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 μr is also used to characterize magnetic materials
(2.6)
so
(2.7)
for linear isotropic materials.
Ferromagnetism
Whilst we will consider (in Chapter 3) the possible consequences of biological effects based upon the dia‐ and para‐ magnetic properties of biological structures, ferromagnetic is the most important class of materials for safety within the MR environment due to the strong magnetic forces. Before we consider these, we need to understand more about ferromagnetism. Figure 2.10 shows how the magnetic domains of a ferromagnetic material may align. In the absence of a magnetic field the domains are randomly orientated with no overall magnetization. When an external B‐field (or H) is applied, the domains align and the material becomes highly magnetized. Some materials will retain their magnetism once the external field is removed – these are known as hard ferromagnetic materials, becoming permanent magnets when magnetized. Soft magnetic materials do not retain their domains’ alignment once the external field is removed, or do so to a minor extent which we will neglect.
Figure 2.10 Domains in a ferromagnetic material as the external field is increased from zero to the saturation point.
The B‐field in the material increases in the presence of an external field H (or B). The slope of the curve gives the magnetic permeability μ, its value depending upon the strength of H applied. For low values of external field, the magnetization is reversible. Above the saturation point the material becomes unable to sustain a higher magnetization no matter how large the applied field is. This material is magnetically saturated. For most ferromagnetic materials this occurs below 1.5 T, so it is likely that a potential projectile will be saturated when very close to the magnet bore entrance. Figure 2.11 shows the B‐H curve for series 416 stainless steel, a material commonly used in domestic goods. Also shown is the dependence of its magnetic permeability μ upon the external field H.
Figure 2.11 B‐H curve for 416 stainless steel (blue line) and its magnetic permeability μ (red line). μ is a function of H. The metal saturates at 1.85 T. The external field H = B0/μ0.
As the applied H‐field is reduced (or the material is removed from the external B0‐field of your magnet) the internal B within the material decreases. Due to hysteresis, it does not decrease exactly along the path of its increase (Figure 2.12). With a hard ferromagnetic material significant B remains once the external field has been reduced to zero. This is known as the remanence, Brem. Permanent magnets have high remanence. If the H is applied in the opposite direction (i.e. is made negative) the material’s B continues to fall. The intercept Hc on the ‐H axis is called the coercivity. Soft materials have low coercivity and remanence with a slim B‐H (or M‐H) curve. In hard ferromagnetic materials both are large and the hysteresis curve is broader. Above the Curie temperature, metals lose their ferromagnetic properties. Values of Bsat, Hc and Curie temperatures are shown in Table 2.2.
Figure 2.12 The hysteresis curve for a ferromagnetic material. The orange line represents increases in field which are reversible. Soft ferromagnetic materials have a slim curve with low remanence and coercivity. Hard ferromagnetic materials have a broader curve with higher remanence and coercivity.
Table 2.2 Properties of ferromagnetic metals.
| Soft Ferromagnetic | HC (A M−1) | Bsat (T) | Curie temperature (K) |
| Silicon steel | 40–70 | 2.0 | 750 |
|
Mumetal (Ni-Fe
|