What are the specific physical meanings of parameters such as residual magnetism (Br), coercive force (Hc), and maximum magnetic energy product (BHmax)? How to judge the quality of magnets through these parameters?

1. Residual Magnetism (Br)

Physical Meaning

Residual magnetism (Br), also called remanence, is the magnetic flux density (B) remaining in a magnet after it has been magnetized to saturation and then the external magnetic field (H) is reduced to zero. It is measured in Tesla (T) or Gauss (G) (1 T = 10,000 G).

• Origin: Br arises from the alignment of magnetic domains in the material during magnetization. When the external field is removed, some domains remain aligned due to strong magnetocrystalline anisotropy and exchange interactions, retaining a net magnetic moment.
• Significance: Br represents the magnet's "output strength" in the absence of an external field. A higher Br means the magnet can generate a stronger magnetic field without assistance.

Factors Affecting Br

• Material composition: Pure Nd₂Fe₁₄B has a high Br (~1.3–1.4 T), but alloying with Dy or Tb can slightly reduce Br while improving coercivity.
• Crystal structure: The tetragonal structure of NdFeB provides strong uniaxial anisotropy, enhancing Br.
• Microstructure: Grain size, orientation, and defects influence domain alignment. Single-crystal or highly oriented polycrystalline magnets exhibit higher Br.
• Temperature: Br decreases with increasing temperature due to thermal agitation disrupting domain alignment.

Typical Values

• NdFeB (N52 grade): Br ≈ 1.45–1.50 T
• SmCo (2:17 type): Br ≈ 1.00–1.15 T
• Ferrite (SrFe₁₂O₁₉): Br ≈ 0.35–0.45 T

2. Coercive Force (Hc)

Physical Meaning

Coercive force (Hc) is the external magnetic field (H) required to reduce the residual magnetism (Br) to zero after saturation. It is measured in A/m or Oersted (Oe) (1 A/m ≈ 0.0125 Oe).

• Types:
  • Normal coercivity (Hcb): The field needed to demagnetize the magnet along its easy axis (c-axis in NdFeB).
  • Intrinsic coercivity (Hci): The field required to reverse the magnetization of individual grains, reflecting the material's resistance to irreversible demagnetization. Hci is always ≥ Hcb.
• Significance: Hc determines the magnet's ability to resist demagnetization from external fields, thermal fluctuations, or mechanical stress. A high Hc is crucial for applications involving reverse fields or high temperatures.

Factors Affecting Hc

• Magnetocrystalline anisotropy: Materials with high anisotropy (e.g., NdFeB, SmCo) have higher Hc.
• Grain boundary phase: In sintered NdFeB magnets, the Nd-rich grain boundary phase isolates grains, reducing intergranular exchange coupling and increasing Hc.
• Heavy rare-earth (HRE) doping: Adding Dy or Tb forms (Nd,Dy)₂Fe₁₄B phases with higher anisotropy, boosting Hci.
• Temperature: Hc decreases with temperature due to reduced anisotropy energy barriers.

Typical Values

• NdFeB (N52 grade): Hcb ≈ 955 kA/m (12 kOe), Hci ≈ 2100 kA/m (26.4 kOe)
• SmCo (2:17 type): Hcb ≈ 796 kA/m (10 kOe), Hci ≈ 1592 kA/m (20 kOe)
• Ferrite: Hcb ≈ 159–239 kA/m (2–3 kOe)

3. Maximum Magnetic Energy Product (BHmax)

Physical Meaning

The maximum magnetic energy product (BHmax) is the peak value of the product of magnetic flux density (B) and magnetic field strength (H) on the demagnetization curve (B-H curve). It is measured in J/m³ or MGOe (1 MGOe ≈ 7.96 kJ/m³).

• Physical Interpretation: BHmax represents the maximum energy stored in the magnetic field per unit volume. A higher BHmax means the magnet can deliver more mechanical work (e.g., in motors) or sustain a stronger field with less material.
• Calculation: BHmax is found by multiplying B and H at each point on the demagnetization curve and identifying the maximum value.

Significance

• Efficiency: BHmax is the most critical parameter for evaluating magnet performance. A magnet with high BHmax requires less volume to achieve the same field strength, saving space and weight.
• Cost-effectiveness: Higher BHmax magnets often justify their higher cost due to reduced material usage.

Factors Affecting BHmax

• Br and Hc balance: BHmax is maximized when the magnet operates near the "knee" of the demagnetization curve, where both B and H are high. This requires an optimal balance between Br and Hc.
• Material purity: Impurities reduce BHmax by introducing defects that disrupt domain alignment.
• Manufacturing process: Hot pressing, die-upsetting, or grain boundary diffusion can enhance BHmax by improving microstructural uniformity.

Typical Values

• NdFeB (N52 grade): BHmax ≈ 400–420 kJ/m³ (50–52 MGOe)
• SmCo (2:17 type): BHmax ≈ 240–280 kJ/m³ (30–35 MGOe)
• Ferrite: BHmax ≈ 28–36 kJ/m³ (3.5–4.5 MGOe)

4. Judging Magnet Quality Using These Parameters

Key Criteria

1. High Br: Indicates strong magnetic field generation.
2. High Hc (especially Hci): Ensures resistance to demagnetization.
3. High BHmax: Reflects overall energy density and efficiency.

Trade-offs and Optimization

• Br vs. Hc: Increasing Hc (e.g., by adding Dy) often reduces Br due to the lower magnetic moment of Dy compared to Nd. Manufacturers must balance these for specific applications.
• Temperature stability: High-temperature magnets (e.g., for electric vehicle traction motors) prioritize Hci over Br, accepting slightly lower BHmax.
• Cost constraints: High-performance NdFeB magnets (e.g., N52SH grade) are expensive due to HRE additions. Lower-grade magnets (e.g., N35) may suffice for less demanding applications.

Demagnetization Curve Analysis

The B-H curve (or hysteresis loop) provides a complete picture of magnet performance:

• Squareness ratio (Br/Bsat): A ratio close to 1 indicates minimal domain wall movement, reflecting high coercivity.
• Reversibility: A linear B-H curve near the origin suggests good thermal stability.
• Knee point: The BHmax occurs near the "knee" where the curve bends sharply downward, indicating the onset of irreversible demagnetization.

Practical Examples

• Electric vehicle motors: Require high BHmax (>400 kJ/m³) and Hci (>2000 kA/m) to operate efficiently at elevated temperatures.
• Speaker magnets: Prioritize high Br (>1.2 T) for strong sound output, with moderate Hc (~800 kA/m).
• Refrigerator seals: Use low-cost ferrite magnets with sufficient Br (~0.3 T) and Hc (~200 kA/m) for basic magnetic holding.

5. Advanced Considerations

Temperature Coefficients

• Br temperature coefficient (α): Typically -0.12 to -0.10 %/°C for NdFeB, meaning Br decreases by ~1% per 10°C rise.
• Hc temperature coefficient (β): More negative than α (e.g., -0.6 %/°C for NdFeB), making Hc highly temperature-sensitive.
• Compensation: High-temperature grades (e.g., N52SH) use HRE doping to reduce β.

Corrosion Resistance

• NdFeB is prone to oxidation due to its reactive Nd content. Coatings (Ni, Zn, epoxy) or alloying with Cu/Al improve durability but do not affect Br, Hc, or BHmax directly.

Mechanical Properties

• Brittle materials like NdFeB require careful handling during assembly. Flexible magnets (e.g., bonded NdFeB) trade off some BHmax for improved machinability.

Conclusion

The parameters Br, Hc, and BHmax are fundamental to evaluating permanent magnet quality:

• Br determines field strength.
• Hc ensures resistance to demagnetization.
• BHmax reflects overall energy density and efficiency.

High-quality magnets optimize these parameters for specific applications, balancing trade-offs between performance, temperature stability, and cost. Advanced techniques like grain boundary diffusion and additive manufacturing continue to push the limits of magnet performance, enabling innovations in renewable energy, transportation, and medical technologies. Understanding these parameters is essential for selecting the right magnet for any given application.