Phase-Transition Energies, New Characterization of Solid Materials and Anisotropy

Abstract

Non-iterative analysis of indentation results allows for the detection of phase transitions under load and their transition energy. The closed algebraic equations have been deduced on the basis of the physically founded normal force ∝ depth 3/2 relation. The precise transition onset position is obtained by linear regression of the F N = kh 3/2 plot, where k is the penetration resistance, which also provides the axis cuts of both polymorphs of first order phase transitions. The phase changes can be endothermic or exothermic. They are normalized per µN or mN normal load. The analyses of indentation loading curves with self-similar diamond indenters are used as validity check of the loading curves, also from calibration standards that exhibit previously undetected phase-transitions and are thus incorrect. The phase-transition energies for fused quartz are determined from the loading curves from instrument provider handbooks. The anisotropic behavior of phase transition energies is studied for the first time. Quartz is a useful test object. The reasons for the packing-dependent differences are discussed on the basis of the local crystal structure under and around the inserting tip.

Indentation onto Stishovite (SiO<sub>2</sub>), MgO, and a Covered Superalloy: “Pop-In” Repair, Phase-Transition Onsets, Polymorph Energies, and Transition-Energies

“…They were directly loaded to Excel ® for the calculation of Figure 1 through Figure 3 and listed in Table 1. The calculations according to the already repeatedly published short and easily proved equations (numbers 3 -7 in [5]) must not be repeated here. Due to high sensitivity and for avoiding rounding errors, all values throughout were calculated with 10 significant figures, for reasonable rounding in Table 1 and at the final results in the text.…”

“…This avoids a complication of formulas. 0.2 F N is the universal requirement for the elastic + plastic work of conical, pyramidal and wedged indentations [5].…”

“…The big advantage of indentation is the energetic characterization that is only possible with this technique. The reason why (post)Stishovite does not exothermic react to give the 4-fold coordination of Coesite etc, or α-quartz that transforms exothermally to an amorphous phase with k 1 = 2.5443 and k 2 = 1.8609 µN/nm 3/2 [5] is their enormous density due to 6-fold coordination of Si. That makes any internal expansion difficult and prefers cooperative transitions with minimal internal movements by retaining the 6-fold coordination and retaining the high density.…”

“…Almost all actually occurring phase-transitions remain unknown, if the physical Kaupp-plot analysis [1] is avoided for historical reasons. This proved already extremely dangerous, as polymorph interfaces upon phase-transition are nucleation sites for initially small cracks that upon further force produce catastrophic cracking for example in airliners [3] [4] [5]. Remedy is indispensable for e.g.…”

“…Also the necessity for precise direct calibrations will be stressed. Unfortunately, the ISO "standards" that were obtained with false force calibration, materials' mix-up, inconsideration of the phase-transitions, and excessive multi-parameter iterations (as revealed in [5]) are unacceptable. But fortunately, these standards are not required at all.…”