The critical size limit of electric polarization remains a fundamental question in nanoscale ferroelectric research 1 . As such, the viability of ultrathin ferroelectricity greatly impacts emerging low-power logic and nonvolatile memories 2 . Size effects in ferroelectrics have been thoroughly investigated for perovskite oxides -the archetypal ferroelectric system 3 . Perovskites, however, have so far proved unsuitable for thickness-scaling and integration with modern semiconductor processes 4 . Here, we report ultrathin ferroelectricity in doped-HfO2, a fluorite-structure oxide grown by atomic layer deposition on silicon. We demonstrate the persistence of inversion symmetry breaking and spontaneous, switchable polarization down to 1 nm. Our results indicate not only the absence of a ferroelectric critical thickness, but also enhanced polar distortions as film thickness is reduced, contradictory to perovskite ferroelectrics. This work shifts the focus on the fundamental limits of ferroelectricity to simpler transition metal oxide systems -from perovskite-derived complex oxides to fluoritestructure binary oxides -in which 'reverse' size effects counter-intuitively stabilize polar symmetry in the ultrathin regime.Ferroelectric materials exhibit stable states of collectively ordered electrical dipoles whose polarization can be reversed under an applied electric field 5 . Consequently, ultrathin ferroelectrics are of great technological interest for high-density electronics, particularly field-effect transistors and nonvolatile memories 2 . However, ferroelectricity is typically suppressed at the few nanometer scale in the ubiquitous perovskite oxides 6 . First-principles calculations predict six unit cells as the critical thickness in perovskite ferroelectrics 1 due to incomplete screening of depolarization fields 3 . Atomic-scale ferroelectricity in perovskites often fail to demonstrate polarization switching 7,8 , a crucial ingredient for application. Furthermore, attempts to synthesize ferroelectric perovskite films on silicon 9,10 are plagued by chemical incompatibility 4,11 and high temperatures required for epitaxial growth. Since the discovery of ferroelectricity in HfO2-based thin films in 2011 12 , fluorite-structure binary oxides (fluorites) have attracted considerable interest 13 as they enable lowtemperature synthesis and conformal growth in three-dimensional (3D) structures on silicon 14,15 , thereby overcoming many of the issues that restrict its perovskite counterparts in terms of complementary metal-oxide-semiconductor (CMOS) compatibility and thickness scaling 16 .

Quantifying uncertainty in measured properties of nanomaterials is a prerequisite for the manufacture of reliable nanoengineered materials and products. Yet, rigorous uncertainty quantification (UQ) is rarely applied for material property measurements with the atomic force microscope (AFM), a widely used instrument that can measure properties at nanometer scale resolution of both inorganic and biological surfaces and nanomaterials. We present a framework to ascribe uncertainty to local nanomechanical properties of any nanoparticle or surface measured with the AFM by taking into account the main uncertainty sources inherent in such measurements. We demonstrate the framework by quantifying uncertainty in AFM-based measurements of the transverse elastic modulus of cellulose nanocrystals (CNCs), an abundant, plant-derived nanomaterial whose mechanical properties are comparable to Kevlar fibers. For a single, isolated CNC the transverse elastic modulus was found to have a mean of 8.1 GPa and a 95% confidence interval of 2.7-20 GPa. A key result is that multiple replicates of force-distance curves do not sample the important sources of uncertainty, which are systematic in nature. The dominant source of uncertainty is the nondimensional photodiode sensitivity calibration rather than the cantilever stiffness or Z-piezo calibrations. The results underscore the great need for, and open a path towards, quantifying and minimizing uncertainty in AFM-based material property measurements of nanoparticles, nanostructured surfaces, thin films, polymers and biomaterials.

The development of metrology for nanoparticles is a significant challenge. Cellulose nanocrystals (CNCs) are one group of nanoparticles that have high potential economic value but present substantial challenges to the development of the measurement science. Even the largest trees owe their strength to this newly appreciated class of nanomaterials. Cellulose is the world's most abundant natural, renewable, biodegradable polymer. Cellulose occurs as whisker-like microfibrils that are biosynthesized and deposited in plant material in a continuous fashion. The nanocrystals are isolated by hydrolyzing away the amorphous segments leaving the acid resistant crystalline fragments. Therefore, the basic raw material for new nanomaterial products already abounds in nature and is available to be utilized in an array of future materials. However, commercialization requires the development of efficient manufacturing processes and nanometrology to monitor quality. This paper discusses some of the instrumentation, metrology and standards issues associated with the ramping up for production and use of CNCs.

Technologies surrounding utilization of cellulosic materials have been integral to human society for millennia. In many materials, controlled introduction of defects provides a means to tailor properties, introduce reactivity, and modulate functionality for various applications. The importance of defects in defining the behavior of cellulose is becoming increasingly recognized. However, fully exploiting defects in cellulose to benefit biobased materials and conversion applications will require an improved understanding of the mechanisms of defect induction and corresponding molecular-level consequences. We have identified a fundamental relationship between the macromolecular structure and mechanical behavior of cellulose nanofibrils whereby molecular defects may be induced when the fibrils are subjected to bending stress exceeding a certain threshold. By nanomanipulation, imaging, and molecular modeling, we demonstrate that cellulose nanofibrils tend to form kink defects in response to bending stress, and that these macromolecular features are often accompanied by breakages in the glucan chains. Direct observation of deformed cellulose fibrils following partial enzymatic digestion reveals that processive cellulases exploit these defects as initiation sites for hydrolysis. Collectively, our findings provide a refined understanding of the interplay between the structure, mechanics, and reactivity of cellulose assemblies.