The Solid State (Electrical And Magnetic Properties)

Electrical Properties

The electrical properties of solids are primarily determined by the nature of bonding and the arrangement of electrons within the crystal lattice.

Conduction Of Electricity In Metals:

Metals are excellent conductors of electricity and heat.

• Mechanism of Conduction: Metals have a crystal lattice structure where valence electrons are delocalized and form a "sea of electrons" that can move freely throughout the lattice. When an electric field is applied, these free electrons drift towards the positive electrode, resulting in an electric current.
• Electrical Conductivity ($\sigma$): Metals have very high electrical conductivity, typically in the range of $10^6$ to $10^7$ $S/m$.
• Temperature Dependence: The conductivity of metals decreases with increasing temperature because the increased thermal vibrations of the lattice ions impede the movement of electrons.
• Band Theory Explanation: In metals, the valence band and the conduction band overlap or are partially filled. This allows electrons to move easily from the valence band to the conduction band with very little energy input, enabling high conductivity.

Conduction Of Electricity In Semiconductors:

Semiconductors are materials whose electrical conductivity lies between that of metals and insulators.

• Mechanism of Conduction: In semiconductors, the valence band is completely filled, and the conduction band is empty, separated by a small energy gap ($E_g$). At absolute zero temperature, semiconductors behave as insulators. However, at higher temperatures or upon doping, electrons gain enough thermal energy to jump the gap into the conduction band, leaving behind "holes" in the valence band. Both electrons (in the conduction band) and holes (in the valence band) contribute to electrical conduction.
• Electrical Conductivity ($\sigma$): The conductivity of intrinsic semiconductors is low (e.g., $10^{-4}$ to $10^{-6}$ $S/m$).
• Temperature Dependence: The conductivity of semiconductors increases significantly with increasing temperature because more charge carriers (electrons and holes) are generated as the temperature rises.
• Intrinsic vs. Extrinsic Semiconductors:
  • Intrinsic Semiconductors: Pure semiconductors (e.g., Si, Ge) with conductivity dependent on temperature and intrinsic properties.
  • Extrinsic Semiconductors: Doped semiconductors where impurities are intentionally added to increase conductivity.
    • n-type Semiconductor: Doped with pentavalent impurities (e.g., Phosphorus in Silicon), where electrons are the majority charge carriers.
    • p-type Semiconductor: Doped with trivalent impurities (e.g., Boron in Silicon), where holes are the majority charge carriers.
• Band Theory Explanation: A small energy gap ($E_g$) between the valence band and conduction band allows electrons to move to the conduction band with moderate thermal energy.

Insulators: In insulators, the energy gap ($E_g$) between the valence band and conduction band is very large (typically $> 3$ eV), preventing electrons from moving to the conduction band, hence their very low conductivity.

Magnetic Properties

Magnetic properties of solids arise from the orbital motion and spin of electrons. Each electron behaves like a tiny magnet. When placed in an external magnetic field, different materials respond differently, leading to various magnetic properties.

Diamagnetism:

• Cause: Diamagnetism arises from the orbital motion of electrons. When an external magnetic field is applied, it induces a magnetic moment in the opposite direction of the field, causing a weak repulsion. All substances exhibit diamagnetism, but it is often masked by stronger magnetic effects like paramagnetism or ferromagnetism.
• Electron Configuration: Occurs in substances where all electrons are paired.
• Response to Magnetic Field: Weakly repelled by an external magnetic field.
• Magnetic Susceptibility ($\chi$): Negative and very small (typically $-10^{-5}$ to $-10^{-6}$).
• Examples: Water ($H_2O$), Sodium Chloride ($NaCl$), Benzene ($C_6H_6$), Copper ($Cu$).

Paramagnetism:

• Cause: Paramagnetism arises from the presence of unpaired electrons, which possess permanent magnetic dipole moments. These moments tend to align themselves with the external magnetic field, resulting in a weak attraction.
• Electron Configuration: Occurs in substances with one or more unpaired electrons.
• Response to Magnetic Field: Weakly attracted by an external magnetic field. The attraction disappears when the external field is removed.
• Magnetic Susceptibility ($\chi$): Positive and small (typically $10^{-3}$ to $10^{-5}$).
• Temperature Dependence: Paramagnetism decreases with increasing temperature (Curie's Law: $\chi \propto 1/T$).
• Examples: Oxygen ($O_2$), Aluminium ($Al$), Chromium ($Cr$), $Cu^{2+}$ salts.

Ferromagnetism:

• Cause: Ferromagnetism arises from the spontaneous alignment of magnetic moments of unpaired electrons in a specific direction due to strong interatomic interactions (exchange coupling). This alignment occurs even in the absence of an external magnetic field, resulting in a strong permanent magnetism.
• Electron Configuration: Occurs in substances with a large number of unpaired electrons and strong exchange interactions.
• Response to Magnetic Field: Strongly attracted by an external magnetic field. Can retain magnetism even after the external field is removed (forming permanent magnets).
• Magnetic Susceptibility ($\chi$): Large and positive (typically $> 100$).
• Temperature Dependence: Ferromagnetic materials lose their ferromagnetism above a critical temperature known as the Curie Temperature ($T_C$), above which they become paramagnetic.
• Examples: Iron (Fe), Nickel (Ni), Cobalt (Co), Gadolinium (Gd).

Ferromagnetic materials exhibit magnetic domains, regions where magnetic moments are aligned in the same direction. In the absence of an external field, these domains may be randomly oriented, resulting in no net magnetism. Upon applying an external field, the domains align, leading to strong magnetization.

Antiferromagnetism:

• Cause: In antiferromagnetic materials, the magnetic moments of adjacent atoms or ions are aligned in a way that they oppose each other, resulting in a net magnetic moment close to zero.
• Electron Configuration: Occurs when there are unpaired electrons and a specific arrangement that leads to opposing alignments.
• Response to Magnetic Field: Weakly attracted by an external magnetic field, but their magnetic susceptibility is generally lower than that of paramagnetic materials.
• Temperature Dependence: Antiferromagnetism is observed below a certain temperature, called the Néel Temperature ($T_N$). Above $T_N$, the material becomes paramagnetic.
• Examples: Manganese(II) oxide ($MnO$), Iron(II) oxide ($FeO$), Nickel(II) oxide ($NiO$).

Ferrimagnetism:

• Cause: Ferrimagnetic materials have magnetic moments that are aligned in opposite directions, similar to antiferromagnetic materials, but the opposing moments are unequal in magnitude. This results in a net magnetic moment, and thus they exhibit spontaneous magnetism, similar to ferromagnetism but generally weaker.
• Electron Configuration: Occurs in compounds with different types of ions or ions with different magnetic moments arranged in opposing magnetic sublattices.
• Response to Magnetic Field: Strongly attracted by an external magnetic field and can retain magnetism, but generally weaker than ferromagnetic materials.
• Temperature Dependence: Ferrimagnetic materials also exhibit a transition temperature (similar to Curie temperature) above which they become paramagnetic.
• Examples: Ferrites (e.g., $Fe_3O_4$, Magnetite; $NiFe_2O_4$, $MgFe_2O_4$). These are ceramic materials with mixed metal oxides.