## 3 Results and Discussion
### Physical Properties with Theoretical Discussion  
In order to investigate the effect of Ho\({}^{3+}\) doping on the physical and optical properties of the prepared glasses, various physical and optical parameters, such as, density, molar volume, average boron-boron separation, packing density, oxygen packing density (OPD), average coordination number, concentration of holmium ions (\(C_{H_{0}{}^{3+}}\)), holmium inter-ionic distance (r\({}_{i}\)), polaron radius (r\({}_{p}\)), field strength (F) of holmium field, molar refractivity, polarizability, reflection loss, transmission coefficient, and dielectric constant were evaluated using the various theoretical formulae [18; 21; 22; 23] and experimentally acquired results. The estimated values are presented in Table 1. We observed the variation in the values of the density of the B0H set due to the incorporation of Ho\({}^{3+}\) that was added to the host glass matrix to improve structure compactness, as illustrated in Table 1. Furthermore, holmium molecular weight (377.68 g/mol) differs from borate mass (69.63 g/mol); holmium M.W, in particular, is higher, which results in enhanced formation of non-bridging oxygen's (NBOs). However, in the B0H, the volume of the molar reduces with the increased holmium concentration due to the shrinking bond length. Due to the difference in holmium ionic radii (0.91 A) and borate (0.27 A), a variance in the molar volume can also be expected. Further, with increase in the holmium concentration, the \(<\)d\({}_{\text{B-B}}\)\(>\) also enhanced which supports the variation observed in molar volume. It is found that Li\({}_{2}\)O, Bi\({}_{2}\)O\({}_{3}\), B\({}_{2}\)O\({}_{3}\)  
Figure 1: XRD patterns of the Ho doped lithium boro-phosphate glasses. P\({}_{2}\)O\({}_{5}\), and Ho\({}_{2}\)O\({}_{3}\) have packing factors of 9.14 cm\({}^{3}\)/mol, 26.28 cm\({}^{3}\)/mol, 20.87 cm\({}^{3}\)/mol, 34.89 cm\({}^{3}\)/mol, and 24.46 cm\({}^{3}\)/mol, respectively. The packing density for the whole B0H set was determined using the packing factor, and the difference in the packing density shows that the oxide glass' rigidity increases as the holmium concentration. The creation of non-bridging oxygen (NBO) after the addition of holmium to the B0H set is explained by OPD variations. The increase in OPD leads to a rise in glass hardness as holmium concentration increases. It is observed that the number of bonds per unit length in the B0H set also decreased as the holmium concentration increased. There is a difference in Ri and an increase in the molecular weight also with the holmium content in the B0H glasses. This has led to the development of a densely packed glass network. We would expect to increase field strength in B0H close to Ho\({}^{3+}\) ions, as r\({}_{\rm P}\) decreases. The results were the same as the estimated values. With holmium concentrations increased greatly, the refractive index of B0H glasses suggested that optical not-linearity was improved in the produced glasses. Thus, effective polarisation and molar repressiveness decreases were found from B01H to B05H. The R\({}_{\rm L}\) value of B0H set signified that the low reflection loss resulted in the high transmission coefficient. The conduction width would increase as the holmium concentration in B0H rises. As a result, the metallization requirement is less than 1, implying that the B0H set of materials is insulating [23; 24; 25].