The overlooked role of grain boundary thickness in shaping mechanical properties of solid material

The world of solid materials is not composed solely of perfectly ordered crystals and completely disordered glasses. Between these two fundamental states, there naturally exists a vast transitional region—structures consisting of crystalline grains surrounded by disordered boundaries. When the disordered region is as thin as a single atomic layer, it forms the common polycrystals; when it has a certain thickness, it constitutes the more general crystalline-amorphous composites.

Geometrically, the mean diameter of crystalline grains (D) and the mean grain boundary thickness (l) should be the two fundamental parameters describing the structure of such materials. How the grain diameter affects mechanical properties has been intensively studied for polycrystals. For example, as the crystallite diameter decreases, the yield strength σ_y of polycrystals first increases (the famous Hall–Petch relationship) and then decreases (the inverse Hall–Petch relationship).

“Surprisingly, how the grain boundary thickness, an equally important structural parameter, affects material properties has rarely been studied. The lack of experimental research is understandable, as preparing a series of samples with varying grain boundary thicknesses is highly challenging.” commented by Yilong Han. “However, computer simulations are not difficult, so why is there also a lack of research? This may be due to terminology barriers and mindset differences between different fields: the crystalline-amorphous composites field typically uses the crystalline fraction as a parameter, without considering D and l; while the polycrystals field only treats D as a parameter, considering grain boundaries as interfaces only one or two atomic layers thick.”

Addressing this blind spot, a team led by Prof. Yilong Han from the Hong Kong University of Science and Technology used computer simulations to systematically study key mechanical properties of materials—such as strength, toughness, and elastic modulus—for the first time across the complete (D, l) parameter space. This research was published in September 2025 in National Science Review, with postdoctoral researcher Zhibin Xu as the first author.

By simulating different particle systems, the team extended the classical Hall–Petch and inverse Hall–Petch relationships σy(l) to σ𝑦(𝐷, 𝑙). The results show that in single-component face-centered cubic materials, the material strength peaks when the grain boundary thickness is about 6 atoms (Image), and the ductility also reaches its maximum. This means that increasing the grain boundary thickness up to about 6 atoms can simultaneously enhance both strength and ductility, avoiding the common "strength-ductility tradeoff ". However, for body-centered cubic or multi-component face-centered cubic materials, increasing the grain boundary thickness continuously softens the material.

“These behaviors stem from the competition between two types of plastic mechanisms: dislocation-dominated crystalline plasticity and shear transformation-dominated plasticity in the amorphous regions.” Zhibin Xu explained. “In single-component face-centered cubic materials, thick grain boundaries can inhibit dislocation nucleation and absorb gliding dislocations, thereby simultaneously improving strength and ductility. In body-centered cubic or multi-component materials, due to the high friction stress of dislocations, plastic deformation is primarily borne by the amorphous regions; therefore, thickening the grain boundaries only softens the material.”

In recent years, some alloys with thick grain boundaries have been successfully fabricated experimentally, some of which can exceed the maximum strength of their polycrystalline counterparts, while others cannot. This study provides a reasonable explanation for these seemingly contradictory experimental phenomena. By studying the influence of (D, l) as a pair of independent variables on materials, it offers new insights for the future design of solid materials with superior properties such as high strength and high ductility.

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