(a) Classify diamagnetic, paramagnetic and ferromagnetic materials in terms of their magnetic susceptibility (χ). Plot and…

(a) Magnetic materials and susceptibility

Susceptibility is defined by χ = M/H.

Classification by susceptibility. Diamagnetic materials have no permanent atomic moment; the applied field induces a weak opposing moment, so χ is small and negative (χ < 0), typically −10⁻⁵, and is essentially independent of temperature. Paramagnetic materials possess permanent moments that are randomly oriented by thermal agitation; the field partially aligns them, giving a small positive χ (≈10⁻³–10⁻⁵) that falls as temperature rises, following the Curie law χ = C/T. Ferromagnetic materials have strongly coupled moments that align spontaneously below the Curie temperature T_C, giving χ ≫ 0 and very large (10²–10⁶); above T_C they obey the Curie–Weiss law χ = C/(T − θ), where the paramagnetic Curie temperature θ is close to (slightly above) T_C. Examples: Cu, Bi and water (diamagnetic); Al, Pt and O₂ (paramagnetic); Fe, Co and Ni (ferromagnetic).

Variation of 1/χ with T. For a diamagnet, 1/χ is a horizontal line at a negative value, since χ is constant and negative. For a paramagnet, 1/χ = T/C, a straight line passing through the origin with slope 1/C. For a ferromagnet, above T_C, 1/χ = (T − T_C)/C, a straight line extrapolating to intercept T_C on the temperature axis; below T_C the relation breaks down as domains align spontaneously. The intercept thus directly yields the Curie temperature.

The 1/χ versus T behaviour is plotted below:

(b) X-ray diffraction

X-ray diffraction. When monochromatic X-rays of wavelength λ strike a crystal, they scatter from parallel atomic planes of spacing d; constructive interference occurs when the path difference satisfies Bragg's law, nλ = 2d sinθ. In the powder method, randomly oriented crystallites give cones of diffracted intensity recorded as peaks of 2θ.

Structure determination. Each peak corresponds to a set of planes (hkl). Using Bragg's law, d is obtained from θ; the d-spacings and systematic absences (from the structure factor) reveal the lattice type (SC, BCC, FCC) and, via indexing, the lattice parameter a. Intensities give atomic positions. Comparison with standard JCPDS (ICDD) tables identifies the phase. For cubic crystals, sin²θ ∝ (h² + k² + l²); for example, FCC shows only reflections with h, k, l all odd or all even (111, 200, 220 ...), and BCC only those with h + k + l even (110, 200, 211 ...). Peak broadening also gives crystallite size through the Scherrer equation.

(c)(i) Microprocessor

Microprocessor. A microprocessor is the CPU fabricated on a single chip. Its blocks are the ALU (arithmetic/logic), control unit (timing and control signals), register array (accumulator, program counter, instruction register), and internal buses, interfaced to memory and I/O through address, data and control buses. It repeatedly executes the fetch–decode–execute cycle: fetch the instruction from memory, decode it in the control unit, execute it in the ALU, and store the result.

The internal block arrangement is shown below:

(c)(ii) Thermistors vs solar cells

Thermistors vs solar cells. A thermistor is a metal-oxide semiconductor whose resistance changes sharply with temperature (usually negative coefficient); it is a two-terminal resistive device. A solar cell is a p–n junction with a depletion region; photons create electron–hole pairs that the built-in field separates, producing a photovoltage (photovoltaic effect). Thermistors are passive sensors that need an external current and sense temperature; solar cells are active sources that convert light to electricity. A thermistor's resistance change comes from thermally generated carriers (NTC) or a structural transition (PTC), while a solar cell is characterised by its I–V curve, open-circuit voltage, short-circuit current, fill factor and efficiency.