The Ti-Mn system revisited: experimental investigation and thermodynamic modelling.

As the Ti-Mn phase diagram is part of numerous ternary and higher order systems of technological importance, the present paper defines phase relations which have been experimentally established throughout this work from 800 °C to the melting range based on Differential Thermal Analyses (DTA), X-ray powder diffraction, metallography and Electron Probe Micro Analysis (EPMA) techniques on ∼50 alloys, which were prepared by arc melting or high frequency melting under high purity argon starting from freshly cleaned metal ingots. Novel compounds were identified and reaction isotherms were redefined accordingly. In the Ti-rich region a novel compound TiMn was detected, sandwiched between the known phases: TiMn1-x (∼45 at% Mn) and TiMn1+x (∼55 at% Mn). In the Mn-rich region the hitherto unknown crystal structure of TiMn∼3 was solved from X-ray single crystal diffraction data and found to be of a unique structure type Ti6(Ti1-xMnx)6Mn25 (x = 0.462; space group Pbam (#55); a = 0.79081(3) nm, b = 2.58557(9) nm, c = 0.47931(2) nm), which consists of two consecutive layers of the hexagonal MgZn2-type Laves phase (TiMn2) and a combined layer of alternate structure blocks of MgZn2 type and Zr4Al3 type. Whereas TiMn can be considered as a line compound (solubility range <∼1 at%), the homogeneity regions of the Ti-Mn compounds are significant (determined by EPMA): TiMn1-x (44.0 to 46.6 at% Mn), TiMn1+x (54.6 to 56.3 at% Mn), Ti1+xMn2-x (MgZn2-type, 59 to 69 at% Mn at 1000 °C: -0.08 < x < 0.23), TiMn∼3 (unique type; 74 to 76.5 at% Mn) and TiMn∼4 (R-phase: Ti8(TixMn1-x)6Mn39, 80 to 84 at% Ti). Supported by ab initio calculations of the ground state energy for the Laves phase, the new experimental results enabled thermodynamic modelling of the entire Ti-Mn phase diagram providing a complete and novel set of thermodynamic data thus providing a sound basis for future thermodynamic predictions of higher order Ti-Mn-X-Y systems.

End-point evaluation in instrumental titrimetry-I Linear extrapolation of hyperbolic titration curves.

A method is described for the estimation of a systematic titration error which is introduced by linear extrapolation of hyperbolic titration curves in amperometric, photometric, and other instrumental titrations. It is assumed that the titration is based upon a single-step ion-association reaction mA + nB right harpoon over left harpoon A(m)B(n) and that the measured physical property falls within known minimum and maximum values. The procedure is suitable for end-point determination, even when the titration curves have extensive curvature, and for predicting the choice of optimum experimental conditions for a given titration.