The atomic packing factor (APF) and coordination number of these structures dictate mechanical ductility and slip systems. Reciprocal Lattice and Diffraction
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A compact guide suitable for quick reference, available here . Conclusion The atomic packing factor (APF) and coordination number
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Materials engineers must first understand the periodic arrangement of atoms. This section covers: Bravais lattices, Miller indices.
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Pure materials (like silicon or germanium) where the electron concentration ( ) exactly equals the hole concentration ( ). Conductivity is highly temperature-dependent.
Introduces a weak periodic potential from the ion cores. This perturbation splits the continuous energy spectrum, creating band gaps where electron waves experience destructive interference and cannot exist. Tight-Binding Model
). Constructive interference occurs when the change in the wave vector ( ) equals a reciprocal lattice vector: This is where the search for the right
Strong, spontaneous alignment of spins below a critical temperature (the Curie Temperature ), driven by quantum mechanical exchange interactions. This is critical for transformers, electric motors, and magnetic storage. Optical Properties
The highest occupied band is only partially filled, or the valence and conduction bands overlap. Electrons move freely under an applied electric field.
: Shared localized electrons result in high hardness and wide band gaps (e.g., diamond, silicon).
: Pure semiconductor where the electron concentration ( ) equals the hole concentration (