Table A.1. Thermodynamic phenomena and associated graphical behavior of points and regions of interest for thixoformability analysis on the fl vs. T curve and its first-order and second-order derivatives with respect to temperature. Point or Numerical operation and respective graphical behavior region on Associated thermodynamic None (original First-order Second-order the fl vs. T phenomenon curve) differentiation differentiation curve Point A Maximum sensitivity Inflection Peak Sign inversion (Peak of phase (concave convex) =0° (positive negative) θA transformation) = maximum Maximum value =0° θA θA Null value Points Minimum sensitivity Inflection (convex Valley Sign inversion I and F (Start and end of phase concave) = = =0° (negative positive) θI θF θI θF transformation) =0° Minimum values = =0° θI θF Minimum and Null values maximum values Region IA Increase in sensitivity Increase in Transition (valley Positive region (Start peak of phase curvature peak) (around a peak) transformation) Region AF Decrease in sensitivity Decrease in Transition (peak Negative region (Peak end of phase curvature valley) (around a valley) transformation) Point B Maximum positive Not identifiable Inflection Peak sensitivity change rate (concave =0° θB (Maximum of convex) Maximum value “acceleration” the phase transformation) = maximum θB IA “Inverted knee” Point Maximum negative Not identifiable Inflection (convex Valley B’ sensitivity change rate concave) =0° θB’ (Maximum = maximum Minimum value θB’ “deceleration” of the phase AF transformation) “Knee” Regions Positive variation in Not identifiable Increase in Transition (zero IB and sensitivity change rate curvature peak/valley) AB’ (Increase in “acceleration/deceleration”) Regions Negative variation in Not identifiable Decrease in Transition BA and sensitivity change rate curvature (peak/valley zero) B’F (Decrease in “acceleration/deceleration”)
Table A.1. Thermodynamic phenomena and associated graphical behavior of points and regions of interest for thixoformability analysis on the fl vs. T curve and its first-order and second-order derivatives with respect to temperature. Point or region on the fl vs. T curve Associated thermodynamic phenomenon Numerical operation and respective graphical behavior None (original curve) First-order differentiation Second-order differentiation Point A Maximum sensitivity (Peak of phase transformation) Inflection (concave convex) θA = maximum Peak θA =0° Maximum value Sign inversion (positive negative) θA =0° Null value Points I and F Minimum sensitivity (Start and end of phase transformation) Inflection (convex concave) θI = θF =0° Minimum and maximum values Valley θI = θF =0° Minimum values Sign inversion (negative positive) θI = θF =0° Null values Region IA Increase in sensitivity (Start peak of phase transformation) Increase in curvature Transition (valley peak) Positive region (around a peak) Region AF Decrease in sensitivity (Peak end of phase transformation) Decrease in curvature Transition (peak valley) Negative region (around a valley) Point B Maximum positive sensitivity change rate (Maximum “acceleration” of the phase transformation) “Inverted knee” Not identifiable Inflection (concave convex) θB = maximum IA Peak θB =0° Maximum value Point B’ Maximum negative sensitivity change rate (Maximum “deceleration” of the phase transformation) “Knee” Not identifiable Inflection (convex concave) θB’ = maximum AF Valley θB’ =0° Minimum value Regions IB and AB’ Positive variation in sensitivity change rate (Increase in “acceleration/deceleration”) Not identifiable Increase in curvature Transition (zero peak/valley) Regions BA and B’F Negative variation in sensitivity change rate (Decrease in “acceleration/deceleration”) Not identifiable Decrease in curvature Transition (peak/valley zero)
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