## 1 Introduction  
Phosphate glasses are a group of materials that possess many applications. Their properties change in a very broad range and are strongly dependent on the structural features of glass networks and chemical composition. The addition of rare earth oxides makes them a good candidate for applications in optoelectronic devices [1; 2; 3; 4]. Phosphate glasses containing calcium and/or strontium are biocompatible and may be used as dental or bone implants [5; 6; 7]. Glasses with a high P\({}_{2}\)O\({}_{5}\) content have low water resistance [8]. The introduction of iron or aluminum strongly increases durability, and hence, glasses of excellent chemical resistance can be produced [9]. Thus, by changing the iron content, materials of controlled dissolution in water can be obtained. One of the possible applications of phosphate glasses is their use as a matrix for the immobilization of waste. Binary iron phosphate glasses containing c.a. 30-40 mol% of Fe\({}_{2}\)O\({}_{3}\) (IPG) are characterized by excellent chemical durability and lower melting temperatures compared to conventional silicate. This predisposes them to the process of waste vitrification, and they are now considered for the immobilization of radioactive waste. The IPG can be used to vitrify so-called \"difficult waste\" that cannot be immobilized in conventional borosilicate glasses. Such waste has a high concentration of elements whose solubility in silicate glasses is strongly limited. The species may be sulfur and salty waste containing a high concentration of sulfates that cannot be utilized in conventional waste glasses. The solubility of salts is much higher in phosphate glasses [10; 11; 12; 13]. In IPG glasses, the main pure network former oxide is P\({}_{2}\)O\({}_{5}\). The phosphorus cations are placed in the middle of the oxygen tetrahedron. Due to the pentavalency of P, one of four oxygen atoms forms a double bond to fulfill the charge neutrality of [PO\({}_{4}\)] tetrahedrons. The tetrahedrons join each other by common vertices, creating P-O-P bridges. Thus, a continuous phosphate network is achieved [14; 15; 16; 17; 18]. The role of iron is more difficult. Fe\({}_{2}\)O\({}_{3}\) is an intermediate oxide. Thus, depending on the chemical environment of the network, it may occupy network or modifier positions. In the network, the positions form [FeIIIO\({}_{4}\)]\({}^{-}\) tetrahedrons that are negatively charged. To compensate for the charge, the tetrahedrons join the positively charged modifiers, which change their role from modifier to charge compensator. During glass synthesis, part of FeIII is frequently reduced to FeII. FeII is commonly considered a pure modifier of the glass network [19; 20; 21; 22; 23; 24]. Strontium oxide in glasses is a typical divalent glass network modifier. It plays a crucial role in new bone formation by increasing osteoblast proliferation and inhibitory effects on osteoclasts. As such, bioactive glasses can induce the healing of osteoporotic tissues and promote bone densification. On the other hand, the \({}^{90}\)Sr isotope is one of the major sources of nuclear waste activity and \(\beta\) radiation. Due to its high solubility, it can enter groundwater from waste, and the radionuclide can be incorporated into bones and thus remain in the body [11; 13]. Computer simulations have become a very important and accurate method that offers the possibility to predict the properties of new materials. This gives the possibility to check at relatively low costs the potential application possibilities of different materials in specific conditions or processes. In the case of waste vitrification, the final waste form should be very stable and prone to different environmental conditions for a very long time. One of the parameters that may limit the potential usefulness of specific materials in waste immobilization is the migration of elements in the structure. Thus, a description of the self-diffusion mechanism could be an important factor in glass composition optimization for waste immobilization.