Final answer:
Planar discontinuities are generally more critical and are more likely to lead to serious defects in structures compared to spherical ones due to their potential impact on mechanical properties at the grain boundaries.
Step-by-step explanation:
When evaluating the types of structural discontinuities and their propensity to lead to serious defects, planar discontinuities are generally more concerning than spherical ones. Planar defects occur along two-dimensional surfaces and can take various forms, such as grain boundaries, where the properties can significantly differ from the grain itself. Grain boundaries, for example, arise when individual crystal grains grow and meet, and at these junctions, mechanical properties can be weakened, leading to potential failure under stress.
On the other hand, spherical shapes, especially in the context of optics, generally do not introduce the same level of structural weakness as planar defects. In lenses or mirrors, spherical aberrations can occur, but these typically affect image quality rather than structural integrity. Therefore, in the context of structural engineering and materials science, planar defects are more critical and likely to lead to serious defects compared to spherical discontinuities.