Statistical size scaling of ceramic strength

Abstract

This work is based on the belief that the uniform spatial distribution of flaws underlying Weibull statistics is not necessarily always true for all ceramics. The weakest-link statistics for a power-law spatial distribution of flaws is adopted to synchronize the size dependence and random variation of ceramic strength. Three sets of published strength data of ceramics from different sized specimens are used for this purpose. The assumption of power-law spatial distribution of flaws in ceramics is validated, with both uniform and nonuniform spatial distributions being showcased possible. For all the three case studies, there exists a master curve to correlate a compound parameter encompassing cumulative failure probability and size effect with the nominal fracture strength. K E Y W O R D Sceramics, size effect, statistical model, strength

Up-conversion luminescence and Judd–Ofelt analysis of Nd2O3-doped yttria stabilized zirconia single crystals

“…This then decays initially to the 4 F 3/2 energy level by a NR process, then decays further to the 4 I 9/2 , 4 I 11/2 and 4 I 13/2 energy states with photon emission. 46,47 The 4 I 11/2 and 4 I 13/2 states eventually decay to the 4 I 9/2 ground state by MPR and NR processes.…”

Statistical size scaling of breakage strength of irregularly-shaped particles

“…If β = 1, it is a perfect uniform distribution; if 0 < β < 1, defects are less dense than uniform distribution and are nonuniform; if β > 1, defects are more dense than uniform distribution and are nonuniform. Combining the 4 materials in this study which are irregular shaped, and other materials investigated in Lei [11,13,14], the following observations can be made: (1) Nonuniform spatial defect distributions are more often found in natural materials such as sugar, wood, coal, rocks and other mineral materials than in modern technological materials; Modern technological materials such as steels and classical concrete materials have been developed with a special focus on eliminating all nonuniform types for desired performance. (2) Porous structures are more susceptible to nonuniform defect distribution, such as wood, aluminum foam and some ceramics; (3) Materials easier to take inter-granular fracture than transgranular fracture, such as sugar, inter-metallics.…”

“…Specifically, in Lei [11], it was found that wood and coal as natural materials, and gamma titanium aluminum alloy, aluminum foam and nuclear grade graphite as technological materials, can be better described with this nonuniform defection distribution based statistical model. In Lei [13], it was reported that the statistical distribution of defects in different ceramic materials can fit either β = 1, β > 1 or 0 < β < 1.…”

Advances in Molten Salt Synthesis of Non‐oxide Materials

“…The target products undergo two processes of nucleation and growth in molten salt. Generally, the reaction mechanisms are considered as "template mode" or "dissolution-precipitation mode" (Figure 1) [12][13][14][15] according to the different dissolution and diffusion of reactants in molten salt. The principle of template synthesis mechanism is that the solubility of reactants in molten salt is greatly different, so the reactants with large solubility dissolve and diffuse to the reactants with small solubility, and then, the target product is generated with it as template, so the target product morphology will be similar to that of the reactants with small solubility.…”

“…[16][17][18][19] Molten salt synthesis is an important method for the preparation of inorganic materials, which has been greatly developed due to a series of unique advantages. At present, molten salt synthesis has been widely used in the preparation of oxide materials, [20,21] including binary oxides: Ti 4 O 7 , [22] Mn 2 O 3 , [23] and SnO 2 ; [24] perovskite: CaZrO 3 [14] and BaTiO 3 ; [25] composite oxides: MgAl 2 O 4 , [13,26] LaAlO 3 , [15] Lu 2 Ti 2 O 9 , [27] and Bi 3.15 Nd 0.85 Ti 2 CoO 12 ; [28] and battery materials: LiCoO 2 , [29] (La, Sr)FeO 3 , [30] LaMnO 3 -δ, [31] etc. At the same time,…”