We present the Hall–Petch correlation between microhardness values and grain sizes for single, binary (50-50 vol.%), and ternary (33-33-33 vol.%) phase composites of yttria-stabilized zirconia (8Y–ZrO₂), spinel (MgAl₂O₄), and alumina (Al₂O₃) samples produced by spark plasma sintering. Both the intrinsic grain microhardness values and the Hall–Petch constants were found to be significantly higher for alumina among the single-phase samples, and for the alumina-containing composites for the multiphase specimens. The microhardness values of all binary and ternary composites were observed to follow a rule of mixtures for both sub-micron (250–400 nm) and micrometer (1–1.5 μm) grain sizes. The fracture toughness values for all the specimens were also determined using the Vickers indentation method. Among all studied ceramic composites, single phase Al₂O₃ and a binary composite of 8Y–ZrO₂/Al₂O₃ attained the highest hardness and toughness values of 20 GPa and 5.8 MPa•m^1/2, respectively. The number of slip systems could be the main reason for the improved mechanical performance of the alumina and alumina-containing composites. Particularly, alumina consists of only 17 slip systems, while both zirconia and spinel are more ductile and contain 12 principal and 24 secondary, and 24 slip systems, respectively. These results are of significant interest, since they connect the grain sizes of the materials produced to their corresponding mechanical response.

我们介绍了钇稳定氧化锆（8Y–ZrO ₂）的单相，二元（50-50％（体积））和三元（33-33-33％（体积））复合物的显微硬度值与晶粒尺寸之间的霍尔-帕奇相关性。），尖晶石（MgAl ₂ O ₄）和氧化铝（Al ₂ O ₃）火花等离子体烧结产生的样品。发现单相样品中的氧化铝和多相样品中的含氧化铝复合材料的固有晶粒显微硬度值和Hall-Petch常数均显着较高。观察到所有二元和三元复合材料的显微硬度值均遵循亚微米（250-400 nm）和微米（1-1.5μm）晶粒尺寸的混合规则。还使用维氏压痕法确定所有样品的断裂韧性值。在所有研究的陶瓷复合材料中，单相Al ₂ O ₃和8Y–ZrO ₂ / Al ₂ O ₃二元复合材料最高硬度和韧性值分别达到20 GPa和5.8 MPa•m ^1/2。滑动系统的数量可能是改善氧化铝和含氧化铝复合材料机械性能的主要原因。特别是，氧化铝仅包含17个滑移系统，而氧化锆和尖晶石则更具延展性，分别包含12个主滑移系统和24个滑移系统。这些结果令人关注，因为它们将所生产材料的晶粒尺寸与其相应的机械响应联系起来。