Understanding how the structure of materials affects their properties is a cornerstone of materials science and engineering. However, traditional methods have struggled to accurately describe the quantitative structure-property relationships for complex structures. In our study, we bridge this gap by leveraging machine learning to analyze images of materials' microstructures, thus offering a novel way to understand and predict the properties of materials based on their microstructures. We introduce a method known as FAGC (Feature Augmentation on Geodesic Curves), specifically demonstrated for Cu-Cr-Zr alloys. This approach utilizes machine learning to examine the shapes within images of the alloys' microstructures and predict their mechanical and electronic properties. This generative FAGC approach can effectively expand the relatively small training datasets due to the limited availability of materials images labeled with quantitative properties. The process begins with extracting features from the images using neural networks. These features are then mapped onto the Pre-shape space to construct the Geodesic curves. Along these curves, new features are generated, effectively increasing the dataset. Moreover, we design a pseudo-labeling mechanism for these newly generated features to further enhance the training dataset. Our FAGC method has shown remarkable results, significantly improving the accuracy of predicting the electronic conductivity and hardness of Cu-Cr-Zr alloys, with R-squared values of 0.978 and 0.998, respectively. These outcomes underscore the potential of FAGC to address the challenge of limited image data in materials science, providing a powerful tool for establishing detailed and quantitative relationships between complex microstructures and material properties.

Mechanical THz vibrations in nanocrystals have recently been harnessed for quantum sensing and thermal management. The free boundaries of nanocrystals introduce new surface wave solutions, analogous to the seismic waves on Earth, yet the implications of these surface waves on nanocrystals have remained largely unexplored. Here, we use atomistic molecular dynamics simulations and experimental neutron spectroscopy to elucidate these THz-scale features in nanodiamond. Our key insight is that thermally induced Rayleigh surface phonons, which have a low group velocity and an amplitude that decays exponentially away from the surface, are responsible for the previously observed but unexplained linear scaling of the low-energy vibrational density of states in nanocrystals. Large thermal atomic displacements, relative to the nanoparticle radius, induce perpetual surface quakes, even at ambient conditions. Normalised to the radius, the surface displacement ratio in diamond nanocrystals exceeds that of the largest recorded earthquakes by a factor of $10^{5\pm1}$. We explicate how these dramatic Rayleigh waves coexist with other distinctive features including confined lattice phonons, soft surface modes, the acoustic gap, Love waves, and Lamb modes, thereby offering a complete framework for the vibrational dynamics of nanocrystals.