Hrdmagnetiska material permanent magnet materials Magnetiseras frst med

Hårdmagnetiska material / permanent magnet materials Magnetiseras först med stort magnetfält H 1 (ofta pulsat), när det yttre fältet är bortaget finns fortfarande det avmagnetiserande fältet Hd och arbetsinduktionen (-magnetiseringen) är Bd (Md)

Tillämpningar delas in i 3 kategorier i) elektrisk-till-mekanisk omvandling ii) mekanisk-till-elektrisk omvandling iii) magnetisk kraft

Hard magnetic materials Always used as passive component, the energy is stored in the material before use by applying and removing a large magnetic field, the magnetization is < MR after field removal. Desired properties: high (large magnetic anisotropy), high and high. Coercive field A material is classified as magnetically hard if Hc > 104 A/m, distinguish between I Hci defined by M vs. Hi curve and II Hc defined by B vs. Hi curve, Hc < Hci. Good permanent magnets like Nd 2 Fe 14 B or Sm. Co 5 have Hci ≥ 106 A/m. Remanence MR defined for closed magnetic circuit (no demagnetizing field), applications require open circuit → magnetization for a permanent magnet when used in an application always smaller than MR. Good permanent magnets like Nd 2 Fe 14 B or Sm. Co 5 MR ~ 106 A/m. Saturation magnetization Desired to have MR / Ms ~ 1, implies rectangular hysteresis curve. Nd 2 Fe 14 B have Ms ~ 1. 2 106 A/m.

Curie temperature Working temperature << Tc , otherwise (strongly) temperature dependent magnetic parameters, risc that the permanent magnet material ages and in the worst case the material will be demagnetized; producers give information. . . +- Energy product +- B, M Ampere's circulation law (i = 0) H ideal magnetic circuit, the core is a permanent magnet material and the field in the material is a demagnetizing field Field equations Energy/unit area in air-gap where B and H are the magnetic flux density and magnetic field in the material, respectively, B∙H is called energy product, SI unit is [J/m 3]. Note that CGS units: [M G Oe] 1 M G Oe = 7. 96 k. J/m 3

The working point for a permanent magnet in an application is always found in the second quadrant of the hysteresis curve (the magnetic field is a demagnetizing field). How large is the energy product for the ideal permanent magnet material with a “rectangular” hysteresis curve? m 0 M , B m 0 Ms B m 0 Hi -m 0 Ms/2 Maximum? The maximum energy product thus is

How large can the energy product become? Fe-Co alloy has Ms = 1. 96 106 A/m → J/m 3. Today we have reached k. J/m 3. To reach higher values, we must improve… The demagnetizing curve Defined as the second quadrant of the hysteresis curve, contains all information being important for a permanent magnet. Geometrical considerations determine the working point in an application, since the demagnetizing field is determined by the geometrical shape of the material. Two cases (i = 0): i) M vs. Hi ; ii) B vs. Hi ; B load line is called permeance coefficient working point Hi For B vs. Hi the load line is defined by = .

Demagnetizing curves, lines of constant energy product and permeance coefficients in the same figure How should one choose the permanent magnet material for a specific application? Always the material exhibiting the largerst ? No! Given a value for the permeance coefficient, choose the material exhibiting the largest energy product at the working point for the material! 0. 0244

Stoner-Wohlfarth model Model that was developed ~ 1950, guided the search for new permanent magnet materials at that time. Start out by assuming uniaxial anisotropy (magnetocrystalline or shape anisotropy) Ms easy axis q 2 a q 0 z H y q 0+p x 2 b and that the material is built up of single domain particles (implies a magnetization process governed only by. . . ) Uniaxial magnetocrystalline or shape anisotropy (lecture 4) In case of shape anisotropy, the anisotropy axis is given by the long axis and the anisotropy constant by

Back to the Stoner-Wohlfarth model. The total energy is for + fields - fields At equilibrium it holds + fields (1) - fields where . q thus determined is used to calculate the magnetization as Moreover, holds for energy minimum, and for – fields towards the field and decreases, instability for when rotates with increasing field.

where H 0 corresponds to the critical field. For every value of At the instability of , (1) and (2) can be written where … after some work we obtain Relation there exists a corresponding H 0.

Hysteresis curves for different q 0 M/Ms H/Han Starting condition, angle between field and easy axis of magnetization, field decreases from a large positive value: I. For positive fields, the magnetization first rotates reversibly away from the field direction; at zero field the magnetization is along the easy axis. II. For negative fields, the magnetization continues to rotate reversibly towards the field direction, when the field magnitude reaches the magnetization rotates irreversibly to a new equilibrium direction. III. Finally, there is a reversible rotation of the magnetization towards the applied field direction.

Ms Ms Ms H H ≈0 Ms Ms H H 0 Instabilt läge för Ms → irreversibel rotation IV. If the field decreases from a H Ms large negative value, the behavior of the magnetization is repeated and the irreversible rotation occurs at H Ms .

For a polycrystalline material consisting of grains exhibiting uniaxial anisotropy, averaging over a random distribution of (random with respect to…) yields By aligning the grains during fabrication (how? ), the coercive field can be increased to Grain aligning also yields a material exhibiting . The S-W model has been useful as a guide when researching for new permanent magnet materials and is also useful for e. g. magnetic storage media consisting of single domain magnetic particles. Modern permanent magnet materials are best explained by domain wall motion and/or nucleation of domains with reverse magnetization. Materials Alnico Was developed in ~ 1930, Fe-Co-Ni-Al alloy, small amount of other elements may also be used.

Steps in fabrication • heat to 1250 o. C to form a homogeneous solid solution • cool at a rate of ~ 1 o. C/sec to about 500 o. C • reheat at 600 o. C for a few hours Sintered bcc material, mixed two-phase material: I. Fe-Co phase strongly magnetic II. Ni-Al phase weakly magnetic/paramagnetic The magnetic properties can be improved by precipitation (step 2) in magnetic field and/or columnar growth of grains.

The a 2 phase pins domain walls; the a 1 phase consists of elongated single domain grains (long axis // [100]), l / d ~ 600 nm / 30 nm, shape anisotropy. Distinguish between isotropic (1 -4) and oriented Alnico (5 -9), oriented Alnico contain somewhat more Co, 20 -40 weight-%, and a small amount Ti, 5 -8 weight-% (increases Hc). Energy product for oriented Alnico is 40 -100 k. J/m 3, Alnico it is 5 -10 k. J/m 3, k. A/m, while for isotropic

Hard ferrites Developed in the 50'th (Stoner-Wohlfarth model), sintered material, hexagonal crystal structure and plate like grains with size ~ 1 mm, which is larger than the single domain limit, c-axis perpendicular to plate, magnetocrystalline anisotropy dominates, K 1 = 3. 3∙ 105 J/m 3. Most common are Ba. O-6 Fe 2 O 3 and Sr. O-6 Fe 2 O 3, cheap to produce – large industry. Larger Hc compared to Alnico, k. A/m, but smaller energy product k. J/m 3. coercivity governed by domain wall nucleation and motion Sm-Co Intensive research in the 60'th to find compounds based on rare-earth (4 f) and transition metal (3 d) elements, highest anisotropy for Co-RE, moreover higher Ms for light RE-elements.

Sm. Co 5 Tc = 720 o. C. m 0 MR ≈ 0. 9 T, m 0 Hc ≈1 T (m 0 Hci ≈ 2 T) and k. J/m 3 and Hexagonal crystal structure, sintered material, grain size 3 -10 mm, magnetocrystalline anisotropy dominates, experimental results obtained for single crystals (H // hard direction) show that Sm 2 Co 17 m 0 MR ≈ 1. 1 T, m 0 Hc ≈1 T and k. J/m 3, consists of bands of Sm. Co 5 separating regions of Sm. Co 17, higher Tc compared to pure Sm. Co 5 (Tc = 820 o. C). grains larger than the single domain limit

Coercivity controlled by nucleation of reverse domains or by pinning of domain walls, Sm. Co 5 is one example of nucleation controlled coercivity The Sm 2 Co 17 magnets consists of Sm. Co 5 bands separating regions of Sm 2 Co 17 Sm. Co 5 Sm 2 Co 17

Nd-Fe-B Was developed in the 80'th, Nd 2 Fe 14 B, the magnetic properties are sensitive to details of the fabrication process, two methods are commonly used: I. Sintered material with grain size ~ 3 mm and II. 'melt-spun' material with grain size 20 -80 nm. Tetragonal structure, strong magnetocrystalline anisotropy K 1 ≈ 5· 106 J/m 3. m. MR ≈1. 2 T, m 0 Hc ≈1 T (m 0 Hci ≈ 1 - 2 T) and k. J/m 3 for oriented material. One problem with this material is the comparably low Curie-temperature, Tc ≈ 300 o. C. tillsatser av Co och Dy vanliga. . .

Stability of permanent magnets against external field and temperature changes (page 495 -497) Rectangular M vs Hi curve may be a problem in this case but not in this case Irreversible changes for sufficiently large temperature increase, e. g. for Nd. Fe. B the temperature limit is 150 – 200 o. C

Mål • Känna till hur hårdmagnetiska material förbereds för att kunna användas i tillämpningar • Känna till önskvärda egenskaper för hårdmagnetiska material • Känna till vad energiprodukten innebär och hur man utifrån magnetisering/magnetisk induktion versus inre fält kan beräkna energiprodukten • Känna till begreppen avmagnetiseringskurva, arbetslinje och permeanskoefficient och vad de innebär • Känna till Stoner-Wohlfarth modellen, inte härledningar men vad modellen beskriver • Känna till egenskaper hos Alnico, hårdferriter, Sm. Co och Nd. Fe. B permanentmagneter • Känna till hur man utifrån hystereskurvan kan avgöra om koercivfältet bestäms av nukleering av omvända domäner eller fastlåsning av domänväggar