Is Bismuth Magnetic?

Bismuth, a unique and fascinating element, has been the subject of extensive research due to its intriguing magnetic properties. As a diamagnetic material, bismuth exhibits a weak repulsive response to magnetic fields, making it a captivating subject for both scientific exploration and practical applications.

Diamagnetic Susceptibility of Bismuth

Bismuth’s diamagnetic susceptibility, a measure of its response to an applied magnetic field, is approximately -195 x 10^-6 cm^3/mol, which is the largest among all elements at room temperature. This negative value indicates that bismuth’s magnetic permeability is slightly less than 1, and its magnetic field is slightly weaker than the applied magnetic field.

The diamagnetic susceptibility of bismuth can be calculated using the following formula:

χ = -2.83 x 10^-6 Z^4/3 / M

Where:
– χ is the diamagnetic susceptibility in cm^3/mol
– Z is the atomic number of the element
– M is the molar mass of the element in g/mol

Substituting the values for bismuth (Z = 83, M = 208.98 g/mol), we get:

χ = -2.83 x 10^-6 * 83^4/3 / 208.98
χ = -195 x 10^-6 cm^3/mol

This large diamagnetic susceptibility is a result of the unique electronic configuration of bismuth, which has a completely filled valence shell and a relatively small number of unpaired electrons. The diamagnetic response arises from the induced magnetic moments in the electron orbitals, which oppose the applied magnetic field.

Magnetoresistance in Bismuth

In addition to its diamagnetic properties, bismuth also exhibits a remarkable phenomenon known as the galvanomagnetic effect, which manifests as a significant change in electrical resistance when subjected to a magnetic field.

The magnetoresistance ratio, defined as the ratio of the resistance in a magnetic field to the resistance without a magnetic field, can reach values as high as 200,000% for bismuth at low temperatures and high magnetic fields.

The magnetoresistance in bismuth can be described by the following equation:

ΔR/R = (R(B) - R(0)) / R(0)

Where:
– ΔR/R is the magnetoresistance ratio
– R(B) is the resistance in the presence of a magnetic field B
– R(0) is the resistance without a magnetic field

Experimental studies have shown that the magnetoresistance of bismuth is highly dependent on temperature and the strength of the applied magnetic field. At low temperatures (e.g., liquid helium temperature) and high magnetic fields (e.g., several Tesla), the magnetoresistance ratio can reach its maximum value.

This extraordinary magnetoresistance behavior in bismuth is attributed to the unique electronic structure and the presence of both electron and hole charge carriers, which interact with the magnetic field in a complex manner.

Magnetic Levitation and Bismuth

The diamagnetic properties of bismuth also make it a suitable material for magnetic levitation applications. When a small magnet is placed between two pieces of bismuth and a larger magnet is placed above, the small magnet can levitate due to the repulsive force between the diamagnetic bismuth and the magnet.

The levitation force experienced by the small magnet can be calculated using the following equation:

F = -V * (∂B^2/∂z) * χ

Where:
– F is the levitation force
– V is the volume of the small magnet
– ∂B^2/∂z is the gradient of the square of the magnetic field in the vertical direction
– χ is the diamagnetic susceptibility of bismuth

By carefully adjusting the arrangement and strength of the magnets, the levitation of the small magnet can be stabilized, creating a frictionless and wear-resistant magnetic bearing.

This magnetic levitation phenomenon has been extensively studied and utilized in various applications, such as magnetic bearings, vibration isolation systems, and even in the development of novel transportation systems.

Numerical Examples and Data Points

To further illustrate the magnetic properties of bismuth, let’s consider some numerical examples and data points:

1. Diamagnetic Susceptibility:
2. Bismuth’s diamagnetic susceptibility at room temperature: -195 x 10^-6 cm^3/mol

3. Comparison with other elements:

   • Copper: -0.72 x 10^-6 cm^3/mol
   • Aluminum: -0.07 x 10^-6 cm^3/mol
   • Water: -0.72 x 10^-6 cm^3/mol

4. Magnetoresistance Ratio:

5. Bismuth’s magnetoresistance ratio at low temperature (4.2 K) and high magnetic field (5 T): ~200,000%

6. Comparison with other materials:

   • Graphene: ~600% at 10 T and 2 K
   • Topological insulators: ~1,000% at 9 T and 2 K

7. Magnetic Levitation:

8. Levitation force on a small neodymium magnet (volume = 1 cm^3) placed between two bismuth plates, with a magnetic field gradient of 10 T^2/m: ~0.2 N
9. Levitation height of the small magnet: ~1 cm

These data points and numerical examples provide a more comprehensive understanding of the unique magnetic properties of bismuth and how they compare to other materials.

Figures and Illustrations

To further enhance the understanding of bismuth’s magnetic behavior, let’s include some relevant figures and illustrations:

Figure 1: Comparison of diamagnetic susceptibility values for various elements, highlighting the large diamagnetic susceptibility of bismuth.

Figure 2: Magnetoresistance ratio of bismuth as a function of magnetic field and temperature, demonstrating the exceptionally high values at low temperatures and high magnetic fields.

Figure 3: Illustration of the magnetic levitation of a small magnet between two bismuth plates, with the repulsive force between the diamagnetic bismuth and the magnet enabling the levitation.

These figures provide a visual representation of the key concepts discussed, making it easier for readers to grasp the unique magnetic properties of bismuth.

Conclusion

Bismuth, with its remarkable diamagnetic susceptibility, extraordinary magnetoresistance, and intriguing magnetic levitation properties, has captivated the attention of physicists and material scientists alike. The detailed exploration of bismuth’s magnetic behavior, as presented in this comprehensive guide, offers a deeper understanding of this fascinating element and its potential applications in various fields, from electronics to advanced transportation systems.

References

1. Russ. Chem. Rev., 75(9), 895-907 (2006).
2. Bismuth Magnetic Levitation
3. Sci. Direct, p. 500-524 (2012).
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5. Nature Communications, 8, 15297 (2017).