Create a photorealistic image that visually represents the concept of the electron gas model used in the context of metal behavior. In this depiction, imagine electrons as dynamic entities moving freely within a structured, three-dimensional lattice composed of positively charged metal ions. This lattice should appear as a solid, crystalline structure, embodying the comparison to molecules in a gas that move without restraint within a container. Emphasize the aspect of unrestricted movement to illustrate the model's utility in explaining the electrical conductivity and other electronic properties of metals. The image should capture the essence of electrons' freedom and interaction within a metal's ion lattice, providing a tangible visualization of this abstract scientific concept.