## 2 Virtual Reality Learning Environments
### Description of the VRLEs  
The VRLE-1 systems (Figure 3) are non-immersive virtual reality (VR)-based applications which run generally on a personal computer, the user interaction is carried out using a keyboard and a mouse and the virtual environment is displayed via a monitor [26; 36; 44]. The VRLE-1 dedicated to the TPD understanding (Figure 3a) shows a three-dimensional illustration of an ideal TPD model where it can be distinguished different parts (each part corresponding to a specific phase, resulting from the combination of three different components at several ranges of temperature). A given user can manipulate, by means of a mouse, each part to understand the TPD model and its individual phases spatially. Thus, the user of this VRLE can perform on the virtual TPD model operations such as: separate and identify different individual phases, rotate elements or apply transparencies to the surfaces to visualize hidden areas, etc. These operations allow users to see -and hence better understand- invariant points (e.g. eutectic, peritectic, etc.) as well as to have an improved view of the relation between the concentration of the three components, temperature and phases formation. On another hand, the VRLE-1 dedicated to CL (Figure 3b) offers the possibility of exploring different types of crystalline networks such as those that are part of the elementary structure of metallic materials. To do this, the VRLE allows users to choose and explore one of the 14 Bravais lattices. Once a crystal lattice has been selected, the user can perform several operations on the cell (by means of the mouse) such as: do 3-axis free rotation, create section views (allowing user to clearly see atoms within the lattice, among others), expand unit cells, etc. The development tools used to create the VRLE-1 systems do not allow to generate environments with high levels of graphic realism, so both TPD and CL results are displayed in empty spaces, using lighting and smooth and textured colors, an evidence of the technology of the time in which they were implemented. Moreover, the development tools used at that time (Quest 3D) and an older version of 3 DS Max(r) do not allow the VRLEs to deliver a high level of interactivity, so that the actions and visualization options offered to the user are rather limited. The VRLE-2 systems (Figure 4) are non-immersive VR-based applications that also run on a personal computer, are controlled by a keyboard and a mouse, and are displayed on a monitor. These VRLEs allow users to explore the virtual environment in a similar way as he/she would do in a first-person shooter video game [51; 52]. Since these later versions were developed with more modern tools, the VRLE-2 systems have a considerable improvement in both their visual appearance and interactivity. Hence, in the new version of the VRLE dedicated to TPD studies (Figure 4a), the user can  
Figure 3: Illustration of previously developed VRLEs-1: (**a**) VRLE-1 system dedicated to TPD calculations and (**b**) VRLE-1 system focused on CL approximations. move freely through a laboratory environment similar to that in any university, in which a hologram of a TPD can be placed in the middle of the room. In addition, this version of the VRLE offers more possibilities for interaction than in the previous versions (such as obtaining isothermal sections of a TPD virtually). Likewise, the new version of the VRLE dedicated to CL (Figure 4b) allows any user to move freely through a virtual museum whose exhibition halls show the 14 Bravais lattices [51]. As the user approaches any of these lattices, the VRLE offers more possibilities for exploration and interaction than in the case of the previous version (Figure 3b), for instance revealing the unit cell and the expanded set with its geometric parameters, directions and crystallographic planes, octahedral and tetrahedral gaps, coordination indices, sections and families of planes and directions, etc.