Mechanoluminescent materials, which emit light in response to elastic deformation, are demanded for use as in situ stress sensors. ZnS doped with Mn is known to exhibit one of the lowest reported thresholds for appearance of mechanoluminescence, with repeatable light emission under contact pressure <10 MPa. The physical basis for such behavior remains as yet unclear. Here, reliable microscopic detection of mechanoluminescence of single ZnS:Mn microparticles, in combination with nanoscale structural characterization, provides evidence that the mechanoluminescent properties of these particles result from interplay between a non-centrosymmetric crystal lattice and its defects, viz., dislocations and stacking faults. Statistical analysis of the distributions of mechanoluminescence energy release trajectories reveals two distinct mechanisms of excitation: one attributable to a piezo-phototronic effect and the other due to dislocation motion. At pressures below 8.1 MPa, both mechanisms contribute to mechanoluminescent output, with a dominant contribution from the piezo-phototronic mechanism. In contrast, above 8.1 MPa, dislocation motion is the primary excitation source. For the piezo-phototronic mechanism, we propose a specific model that accounts for elastic ZnS:Mn mechanoluminescence under very low pressure. The charged interfaces in stacking faults lead to the presence of filled traps, which otherwise would be empty in the absence of the built-in electric field. Upon application of external stress, local enhancement of the piezoelectric field at the stacking faults' interfaces facilitates release of the trapped carriers and subsequent luminescence. This field enhancement explains how <10 MPa pressure produces thousands of photons.

Growth laws emerging from studies of cell populations provide essential constraints on the global mechanisms that coordinate cell growth^1-3. The foundation of bacterial cell cycle studies relies on two interconnected dogmas that were proposed more than 50 years ago-the Schaechter-Maaloe-Kjeldgaard growth law that relates cell mass to growth rate¹ and Donachie's hypothesis of a growth-rate-independent initiation mass⁴. These dogmas spurred many efforts to understand their molecular bases and physiological consequences^5-14. Although they are generally accepted in the fast-growth regime, that is, for doubling times below 1 h, extension of these dogmas to the slow-growth regime has not been consistently achieved. Here, through a quantitative physiological study of Escherichia coli cell cycles over an extensive range of growth rates, we report that neither dogma holds in either the slow- or fast-growth regime. In their stead, linear relations between the cell mass and the rate of chromosome replication-segregation were found across the range of growth rates. These relations led us to propose an integral-threshold model in which the cell cycle is controlled by a licensing process, the rate of which is related in a simple way to chromosomal dynamics. These results provide a quantitative basis for predictive understanding of cell growth-cell cycle relationships.