Long period structures in Ti1+xAl3- x alloys : experimental evidence of a devil's staircase ?

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Abstract
Long period antiphase boundary structures based on the Ll2 type structure have been studied in Ti1+xAl3-x alloys by electron diffraction and high resolution electron microscopy. The domain of existence of these structures is determined as a function of concentration and temperature. The structures are found to be commensurate, with rational values of the average antiphase domain size M (4/3 ≤ M ≤ 7/4) and they are always uniform mixings of two types of antiphase domains : domains 1 of one Ll2 cell wide, and domains 2 of two Ll2 cells wide. The uniformity criterion, first introduced by Fujiwara, together with a representation of such structures by a regular step (or square-wave) function is discussed in detail. It is shown in particular that the defects observed in these structures at finite temperature can be accounted for, using a slightly smoothed step function. The mean domain size M depends on temperature; this dependence corresponds to a simple (harmless) staircase below 900 °C, with a few simple structures, while above 1 000 °C, the results strongly suggest the existence of a so-called devil's staircase. The experimental results are compared with those obtained in Ag3Mg and in magnetic systems such as CeSb. Finally, some theoretical approaches are briefly discussed