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Ti2ReCu crystallizes in the orthorhombic Immm space group. The structure is one-dimensional and consists of two Ti2ReCu ribbons oriented in the (1, 0, 0) direction. Ti is bonded in a linear geometry to one Re and one Cu atom. The Ti–Re bond length is 2.19 Å. The Ti–Cu bond length is 2.57 Å. Re is bonded in a linear geometry to two equivalent Ti atoms. Cu is bonded in a linear geometry to two equivalent Ti atoms.
Ti2ReCu is Heusler structured and crystallizes in the cubic Fm-3m space group. The structure is three-dimensional. Ti is bonded in a body-centered cubic geometry to four equivalent Re and four equivalent Cu atoms. All Ti–Re bond lengths are 2.69 Å. All Ti–Cu bond lengths are 2.69 Å. Re is bonded in a body-centered cubic geometry to eight equivalent Ti atoms. Cu is bonded in a body-centered cubic geometry to eight equivalent Ti atoms.