with the increase in molar volume (Vm) (i.e. open structure) and increase in oxygen molar volume (VO) due to the addition of Al2O3 as a glass former at the expense of Na2O (see Table 2), caused the decrease in N4 value and consequently the decrease in all elastic moduli values When the volume change occurs without change in the nature of the bonding or change in the coordination polyhedra, (Ke)(Vm) plots generally are linear, as shown in Fig. 9. with the increase in molar volume (Vm) (i.e. open structure) and increase in oxygen molar volume (VO) due to the addition of Al2O3 as a glass former at the expense of Na2O (see Table 2), caused the decrease in N4 value and consequently the decrease in all elastic moduli values When the volume change occurs without change in the nature of the bonding or change in the coordination polyhedra, (Ke)(Vm) plots generally are linear, as shown in Fig. 9. Since the molar volume represents the spatial distribution of the structural units and ions in a glass network, therefore it deals directly with the spatial structure of the glass. So, it is better to discuss the observed changes in a glass structure in terms of its molar volume. The calculated molar volume values (Table 4) show approximately a stable value for each glass system, and this reflects an approximate structural stability for the obtained glassy phase. This can be taken as an evidence for the supposition that there is no any crystalline phase or any precipitated phase appeared anywhere. (A.G. Mostafa et al. / Solid State Communications 131 (2004) 729734)****with the increase in molar volume (Vm) (i.e. open structure) and increase in oxygen molar volume (VO) due to the addition of Al2O3 as a glass former at the expense of Na2O (see Table 2), caused the decrease in N4 value and consequently the decrease in all elastic moduli values When the volume change occurs without change in the nature of the bonding or change in the coordination polyhedra, (Ke)(Vm) plots generally are linear, as shown in Fig. 9. The observed increase in bulk modulus in spite of the decrease in volume shows that in addition to volume, the type of bonding is also important in determining the composition dependence of bulk modulus in these glasses. Therefore, the increase in bulk modulus with ZnO content in the aluminium sodium diborate glass network led one to conclude that Zn2+ ions try to form ring structures in the form of regular ZnO4 tetrahedral coordination as a network former [16], and compensate for the decrease in the average coordination number of boron atoms (the decrease in N4 values). Such an increasing bulk modulusvolume relationship was observed in some other types of glasses [M.S. Gaafar et al. / Journal of Alloys and Compounds 475 (2009) 535542 ]***This decrease is associated with a decrease in the number of non-bridging oxygens and with acontracting effect of the network due to the formation of Fig. [GeO6] structural units which are slightly larger in size than the [GeO4] species. For the sample with x10 mol% MoO3,the formation of [GeO6] octahedral structural units in the network results in better packing and hence the increase of density. [492]****decrease in the density; this is indicative of decreasing structural compactness of the material. In general, the structural compactness, the modification of the geometrical configuration of the glassy network, the change in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial holes are the factors that influence the density of the glass ceramic material [493]

***The replacement of an intermediate/modifier CdO with Na2O which is a modifier only, develops more nonbridging oxygen than bridging oxygen in the glass network.17,18 The development of nonbridging oxygen may inflate the glass system and thus increases its molar volume. The increase in molar volume may cause decrease in oxygen packing density and mass density [582]****alkali metal oxide cleaves the structure and disturbs the bonding between glass forming cations and oxygen anions. This increases the number of nonbridging oxygens and thus develops a more open structure. Consequently, the expansion of the structure increases the molar volume which causes a decrease in the oxygen packing density and hence a decrease in the density of the glass sample. The decrease in oxygen packing density along with the decrease of mass density and increase of molar volume of these glasses make them less resistive mechanically. This may have caused an increase in the coefficient of linear expansion and decrease in the transition temperature and the softening temperature [585] ****The observed nearly linear compositional dependences of the density and molar volume on TeO2 content (see Table 1) indicates that there are no anomalous structural changes with increasing TeO2 concentration in the glasses. The observed decrease in the molar volume can be attributed to an increase of the atom packing density in the glass network [976]***From the structural point of view, the molar volume, V M=r; where M is the molecular weight of the glass and r the mass density, has frequently been used [6,7]. Molar volume is more sensitive to structural differences between glasses than to density because it normalises for atomic weights of different glass constituents. This normalisation leads to the non-linearity observed in the variation of the molar volume [1090]

The systematic decrease in molar volume indicates that the silver ions do not expand the glass network, instead filling the free volume within the glass structure, which also contributes to the increase in glass density [1377]

The observed decrease in the molar volume (Fig. 7) with increasing alumina content indicates a decrease in the free space in the glass. This is consistent with reports that Al31 strengthens the glass network by cross-linking phosphate chains.16,38,39 The competition between weight and volume effects may be responsible for the presence of the density maxima. [1757]

Calculation of molar volume enables packing density of the glass to be examined independent of effects of ion mass.The increase in molar volume suggests the increased free space within the glass structure [1944]

This behavior is generally observed when increasing the content of amodifier oxide in metaphosphate glasses. The change in density of such systems is related to the density of the formed structural units when introducing the modifier oxide. The molar volume VM decreases linearly with increasing the content, confirming that the copper does reticule the network. [2323] The density of these glasses first increases and then decreases with the content of TiO2 while corresponding molar volume first decreases and then increases. The density of these glasses should decrease due to replacement of high molecular weight P2O5 by low molecular weight TiO2. But it is found that the density of these glasses increases with addition of TiO2 and correspondingly molar volume decreases, indicating that the titanium polyhedra form some new interconnections within the structural network and thus stabilize the glass structure [2340] thus the addition of WO3 can promote a relatively open structure causing an increase in the molar volume. is behaviour was observed in the present case, where the molar volume of the glass systems increases with the growth of the WO3 concentration, suggesting that the molecular volume is inuenced by the number of O2 ions per unit of volume. Apparently, while substituting A2O by WO3, the molar volume should decrease because two cations per unit found for A2O are replaced by a single cation in WO3. e increase of molar volume in tungsten-glasses suggests that the excess of oxygen, due to the substitution of Li2O or Na2O by WO3, induces the formation of additional nonbridging oxygen and/or the formation of voluminous niobium and/or tungsten structural units such as WO6/NbO6 octahedron in the glass network. [2472]

This explanation is in line with the results of the density and the calculated molar volume of the glasses (tabulated in Table 1) which clearly indicates network expansion on account of participating magnesium ions in the glassy matrix and increase the network connectivity. Such asymmetric bridging oxygen formation leads to a length shortening of the phosphate chains and strengthen the cross-linking between the shorter phosphate chains in the glass structure [3112]

Generally, the density and the molar volume show opposite behaviors, but in this study, different resultswere obtained. In this glass, the substitution of phosphorus by lead causes an expansion of the network. Similar trends for densities and molar volumes have already been reported elsewhere for other glass systems [4318]

It is clear that by increasing PbO, the molar volume increases, which is similar to the variation density that occurs with increasing PbO content. The Pb ions may enter the glass network interstitially; hence, some network P\O\P bonds are broken and replaced by ionic bonds between Pb ions and singly bonded oxygen atoms. Therefore, if one assumed that the only effect of adding Pb cations was to break down the network P\O\P bonds, then an increase in the molar volume with PbO content would be expected for the entire vitreous range of the studied glass system. [4318]

This simplified structural model is consistent with the results of the oxygen molar volume, Vom, and the PDof the studied glasses as a function of the O/P ratio, figures 10 and 11 respectively. The continuous decrease in Vom and the slight increase of PD confirm the gradual reduction in the concentration of bridging POP bonds with an increasing O/P ratio [522]

Volumetric studiesVolumetric properties of the glasses are vital for understanding the microscopic structural transformations in the glass matrix [69]. Molar volume is more sensitive to structural differences between glasses than to density because it normalises for atomic weights of different glass constituents. These parameters of the glassy material are influenced by the structural compactness, the modification of the geometrical configuration of the glassy network, the changes in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial hole. Even though the density of the sample depends on the densities of its individual constituents [70], in the case of glasses many other factors like their preparation, thermal history of the sample, creation of non-bridging oxygens, field strength of the modifier etc. also influence the final density of the sample [70] to a greater extent. From the measured densities () at room temperature and effective molar molecular weights (), the physical parameters like molar volume (Vm), oxygen molar volume (VO), oxygen packing density (OPD), cobalt ion concentration (Ni), interionic distance (ri), polaron radius (rp) and field strength (F) are computed using the relations mentioned in the literature [71,72] and are presented in Table 2. The quantitative understanding of these parameters is essential for exploring the basic structural modifications that take place in ZnO-CaF2-P2O5 glasses with the variation of NiO content. Fig. 2 shows the variation of density, oxygen packing density, molar volume and oxygen molar volume of ZnO-CaF2-P2O5 glasses on NiO content. It is observed that the density decreases initially from 2754 (pure glass) to 2739 kgm-3 with the addition of 0.2 mol% of NiO into the glass and then increases nonlinearly with the increase of NiO content and reaches the maximum value of 2831 kgm-3 for 1.0 mol% of NiO doped glass. Also, it is noticed that oxygen packing density showed the same trend while molar volume and oxygen molar volume followed an opposite trend. The nonlinear compositional dependence of these parameters on NiO content indicates that there are structural changes in the glasses with the increasing NiO concentration. As evident from x-ray diffraction patterns and infrared spectra, these glass samples are still in an amorphous state indicating that there is no detectable change to crystallization. Hence, the variation in these parameters can be attributed only to the differences in linkages between different structural species [73] due to the formation of more non-bridging oxygens than bridging oxygens in the glass network and the modification of less stable P-O-P bonds.Volumetric studiesThe initial decrease in the density and oxygen packing density (Fig. 2) of the glasses, an indicative of decreasing structural compactness of the material with the addition of 0.2 mol% of NiO is unpredicted as NiO has a higher density than P2O5. This anomaly of the glasses indicating the loose packing of the atoms in the glass structure is due to the expansion of phosphate Q3 network to accommodate Ni2+ ions in the interstices of PO4 network indicating the formation of PONi2+ bonds which may be due to the disproportionation [65,74] of different phosphate groups present in the glass matrix. Also, this initial decrease in the density can be attributed to the formation of more NiO6 octahedral units than NiO4 tetrahedral units in the ZCP:Ni 0.2 network. On the other hand, NiO cleaves the structure and disturbs the bonding between glass forming cations and anions. This decreases the number of non-bridging oxygens and thus develops a more open structure. Consequently, the expansion of the structure increases the molar volume which causes a decrease in the oxygen packing density and hence a decrease in the density of the glass sample. The observed increase in the density from 2754 kg m-3 (pure glass) to 2802 kg m-3 (0.6 mol% of CoO) and oxygen packing density from 75.28 (pure) to 76.43 x 103 mol m-3 (0.6 mol% of CoO) along with the decrease in the molar volume (Vm) and oxygen molar volume (Vo) up to 0.6 mol% of CoO suggest that cobalt ions are filling the interstices of the glass network indicating the formation of PONi linkages. Also, cobalt ions in glass network exist in both four (Co2+) and six (Co2+, Co3+) fold coordinations, whereas P5+ ion in glass network is in four fold coordination [61]. Therefore, average coordination number of the cation in the glass network increases with increasing CoO content up to 0.6 mol%, which improves glass compactness [61]. Hence, an increase in the density and oxygen packing density can be expected up to 0.6 mol% of CoO. The increase in the density up to 0.6 mol% of CoO may also be attributed to the formation of CoO4 tetrahedral structural units and the conversion of CoO6 octahedral structural units to CoO4 tetrahedral structural units through the formation of some more CoOP bonds which probably results in better packing causing strengthening of the glass network. Also, the decrease in molar volume, which represents the spatial distribution of the ions in the glass structure up to 0.6 mol% of CoO is an indication of the increased compactness of the glass due to the increased cross-linking density. This increase in oxygen packing density along with the increase of mass density and decrease of molar volume of these glasses make them more resistive mechanically.The replacement of P2O5 with CoO develops more non-bridging oxygens than bridging oxygens in the glass network due to the replacement of less stable P-O-P bonds by chemically durable P-O-Co bonds. The observed increase in the density with the increase of CoO up to 0.6 mol% may be due to increase in non-bridging oxygens in the glass network indicating the increasing crosslinking of various units leading to a decrease in its molar volume [73]. The decrease in molar volume may cause an increase in oxygen packing density and mass density. This is due to the fact that the divalent cobalt ions form higher number of NBOs than the trivalent cobalt ions. For better understanding of the structural variations in the glass, a qualitative and quantitative analysis is carried out by theoretical estimation of mass density and excess molar volume of these glasses. Theoretical values of the density are estimated using the relation th = ixi where i and xi are the density and mol% of the glass components respectively. The estimated and the measured values of density of these glasses are depicted in Fig. 3a as a function of CoO concentration. The difference in values of density may be due to the variation in atomic arrangement between the structure of glass and component molecules. Excess volume () is a quantity derived from the molar volume of the sample (Vm) and molar volumes of the individual components (Vi) of the glass. is calculated using [70]:(3) Fig. 3b represents the variation of the excess molar volume of CoO doped ZCP glasses. It is an established fact in the case of liquid mixtures that the negative values of excess molar volume , suggest specific interactions [75,76] between the mixing components while its positive values suggest dominance of dispersion forces [76,77] between them. In the present study, the negative values (Fig. 3b, Table 2) indicate the presence of specific interactions between the mixing components of the glass leading to structural strengthening of the glass. The largest negative value of for 0.6 mol% of CoO doped ZCP glass indicates the closed packing of the atoms of the components of this glass. Since the molar volume represents the spatial distribution of the structural units and ions in a glass network, therefore it deals directly with the spatial structure of the glass. So, it is better to discuss the observed changes in a glass structure in terms of its molar volume. The calculated molar volume values (Table 4) show approximately a stable value for each glass system, and this reflects an approximate structural stability for the obtained glassy phase. This can be taken as an evidence for the supposition that there is no any crystalline phase or any precipitated phase appeared anywhere. (A.G. Mostafa et al. / Solid State Communications 131 (2004) 729734)****with the increase in molar volume (Vm) (i.e. open structure) and increase in oxygen molar volume (VO) due to the addition of Al2O3 as a glass former at the expense of Na2O (see Table 2), caused the decrease in N4 value and consequently the decrease in all elastic moduli values When the volume change occurs without change in the nature of the bonding or change in the coordination polyhedra, (Ke)(Vm) plots generally are linear, as shown in Fig. 9. The observed increase in bulk modulus in spite of the decrease in volume shows that in addition to volume, the type of bonding is also important in determining the composition dependence of bulk modulus in these glasses. Therefore, the increase in bulk modulus with ZnO content in the aluminium sodium diborate glass network led one to conclude that Zn2+ ions try to form ring structures in the form of regular ZnO4 tetrahedral coordination as a network former [16], and compensate for the decrease in the average coordination number of boron atoms (the decrease in N4 values). Such an increasing bulk modulusvolume relationship was observed in some other types of glasses [M.S. Gaafar et al. / Journal of Alloys and Compounds 475 (2009) 535542 ]***This decrease is associated with a decrease in the number of non-bridging oxygens and with acontracting effect of the network due to the formation of Fig. [GeO6] structural units which are slightly larger in size than the [GeO4] species. For the sample with x10 mol% MoO3,the formation of [GeO6] octahedral structural units in the network results in better packing and hence the increase of density. [492]****decrease in the density; this is indicative of decreasing structural compactness of the material. In general, the structural compactness, the modification of the geometrical configuration of the glassy network, the change in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial holes are the factors that influence the density of the glass ceramic material [493]

***The replacement of an intermediate/modifier CdO with Na2O which is a modifier only, develops more nonbridging oxygen than bridging oxygen in the glass network.17,18 The development of nonbridging oxygen may inflate the glass system and thus increases its molar volume. The increase in molar volume may cause decrease in oxygen packing density and mass density [582]****alkali metal oxide cleaves the structure and disturbs the bonding between glass forming cations and oxygen anions. This increases the number of nonbridging oxygens and thus develops a more open structure. Consequently, the expansion of the structure increases the molar volume which causes a decrease in the oxygen packing density and hence a decrease in the density of the glass sample. The decrease in oxygen packing density along with the decrease of mass density and increase of molar volume of these glasses make them less resistive mechanically. This may have caused an increase in the coefficient of linear expansion and decrease in the transition temperature and the softening temperature [585] ****The observed nearly linear compositional dependences of the density and molar volume on TeO2 content (see Table 1) indicates that there are no anomalous structural changes with increasing TeO2 concentration in the glasses. The observed decrease in the molar volume can be attributed to an increase of the atom packing density in the glass network [976]***From the structural point of view, the molar volume, V M=r; where M is the molecular weight of the glass and r the mass density, has frequently been used [6,7]. Molar volume is more sensitive to structural differences between glasses than to density because it normalises for atomic weights of different glass constituents. This normalisation leads to the non-linearity observed in the variation of the molar volume [1090]

The systematic decrease in molar volume indicates that the silver ions do not expand the glass network, instead filling the free volume within the glass structure, which also contributes to the increase in glass density [1377]

The observed decrease in the molar volume (Fig. 7) with increasing alumina content indicates a decrease in the free space in the glass. This is consistent with reports that Al31 strengthens the glass network by cross-linking phosphate chains.16,38,39 The competition between weight and volume effects may be responsible for the presence of the density maxima. [1757]

Calculation of molar volume enables packing density of the glass to be examined independent of effects of ion mass.The increase in molar volume suggests the increased free space within the glass structure [1944]

This behavior is generally observed when increasing the content of amodifier oxide in metaphosphate glasses. The change in density of such systems is related to the density of the formed structural units when introducing the modifier oxide. The molar volume VM decreases linearly with increasing the content, confirming that the copper does reticule the network. [2323] The density of these glasses first increases and then decreases with the content of TiO2 while corresponding molar volume first decreases and then increases. The density of these glasses should decrease due to replacement of high molecular weight P2O5 by low molecular weight TiO2. But it is found that the density of these glasses increases with addition of TiO2 and correspondingly molar volume decreases, indicating that the titanium polyhedra form some new interconnections within the structural network and thus stabilize the glass structure [2340] thus the addition of WO3 can promote a relatively open structure causing an increase in the molar volume. is behaviour was observed in the present case, where the molar volume of the glass systems increases with the growth of the WO3 concentration, suggesting that the molecular volume is inuenced by the number of O2 ions per unit of volume. Apparently, while substituting A2O by WO3, the molar volume should decrease because two cations per unit found for A2O are replaced by a single cation in WO3. e increase of molar volume in tungsten-glasses suggests that the excess of oxygen, due to the substitution of Li2O or Na2O by WO3, induces the formation of additional nonbridging oxygen and/or the formation of voluminous niobium and/or tungsten structural units such as WO6/NbO6 octahedron in the glass network. [2472]

This explanation is in line with the results of the density and the calculated molar volume of the glasses (tabulated in Table 1) which clearly indicates network expansion on account of participating magnesium ions in the glassy matrix and increase the network connectivity. Such asymmetric bridging oxygen formation leads to a length shortening of the phosphate chains and strengthen the cross-linking between the shorter phosphate chains in the glass structure [3112]

Generally, the density and the molar volume show opposite behaviors, but in this study, different resultswere obtained. In this glass, the substitution of phosphorus by lead causes an expansion of the network. Similar trends for densities and molar volumes have already been reported elsewhere for other glass systems [4318]

It is clear that by increasing PbO, the molar volume increases, which is similar to the variation density that occurs with increasing PbO content. The Pb ions may enter the glass network interstitially; hence, some network P\O\P bonds are broken and replaced by ionic bonds between Pb ions and singly bonded oxygen atoms. Therefore, if one assumed that the only effect of adding Pb cations was to break down the network P\O\P bonds, then an increase in the molar volume with PbO content would be expected for the entire vitreous range of the studied glass system. [4318]

This simplified structural model is consistent with the results of the oxygen molar volume, Vom, and the PDof the studied glasses as a function of the O/P ratio, figures 10 and 11 respectively. The continuous decrease in Vom and the slight increase of PD confirm the gradual reduction in the concentration of bridging POP bonds with an increasing O/P ratio [522]

Volumetric studiesVolumetric properties of the glasses are vital for understanding the microscopic structural transformations in the glass matrix [69]. Molar volume is more sensitive to structural differences between glasses than to density because it normalises for atomic weights of different glass constituents. These parameters of the glassy material are influenced by the structural compactness, the modification of the geometrical configuration of the glassy network, the changes in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial hole. Even though the density of the sample depends on the densities of its individual constituents [70], in the case of glasses many other factors like their preparation, thermal history of the sample, creation of non-bridging oxygens, field strength of the modifier etc. also influence the final density of the sample [70] to a greater extent. From the measured densities () at room temperature and effective molar molecular weights (), the physical parameters like molar volume (Vm), oxygen molar volume (VO), oxygen packing density (OPD), cobalt ion concentration (Ni), interionic distance (ri), polaron radius (rp) and field strength (F) are computed using the relations mentioned in the literature [71,72] and are presented in Table 2. The quantitative understanding of these parameters is essential for exploring the basic structural modifications that take place in ZnO-CaF2-P2O5 glasses with the variation of NiO content. Fig. 2 shows the variation of density, oxygen packing density, molar volume and oxygen molar volume of ZnO-CaF2-P2O5 glasses on NiO content. It is observed that the density decreases initially from 2754 (pure glass) to 2739 kgm-3 with the addition of 0.2 mol% of NiO into the glass and then increases nonlinearly with the increase of NiO content and reaches the maximum value of 2831 kgm-3 for 1.0 mol% of NiO doped glass. Also, it is noticed that oxygen packing density showed the same trend while molar volume and oxygen molar volume followed an opposite trend. The nonlinear compositional dependence of these parameters on NiO content indicates that there are structural changes in the glasses with the increasing NiO concentration. As evident from x-ray diffraction patterns and infrared spectra, these glass samples are still in an amorphous state indicating that there is no detectable change to crystallization. Hence, the variation in these parameters can be attributed only to the differences in linkages between different structural species [73] due to the formation of more non-bridging oxygens than bridging oxygens in the glass network and the modification of less stable P-O-P bonds.Volumetric studiesThe initial decrease in the density and oxygen packing density (Fig. 2) of the glasses, an indicative of decreasing structural compactness of the material with the addition of 0.2 mol% of NiO is unpredicted as NiO has a higher density than P2O5. This anomaly of the glasses indicating the loose packing of the atoms in the glass structure is due to the expansion of phosphate Q3 network to accommodate Ni2+ ions in the interstices of PO4 network indicating the formation of PONi2+ bonds which may be due to the disproportionation [65,74] of different phosphate groups present in the glass matrix. Also, this initial decrease in the density can be attributed to the formation of more NiO6 octahedral units than NiO4 tetrahedral units in the ZCP:Ni 0.2 network. On the other hand, NiO cleaves the structure and disturbs the bonding between glass forming cations and anions. This decreases the number of non-bridging oxygens and thus develops a more open structure. Consequently, the expansion of the structure increases the molar volume which causes a decrease in the oxygen packing density and hence a decrease in the density of the glass sample. The observed increase in the density from 2754 kg m-3 (pure glass) to 2802 kg m-3 (0.6 mol% of CoO) and oxygen packing density from 75.28 (pure) to 76.43 x 103 mol m-3 (0.6 mol% of CoO) along with the decrease in the molar volume (Vm) and oxygen molar volume (Vo) up to 0.6 mol% of CoO suggest that cobalt ions are filling the interstices of the glass network indicating the formation of PONi linkages. Also, cobalt ions in glass network exist in both four (Co2+) and six (Co2+, Co3+) fold coordinations, whereas P5+ ion in glass network is in four fold coordination [61]. Therefore, average coordination number of the cation in the glass network increases with increasing CoO content up to 0.6 mol%, which improves glass compactness [61]. Hence, an increase in the density and oxygen packing density can be expected up to 0.6 mol% of CoO. The increase in the density up to 0.6 mol% of CoO may also be attributed to the formation of CoO4 tetrahedral structural units and the conversion of CoO6 octahedral structural units to CoO4 tetrahedral structural units through the formation of some more CoOP bonds which probably results in better packing causing strengthening of the glass network. Also, the decrease in molar volume, which represents the spatial distribution of the ions in the glass structure up to 0.6 mol% of CoO is an indication of the increased compactness of the glass due to the increased cross-linking density. This increase in oxygen packing density along with the increase of mass density and decrease of molar volume of these glasses make them more resistive mechanically.The replacement of P2O5 with CoO develops more non-bridging oxygens than bridging oxygens in the glass network due to the replacement of less stable P-O-P bonds by chemically durable P-O-Co bonds. The observed increase in the density with the increase of CoO up to 0.6 mol% may be due to increase in non-bridging oxygens in the glass network indicating the increasing crosslinking of various units leading to a decrease in its molar volume [73]. The decrease in molar volume may cause an increase in oxygen packing density and mass density. This is due to the fact that the divalent cobalt ions form higher number of NBOs than the trivalent cobalt ions. For better understanding of the structural variations in the glass, a qualitative and quantitative analysis is carried out by theoretical estimation of mass density and excess molar volume of these glasses. Theoretical values of the density are estimated using the relation th = ixi where i and xi are the density and mol% of the glass components respectively. The estimated and the measured values of density of these glasses are depicted in Fig. 3a as a function of CoO concentration. The difference in values of density may be due to the variation in atomic arrangement between the structure of glass and component molecules. Excess volume () is a quantity derived from the molar volume of the sample (Vm) and molar volumes of the individual components (Vi) of the glass. is calculated using [70]:(3) Fig. 3b represents the variation of the excess molar volume of CoO doped ZCP glasses. It is an established fact in the case of liquid mixtures that the negative values of excess molar volume , suggest specific interactions [75,76] between the mixing components while its positive values suggest dominance of dispersion forces [76,77] between them. In the present study, the negative values (Fig. 3b, Table 2) indicate the presence of specific interactions between the mixing components of the glass leading to structural strengthening of the glass. The largest negative value of for 0.6 mol% of CoO doped ZCP glass indicates the closed packing of the atoms of the components of this glass. Since the molar volume represents the spatial distribution of the structural units and ions in a glass network, therefore it deals directly with the spatial structure of the glass. So, it is better to discuss the observed changes in a glass structure in terms of its molar volume. The calculated molar volume values (Table 4) show approximately a stable value for each glass system, and this reflects an approximate structural stability for the obtained glassy phase. This can be taken as an evidence for the supposition that there is no any crystalline phase or any precipitated phase appeared anywhere. (A.G. Mostafa et al. / Solid State Communications 131 (2004) 729734)****with the increase in molar volume (Vm) (i.e. open structure) and increase in oxygen molar volume (VO) due to the addition of Al2O3 as a glass former at the expense of Na2O (see Table 2), caused the decrease in N4 value and consequently the decrease in all elastic moduli values When the volume change occurs without change in the nature of the bonding or change in the coordination polyhedra, (Ke)(Vm) plots generally are linear, as shown in Fig. 9. The observed increase in bulk modulus in spite of the decrease in volume shows that in addition to volume, the type of bonding is also important in determining the composition dependence of bulk modulus in these glasses. Therefore, the increase in bulk modulus with ZnO content in the aluminium sodium diborate glass network led one to conclude that Zn2+ ions try to form ring structures in the form of regular ZnO4 tetrahedral coordination as a network former [16], and compensate for the decrease in the average coordination number of boron atoms (the decrease in N4 values). Such an increasing bulk modulusvolume relationship was observed in some other types of glasses [M.S. Gaafar et al. / Journal of Alloys and Compounds 475 (2009) 535542 ]***This decrease is associated with a decrease in the number of non-bridging oxygens and with acontracting effect of the network due to the formation of Fig. [GeO6] structural units which are slightly larger in size than the [GeO4] species. For the sample with x10 mol% MoO3,the formation of [GeO6] octahedral structural units in the network results in better packing and hence the increase of density. [492]****decrease in the density; this is indicative of decreasing structural compactness of the material. In general, the structural compactness, the modification of the geometrical configuration of the glassy network, the change in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial holes are the factors that influence the density of the glass ceramic material [493]

***The replacement of an intermediate/modifier CdO with Na2O which is a modifier only, develops more nonbridging oxygen than bridging oxygen in the glass network.17,18 The development of nonbridging oxygen may inflate the glass system and thus increases its molar volume. The increase in molar volume may cause decrease in oxygen packing density and mass density [582]****alkali metal oxide cleaves the structure and disturbs the bonding between glass forming cations and oxygen anions. This increases the number of nonbridging oxygens and thus develops a more open structure. Consequently, the expansion of the structure increases the molar volume which causes a decrease in the oxygen packing density and hence a decrease in the density of the glass sample. The decrease in oxygen packing density along with the decrease of mass density and increase of molar volume of these glasses make them less resistive mechanically. This may have caused an increase in the coefficient of linear expansion and decrease in the transition temperature and the softening temperature [585] ****The observed nearly linear compositional dependences of the density and molar volume on TeO2 content (see Table 1) indicates that there are no anomalous structural changes with increasing TeO2 concentration in the glasses. The observed decrease in the molar volume can be attributed to an increase of the atom packing density in the glass network [976]***From the structural point of view, the molar volume, V M=r; where M is the molecular weight of the glass and r the mass density, has frequently been used [6,7]. Molar volume is more sensitive to structural differences between glasses than to density because it normalises for atomic weights of different glass constituents. This normalisation leads to the non-linearity observed in the variation of the molar volume [1090]

The systematic decrease in molar volume indicates that the silver ions do not expand the glass network, instead filling the free volume within the glass structure, which also contributes to the increase in glass density [1377]

The observed decrease in the molar volume (Fig. 7) with increasing alumina content indicates a decrease in the free space in the glass. This is consistent with reports that Al31 strengthens the glass network by cross-linking phosphate chains.16,38,39 The competition between weight and volume effects may be responsible for the presence of the density maxima. [1757]

Calculation of molar volume enables packing density of the glass to be examined independent of effects of ion mass.The increase in molar volume suggests the increased free space within the glass structure [1944]

This behavior is generally observed when increasing the content of amodifier oxide in metaphosphate glasses. The change in density of such systems is related to the density of the formed structural units when introducing the modifier oxide. The molar volume VM decreases linearly with increasing the content, confirming that the copper does reticule the network. [2323] The density of these glasses first increases and then decreases with the content of TiO2 while corresponding molar volume first decreases and then increases. The density of these glasses should decrease due to replacement of high molecular weight P2O5 by low molecular weight TiO2. But it is found that the density of these glasses increases with addition of TiO2 and correspondingly molar volume decreases, indicating that the titanium polyhedra form some new interconnections within the structural network and thus stabilize the glass structure [2340] thus the addition of WO3 can promote a relatively open structure causing an increase in the molar volume. is behaviour was observed in the present case, where the molar volume of the glass systems increases with the growth of the WO3 concentration, suggesting that the molecular volume is inuenced by the number of O2 ions per unit of volume. Apparently, while substituting A2O by WO3, the molar volume should decrease because two cations per unit found for A2O are replaced by a single cation in WO3. e increase of molar volume in tungsten-glasses suggests that the excess of oxygen, due to the substitution of Li2O or Na2O by WO3, induces the formation of additional nonbridging oxygen and/or the formation of voluminous niobium and/or tungsten structural units such as WO6/NbO6 octahedron in the glass network. [2472]

This explanation is in line with the results of the density and the calculated molar volume of the glasses (tabulated in Table 1) which clearly indicates network expansion on account of participating magnesium ions in the glassy matrix and increase the network connectivity. Such asymmetric bridging oxygen formation leads to a length shortening of the phosphate chains and strengthen the cross-linking between the shorter phosphate chains in the glass structure [3112]

Generally, the density and the molar volume show opposite behaviors, but in this study, different resultswere obtained. In this glass, the substitution of phosphorus by lead causes an expansion of the network. Similar trends for densities and molar volumes have already been reported elsewhere for other glass systems [4318]

It is clear that by increasing PbO, the molar volume increases, which is similar to the variation density that occurs with increasing PbO content. The Pb ions may enter the glass network interstitially; hence, some network P\O\P bonds are broken and replaced by ionic bonds between Pb ions and singly bonded oxygen atoms. Therefore, if one assumed that the only effect of adding Pb cations was to break down the network P\O\P bonds, then an increase in the molar volume with PbO content would be expected for the entire vitreous range of the studied glass system. [4318]

This simplified structural model is consistent with the results of the oxygen molar volume, Vom, and the PDof the studied glasses as a function of the O/P ratio, figures 10 and 11 respectively. The continuous decrease in Vom and the slight increase of PD confirm the gradual reduction in the concentration of bridging POP bonds with an increasing O/P ratio [522]

Volumetric studiesVolumetric properties of the glasses are vital for understanding the microscopic structural transformations in the glass matrix [69]. Molar volume is more sensitive to structural differences between glasses than to density because it normalises for atomic weights of different glass constituents. These parameters of the glassy material are influenced by the structural compactness, the modification of the geometrical configuration of the glassy network, the changes in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial hole. Even though the density of the sample depends on the densities of its individual constituents [70], in the case of glasses many other factors like their preparation, thermal history of the sample, creation of non-bridging oxygens, field strength of the modifier etc. also influence the final density of the sample [70] to a greater extent. From the measured densities () at room temperature and effective molar molecular weights (), the physical parameters like molar volume (Vm), oxygen molar volume (VO), oxygen packing density (OPD), cobalt ion concentration (Ni), interionic distance (ri), polaron radius (rp) and field strength (F) are computed using the relations mentioned in the literature [71,72] and are presented in Table 2. The quantitative understanding of these parameters is essential for exploring the basic structural modifications that take place in ZnO-CaF2-P2O5 glasses with the variation of NiO content. Fig. 2 shows the variation of density, oxygen packing density, molar volume and oxygen molar volume of ZnO-CaF2-P2O5 glasses on NiO content. It is observed that the density decreases initially from 2754 (pure glass) to 2739 kgm-3 with the addition of 0.2 mol% of NiO into the glass and then increases nonlinearly with the increase of NiO content and reaches the maximum value of 2831 kgm-3 for 1.0 mol% of NiO doped glass. Also, it is noticed that oxygen packing density showed the same trend while molar volume and oxygen molar volume followed an opposite trend. The nonlinear compositional dependence of these parameters on NiO content indicates that there are structural changes in the glasses with the increasing NiO concentration. As evident from x-ray diffraction patterns and infrared spectra, these glass samples are still in an amorphous state indicating that there is no detectable change to crystallization. Hence, the variation in these parameters can be attributed only to the differences in linkages between different structural species [73] due to the formation of more non-bridging oxygens than bridging oxygens in the glass network and the modification of less stable P-O-P bonds.Volumetric studiesThe initial decrease in the density and oxygen packing density (Fig. 2) of the glasses, an indicative of decreasing structural compactness of the material with the addition of 0.2 mol% of NiO is unpredicted as NiO has a higher density than P2O5. This anomaly of the glasses indicating the loose packing of the atoms in the glass structure is due to the expansion of phosphate Q3 network to accommodate Ni2+ ions in the interstices of PO4 network indicating the formation of PONi2+ bonds which may be due to the disproportionation [65,74] of different phosphate groups present in the glass matrix. Also, this initial decrease in the density can be attributed to the formation of more NiO6 octahedral units than NiO4 tetrahedral units in the ZCP:Ni 0.2 network. On the other hand, NiO cleaves the structure and disturbs the bonding between glass forming cations and anions. This decreases the number of non-bridging oxygens and thus develops a more open structure. Consequently, the expansion of the structure increases the molar volume which causes a decrease in the oxygen packing density and hence a decrease in the density of the glass sample. The observed increase in the density from 2754 kg m-3 (pure glass) to 2802 kg m-3 (0.6 mol% of CoO) and oxygen packing density from 75.28 (pure) to 76.43 x 103 mol m-3 (0.6 mol% of CoO) along with the decrease in the molar volume (Vm) and oxygen molar volume (Vo) up to 0.6 mol% of CoO suggest that cobalt ions are filling the interstices of the glass network indicating the formation of PONi linkages. Also, cobalt ions in glass network exist in both four (Co2+) and six (Co2+, Co3+) fold coordinations, whereas P5+ ion in glass network is in four fold coordination [61]. Therefore, average coordination number of the cation in the glass network increases with increasing CoO content up to 0.6 mol%, which improves glass compactness [61]. Hence, an increase in the density and oxygen packing density can be expected up to 0.6 mol% of CoO. The increase in the density up to 0.6 mol% of CoO may also be attributed to the formation of CoO4 tetrahedral structural units and the conversion of CoO6 octahedral structural units to CoO4 tetrahedral structural units through the formation of some more CoOP bonds which probably results in better packing causing strengthening of the glass network. Also, the decrease in molar volume, which represents the spatial distribution of the ions in the glass structure up to 0.6 mol% of CoO is an indication of the increased compactness of the glass due to the increased cross-linking density. This increase in oxygen packing density along with the increase of mass density and decrease of molar volume of these glasses make them more resistive mechanically.The replacement of P2O5 with CoO develops more non-bridging oxygens than bridging oxygens in the glass network due to the replacement of less stable P-O-P bonds by chemically durable P-O-Co bonds. The observed increase in the density with the increase of CoO up to 0.6 mol% may be due to increase in non-bridging oxygens in the glass network indicating the increasing crosslinking of various units leading to a decrease in its molar volume [73]. The decrease in molar volume may cause an increase in oxygen packing density and mass density. This is due to the fact that the divalent cobalt ions form higher number of NBOs than the trivalent cobalt ions. For better understanding of the structural variations in the glass, a qualitative and quantitative analysis is carried out by theoretical estimation of mass density and excess molar volume of these glasses. Theoretical values of the density are estimated using the relation th = ixi where i and xi are the density and mol% of the glass components respectively. The estimated and the measured values of density of these glasses are depicted in Fig. 3a as a function of CoO concentration. The difference in values of density may be due to the variation in atomic arrangement between the structure of glass and component molecules. Excess volume () is a quantity derived from the molar volume of the sample (Vm) and molar volumes of the individual components (Vi) of the glass. is calculated using [70]:(3) Fig. 3b represents the variation of the excess molar volume of CoO doped ZCP glasses. It is an established fact in the case of liquid mixtures that the negative values of excess molar volume , suggest specific interactions [75,76] between the mixing components while its positive values suggest dominance of dispersion forces [76,77] between them. In the present study, the negative values (Fig. 3b, Table 2) indicate the presence of specific interactions between the mixing components of the glass leading to structural strengthening of the glass. The largest negative value of for 0.6 mol% of CoO doped ZCP glass indicates the closed packing of the atoms of the components of this glass. Since the molar volume represents the spatial distribution of the structural units and ions in a glass network, therefore it deals directly with the spatial structure of the glass. So, it is better to discuss the observed changes in a glass structure in terms of its molar volume. The calculated molar volume values (Table 4) show approximately a stable value for each glass system, and this reflects an approximate structural stability for the obtained glassy phase. This can be taken as an evidence for the supposition that there is no any crystalline phase or any precipitated phase appeared anywhere. (A.G. Mostafa et al. / Solid State Communications 131 (2004) 729734)****with the increase in molar volume (Vm) (i.e. open structure) and increase in oxygen molar volume (VO) due to the addition of Al2O3 as a glass former at the expense of Na2O (see Table 2), caused the decrease in N4 value and consequently the decrease in all elastic moduli values When the volume change occurs without change in the nature of the bonding or change in the coordination polyhedra, (Ke)(Vm) plots generally are linear, as shown in Fig. 9. The observed increase in bulk modulus in spite of the decrease in volume shows that in addition to volume, the type of bonding is also important in determining the composition dependence of bulk modulus in these glasses. Therefore, the increase in bulk modulus with ZnO content in the aluminium sodium diborate glass network led one to conclude that Zn2+ ions try to form ring structures in the form of regular ZnO4 tetrahedral coordination as a network former [16], and compensate for the decrease in the average coordination number of boron atoms (the decrease in N4 values). Such an increasing bulk modulusvolume relationship was observed in some other types of glasses [M.S. Gaafar et al. / Journal of Alloys and Compounds 475 (2009) 535542 ]***This decrease is associated with a decrease in the number of non-bridging oxygens and with acontracting effect of the network due to the formation of Fig. [GeO6] structural units which are slightly larger in size than the [GeO4] species. For the sample with x10 mol% MoO3,the formation of [GeO6] octahedral structural units in the network results in better packing and hence the increase of density. [492]****decrease in the density; this is indicative of decreasing structural compactness of the material. In general, the structural compactness, the modification of the geometrical configuration of the glassy network, the change in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial holes are the factors that influence the density of the glass ceramic material [493]

***The replacement of an intermediate/modifier CdO with Na2O which is a modifier only, develops more nonbridging oxygen than bridging oxygen in the glass network.17,18 The development of nonbridging oxygen may inflate the glass system and thus increases its molar volume. The increase in molar volume may cause decrease in oxygen packing density and mass density [582]****alkali metal oxide cleaves the structure and disturbs the bonding between glass forming cations and oxygen anions. This increases the number of nonbridging oxygens and thus develops a more open structure. Consequently, the expansion of the structure increases the molar volume which causes a decrease in the oxygen packing density and hence a decrease in the density of the glass sample. The decrease in oxygen packing density along with the decrease of mass density and increase of molar volume of these glasses make them less resistive mechanically. This may have caused an increase in the coefficient of linear expansion and decrease in the transition temperature and the softening temperature [585] ****The observed nearly linear compositional dependences of the density and molar volume on TeO2 content (see Table 1) indicates that there are no anomalous structural changes with increasing TeO2 concentration in the glasses. The observed decrease in the molar volume can be attributed to an increase of the atom packing density in the glass network [976]***From the structural point of view, the molar volume, V M=r; where M is the molecular weight of the glass and r the mass density, has frequently been used [6,7]. Molar volume is more sensitive to structural differences between glasses than to density because it normalises for atomic weights of different glass constituents. This normalisation leads to the non-linearity observed in the variation of the molar volume [1090]

The systematic decrease in molar volume indicates that the silver ions do not expand the glass network, instead filling the free volume within the glass structure, which also contributes to the increase in glass density [1377]

The observed decrease in the molar volume (Fig. 7) with increasing alumina content indicates a decrease in the free space in the glass. This is consistent with reports that Al31 strengthens the glass network by cross-linking phosphate chains.16,38,39 The competition between weight and volume effects may be responsible for the presence of the density maxima. [1757]

Calculation of molar volume enables packing density of the glass to be examined independent of effects of ion mass.The increase in molar volume suggests the increased free space within the glass structure [1944]

This behavior is generally observed when increasing the content of amodifier oxide in metaphosphate glasses. The change in density of such systems is related to the density of the formed structural units when introducing the modifier oxide. The molar volume VM decreases linearly with increasing the content, confirming that the copper does reticule the network. [2323] The density of these glasses first increases and then decreases with the content of TiO2 while corresponding molar volume first decreases and then increases. The density of these glasses should decrease due to replacement of high molecular weight P2O5 by low molecular weight TiO2. But it is found that the density of these glasses increases with addition of TiO2 and correspondingly molar volume decreases, indicating that the titanium polyhedra form some new interconnections within the structural network and thus stabilize the glass structure [2340] thus the addition of WO3 can promote a relatively open structure causing an increase in the molar volume. is behaviour was observed in the present case, where the molar volume of the glass systems increases with the growth of the WO3 concentration, suggesting that the molecular volume is inuenced by the number of O2 ions per unit of volume. Apparently, while substituting A2O by WO3, the molar volume should decrease because two cations per unit found for A2O are replaced by a single cation in WO3. e increase of molar volume in tungsten-glasses suggests that the excess of oxygen, due to the substitution of Li2O or Na2O by WO3, induces the formation of additional nonbridging oxygen and/or the formation of voluminous niobium and/or tungsten structural units such as WO6/NbO6 octahedron in the glass network. [2472]

This explanation is in line with the results of the density and the calculated molar volume of the glasses (tabulated in Table 1) which clearly indicates network expansion on account of participating magnesium ions in the glassy matrix and increase the network connectivity. Such asymmetric bridging oxygen formation leads to a length shortening of the phosphate chains and strengthen the cross-linking between the shorter phosphate chains in the glass structure [3112]

Generally, the density and the molar volume show opposite behaviors, but in this study, different resultswere obtained. In this glass, the substitution of phosphorus by lead causes an expansion of the network. Similar trends for densities and molar volumes have already been reported elsewhere for other glass systems [4318]

It is clear that by increasing PbO, the molar volume increases, which is similar to the variation density that occurs with increasing PbO content. The Pb ions may enter the glass network interstitially; hence, some network P\O\P bonds are broken and replaced by ionic bonds between Pb ions and singly bonded oxygen atoms. Therefore, if one assumed that the only effect of adding Pb cations was to break down the network P\O\P bonds, then an increase in the molar volume with PbO content would be expected for the entire vitreous range of the studied glass system. [4318]

This simplified structural model is consistent with the results of the oxygen molar volume, Vom, and the PDof the studied glasses as a function of the O/P ratio, figures 10 and 11 respectively. The continuous decrease in Vom and the slight increase of PD confirm the gradual reduction in the concentration of bridging POP bonds with an increasing O/P ratio [522]

Volumetric studiesVolumetric properties of the glasses are vital for understanding the microscopic structural transformations in the glass matrix [69]. Molar volume is more sensitive to structural differences between glasses than to density because it normalises for atomic weights of different glass constituents. These parameters of the glassy material are influenced by the structural compactness, the modification of the geometrical configuration of the glassy network, the changes in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial hole. Even though the density of the sample depends on the densities of its individual constituents [70], in the case of glasses many other factors like their preparation, thermal history of the sample, creation of non-bridging oxygens, field strength of the modifier etc. also influence the final density of the sample [70] to a greater extent. From the measured densities () at room temperature and effective molar molecular weights (), the physical parameters like molar volume (Vm), oxygen molar volume (VO), oxygen packing density (OPD), cobalt ion concentration (Ni), interionic distance (ri), polaron radius (rp) and field strength (F) are computed using the relations mentioned in the literature [71,72] and are presented in Table 2. The quantitative understanding of these parameters is essential for exploring the basic structural modifications that take place in ZnO-CaF2-P2O5 glasses with the variation of NiO content. Fig. 2 shows the variation of density, oxygen packing density, molar volume and oxygen molar volume of ZnO-CaF2-P2O5 glasses on NiO content. It is observed that the density decreases initially from 2754 (pure glass) to 2739 kgm-3 with the addition of 0.2 mol% of NiO into the glass and then increases nonlinearly with the increase of NiO content and reaches the maximum value of 2831 kgm-3 for 1.0 mol% of NiO doped glass. Also, it is noticed that oxygen packing density showed the same trend while molar volume and oxygen molar volume followed an opposite trend. The nonlinear compositional dependence of these parameters on NiO content indicates that there are structural changes in the glasses with the increasing NiO concentration. As evident from x-ray diffraction patterns and infrared spectra, these glass samples are still in an amorphous state indicating that there is no detectable change to crystallization. Hence, the variation in these parameters can be attributed only to the differences in linkages between different structural species [73] due to the formation of more non-bridging oxygens than bridging oxygens in the glass network and the modification of less stable P-O-P bonds.Volumetric studiesThe initial decrease in the density and oxygen packing density (Fig. 2) of the glasses, an indicative of decreasing structural compactness of the material with the addition of 0.2 mol% of NiO is unpredicted as NiO has a higher density than P2O5. This anomaly of the glasses indicating the loose packing of the atoms in the glass structure is due to the expansion of phosphate Q3 network to accommodate Ni2+ ions in the interstices of PO4 network indicating the formation of PONi2+ bonds which may be due to the disproportionation [65,74] of different phosphate groups present in the glass matrix. Also, this initial decrease in the density can be attributed to the formation of more NiO6 octahedral units than NiO4 tetrahedral units in the ZCP:Ni 0.2 network. On the other hand, NiO cleaves the structure and disturbs the bonding between glass forming cations and anions. This decreases the number of non-bridging oxygens and thus develops a more open structure. Consequently, the expansion of the structure increases the molar volume which causes a decrease in the oxygen packing density and hence a decrease in the density of the glass sample. The observed increase in the density from 2754 kg m-3 (pure glass) to 2802 kg m-3 (0.6 mol% of CoO) and oxygen packing density from 75.28 (pure) to 76.43 x 103 mol m-3 (0.6 mol% of CoO) along with the decrease in the molar volume (Vm) and oxygen molar volume (Vo) up to 0.6 mol% of CoO suggest that cobalt ions are filling the interstices of the glass network indicating the formation of PONi linkages. Also, cobalt ions in glass network exist in both four (Co2+) and six (Co2+, Co3+) fold coordinations, whereas P5+ ion in glass network is in four fold coordination [61]. Therefore, average coordination number of the cation in the glass network increases with increasing CoO content up to 0.6 mol%, which improves glass compactness [61]. Hence, an increase in the density and oxygen packing density can be expected up to 0.6 mol% of CoO. The increase in the density up to 0.6 mol% of CoO may also be attributed to the formation of CoO4 tetrahedral structural units and the conversion of CoO6 octahedral structural units to CoO4 tetrahedral structural units through the formation of some more CoOP bonds which probably results in better packing causing strengthening of the glass network. Also, the decrease in molar volume, which represents the spatial distribution of the ions in the glass structure up to 0.6 mol% of CoO is an indication of the increased compactness of the glass due to the increased cross-linking density. This increase in oxygen packing density along with the increase of mass density and decrease of molar volume of these glasses make them more resistive mechanically.The replacement of P2O5 with CoO develops more non-bridging oxygens than bridging oxygens in the glass network due to the replacement of less stable P-O-P bonds by chemically durable P-O-Co bonds. The observed increase in the density with the increase of CoO up to 0.6 mol% may be due to increase in non-bridging oxygens in the glass network indicating the increasing crosslinking of various units leading to a decrease in its molar volume [73]. The decrease in molar volume may cause an increase in oxygen packing density and mass density. This is due to the fact that the divalent cobalt ions form higher number of NBOs than the trivalent cobalt ions. For better understanding of the structural variations in the glass, a qualitative and quantitative analysis is carried out by theoretical estimation of mass density and excess molar volume of these glasses. Theoretical values of the density are estimated using the relation th = ixi where i and xi are the density and mol% of the glass components respectively. The estimated and the measured values of density of these glasses are depicted in Fig. 3a as a function of CoO concentration. The difference in values of density may be due to the variation in atomic arrangement between the structure of glass and component molecules. Excess volume () is a quantity derived from the molar volume of the sample (Vm) and molar volumes of the individual components (Vi) of the glass. is calculated using [70]:(3) Fig. 3b represents the variation of the excess molar volume of CoO doped ZCP glasses. It is an established fact in the case of liquid mixtures that the negative values of excess molar volume , suggest specific interactions [75,76] between the mixing components while its positive values suggest dominance of dispersion forces [76,77] between them. In the present study, the negative values (Fig. 3b, Table 2) indicate the presence of specific interactions between the mixing components of the glass leading to structural strengthening of the glass. The largest negative value of for 0.6 mol% of CoO doped ZCP glass indicates the closed packing of the atoms of the components of this glass. Since the molar volume represents the spatial distribution of the structural units and ions in a glass network, therefore it deals directly with the spatial structure of the glass. So, it is better to discuss the observed changes in a glass structure in terms of its molar volume. The calculated molar volume values (Table 4) show approximately a stable value for each glass system, and this reflects an approximate structural stability for the obtained glassy phase. This can be taken as an evidence for the supposition that there is no any crystalline phase or any precipitated phase appeared anywhere. (A.G. Mostafa et al. / Solid State Communications 131 (2004) 729734)****with the increase in molar volume (Vm) (i.e. open structure) and increase in oxygen molar volume (VO) due to the addition of Al2O3 as a glass former at the expense of Na2O (see Table 2), caused the decrease in N4 value and consequently the decrease in all elastic moduli values When the volume change occurs without change in the nature of the bonding or change in the coordination polyhedra, (Ke)(Vm) plots generally are linear, as shown in Fig. 9. The observed increase in bulk modulus in spite of the decrease in volume shows that in addition to volume, the type of bonding is also important in determining the composition dependence of bulk modulus in these glasses. Therefore, the increase in bulk modulus with ZnO content in the aluminium sodium diborate glass network led one to conclude that Zn2+ ions try to form ring structures in the form of regular ZnO4 tetrahedral coordination as a network former [16], and compensate for the decrease in the average coordination number of boron atoms (the decrease in N4 values). Such an increasing bulk modulusvolume relationship was observed in some other types of glasses [M.S. Gaafar et al. / Journal of Alloys and Compounds 475 (2009) 535542 ]***This decrease is associated with a decrease in the number of non-bridging oxygens and with acontracting effect of the network due to the formation of Fig. [GeO6] structural units which are slightly larger in size than the [GeO4] species. For the sample with x10 mol% MoO3,the formation of [GeO6] octahedral structural units in the network results in better packing and hence the increase of density. [492]****decrease in the density; this is indicative of decreasing structural compactness of the material. In general, the structural compactness, the modification of the geometrical configuration of the glassy network, the change in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial holes are the factors that influence the density of the glass ceramic material [493]

***The replacement of an intermediate/modifier CdO with Na2O which is a modifier only, develops more nonbridging oxygen than bridging oxygen in the glass network.17,18 The development of nonbridging oxygen may inflate the glass system and thus increases its molar volume. The increase in molar volume may cause decrease in oxygen packing density and mass density [582]****alkali metal oxide cleaves the structure and disturbs the bonding between glass forming cations and oxygen anions. This increases the number of nonbridging oxygens and thus develops a more open structure. Consequently, the expansion of the structure increases the molar volume which causes a decrease in the oxygen packing density and hence a decrease in the density of the glass sample. The decrease in oxygen packing density along with the decrease of mass density and increase of molar volume of these glasses make them less resistive mechanically. This may have caused an increase in the coefficient of linear expansion and decrease in the transition temperature and the softening temperature [585] ****The observed nearly linear compositional dependences of the density and molar volume on TeO2 content (see Table 1) indicates that there are no anomalous structural changes with increasing TeO2 concentration in the glasses. The observed decrease in the molar volume can be attributed to an increase of the atom packing density in the glass network [976]***From the structural point of view, the molar volume, V M=r; where M is the molecular weight of the glass and r the mass density, has frequently been used [6,7]. Molar volume is more sensitive to structural differences between glasses than to density because it normalises for atomic weights of different glass constituents. This normalisation leads to the non-linearity observed in the variation of the molar volume [1090]

The systematic decrease in molar volume indicates that the silver ions do not expand the glass network, instead filling the free volume within the glass structure, which also contributes to the increase in glass density [1377]

The observed decrease in the molar volume (Fig. 7) with increasing alumina content indicates a decrease in the free space in the glass. This is consistent with reports that Al31 strengthens the glass network by cross-linking phosphate chains.16,38,39 The competition between weight and volume effects may be responsible for the presence of the density maxima. [1757]

Calculation of molar volume enables packing density of the glass to be examined independent of effects of ion mass.The increase in molar volume suggests the increased free space within the glass structure [1944]

This behavior is generally observed when increasing the content of amodifier oxide in metaphosphate glasses. The change in density of such systems is related to the density of the formed structural units when introducing the modifier oxide. The molar volume VM decreases linearly with increasing the content, confirming that the copper does reticule the network. [2323] The density of these glasses first increases and then decreases with the content of TiO2 while corresponding molar volume first decreases and then increases. The density of these glasses should decrease due to replacement of high molecular weight P2O5 by low molecular weight TiO2. But it is found that the density of these glasses increases with addition of TiO2 and correspondingly molar volume decreases, indicating that the titanium polyhedra form some new interconnections within the structural network and thus stabilize the glass structure [2340] thus the addition of WO3 can promote a relatively open structure causing an increase in the molar volume. is behaviour was observed in the present case, where the molar volume of the glass systems increases with the growth of the WO3 concentration, suggesting that the molecular volume is inuenced by the number of O2 ions per unit of volume. Apparently, while substituting A2O by WO3, the molar volume should decrease because two cations per unit found for A2O are replaced by a single cation in WO3. e increase of molar volume in tungsten-glasses suggests that the excess of oxygen, due to the substitution of Li2O or Na2O by WO3, induces the formation of additional nonbridging oxygen and/or the formation of voluminous niobium and/or tungsten structural units such as WO6/NbO6 octahedron in the glass network. [2472]

This explanation is in line with the results of the density and the calculated molar volume of the glasses (tabulated in Table 1) which clearly indicates network expansion on account of participating magnesium ions in the glassy matrix and increase the network connectivity. Such asymmetric bridging oxygen formation leads to a length shortening of the phosphate chains and strengthen the cross-linking between the shorter phosphate chains in the glass structure [3112]

Generally, the density and the molar volume show opposite behaviors, but in this study, different resultswere obtained. In this glass, the substitution of phosphorus by lead causes an expansion of the network. Similar trends for densities and molar volumes have already been reported elsewhere for other glass systems [4318]

It is clear that by increasing PbO, the molar volume increases, which is similar to the variation density that occurs with increasing PbO content. The Pb ions may enter the glass network interstitially; hence, some network P\O\P bonds are broken and replaced by ionic bonds between Pb ions and singly bonded oxygen atoms. Therefore, if one assumed that the only effect of adding Pb cations was to break down the network P\O\P bonds, then an increase in the molar volume with PbO content would be expected for the entire vitreous range of the studied glass system. [4318]

This simplified structural model is consistent with the results of the oxygen molar volume, Vom, and the PDof the studied glasses as a function of the O/P ratio, figures 10 and 11 respectively. The continuous decrease in Vom and the slight increase of PD confirm the gradual reduction in the concentration of bridging POP bonds with an increasing O/P ratio [522]

Volumetric studiesVolumetric properties of the glasses are vital for understanding the microscopic structural transformations in the glass matrix [69]. Molar volume is more sensitive to structural differences between glasses than to density because it normalises for atomic weights of different glass constituents. These parameters of the glassy material are influenced by the structural compactness, the modification of the geometrical configuration of the glassy network, the changes in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial hole. Even though the density of the sample depends on the densities of its individual constituents [70], in the case of glasses many other factors like their preparation, thermal history of the sample, creation of non-bridging oxygens, field strength of the modifier etc. also influence the final density of the sample [70] to a greater extent. From the measured densities () at room temperature and effective molar molecular weights (), the physical parameters like molar volume (Vm), oxygen molar volume (VO), oxygen packing density (OPD), cobalt ion concentration (Ni), interionic distance (ri), polaron radius (rp) and field strength (F) are computed using the relations mentioned in the literature [71,72] and are presented in Table 2. The quantitative understanding of these parameters is essential for exploring the basic structural modifications that take place in ZnO-CaF2-P2O5 glasses with the variation of NiO content. Fig. 2 shows the variation of density, oxygen packing density, molar volume and oxygen molar volume of ZnO-CaF2-P2O5 glasses on NiO content. It is observed that the density decreases initially from 2754 (pure glass) to 2739 kgm-3 with the addition of 0.2 mol% of NiO into the glass and then increases nonlinearly with the increase of NiO content and reaches the maximum value of 2831 kgm-3 for 1.0 mol% of NiO doped glass. Also, it is noticed that oxygen packing density showed the same trend while molar volume and oxygen molar volume followed an opposite trend. The nonlinear compositional dependence of these parameters on NiO content indicates that there are structural changes in the glasses with the increasing NiO concentration. As evident from x-ray diffraction patterns and infrared spectra, these glass samples are still in an amorphous state indicating that there is no detectable change to crystallization. Hence, the variation in these parameters can be attributed only to the differences in linkages between different structural species [73] due to the formation of more non-bridging oxygens than bridging oxygens in the glass network and the modification of less stable P-O-P bonds.Volumetric studiesThe initial decrease in the density and oxygen packing density (Fig. 2) of the glasses, an indicative of decreasing structural compactness of the material with the addition of 0.2 mol% of NiO is unpredicted as NiO has a higher density than P2O5. This anomaly of the glasses indicating the loose packing of the atoms in the glass structure is due to the expansion of phosphate Q3 network to accommodate Ni2+ ions in the interstices of PO4 network indicating the formation of PONi2+ bonds which may be due to the disproportionation [65,74] of different phosphate groups present in the glass matrix. Also, this initial decrease in the density can be attributed to the formation of more NiO6 octahedral units than NiO4 tetrahedral units in the ZCP:Ni 0.2 network. On the other hand, NiO cleaves the structure and disturbs the bonding between glass forming cations and anions. This decreases the number of non-bridging oxygens and thus develops a more open structure. Consequently, the expansion of the structure increases the molar volume which causes a decrease in the oxygen packing density and hence a decrease in the density of the glass sample. The observed increase in the density from 2754 kg m-3 (pure glass) to 2802 kg m-3 (0.6 mol% of CoO) and oxygen packing density from 75.28 (pure) to 76.43 x 103 mol m-3 (0.6 mol% of CoO) along with the decrease in the molar volume (Vm) and oxygen molar volume (Vo) up to 0.6 mol% of CoO suggest that cobalt ions are filling the interstices of the glass network indicating the formation of PONi linkages. Also, cobalt ions in glass network exist in both four (Co2+) and six (Co2+, Co3+) fold coordinations, whereas P5+ ion in glass network is in four fold coordination [61]. Therefore, average coordination number of the cation in the glass network increases with increasing CoO content up to 0.6 mol%, which improves glass compactness [61]. Hence, an increase in the density and oxygen packing density can be expected up to 0.6 mol% of CoO. The increase in the density up to 0.6 mol% of CoO may also be attributed to the formation of CoO4 tetrahedral structural units and the conversion of CoO6 octahedral structural units to CoO4 tetrahedral structural units through the formation of some more CoOP bonds which probably results in better packing causing strengthening of the glass network. Also, the decrease in molar volume, which represents the spatial distribution of the ions in the glass structure up to 0.6 mol% of CoO is an indication of the increased compactness of the glass due to the increased cross-linking density. This increase in oxygen packing density along with the increase of mass density and decrease of molar volume of these glasses make them more resistive mechanically.The replacement of P2O5 with CoO develops more non-bridging oxygens than bridging oxygens in the glass network due to the replacement of less stable P-O-P bonds by chemically durable P-O-Co bonds. The observed increase in the density with the increase of CoO up to 0.6 mol% may be due to increase in non-bridging oxygens in the glass network indicating the increasing crosslinking of various units leading to a decrease in its molar volume [73]. The decrease in molar volume may cause an increase in oxygen packing density and mass density. This is due to the fact that the divalent cobalt ions form higher number of NBOs than the trivalent cobalt ions. For better understanding of the structural variations in the glass, a qualitative and quantitative analysis is carried out by theoretical estimation of mass density and excess molar volume of these glasses. Theoretical values of the density are estimated using the relation th = ixi where i and xi are the density and mol% of the glass components respectively. The estimated and the measured values of density of these glasses are depicted in Fig. 3a as a function of CoO concentration. The difference in values of density may be due to the variation in atomic arrangement between the structure of glass and component molecules. Excess volume () is a quantity derived from the molar volume of the sample (Vm) and molar volumes of the individual components (Vi) of the glass. is calculated using [70]:(3) Fig. 3b represents the variation of the excess molar volume of CoO doped ZCP glasses. It is an established fact in the case of liquid mixtures that the negative values of excess molar volume , suggest specific interactions [75,76] between the mixing components while its positive values suggest dominance of dispersion forces [76,77] between them. In the present study, the negative values (Fig. 3b, Table 2) indicate the presence of specific interactions between the mixing components of the glass leading to structural strengthening of the glass. The largest negative value of for 0.6 mol% of CoO doped ZCP glass indicates the closed packing of the atoms of the components of this glass. Since the molar volume represents the spatial distribution of the structural units and ions in a glass network, therefore it deals directly with the spatial structure of the glass. So, it is better to discuss the observed changes in a glass structure in terms of its molar volume. The calculated molar volume values (Table 4) show approximately a stable value for each glass system, and this reflects an approximate structural stability for the obtained glassy phase. This can be taken as an evidence for the supposition that there is no any crystalline phase or any precipitated phase appeared anywhere. (A.G. Mostafa et al. / Solid State Communications 131 (2004) 729734)****with the increase in molar volume (Vm) (i.e. open structure) and increase in oxygen molar volume (VO) due to the addition of Al2O3 as a glass former at the expense of Na2O (see Table 2), caused the decrease in N4 value and consequently the decrease in all elastic moduli values When the volume change occurs without change in the nature of the bonding or change in the coordination polyhedra, (Ke)(Vm) plots generally are linear, as shown in Fig. 9. The observed increase in bulk modulus in spite of the decrease in volume shows that in addition to volume, the type of bonding is also important in determining the composition dependence of bulk modulus in these glasses. Therefore, the increase in bulk modulus with ZnO content in the aluminium sodium diborate glass network led one to conclude that Zn2+ ions try to form ring structures in the form of regular ZnO4 tetrahedral coordination as a network former [16], and compensate for the decrease in the average coordination number of boron atoms (the decrease in N4 values). Such an increasing bulk modulusvolume relationship was observed in some other types of glasses [M.S. Gaafar et al. / Journal of Alloys and Compounds 475 (2009) 535542 ]***This decrease is associated with a decrease in the number of non-bridging oxygens and with acontracting effect of the network due to the formation of Fig. [GeO6] structural units which are slightly larger in size than the [GeO4] species. For the sample with x10 mol% MoO3,the formation of [GeO6] octahedral structural units in the network results in better packing and hence the increase of density. [492]****decrease in the density; this is indicative of decreasing structural compactness of the material. In general, the structural compactness, the modification of the geometrical configuration of the glassy network, the change in the coordination of the glass forming ions and the fluctuations in the dimensions of the interstitial holes are the factors that influence the density of the glass ceramic material [493]

***The replacement of an intermediate/modifier CdO with Na2O which is a modifier only, develops more nonbridging oxygen than bridging oxygen in the glass network.17,18 The development of nonbridging oxygen may inflate the glass system and thus increases its molar volume. The increase in molar volume may cause decrease in oxygen packing density an