# An Interpretable XGBoost Framework for Predicting Oxide Glass Density
## 1 Introduction  
Amorphous materials, particularly glasses, play an important role in modern engineering and technology, with critical applications in optics, electronics, construction, and medicine. Among their fundamental characteristics, density is a one of the key properties that not only determine the final weight of a component but also influence other crucial parameters such as the refractive index, mechanical properties, thermal stability, etc. [1, 2, 3]. The density of a glass is intrinsically tied to the efficiency of atomic packing within its disordered, non-periodic network. Unlike crystalline materials, which feature a highlyregular and repeating lattice structure that minimizes volume, glasses possess a more open and random arrangement of atoms. This inherent disorder results in the presence of free volume--interstitial spaces and voids within the atomic network. Consequently, a glass will almost always be less dense than its crystalline counterpart of the same chemical composition. For example, crystalline silica (quartz) has a density of 2.65 g/cm\({}^{3}\), whereas its amorphous form, fused silica glass, has a density of only 2.20 g/cm\({}^{3}\)[1; 2; 3]. One of the most important factors governing the density of a glass is its chemical composition. The vast range of possible glass formulations leads to an equally broad range of densities, typically spanning from as low as 2.0 g/cm\({}^{3}\) to over 8.0 g/cm\({}^{3}\). The mass of the constituent atoms plays a direct role; incorporating heavy element oxides, such as lead(II) oxide (PbO), barium oxide (BaO), or lanthanum oxide (La\({}_{2}\)O\({}_{3}\)), significantly increases density. This is evident when comparing common soda-lime-silica glass used for windows (c.a. 2.5 g/cm\({}^{3}\)) with heavy flint glasses used in high-end optics or traditional lead crystal glass, whose densities can easily exceed 4.0 or 6.0 g/cm\({}^{3}\). The structural role of these elements--whether they act as network formers (like Si, B, P) that create the glass network or as network modifiers (like Na, K, Ca) that disrupt and alter the network--also subtly influences the packing efficiency and final density [1; 2; 3; 4]. While composition is the primary determinant, the thermal history of the glass is also a significant factor. The final density is influenced by the cooling rate from the molten state; more rapid quenching corresponds to a structure that is \"frozen-in\" from a higher-temperature, less-relaxed state. This leads to a more open network with greater free volume and, therefore, a lower density. Conversely, slow cooling or subsequent annealing allows the structure to relax into a more compact arrangement. Furthermore, the pressure under which the glass is formed can also affect its final density, with higher pressures leading to more compact, denser structures [1; 2; 3; 4]. Given the strong dependence of density on composition, various empirical models to predict this property were proposed. These models are generally based on the principle of additivity, where the total molar volume (V\({}_{\text{M}}\)) of the glass is calculated by summing the contributions of its constituent oxides based on their mole fractions. From the molar volume and the average molar mass (M), the density can be easily calculated as the quotient of the V\({}_{\text{M}}\) to M. Classic examples include the models developed by [PERSON] and [PERSON] [5; 6], who assigned specific volume coefficients to each oxide. A more physically grounded approach was later proposed by [PERSON] and [PERSON] [7; 8], who related the molar volume to the packing fractions of the constituent ions and the dissociation energies of the oxides. These models remain valuable tools for designing new glasses with tailored properties. The ability to accurately predict the density of a glass from its chemical composition is therefore essential for designing novel materials with tailored properties, significantly accelerating the research and development cycle by saving time and experimental resources.