**1. Introduction**

To underscore the relevance of the current topic, a number of example engineering-based references are provided for micro- and nano-crystal mechanical property measurements and the applications of them [1–5]. In brief, the topics relate to crystal size effects in manufacturing; strength measurements relating to MEMS applications; micro-forming of foils; nano-metric machining defects; and advanced machine tool manufacturing. Such observations involving extremely small dimensionally-dependent mechanical property measurements have followed a pioneering report by Brenner [6] of greatly-enhanced strength levels being achieved for smaller diameter "whisker" materials. This was later established for nano-grained steel wire [7], micro-pillarα-iron [8], and copper [9] materials. The strength levels have been attributed either to higher applied stresses being needed to nucleate individual dislocations within a dislocation-free environment or because of the need for internal stress concentrations to be produced by small dislocation pile-ups [10–12], for example, as established in the description of higher micro-hardness levels reached for nano-grained nickel material [13].

Here, we consider four example cases in more detail, spanning micro- and nano-scale strength levels and their connection with conventional crystal strength properties, as follows: (1) hardness-based nano-indentation load, *P*, values vs. corresponding respective contact diameters, *di*, for silicon crystals; (2) theoretical-limiting strength levels achieved for the mentioned ultrafine grain size iron and steel materials; (3) dislocation pile-up characterizations of strength levels at nano-scale dimensions relating to the Griffith-based theory of brittle cleavage fracturing; and (3) order-of-magnitude increases in the thermally-dependent strain rate sensitivity properties of nano-crystalline copper and nickel materials associated both with grain size strengthening and grain size-dependent weakening behaviors, in the latter case, connected most often with high temperature creep behavior.
