  We present the results of ab initio modeling of structure of dilute Ti-Fe, a
typical representative of quenched Ti-based transition-metal alloys. We have
demonstrated that beyond the solubility limit this alloy cannot be described in
common terms of substitutional and interstitial alloys. Instead, very stable
local clusters are formed in both low-temperature hcp and high-temperature bcc
phases of alloys, with almost identical local structures. This gives an example
of geometrically frustrated state and explains unusual concentration behavior
of M\"ossbauer spectra discovered long ago for this system.
