Briefly explain (a) why there may be significant scatter in the fracture strength for some given ceramic material, and (b) why fracture strength increases with decreasing specimen size.

The microstructural flaws in ceramics are imperfections within the material that significantly affect their mechanical properties. These flaws, such as pores, cracks, or inclusions, originate from various stages of the ceramic production process, including powder processing, shaping, and sintering.

Microstructural flaws act as stress concentrators, meaning they localize stress and can drastically reduce the strength of the ceramic. Under applied stress, these flaws can propagate, leading to the growth of cracks and ultimately causing fracture. The scatter in fracture strength observed in ceramic materials is largely due to the unpredictable nature of these flaws. No two ceramic pieces are identical at the microstructural level, thus creating a variance in their strength.

Understanding the role of microstructural flaws is crucial for improving the strength of ceramics. Manufacturers strive to control the processing conditions to minimize these flaws and increase the reliability and performance of ceramic components in applications such as aerospace, biomedical implants, and electronics.

Brittleness is one of the defining characteristics of ceramic materials. It describes their inability to deform plastically before fracture, unlike metals that can typically bend or stretch to some extent. This brittleness stems from the strong ionic and/or covalent bonds in ceramics, which don't allow for the dislocation movements that accommodate plastic deformation in metals.

When subjected to stress, a ceramic material with microstructural flaws will fracture at the flaws without much warning or prior deformation. The brittleness of ceramics is a double-edged sword; while it leads to high hardness and wear resistance, it also means that ceramics are more susceptible to catastrophic failure when a critical stress is reached. This is why the fracture strength of ceramics can vary widely based on the presence and severity of microstructural flaws, and it's also why such materials are more commonly used in applications where high strength, but low deformability, is required.

The size effect on the fracture strength of ceramic materials is a well-observed phenomenon. As the size of the ceramic specimen decreases, the chance of containing a critical flaw within it also reduces. This has a direct impact on increasing the fracture strength of smaller ceramic samples.

Moreover, smaller samples have a reduced volume, and, consequently, less material is likely to be affected by any given flaw. This size effect is significant in applications that require high precision and reliability. For example, in the cutting edge technology of microelectronics and medical devices, smaller ceramic components can offer superior performance and durability due to their increased fracture strength. Understanding and utilizing the size effect allows engineers to design ceramic parts that capitalize on the mechanical properties of these materials for optimal performance.