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The density, molar volume and refractive index of the glasses were found to increase with the increase in CaO content. Structural investigation by FTIR spectroscopy revealed that the substitution of P2O5 by CaO depolymerizes the phosphate glass network by systematic conversion of Q3 structural units into Q2 structural units by breaking the P-O-P links. From the optical absorption studies, the optical band gap values were found to decrease with increasing CaO content which can be due to increase in the number of nonbridging oxygens in the glass network. Vickers hardness increased with the calcium oxide content due to densification. The fracture toughness decreased with increase in CaO content due to the increase in the bond density between the modifying cations and the nonbridging oxygens in the glass network. It was observed that brittleness increase with the addition of CaO content can be mainly attributed to the decrease in the molar volume.
Phosphate glasses possess remarkable functional properties such as low viscosity, low dispersion, lower melting temperature (compared to silicate and borate glasses), high refractive indices, high thermal expansion coefficient and the high transparency in the ultraviolet range which make them excellent candidates for glass to metal sealing applications, vitrification of radioactive waste, and photonics [1-4]. The main disadvantage of phosphate glass is poor chemical durability. The properties of the phosphate glasses can be modified and the chemical durability can be improved significantly by the addition of alkali and alkaline earth oxides into the glassy network .
Various types of bioactive glasses and ceramics based on calcium phosphates have been of considerable interest for artificial bone and tooth materials . For technical and biomedical applications such as temporary implants for bone repair and reconstruction require knowledge on their mechanical properties. Vickers hardness and fracture toughness are important parameters required for the prediction of the mechanical properties of brittle materials [7-9]. The cracks generated by Vickers indentations are widely used to determine the fracture toughness and brittleness of glasses. The mathematical analysis of fracture mechanics particularly for brittle materials was outlined in many investigations [10-11]. These analyses can be used for phosphate glasses as they are brittle in nature.
In the present work, calcium phosphate glasses in the ultra region were prepared and characterized using X-ray diffraction, optical method and FTIR. Density and molar volume of these materials were measured and compared with their composition. Refractive index of these glasses also showed composition dependence. Further, mechanical properties like microhardness, fracture toughness and brittleness were evaluated for different mole% of CaO.
2. Experimental procedure
Glasses were prepared by the conventional melt quenching method using high purity chemicals such as CaO (99.9%), and P2O5 (≥ 98%) supplied by Alfa Aesar as starting materials. A batch of 20g was weighed, thoroughly mixed in agate mortar, and then placed into a silica crucible and melted at 1,200 °C for 1 h in a muffle furnace. After retaining the melt at that temperature, it was cast into copper plates. The obtained glass samples were annealed at 400 °C for 5 hours to relieve any residual stress developed during glass quenching and then slowly cooled to room temperature. Glasses were ground and polished with different grades of emery paper for optical and mechanical measurements. The compositions of the studied glasses are shown in Table 1.
The X-ray diffraction studies of the prepared glass samples were carried out using JEOL, JDX-8P-X-ray diffractometer with Cu-kα radiation in the diffraction angle (2θ) range from 20°-80°. The x-ray tube was operated at 40 kV and 30 mA. Density measurements were carried out by Archimedes method using xylene as an immersion fluid. The corresponding molar volume of each sample was calculated by using the relation, where M is the glass molecular weight and ρ is the density of the corresponding glass samples. The refractive indices of the samples were measured at room temperature using an Abbe (MAR-33) Refractometer with an accuracy of ± 0.001.The structural investigation was performed using Thermo Nicolet Avatar 330 FTIR spectrometer range from 400-4000 cm-1. The optical absorption spectra were recorded using fibre optic spectrometer (model SD 2000, Ocean optics inc., USA) in a spectral range of 250nm - 850nm. The Vickers hardness of the glasses was measured using Vickers diamond pyramid indentation technique (Clemex micro hardness tester, MMT X7, Matsuzawa Seiki Corp., Japan) by applying 0.98N for 10s. For the fracture toughness measurements, indentations were performed on glass samples at 19.6 N to obtain median cracking. The obtained crack length was measured using optical microscope. The indentations with cracks were observed under scanning electron microscopy (JEOL JSM 6380LA system).
3. Results and Discussion
3.1 Density, Molar volume and Refractive index
XRD pattern of prepared glasses is shown in Fig. 1. No sharp diffraction peaks in the spectra can be observed which indicates that the samples are indeed amorphous in nature. Density and molar volume of the binary calcium phosphate glasses are shown in Fig. 2. The density of the glasses increases with the increase of CaO content. This may be due to the reduction in connecting P-O-P bonds of the network or cross linking between newly formed phosphate chains. This increase in density agrees with the results reported on density of calcium phosphate glasses . The observed decrease in the molar volume with increasing CaO content indicates a decrease in the free space in the glass structure. The density depends on the mass of the constituents and the volume that they occupy in the glass matrix and these properties depend on the nature of the modifier cations which eventually changes the glass network, leading to the formation of non bridging oxygen atoms.
The compositional effects on the refractive index with modifying cation mole% of glasses are depicted in Fig. 3. The results show that the refractive index of the prepared glasses increases with CaO mole%. The obtained values are reported in Table 1.This increase in refractive index is consistent with the results reported in the literature . The refractive index depends on the electron density and polarizability of anions present in the glass. The contribution to the refractive index from the oxygen ions is very important. Particularly, nonbridging oxygens are more polarisable than bridging oxygens and contribute to a larger refractive index. The addition of network modifiers such as CaO to the phosphate glasses breaks the P-O-P linkages and generates the nonbridging oxygens and electic dipoles that can contribute to an increase of refractive index. The refractive index also depends on glass composition, density, molar and ionic refractivity .
3.2 FTIR spectra
Typical infrared spectra in the frequency range between 400 and 1600 cm-1 of xCaO-(100-x) P2O5 glasses are shown in Fig. 4. As seen from this figure, the band at about 1268-1289 cm-1 is assigned to asymmetric stretching modes, νas (PO2) of the two non bridging oxygen atoms bonded to a phosphorus atom in Q2 phosphate tetrahedron. The absorption bands νas (P-O-P) and νs (P-O-P) occurring about 898-910 cm-1 and 739-767 cm-1 are assigned, respectively to the asymmetric and symmetric stretching of the bridging oxygen atoms bonded to a phosphorus atom in Q2 phosphate tetrahedron. The bands at around 444-462 cm-1 can be ascribed to deformation modes of PO43- groups. The band assignments shown in fig. 3 are consistent with the reported literature .
The hygroscopic nature of the prepared glasses was confirmed by the presence of absorption bands due to O-H groups which are observed in the frequency range between 4000-1600 cm-1. The broad band around 3345-3416 cm-1 is due to the symmetric stretching of O-H groups, and the band around 1638 cm-1 is due to the deformation modes of O-H groups, νs (H-O-H) and absorbed water molecules, δ (H-O-H). Bands assignment for all the prepared glasses are summarized in Table 2.
When a modifier cation is incorporated into phosphate glasses, depolymerisation takes place through the breaking of long chains. Thus it may form ionic cross linking between the broken phosphate chains in the glass network. The considerable shift towards lower frequencies of (PO2)as was observed with increase of CaO content . Decrease in the intensity of the (PO2)as stretching band as the CaO content increases, may be due to a decrease of the length of phosphate chains with increasing CaO content and is attributed to depolymerisation of the phosphate network. The analysis of the IR spectra of the studied glasses reveals that the total content of P-O-P bridges with ring structures (896-910cm-1) decreases with the increase of CaO content. The decreasing intensity of P-O-P absorption band indicates that the calcium ions may act as a glass modifier. The broad IR feature at 739-767 cm-1 is assigned to symmetric stretching modes of P-O-P linkages. These band shift to higher wave number with increase in CaO content indicates the shortening of phosphate chain length. For the glass with 50 mol% CaO, the absorption band near 1080cm-1 may be due to the stretching mode of P-O-Ca as shown fig.4 similar to those reported in the literature . But there is no sufficient evidence for the existence of covalent P-O-Ca band linkage in the literature. The overlapping of absorption bands gives rise to difficulties in analysis. It was shown that the absorption bands at around 444-462 cm-1 can be ascribed to deformation modes of PO43- groups are shifted to higher wave number with increasing CaO content.
3.3 Optical absorption
Tauc plot for binary calcium phosphate glasses are shown in Fig. 5. The absorption coefficient in these glasses can be related to optical band gap energy values of the glass by power law suggested by Davis and Mott , which can be expressed as the following equation.
where B is a constant, is the optical energy band gap, is the photon energy of incident beam, α (ω) is the absorption coefficient at an angular frequency and index which can assume values of 1/2, 3/2, 2 and 3, depending on the mechanism of interband transitions. The value of is equal to 1/2 for allowed direct transitions, 3/2 for direct forbidden transitions, 2 for allowed indirect transitions and 3 for forbidden indirect transitions. As reported by Tauc  and Davis and Mott  for indirect transitions of glassy materials, the value of can be assumed to be 2 so, a value of r=2 has been used in the present analysis. The values of optical band gap energy obtained from extrapolation of linear regions of the plot to () 1/2 = 0 as shown in Fig. 5. The values are listed in Table 3.
In the present investigation the decrease of to lower energies with increase in calcium oxide content is probably related to the conversion of bridging oxygens (BO) to non bridging oxygen (NBO). The optical band gap energy of glasses depends on the nature and relative concentration of bridging and non bridging oxygens. The optical transitions in these glasses may be due to the excitation of electrons from the energy levels, mainly constituted by oxygen atoms to the levels made by the metal ions. Non bridging oxygen atoms are associated with negative charge which helps the excitation of its electrons to the higher energy level in comparison with bridging oxygen atoms in which there is no negative charge. Hence, an increase in concentration of nonbridging oxygen atoms is associated with a decrease in values. A similar decrease in values with an increase in the number of nonbridging oxygen atoms has been reported for phosphate glasses .
The absorption coefficient near the band edge shows an exponential dependence on photon energy. The fundamental absorption edge usually follows the Urbach rule,  given by
where is a constant and is the Urbach energy which indicates the width of the band tails of the localized states. Urbach energy is determined from the reciprocals of the slopes of the linear portion of the ln versus photon energy ( curves in the lower photon energy regions as shown in Fig 6. The origin of Urbach energy in amorphous materials may be due to the stronger broadening of absorption edge compared with crystals. This origin can be attributed to the lack of long range order, density fluctuations, phonon-assisted indirect electron transitions and charged impurities . The values of Urbach energy are included in Table 3 for all the prepared samples.
3.4 Vickers hardness, Fracture toughness and Brittleness
Vickers hardness of binary phosphate glasses are shown in Fig. 7. Vickers hardness is calculated from the following equation.
where is the Vickers hardness in GPa, is the indentation load (0.98N) and is the half of the average length of two diagonals of the indentation measured with a precision of 0.1µm. The Vickers hardness of the glasses increases with the CaO content which indicates the stacking of phosphate chains are more compact and cross linking strength has increased in the glass network . The measured values of Vickers hardness are reported in Table 3. In hardness measurements, glass is subjected to undergo both compression and shear which results in the elastic deformation, plastic flow and densification caused by the high stresses developed during the indentation process. Yamane and Mackenzie  state that the ratio of the contribution of various possible deformation mechanisms to the formation of indentation load is not the same but varies with the volume ratio of the glass composition. Generally, in brittle materials, fracture is caused by a propagating crack, which often originates from flaws and extends when the applied stress exceeds a certain threshold. Vickers diamond pyramidal indenter produces palmqvist or radial cracks. Radial cracks that occur on the surface of the specimen outside the plastic zone and at the four corners of the indentation pattern. Half-penny shaped crack patterns generated by Vickers indentations are widely used to determine the fracture toughness (KIC) of glasses. The following equation is proposed by Anstis .
where , , C and are Young's modulus (Gpa), Vickers hardness (GPa), the crack length (microns) and applied load (19.6 N), Young's modulus of glass compositions was calculated using Makishima and Mackenzie model . The evaluated fracture toughness values are listed in Table 2.
Fig. 8 shows, a decrease in the fracture toughness which is due to the increase in Young's modulus and crack length with the increase in CaO content. Fracture toughness is a property concerned with the mean bond strength and it changes with Young's modulus. According to Osaka and Takahasi  results on binary glasses, the bond strengths between the modifying cation and non bridging oxygen were much weaker than the bond strengths between the phorphous and bridging oxygens or phrosphorus and nonbridging oxygens. It is concluded that propagating cracks in these glasses may be due to the breakage of weakest bonds between the nonbridging oxygens and modifying cations. Lawn and Marshall  have proposed a useful approach for the quantification of the brittleness, in which a simple index of brittleness B is derived in terms of hardness and fracture toughness parameters as,
where Hv is the Vickers hardness and KIC is the Vickers indentation fracture toughness. The brittleness of studied glasses as a function of CaO content is shown in Fig. 8. It increased with the increase in CaO content. This is mainly due to an increase in density and decrease in the molar volume. From these results, the reason for increase in brittleness as the CaO content increases can be explained since a higher CaO content makes the glass structure more rigid. When indented, more rigid glass structure allows less deformation and it shows more brittle nature. A lower deformation results in increase of median cracking and thus an increase in the brittleness. Seghal and oto  found that a lower molar volume is a key factor for increase in brittleness (i.e. increasing hardness and decreasing fracture toughness) in soda lime silicate glasses and they believed that brittleness is dependent on the densification and plastic flow modes of deformation before crack initiation.
Fig. 9 shows the SEM micrographs of the indents made at 19.6 N load on glass samples with 30mol% and 50mol% CaO. Straight cracks were generated from the four corners of the pyramidal Vickers indentation which confirms that fracture pattern for the glasses were penny-like radial/median cracks (C/d ratio ≥ 2.5). EDX analysis shown in fig 9(b) indicates the presence of P,Ca and O atoms in the glass matrix. The presence of shear lines, which are indicative of plastic flow, can be observed for all the glasses. 50mol% CaO glass shows more shear lines compared to 30mol% CaO glass due to more plastic flow which indicates that densification mode of deformation is difficult, thus increasing the brittleness. It was also found that for minimum brittleness glasses show lesser hardness and more fracture toughness.
Binary calcium phosphate glasses of the composition range from 30 to 50 mol% of CaO are prepared by melt quenching technique. The properties of calcium phosphate glasses show composition dependence. The values of density increased from 2.528 to 2.621 (gm/cm3) while the molar volume decreased from 45.95 to 37.92 (cm3/mol) and the refractive index increased from 1.527 to 1.543 with the increase in CaO content. The phosphate glass structure was significantly changed by the addition of appropriate modifier cations that cause the depolymerisation of the glass network structure by converting bridging oxygens into nonbridging oxygens by breaking P-O-P links. The values of optical band gap energies for the binary series deceased from 3.67 to 3.49 eV while Urbach energy increased from 0.233 to 0.336 eV with the increase in CaO content. The optical band gap and Urbach energy were found to be strongly dependent on the glass composition. It was found that Vickers hardness increased from 3.47 to 3.72GPa with the calcium oxide content due to densification. The fracture toughness decreased from 1.03 to 0.63 MPam1/2 and brittleness increased from 2.65 to 4.19 µm-1/2 with increase in CaO content.