It is possible to cut on-grain pieces from neckties (which are cut on the bias).  The on-grain weave is what you have on the edges of the tie points, so you can cut on-grain strips by cutting parallel to one edge of the tie point.  Narrow strips cut on-grain (1" - 1 1/2") can then be used for tiny log cabin blocks or any other small application.  Be aware that these small pieces will fray very easily, so handle with care!