XRD, FTIR and ultrasonic investigations of cadmium lead bismuthate glasses

Cadmium lead bismuthate glasses in the system xCdO–(1−x)[0.5PbO + 0.5Bi2O3](40 mol% ≤ x ≤ 90 mol%) were successfully prepared by melt-quenching method. The structural and elastic properties have been investigated using XRD, FTIR and ultrasonic pulse–echo techniques. The XRD patterns confirmed the amorphous nature of the samples prepared. Density and ultrasonic velocity data were used to evaluate various elastic properties. Addition of CdO gave rise to decreased density and molar volume and increased elastic moduli, micro-hardness, and Debye temperature. The FTIR analysis revealed that increasing CdO content enhances the BiO6 octahedral sites at the expense of the BiO3 and PbO4 units. This results in the formation of Pb–O–Bi(6) and Bi(3)–O–Bi(6) linkages in the glass network, which stiffen the structure and improve the elastic properties. A correlation between elastic and compositional parameters was achieved on the basis of theories and approaches in the field.


Experimental
Sample preparation.The investigated glass samples in the present study were prepared from laboratory chemicals with purity > 99%, including cadmium carbonate CdCO 3 (Fluka, Germany) for CdO, lead tetroxide Pb 3 O 4 (TECHNO FARMACHEM, India) for PbO and Bi 2 O 3 (Fluka, Germany) was added as such.The required amount of different chemicals for producing 100 g glass melt was weighed using a single pan balance having an accuracy of ± 0.001 g.The chemical composition and code of the prepared samples are listed in Table 1.The mixture is put in a porcelain crucible and heated inside a SiC-heated furnace (Vecstar, UK) to 1050 °C for 2 h for melting.The melts were rotated at intervals of 20 min to arrive complete mixing and acceptable homogeneity.The homogeneous molten mixtures were casted into a warmed stainless-steel mold to get the required dimensions.Then the prepared samples were immediately transferred to an annealing muffle furnace regulated at 320 °C-less than the glass transition temperature-to avoid the mechanical strain developed during the quenching process.The muffle was switched off after 1 h and left to cool with the glass inside to room temperature at a rate of 30 °C/h.Finally, the prepared glass samples were polished and their surfaces were made perfectly parallel and smoothened by diamond disc and diamond powder.The samples prepared were non-hygroscopic and chemically stable.Figure 1 shows the photograph of glass samples prepared in the present work.

X-ray diffraction (XRD) analysis.
The preparedglass samples were subjected to powder X-ray diffraction (XRD), using Bruker AXA diffractometer (Germany) with graphite monochromatized Cu-Kα radiation operating at 40 kV and 10 mA and scanning rate 10°/min was used for x-ray measurements.The measurements were carried out in the range 5° ≤ 2θ ≥ 80°.Table 1.Chemical compositions (in mol%) and codes of the prepared glass samples.www.nature.com/scientificreports/Fourier transform infrared (FTIR) absorption measurements.FTIR technique is one of the spectroscopic techniques used to identify the basic building units in the glass network.FTIR absorption spectra of glasses prepared were recorded at room temperature in the wave number range from 400 to 1500/cm by a Fourier transform computerized IR spectrometer type FTIR 4600 JASCO Corp (Japan) using the KBr disc technique.The glasses were examined in the form of pulverized powder which was mixed with KBr with the ratio 1:100 mg glass powder to KBr, respectively.The weighed mixtures were then subjected to a pressure of 5 tons/ cm 2 to produce clear homogeneous discs.
Density measurement and molar volume calculation.The densities of the samples that were prepared were determined at room temperature using an analytical balance A&D company limited, model GR-200, with a repeatability of 0.1 mg, and a density determination kit based on the standard test method ASTM-D792-13.The Archimedes technique was used, with distilled water as the buoyant liquid, and the following formula was applied: where ρ w represents the density of distilled water at room temperature, while W a and W w represent the weights of the sample in air and distilled water, respectively.In order to assess the uncertainty associated with the density (ρ) and molar volume (Vm), three measurements were taken for each sample.The formula used to determine the uncertainty in densities and molar volume is based on the standard deviation (σ) and the number of independent observations (n).The standard uncertainty can be calculated using the following expression 15 : u = σ √ n .Empirical densities (crystalline densities) were calculated using equation ρ C = i x i ρ i , where ρ i is the density of ith oxide component in the crystalline phase and x i is its molar fraction.The molar volume deals directly with the spatial structure of the glass network.The molar volume of each glass sample was calculated with the help of the following equation: where M i is the ith component molecular weight.The volume occupied by crystalline phases in the glass network is known as empirical (crystalline) molar volume.Assuming the mixture of oxide components to be an ideal solution we also calculated the empirical molar volume for each glass composition using the relation

Ultrasonic measurements.
The ultrasonic pulse-echo technique is a non-damaging technique that capable of determining elastic properties of glasses.The measurements of longitudinal and shear ultrasonic wave velocities in the prepared glass samples were made at room temperature and at 4 MHz frequency.The ultrasonic pulse travels through the sample bonded to the transducer and the echo is registered each time it returns to the transducer.The flaw detector (KRAUTKRAMER USM 36) was applied to measure the time interval between the pulse and its echo (or two successive echoes) ( t ).Ultrasonic velocities were determined by dividing the thickness of the sample by t.
Elastic properties are informative because they are related to the structure of the glass network.The ultrasonic velocities and density data allow the determination of various elastic properties using the standard relations; longitudinal modulus In these relations, V l and V s are the respective longitudinal and shear ultrasonic veloci- ties, N a is Avogadro's number, B is Boltzmann's constant, h is Planck's constant and is the mean ultrasonic velocity.

Results and discussion
X-ray diffraction (XRD) analysis.X-ray diffraction is one of the simplest techniques, which was used by researchers to establish the amorphous nature of oxide glasses 16 .Figure 2 depicts the X-ray diffraction patterns for Cd40, Cd70 and Cd90 glass samples.The absence of sharp Bragg peaks and presence of broad humps confirms the amorphous nature of these samples 16 .The samples lack in long-range atomic periodicity in their networks.
FTIR spectral analysis.IR spectroscopy studies were used to get essential information about the arrangement of the structural units of the glass samples.Figure 3 shows the measured FTIR absorption spectra of xCdO-(1−x)[0.5PbO−0.5Bi 2 O 3 ] glass samples under investigation.These spectra are dominated by two broad absorption bands in the range 400-550/cm and 750-1050/cm and a small but well-distinguished band centered at 717/cm.The broad band extending from 400 to 550/cm is attributed to bending vibration of Bi-O bonds in BiO 6 octahedral units and symmetric bending vibration of Pb-O bonds in PbO 4 tetragonal pyramids 17,18 .The presence of this band confirms the former role of PbO and Bi 2 O 3 in the matrix of the studied glasses.Some author's attributed the FTIR band at 720/cm in the ZnO modified bismuth silicate glasses 19 and that at 715/cm in ternary Bi 2 O 3 -B 2 O 3 -CuO glasses 20 to the symmetric stretching vibrations of Bi-O bond in BiO 3 structural www.nature.com/scientificreports/units.The appearance of this band in investigated glasses at 717/cm (Fig. 3) evidences the existence Bi 3+ ions not only as BiO 6 units but also as BiO 3 units.The broad band in the wavenumber range 750-1050/cm is assigned to the vibrations of Bi-O-Bilinkages 19 .With increasing CdO content, the intensity of this band has been observed to increase whereas that of BiO 3 units decreases.This suggests that the gradual increase in the concentration of cadmium oxide in xCdO-(1−x)[0.5PbO−0.5Bi 2 O 3 ] glasses enhances the BiO 6 octahedral sites in the glass matrix at the expense of BiO 3 groups.The low frequency peak at 418/cm, which was observed in all samples is may be attributed to vibrations of Cd 2+ metal cations.
Because the observed bands are very broad and asymmetric, the deconvolution process should be applied to the measured FTIR spectra to decompose each broad absorption band to deconvoluted peaks (component bands).Each peak has two characteristic parameters, which are the center (C) and the relative area (A).The center is related to some type of vibrations of a specific structural group, whereas the relative area (A) is proportional to the concentration of this structural group.Figure 4 displays the deconvoluted peaks for Cd40, Cd80 and Cd90 glass samples.The Gaussian distribution was applied in the present deconvolution.The peak centers and their corresponding assignments are shown in Table 2.
The general characteristics of the fitted FTIR absorption spectra for the investigated xCdO-(1−x) [0.5PbO + 0.5Bi 2 O 3 ] glasses can be summarized as follows; 1.The broad band extending from 400 to 550/cm was deconvoluted to two peaks at about 428 and 476/cm, which are related to BiO 6 and PbO 4 units, respectively.The intensity of these peak has been observed to increase with increasing CdO. 2. The broad band extending from 550 to 1100/cm was deconvoluted to four peaks at about 690, 733, 831 and 916/cm.An additional absorption peak centered at 636/cm was observed only in Cd90 sample.This may be  www.nature.com/scientificreports/attributed to the metal-oxygen starching of CdO.The peak centered at 620/cm has been assigned to Cd-O bonds 23 .
The most important condition for the formation of BiO 3 structural units in the glass network is the appearance of the 830/cm band in the FTIR spectra 17 .In the present study, this band appears in the wave number range 831-843/cm, which proofs the coexistence of BiO 6 and BiO 3 units in the structure of xCdO-(1−x) [0.5PbO + 0.5Bi 2 O 3 ] glasses.Figure 5 shows that the relative area of BiO 3 -and PbO 4 -relating absorption bands  www.nature.com/scientificreports/decrease whereas that of bands characterizing BiO 6 units and Pb-O-Bi(6), and Bi(3)-O-Bi(6) linkages increase with the addition CdO.This may be explained by accepting the assumption that the addition of the cadmium oxide declines the formation of BiO 3 and PbO 4 units in favor of the formation of BiO 6 units in the glass.The presence of extra BiO 6 units and formation of Pb-O-Bi(6), and Bi(3)-O-Bi(6) linkages is expected to increase the compactness of the glass structure with increasing CdO content.This reflected the glass modifier role of CdO, which results in the change in the coordination number of bismuth ions from three to six.The structure of the studied glasses is assumed to be built up by BiO 3 , BiO 6 , and PbO 4 structural units.These structural units are connected to each other through Pb-O-Bi, and Bi-O-Bi linkages.
Density and molar volume.The density is one of the simplest tools used to detect changes in the glass structure [26][27][28][29] .Also, the molar volume can be preferably used to describe the network structure and the arrangement of the building units in glasses [26][27][28][29] .Table 3    ] glasses under investigation.The variation of measured and empirical densities with the molar fraction of CdO is shown in Fig. 6.As clearly observed, the measured density values decrease monotonically from 7.4888 to 5.2401 g/cm 3 with increasing the molar ratio of CdO from 40 to 90 mol%.This behavior is not only attributed to the lighter molar mass of CdO (128.41 g/mol) than that of Bi 2 O 3 (465.96g/mol) and PbO (223.20 g/mol) but also attributed to the relative changes in the density values between CdO (8.15 g/cm 3 ), Bi 2 O 3 (8.9g/cm 3 ) and PbO (9.53 g/cm 3 ).The empirical density values also decreased, but with a slower rate, over the entire composition range studied.As a result (ρ − ρ C ) value increases with increasing CdO content, which sup- ports the amorphous nature of samples as confirmed from the XRD results in section "X-ray diffraction (XRD) analysis".
In the present investigation, the molar volume of xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses decreased monotonically from 34.47 to 28.63 cm 3 /mol with increasing CdO content from 40 to 90 mol% (Fig. 7).The empirical molar volume V C behaves the same trend but with a higher rate of decrease.This indicates structure compactness with CdO addition.This parallel behavior of density and molar volume with composition was reported in the literature for numerous glasses [30][31][32][33] .Change in the molar volume might be ascribed to the lattice rearrangements caused by the substitution of PbO and Bi 2 O 3 by CdO resulting in decreasing the ring size, leading to the structural closure.Thus, the decrease in molar volume with increasing CdO content can be explained in two ways as follows:  www.nature.com/scientificreports/ 1.The atomic radii of ingredient elements were changed in the order Cd (1.52 nm) < Pb (1.63 nm) < Bi (1.81 nm).Moreover, the ionic radius values were 0.119 nm for Pb 2+ ion and 0.103 nm for Cd 2+ and Bi 3+ ions.Thus, the substitution of Pb 2+ and Bi 3+ ions by Cd 2+ ion is expected to contracts the structure and decreased the molar volume.2. Based on FTIR data obtained, the addition of CdO declines the presence of the structural units BiO The increase in the difference between glass and crystalline molar volumes with increasing CdO content in the glass confirms the amorphous nature of samples.

Ultrasonic velocity and elastic properties.
Changes in the glass structure due to addition of a network modifier and/or a network former can be directly reflected in ultrasonic velocities and elastic properties.Thus, the composition dependence of ultrasonic velocities and elastic moduli may yield information about the dimensionality and nature of bonding in the glass.The results of longitudinal and shear ultrasonic velocities measurements, along with the determined values of elastic moduli, micro-hardness, Debye temperature and Poison's ratio are listed in Table 4 for xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses studied.One can observe from Fig. 8 that both longitudinal and shear velocities increase linearly with the substitution of (0.5PbO + 0.5Bi 2 O 3 ) by CdO.Also, the elastic moduli (Fig. 9) and micro-hardness (Fig. 10) are improved with the progressive addition of CdO.Generally, elastic moduli of the glass are strongly dependent on the concentration of basic structural units of the constituent oxides and types of bonds between these units.The FTIR results obtained indicated that the increase in the concentration of cadmium oxide enhances the BiO 6 octahedral sites in the glass matrix at the expense of BiO 3 and PbO 4 groups.As shown in Fig. 5, the relative areas of absorption band characterizing BiO 3   36 .However, the BiO 6 , PbO 4 and BiO 3 structural units have a cross-link density of 4, 2 and 1, respectively.Thus, the presence of extra covalent bonds due to the formation of Pb-O-Bi (6) and Bi(3)-O-Bi(6) linkages at the expense of Pb-O-Bi(3) linkages is expected to increase the average cross-link density and number of network bonds per unit volume.This increases the rigidity and resists the deformation of glassy structure with increasing CdO content as evidenced by the increase in ultrasonic velocity, elastic moduli and micro-hardness.

Sample code
Poisson's ratio plays a dominant role in exploring the degree of connectivity and cross-link density of the glass structure.It is reported that, if the solid material has Poisson's ratio < 0.3, then it has been counted in high crosslinking density materials 37 .Otherwise, it is considered in low cross-linking density materials.Three-dimensional glasses (high cross-link density materials) have Poisson's ratio values extending from 0.1 to 0.2, meanwhile, two-dimensional glasses have Poisson's ratio values extending from 0.3 to 0.5 37 .It can be seen from Table 3 that xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses have Poisson's ratio values < 3.0, which suggest that these glasses have high cross-linking density.These cross-links generate covalent bonds and resisting the transverse deformation.This evidenced the presence of PbO 4 , BiO 3 and BiO 6 structural units within the matrix of these glasses.
Debye temperature is an important thermal parameter in the determination of elastic properties and atomic vibrations of solids.The increasing trend of Debye temperature in xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses  www.nature.com/scientificreports/(Fig. 12) implies an enhancement in the compactness and rigidity with the substitution of (0.5PbO + 0.5Bi 2 O 3 ) by CdO.This behavior is in consistent with the results of molar volume, ultrasonic velocities, elastic moduli, and micro-hardness.Gopal et al. 38 and Rajendran et al. 39 38 and Rajendran et al. 39 approaches.
Fractal bond connectivity ( d = 4 S /K ) can give information about the dimensionality of the glass structure 43 .This parameter testified the glass rigidity and mostly its values lie between 1 and 3.It has been found that, d = 1 for 1D chain structure, d = 2 for 2D layer network and d = 3 for 3D network 43 .The d values of the present xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses lie between 1.99 and 2.18, which suggests 2D structures.One way to determine the elasticity of glasses is by studying Poisson's ratio-fractal bond connectivity correlation on the basis of Abd El-Moneim's approach 44 , according to the following equation: www.nature.com/scientificreports/where A and z are two constant, their values depend strongly on the glass network 44 .Figure 14  glasses (A = 0.466 and z = 0.09) 46 , Li 2 O-PbO-B 2 O 3 glasses (A = 0.469 and z = 0.091) 47 and PbO-CuO-B 2 O 3 glasses (A = 0.473 and z = 0.094) glasses 48 .This supports the suitability of Abd El-Moneim's approach 44 for understanding the Poisson's ratio data of glasses.
Understanding the obtained elastic moduli values of xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses is based on the Makishima-Mackenzie's theory 49,50 .It is a well-known fact that closely packed structures are rigid and have high values of packing density, whereas loosely packed structures are soft and have small values of packing density 49,50 .According to Makishima-Mackenzie's theory 49,50 , elastic moduli of glasses should show a forward relations with two compositional parameters, which are the total packing density ( C t =   49,50 for predicting the elastic moduli of the investigated glasses.
The following equation, which correlating bulk modulus with the total packing density and Young's modulus of ionic solid, was reported 49,50 : In these equations, m and n are constants in Mie's atomic potential-energy equation ( ϕ(r) = − a r m + b r n ,a and b are two constants and r is the distance between cation and anion), β = (r A + r O ) 3 y r 3 A + z r 3 O is a factor for an oxide A y O z with cation ionic radius r A and oxygen ionic radius r O .It is important to demonstrate the applicability of Eq. ( 4) for the present glasses.Figure 17 shows how the experimental bulk modulus varies with the quantity C t E exp .As can be seen, the K exp −C t E exp relationship reveals a linear proportionality.The fitted curve in the figure can be represented by the following semi-empirical formula: with R 2 = 0.996 and [(m − n) m/24π] β = 1.49 .These results show that the correlation between bulk and Young's moduli of xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses can be achieved through the total theoretical packing density.

Figure 5 .
Figure 5. Composition dependence of the relative area of BiO 3 , BiO 6 , and PbO 4 structural units and Pb-O-Bi and Bi-O-Bi linkages.
3 and PbO 4 in favor of the presence of BiO 6 structural units in the glass network.This results in the formation of Bi(3)-O-Bi(6) and Pb-O-Bi(6) linkages at the expense of Pb-O-Bi(3) linkages.The curves of the radial distribution function (RDF) obtained by the Fourier transformation for PbO-B 2 O 3 glasses concluded that the well-separated peaks due to Pb-O and Pb-Pb correlations appear at about 0.23-0.25 and 0.40 nm, respectively34 .Also, X-ray diffraction studies of binary Bi 2 O 3 -B 2 O 3 glasses revealed two groups of Bi-O distances at about 0.19 and 0.25 nm35 .In the light of these data, the formation of Bi(3)-O-Bi(6) and Pb-O-Bi(6) linkages at the expense of Pb-O-Bi(3) linkages in the present xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses is expected to increase the compactness of their structure and decrease the molar volume.
suggested bulk modulus-molar volume correlation according to the equation K V b M = C .In this relation b and C are two constants, their values are determined by the nature of bond- ing, and co-ordination polyhedral that are present in the glass structure.As shown in Fig. 13, the bulk modulusmolar volume relationship revealed an inverse proportionality for xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses.The equation of the fitted curve is given by K V 3.21 M = 5 × 10 6 , with b = 3.21 , C = 5 × 10 6 and R 2 = 0.963.A good bulk modulus-molar volume correlation was achieved in alkaline earth aluminoborate RO-Al 2 O 3 -B 2 O 3 (R = Mg, Ca, Sr) glasses ( b = 1.92 and C = 3.7 × 10 4 40 , TiO 2 -doped borate CaO-Al 2 O 3 -B 2 O 3 glasses ( b = 4.38 and C = 8.8 × 1 0 7 41 , fluorotellurite BaF 2 -TeO 2 glasses ( b = 1.05 and C = 1.0125 × 10 3 42 .This dependence of b and C values on the glass network supports Gopal et al.
shows an inverse linear proportionality between µ and d , which confirms the validity of the semi-empirical Eq. (3) for the present xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses.The equation of the fitted curve in this figure is given by µ = 0.468 − 0.091 d , with R 2 = 0.994.The present glasses have A and zvalues agree very well those reported previously for different glasses, like Li 2 O-V 2 O 5 -B 2 O 3 glasses (A = 0.447 and z = 0.082) 45 , WO 3 -B 2 O 3 -MgO-TeO 2

Figure 17 .
Figure 17.Relation between experimental bulk modulus and quantity C t E exp in xCdO-(1−x) [0.5PbO + 0.5Bi 2 O 3 ] glasses.The solid line represents the least-square fitting of the data.
PbO 4 units decrease, whereas that of BiO 6 units increases.The fraction of the six coordinated bismuth atoms (or fraction of BiO 6 units) was calculated from the relationN 6 = A 6 / (A 3 + A 6 ), where A 6 is the area under IR peaks characterizing BiO 6 and A 3 is that under IR peaks characterizing BiO 3 units.The N 6 values changed from 0.0081 in Cd40 sample to 0.1855 in Cd90 sample as shown Fig.11.This behavior is quite similar to those of ultrasonic velocities and elastic moduli.It is well known that bulk modulus is a function of the cross-link density (coordination number of a network former cation minus 2) and number of network bonds per unit volume of the glass Vl Vs Figure 8. Composition dependence of ultrasonic velocities in xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses.Vol.:(0123456789) Scientific Reports | (2023) 13:12788 | https://doi.org/10.1038/s41598-023-39489-5www.nature.com/scientificreports/and [0.5PbO + 0.5Bi 2 O 3 ] glasses are listed in Table3.For CdO, PbO and Bi 2 O 3 oxides, we have applied C i values of 0.5204, 0.3843 and 0.4985, respectively, whereas the applied G i values were 7.94, 6.05 and 7.56 kcal/cm 3 respectively 51 .It was found that both C t and G t show an increase with the substitution of (0.5PbO + 0.5Bi 2 O 3 ) mole by mole with CdO.These results agree well with the elastic moduli (Figs.15 and 16), micro-hardness and Debye temperature results, which suggested an increase in the rigidity of the glass matrix with increasing CdO content.This confirms the applicability of Makishima-Mackenzie theory Figure 14.Poisson's ratio-fractal bond connectivity correlation in xCdO-(1−x)[0.5PbO+ 0.5Bi 2 O 3 ] glasses.Vol:.(1234567890)Scientific Reports | (2023) 13:12788 | https://doi.org/10.1038/s41598-023-39489-5www.nature.com/scientificreports/