Solved Examples: Finding the Curie Temperature of Different Materials

📚 Quick Study Guide

• 🌡️ The Curie temperature ($T_c$) is the temperature at which a ferromagnetic material transitions to paramagnetic behavior. Above $T_c$, the material loses its spontaneous magnetization.
• ⚛️ Ferromagnetism arises from the alignment of atomic magnetic moments. In paramagnetism, these moments are randomly oriented.
• 🧲 The Curie temperature is material-specific. For example, Iron (Fe) has a $T_c$ of 1043 K, Nickel (Ni) has a $T_c$ of 627 K, and Cobalt (Co) has a $T_c$ of 1388 K.
• 📐 The temperature dependence of magnetization ($M$) near the Curie temperature follows a power law: $M \propto (T_c - T)^{\beta}$, where $\beta$ is a critical exponent.
• 📈 Factors affecting $T_c$ include: material composition, crystal structure, and applied pressure.
• 🧪 Experimental methods for determining $T_c$ involve measuring magnetization as a function of temperature using techniques like SQUID magnetometry.

Practice Quiz

1. Which of the following best describes the Curie temperature?
   1. (A) The temperature at which a superconductor loses its superconductivity.
   2. (B) The temperature at which a ferromagnetic material becomes paramagnetic.
   3. (C) The temperature at which water boils.
   4. (D) The temperature at which a paramagnetic material becomes ferromagnetic.
2. What happens to the magnetic moments in a ferromagnetic material above its Curie temperature?
   1. (A) They align perfectly.
   2. (B) They become randomly oriented.
   3. (C) They disappear entirely.
   4. (D) They become stronger.
3. What is the approximate Curie temperature of Iron (Fe)?
   1. (A) 298 K
   2. (B) 627 K
   3. (C) 1043 K
   4. (D) 1388 K
4. Which factor does NOT significantly affect the Curie temperature of a material?
   1. (A) Material composition
   2. (B) Crystal structure
   3. (C) Applied pressure
   4. (D) Color of the material
5. Near the Curie temperature, the magnetization ($M$) is proportional to $(T_c - T)^{\beta}$. What is $\beta$ called?
   1. (A) Curie constant
   2. (B) Critical exponent
   3. (C) Boltzmann constant
   4. (D) Proportionality constant
6. Which experimental technique is commonly used to measure the magnetization of a material as a function of temperature to determine its Curie temperature?
   1. (A) Optical microscopy
   2. (B) SQUID magnetometry
   3. (C) X-ray diffraction
   4. (D) Atomic force microscopy
7. Compared to Iron and Nickel, Cobalt has:
   1. (A) A lower Curie temperature.
   2. (B) A similar Curie temperature.
   3. (C) A higher Curie temperature.
   4. (D) No Curie temperature.