1、磁性测量中的几个问题第二部分:参数磁化率的测量居里温度的测量饱和值的测量磁性测量讲座2007年磁学国家重点实验室磁化率2021TFHMHMH=?磁化率的定义:磁化强度M与磁场强度H的依赖关系初始磁化率磁化率质量(比)磁化率摩尔(克分子)磁化率张量磁化率H的大小M的计量单位H、M的空间分布磁化率MH=?磁化率的量纲与单位:磁场强度H的单位:A/m 的单位 的量纲M 的单位m3/molL3N1Am2/mol摩尔磁化率m3/kgL3M1Am2/kg质量磁化率11A/m磁化率磁化率MH=?磁化率的数值:闭合磁路开放磁路磁路励磁交流励磁直流励磁质量样品:几何形状体积测量方法:磁化率MH=?磁化率的数值:
2、不要求精确数值:略适用:直流磁化率交流磁化率根据磁化率计算其它参数:220(1)3JBBNg J JCk+=必须注意:H(样品内部的磁场)退磁效应 退磁效应、退磁场、退磁因子HextMintextdHHH=+?Hint样品内部磁场:ddHN M=??样品的磁化率:intintMH=dNextMH=int1dddNNN=intint1ddNN=+int11dNdN=退磁效应的理论处理 静磁学边值问题设空间充满磁导率为 2的介质,在此空间存在一均匀的平行磁场H0,将某一磁导率为 1的任意形状物体放置在此空间中,求解该物体内部感生的磁化强度和磁场强度。退磁效应的理论处理 求解依据:t=+DHJ1、M
3、axwell方程:0=H(J0,静磁学)()12-0=?nBB2、唯一性边界条件:0()=+BHHM3、磁化方程:00=MH退磁效应的理论处理 求解方法:0=H分离变量法32210iiiiguhu=Laplace方程:22221 23,iiiixyzhghh huuu=+=321()1()()44VSdd=+M rn M rrrrr-rr-r磁标势均匀磁化:0退磁效应的理论处理 求解方法:0=H1、引力势:Poisson:旋转椭球体R.I.Joseph2、磁标势级数展开:intintM?HD.X.Chen3、电感方法:A.S.Arrott4、能量方法:Magnetostatic princip
4、les in ferromagnetismW.F.Brown,Jr.,1962,North-Holland Publishing Company,Amsterdam退磁因子 旋转椭球体:精确解(解析解)bac1GGcGabNNN+=真空中:定义椭率:ccrab扁椭球(oblate spheroid)长椭球(prolate spheroid)(绕c轴旋转)()2211arccos11crNrrr=()2221ln1111crNrrrr=+r 1r=()()()22archln1arsh1rrrr+=sh,ch22xxxxeeeexx+=()()22arshln1,archln1xxxxxx=+=
5、+旋转椭球体的退磁因子0.10873.00.47580.61/31.00.75050.20.17362.00.52720.50.05585.00.43210.70.21871.60.58820.40.23301.50.66140.30.36180.90.86080.10.39440.81.0000.0NcrNcrccrab其它形状的退磁因子H=?均匀磁化假设:均匀退磁场假设:通量退磁因子Nf(the fluxmetric(ballistic)demagnetizing factor)xyzNf中心截面的平均磁化强度与平均退磁场强度之比Nm整个样品的平均磁化强度与平均退磁场强度之比强度退磁因子N
6、m(the magnetometric demagnetizing factor)圆柱体的退磁因子 均匀磁化:(h方向)h2a2hra定义长径比:21()()fffrNK kE kk=22414fkr=+222411()(1)()13mmmNrr K krE kr=+22111mkr=+12222222001 1(),;1;,122 2(1)(1)1sindxdyK kFkkxk xky=221222220011 1()1sin,;1;,1122 2k xE kdxdykyFkkx=20时:211FiorillofrNr=+r 1(细长圆柱体)时22413251,1228fNrrrr+241,
7、138mNrrrr 1(短粗圆柱体)时281ln1,1frNrr 2411ln,12mrNrr 薄片状22211arctanlnln(1),24mrrNrrbacrr=+()222223222221 121211lnln21ln2111122arctan12(1)2(21)132mrrrNrrrrrrrrrrrr r+=+craaac四方体长方体的退磁因子 退化情况下:如果:a b()()()2222222222428arctan2482ln28424frrrNrrrr rrr+=+四方体的退磁因子 简化公式:aac四方体craa b112SatomNr=+21arcsin1Fiorillom
8、Nr=+cra四方体的退磁因子0.02360.05860.11090.15090.16390.25870.28620.3178Nf0.35440.39710.44730.50730.58030.67170.79331.000Nf0.14043.00.45250.61/31.00.69420.20.19832.00.49590.50.08835.00.41570.70.23711.60.54820.40.24921.50.61240.30.35710.90.80510.10.38430.81.0000.0NmrNmr正确处理退磁效应 退磁效应的影响程度 如何确定退磁因子 规则形状的退磁因子 非规
9、则形状的退磁因子退磁效应对什么量有影响(Hext,M)所 有 与 Hint有 关 的 量!(Hint,M)MHextHdKittel公式旋转椭球体的一致进动本征频率:()()000 xzSyzSHNNMHNNM=+仅为教学使用10-310-210-110010110210310410510610-310-210-11001011021031.0000.1000.0100.00100102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137
10、138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237
11、23823924024124224324424524624724824925025125225325425525625725825926026126226326426526626726826927027127227327427527627727827928028128228328428528628728828929029129229329429529629729829930030130230330430530630730830931031131231331431531631731831932032132232332432532 3VWCXCYCZDADBDCDDDEDFDGDHDIDJDKDL
12、DMDNDODPDQDRDSDTDUDVDWDXDYDZEAEBECEDEEEFEGEHEIEJEKELEMENEOEPEQERESETEUEVEWEXEYEZFAFBFCFDFEFFFGFHFIFJFKFLFMFNFOFPFQFRFSFTFUFVFWFXFYFZGAGBGCGDGEGFGGGHGIGJGKGLGMGNGOGPGQGRGSGTGUGVGWGXGYGZHAHBHCHDHEHFHGHHHI HJHKHLHMHNHOHPHQHRHSHTHUHVHWHXHYHZ IA IB IC ID IE IF IG IH II IJ IK IL IM IN IO IP IQ IR IS IT IU
13、 IV IW IX IY IZ JA JBJCJD JE JF JGJH JI JJ JK JL JMJNJOJPJQJR JS JT JU JVJWJX JY JZKAKBKCKDKEKFKGKH KI KJ KKKLKMKNKOKPKQKRKSKTKUKVKWKXKYKZLALBLCLDLE LFLGLH LI LJ LK LLLMLNLwcxcyczdadbdcdddedfdgdhdidjdkdldmdndodpdqdrdsdtdudvdwdxdydzeaebecedeeefegeheiejekelemeneoepeqereseteuevewexeyezfafbfcfdfefffgfhf
14、ifjfkflfmfnfofpfqfrfsftfufvfwfxfyfzgagbgcgdgegfggghgigjgkglgmgngogpgqgrgsgtgugvgwgxgygzhahbhchd hehfhg hh hi hj hk hl hmhn ho hp hq hr hs ht hu hv hw hx hy hz ia ib ic id ie if ig ih iiij ik il im in io ip iq ir is it iu iv iw ix iy iz ja jb jc jd je jf jg jh jijj jk jl jm jn jo jp jq jr js jt ju jv
15、 jw jx jy jz ka kb kc kd ke kf kg kh ki kj kk kl km kn ko kp kq kr ks kt ku kv kw kx ky kz la lb lc ld le lf lg lh lilj lkll lm lnN N=0.001 N=0.002 N=0.003 N=0.004 N=0.005 N=0.006 N=0.007 N=0.008 N=0.009 N=0.010 N=0.020 N=0.030 N=0.040 N=0.050 N=0.060 N=0.0701 N=0.080A N=0.090a N=0.100 N=0.200 N=0.2
16、93 N=0.333 N=0.500 N=1.000Demagnetization factor N1+NN=修正未修正影响程度D1E-41E-30.010.111010010001E-71E-61E-51E-41E-30.010.11123456 7 8 9100.010.1Demagnetizing factors N(Nf,Nm)Aspect Ratio r(c/a or h/2a)N-Ellipsoid(-exact)Nf-Cylinder(-exact)Nm-Cylinder(-exact)Ndf-Cylinder(-Fiorillo)Nf-Rectangular Prism(-exact)Nm-Rectangular Prism(-exac)Ndm-Rectangular Prism(-Fiorillo)Ndm-Rectangular Prism(-Sato)规则形状非规则形状 学习微磁学W.F.Brown,Jr.,Magnetostatic principles in ferromagnetism,1962,North-Holland Publishing Company
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