alt="Schematic illustration of the domains in a ferromagnetic material as the external field is increased from zero to the saturation point."/>
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 alloy) | 0.6–1.0 | 0.77 | 350 |
| Iron | 12–400 | 1.7–2.2 | 770 |
| Nickel | 400 | 0.62 | 358 |
| 400 series stainless steels | 130–480 | 1.2–1.4 | – |
| Hard Ferromagnetic | |||
| 5% Chromium steel | 5×103 | 0.94 | 760–850 |
| Alnico (Al-Ni-Co alloy) | 50×103 | 0.56–1.35 | 973–1133 |
| Supermagloy (Sm-Co alloy) | 700×103 | 1.50 | 993–1073 |
Demagnetizing field and factors
An object’s shape adds a further layer of complexity with great significance for magnetic forces and torques, and hence for MRI safety. Figure 2.13 shows how magnetization of the object in an external B0 generates “virtual poles”, resulting in a “de‐magnetization field” which reduces the apparent value of susceptibility χapp:
(2.8)
Figure 2.13 Demagnetization field within objects magnetized by an external magnetic field: the flatter object (left) creates more ‘virtual poles’ and develops a greater degree of demagnetization.
where di is the demagnetizing factor. For simple shapes (ellipsoids of rotation, cuboids and cylinders) there are three demagnetizing factors: d1 along the principal axis, d2 and d3 along the minor axes. Representative values are shown in Table A1.1 in Appendix 1. Figure 2.14 shows the values of 1/d1 for the axial and 1/d2 (=1/d3) for the radial axes of cylindrical objects. It is the demagnetizing factor that determines the level of magnetization of a ferromagnetic object, rather than the value of χ. For an unsaturated sphere the internal B field is three times the external B0. For elongated objects the internal B can be significantly greater. As a simple rule of thumb, for a cylinder whose length is aligned with B0
