Activation energy of the low-load NaCl transition from nanoindentation loading curves

Abstract

Access to activation energies E(a) of phase transitions is opened by unprecedented analyses of temperature dependent nanoindentation loading curves. It is based on kinks in linearized loading curves, with additional support by coincidence of kink and electrical conductivity of silicon loading curves. Physical properties of B1, B2, NaCl and further phases are discussed. The normalized low-load transition energy of NaCl (Wtrans/µN) increases with temperature and slightly decreases with load. Its semi-logarithmic plot versus T obtains activation energy E(a)/µN for calculation of the transition work for all interesting temperatures and pressures. Arrhenius-type activation energy (kJ/mol) is unavailable for indentation phase transitions. The E(a) per load normalization proves insensitive to creep-on-load, which excludes normalization to depth or volume for large temperature ranges. Such phase transition E(a)/µN is unprecedented material's property and will be of practical importance for the compatibility of composite materials under impact and further shearing interactions at elevated temperatures.

The ISO Standard 14577 for Mechanics Violates the First Energy Law and Denies Physical Dimensions

“…Only the quantitative indentation on the physical basis reveals numerous otherwise impossible applications. Examples are phase change [4,5,16], conversion energies [4,16] and activation energies [16] of materials, all on the basis of the so-called Kaupp-plot (1) that also checks for correctly performed indentations and provides extrapolation facility up to recognized phase change qualities under pressure. Furthermore, it reveals a large number of special materials' properties and indentation errors that are named above.…”

Important Consequences of the Exponent 3/2 for Pyramidal/Conical Indentations-New Definitions of Physical Hardness and Modulus

“…Only rarely and exceptionally were phase transitions concluded from "elbows" in unloading curves, but then without any transition-onset information. A widely studied example, also with more advanced techniques, is silicon [7]. Original material is characterized by the penetration resistance k 1 before the kink in linearized loading curves.…”

“…After the kink the k 2 -value is obtained for transformed material in a matrix of the original one [4]. It provides an important bargain when both k 1 and k 2 (mN/µm 3/2 ) are known: The transition energy [6], and temperature dependent also the activation energy of the transition are revealed [7]. When the onset of phase changes is not uncovered, there is often a risk that such transition-onset has occurred before the applied (not italicized for distinction from physical k values) for varying depths onto fused quartz for proposing varying depth/exponent and depth/k relations.…”

“…Such long-range processes convert or store energy that is lost for the impression. The denial of such loss inexcusably violates the basic first energy law (applied work = produced work/energy): Equation (1) and simple algebra deduce that precisely 20% of the applied work (for all materials) is used for the sum of long-range effects and lost for the indentation depth [6][7][8][9][10]. The energy loss for the penetration as deduced in [6], is summarized in the basic Figure 2.…”

“…1) with excellent linear regression reveals surface effects (including tip rounding), influence of tip angle and radius on k, gradients, mechanical pretreatment, alternating layers, elbows, nanopores, phase transitions under load, transition energies, activation energies, and correct adhesion energies, all by simple mathematics without iterations (Eq. 1) [4,[6][7][8][9].…”