Magnetic Properties of Metals

Transcription

1 Landolt-Bernstein Numerical Data and Functional Relationships in Science and Technology New Series / Editors in Chief: 0. Madelung and W. Martienssen Group III: Solid State Physics Volume 19 Magnetic Properties of Metals Subvolume i 1 Magnetic Alloys for Technical Applications. Soft Magnetic Alloys, Invar and Elinvar Alloys Editor: HI? J. Wijn Contributors: G. Bertotti, A.R. Ferchmin, F. Fiorillo, K. Fukamichi S.Kobe, S.Roth Springer-Verlag Berlin Heidelberg NewYork London Paris Tokyo Hong Kong Barcelona Budapest

2 ISSN (Solid State Physics) ISBN o Springer-Verlag Berlin Heidelberg New York ISBN O Springer-Verlag New York Berlin Heidelberg LibraryofCongressCalilloginginPubliwtionData Zahlenwerteund FunktionenausNaturwissenschafIenundTechnik,NeueSerie Editorsin Chief: 0. Madelung. W. Martienssen Vol. Hi/I 9i I : Edited by H.P.J. Wijn AtheadofIiIle:LandolI-BBmstein. Addedt.p.:Numericilldataandfunctionalmlationshipsinscienceandlechnology TubleschieflyinEnglish. JntendedtosupenedethePhysikalisch-che~scheTa~~lenbyH.H.~do~I~dR. Btimsteinofwhichthe6thed. beganpublicationin 1950un&rtiIle:ZahlenwerteundFunkIionenausPhysik,Chemie,Ashonomie, GeophysikundTechnik. Vols. published afierv. 1 of group I have imprini: Berlin, NewYork, Springer-Verlag Includesbibliographies. l.physics--tables.2.chemistry--tabies.3. Engineering--Tables. I.BSrnstein,R.(Richad), II.LandoII.H.(Hans),l Physikalisch-chemischeTabeIlen. IV.TiIle:Numen caldaiaandfunciionalrelationshipsinsci~nceand technology. QC This work is subject IO copyright. All rights are reserved, whelher the whole or part of this material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasring, reproduction on microfilmor in other ways, and storage in data banks. Duplication of this publication or parts thereof is permilted only under the provisions of thegermancopyrightlawofseptember ,initscurrentversion,andpermissionforusemustalwaysbeobrainedfrom Springer-Verlag. Violations are liable for prosecution act under German Copyright 1994 Printed in Germany Tbe use of general descriptive names, registered names Irademarks, etc. in this publicaton does not imply, even in the absence of a specific statement, that such names are exempt from Ihe relevant protective laws and regulations and therefore free for general use. Product Liability: The data and otherinformaiion in this handbook have been carefully exlracted andevaluated by experts from the original literature. Furthermore they have been checked for correctness by the authors and Iheeditorial staff before printing. NevenhelessthepublishercangivenogunranIeeforthecorrecInessoftbedaIaandinformationprovided.Inany individual case of application the respective user must check Ibe correctness by consulting other relevant sources of information. Production:PRODUservSpringerProduktions-Gesellscbaft.Berlin TypeseIIing:MacmillanIndiaLtd. Printing:DmckhausLangenscheidtKG,Berlin Binding:LUderitz&Bauer,Berlin SPIN / Printed on acid-free paper

3 Editor H.P.J. Wijn Institut für Werkstoffe der Elektrotechnik der Rheinisch-Westfälischen Technischen Hochschule Aachen, Templergraben 55, D Aachen, Germany Contributors G. Bertotti Istituto Elettrotecnico Nazionale Galileo Ferraris, Corso Massimo d Azeglio, 42, I Torino, Italy A.R. Ferchmin Instytut Fizyki Molekularnej, Polskiej Akademii Nauk, ul. Smoluchowskiego 17/19, PL Poznan, Poland F. Fiorillo Istituto Elettrotecnico Nazionale Galileo Ferraris, Corso Massimo d Azeglio, 42, I Torino, Italy K. Fukamichi Department of Materials Science, Faculty of Engineering, Tohoku Universtity, Sendai 980, Japan S. Kobe Institut für Theoretische Physik, Fakultät für Naturwissenschaften und Mathematik, Technische Universität Dresden, Mommsenstr. 13, D Dresden, Germany S.Roth Institut für Metallische Werkstoffe, Institut für Festkörper- und Werkstofforschung, Technische Universität Dresden, Helmholtzstr. 20, D Dresden, Germany

4 Preface Since the appearance in 1962 of Landolt-Bornstein (6th Edition), Volume II, part 9, dealing with the magnetic properties of a wide variety of substances, the number of alloys and compounds with interesting magnetic properties has enormously increased. The preparation of these substances aimed, in the first place, at a better understanding of the magnetic behaviour of the already well-known substances, but it also accelerated the industrial development of new magnetic materials with optimized properties for various applications. Progress in electronics as well as the development of new measuring techniques has also led to an enormous extension of the knowledge of intrinsic magnetic properties. Since 1970 several volumes of the Landolt-Bernstein New Series have been devoted to, or at least contain data about, the magnetic properties of some special groups of substances. The present Volume 19 of Group III (Crystal and Solid Physics) will deal with the magnetic properties of metals, alloys and metallic compounds which contain at least one transition element. It was not attempted, however, to be very critical about the metallic character of the substances discussed. Where appropriate, semiconductors and even insulators have been included. Regarding the properties to be listed, not only data on magnetic properties but also on those nonmagnetic properties have been included which, to some extent, depend on the magnetic state of the metallic system. The literature that appeared until about one year before the publication of each subvolume has been covered. The amount of information available has become so substantial that a larger number of subvolumes is needed to cover the reliable data on magnetic properties of metals. The data are not arranged according to specific magnetic properties, but rather follow the lines of the various groups of magnetic substances. It appeared during the organization of the work that in this way the largest coherence within the contents could be obtained. This was also reflected in the experience that in this way competent authors could be found who, in their contributions to this volume, covered important groups of metals, instead of a single, narrowly defined magnetic property. A survey of the contents of all subvolumes is printed on the inside front cover. The subvolumes 111/19a to III/l 9f deal with the intrinsic magnetic properties of metals, i.e. data on those magnetic properties are represented in tables and figures which depend only on the chemical composition and on the crystal structure of the metal. Data on properties that, in addition, depend on the preparation of the samples used in the measurements, as is for instance the case for thin films, amorphous alloys, and above all for the magnetic alloys used in technical applications, are given in the final subvolumes 111/19g, 111/19h and 111/19i. A clean-cut division is of course illusory for at least two reasons. In the first place the properties of metals and alloys may depend on the chemical purity and on the physical quality of the crystal. And moreover, in alloys the ordering of the various atoms in the crystal lattice may in some cases influence the magnetic properties. This subvolume III/lBil deals with the magnetic properties of soft magnetic alloys which are the subject of investigations in relation with their potential usefulness for technical applications. The large fields of high-induction alloys and Invar and Elinvar alloys are covered. The relation between the magnetic properties and the various preparation techniques of the alloys with the consequences for their physical structure have obtained special attention. In the field of magnetism, there is a gradual transition from the use of cgs/emu units to SI units. It was, however, not intended to represent all data in the units of one system, regardless of how nice this would have been from a systematic point of view. Instead, mostly preference was given to the system of units that was originally used by the authors whose work is quoted. Thus cgs/emu units occur most frequently. Of course the user of the tables and figures is helped in several ways to convert the data to the units which he is most

5 Preface VII familiar with, see, e.g., the list of definitions, units and conversion factors for the magnetic quantities occurring most frequently. Many thanks are due to the authors for the agreeable cooperation, the Landolt- Bornstein editorial office in Darmstadt, especially Dr. W. Finger and Frau G. Burfeindt for the great help with the editorial work, and to the Springer-Verlag for the carefulness with respect to the publication of this volume. Like all other volumes of Landolt-Bornstein, this volume is published without outside financial support. Aachen, July The Editor

6 List of symbols Italic letters preceding page numbers indicate the respective subvolume of volume III/19. Symbol Unit Quantity Introduced in Sect. Page A J m -1 exchange constant A s % surface area ratio of supplementary domains a T A -1 m first Rayleigh constant a, b, c nm lattice parameters B Pa bulk modulus B T, G magnetic induction XV B T peak magnetic induction B 3 /B 1 ratio of third harmonic to fundamental component of magnetic induction B 10 T magnetic induction at a magnetic field of 10 Oe B eff T effective magnetic induction B r T remanent magnetic induction B s T saturation magnetic induction b T A -2 m 2 second Rayleigh constant C p J kg -1 K -1 heat capacity at constant pressure c at %, wt % solute concentration c ij Pa elastic constants c L Pa linear combination of elastic constants D mm 180 domain wall spacing D m 2 s -1 diffusion coefficient D 0 m 2 s -1 diffusion constant d mm thickness d 0 mm Bloch wall thickness parameter d s mm distance from surface sheet E Pa Young s modulus E 0 Pa Young s modulus at zero magnetization E a J m -3 anisotropy energy E s Pa Young s modulus at saturation magnetization E u J m -3, J kg -3 free energy of uniaxial anisotropy e K -1 temperature coefficient of Young s modulus F precipitated fraction of impurities fraction of C released with decarburization F C F γ fraction of γ-phase in FeSi f Hz magnetizing frequency G Pa shear modulus G 0 Pa shear modulus at zero magnetization G s Pa shear modulus at saturation magnetization g K -1 temperature coefficient of shear modulus H A m -1, Oe magnetic field XV H A m -1 peak magnetic field H c A m -1 coercive field H cr A m -1 in wasp-waisted hysteresis loops: critical magnetic field at which differential permeability increases H eff A m -1 effective magnetic field

7 List of symbols XI Symbol Unit Quantity Introduced in Sect. Page H v A m domain-wall stabilization field due to after-effect; in magnetic viscosity measurements: maximum magnetic field difference between relaxed and unrelaxed magnetization curves H V Vickers hardness h, k, l Miller indices h b µm burr height in punched lamination I T intensity of magnetization: I = B µ 0 H I s T intensity of saturation magnetization relative <uvw> direction intensity of magnetization I <uvw> I (hkl) relative density of crystallographic plane (hkl) J s T saturation magnetic polarization K 1, K 2 J m -3 magnetocrystalline anisotropy constants a 41 K eff J m -3 effective magnetic anisotropy constant K u J m -3 maximum uniaxial magnetic anisotropy constant k recrystallization fraction k B J K -1 Boltzmann constant L J m -3 magnetic anisotropy torque L W kg -1, W m -3 magnetic loss L e W m -3 eddy current loss L h W s m -3 hysteresis loss per magnetizing cycle L m W kg -1 power loss per unit mass L p W s m -3 pulse loss L s mm supplementary lancet domain length L V W m -3 power loss per unit volume l/l linear magnetostriction M A m -1, T, G magnetization XV M r A m -1 remanent magnetization M s A m -1 saturation magnetization n g normalized grain size distribution n i mm -2 inclusion density n s number of strokes in lamination punching n s mm -1 supplementary lancet domain density P W kg -1, W m -3 power loss P c W kg -1, W m -3 classical power loss P d W kg -1, W m -3 dynamic power loss P e W kg -1, W m -3 excess power loss P h W kg -1, W m -3 hysteresis power loss P R W kg -1, W m -3 rotational power loss R P c R P e R P h W kg -1, W m -3 W kg -1, W m -3 rotational classical power loss rotational excess power loss W kg -1, W m -3 rotational hysteresis power loss p Pa pressure ph O/ p 2 H2 partial pressure ratio in wet H 2 atmosphere Q ev activation energy for interstitial diffusion Q a ev activation energy Q -1 damping coefficient

8 XII List of symbols Symbol Unit Quantity Introduced in Sect. Page Q m 1 magnetomechanical damping coefficient R recrystallized fraction R % cold-reduction in area R C Rockwell hardness (C scale) r A m -1 T -1 reluctivity S VAkg -1 exciting power S m VAkg -1 exciting power per unit mass S V VAm -3 exciting power per unit volume s mm average grain diameter s i µm size of inclusions T K, C temperature T a K annealing temperature T C K Curie temperature T m K, C melting point temperature T N K Néel temperature T X K crystallization temperature T Q K quenching temperature T αγ - K, C α-γ phase transformation temperature T γδ - K, C γ-δ phase tranformation temperature t s time t a s annealing time tan δ loss factor t s µm subscale layer thickness u, v, w lattice direction indices V m 3 volume; unit cell volume V s % volume fraction of supplementary domains v m s domain-wall velocity W h J kg -1 dc energy loss per magnetizing cycle x, y, z solute concentrations x µm 180 -domain-wall displacement α deg angle; in (110)[001] crystals: angle between the projection of the [001] axis on the crystal surface and the longitudinal specimen axis α K -1 linear thermal expansion coefficient β deg angle; in (110)[001] crystals: tilt angle of the [001] axis out of the crystal surface β K -1 volumetric thermal expansion coefficient β 1 ( C) -1 linear thermal expansion coefficient β 2 ( C) -2 quadratic thermal expansion coefficient γ shear strain γ 0 J m domain-wall energy δ phase shift between magnetic induction and magnetic field δ Å inclusion diameter

9 List of symbols XIII Symbol Unit Quantity Introduced in Sect. Page δ kg m -3 mass density ε relative thickness reduction; strain amplitude ε s -1 strain rate ε p plastic strain amplitude θ, ϑ deg angles λ W m -1 K -1 thermal conductivity λ magnetostriction λ 100, λ 111 magnetostriction constants a 48 λ 0-p magnetostriction difference between the peak induction under consideration and B = 0 λ p-p peak-to-peak magnetostriction for the peak induction under consideration λ s saturation magnetostriction constant λ magnetostriction parallel to the direction of the magnetization λ magnetostriction perpendicular to the direction of the magnetization µ relative permeability µ T m A -1 permeability µ 0 T m A -1 permeability of the vacuum XV µ a relative amplitude permeability µ eff relative effective permeability µ i relative initial permeability µ i T m A -1 initial permeability µ max T m A -1 maximum permeability µ r relative permeability µ real part of the complex relative permeability µ imaginary part of the complex relative permeability ν Poisson s ratio ρ cm -2 dislocation density ρ kg m -3 mass density ρ Ω m electrical resistivity σ Pa, kp mm -2 stress, tensile stress σ Pa work-hardening σ c Pa compressive stress σ i internal strain σ T Pa tensile strength σ y Pa yield strength τ Pa resolved shear stress τ s relaxation time τ 0 s relaxation time constant τ y Pa critical resolved shear stress φ, ϕ deg angles ϕ 3 deg phase shift of third harmonic induction χ magnetic susceptibility XV

10 XIV List of symbols Symbol Unit Quantity Introduced in Sect. Page χ magnetic susceptibility of a ribbon sample annealed in a magnetic field parallel to the ribbon axis χ magnetic susceptibility of a ribbon sample annealed in a magnetic field perpendicular to the ribbon axis

11 List of abbreviations ac at CGO CINDAS dc fcc GO HGO IEC max NO ODF ppm RD rpm RRR RT surf. TD TM vol. wt alternating current atom conventional grain-oriented steel Center for Information and Numerical Data Analysis and Synthesis direct current face-centered cubic grain-oriented steel high permeability grain-oriented steel International Electrotechnical Commission maximum nonoriented steel orientation distribution function parts per million rolling direction rotations per minute residual resistivity ratio room temperature surface transverse direction transition-metal element volume weight

12 Definitions, units and conversion factors Units are given for the cgs/emu system and SI, for defining relations of the magnetization, B = H + 4πM, B = µ 0 (H + M) and B = µ 0 H + M, respectively. µ 0 = 4π 10 7 VsA 1 m 1, A: molar mass, ρ : mass density. Quantity cgs/emu SI B G = (erg cm 3 ) 1/2 1 G H 1 Oe = (erg cm 3 ) 1/2 1 Oe M B = H + 4πM G 1 G T = Vs m T A m /4π A m 1 B = µ 0 (H + M) A m A m 1 B = µ 0 H + M T 4π 10 4 T P σ σ m P = MV G cm 3 1 G cm 3 σ = M/ρ G cm 3 g 1 1 G cm 3 g 1 σ m = σa G cm 3 mol 1 1 G cm 3 mol 1 P = MV A m A m 2 σ = M/ρ A m 2 kg 1 1 A m 2 kg 1 σ m = σa A m 2 mol A m 2 mol 1 P = MV V s m 4π V s m σ = M/ρ V s m kg 1 4π 10 7 V s m kg 1 σ m = σa V s m mol 1 4π V s m mol 1 χ χ V P = χh cm 3 1 cm 3 χ V = χ/v cm 3 cm 3 1 cm 3 cm 3 χ g χ g = χ V /ρ cm 3 g 1 χ m 1 cm 3 g 1 χ m = χ g A cm 3 mol 1 1 cm 3 mol 1 P = χh m 3 4π 10 6 m 3 χ V = χ/v m 3 m 3 4π m 3 m 3 χ g = χ V /ρ m 3 kg 1 4π 10 3 m 3 kg 1 χ m = χ g A m 3 mol 1 4π 10 6 m 3 mol 1 P = χµ 0 H m 3 4π 10 6 m 3 χ V = χ/v m 3 m 3 4π m 3 m 3 χ g = χ V /ρ m 3 kg 1 4π 10 3 m 3 kg 1 χ m = χ g A m 3 mol 1 4π 10 6 m 3 mol 1 R 0, R s ρ H = R 0 B + 4πR s M s Ω cm G 1 1 Ω cm G 1 ρ H = R 0 B + µ 0 R s M s m 3 C m 3 C 1 ρ H = R 0 B + R s M s m 3 C m 3 C 1