下载文档原格式
STEEL FORMING AND HEAT TREATING HANDBOOKAntonio Augusto GorniSão Vicente, Brazilwww.gorni.eng.brRelease #12 – 12 April 2005USEFUL METALLURGICAL FORMULAS- Austenite Formation Temperatures. GrangeAe Mn Si Cr Ni 1133325404226=−++−Notation:Ae 1: Equilibrium Temperature for Austenitization Start [°F]Alloy Content : [weight %]Ae C Mn Si Cr Ni 315703232580332=−−+−−Notation:Ae 3: Equilibrium Temperature for End of Austenitization [°F]Alloy Content : [weight %]Source: GRANGE, R.A. Metal Progress , April 1961, 73.Ae Mn Si Cr Ni As W 1723107291169169290638=−++−++,,,,,Notation:Ae 1: Equilibrium Temperature of Austenitization Start [°C]Alloy Content : [weight %]. AndrewsNotation:Ae 3: Equilibrium Temperature for End of Austenitization [°C]Alloy Content : [weight %]Notes:- Both formulas are valid for low alloy steels with less than 0,6%C.Source: ANDREWS, K.W. Empirical Formulae for the Calculation of Some Transformation Temperatures. Journal of theIron and Steel Institute , 203, Part 7, July 1965, 721-727.. RobertsAe Mn Cr Cu Si P Al F n 391025112060700250=−−−++−−Notation:Ae 3: Equilibrium Temperature for End of Austenitization [°C]Alloy Content : [weight %]F n : value defined according to the table below:C F n0,05 240,10 480,15 64 0,20 800,25 930,30 1060,35 1170,40 128Source: ROBERTS, W.L.: Flat Processing of Steel ; Marcel Dekker Inc., New York, 1988.. EldisAe Mn Ni Si Cr Mo 171217819120111998=−−+++,,,,,Notation:Ae 1: Equilibrium Temperature of Austenitization Start [°C]Alloy Content : [weight %]Notation:Ac 3: Equilibrium Temperature for End of Austenitization [°C]Alloy Content : [weight %]Notes:- Both formulas were proposed by ELDIS for low alloy steels with less than 0,6%C.Source: BARRALIS, J. & MAEDER, G. Métallurgie Tome I: Métallurgie Physique. Collection Scientifique ENSAM ,1982, 270 p.- Austenite Transformation Temperatures. BorattoNotation:T nr : Temperatura of No-Recrystallization [°C]Alloy Content : [weight %]Source: BORATTO, F. et al.: In: THERMEC ‘88. Proceedings. Iron and Steel Institute of Japan, Tokyo, 1988, p. 383-390.. OuchiAr C Mn Cu Cr Ni Mo h 391031080201555800358=−−−−−−+−,()Notation:Ar 3: Start Temperature of the Transformation Austenite → Ferrite [°C]Alloy Content : [weight %]h : Plate Thickness [mm]Notes:- This formula was determined using data got from samples cooled directly from hot rolling experiments. Thus it includes the effects of hot forming over austenite decomposition.Source: OUCHI, C. et al.: Transactions of the ISIJ , March 1982, 214-222.. ChoquetAr C Mn Si 39025276260=−−+Notation:Ar 3: Start Temperature of the Transformation Austenite → Ferrite [°C]Alloy Amount : [weight %]Notes:- This formula was determined using data got from samples cooled directly from hot rolling experiments. Thus it includes the effects of hot forming over austenite decomposition.Source: CHOQUET, P. et al.: Mathematical Model for Predictions of Austenite and Ferrite Microstructures in Hot RollingProcesses. IRSID Report , St. Germain-en-Laye, 1985. 7 p.. Nippon Steel 1Ar C Mn Si P 3879451616573802747=−−++,,,,,Notation:Ar 3: Start Temperature of the Transformation Austenite → Ferrite [°C]Alloy Content : [weight %]Ar C Mn 1706435041182=−−,,,Notation:Ar 1: Final Temperature of the Transformation Austenite → Ferrite [°C]Alloy Content : [weight %]Notes:- It is unknown the previous conditioning of the steel samples that supplied data for the deduction of this formula.- Samples cooled at 20°C/s.Source: R&D Team of the Kimitsu Steelworks of Nippon Steel , 2003.. Nippon Steel 2Cr Al P Si Mn C Ar 204028733923259013−+++−−=Notation:Ar 3: Start Temperature of the Transformation Austenite → Ferrite [°C]Alloy Content : [weight %]Notes:- It is unknown the previous conditioning of the steel samples that supplied data for the deduction of this formula.Source: R&D Team of the Kimitsu Steelworks of Nippon Steel , 2003.. StevenB C Mn Cr Ni Mo s =−−−−−152648616212667149B Bs 50108=−B Bs 100216=−Notation:B s : Start Temperature of the Bainitic Transformation [°F]Alloy Amount : [% em peso]B x : Temperature Required for the Formation of x% of Bainite [°F]Source: STEVEN, W. et al. Journal of the Iron and Steel Institute , 183, 1956, 349.. SuehiroB C Mn s =−−718425425.Notation:B s : Start Temperature of the Bainitic Transformation [°F]Alloy Amount : [weight %]Source: SUEHIRO, M. et al. Tetsu-to-Hagané, 73 (1987), p. 1026-1033.. RowlandM C Mn Si Cr Ni Mo W s =−−−−−−−930600602050302020Notation:M s : Start Temperature of the Martensitic Transformation [°F]Alloy Amount : [% em peso]Source: ROWLAND, E.S. et al. Transactions ASM , 37, 1946, 27.. StevenM Ms 1018=−M Ms 5085=−M Ms 90185=−M Ms 100387=−Notation:M x : Temperature Required for the Formation of x% of Martensite [°F]Source: STEVEN, W. et al. Journal of the Iron and Steel Institute , 183, 1956, 349.. AndrewsM C Mn Ni Cr Si Mo s =−−−−−−53942330417712111070,,,,,Notation:M s : Start Temperature of the Martensitic Transformation [°C]Alloy Content : [weight %]Notes:- Formula valid for low alloy steels with less than 0,6%C.Source: ANDREWS, K.W. Empirical Formulae for the Calculation of Some Transformation Temperatures. Journal of theIron and Steel Institute , 203, Part 7, July 1965, 721-727.. EldisM C Mn Ni Cr s =−−−−5313912433218162,,,,Notation:M s : Start Temperature of the Martensitic Transformation [°C]Alloy Content : [weight %]Notes:- Equation developed by Eldis- Equation valid for steels with chemical composition between the following limits: 0.1~0.8% C; 0.35~1.80% Mn; <1.50% Si; <0.90% Mo; <1.50% Cr; <4.50% Ni .Source: BARRALIS, J. & MAEDER, G. Métallurgie Tome I: Métallurgie Physique. Collection Scientifique ENSAM , 1982, 270 p.. KraussM C Mn Cr Ni Mo s =−−−−−56147433171721Notation:M s: Start Temperature of the Martensitic Transformation [°C]Alloy Amount: [% em peso]Source: KRAUSS, G. Principles of Heat Treatment and Processing of Steels, ASM International, 1990, p. 43-87.- Austenitization Time-Temperature Equivalency Parameter. Isothermal AustenitizingNotation:P a: Austenitization Time-Temperature Equivalence Parameter in Terms of Grain Size [K]T a: Austenitization Temperature [K]R: Molar Gas Constant, 8.314 JK-1mol-1t a: Soaking time under T a∆H a: Activation Energy of Austenitic Grain Coarsening, 460 kJmol-1 for low alloy steels. Anisothermal AustenitizingIn this case P a is the period of heating/cooling time between T max and T min, whereT max: maximum temperature during the austenitizing treatment;T min : temperature calculated according to the following equation:Source: BARRALIS, J. & MAEDER, G. Métallurgie Tome I: Métallurgie Physique. Collection Scientifique ENSAM ,1982, 270 p.- Equivalent Carbon – H.A.Z. Hardenability. Dearden & O’Neill (1940)2001200_max −=Dearden EQ C HVNotation:C EQ_Dearden : Equivalent Carbon (Dearden) [%]Alloy Content : [weight %]HV max = Dureza Máxima [Vickers]Source: Y URIOKA, N.: Physical Metallurgy of Steel Weldability . ISIJ International , 41:6, June 2001, 566-570.. IIW - International Institute of WeldingNotation:C EQ_IIW : Equivalent Carbon (IIW) [%]Alloy Content : [weight %]Source: H EISTERKAMP, F. et al.: Metallurgical Concept And Full-Scale Testing of High Toughness, H 2S Resistant0.03%C - 0.10%Nb Steel . C.B.M.M. Report , São Paulo, February 1993.. BastienBastien EQ m C CR _6,109,13)ln(−=Notation:C EQ_Bastien : Equivalent Carbon (Bastien) [%]Alloy Content : [weight %]CR m : Critical Cooling Rate at 700°C [°C/s] (that is, minimum cooling rate that produces a fully martensitic structure)Source: Y URIOKA, N.: Physical Metallurgy of Steel Weldability . ISIJ International , 41:6, June 2001, 566-570.. Yurioka et al.8,46,10)log(_−=Yurioka EQ m C tNotation:C EQ_Yurioka : Equivalent Carbon (Yurioka) [%]Alloy Content : [weight %]t m : Critical Cooling Time from 800 to 500°C [s] (that is, maximum cooling time that produces a fully martensiticstructure)Source: Y URIOKA, N.: Physical Metallurgy of Steel Weldability . ISIJ International , 41:6, June 2001, 566-570.. Kihara et al.Notation:C EQ_Kihara : Equivalent Carbon (Kihara) [%]Alloy Content : [weight %]Source: Y URIOKA, N.: Physical Metallurgy of Steel Weldability . ISIJ International , 41:6, June 2001, 566-570.- Equivalent Carbon – Hydrogen Assisted Cold Cracking. DNVNotation:C EQ_DNV: Equivalent Carbon (DNV) [%]Alloy Content: [weight %]Source: Y URIOKA, N.: Physical Metallurgy of Steel Weldability. ISIJ International, 41:6, June 2001, 566-570. . Uwer & HohneNotation:C EQ_Uwer: Equivalent Carbon (Uwer & Hohne) [%]Alloy Content: [weight %]Source: Y URIOKA, N.: Physical Metallurgy of Steel Weldability. ISIJ International, 41:6, June 2001, 566-570.Mannesmann.Notation:C EQ_PLS: Equivalent Carbon for Pipeline Steels [%]Alloy Content: [weight %]Notes:-Formula deduced for pipeline steels- A version of this formula divides V by 15Source: H EISTERKAMP, F. e outros: Metallurgical Concept And Full-Scale Testing of High Toughness, H2S Resistant0.03%C - 0.10%Nb Steel. C.B.M.M. Report, São Paulo, February 1993.. GravilleNotation:C EQ_HSLA: Equivalent Carbon (Uwer & Graville) [%]Alloy Content: [weight %]Notes:-Formula deduced for pipeline steelsSource: Y URIOKA, N.: Physical Metallurgy of Steel Weldability. ISIJ International, 41:6, June 2001, 566-570.. Bersch & KochNotation:C EQ_Bersh: Equivalent Carbon for Pipeline Steels [%]Alloy Content: [weight %]Notes:- Formula deduced for pipeline steelsSource: P ATCHETT, B.M. et al.: Casti Metals Blue Book: Welding Filler Metals. Casti Publishing Corp., Edmonton, February 1993, 608 p. (CD Edition).. Ito & Bessyo (I)Notation:P cm: Cracking Parameter [%]Alloy Content: [weight %]Notes:- Formula deduced for pipeline steels with C < 0,15%- This is the most popular formula for this kind of material.Source: H EISTERKAMP, F. e outros: Metallurgical Concept And Full-Scale Testing of High Toughness, H2S Resistant0.03%C - 0.10%Nb Steel. C.B.M.M. Report, São Paulo, February 1993.. Ito & Bessyo (II)Notation:P c: Cracking Parameter [%]Alloy Content: [weight %], exceptH: Hydrogen amount in the weld metal, [cm³/100 g]d: Plate Thickness, [mm]Source: I TO, Y. e outros: Weldability Formula of High Strength Steels. I.I.W. Document IX-576-68.Yurioka.[]07502520012=+−A C C(),,tanh(,)Notation:C EQ_Yurioka: Equivalent Carbon for Pipeline Steels [%]Alloy Content: [weight %]Notes:- Formula for C-Mn and microalloyed pipeline steels- This formula combines Carbon Equivalent equations from IIW and P cmSource: P ATCHETT, B.M. et al.: Casti Metals Blue Book: Welding Filler Metals. Casti Publishing Corp., Edmonton, February 1993, 608 p. (CD Edition).- Equivalent Carbon – Bake Hardenability CapabilityMelco.Notation:C eq_bh: Equivalent Carbon Expressed As Bake Hardenability [%]Alloy Content: [weight %]Source: M itsubishi Electric Co., 1998.- Hot Strength of Steel. Tselikov2013792 E+−CCSi+=+Mn−+−−T17400012000P6,,05289225S308250T 4292414400020525Notation:E: Young Modulus [kgf/cm²]C: C content [weight %]Mn: Mn content [weight %]Si: Si content [weight %]P: P content [weight %]S: S content [weight %]T:Temperature [°C]Note:- Valid for carbon, alloy and stainless steels between 20 and 900°C.Source: ROYZMAN, S.E. Thermal Stresses in Slab Solidification. Asia Steel, 1996, 158-162.. MisakaNotation:σ: Steel Hot Strength [kgf/mm²]C: C content [weight %]T: Absolute Temperature [K]ε: True Straint: Time [s]Source: MISAKA, Y. et al. Formulatization of Mean Resistance to Deformation of Plain C Steels at Elevated Temperature.Journal of the Japan Society for the Technology of Plasticity, 8, 79, 1967-1968, 414-422.. ShidaCalculation algorithm expressed in Visual Basic:Function Shida(C, T, Def, VelDef)Dim nShida, Td, g, Tx, mShida, SigF As SinglenShida = 0.41 – 0.07 * CTd = 0.95 * (C + 0.41) / (C + 0.32)T = (T + 273) / 1000If T >= Td Theng = 1Tx = TmShida = (-0.019 * C + 0.126) * T + (0.075 * C – 0.05)Elseg = 30 * (C + 0.9) * (T – 0.95 * (C + 0.49) / (C + 0.42)) ^ 2 + (C + 0.06) / (C + 0.09)Tx = TdmShida = (0.081 * C – 0.154) * T + (-0.019 * C + 0.207) + 0.027 / (C + 0.32)End IfSigF = 0.28 * g * Exp(5 / Tx – 0.01 / (C + 0.05))Shida = 2 / Sqr(3) * SigF * (1.3 * (Def / 0.2) ^ nShida – 0.3 * (Def / 0.2)) * _(VelDef / 10) ^ mShidaEnd FunctionNotation:σ: Steel Hot Strength [kgf/mm²]C: C content [weight %]T: Temperature [°C]Def: True StrainVelDef: Strain Rate [s-1]Source: SHIDA, S. Effect of Carbon Content, Temperature and Strain Rate on Flow Stress of Carbon Steels.Hitachi Technical Report, 1974, 14 p.- Liquidus Temperature of Steels[]T C Si Mn P S Cu Ni Cr Al Mo V Ti Liq =−+++++++++++1536787649343053113362218,,,,,Notation:T Líq : Steel Melting Temperature [°C]Alloy Content : [weight %]Source: GUTHMANN, K. Stahl und Eisen , 71(1951), 8, 399-402.- Niobium Solubilization in Microalloyed Steels. IrvineNotation:T : Temperature [°C]Alloy Content : [weight %]Source: I RVINE, K.J. et al.: Journal of the Iron and Steel Institute , 205, 1967, 161.. SicilianoNotation:T : Temperature [°C]Alloy Content : [weight %]Source: S ICILIANO JR., F..: Mathematical Modeling of the Hot Strip Rolling of Nb Microalloyed Steels Ph.D. Thesis ,McGill University, February 1999, 165 p.- Relationships Between Chemical Composition x Microstructure x Mechanical Properties. C-Mn Steelsεunif sol Perl Mn Si Sn N =−−−−−027001600150040004310,,,,,,Notation:LE: Yield Strength at 0,2% Real Strain [MPa]LR: Tensile Strength [MPa]dσ/dε: Strain Hardening Coefficient at 0,2% Real Strain [1/MPa]εunif: Uniform Elongation, Expressed as Real (Logarithmic) Strainεtot: Total Elongation, Expressed as Real (Logarithmic) StrainPerl: Pearlite Fraction in Microstructure [%]T trans: Fracture Appearance Transition Temperature [°C]Alloy Content: [weight %]d: Grain Size [µm]Source: P ICKERING, F.B.: The Effect of Composition and Microstructure on Ductility and Toughness; in: Towards Improved Ductility and Toughness, Climax Molybdenum Company, Tokyo, 1971, p. 9-32Notation:LE: Yield Strength at 0,2% Real Strain [MPa]LR: Tensile Strength [MPa]Perl: Pearlite Fraction Present in Microstructure [%]Alloy Contents: [weight %]d: Grain Size [µm]Source: P ICKERING, F.B.: Physical Metallurgy and the Design of Steels. Allied Science Publishers, London, 1978, 275 p.Notation:50% ITT: Impact Transition Temperature for 50% Tough Fracture [°C]Perl: Pearlite Fraction Present in Microstructure [%]Alloy Contents: [weight %]d: Grain Size [µm]Source: PICKERING, F.B. & GLADMAN, T.: In Metallurgical Developments in Carbon Steels. The iron and Steel Institute, London, 1961, 10-20. V-Ti-N Steels Processed by Recrystallization Controlled RollingNotation:LE: Yield Strength at 0,2% Real Strain [MPa]LR: Tensile Strength [MPa]Alloy Content: [weight %]h f: Plate Thickness [mm]Notes:- Formula Derived for Steels with Al Content over 0,010% and Si Content between 0,25 and 0,35%.- Precision of the formulas: ± 40 MPa.Source: M ITCHELL, P.S. et al.: In: Low Carbon Steels for the 90’s. Proceedings. American Society for Metals/The Metallurgical Society, Pittsburgh, Oct. 1993..Dual Phase SteelsSource: G ORNI, A.A.: Efeito da Temperatura de Acabamento e Velocidade de Resfriamento na Microestrutura e Propriedades Mecânicas de um Aço Bifásico ao Mn-Si-Cr-Mo; Dissertação de Mestrado, Departamento de Engenharia Metalúrgica e de Materiais da Escola Politécnica da Universidade de São Paulo, São Paulo, 1989, 184 p.NotationLE: Yield Strength [MPa]LR: Tensile Strength [MPa]dσ/dε: Strain Hardening Coefficient at Uniform Elongation [1/MPa]a unif: Uniform Elongation [%]Lαα: Mean Ferritic Free Path [µm]dβ: Mean Diameter of Martensite Islands [µm]- Solidus Temperature of Steels[]Al Cr Ni S P Mn Si C T Sol 1,44,13,49,1835,1248,63,125,4151536+++++++−=Notation:T Líq : Steel Melting Temperature [°C]Alloy Content : [weight %]Source: TAKEUCHI, E. & BRIMACOMBE, J.K. Effect of Oscillation-Mark Formation on the Surface Quality of ContinuouslyCast Steel Slabs . Metallurgical Transactions B , 16B, 9, 1985, 605-25.USEFUL DATA AND CONSTANTS - Steel Scale Density: 4,86 g/cm³ (Combustol)GENERAL STATISTICAL FORMULAS- Correlation CoefficientNotation:r : Correlation CoefficientY : Raw DataY est : Estimated Data Calculated by the Fitted EquationY _: Mean of the Raw DataSource: SPIEGEL, M.R. Estatística , Editora McGraw-Hill do Brasil Ltda., São Paulo, 1976, 580 p.- Standard Error of EstimationNotation:σ: Standard Error of EstimationY est : Estimated Data Calculated by the Fitted EquationY _: Mean of the Raw Datan : Number of Points of DataSource: SPIEGEL, M.R. Estatística , Editora McGraw-Hill do Brasil Ltda., São Paulo, 1976, 580 p.。
a rXiv:h ep-ph/4317v11Mar24Particle and spin motion in polarized media A.J.Silenko Institute of Nuclear Problems,Belarusian State University,Minsk,Belarus E-mail:silenko@inp.minsk.by Abstract Quantum mechanical equations of motion are obtained for particles and spin in media with polarized electrons in the presence of external fields.The motion of elec-trons and their spins is governed by the exchange interaction,while the motion of positrons and their spins is governed by the annihilation interaction.The equations obtained describe the motion of particles and spin in both magnetic and nonmag-netic media.The evolution of positronium spin in polarized media is investigated.Media with polarized electrons can be used for polarization of positronium beams.1IntroductionThe quantum mechanical description of the motion of particles and spin in matter is a very important problem.The classical theory of motion of particles and spin has been developed in great detail (see [1,2])).A quantum mechanical equation of motion of relativistic particles in an electromagnetic field was derived by Derbenev and Kondratenko[3].The motion of the spin of relativistic particles in an electromagnetic field is described by the Bargmann–Michel–Telegdi (BMT)equation [4].The Lagrangian with an allowance for terms quadratic in spin was obtained in [5,6].The corresponding equation of spin motion was presented in [7].The interaction between polarized particles and polarized matter was analyzed in [8,9].In the present paper,we find quantum mechanical equations of motion of particles and spin for relativistic particles with arbitrary spin that move in media with polarized electrons in the presence of external fields.The system of units ¯h =c =1is used.2Hamiltonian for particles in polarized mediaFor particles with arbitrary spin,the Hamiltonian can be derived with the use of the interaction Lagrangian L ,obtained in [5,6].This Lagrangian contains terms that are linear (L 1)and quadratic (L 2)in spin:L =L 1+L 2,L 1=eγ (S ·B )−(g −2)γγ+1(S ·[E ×v ]) ,L 2=Qγ+1(S ·v )(v ·∇) (S ·E )−γ2m 2γγ (S ·B )−(g −1)γγ+1 (S ·[E ×v ]) ,γ=11−v 2,(1)where g =2µm/(eS ),v is the velocity operator,γis the Lorentz factor,Q is the quadrupole moment,and S is the spin operator.The Hermitian form of formula (1)is obtained by the substitution L →(L +L †)/2.The total Hamiltonian is given byH =√1)Recall that the exchange interaction is responsible for the ferromagnetism.field for electrons should be replaced in (2)by the effective quasimagnetic field [8]B →G e =B +H c eff +H m eff ,H c eff =−4π|e |Nm (P ·n )n ,(3)where N and P =<σ′>are the polarization density and vector (average spin),respec-tively,of polarized matter electrons and n =v /v .The main contribution to the effective quasimagnetic field,H c eff ,is made by the Coulomb exchange interaction,or the Coulomb scattering.The exchange magnetic scattering yields the lesser contribution,H m eff .For nonrelativistic positrons in polarized media,the effective field with an allowance for the annihilation interaction,H a eff ,is determined byG p =B +H a eff =B −π|e |Nv 2M −4π(M ·n )n ,G p =B +2πM ,M =−|e |Nµm v 2B −µm −12µm B .(6)An appropriate expression for the Hamiltonian is expressed as (G =G e ,G p )[9]H =√2m g (S ·G )+(g −1)(S ·[E ×v ]) .(7)3Equations of motion of particles and spinThe equation of particle motion in both polarized and unpolarized media is the same if the Hamiltonian remains unchanged.For electrons and positrons,the equation of particle motion is given by [9]d π2m ∇ g (S ·G )+(g −1)(S ·[E ×v ]) .(8)For particles with arbitrary spin,the equation of spin motion with regard to the terms quadratic in spin is given in [7].For nonrelativistic electrons and positrons,the equation of the spin motion takes the form [9]d S2m g [S ×G ]+(g −1)[S ×[E ×v ]] .(9)The effect of the exchange interaction on the spin motion is stronger than that on the particle motion.The equations can be used for dia-,para-,and ferromagnetic media.4Polarization of positronium beams by polarized mediaPositronium beams can be polarized under passing through the polarized medium. Such a possibility takes place due to a dependence of the ortho-para-conversion(spin-conversion)rate on the polarization of the positronium.Positronium atoms have spin0(para-positronium,p-Ps)or1(ortho-positronium,o-Ps).Only o-Ps atoms pass through the medium because p-Ps atoms annihilate very quickly.As a rule,the positronium energy does not exceed several eV.In the matter,the o-Ps lifetime can be shortened by several processes,namely,the pick-offannihilation,the ortho-para-conversion that is the spin-conversion,and chemical reactions[10].The spin-conversion takes place in para-and ferromagnetic media,whose molecules contain unpaired electrons.In these media,the spin-conversion rate is generally much more than the rates of the pick-offannihilation and other processes.As particular,in the oxygen gas the spin-conversion rate is dozens of times larger than the pick-offannihilation one[11].The same conclusion can be made from an analysis of experimental data on the spin-conversion in solutions of HTMPO[12].We consider the simplified description of the positronium polarization process.For a more detailed description,the method and results obtained in Ref.[13]can be used.Let all the unpaired electrons of the matter be polarized along the z-axis(Fig.1). The spin exchange interaction can cause changing the o-Ps spin or its projection.This process can result in both the ortho-para-conversion and the prompt annihilation of the o-Ps.However,the simple analysis shows that the ortho-para-conversion is only possible when the o-Ps spin projection onto the z-axis equals either−1or0(see Figs.1a,b). When it equals1,flipping the spin is forbidden(see Fig.1c).The operator of the spin exchange interaction has the formP=−J(1+4s·s′)/2,(10) where s and s′are the spin operators of the o-Ps electron and the matter electron,re-spectively,and J is the exchange integral that determines splitting energy levels.The operator P mixes the states of the o-Ps and p-Ps.The o-Ps with S z=−1interacting with a matter electron(s z=1/2)is described by the spin wave function|1,−1;1/2,1/2 .As a result of simultaneousflipping the spins of the o-Ps electron and the matter one,the o-Ps can convert into the p-Ps with the spin wave function|0,0;1/2,−1/2 .This process is characterized by the matrix element2)0,0;1/2,−1/2|P|1,−1;1/2,1/2 =−J/√2.Analogous processes take place for the o-Ps with S z=0.The spin exchange interaction between the o-Ps electron and the matter one with and without the ortho-para-conversion is described by the matrix elements0,0;1/2,1/2|P|1,0;1/2,1/2 =−J/2and 1,1;1/2,−1/2|P|1,0;1/2,1/2 =−J/√2)All the matrix elements of the operator s·s′are given,e.g.,in Ref.[14].respectively.Coupled electrons do not contribute to the spin-conversion because matrixelements characterizing the exchange interaction between the o-Ps and the pair of coupledelectrons are zero.For the o-Ps with S z=1,all the corresponding matrix elements are zero.Therefore,the majority of o-Ps atoms passes through the medium without the annihilation.Thepick-offannihilation is possible for the o-Ps atoms with any spin projection.The o-Ps lifetime is changed by a magneticfield into the medium.Thisfield can bestrong enough.As is known,such afield does not change the lifetime of the o-Ps with S z=±1and shortens the lifetime of the o-Ps with S z=0(see Ref.[10]).This circumstance accelerates the process of polarization of the o-Ps beam.However,the evaluation showssuch an acceleration is not very significant.For example,the pick-offannihilation shortens the o-Ps lifetime more greatly than the magneticfield in ferromagnetic media.5Discussion and conclusionsMagnetic crystals can be effectively used for the rotation of the polarization vectorof particles.Even for neutrons,whose magnetic moment is relatively small,for B∼1T,the angle of rotation of the polarization vector per unit length is of the order of ∆Φ/∆l∼(c/v)×10−3rad/cm.The rotation of the polarization vector in magnetic crystals reaches especially large values for nonrelativistic electrons.It follows from(6)and(7)that the angular velocity of the spin precession of nonrelativistic electrons is increased by the factor of(c/v)2due to the exchange interaction.For B∼1T,we have∆Φ/∆l∼(c/v)3×1rad/cm in order of magnitude.In particular,when v/c∼0.1,we have∆Φ/∆l∼103rad/cm.The use of magnetic crystals may also be sufficiently effective for the rotation of the polarization vector of relativistic electrons.The Stern–Gerlach force,which splits beams according to the polarization of particles,is considerably increased.However,the use of polarized media for splitting electron beams according to the polarization is seriously hampered by the small value of the energy of interaction between the spin of electrons and a quasimagneticfield W(s)(of the order of 1eV or less)and a multiple scattering that increases the transverse energy of electrons. If the transverse energy of electrons is greater than|W(s)|,splitting the beam according to the polarization becomes impossible.The formulas obtained in this work are also valid for beams of polarized nuclei.Media with polarized electrons can be used for the polarization of positronium beams.The spin direction of positroniums coincides with the spin direction of polarized electrons.The considered effect of the polarization of positronium beams is more importantfor para-and ferromagnetic media without conductivity electrons,e.g.,ferrites.The spinexchange interaction of o-Ps atoms with conductivity electrons leads to the spin-conversion that does not depend on the o-Ps polarization.As a result,a presence of conductivity electrons can cause a strong background making the effect unobservable.It is important that the intensity of the positronium beam passing through two samplesmagnetized in different directions,depends on the angleφbetween the magnetization axes.This effect is similar to passing the unpolarized light through two polarizers when their axes do not coincide.Polarized positronium beams can be used for an investigation of magnetic media.Theinvestigation can include monitoring the process of magnetization and determining the magnetic structure of materials.The work is supported by the grant of the Belarusian Republican Foundation for Fundamental Research No.Φ03-242.References[1]I.M.Ternov and V.A.Bordovitzyn,Usp.Fiz.Nauk132,345(1980)[p. 23,679(1980)].[2]K.Yee,M.Bander,Phys.Rev.D48,2797(1993).[3]Ya.S.Derbenev and A.M.Kondratenko,Zh.Eksp.Teor.Fiz.64,1918(1973)[Sov. Phys.JETP37,968(1973)].[4]V.Bargmann,L.Michel,and V.L.Telegdi,Phys.Rev.Lett.2,435(1959).[5]A.A.Pomeransky and I.B.Khriplovich,Zh.Eksp.Teor.Fiz.113,1537(1998)[JETP 86,839(1998)].[6]A.A.Pomeransky and R.A.Sen’kov,Phys.Lett.B468,251(1999).[7]A.J.Silenko,Yader.Fiz.64,1054(2001)[Phys.At.Nucl.64,983(2001)].[8]V.G.Baryshevsky,Nuclear Optics of Polarized Media,Evergoatomizdat,Moscow, 1995.[9]A.J.Silenko,Zs.Eksp.Teor.Fiz.123,688(2003)[JETP96,610(2003)].[10]V.I.Goldanskii,Chemical Reactions of Positronium,Univ.of Newcastle upon Tyne, Newcastle-upon-Tyne(1968).[11]N.Shinohara,N.Suzuki,T.Chang,and T.Hyodo,Phys.Rev.A64,042702(2001); arXiv:physics/0011054.[12]J.Major,H.Schneider,A.Seeger et al.,J.Radioanal.Nucl.Chem.190,481(1995).[13]M.Senba,Can.J.Phys.74,385(1996);75,117(1997).[14]ndau and E.M.Lifshitz,Quantum Mechanics:Non-relativistic Theory,3rd ed.,Pergamon Press,Oxford(1977).。
Organometallic Compounds有机金属试剂有机金属试剂主族金属试剂：Li,Na, Mg, Cu, Zn, Cd过渡金属有机化合物：Pd,W,Mo,Ni,Sn稀土金属有机化合物: Sm,La,Yb,Ru,Rh,ScI. Concepts and principles Compounds with C-M bond. M = metalAs electrophilic reagents,attacked by nucleophilesAs nucleophilicreagents, attackelectrophiles Organometellic compoundsOrganometellic compoundsThe reactivity depends on the nature of the metal atom. Electropositive characterA. Preparation1. From metals and organic halides2. Metal-halogen exchangeSolventEquilibrium 利于形成与电负性更大的碳原子相连的有机金属试剂3. Metal-metal exchange4. Metalation of hydrocarbonsEquilibrium/ 利于形成含更小电正性金属的试剂A acidic C-H bond, formation a stable carbanionB. General reactions of organometallic compounds1. Substitution ( nucleophilic )2. Addition to double bondsNucleophiliesII. Organomagnesium compounds(Grignard reagents)♣1901, Grignard reagent was discovered; ♣1912, Nobel PrizeX = Cl, Br, IR = alkyl, aryl, alkenylPreparation:Order of reactivity: RI > RBr > RCl >> RF ♦Magnesium metal♦Alkyl halide: ♦Solvent: 乙醚, THF ，（丁醚, 异戊醚），甲基叔丁基醚⨯♦O 2, CO 2, H 2O should be rigorously excluded 1o RX > 2o RX > 3o RX♦反应的引发：碘或者CH 2Br 2♦反应的淬灭：氯化铵水溶液Vinyl halidesAcetylenic halidesAlkyl Chlorides Reactions of Grignard reagentsA. Formation of carbon-carbon bonds 1. Formation of Hydrocarbons 延长碳链烷基化卤代烃、磺酸酯、硫酸酯2. Formation of AlcoholsTertiary alcoholPrimary alcoholSecondary alcohol酮甲醛醛格氏试剂与醛酮的反应提供了一条由简单醇制备复杂醇的路线收率-----电性因素立体因素√Less bulky Grignard reagent is preferableAlternative methods for synthesizing alcoholsa. With acyl halides控制投料比,可控制产物的结构状态低温, 等当量投料立体位阻？b. With carboxylic esters3o 醇有两个相同烃基的醇甲酸酯对称的仲醇2o 醇六甲基磷酰胺HMPA有两个相同取代基的二醇c. With epoxide增加两个碳的醇不对称环氧化物3. Formation of Aldehydes原酸酯4. Formation of Ketones腈酰胺5. Formation of Caboxylic acids 与CO 2的反应B. Reaction at elements other than carbon1. Hydroperoxides 氢过氧化物2. Thiols过氧醇硫醇3. Sulfinic acids4. Alkyl Iodides烷基亚磺酸5. Amines6. Derivatives of phosphorus, boron, and siliconC. Some abnormal reactions of Grignard reagents1. Allylic and Benzylic Grignard reagentMajorminorAllyl Grignard reagentAllylic-type Grignard reagentReaction through six-membered cyclic transition stateBenzylic Grignard reagentsPyrrole2-position3-positionIndole2. 1,4 -Additionα, β-不饱和醛, 1,2-additionGrignard reagent, with a large bulky group1, 2-addition1,4-addition75%25%α, β-不饱和酮, 1,4-additionOrganic SynthesisA large bulky group in 4-positionA large bulky group in α-positionCu +, Cu 2+催化1,4-加成反应CuCl, Cu(OAc)2,CuCN3. Undesirable reactions of Grignard reagentDecomposition of Grignard reagentα-Hydrogen atomenolizationAs a baseReductionA hydrogen atom at β-carbonHydride-ion transferSix-memberedCyclic transition stateStereoselectivityMechanism of Grignard Reaction Barbier reactionIII. Organolithium compounds♦作为强碱;♦作为强的亲核试剂, 活性高于Grignard 试剂;♦发生一些不同于Grignard 试剂的反应Wurtz coupling reaction♦RX/Li干燥, 溶剂, 隔绝空气, 温度低温反应♦金属-卤素交换芳基、乙烯基卤代物♦锂-氢交换较强酸性的烃C-H键涉及有机锂试剂的实验装置RLi 过滤、转移装置反应装置无水溶剂蒸馏转移装置涉及有机锂试剂的实验装置B. ReactionsSimilar as the Grignard reagents, but more effective.The differences from Grignard reagentsLess readily prevented by steric hindrance from reacting at carbonyl groups.1. Reaction with Carbonyl Groups2. 1,2-addition , with unsaturated ketones1,4-addition1,2-addition3. Wurtz coupling 烃基取代反应4. Carbon dioxide 形成羧酸、酮的反应羧酸5. Addition to cyclic ether6. Reaction with Carboxylic DerivativesIV. Organocopper compoundsA. PreparationOrganocoper compoundsLithium organocuprates二烷基铜锂试剂R = alkyl, alkenyl, arylB. Reactions1. With alkyl halides较少重排、消除副反应2. Coupling reaction with Carbonyl halides形成酮，温和，收率较高3. Reaction with α-Bromo-ketones酮的α-烃化碱催化, 与卤代烃反应/ 消除, 缩合烷基铜锂试剂仅与卤代烃反应, 而不与醛酮羰基反应4. With α,β-unsaturated carbonyl compoundsReacts exclusively by 1,4-addition, Michael addition---------高度的区域选择性, 将烷基、芳基引入α、β-不饱和羰基化合物的β-位RMgBr: 1,2-and 1,4-additionRLi: 1,2-addition R2CuLi: 1, 4-additionCis-加成5. Addition to Epoxides反应条件温和，生成增加2个碳的醇；加成反应的位点α, β-不饱和环氧化物1, 4-additionTrans-addition活性顺序：酰氯> 醛> 环氧化物>RX>酮>酯>腈6. Copper(I) catalyzed formation of cyclopropanesA copper-carbene complex may be involved V. Organocadmium compoundsA. Preparation金属试剂与金属离子交换, 生成更稳定的金属试剂R = alkyl, aryl 反应活性比RMgX, RLi低, 毒性B. ReactionDo not react with ketones and esters.分子中引入酮基, 对其它功能团没有影响VI. Organozinc compounds A. Preparation1. With acyl chlorideB. ReactionsKetones2. With aldehydes and ketonesReformatsky reaction3. With nitriles4. The Simmons-Smith reactionCarbenoidZinc-copper alloyVII. Organonickel compoundsA. PreparationThe 3-allyl complex dimerizationAllyl halideB. ReactionsCoupling reaction with alkyl halidesDihydrocoumarinsTerpenesB. ReactionsVIII. Organoferric compoundsA. PreparationCollman’s reagentCarbonyl complexSynthesis of cyclic ketonesFerrocene二茂铁。
equilibrium英文解释Equilibrium is a fundamental concept in physics, chemistry, economics, and other fields, referring to a state of balance or stability where opposing forces or influences are balanced, resulting in no net change or motion. In other words, it is a state where the system is at rest or in a constant state of motion, with no tendency to change.In physics, equilibrium is often described as the state where a system is in a state of dynamic balance, with all forces acting on it canceled out by opposing forces. This can be seen in mechanical systems, where objects are atrest or moving with constant velocity, or in thermodynamic systems, where the system is in a state of thermal balance, with no net heat flow.In chemistry, equilibrium is typically referred to as a state where a chemical reaction proceeds in both directions at the same rate, resulting in no net change in theconcentrations of the reactants and products. This state is known as chemical equilibrium, and it is described by the law of mass action, which states that the rate of a chemical reaction is proportional to the product of the concentrations of the reactants.In economics, equilibrium is often described as a state where the supply and demand for a particular good or service are balanced, resulting in a stable price. This state is known as market equilibrium, and it is described by the law of supply and demand, which states that the price of a good or service will adjust to balance the quantity supplied with the quantity demanded.In all these fields, equilibrium is an important concept because it represents a state of stability and predictability. When a system is in equilibrium, it is generally easier to understand and predict its behavior than when it is in a state of flux or change. Additionally, equilibrium states often correspond to optimal or most efficient conditions, making them important targets for engineering, economic policy, and other applications.However, it is important to note that equilibrium is not always a static or unchanging state. In many systems, equilibrium is a dynamic state, with small fluctuations or perturbations constantly occurring. These fluctuations can be caused by external influences, internal fluctuations in the system, or random events. In these cases, the system will continually adjust to maintain the balance orstability of the equilibrium state.Additionally, it is worth noting that achieving or maintaining an equilibrium state can often be challenging. In many cases, it requires careful control or management of the system, as well as an understanding of the interactions and dependencies within the system. For example, in economic systems, maintaining market equilibrium often requires government intervention or regulation to prevent market failures or excesses. In physical systems, achieving equilibrium may require precise control of external conditions or the manipulation of system parameters.In conclusion, equilibrium is a fundamental conceptthat describes a state of balance or stability in various fields. It represents a state where opposing forces or influences are balanced, resulting in no net change or motion. While equilibrium may be seen as a static or unchanging state in some cases, it is often a dynamic state that requires careful management and control to maintain. Understanding and manipulating equilibrium states iscrucial in many fields, including physics, chemistry, economics, and engineering, and has important applications in real-world scenarios.。
Journal of Magnetism and Magnetic Materials242–245(2002)1277–1283Invited paperNanocrystalline high performance permanent magnets O.Gutfleisch*,A.Bollero,A.Handstein,D.Hinz,A.Kirchner,A.Yan,K.-H.M.uller,L.SchultzInstitute of Solid State and Materials Research,IFW Dresden,P.O.Box270016,01171Dresden,GermanyAbstractRecent developments in nanocrystalline rare earth–transition metal magnets are reviewed and emphasis is placed on research work at IFW Dresden.Principal synthesis methods include high energy ball milling,melt spinning and hydrogen assisted methods such as reactive milling and hydrogenation-disproportionation-desorption-recombination. These techniques are applied to NdFeB-,PrFeB-and SmCo-type systems with the aim to produce high remanence magnets with high coercivity.Concepts of maximizing the energy density in nanostructured magnets by either inducing a texture via anisotropic HDDR or hot deformation or enhancing the remanence via magnetic exchange coupling are evaluated.r2002Elsevier Science B.V.All rights reserved.Keywords:Permanent magnets;Nanocrystalline materials;Exchange coupling;Texture;Hydrogen absorption1.IntroductionNanocrystalline materials,including those of mag-netic materials,have been at the centre of numerousR&D activities during the last decade because of theirparticular scientific and technological properties.In thecase of hard magnetic rare earth–transition metal(R–T)compounds,it is the grain size and the presence orabsence of intergranular phases which give rise tounusual magnetic properties because of surface/interfaceeffects different from those of bulk or microcrystallinerge coercivities can be obtained once thegrain size is below a certain threshold where thecrystallites become single domain.In most of the R–T-compounds discussed here,the critical single-domainparticle size d c is a fraction of a micron.Assuming idealized microstructures,three prototypesof NdFeB-type magnets can be distinguished on thebasis of the ternary phase diagram[1]:Type(I)israre earth rich and the individual crystallites are sepa-rated by a thin paramagnetic layer,the rare earth-richintergranular phase.This structure leads to a decouplingof the hard magnetic grains resulting in high coercivities.Type(II)is obtained using the stoichiometric R2Fe14Bcomposition and the hard magnetic grains are in directcontact with each other(‘single-phase exchange coupledmagnets’)[2].Type(III)nanocomposite magnets are Rdeficient(i.e.,R concentrations o11.76at%)and thecoupling occurs between the R2Fe14B grains(to providehigh coercivity)and soft magnetic Fe3B or Fe rich grains(to provide high magnetisation;e.g.J sða2FeÞ¼2:16T).The exchange interaction between the grains of thedifferent phases leads to single-phase demagnetisationcurves despite a multi-phase microstructure providedgrain sizes are below a certain threshold and para-magnetic intergranular phases are absent[3–5].En-hanced remanences of the isotropic hard magneticmaterials,larger than those predicted by the Stoner-Wohlfarth theory[6]for systems of isotropicallyoriented,magnetically uniaxial,non-interacting singledomain particles where M r=M S p0:5;are the conse-quence.The development of melt-spun or rapidly quenchedNd–Fe–B magnets by Croat and Herbst[7]coincidedwith that of sintered magnets by Sagawa[8].Nanocrys-talline structures can also be synthesised by mechanical *Corresponding author.Tel.:+49-351-4659-664;fax+49-351-4659-781.E-mail address:o.gutfleisch@ifw-dresden.de(O.Gutfleisch).0304-8853/02/$-see front matter r2002Elsevier Science B.V.All rights reserved.PII:S0304-8853(01)00989-1alloying [9],intensive milling or hydrogenation dispro-portionation desorption and recombination (HDDR)processing [10,11].These nanostructures,provide energy barriers preserving the metastable,permanently magne-tised state.The resulting isotropic powders are most commonly used for the production of bonded magnets,where they are usually mixed with polymer resin and are then injection or compression moulded.Bonded mag-nets have the advantage of easily accomplished near net-shape processing,the avoidance of eddy-currents and good mechanical properties.The disadvantage being the dilution of magnetic properties due to the polymer binder.The randomly oriented grain structure results in magnetically isotropic magnets,with the remanent polarisation,J r ;and (BH )max limited to 0.5and 0.25,respectively,of the values obtainable for ideal micro-structures consisting of single domain grains and with full crystallographic alignment.Therefore various con-cepts have to be developed in order to increase remanence as shown in Fig.1.The three most relevant ways of maximising the energy density (BH )max are hot deformation [12,13],inducement of texture via ‘aniso-tropic’HDDR [14]or thirdly,remanence enhancement via exchange coupling [3,4].In summary,the task of transferring good intrinsic properties such as high values of Curie temperature (T C >500K),high saturation magnetisation (M s >1T)and high anisotropy field,H A into useful extrinsic properties of nanocrystalline magnets such as coercive field H C ;remanent magnetisation B r and maximum energy density (BH )max by appropriate processing is described in this paper.2.Maximising the energy density (BH)max 2.1.High energy ball millingAs a non-equilibrium processing technique,mechan-ical alloying circumvents,like rapid quenching,many limitations of conventional alloying and thus can be used for the preparation of metastable alloys.The mixing of the elements is achieved by an interdiffusional reaction,enabled by the formation of ultrafine layered composite particles during high energy ball milling.Depending on the thermodynamics of the alloy system,energy input and the mechanical workability of the starting powders,the alloying can take place during milling or during a subsequent heat treatment [9].A variation of this high energy ball milling technique is intensive milling,where an alloy is exposed to high energy ball milling rather than the elemental powders.Here,an example is given for the intensive milling of a Pr–Fe–B-based alloy.Pr 2Fe 14B-type alloys are compar-able in terms of their intrinsic magnetic properties [15]and phase relations with the advantage of a much lower spin reorientation temperature.An alloy with the nominal composition Pr 9Nd 3Dy 1Fe 72Co 8B 6.9Zr 0.1has been milled for 60h (leading to a type II magnet)and also with various amounts of Fe powder (leading to type III magnets)and subsequently annealed at 6001C for 30min.The partly amorphous structure after milling is illustrated in Fig.2.The Curie-temperature of the alloy is T C ¼3801C.The magnetic properties of various annealed powders are shown in Fig.3.Optimised valued for (BH )max were above 175kJ/m 3when adding 20–25wt%Fe (B r ¼1:18T and i H c ¼0:66T).A key issueFig.1.Flow chart illustrating the principal processing routes of high energy density magnets based on micro-and nano-crystalline powders.The right branch shows the three principal ways of maximizing the energy product (BH )max of nanocrystalline magnets.O.Gutfleisch et al./Journal of Magnetism and Magnetic Materials 242–245(2002)1277–12831278for the effectiveness of the exchange coupling and thus the degree of remanence enhancement is the develop-ment of a uniform nanoscale microstructure of hard and soft magnetic grains.This can be realised by micro-alloying using additions such as Zr and Co having grain growth inhibiting effects [16,17]or leading to a modification of the tie lines in the phase diagram and thus changed volume fractions of the different phases [18].An effective coupling occurs when the soft regions with a small anisotropy are no bigger than a few times the exchange length l ex ;i.e.o 20nm and thus a complete coupling of the soft magnetic grain occurs.The crystal-lite size of the annealed sample was evaluated from the broadening of the X-ray diffraction peaks (see Fig.3)using the Williamson-Hall method [19]and it was found to be around 20nm.Remanence enhanced high energy density magnets,synthesised by melt spinning or ball milling techniques,are of great commercial interest because no magnetic alignment and less of the costly rare earth element arerequired and an improved corrosion behaviour can be expected.2.2.Rapid quenchingCurrently,rapidly quenched Nd–Fe–B forms the basis for almost the entire bonded magnet industry.The flexibility of bonded Nd–Fe–B-type magnets in proces-sing,shape and magnetic properties and the highly stable nature of the ribbons contribute to its success in a fast growing permanent magnet market [20–22].De-pending on the wheel speed,ejection conditions and melt temperature substantial undercooling below the equili-brium freezing temperature and,consequently,a very high frequency of crystal nucleation are achieved (‘‘over-quenching’’).Lower wheel speeds can lead directly to nano-crystalline material (‘‘direct-quenching’’).The inset of Fig.4shows the DSC curves on first heating of melt-spun Nd 15DyFe 75.9B 8Zr 0.1and Pr 15Dy-Fe 75.9B 8Zr 0.1alloys.XRD patterns of both melt-spun materials showed a partly amorphous structure which explains the presence of a second order thermodynamic phase transition around 3101C and 2951C,respectively,during first heating corresponding to the Curie-tem-perature of the remaining R 2Fe 14B phase.A comparison of the onset of crystallization of both alloys prepared by this technique and by intensive milling showed lower values in the case of the latter method:5801C for the Nd-based alloy and 5301C for the Pr-based alloy whereas values of 6001C and 5751C,respectively,were obtained when using melt-spinning [23].Annealing of the melt-spun alloys at 6501C leads to the com-plete formation of the R 2Fe 14B phase achieving coerciv-ities as high as 2.7T for PrDyFeBZr and 2.37T for3035404550556065707580••600˚Cafter millingi n t e n s i t y (a .u .)2 theta (degree)Fig.2.XRD patterns of Pr 9Nd 3Dy 1Fe 72Co 8B 6.9Zr 0.1after 60h of intensive milling in argon and after annealing at 6001C for 30min.Intensity peaks of a –Fe ( )are indicated.-1.5-1.0-0.50.00.51.01.5P o l a r i s a t i o n J ( T )Applied field µ0H ( T )Fig.3.Hysteresis loops of intensively milled (with various amounts of Fe)and annealed Pr 9Nd 3Dy 1Fe 72Co 8B 6.9Zr 0.1.P o l a r i s a t i o n J ( T )Applied field µ0H ( T )Fig.4.Demagnetisation curves of melt-spun NdDyFeBZr and PrDyFeBZr materials annealed at 6501C for 10min (inset:DSC curves on first heating (40K/min)of melt-spun NdDyFeBZr and PrDyFeBZr showing Curie temperature,T C ;and crystal-lization onset,T x ).O.Gutfleisch et al./Journal of Magnetism and Magnetic Materials 242–245(2002)1277–12831279NdDyFeBZr (see Fig.4).The room temperature aniso-tropy field of Pr 2Fe 14B is around 25%larger than of its Nd counterpart,and the saturation magnetisation is only slightly lower.Melt-spun precipitation hardened Sm 2(Co,Cu,-Fe,Zr)17magnets have been produced using single roller melt-spinning at low velocity and their magnetic proper-ties in the as-spun state and after hardening are shown in Fig.5.Coercivity is developed only during the complex annealing treatment leading to the formation of a cellular structure (see inset in Fig.5)similar to that in sintered 2:17-type magnets.However,the resulting powder in this case is isotropic.It has been found that this type of material can show an abnormal temperature dependence of the coercivity [24]leading to excellent high temperature magnetic properties also reported for sintered magnets [25,26].Another interesting aspect is the production of magnetically anisotropic SmCo 5-type ribbons also using low wheel speeds [27]and a (BH )max of 146kJ/m 3was obtained for Sm 1.1Co 5[28].The c -axis of the crystallites after direct-quenching were found to be parallel to the longitudinal axis of the ribbon.This phenomenon is shown here for various Sm 2(Co)17-type alloys with the successive addition of Fe,Zr and Cu.XRD patterns of Fig.6show that the degree of texture decreases when adding Zr and Cu.This is illustrated by the weaker (110)and (200)and stronger (111)and (002)peaks for the Sm 2(Co,Cu,Fe,Zr)17alloy.2.3.Hydrogen assisted processingThe HDDR process is established as a processing technique for the production of highly coercive Nd 2Fe 14B [10,11]and Sm 2Fe 17N y magnets [29,30].A special type of powder suitable for bonded magnets is the anisotropic powder made by HDDR [14]which could close the gap in the market for high energyproduct bonded magnets.Very recently,excellent magnetic values of B r ¼1:38T,i H c ¼1122kA/m and (BH )max =342kJ/m 3have been obtained for NdFe-GaNbB using a process which controls the reaction rates during exothermic hydrogen absorption (dispro-portionation)and endothermic desorption (recombina-tion)by pressure adjustments [31,32].This multistage HDDR process is beneficial to optimise remanence and coercivity without expensive additions such as Co.Strictly,HDDR does not lead to nanoscale (usually defined as o 100nm)material,as the final product resulting from the reversible,hydrogen-induced chemi-cal reaction shows typical grain sizes of around 300nm.The disproportionated state is certainly nanoscale and it is this intermediate product which should clarify the mechanism of the inducement of texture.Various models have been suggested and they have been detailed in a recent review [33].Intermediate boride phases have been linked with the transfer of the original cast grain orientation to that of the recombined 2-14-1-type grains in both,NdFeCoGaB [34]and NdFeB [35]alloys.The HRSEM micrograph in Fig.7shows the solid-dispro-portionated state of a Nd 16.2Fe 78.2B 5.6alloy.The eutectoid-type decomposition into NdH 27x rods of appr.20nm and Fe and a build-up of finely dispersed Fe 3B particles of 10–50nm diameter in the intercolony regions due to an ejection of this phase from the rod-like areas can be observed.The principal solid-disproportionation reactions of the R 2Fe 14B (with R=Nd or Pr)phases can be described as follows:R 2Fe 14B þð27x ÞH 2)2RH 27x þ11Fe þFe 3B )2RH 27x þ12Fe þFe 2B :ð1ÞIn the case of a Pr 13.7Fe 63.5Co 16.7Zr 0.1B 6alloy a new intermediate boride phase,Pr(Fe,Co)12B 6(R3m),has been found recently after solid-disproportionation[36]Fig.5.Hysteresis loops of as-spun and precipitation hardened (T h =11601C,1h,T a =8501C,20h,cooling to 4001C with 0.75K/min)Sm(Co 0.74Cu 0.12Fe 0.1Zr 0.04)7.5(inset:TEM bright field image of the latter).3035404550556065707580Sm 2Co 17Sm 2(Co 0.9Fe 0.1)17Sm 2(Co 0.86Fe 0.1Zr 0.04)17Sm 2(Co 0.74Fe 0.1Cu 0.12Zr 0.04)17(201)(002)(111)(110)(200)I n t e n s i t y (a .u .)2 theta (degree)Fig.6.XRD patterns of as-spun (using a low wheel speed)Sm 2(Co)17-type alloys with the successive addition of Fe,Zr and Cu.O.Gutfleisch et al./Journal of Magnetism and Magnetic Materials 242–245(2002)1277–12831280and a high degree of texture has also been reported for this type of alloys after conventional processing [37].The application of the HDDR process to the Nd–Co–B or Sm–Co systems requires more severe hydrogena-tion conditions which is due to the higher thermo-dynamic stability of the R–Co phases against the disproportionation by hydrogen compared to those of the Nd 2Fe 14B and Sm 2Fe 17phases.Recently,it was shown that HDDR in thermodynamically stabilised compounds such as Sm 2Fe 16Ga,SmCo 5,Sm 2Co 17and Nd 2Co 14B is successful when using high hydrogen pressures [38]or reactive milling in hydrogen [39].In case of Sm 2Co 17,the latter mechanically activated gas-solid reaction leads to the disproportionation of the rhombohedral 2:17phase into Sm-hydride and FCC Co according to the following equation:Sm 2Co 17þð27x ÞH 232SmH 27x þ17Co :ð2ÞIntimate mixtures of R-hydride with grain sizes o 10nm and BCC Fe or FCC Co are obtained after reactive milling which is not possible when applying the conventional HDDR process [33].For SmCo-type alloys,the following desorption treatment at tempera-tures as low as 5001C leads to the recombination to the original structure either of CaCu 5and Th 2Zn 17type.In dependence on Sm content,milling parameters and desorption temperature additional phases are synthe-sised,partly of metastable character,such as the Sm 2Co 7phase.The recombined multiphase material exhibits grain sizes of the scale o 30nm (compare Fig.8)which makes an effective exchange coupling and thus rema-nence enhancement possible.Magnetically single phase demagnetisation loops are observed and a clear tendency of increased coercivity and decreased reman-cence with increasing Sm content is found [40].2.4.Hot deformationHot deformation-induced texturing of nano-grained materials is an option for producing fully dense,anisotropic magnets with maximised energy densities.A grain alignment along the c -axis of the tetragonal 2:14:1phase based on either Nd–Fe–B or Pr–Fe–B alloys perpendicular to the plastic flow is achieved after high temperature compressive deformation [12,13].The production of a fully dense isotropic precursor at about 7251C is followed by placing this compact in an oversized die-cavity where die-upsetting is carried out at similar temperatures.After this second step,an anisotropic magnet is obtained with the alignment of the crystallographic c -axis parallel to the pressing direction.Alternatively,backward extrusion [41]can be carried out as a second step to produce near net-shape ring magnets which can show,especially for smaller dimensions,superior magnetic properties to sintered magnets.A radial preferential orientation is obtained,again with the c -axis alignment perpendicular to the material flow.Small variations in the magnetic properties have been observed along the cross-section and along the axial direction of the ring magnets which were attributed to inhomogeneities in material flow inherent to the deformation process [42].Additions of Co are used to improve the thermal stability and to increase the Curie-temperature in sintered NdFeB magnets.Simultaneously the coercivity is reduced,which again can be compensated by small additions of Ga.The same positive effect of Co and Ga was found in hot deformed NdFeB magnets,prepared from melt-spun material (MQU-F).The addition of Ga decreases melting point and viscosity of the Nd-rich grain boundary phase.This accelerates mass transfer through the liquid and improves the isolation of the grains leading to enhanced coercivities.TEM-EDX analysis showed a preferential solution of Ga intotheFig.8.TEM bright field image of reactively milled and recombined Sm 2Co 17powder.Fig.7.Scanning electron microscopy image in the backscat-tered mode showing the rod-like structure of NdH 27x (A)and a –Fe (B)and finely dispersed Fe 3B (C)obtained after 15min of solid-disproportionation at 9001C.O.Gutfleisch et al./Journal of Magnetism and Magnetic Materials 242–245(2002)1277–12831281Nd-rich grain boundary phase,now a neodymium–iron–gallium phase.Ga reduces the surface energy of this phase resulting in smoothed grain boundaries and a more uniform distribution [43].Thus,lower deformation forces are required for hot deformation and higher B r material can be produced because of an increased volume fraction of the hard magnetic 2:14:1phase with a commensurate reduction in the non-ferromagnetic grain boundary material.Demagnetisation curves of hot pressed and die-upset melt-spun NdFeB-type powders are shown in Fig.9.As a comparison,hot pressed and die-upset intensively milled Pr 14.7Fe 77.3B 8.0powder is also included.The already mentioned much lower spin reorientation temperature make them attractive for low temperature applications such as superconducting bearings.Opti-mised deformation conditions were used for the production of MQ-type magnets [43]and remarkably higher coercivities were found in hot pressed and in hot deformed MQU-F magnets.A reduction in coercivity after die-upsetting can be observed which amounts to 25%in MQU-F magnets and to 40%in MQP-A.The higher coercivity in MQU-F magnets is due to the beneficial effect of the additives resulting in smaller grains after hot deformation.A remanence of B r ¼1:3T and a (BH )max =326kJ/m 3were measured for the MQU-F die-upset magnet.The loop shape ((BH )max =307kJ/m 3)and the hot workability of the Pr 14.7Fe 77.3B 8.0die-upset magnet made from intensively milled powder are excellent and it can be expected that compositional modifications will improve the magnetic properties further.3.ConclusionsNowadays about 85%of the limit for the energy density (BH )max (based on the Nd 2Fe 14B phase)can beachieved in commercially produced sintered Nd–Fe–B grades [44,45].Coercivity values however,rarely exceed 20–30%of the anisotropy field H A .Recent exciting developments include excellent anisotropic HDDR powders for polymer bonded magnets and SmCo-type magnets for application temperatures as high as 5501C.In terms of maximised energy densities,there is still a lot of scope for improvement for bonded and fully dense nanocrystalline magnets,especially considering multi-component systems.In this context,it is just to state that computational micromagnetism based on realistic mi-cro-and nano-structures and modelling of phase diagrams will be of increased importance in order to map the vast number of ternary,quaternary,etc.equilibrium and non-equilibrium phases.Novel proces-sing techniques and microalloying should allow more freedom for tailoring magnetic and non-magnetic properties of nanocrystalline high performance perma-nent magnets.AcknowledgementsThe support of parts of this work by the Deutsche Forschungsgemeinschaft (SFB 463),SfP (Science for Peace,Nato)and the EU (HITEMAG)is gratefully acknowledged.References[1]K.H.J.Buschow,in:K.H.J.Buschow (Ed.),Handbook ofMagnetic Materials,Vol.10,Elsevier Science,North Holland,Amsterdam,1997(Chapter 4).[2]G.B.Clemente,K.E.Keem,J.P.Bradley,J.Appl.Phys.64(1988)5299.[3]R.Coehoorn, D.B.Mooji,J.P.Duchateau,K.H.J.Buschow,J.Phys.49(C8)(1988)669.[4]E.F.Kneller,R.Hawig,IEEE Trans.Magn.27(1991)3588.[5]K.H.M .uller,D.Eckert,A.Handstein,M.Wolf,S.Wirth,L.L.M.Martinez,Proceedings of the Eighth International Symposium Magn.Anisotropy and Coercivity in RE-TM Alloys,Birmingham,UK,1994,p.179.[6]E.C.Stoner, E.P.Wohlfarth,Philos.Trans.R.Soc.London,Ser.A 240(1948)599.[7]J.J.Croat,J.F.Herbst,R.W.Lee,F.E.Pinkerton,J.Appl.Phys.55(1984)2078.[8]M.Sagawa,S.Fujimori,M.Togawa,Y.Matsuura,J.Appl.Phys.55(1984)2083.[9]L.Schultz,J.Wecker, E.Hellstern,J.Appl.Phys.61(1987)3583.[10]T.Takeshita,R.Nakayama,Proceedings of the 10thInternational Workshop on RE Magnets and their Appl.,Kyoto,Japan,1989,p.551.[11]P.J.McGuiness,X.J.Zhang,X.J.Yin,I.R.Harris,J.Less-Common Met.158(1990)379.[12]R.K.Mishra,R.W.Lee,Appl.Phys.Lett.48(1986)733.-3.0-2.5-2.0-1.5-1.0-0.50.00.00.20.40.60.81.01.21.4P o l a r i z a t i o n J (T )Applied field µ0H (T)Fig.9.Demagnetisation curves of hot pressed and die-upset melt-spun NdFeB-type and intensively milled PrFeB-type materials.O.Gutfleisch et al./Journal of Magnetism and Magnetic Materials 242–245(2002)1277–12831282[13]J.J.Croat,IEEE Trans.Magn.25(1989)3550.[14]T.Takeshita,R.Nakayama,12th International Workshopon RE Magnets and their Appl.,Canberra,1992,p.670.[15]S.Hirosawa,Y.Matsuura,H.Yamamoto,S.Fujimura,M.Sagawa,H.Yamauchi,J.Appl.Phys.59(1986)873.[16]V.Neu,U.Klement,R.Sch.a fer,J.Eckert,L.Schultz,Mater.Lett.26(1996)167.[17]H.A.Davies,J.Magn.Magn.Mater.157/158(1996)11.[18]N.Sano,T.Tomida,S.Hirosawa,M.Uehara,H.Kanekiyo,Mater.Sci.Eng.A250(1998)146.[19]G.K.Williamson,W.H.Hall,Acta Metall.1(1953)22.[20]V.Panchanathan,Proceedings of the16th InternationalWorkshop on RE Magnets and their Appl.,Sendai,Japan, 2000,p.431.[21]G.C.Hadjipanayis,W.Gong,J.Appl.Phys.64(1988)5589.[22]H.A.Davies,C.L.Harland,J.I.Betancourt,G.Menoza,MRS Symp.Proceedings‘Advanced Hard and Soft Magnets’,Vol.577,1999,p.27.[23]A.Bollero,A.Kirchner,O.Gutfleisch,K.H.M.uller,L.Schultz,IEEE Trans.Magn.37(2001)2483.[24]D.Goll,I.Kleinschroth,W.Sigle,H.Kronm.uller,Appl.Phys.Lett.76(2000)1054.[25]C.Chen,M.S.Walmer,M.H.Walmer,S.Liu,G.E.Kuhl,G.K.Simon,MRS Symp.Proceedings of the‘AdvancedHard and Soft Magnets,’Vol.577,1999,p.277.[26]J.F.Liu,Y.Zhang,D.Dimitrov,G.C.Hadjipanayis,J.Appl.Phys.85(1999)2800.[27]A.Yan,W.Y.Zhang,H.W.Zhang,B.Shen,J.Magn.Magn.Mater.210(2000)L10.[28]A.Yan,W.Y.Zhang,H.W.Zhang,B.Shen,Mater.Sci.Eng.B68(1999)111.[29]H.Nakamura,S.Sugimoto,M.Okada,M.Homma,Mater.Chem.Phys.32(1992)280.[30]C.N.Christodoulou,T.Takeshita,J.Alloys Comp.196(1993)155.[31]C.Mishima,N.Hamada,H.Mitarai,Y.Honkua,Proceedings of the16th International Workshop on RE Magnets and their Appl.,Sendai,Japan,2000,p.873. [32]C.Mishima,N.Hamada,H.Mitarai,Y.Honkua,IEEETrans.Magn.37(2001)2467.[33]O.Gutfleisch,J.Phys.D33(2000)R157.[34]T.Tomida,N.Sano,K.Hanafusa,H.Tomizawa,S.Hirosawa,Acta Metall.47(1999)875.[35]O.Gutfleisch, B.Gebel,N.Mattern,J.Magn.Magn.Mater.210(2000)5.[36]O.Gutfleisch,A.Teresiak,B.Gebel,K.-H.M.uller,N.B.Cannesan,D.N.Brown,I.R.Harris,IEEE Trans.Magn.37(2001)2471.[37]R.N.Faria,A.J.Williams,I.R.Harris,J Alloys Comp.287(1999)L10.[38]M.Kubis,O.Gutfleisch,K.H.M.uller,I.R.Harris,L.Schultz,J.Appl.Phys.83(1998)6905.[39]O.Gutfleisch,M.Kubis,A.Handstein,K.-H.M.uller,L.Schultz,Appl.Phys.Lett.73(1998)3001.[40]O.Gutfleisch,A.Bollero,D.Eckert,B.Gebel,M.Kubis,K.-H.M.uller,L.Schultz,Proceedings of the16th International Workshop on RE Magnets and their Appl., Sendai,Japan,2000,p.883.[41]N.Yoshikawa,H.Yamada,Y.Iwasaki,K.Nagata,Y.Kasai,Proceedings of the13th International Workshop on RE Magnets and their Appl.,Birmingham,UK,1994, p.635.[42]W.Gr.unberger,D.Hinz,D.Schl.a fer,L.Schultz,J.Magn.Magn.Mater.157/158(1996)41.[43]A.Kirchner,D.Hinz,V.Panchanathan,O.Gutfleisch,K.H.M.uller,L.Schultz,IEEE Trans.Magn.36(2000) 3288.[44]Y.Kaneko,IEEE Trans.Magn.36(2000)3275.[45]W.Rodewald,R.Blank,B.Wall,G.W.Reppel,H.D.Zilg,Proceedings of16th International Workshop on RE Magnets and their Appl.,Sendai,Japan,2000,p.119.O.Gutfleisch et al./Journal of Magnetism and Magnetic Materials242–245(2002)1277–12831283。
