Amorphous materials do not have a regular crystal lattice structure, unlike cubic, tetragonal, and hexagonal lattices.

Miller indices (h, k, l) represent the intercepts of the crystal plane with the crystallographic axes a, b, and c, respectively.

Bragg's Law describes the relationship between the wavelength of X-rays and the diffraction angle in X-ray crystallography.

X-ray diffraction is the most widely used technique for determining the crystal structure of materials.

Crystal engineering is the process of designing and synthesizing materials with specific crystal structures to achieve desired properties.

Bulk materials are not considered nanomaterials, as they do not have dimensions in the nanometer range.

Nanosynthesis refers to the process of synthesizing nanomaterials with controlled properties.

Toughness is typically not enhanced in nanomaterials compared to their bulk counterparts.

Quantum confinement refers to the phenomenon where the properties of a material change significantly at the nanoscale due to quantum effects.

Construction is not a typical application of nanomaterials.

Nanomaterial optimization refers to the process of modifying the properties of nanomaterials to achieve desired outcomes.

X-ray diffraction is not commonly used for characterizing nanomaterials due to their small size.

Nanomaterial aging refers to the phenomenon where the properties of a nanomaterial change over time due to interactions with the environment.

Scalability is not a typical challenge associated with the use of nanomaterials.

Optimization in materials science is the field that combines optimization techniques with materials science to improve the properties and performance of materials.