Читать книгу Materials for Biomedical Engineering - Mohamed N. Rahaman - Страница 150

Diamagnetism and paramagnetism are weak forms of magnetism and, consequently, materials that show these two types of behavior are often considered nonmagnetic. Certain materials that contain paramagnetic atoms or ions, however, do show a strong permanent magnetization even in the absence of a magnetic field. This type of response, called ferromagnetism, is shown by materials composed of atoms of certain transition elements such as iron and cobalt, and certain rare earth elements such as gadolinium. In ferromagnetic materials, a special type of coupling occurs between adjacent atoms, resulting in cooperative alignment of their magnetic moment throughout the crystal. This coupling is purely a quantum mechanical effect that cannot be adequately explained in terms of classical physics. It leads to a high net magnetic moment of the material even in the absence of a magnetic field. Ferromagnetism is a property not just of the individual atoms but is a result of the interaction of each atom with its neighbors in the crystal lattice of the solid. Although the magnetization can vary with the magnetic field, magnetic susceptibility χ_m values as high as 10⁶ are possible for ferromagnetic materials.

Another property of ferromagnetism is that each grain in a polycrystalline material (or the whole crystal of a single crystalline material) is made up of a number of magnetic domains, tiny regions in which the atomic dipoles are essentially perfectly aligned. These domains are originally oriented in such a way that they cancel each other as far as their external magnetic effects are concerned (Figure 4.19a). However, when a ferromagnetic material is subjected to an applied magnetic field of gradually increasing strength, the domains that are favorably oriented grow at the expense of those that are not, and the material becomes highly magnetized (Figure 4.19b).

Figure 4.19 Schematic illustration of magnetic domains in a ferromagnetic material: (a) Randomly oriented domains in an unmagnetized material. (b) The domains become oriented upon application of a magnetic field, resulting in a highly magnetized material. Each arrow represents a huge number of atoms.

The maximum possible magnetization of a ferroelectric material, called the saturation magnetization M_max, corresponds to the magnetization that would result if all the atomic dipoles of the material were completely aligned with the magnetic field. There is also a saturation magnetic flux density, B_max (Eq. (4.40)). For the transition metal atoms (those with a partially filled d electron subshell), the contribution from the orbital angular momentum is negligible and, thus, the magnetic moment of the atom is determined by the number of unpaired electrons. Consequently, in the transition metals where the 3d shells of the atoms are partially filled, we can determine the magnetic moment of the atoms by filling the 3d shell with aligned spins up to a maximum of five beyond which the spins must have an opposite or antiparallel alignment to the first five. This is required by the Pauli exclusion principle. In the iron (Fe) atom, for example, the net number of unpaired electrons is four and, thus, the net magnetic moment of the atom is 4 μ_B, where μ_B is the Bohr magneton. Experimental magnetization curves of M (or B) versus H show a saturation magnetization that is lower than the ideal value due to microstructural factors and pinning of the domain walls by defects such as grain boundaries.