Читать книгу Essentials of MRI Safety - Donald W. McRobbie - Страница 63

The previous section showed how a B‐field can be generated in free space or air. Now we consider how materials or physical media respond to an external magnetic field. At the atomic level the electrons in their shells orbiting the nucleus have intrinsic magnetic moments. In most atoms the magnetic moments from the electrons’ spin and orbital motion cancel. This is diamagnetism, the default “non‐magnetic” state. If the cancellation is incomplete then the material is paramagnetic. In ferromagnetic ¹ materials, such as iron or steel, the electron spins become aligned in large groups or domains and their effect is significantly greater. Figure 2.9 shows the magnetic susceptibility spectrum covering a range of materials [1]. This is an enormous range extending over ten orders of magnitude (10¹⁰); each step in the chart represents a factor of ten.

Figure 2.9 Magnetic susceptibility spectrum.

When an object is placed in an external magnetic field, it becomes magnetized. Each of the types of material: dia‐, para‐, and ferromagnetic behave differently in the field, but because of Maxwell’s equations, the underlying physics is similar. In an external field, the magnetization of the material M (a vector) is

(2.4)

H is the magnetic field strength (A m⁻¹) and χ is the magnetic susceptibility which is dimensionless². Table 2.1 shows some values of χ_. In isotropic media χ is independent of orientation or position and is a simple scalar number. If the material is linear and isotropic we can say

(2.5)

Table 2.1 Magnetic susceptibility of common materials.

Type of material	Behavior	Material	χ1
Diamagnetic	M opposes H and external B0. Repulsive force.	Water and soft tissueCortical boneDe‐oxygenated red blood cellsCopperSuperconductors	–9.05×10−6 –8.86×10−6 –6.52 ×10−6 –9.63×10−6 –1
Paramagnetic	M parallel to H and external B0. Attractive force.	AirMagnesiumAluminiumTitaniumCoCrMo alloy	0.36 ×10−6 11.7×10−6 20.7×10−6 182×10−6 920×10−6
Ferromagnetic	M parallel to H and external B0. Strong attractive force. Can become permanently magnetized. Displays hysteresis.	Martensitic stainless steelSilicon steelMumetalPure iron	~ 103 103–104 104–105 ~105

1 Values from [1,2]

The total field within the material is the sum of the external field plus the field resulting from the magnetization of the material.

The relative permeability μ_r is also used to characterize magnetic materials

(2.6)

so

(2.7)

for linear isotropic materials.