoted D + E (see Figure 4a).The Gaussian multi-peak fitting of the optical absorption spectra showed the components of the broad absorption bands (Figure 4b).The optical absorption spectra of various concentrations of the Pb 2+ : BaF2 crystals r vealed three absorption bands: A, D, and E (Figure 4a).The intensity of the E band vari with the PbF2 concentration.For a concentration > 0.05 mol% PbF2, this band overlapp with the components of the D band, resulting in a broad absorption band, denoted D + (see Figure 4a).The Gaussian multi-peak fitting of the optical absorption spectra show the components of the broad absorption bands (Figure 4b).The optical absorption spectra of various concentrations of the Pb 2+ : BaF2 crystals revealed three absorption bands: A, D, and E (Figure 4a).The intensity of the E band varied with the PbF2 concentration.For a concentration > 0.05 mol% PbF2, this band overlapped with the components of the D band, resulting in a broad absorption band, denoted D + E (see Figure 4a).The Gaussian multi-peak fitting of the optical absorption spectra showed the components of the broad absorption bands (Figure 4b).As the Pb 2+ ion concentration increased, the A band conserved its shape but the shape of the D band modified (Figure 4b).For all concentrations, the A band was the strongest In Figure 5a we show the Gaussian multi-peak fitting of the A band for two different PbF2concentration BaF2 crystals.The absorption coefficient of the maximum of the A band (taken from the spectra) increased linearly as the Pb 2+ ion concentration increased (Figure As the Pb 2+ ion concentration increased, the A band conserved its shape but the shape of the D band modified (Figure 4b).For all concentrations, the A band was the strongest.In Figure 5a we show the Gaussian multi-peak fitting of the A band for two different PbF 2 -concentration BaF 2 crystals.The absorption coefficient of the maximum of the A band (taken from the spectra) increased linearly as the Pb 2+ ion concentration increased (Figure 5b).The Gaussian multi-peak fitting of this band revealed two components, labeled A 1 and A 2 (Figure 5a).The obtained results are summarized in Table 2.
5b).The Gaussian multi-peak fitting of this band revealed two components, labeled A1 and A2 (Figure 5a).The obtained results are summarized in Table 2.The C band observed in the Pb 2+ :CaF2 crystals was assigned to symmetry and a spinallowed 1 S0-1 P1 transition; this band was missing in our Pb 2+ :BaF2 crystals (Figures 3a and  4a).The A, B, and C bands were due to the electronic excitation of the Pb 2+ ions from the ground state to the 6s 1 6p 1 excited states.It is possible that another excitation transition corresponded with the D band.The origin of the D band is not yet understood.
In Figure 6a we show the Gaussian multi-peak fitting of the last band, (D + E), for two samples: BaF2:0.05mol% PbF2 and BaF2:0.5 mol% PbF2.For the CaF2 crystal, the E band (194 nm) was clearly visible in the spectrum (Figures 3a and 6c), while in the case of the BaF2 host, for a concentration > 0.05 mol% PbF2, the components of the D and E bands overlapped, giving rise to a broad band, (D + E) (Figures 4a and 6a).For both hosts (BaF2 and CaF2), the components of the D band for the same PbF2 content are listed in Table 3.The C band observed in the Pb 2+ :CaF 2 crystals was assigned to symmetry and a spin-allowed 1 S 0 -1 P 1 transition; this band was missing in our Pb 2+ :BaF 2 crystals (Figures 3a and 4a).The A, B, and C bands were due to the electronic excitation of the Pb 2+ ions from the ground state to the 6s 1 6p 1 excited states.It is possible that another excitation transition corresponded with the D band.The origin of the D band is not yet understood.
In Figure 6a we show the Gaussian multi-peak fitting of the last band, (D + E), for two samples: BaF 2 :0.05 mol% PbF 2 and BaF 2 :0.5 mol% PbF 2 .For the CaF 2 crystal, the E band (194 nm) was clearly visible in the spectrum (Figures 3a and 6c), while in the case of the BaF 2 host, for a concentration > 0.05 mol% PbF 2 , the components of the D and E bands overlapped, giving rise to a broad band, (D + E) (Figures 4a and 6a).For both hosts (BaF 2 and CaF 2 ), the components of the D band for the same PbF 2 content are listed in Table 3.The dependence of the intensity of the D band components on the PbF 2 concentration is shown in Figure 6b.The Pb 2+ ion concentration dependence of the D 1 and D 2 components was exponential rather than linear.As the Pb 2+ ion concentration increased the D 1 component increased more than the D 2 component.These bands were probably due to a disturbed exciton or to the charge transfer from the ligand orbitals of the halogen to the orbitals of a vacant cation.The dependence of the intensity of the D band components on the PbF2 concentration is shown in Figure 6b.The Pb 2+ ion concentration dependence of the D1 and D2 components was exponential rather than linear.As the Pb 2+ ion concentration increased the D1 component increased more than the D2 component.These bands were probably due to a disturbed exciton or to the charge transfer from the ligand orbitals of the halogen to the orbitals of a vacant cation.

Distribution of the Pb 2+ Ions along the Crystal
The segregation coefficient was defined by the relation k = CS/C0, where CS is the dopant concentration of the as-grown crystal and C0 is the dopant concentration in the initial melt.At a given growth rate, the effective distribution coefficient (keff) was defined as keff = CS(z)/C0, where CS(z) is the dopant concentration at the distance z from the tip of the asgrown crystal.The Scheill relation [35] gives information about the CS(z) value at the given position, (z), along the growth axis of the as-grown crystal: where g = g(z) = V t/L = z/L is the crystallized fraction of the melt, V is the crystal growth rate, t is the growth time, Vt is the grown-crystal length, (z), at the moment t, and L is the crystal final length.If we can measure the CS(z) value, the keff can be obtained from this relation.The value of CS can be measured by various methods or estimated from optical absorption measurements [36][37][38].In order to study the distribution of Pb 2+ ion concentration along the crystal and to calculate the distribution coefficient, we chose the method described by [36].The value of CS(z) was estimated from the optical absorption measurements.Taking into account the Beer-Lambert law, the absorption coefficient (α) was proportional with the concentration of the dopant (α = a CS, so CS(z) ~ α(z)), so the dopant distribution along the crystal could be estimated by studying the optical absorption spectrum of slices cut along the crystal.The Scheill relation could be written as: log α(z) = (keff − 1) log (1 − g) + log (a keff C0) [36].The distribution coefficient, keff, was calculated from the slope of the fitting line of log α(z) versus log (1-g).The solidification fraction, g = z/L, indicated the position of the slice in the ingot.
The crystals were cleaved from the bottom to the top into various numbers of slices (Figure 1) of ≈ 2 mm thickness.The optical absorption coefficient, α (z), of every slice was

Distribution of the Pb 2+ Ions along the Crystal
The segregation coefficient was defined by the relation k = C S /C 0 , where C S is the dopant concentration of the as-grown crystal and C 0 is the dopant concentration in the initial melt.At a given growth rate, the effective distribution coefficient (k eff ) was defined as k eff = C S (z)/C 0 , where C S (z) is the dopant concentration at the distance z from the tip of the as-grown crystal.The Scheill relation [35] gives information about the C S (z) value at the given position, (z), along the growth axis of the as-grown crystal: where g = g(z) = V t/L = z/L is the crystallized fraction of the melt, V is the crystal growth rate, t is the growth time, Vt is the grown-crystal length, (z), at the moment t, and L is the crystal final length.If we can measure the C S (z) value, the k eff can be obtained from this relation.The value of C S can be measured by various methods or estimated from optical absorption measurements [36][37][38].In order to study the distribution of Pb 2+ ion concentration along the crystal and to calculate the distribution coefficient, we chose the method described by [36].The value of C S (z) was estimated from the optical absorption measurements.Taking into account the Beer-Lambert law, the absorption coefficient (α) was proportional with the concentration of the dopant (α = a C S , so C S (z) ~α(z)), so the dopant distribution along the crystal could be estimated by studying the optical absorption spectrum of slices cut along the crystal.The Scheill relation could be written as: log α(z) = (k eff − 1) log (1 − g) + log (a k eff C 0 ) [36].The distribution coefficient, k eff , was calculated from the slope of the fitting line of log α(z) versus log (1 -g).The solidification fraction, g = z/L, indicated the position of the slice in the ingot.The crystals were cleaved from the bottom to the top into various numbers of slices (Figure 1) of ≈2 mm thickness.The optical absorption coefficient, α (z), of every slice was estimated from the optical absorption spectrum for the well-shaped and strong characteristic absorption band of the Pb 2+ ions, A = 290 nm.We also used the D band (203 nm) for two crystals (0.05 mol% PbF 2 and 0.1 mol% PbF 2 ).The shape of the A peak (for a given PbF 2 concentration) was the same for various slices cleaved along the crystal; only the absorption coefficient α(z) differed from slice to slice, as shown in Figures 7a and 8a.This behavior was used to determine the effective segregation coefficient by the optical absorption method.estimated from the optical absorption spectrum for the well-shaped and strong char istic absorption band of the Pb 2+ ions, A = 290 nm.We also used the D band (203 nm two crystals (0.05 mol% PbF2 and 0.1 mol% PbF2).The shape of the A peak (for a PbF2 concentration) was the same for various slices cleaved along the crystal; on absorption coefficient α(z) differed from slice to slice, as shown in Figures 7a and 8a behavior was used to determine the effective segregation coefficient by the optical ab tion method.estimated from the optical absorption spectrum for the well-shaped and strong characteristic absorption band of the Pb 2+ ions, A = 290 nm.We also used the D band (203 nm) for two crystals (0.05 mol% PbF2 and 0.1 mol% PbF2).The shape of the A peak (for a given PbF2 concentration) was the same for various slices cleaved along the crystal; only the absorption coefficient α(z) differed from slice to slice, as shown in Figures 7a and 8a.This behavior was used to determine the effective segregation coefficient by the optical absorption method.Figures 7a and 8a,b show the absorption spectra of the slices cleaved from BaF 2 :0.05 mol% PbF 2 and BaF 2 :0.1 mol% PbF 2 crystals.Figure 7c shows the variation of the optical absorption coefficient of the peak at 290 nm along the 0.05 mol% PbF 2 -doped BaF 2 crystal.This behavior also corresponded with the Pb 2+ ion concentration distribution (characterized by the absorption coefficient, α,).As we observed, the distribution of the Pb 2+ ions was not uniform and their concentration decreased toward the end of the crystal and the Pb 2+ ions piled up at the bottom of the sample.For this reason, only the middle of the crystals could be used for different purposes.
In order to calculate the effective segregation coefficient, we used the slopes (m) of the fitting line of log α(z) vs. log (1−g), k eff =1 + m.The obtained effective segregation coefficient for the studied samples is shown in Figures 7b and 8c and Table 4.The effective segregation coefficient did not vary as the Pb 2+ ion concentration increased.The segregation coefficient could be k < 1 or >1, depending on the matrix, on the dopant concentration and on the dopant itself.The more that k eff differed from unity, the larger the dopant concentration gradient along the crystal became and, hence, no homogeneous distribution of Pb 2+ ions in the crystals could be obtained.
The study of Pb 2+ ion distribution along BaF 2 crystals and the determination of the effective segregation coefficient have not previously been reported.

Emission Spectra
The emission spectra of the studied samples were recorded at room temperature for excitation in three absorption bands: λ exc = 290 nm, λ exc = 206 nm, and λ exc = 203 nm.In Figure 9a, the emission spectra under excitation in the A band of the absorption spectrum (λ exc = 290 nm) are shown.Two high intensity bands were present, one in the near UV and one in the visible domain.The intense UV band had two peaks at 304 nm and 320 nm.The visible domain band also had two peaks at 610 nm and 640 nm.The influence of PbF 2 concentration on the peak intensity is shown in Figure 9b.The emission intensity of the band in the visible domain band was twice as weak as the band in the UV domain.The influence of the excitation wavelength on the emission spectra in the near UV domain is shown in Figure 10a.For all concentrations, the most intense emission was obtained for excitation in the A band (λexc = 290 nm).The influence of the PbF2 concentration  The influence of the excitation wavelength on the emission spectra in the near UV domain is shown in Figure 10a.For all concentrations, the most intense emission was obtained for excitation in the A band (λ exc = 290 nm).The influence of the PbF 2 concentration on the emission intensity of the 303 nm and 320 nm peaks for two excitation wavelengths, λ exc = 203 nm and 206 nm, is shown in Figure 10b.The emission of excitation at 203 nm was more intense than that of the excitation at 206 nm (Figure 10b).The influence of the excitation wavelength on the emission intensity in the visible domain is shown in Figure 11a for two concentration samples.The emission bands in the visible domain revealed two components for both excitation wavelengths (203 nm and 290 nm), as shown in Figure 11a.The Gaussian multi-peak fitting of the visible domain emission, for two samples, by excitation at 203 nm showed the two components of the emission band (see Figure 11b).Regardless of the sample PbF 2 concentration or the excitation wavelength, the emission maxima appeared at about the same wavelength (~610 nm and ~640 nm); only the intensity of the maxima differed (Figure 11a,b).In Figure 12a are shown the excitation spectrum monitored for the 320 nm emission peak (λmonitor = 320 nm), the A band optical absorption spectrum, and the emission spectrum under excitation at λexc = 290 nm (A band) for the BaF2:0.05mol% PbF2 sample.The excitation spectrum and the optical absorption spectrum were quite similar.This meant that the emission upon excitation at 290 nm came from the A absorption band from the 3 P1-excited state.
The excitation spectra of the two emission peaks (at 305 nm and 320 nm) are shown in Figure 12b for the BaF2:0.25 mol% PbF2 sample.The excitation spectra of both emission peaks were the same.The Gaussian multi-peak fitting of the excitation bands revealed two components, whose peaks slightly differed for different PbF2 concentrations (Figure 12c).In Figure 12a are shown the excitation spectrum monitored for the 320 nm emission peak (λmonitor = 320 nm), the A band optical absorption spectrum, and the emission spectrum under excitation at λexc = 290 nm (A band) for the BaF2:0.05mol% PbF2 sample.The excitation spectrum and the optical absorption spectrum were quite similar.This meant that the emission upon excitation at 290 nm came from the A absorption band from the 3 P1-excited state.
The excitation spectra of the two emission peaks (at 305 nm and 320 nm) are shown In Figure 12a are shown the excitation spectrum monitored for the 320 nm emission peak (λ monitor = 320 nm), the A band optical absorption spectrum, and the emission spec-trum under excitation at λ exc = 290 nm (A band) for the BaF 2 :0.05 mol% PbF 2 sample.The excitation spectrum and the optical absorption spectrum were quite similar.This meant that the emission upon excitation at 290 nm came from the A absorption band from the 3 P 1 -excited state.Probably, at a PbF2 concentration > 0.5 mol%, the splitting of the excitation bands in two components should be clearly visible in the spectrum.The luminescence of Pb 2+ and other ns 2 configuration ions was investigated in various hosts by [14,[16][17][18][26][27][28], less so in that of BaF2.The UV emission band of the CaF2:0.5 mol% PbF2 sample also consisted of two components under excitation in the A band (307 nm), namely 320 nm and 341 nm [25], but the intensities of the peaks were three times stronger than those of the BaF2:0.5 mol% PbF2 under excitation in the A band (290 nm).The obtained spectroscopic properties of the PbF2-doped BaF2 crystals are summarized in Table 5.
Table 5.The components of the optical absorption A band, the excitation A band components monitored for the 320 nm emission peak, and the UV emission under excitation in the A band (290 nm) 1 .The excitation spectra of the two emission peaks (at 305 nm and 320 nm) are shown in Figure 12b for the BaF 2 :0.25 mol% PbF 2 sample.The excitation spectra of both emission peaks were the same.The Gaussian multi-peak fitting of the excitation bands revealed two components, whose peaks slightly differed for different PbF 2 concentrations (Figure 12c).Probably, at a PbF 2 concentration > 0.5 mol%, the splitting of the excitation bands in two components should be clearly visible in the spectrum.

Discussion
The luminescence of Pb 2+ and other ns 2 configuration ions was investigated in various hosts by [14,[16][17][18][26][27][28], less so in that of BaF 2 .The UV emission band of the CaF 2 :0.5 mol% PbF 2 sample also consisted of two components under excitation in the A band (307 nm), namely 320 nm and 341 nm [25], but the intensities of the peaks were three times stronger than those of the BaF 2 :0.5 mol% PbF 2 under excitation in the A band (290 nm).The obtained spectroscopic properties of the PbF 2 -doped BaF 2 crystals are summarized in Table 5.For the investigated crystals with the PbF 2 concentration range between 0.05 and 0.5 mol%, the distribution of the Pb 2+ ions was not uniform and their concentration decreased toward the end of the crystal, where the Pb 2+ ions piled up at the bottom of the sample.The calculated effective segregation coefficient was >1, having values around 1.3 (see Table 4).Only for the sample with 0.25 mol% PbF 2 concentration did k eff equal 2.4.The segregation coefficient, and consequently the crystal homogeneity, could be more or less controlled by the growth conditions (the temperature gradient in the crystallization zone and the pulling rate during the growth process) [40].Probably, this crystal was grown in improper conditions and the dopant accumulated at the beginning of the crystal, determining such a high k eff .
There have been few reported results regarding the Pb 2+ ion distribution or regarding the segregation coefficient in various crystals [33,41]; rather, the behavior of RE ions has been investigated in the BaF 2 host.The obtained results are mentioned in the introduction.
The emission spectra of all PbF 2 -doped BaF 2 samples had the same behavior under excitation in the three optical absorption peaks, 290 nm, 206 nm, and 203 nm (Figures 9a, 10a and 11a).The emission in the near UV domain consisted of two peaks (at 305 nm and 320 nm).The emission in the visible domain also consisted of two components, ~610 nm and ~640 nm.The emission in the near UV domain was twice as intense than that in the visible domain.The emission intensity was high and slightly depended on the PbF 2 concentration.The observed emissions were assigned to the 3 P 1 -1 S 0 -allowed electronic transition of the Pb 2+ ions.The excitation spectra of both emission peaks (305 nm and 320 nm) were the same (Figure 12b).This indicated that the excited states from which the emissions appeared must have been associated.
The luminescence of Pb 2+ and other ns 2 electronic configuration ions was investigated in various hosts by [14,[16][17][18][26][27][28], less so in that of BaF 2 .The spectroscopic properties of Pb 2+ ions (the optical absorption and the emission) were studied rather in the VUV domain.Arkhangelskaya et al. [20] reported the spectroscopic properties of low concentration PbF 2doped CaF 2 crystals in a 120-220 nm domain.A broad emission band, with maximum intensity at 222 nm at room temperature, was obtained under excitations in all absorption bands.The optical absorption and emission spectra of Pb 2+ and Bi 3+ ions in different alkali earth fluorides in a VUV domain (124-225 nm) were studied by Oboth et al. [22].Excitations under all absorption bands in VUV gave rise to emissions at 217 nm (for A band) and at 175 nm and 217 nm (for C band).Emission at shorter wavelengths was not detected.The spectroscopic properties of X-ray-irradiated PbF 2 -doped CaF 2 , SrF 2, and BaF 2 crystals were investigated by Fockele et al. [23].They observed intense infrared emissions due to the Pb + (1) centers.The luminescence properties of our PbF 2 -doped BaF 2 crystals could be compared only with those of PbF 2 -doped CaF 2 crystals reported by Nicoara et al. [25].They studied the optical absorption and emission spectra of Pb 2+ ions in a UV domain (190-340 nm).Four absorption bands, peaking at ~306 nm (A band), ~259 nm (B band), ~243 nm (C band), ~210 nm (D band), and ~195 nm (E band), were reported.Under excitation in the A band (307 nm) high-intensity emission spectra for all samples, peaks at 320 nm and 341 nm were detected.The PbF 2 -doped BaF 2 crystals investigated in this work revealed only three broad peaks at ~290 nm (A band), ~203 nm (D band), and ~194 nm (E band).The emission spectra under excitation in three optical absorption peaks, 290 nm, 206 nm, and 203 nm, were characterized by two bands: one in the near UV domain, with peaks at 303 nm and 320 nm, and one in the visible domain, with maximum intensities at around 610 nm and 644 nm.The intensity of the emission peaks of the BaF 2 host were three times weaker than those of the CaF 2 : PbF 2 samples.

Conclusions
Various PbF 2 concentration-doped BaF 2 crystals were grown using the conventional Bridgman setup.The quality of the crystals was investigated by using the chemical etching method.In order to prevent the evaporation of the PbF 2, a special procedure was adopted.The absorption spectra revealed the characteristic absorption bands of the Pb 2+ ions.A concentration dependence of the absorption spectra was observed.Using the optical absorption method, the effective segregation coefficient of the Pb 2+ ions in the BaF 2 crystal was determined.The emission spectra of the studied samples under excitation in various absorption bands revealed two strong emissions components in the UV-VIS spectral region.Our luminescence experiments of Pb-doped BaF 2 crystals pointed out strong emissions in the near UV domain.It has been proven that the use of radiation in the UV range is an efficient tool for medical purposes such as the treatment of tissues, such as psoriasis, vitiligo, or lymphoma.It is important to find a laser material with emissions in the near UV in order to design a miniature laser, easy to use by the patient themself.The pure BaF 2 crystals can be used as a fast scintillator involving emissions in the UV domain.The absorption band in the UV can attenuate the fast component.The Pb ions can be in the raw material; during the crystal growth process, they are incorporated in the BaF 2 crystals, changing the optical properties of the crystal.The influence of the lead ions on the optical properties, especially on the sensitivity to the radiation damage, need to be carefully investigated.This will be the next step in our investigations.In order to obtain more uniform Pb ion distribution along the crystal, further studies are necessary, maybe using different pulling rates.

Figure 4 .
Figure 4. Optical absorption spectra.(a) Influence of PbF2 concentration on the absorption spectra (b) Gaussian multi-peak fitting of the absorption spectrum of BaF2: 0.05 mol% PbF2 sample.

Figure 4 .
Figure 4. Optical absorption spectra.(a) Influence of PbF 2 concentration on the absorption spectra; (b) Gaussian multi-peak fitting of the absorption spectrum of BaF 2 : 0.05 mol% PbF 2 sample.

Figure 5 .
Figure 5. (a) Gaussian multi-peak fitting of the A band for two samples; (b) variation of intensity of the A band (290 nm) and of the components A1 and A2 (see the inset) on the PbF2 concentration.

Table 2 .
Maxima of the optical absorption bands of BaF2: x mol% PbF2 crystals as a result of the absorption spectra and by Gaussian multi-peak fitting *.

Figure 5 .Table 2 .
Figure 5. (a) Gaussian multi-peak fitting of the A band for two samples; (b) variation of intensity of the A band (290 nm) and of the components A 1 and A 2 (see the inset) on the PbF 2 concentration.

Figure 6 .
Figure 6.(a) Gaussian multi-peak fitting of the D band for two samples; (b) dependence of the D band component intensity on the PbF2 concentration; (c) the D and E bands decomposed by Gaussian multi-peak fitting of CaF2: 0.5 mol% PbF2.

Figure 6 .
Figure 6.(a) Gaussian multi-peak fitting of the D band for two samples; (b) dependence of the D band component intensity on the PbF 2 concentration; (c) the D and E bands decomposed by Gaussian multi-peak fitting of CaF 2 : 0.5 mol% PbF 2 .

Figure 7 .
Figure 7. (a) Optical absorption spectra of various slices cleaved from 0.05 mol% PbF2-dope crystal (the A and D bands); (b) fitting lines of log α(z) vs. log (1 − g) in order to calculate the eff distribution coefficient; (c) absorption coefficient of Pb 2+ ions for various slice positions in the (the Pb 2+ ion concentration variation along the crystal).

Figure 8 .
Figure 8.(a) Optical absorption spectra (D band) of various slices at different positions in the defined by g = z/L; (b) a band of the slices cleaved from BaF2:0.1 mol% PbF2 crystal; (c) fittin of log α(z) vs. log (1 − g) in order to calculate the effective distribution coefficient.

Figures
Figures 7a and 8a,b show the absorption spectra of the slices cleaved from BaF mol% PbF2 and BaF2:0.1 mol% PbF2 crystals.Figure 7c shows the variation of the o absorption coefficient of the peak at 290 nm along the 0.05 mol% PbF2-doped BaF2 cr

Figure 7 .
Figure 7. (a) Optical absorption spectra of various slices cleaved from 0.05 mol% PbF 2 -doped BaF 2 crystal (the A and D bands); (b) fitting lines of log α(z) vs. log (1 − g) in order to calculate the effective distribution coefficient; (c) absorption coefficient of Pb 2+ ions for various slice positions in the crystal (the Pb 2+ ion concentration variation along the crystal).

Figure 7 .
Figure 7. (a) Optical absorption spectra of various slices cleaved from 0.05 mol% PbF2-doped BaF2 crystal (the A and D bands); (b) fitting lines of log α(z) vs. log (1 − g) in order to calculate the effective distribution coefficient; (c) absorption coefficient of Pb 2+ ions for various slice positions in the crystal (the Pb 2+ ion concentration variation along the crystal).

Figure 8 .
Figure 8.(a) Optical absorption spectra (D band) of various slices at different positions in the crystal defined by g = z/L; (b) a band of the slices cleaved from BaF2:0.1 mol% PbF2 crystal; (c) fitting lines of log α(z) vs. log (1 − g) in order to calculate the effective distribution coefficient.

Figures
Figures 7a and 8a,b show the absorption spectra of the slices cleaved from BaF2:0.05 mol% PbF2 and BaF2:0.1 mol% PbF2 crystals.Figure 7c shows the variation of the optical absorption coefficient of the peak at 290 nm along the 0.05 mol% PbF2-doped BaF2 crystal.

Figure 8 .
Figure 8.(a) Optical absorption spectra (D band) of various slices at different positions in the crystal defined by g = z/L; (b) a band of the slices cleaved from BaF 2 :0.1 mol% PbF 2 crystal; (c) fitting lines of log α(z) vs. log (1 − g) in order to calculate the effective distribution coefficient.

Crystals 2023 , 16 Figure 9 .
Figure 9. (a) Emission spectra of the studied samples under excitation in A band (290 nm); (b) dependence of the emission intensities on the PbF2 concentration for the emission in the UV domain and the visible domain.

Figure 9 .
Figure 9. (a) Emission spectra of the studied samples under excitation in A band (290 nm); (b) dependence of the emission intensities on the PbF 2 concentration for the emission in the UV domain and the visible domain.

Figure 11 .
Figure 11.(a) Influence of the excitation wavelengths, λexc = 203 nm and 290 nm, on emission intensity in the visible domain for two PbF2 concentration samples; (b) Gaussian multi-peak fitting of the emission band in the visible domain, for two samples, by excitation at λexc = 203 nm.

Figure 11 .
Figure 11.(a) Influence of the excitation wavelengths, λexc = 203 nm and 290 nm, on emission intensity in the visible domain for two PbF2 concentration samples; (b) Gaussian multi-peak fitting of the emission band in the visible domain, for two samples, by excitation at λexc = 203 nm.

Figure 11 .
Figure 11.(a) Influence of the excitation wavelengths, λ exc = 203 nm and 290 nm, on emission intensity in the visible domain for two PbF 2 concentration samples; (b) Gaussian multi-peak fitting of the emission band in the visible domain, for two samples, by excitation at λ exc = 203 nm.

Figure 12 .
Figure 12.(a) Optical absorption spectrum, the excitation spectrum monitored for the 320 nm emission peak and the emission spectrum under excitation in the A band (290 nm) is also shown; (b) excitation spectra of BaF2:0.25 mol% PbF2 sample monitored for 305 nm and 320 nm emission peaks; (c) Gaussian multi-peak fitting of the excitation spectra (λmonitor = 320 nm) of two samples with different PbF2 content.

Figure 12 .
Figure 12.(a) Optical absorption spectrum, the excitation spectrum monitored for the 320 nm emission peak and the emission spectrum under excitation in the A band (290 nm) is also shown; (b) excitation spectra of BaF 2 :0.25 mol% PbF 2 sample monitored for 305 nm and 320 nm emission peaks; (c) Gaussian multi-peak fitting of the excitation spectra (λ monitor = 320 nm) of two samples with different PbF 2 content.

Table 3 .
Maxima of the optical absorption bands of CaF2:0.5 mol% PbF2 and BaF2:0.5 mol% PbF2 crystals as a result of the absorption spectra and by Gaussian multi-peak fitting *.

Table 3 .
Maxima of the optical absorption bands of CaF 2 :0.5 mol% PbF 2 and BaF 2 :0.5 mol% PbF 2 crystals as a result of the absorption spectra and by Gaussian multi-peak fitting *.

Table 5 .
The components of the optical absorption A band, the excitation A band components monitored for the 320 nm emission peak, and the UV emission under excitation in the A band (290 nm)1.