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Titanium is an element in the periodic table, hence it doesn't have a "model" in the sense that a car or a gadget would have.
However, in terms of its atomic model, it is element number 22, meaning it has 22 protons in its nucleus. It usually has 26 neutrons and its 22 electrons are arranged in four energy levels, with two in the first level, eight in the second level, ten in the third level, and two in the fourth level.
In terms of crystal structure, titanium forms a hexagonal close-packed (hcp) arrangement at room temperature, transforming into a body-centered cubic (bcc) structure at higher temperatures (882 °C).
Analogs to "models" for titanium would be its numerous alloys and compounds that modify its properties for better use in various applications - for example, Titanium(IV) oxide (Titania) used as a pigment, photocatalyst and a component in solar cells, or Titanium Aluminium Vanadium alloy (Ti-6Al-4V) used in parts of aircrafts and dental implants due to its high specific strength.
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