Scale-coupling and interface-pinning effects in the phase-field-crystal model

Mesoscale Defect Motion in Binary Systems: Effects of Compositional Strain and Cottrell Atmospheres

The velocity of dislocations is derived analytically to incorporate and predict the intriguing effects induced by the preferential solute segregation and Cottrell atmospheres in both two-dimensional and three-dimensional binary systems of various crystalline symmetries. The corresponding mesoscopic description of defect dynamics is constructed through the amplitude formulation of the phase-field crystal model, which has been shown to accurately capture elasticity and plasticity in a wide variety of systems. Modifications of the Peach-Koehler force as a result of solute concentration variations and compositional stresses are presented, leading to interesting new predictions of defect motion due to effects of Cottrell atmospheres. These include the deflection of dislocation glide paths, the variation of climb speed and direction, and the change or prevention of defect annihilation, all of which play an important role in determining the fundamental behaviors of complex defect network and dynamics. The analytic results are verified by numerical simulations.

Mechanical relaxation and fracture of phase field crystals

A computational method is developed for the study of mechanical response and fracture behavior of phase field crystals (PFC), to overcome a limitation of the PFC dynamics which lacks an effective mechanism for describing fast mechanical relaxation of the material system. The method is based on a simple interpolation scheme for PFC (IPFC) making use of a condition of the displacement field to satisfy local elastic equilibration, while preserving key characteristics of the original PFC model. We conduct a systematic study on the mechanical properties of a sample nanoribbon system with honeycomb lattice symmetry subjected to uniaxial tension, for numerical validation of the IPFC scheme and the comparison with the original PFC and modified PFC methods. Results of mechanical response, in both elasticity and fracture regimes, show the advantage and efficiency of the IPFC method across different system sizes and applied strain rates, due to its effective process of mechanical equilibration. A brittle fracture behavior is obtained in IPFC calculations, where effects of system temperature and chirality on the fracture strength and Young's modulus are also identified, with results agreeing with those found in previous atomistic simulations of graphene. The IPFC scheme developed here is generic and applicable to the mechanical studies using different types of PFC free-energy functionals designed for various material systems.

Tip-enhanced Raman spectroscopy - from early developments to recent advances

An analytical technique operating at the nanoscale must be flexible regarding variable experimental conditions while ideally also being highly specific, extremely sensitive, and spatially confined. In this respect, tip-enhanced Raman scattering (TERS) has been demonstrated to be ideally suited to, e.g., elucidating chemical reaction mechanisms, determining the distribution of components and identifying and localizing specific molecular structures at the nanometre scale. TERS combines the specificity of Raman spectroscopy with the high spatial resolution of scanning probe microscopies by utilizing plasmonic nanostructures to confine the incident electromagnetic field and increase it by many orders of magnitude. Consequently, molecular structure information in the optical near field that is inaccessible to other optical microscopy methods can be obtained. In this general review, the development of this still-young technique, from early experiments to recent achievements concerning inorganic, organic, and biological materials, is addressed. Accordingly, the technical developments necessary for stable and reliable AFM- and STM-based TERS experiments, together with the specific properties of the instruments under different conditions, are reviewed. The review also highlights selected experiments illustrating the capabilities of this emerging technique, the number of users of which has steadily increased since its inception in 2000. Finally, an assessment of the frontiers and new concepts of TERS, which aim towards rendering it a general and widely applicable technique that combines the highest possible lateral resolution and extreme sensitivity, is provided.

Phase-field-crystal investigation of the morphology of a steady-state dendrite tip on the atomic scale

Through phase-field-crystal (PFC) simulations, we investigated, on the atomic scale, the crucial role played by interface energy anisotropy and growth driving force during the morphological evolution of a dendrite tip at low growth driving force. In the layer-by-layer growth manner, the interface energy anisotropy drives the forefront of the dendrite tip to evolve to be highly similar to the corner of the corresponding equilibrium crystal from the aspects of atom configuration and morphology, and thus affects greatly the formation and growth of a steady-state dendrite tip. Meanwhile, the driving force substantially influences the part behind the forefront of the dendrite tip, rather than the forefront itself. However, as the driving force increases enough to change the layer-by-layer growth to the multilayer growth, the morphology of the dendrite tip's forefront is completely altered. Parabolic fitting of the dendrite tip reveals that an increase in the influence of interface energy anisotropy makes dendrite tips deviate increasingly from a parabolic shape. By quantifying the deviations under various interface energy anisotropies and growth driving forces, it is suggested that a perfect parabola is an asymptotic limit for the shape of the dendrite tips. Furthermore, the atomic scale description of the dendrite tip obtained in the PFC simulation is compatible with the mesoscopic results obtained in the phase-field simulation in terms of the dendrite tip's morphology and the stability criterion constant.

Incorporating Noise Quantitatively in the Phase Field Crystal Model via Capillary Fluctuation Theory

A tacit assumption underlying most phase field models of nonequilibrium phase transformations is that of scale separation. Stochastic order parameter field theories utilize noise to separate atomic-scale fluctuations from the slowly varying fields that describe microstructure patterns. The mesoscale distribution of such stochastic variables is generally assumed to follow Gaussian statistics, with their magnitude following fluctuation-dissipation relations. However, there is still much debate about how atomic-scale fluctuations map onto the mesoscale upon coarse graining of microscopic theories. This Letter studies interface fluctuations in the phase field crystal (PFC) model and proposes a self-consistent method for relating how the effective noise strength and spectral filtering of the noise in the PFC model, and similar types of microscopic models, should be defined so as to attain the spectrum of mesoscale capillary fluctuations quantitatively.

Scaling of alloy interfacial properties under compositional strain

Complex morphologies and microstructures that emerge during materials growth and solidification are often determined by both equilibrium and kinetic properties of the interface and their crystalline anisotropies. However, limited knowledge is available on alloying and, particularly, compositionally generated elastic effects on these interface characteristics. Here we systematically investigate such compositional effects on the interfacial properties of an alloy model system based on a phase-field-crystal analysis, including the solid-liquid interfacial free energy, kinetic coefficient, and lattice pinning strength. Scaling relations for these interfacial quantities over various ranges of material parameters are identified and predicted. Our results indicate the important effects of couplings among mesoscopic and microscopic length scales of alloy structure and concentration, and the influence of compressive and tensile interface stresses induced by composition variations. The approach developed here provides an efficient way to systematically identify these key material properties beyond the traditional atomistic and continuum methods.

Exploring the complex world of two-dimensional ordering with three modes

The world of two-dimensional crystals is of great significance for the design and study of structural and functional materials with novel properties. Here we examine the mechanisms governing the formation and dynamics of these crystalline or polycrystalline states and their elastic and plastic properties by constructing a generic multimode phase field crystal model. Our results demonstrate that a system with three competing length scales can order into all five Bravais lattices, and other more complex structures including honeycomb, kagome, and other hybrid phases. In addition, nonequilibrium phase transitions are examined to illustrate the complex phase behavior described by the model. This model provides a systematic path to predict the influence of lattice symmetry on both the structure and dynamics of crystalline and defected systems.