Unit 5 | Engineering Physics Notes | AKTU Notes

UNIT 5: Superconductors and Nano-Materials

PART A: SUPERCONDUCTORS

5.1 Temperature Dependence of Resistivity in Superconducting Materials

In normal conductors (like copper), electrical resistance decreases as temperature decreases — but never reaches zero.

In superconductors, something remarkable happens:

• When cooled below a specific temperature called the Critical Temperature (Tc), the electrical resistance drops suddenly and completely to zero.
• Below Tc, the material becomes a superconductor — it conducts electricity with absolutely zero resistance.

Discovery:

• First discovered by Heike Kamerlingh Onnes in 1911 in mercury (Hg).
• Tc of mercury = 4.2 K (−268.8°C).

Critical Temperature (Tc) of some materials:

Material	Critical Temperature (Tc)
Mercury (Hg)	4.2 K
Lead (Pb)	7.2 K
Niobium (Nb)	9.2 K
YBCO (ceramic)	~92 K
HgBaCaCuO	~133 K

5.2 Meissner Effect

The Meissner Effect is one of the most striking properties of superconductors.

What it is:

• When a material becomes superconducting (below Tc), it completely expels all magnetic field from its interior.
• The superconductor becomes a perfect diamagnet — it repels magnetic fields.
• Inside a superconductor: B = 0 always (even if an external field is applied).

How it works:

• Surface currents are induced in the superconductor that exactly cancel the external magnetic field inside.

Demonstration — Magnetic Levitation:

• A magnet placed above a superconductor floats in air — the superconductor repels the magnetic field of the magnet, pushing it upward.
• This is called Maglev — used in maglev trains.

Difference from perfect conductor:

• A perfect conductor (zero resistance) would maintain whatever magnetic flux was inside when it became perfect.
• A superconductor always expels all flux, regardless — this is unique to superconductors.

5.3 Temperature Dependence of Critical Field

A superconductor loses its superconductivity if the applied magnetic field exceeds a critical value called the Critical Magnetic Field (Hc).

• The critical field depends on temperature.
• At T = 0 K: Hc is maximum (Hc₀).
• As temperature increases toward Tc: Hc decreases.
• At T = Tc: Hc = 0 (superconductivity vanishes even without any field).

Formula:

• Hc(T) = Hc₀ [1 − (T/Tc)²]
• This is a parabolic relationship between Hc and T.

5.4 Persistent Current

• If a current is set up in a superconducting ring (below Tc), it flows indefinitely without any energy source.
• This is called a persistent current.
• Since resistance = 0, there is no energy dissipation (no heating) — the current never dies out.
• Experiments have shown persistent currents lasting for years without any measurable decay.
• Application: Superconducting electromagnets that maintain field permanently with no power input.

5.5 Type I and Type II Superconductors

Type I Superconductors:

• Have a single critical field Hc.
• Below Hc: Complete superconductor (R = 0, B = 0 inside — complete Meissner effect).
• Above Hc: Suddenly becomes normal conductor — superconductivity completely disappears.
• Usually pure metals: Lead, Mercury, Aluminum, Tin.
• Critical fields are very low — not suitable for high-field applications.

Type II Superconductors:

• Have two critical fields — lower critical field Hc₁ and upper critical field Hc₂.
• Below Hc₁: Complete superconductor (perfect Meissner effect).
• Between Hc₁ and Hc₂: Mixed state (or vortex state) — magnetic field partially penetrates in quantized flux tubes (vortices). Still has zero resistance.
• Above Hc₂: Normal conductor.
• Usually alloys and compounds: YBCO, Nb₃Sn, NbTi.
• Hc₂ can be very high (tens of Tesla) — suitable for powerful electromagnets.

Property	Type I	Type II
Critical Fields	One (Hc)	Two (Hc₁ and Hc₂)
Meissner Effect	Complete	Complete below Hc₁, partial between Hc₁ and Hc₂
Materials	Pure metals	Alloys and compounds
Critical Field Value	Low	Very high (up to 50 T)
Applications	Limited	MRI machines, particle accelerators

5.6 High Temperature Superconductors

• Traditional superconductors work only at very low temperatures (near absolute zero) — needed expensive liquid helium cooling.
• In 1986, Bednorz and Müller discovered ceramic superconductors that work at higher temperatures — they won the Nobel Prize in 1987.
• These are called High Temperature Superconductors (HTS).
• Example: YBCO (Yttrium Barium Copper Oxide) — Tc ≈ 92 K — works with cheap liquid nitrogen (77 K).
• Current record: HgBaCaCuO — Tc ≈ 133 K at atmospheric pressure.
• Goal: Room temperature superconductor (still not achieved — active research area).

5.7 Properties and Applications of Superconductors

Properties:

• Zero electrical resistance below Tc.
• Complete expulsion of magnetic field (Meissner effect).
• Persistent currents.
• Quantization of magnetic flux.
• Josephson effect (quantum tunneling of Cooper pairs).

Applications:

• MRI Machines: Medical imaging uses superconducting magnets to produce strong, stable magnetic fields.
• Maglev Trains: Magnetic levitation using superconductors — trains float above the track with no friction → very high speeds (Japan's Maglev: 600 km/h).
• Particle Accelerators: CERN's Large Hadron Collider uses superconducting magnets to guide particles.
• Power Transmission: Superconducting cables can transmit electricity with zero loss.
• SQUID: Superconducting Quantum Interference Device — extremely sensitive magnetometer for detecting tiny magnetic fields (used in brain scanning — MEG).
• Josephson Junctions: Used in ultra-sensitive voltage and frequency standards.
• Energy Storage: Superconducting Magnetic Energy Storage (SMES) stores energy in magnetic field of superconducting coil.

PART B: NANO-MATERIALS

5.8 Introduction and Properties of Nano-Materials

Nano-materials are materials with at least one dimension in the nanometer scale (1–100 nm).

• 1 nanometer = 10⁻⁹ meter (1 billionth of a meter).
• For comparison: A human hair is about 80,000 nm wide. A DNA molecule is about 2 nm wide.

Why nano-materials are special:

• At nanoscale, materials show completely different properties from their bulk (large) form.
• Gold in bulk is yellow and inert. Gold nanoparticles can be red, orange, or blue depending on size — and are chemically active.

Reasons for unique properties:

• High surface area to volume ratio: As size decreases, the fraction of atoms on the surface increases dramatically. Surface atoms have different (more reactive) properties than interior atoms.
• Quantum confinement effects: At nanoscale, quantum mechanical effects become dominant — electrons are confined and energy levels become discrete (quantized).

Properties of Nano-materials:

• Optical properties: Different colors based on size (gold nanoparticles), enhanced optical absorption, fluorescence.
• Electrical properties: Can be conducting, semiconducting, or insulating depending on size and structure (e.g., carbon nanotubes).
• Magnetic properties: Bulk gold is non-magnetic but gold nanoparticles show magnetic behavior. Superparamagnetism in iron oxide nanoparticles.
• Mechanical properties: Carbon nanotubes are 100 times stronger than steel at 1/6th the weight.
• Chemical properties: Highly reactive due to large surface area — excellent catalysts.
• Thermal properties: Lower melting points than bulk material.

5.9 Basics of Quantum Dots, Quantum Wires, and Quantum Wells

These are structures where electrons are confined in 1, 2, or 3 dimensions — leading to quantized energy levels.

Quantum Well:

• Confinement in 1 dimension (like a thin layer/film).
• Electrons can move freely in 2 directions but are confined in 1 direction.
• Like a thin sandwich — electron is trapped between two layers.
• Used in: Laser diodes, LED displays, semiconductor transistors.

Quantum Wire:

• Confinement in 2 dimensions (like a thin wire or rod).
• Electrons can move freely in only 1 direction (along the wire).
• Example: Carbon nanotubes, semiconductor nanowires.
• Used in: Nano-sensors, nanoscale transistors.

Quantum Dot:

• Confinement in all 3 dimensions (like a tiny dot/box).
• Electrons have no free directions — completely trapped.
• Also called "artificial atoms" because energy levels are completely discrete (like a real atom).
• Size-tunable properties: By changing size of quantum dot, you can change its color (emission wavelength).
• Used in: QLED TV displays, solar cells, biological imaging, quantum computing.

Structure	Dimensions Confined	Free to Move In	Example
Quantum Well	1D confined	2 directions (plane)	Thin semiconductor film
Quantum Wire	2D confined	1 direction (along wire)	Carbon nanotube, nanowire
Quantum Dot	3D confined	None — fully confined	Semiconductor nanocrystals

5.10 Fabrication of Nano-Materials

There are two main approaches to making nano-materials:

1. Top-Down Approach:

• Start with a large bulk material and break it down (carve, cut, etch) into smaller nanostructures.
• Like sculpting — you remove material to get the desired shape.
• Think of it as: Big → Small.

CVD — Chemical Vapor Deposition (Top-Down method):

• A chemical vapor (gas) containing the desired material is passed over a heated substrate.
• The vapor reacts and deposits a thin film or nanostructure on the substrate.
• Widely used for making carbon nanotubes, graphene, silicon thin films.
• Steps: Vaporize source material → transport vapor to substrate → chemical reaction on substrate → deposit thin film → cool and collect.
• Advantages: Uniform coating, good control over thickness and composition.

2. Bottom-Up Approach:

• Start with individual atoms or molecules and build up nanostructures by assembling them piece by piece.
• Like building with LEGO blocks — atom by atom.
• Think of it as: Small → Big.

Sol-Gel Process (Bottom-Up method):

• A chemical solution (sol) containing the desired materials gradually converts into a gel-like network (gel).
• The gel is then dried and heated to get the final nanostructure material.
• Steps: Prepare sol (liquid) → Gelation (sol converts to gel) → Drying (remove solvent) → Calcination/Sintering (heat to get final product).
• Used for making: silica nanoparticles, metal oxide nanoparticles, ceramic coatings, optical fibers.
• Advantages: Low processing temperature, precise control of composition, can make complex shapes.

Parameter	Top-Down (CVD)	Bottom-Up (Sol-Gel)
Starting point	Bulk material broken down	Atoms/molecules built up
Direction	Big → Small	Small → Big
Control	Good for thin films	Excellent for composition
Cost	Higher equipment cost	Lower cost
Products	Carbon nanotubes, graphene	Silica nanoparticles, ceramics

5.11 Properties and Applications of Nano-Materials

Mechanical Applications:

• Carbon nanotube reinforced composites — ultralight, ultra-strong materials for aerospace and sports equipment.
• Nanocomposite coatings — hard, scratch-resistant coatings for tools and surfaces.

Electronics Applications:

• Nano-transistors — smaller and faster chips (Moore's law extension).
• Carbon nanotube transistors — replacement for silicon in future chips.
• Quantum dot displays (QLED TVs) — brighter, more energy efficient screens.
• Nano-memory — ultra-high density data storage.

Medical and Biomedical Applications:

• Drug delivery — nanoparticles carry drugs directly to tumor cells, reducing side effects of chemotherapy.
• Cancer treatment — gold nanoparticles absorb near-infrared light and heat up, destroying tumor cells (photothermal therapy).
• Diagnostic imaging — quantum dots and iron oxide nanoparticles as contrast agents for MRI and fluorescence imaging.
• Antibacterial coatings — silver nanoparticles kill bacteria on medical devices and hospital surfaces.

Energy Applications:

• High efficiency solar cells using quantum dots.
• Better batteries with nano-structured electrodes (higher capacity, faster charging).
• Hydrogen storage using carbon nanotubes and metal hydride nanoparticles.
• Nano-catalysts for fuel cells.

Environmental Applications:

• Nano-photocatalysts (like TiO₂ nanoparticles) to break down pollutants in water and air.
• Nano-filters for water purification.
• Nano-sensors to detect toxic chemicals at very low concentrations.

Defense and Security:

• Lightweight nanocomposite armor.
• Chemical and biological warfare agent detection using nano-sensors.
• Stealth coatings using nano-structured radar-absorbing materials.