磁性的测量

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2021TFHMHµχ∂≡≡∂∂∂MHχ=GG•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MHχ=GG•磁化率的量纲与单位：磁场强度H的单位：A/mχ的单位χ的量纲M的单位m3/molL3N–1Am2/mol摩尔磁化率m3/kgL3M–1Am2/kg质量磁化率11A/m磁化率磁化率MHχ=GG•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MHχ=GG•磁化率的数值：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)3JBBNgJJCkµµ+=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=+GGGHint样品内部磁场：ddHNM=−GIG？样品的磁化率：intintMHχ=dNextMHχ=int1dddNNNχχχ=−⋅intint1ddNNχχχ=+⋅int11dNdNχχ−=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µ2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µ1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、Maxwell方程：0∇×=H（J＝0，静磁学）()12-0⋅=GGGnBB2、唯一性边界条件：0()µµ==+BHHM3、磁化方程：00µµµ−=MH退磁效应的理论处理•求解方法：∇0×=H分离变量法32210iiiiguhuψψ=∂∂∇=⋅=∂∂∑Laplace方程：2222123,iiiixyzhghhhuuu∂∂∂=++=∂∂∂321(')1(')()''44VSddψππ∇⋅⋅=−+∫∫MrnMrrrrr-r'r-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：intint~MGGHD.X.Chen3、电感方法：A.S.Arrott4、能量方法：MagnetostaticprinciplesinferromagnetismW.F.Brown,Jr.,1962,North-HollandPublishingCompany,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（oblatespheroid）长椭球（prolatespheroid）（绕c轴旋转）()2211arccos11crNrrr=−−−()2221ln1111crNrrrr=+−−−−r1r1r＝1(),112abcNN=−G：几何等价表达式()()22arccosarcsin1arct1an,0rrrrr−=−=()()()22archln1arsh1rrrr+−=−=sh,ch22xxxxeeeexx−−−+==()()22arshln1,archln1xxxxxx=++=±+−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=−∇ΨG•均匀磁化假设：•均匀退磁场假设：通量退磁因子Nf（thefluxmetric(ballistic)demagnetizingfactor）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Nm（themagnetometricdemagnetizingfactor）圆柱体的退磁因子•均匀磁化：（h方向）h2a2hra≡定义长径比：21()()fffrNKkEkkπ=−−22414fkr=+{}222411()(1)()13mmmNrrKkrEkrπ=−++−−22111mkr=[phone](),;1;,1222(1)(1)1sindxdyKkFkkxkxkyππ===−−−∫∫2212222200111()1sin,;1;,11222kxEkdxdykyFkkxππ−==−=−−∫∫第1类完全椭圆积分第2类完全椭圆积分2hra≡圆柱体的退磁因子0.01890.04800.09350.12980.14180.23220.25920.2905Nf0.32730.37050.42210.48420.56040.65650.78451.000Nf0.12783.00.43030.60.31161.00.68020.20.18192.00.47450.50.07995.00.39330.70.21861.60.52810.40.23011.50.59470.30.33490.90.79670.10.36190.81.0000.0NmrNmr圆柱体的退磁因子•简化公式：h2a当r20时：211FiorillofrNr=−+r1（细长圆柱体）时22413251,1228fNrrrr≈−+241,138mNrrrπ≈−r1（短粗圆柱体）时281ln1,1frNrrπ≈−−2411ln,12mrNrrπ≈−−长方体的退磁因子2322221arctan()31[(,,)(,,)(,,)(,,)]2mmmmmabNFFabccabcFabcFbacFcabFcbaabcπππ=++++++−−cab•均匀磁化假设：沿c方向：122224arctan[(,)(,)]244fffabcNFFabFbaabcabcππ=+++++222222214444Facbcabcc=+++−++−33322222222(2)Fabcabcabc=+−++−++()322222222223(2)(2)Fcaaccbbcab=−++−+−[phone](84444)(,)ln(4)(844)fcuvcuuvcFuvuvcucuuc+++++≡++++22222222222222()(22)(,,)ln(22)muwuvvuvFuvwuvuuvwvuvw++++≡+++++长方体的退磁因子•退化情况下：bcra≡如果：b→∞22224arctanln,2frrNbacrrππ+=−薄片状22211arctanlnln(1),24mrrNrrbacrrπ−=+++()222223222221121211lnln21ln2111122arctan12(1)2(21)132mrrrNrrrrrrrrrrrrrπ−+−+−=+++++++++−−+−++−++cra≡aac四方体长方体的退磁因子•退化情况下：如果：a＝b()()()2222222222428arctan2482ln28424frrrNrrrrrrrππ++=++−+−+++++四方体的退磁因子•简化公式：aac四方体cra≡a＝b112SatomNr=+21arcsin1FiorillomNrπ=+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：()()000xzSyzSHNNMHNNMωµγ=+−⋅+−仅为教学使用10-310-210-110010110210310410510610-310-210-11001011021031.0000.1000.0100.00100102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187188189190191192193194195196197198199200201202203204205206207208209210211212213214215216217218219220221222223224225226227228229230231232233234235236237238239240241242243244245246247248249250251252253254255256257258259260261262263264265266267268269270271272273274275276277278279280281282283284285286287288289290291292293294295296297298299300301302303304305306307308309310311312313314315316317318319320321322323324325323VWCXCYCZDADBDCDDDEDFDGDHDIDJDKDLDMDNDODPDQDRDSDTDUDVDWDXDYDZEAEBECEDEEEFEGEHEIEJEKELEMENEOEPEQERESETEUEVEWEXEYEZFAFBFCFDFEFFFGFHFIFJFKFLFMFNFOFPFQFRFSFTFUFVFWFXFYFZGAGBGCGDGEGFGGGHGIGJGKGLGMGNGOGPGQGRGSGTGUGVGWGXGYGZHAHBHCHDHEHFHGHHHIHJHKHLHMHNHOHPHQHRHSHTHUHVHWHXHYHZIAIBICIDIEIFIGIHIIIJIKILIMINIOIPIQIRISITIUIVIWIXIYIZJAJBJCJDJEJFJGJHJIJJJKJLJMJNJOJPJQJRJSJTJUJVJWJXJYJZKAKBKCKDKEKFKGKHKIKJKKKLKMKNKOKPKQKRKSKTKUKVKWKXKYKZLALBLCLDLELFLGLHLILJLKLLLMLNLwcxcyczdadbdcdddedfdgdhdidjdkdldmdndodpdqdrdsdtdudvdwdxdydzeaebecedeeefegeheiejekelemeneoepeqereseteuevewexeyezfafbfcfdfefffgfhfifjfkflfmfnfofpfqfrfsftfufvfwfxfyfz