Theoretical upper limit of dislocation density in slightly-ductile single-crystal ceramics

Abstract

Upper limit of dislocation density without fracture is numerically calculated for slightly- ductile single-crystal ceramics for which the Griffith criterion for fracture and the Bailey-Hirsch type relationship between applied stress and the dislocation density are nearly valid simultaneously in order to obtain useful information to improve functional, electrical, and mechanical properties of ceramics by the introduction of appropriate dislocations. Two models of fracture as a function of dislocation density are constructed; simple model and probability model. If the diameter of pre-existing microcracks is sufficiently small, the dislocation density could be as high as the crystallographic limit (~10^18 m^-2). Even if the typical diameter of pre-existing microcracks is not so small, there is some probability that the dislocation density could be as high as the crystallographic limit if the number of microcracks in the specimen is very small. Accordingly, the increase in ionic conductivity by several orders of magnitude without dendrite formation by introducing appropriate dislocations into single-crystal solid electrolytes with the dislocation density higher than about 10^17 m^-2 theoretically predicted by the authors may be practically possible.

Merits and Demerits of Machine Learning of Ferroelectric, Flexoelectric, and Electrolytic Properties of Ceramic Materials

“…From the numerical results shown in Figure 18, a dislocation density higher than 2.2 × 10 17 m −2 is achievable if the characteristic size 𝑑 0 ́ of pre-existing microcracks in a specimen is smaller than about 1 μm [172]. In Figure 18, 𝑅 = 10 is assumed, where 𝑅 is defined as the ratio of compressive strength to tensile strength [172]. In conclusion, from the physical algebraic equations (Equations ( 33)-( 37)), all-dislocation-ceramics is theoretically discovered, although experimentally it has not yet been achieved.…”

“…Thus, whether high dislocation density such as 2.2 × 10 17 m −2 or more is achievable without the failure of a specimen becomes an issue. In order to study it theoretically, the probability of fracture 𝑃 𝐹 in volume 𝑉 ́ of a specimen given by Equation ( 38) is numerically calculated as shown in Figure 18 [172]. Due to the statistical nature of the number and size of preexisting microcracks in a specimen, the occurrence of fracture is expressed by a probability [172]:…”

“…In the following section, how all-dislocation-ceramics was theoretically discovered is discussed [ 57 , 58 , 172 ]. In the theoretical analysis, parallel straight dislocations in a single-crystal solid electrolyte are considered ( Figure 16 ) [ 57 ].…”

“…Thus, whether high dislocation density such as or more is achievable without the failure of a specimen becomes an issue. In order to study it theoretically, the probability of fracture in volume of a specimen given by Equation (38) is numerically calculated as shown in Figure 18 [ 172 ]. Due to the statistical nature of the number and size of pre-existing microcracks in a specimen, the occurrence of fracture is expressed by a probability [ 172 ]: where is the number concentration of pre-existing microcracks, is the critical diameter of a microcrack for fracture derived by the Griffith criterion, and and are constants which characterize the size distribution of microcracks [ 172 ].…”

The Effect of Sintering Temperature on Phase-Related Peculiarities of the Microstructure, Flexural Strength, and Fracture Toughness of Fine-Grained ZrO2–Y2O3–Al2O3–CoO–CeO2–Fe2O3 Ceramics

“…The flexural strength was measured to be (Figure 6a) 546 ± 45 MPa for the ceramic sintered in mode 1; 558 ± 140 MPa for the ceramic sintered in mode 2; and 606 ± 148 MPa for the ceramic sintered in mode 3. It is known [65][66][67][68] that the flexural strength strongly depends on the size of pre-existing microcracks. As the microcracks are often present at grain boundaries, the size of the microcracks depends on the grain size and is also related to the dislocation density.…”