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Effect of Ball Scribing on Magnetic Shielding Efficiency of Grain-oriented Silicon Steel
JOURNALOFIRON ANDSTEELRESEARCH,INTERNATIONAL２ ０ １ ４,２ １( ７):６ ７ ９ Ｇ ６ ８ ４
Ef f e c to fBa l lS c r i b i ngon Ma t i cSh i e l d i ngEf f i c i e nc f gne yo Gr a i n Ｇ o r i e n t e dS i l i c onS t e e l Hao WANG１ , Chang Ｇ shengLI１ , Ru i Ｇb i n MEI２ , Gang HUO３
( １． S t a t eKeyLabo r a t o r fRo l l i ngandAu t oma t i on,No r t he a s t e r nUn i ve r s i t i aon i ng,Ch i na; yo y,Shenyang１１０８１９,L , , , , ２．No r t he a s t e r nUn i ve r s i t tQi nhuangdaoBr anch No r t he a s t e r nUn i ve r s i t nhuangdao０６６００４ Hebe i Ch i na; ya y Qi , , , , ) ３．Benx iS t e e lPo s c oCo l dS t r i l l i ngCo Lt d Benx i１１７０２１ L i aon i ng Ch i na pRo Ab s t r a c t:Magne t i csh i e l d i ngo fg r a i n Ｇ o r i en t eds i l i c ons t e e lwa si nve s t i t ed． Ba l ls c r i b i ngwi t hspa c i ngo f２t o１６mm ga wa spe r f o rmeda tpe akf l uxdens i t i e so f８ ０mTt o１ ３T．Magne t i csh i e l d i nge f f i c i encywa sc a l cu l a t ed, i nc l ud i ngab Ｇ s o r t i on,r e f l e c t i onandi nne rmu l t i Ｇ r e f l e c t i onsh i e l d i nge f f i c i enc i e s．Ma e t i cs h i e l d i nge f f i c i e n c n c r e a s er a t i o s p gn y (MSE)i a f t e rd i f f e r e n ts c r i b i ngs a c i ngwe r ec omp a r e d,andt h i ckne s sr e i r emen tt oa ch i e veabs o r t i onsh i e l d i ngo f５０dBwa s p qu p a l s oc a l cu l a t ed．Ther e su l t sshowt ha tmagne t i csh i e l d i nge f f i c i enc i e so fC７１１andH６６８s i l i c ons t e e l si nc r e a s eby４ ７９ and３ １５dBr e spe c t i ve l f t e rs c r i b i ngo f１６mm． Be f o r es c r i b i ng,sh i e l d i nge f f i c i encyo fH６６８s t e e lwa sh i rt han ya ghe t ha to fC７１１s t e e l,wh i l ea f t e rs c r i b i ng,bo t habs o r t i onandsh i e l d i nge f f i c i encygapswe r el a r l r i dgedbe twe en p ge yab C７１１and H６６８s t e e l s．P l a t et h i ckne s so fC７１１s t e e lc ou l db er e du c e df r om３ １８mm w i t hou ts c r i b i ngt o２ ２０mma f t e r s c r i b i ngo f１６ mm．The r ei snoappa r en tt h i ckne s sr educ t i ona tl owe rf l uxdens i t i e s;wh i l et hepe akf l uxdens i t s yi above０ ３T,t hesh i e l d i nge f f e c tbe c ome sappa r en t,andt het h i ckne s sc ou l dber educ edf r om２ ２８mm wi t hou ts c r i Ｇ b i ngt o１ ７０ mm wi t hs c r i b i ngspa c i ngo f１６ mm．Magne t i z i ngp r o c e s sandi t se f f e c tonva r i a t i ono fmagne t i csh i e l Ｇ d i ngwe r ea l s oana l z ed． y Ke r d s:magne t i csh i e l d i nge f f i c i ency;g r a i n Ｇ o r i en t eds i l i c ons t e e l;abs o r t i onsh i e l d i ng;r e f l e c t i onsh i e l d i ng;i n Ｇ p ywo ; ne rmu l t i Ｇ r e f l e c t i onsh i e l d i ng t h i ckne s sr educ t i on
Magne t i cf i e l dsmayc aus ec e r t a i nd i s t u rbanc et o a c cur a c fs ens i t i vee l e c t r on i cande l e c t r i c a lequ i Ｇ yo p , men t s． I nduc t i onhe a t i ngs t ems powe rd i s t r i bu Ｇ ys t i on,h i requ i t s,andi ndus t r i a lt r ans Ｇ ghpowe pmen f o rme rc en t e r sc anbeg i vena sexamp l e so fpo s s i b l y d i s t urb i ng magne t i cs ou r c e s,andt heexpo su r e sa t l owf r equenc i e smaya l s ol e adt oequ i tma l f unc Ｇ pmen [ ] t i on１－３ ． Somer e s e a r che r sc onc e rnedabou tt hepos Ｇ s i b l eh e a l t hh a z a r d sf o rhuma nb e i ng se xpo s e dt oe l e c t r i c [ ４,５] and magne t i cf i e l ds ．Magne t i csh i e l d i ngc anbe r equ i r eda l s ot oi nc r e a s et her obus t ne s so ft hes ens i Ｇ t i vee l e c t r on i cande l e c t r i c a lequ i m e n ta a i n s tt h e p g [ ] magne t i cf i e l d６－８ ．Th e r e f o r e,ma e t i cs h i e l d i ngha s gn be en wi de l l i edi n va r i ouss oph i s t i c a t ede i Ｇ y app qu p me n t sa nda l i a n c e s,s u c ha sma e t i cr e s on a n c eima Ｇ pp gn i ng (MRI)s c a n sa nd ma e t i c a l l e v i t a t e dt r a i n s,t o g gn yl
r o t e c thumanbe i ngsandma ch i necomponen t sf r om p [ ] t hei n f l uenc eo fmagne t i cf i e l ds９－１１ ． As h i e l d i ng ma t e r i a li sp l a c e di na ma e t i cf i e l d gn t r an s f e rs a c ei no r d e rt od imi n i s ho rb l o c kt hep r opaga Ｇ p t i ono fe l e c t r omagne t i c wave s,andsomer e s e a r ch wo rkha sbe enc a r r i edou tt oimp r ovet hesh i e l d i ng [ １２－１５] e f f i c i enc ．Duet oi t sapp r op r i a t e me chan i c a l y , r ope r t i e s l ow p r oduc t i on cos tand good e l e c t r i c p andmagne t i ci nduc t i onpe r f o rmanc e s,g r a i n Ｇ o r i en t ed s i l i cons t e e lbe come sapp r op r i a t emagne t i csh i e l d i ng [ ] ma t e r i a l１６－２０ ． Aba l ls c r i b i ngt e chn i oavo i dt her e Ｇ coa t i ng quet r ob l em wa s deve l oped by Eur ope an El e c t r i c a l p S t e e l s,andsomer e s e a r che shavebe enc a r r i edou t [ ２１, ２２] conc e rn i ngsuchat e chn i ． I nt h i spape r,ba l l que s c r i b i ng wa sapp l i edt oi nve s t i t ei t se f f e c tonmag Ｇ ga
Founda t i onI t em: I t em Spons o r edbyNa t i ona lNa t ur a lSc i enc eFounda t i ono fCh i na ( ５１１７４０５７,５１２７４０６２);Na t i ona lHi chno l ogyRe s e a r ch ghTe andDeve l opmen tPr og r amo fCh i na ( ２０１２AA０３A５０３) B i o r aphy: Hao WANG,Do c t o rCand i da t e; E Ｇma i l: nwuwanghao＠gma i l c om; Re c e i v e dDa t e: May２９,２０１３ g Co r r e s i ngAu t ho r:Chang Ｇ shengLI,Do c t o r,Pr o f e s s o r; E Ｇma i l:l i c s＠r a l neu edu cn pond
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２１
６８０
ne t i csh i e l d i nge f f i c i enc y．
１ Exp e r imen t a lMa t e r i a land Me t hod s Conven t i ona lg r a i n Ｇ o r i en t ed ( CGO)s i l i c ons t e e l she e t sandh i rme ab i l i t r a i n Ｇ o r i en t ed (HGO) ghpe yg s i l i cons t e e lshe e t swe r et e s t ed ma t e r i a l si nt h i spa Ｇ , r wh i ch we r enameda sC７１１and H６６８r e spe c Ｇ pe
t i ve l hechemi c a lcompos i t i oni sshowni n y,andt Tab l e１． Thes amp l e swe r e manu f a c t u r e da ss t and a r d Ep Ｇ , s t e i ns amp l e sa ndt h es amp l es i z ei s３ ５ ０mm×３ ０mm× ０ ３ mm．I n i t i a l magne t i cp r ope r t i e so f C７１１ and H６６８s t e e l sa t１ ０Ta r eshowni nTab l e２． Thet e s t e dma t e r i a l swe r es c r i b e dbys e l f Ｇ de s i gned
Tab l e１ Ch emi c a lc ompo s i t i ono fC７１１andH６６８t e s t e dma t e r i a l s ma s s％
Samp l e C７１１
H６６８
S i
３ ０５ ３ ０９
Mn
０ ０６５ ０ ０７２
C
０ ０３２ ０ ０５４
Cu
０ ０２８ ０ ０７５
S
０ ０２０ ０ ０１８
P
０ ０１２ ０ ０１５
Al
Fe
０ ００８
Ba l anc e
０ ０１０
Ba l anc e
Tab l e２ I n i t i a lma e t i cp r op e r t i e so fC７１１andH６６８s t e e l sa t１ ０T gn Samp l e C７１１
H６６８
/( /(Wkg－１) Coe I r onl o s s r c i vef o r c e Am－１) ０ ７１１ ０ ６６８
２８２ ９ ２８７ ６
Re l a t i vepe rme ab i l i t y
MBNrms１)/mV
２４７３ ７
０ ４４７
７９９ ４
０ ３９１
No t e:１)MBNrmsi st heave r agemagne t i cBa rkhaus enno i s e (MBN)amp l i t udei nt heMBNc l e． yc
ba l ls c r i b i ngi ns t rumen t．A s t anda r d Eps t e i ns t r i sg i venbySche l kuno f f２４ p wa ( １) f o rt e s t i ng wa sp l a c ed be twe en t he yoke s,and a Es＝A ＋R ＋B , st hep e n e t r a t i ono rab s o r t i onl o s si ndBi n Ｇ whe r e Ai f e edba ckc on t r o ls t em imp l emen t edi n LabVIEW p ys i d et heb a r r i e r;Ri st het o t a lr e f l e c t i onl o s si ndBf r om wa sus edt oc on t r o lt hef l uxdens i t oob t a i nr epe a t Ｇ s yt [ ] t hs u r f a c e so ft hes h i e l d,n e l e c t i ngt hee f f e c to fmu l Ｇ ab l eandc ompa r ab l e me a su r emen t s２３ ．The who l e bo g ; i l er e f l e c t i on si n s i d et heb a r r i e r andBi sapo s i t i v eo r me a su r emen twa sc onduc t edi na magne t i csh i e l d i ng t p e a t i v ec o r r e c t i ont e rmi ndu c e dbyt her e f l e c t i ngwa v e s r oomandt hec ompu t e rwa spu ti nano t he rr oomt o n g n s i d et hes h i e l d i ngb a r r i e r( mu l t i Ｇ r e f l e c t i on s)． avo i di n t e r f e r enc e．Ea chs t r i smagne t i s edunde r i p wa , s i nuso i da lf l ux dens i t he pe akf l ux dens i t ( y andt y A ＝１３１ ２) ４３ t fμσ wa sf r om８ ０ mTt o１ ３Ta tama e t i s i ngf r e e n c , ; gn qu y whe r e tr e f e r st op l a t et h i ckne s s fs t andsf o rf r e Ｇ o f５０ Hz．Ea ch me a su r emen to f magne t i cp r ope r t y quenc e f e r st or e l a t i vepe rme ab i l i t e Ｇ y;μ r y;andσ r wa smadet hr e et ime sandt henave r aged． Be f o r ee a ch p r e s en t sr e l a t i veconduc t i v i t y． æ ö me a su r emen te a ch s amp l e wa sd r awn ou tand de Ｇ ç fσ μ ÷ ３) ç l g５ ＋０ ３５４＋１ １７×１０－２ ３ ÷÷ ( ３５ ç magne t i z ed．The de t e c t i on po i n t sa r r angemen ti s R ＝２０ rσø è f μ showni nF i １． g whe r e,rr e f e r st od i s t anc ebe twe enmagne t i csour c e andmagne t i csh i e l d i ng ma t e r i a l,andf o rs imp l i c i t y, [ ]
F i １ Ma e t i cs h i e l d i ngandd e t e c t i onpo i n t sa r r ang emen t g gn
２ Re s u l t sandDi s c u s s i on ２ １ The o r e t i c a lba ckg r ound Magne t i csh i e l d i nge f f i c i enc ou l dbeeva l ua t ed yc wi t hEs,wh i chi sexp r e s s edi n de c i be l s( dB)．Es
r wa sf i xeda s１ m． I n magne t i cf i e l d,i nne rmu l t i Ｇ r e f l e c t i onB wa s [ ] de f i nedbySchu l ze ta l ２５ a sf o l l ows (/ ) B ＝２０ l １－１０－ A １０ ( cos ０ ２３０A －js i n０ ２３０A )] g[ ( ４) Fr om Eq ( ４),B wa sc a l cu l a t edaga i na st he f o l l owi ngequa t i on B ＝１０ l １＋１０－０２A －２×１０－０１Acos( ０ ２３０A )] g[ ( ５) ２ ２ To t a lma t i cs h i e l d i nge f f i c i enc r i a t i on gne yva Magne t i c sh i e l d i ng e f f i c i enc i e so f C７１１ and H６６８s t e e l si nc r e a s ef i r s tandde c r e a s ea th i rf l ux ghe , dens i t st hepe akf l uxdens i t s c ends a sshowni n ya ya F i ２,andt hei n c r e a s ei smo r eappa r en ti ns t e e lwi t h g
I s sue７ Ef f e c to fBa l lSc r i b i ngon Magne t i cSh i e l d i ngEf f i c i encyo fGr a i n Ｇ o r i en t edS i l i c onS t e e l
６８１
F i ２ Ma e t i cs h i e l d i nge f f i c i enc i e so fC７１１ ( a)andH６６８ ( b)s t e e l sa td i f f e r en tp e akf l uxd en s i t i e s g gn
l a r rs c r i b i ngspa c i ng．Thee f f e c to fba l ls c r i b i ngi s ge mo r eappa r en ti nC７１１s t e e l,andt hemagne t i csh i e l Ｇ d i nge f f i c i enc simp r oveda tbo t hl owe randh i r yi ghe akf l uxdens i t i e s．At１ ０ T,t he magne t i csh i e l Ｇ pe d i nge f f i c i enc s８ ２４dB wh i l ea f t e rs c r i b i ngo f４ yi and１６ mmt h ee f f i c i e n c e a c h e s１１ １６a nd１３ ０３dB yr r e spe c t i ve l r H６６８s t e e l,wh i l eB ＜０ ３ T ba l l y．Fo s c r i b i ngdoe sno ts howobv i ou se f f e c t,a ndwh i l eB ≥ ０ ３Tb a l ls c r i b i ngg r a du a l l n c r e a s e smagne t i csh i e l Ｇ yi d i nge f f i c i enc ０T,t hemagne t i csh i e l d i nge f Ｇ y．At１ f i c i enc s１０ ９３dBwh i l ea f t e rs c r i b i ngo f４a nd１６mm yi t hee f f i c i e n c e a c h e s１２ ９７a nd１４ ８０dBr e s e c t i v e l yr p y． Ast hes c r i b i ng spa c i ng i nc r e a s e s,pe ak magne t i c sh i e l d i nge f f i c i enc m o v e s t oh i h e r f l u xd e n s i t i e s ． y g Long i t ud i na landt r ans ve r s e pe rme ab i l i t i e so f s i l i cons t e e lva r r e a t l i chi sma i n l oi t s yg y,wh yduet s t r ongc r t a lmagne t i can i s o t r opy．Wh i l et he mag Ｇ ys ne t i z a t i ona l ongr o l l i ngd i r e c t i ona r r i ve sa ti t smax i Ｇ mumr e l a t i vepe rme ab i l i t i l l i ngo fmagne t i cf i e l d y,f l i ne sa ch i eve ss a t u r a t eds t a t uswhe r esh i e l d i ngene r Ｇ l s oh i t si t smax imum．Ast hepe akf l uxdens i t gya y r adua l l nc r e a s e s,r e l a t i vepe rme ab i l i t l ongo t hＧ g yi ya , e rd i r e c t i onssuc c e s s i ve l e a che s max imum wh i ch yr i nc r e a s e st he magne t i can i s o t r opy． I nc r e a s eo fc r Ｇ ys t a lmagne t i can i s o t r opywi l ll e adt of a l lo ft o t a lmag Ｇ ne t i c pe rme ab i l i t r i ng t he magne t i c sh i e l d i ng y．Du oc e s s,t he h i rt he r e l a t i ve pe rme ab i l i t f pr ghe yo r a i n Ｇ o r i en t eds i l i c ons t e e li s,t he mo r er ema rkab l e g t hesh i e l d i ng e f f e c ti s．S i nc et he magne t i cr e l a t i ve rme ab i l i t fg r a i n Ｇ o r i en t eds i l i c ons t e e li st hou Ｇ pe yo s andso ft ime sl a r e r t h a nt h ea i r r e l a t i v e e r m e a b i l Ｇ g p her e l uc t anc eo ft hec av i t s i t y( yi μshield ≫μair ),t muchl a r rt hant ha to fs i l i c ons t e e l( Rair≫Rshield), ge wh i l et heva s tma o r i t fmagne t i cf l uxi nt heou t e r j yo magne t i cf i e l dwi l lt r ave lt hr oughi nne rwa l lo fs i l i Ｇ cons t e e l,s ot he r ewi l lbel i t t l ef l uxdens i t nt he yi
c av i t Φshield≫Φair)．The r e f o r e,i nt hec av i t i e l Ｇ y( ysh dedbyf e r r omagne t i cma t e r i a lt he r ei sa lmos tnoex Ｇ , t e rna lmagne t i cf i e l d andt hr oughba l ls c r i b i ngt he magne t i cr e l a t i ve pe rme ab i l i t l dbe g r e a t l n Ｇ ycou yi c r e a s ed,wh i chwou l da ch i evesoundmagne t i csh i e l Ｇ d i nge f f e c t． ２ ３ Ma t i cs h i e l d i nge f f i c i enc e r a t i on gne ys pa As magne t i csh i e l d i ngcon t a i nst hr e es e c t i ons, abso r t i on,r e f l e c t i on,andmu l t i Ｇ r e f l e c t i onsh i e l d i ng p , e f f i c i enc i e swe r ec a l cu l a t edr e spe c t i ve l a s s h o w n i n y , F i ３． I ncompa r i sonwi t hF i ２ i ti sno t edt ha tab Ｇ g g so rp t i on sh i e l d i ng e f f i c i enc imi l a rt r ends y shows s wi t ht o t a lmagne t i csh i e l d i ngandcon t r i bu t e s mos t r to fsh i e l d i nge f f i c i enc pa y． At１ ０ T,t heabso r t i one f f i c i enc f C７１１ p yo s t e e li s４ ７２dBwh i l ea f t e rs c r i b i ngo f４and１６ mm t hee f f i c i enc e a che s６ ０３and６ ８３dBr e spe c t i ve l yr y． Fo rH６６８s t e e l,wh i l eB ＜０ ３Tba l ls c r i b i ngdoe s , no tshow obv i ouse f f e c t and wh i l eB ≥０ ３ T ba l l s c r i b i ngg r adua l l nc r e a s e s magne t i csh i e l d i nge f f i Ｇ yi c i enc ０ T,t he magne t i csh i e l d i nge f f i c i enc y．At１ y i s６ ３６dB wh i l ea f t e rs c r i b i ngo f４and１６ mmt he e f f i c i enc e a che s７ ５２and８ ５３dBr e spe c t i ve l yr y．At t hel owe rf l uxdens i t i e s,ade c r e a s ei nsh i e l d i nge f f i Ｇ c i enc a r s．Suchde c l i nei nsh i e l d i ng e f f i c i enc yappe y i nd i c a t e st ha ta tl owe rf l uxdens i t i e sr e f l e c t i onsh i e l Ｇ d i ngab i l i t spoo r． I ti sa l sono t edf r om F i ３( a) yi gs and３( b)t ha tt o t a lmagne t i csh i e l d i nge f f i c i enc r Ｇ yva i a t i oni si den t i c a lt ot ha to fabso r t i onsh i e l d i nge f f i Ｇ p c i enc ． R e f l e c t i o no fC ７ １ １s t e e l r e a c h e sl o w e s te f f i Ｇ y c i enc tabou t０ １Tandv a r i e sa a r e n t l st hef l ux ya pp ya dens i t nc r e a s e s．Re f l e c t i one f f i c i enc s４ ４８dBa t yi yi １ ０Twh i l ea f t e rs c r i b i ngo f４and１６mmt hee f f i c i e n c y r e a c he s５ ２５and６ ０１dBr e s e c t i v e l r ei sn e a r l p y．The y nor e f l e c t i oni nc r e a s eo fH６６８s t e e la tl owe rf l uxd e n Ｇ
６８２
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２１
F i ３ Ab s o rp t i on,r e f l e c t i onandi nn e rmu l t i Ｇ r e f l e c t i ons h i e l d i nge f f i c i enc i e so fC７１１ ( a),( c),( e)and g ( ) ,( ) ,( ) H６６８ b d fs t e e l sa td i f f e r en tp e akf l uxd en s i t i e s
s i t i e s,andt her e f l e c t i one f f i c i e n c s４ ５５dBa t１ ０T yi wh i l ea f t e rs c r i b i ngo f４and１６ mm t hee f f i c i ency r e a che s５ ０７ and ５ ７５ dB r e spe c t i ve l nne r y．I mu l t i Ｇ r e f l e c t i ono fC７１１and H６６８s t e e l si nc r e a s e s sha r l i l eB ＜０ １ Tands l i l swh i l e p y wh ght ychange B ≥０１ T．Af t e rs c r i b i ngi nne rmu l t i Ｇ r e f l e c t i ono f C７１１ s t e e li nc r e a s e s appa r en t l i l et ha to f y, wh H６６８s t e e li nc r e a s e son l ６ T．Such y when B ≥０ va r i a t i onco i nc i de s we l lwi t ht her e l a t i onshowna s Eq ( ３)． Asc a nb es e e nf r om F i s ３( c)t o３( f),t hema i n g d i f f e r enc ebe twe enC７１１and H６６８s t e e l sl i e si nr e Ｇ f l e c t i onandi nne r mu l t i Ｇ r e f l e c t i onsh i e l d i ng．Be f o r e s c r i b i ngsh i e l d i nge f f i c i enc f H６６８s t e e li sh i r yo ghe t hant ha to fC７１１s t e e l,wh i l ea f t e rs c r i b i ngbo t hab Ｇ so r t i onandsh i e l d i ng e f f i c i enc r eab r i dged p ygapsa be twe enCGOandHGOs i l i c ons t e e l s．
２ ４ Ma t i cs h i e l d i nge f f i c i enc nc r e a s er a t i oc a l Ｇ gne yi cu l a t i on I no rde rt oh i l i tt hee f f e c to fba l ls c r i b i ng gh gh on magne t i cs h i e l d i nge f f i c i e n c i n c r e a s er a t i o s, y (MSE)
t hei nc r e a s er a t i oo fMSEont heba s i so fun Ｇ s c r i bed , s amp l e swa sc a l cu l a t ed a sshowni nF i ４．MSEi n Ｇ g c r e a s er a t i oo ft heC７１１s t e e la s c endsa st hes c r i b i ng spa c i ngi nc r e a s e s,andt hei nc r e a s er a t i oi sabove , １０％ f a l l i nga f t e rr e a c h i ngp e akpo i n ta t０ ８－１ ０ T． MSEo f H６６８s t e e lv a r i e s mo r ec omp l i c a t e d l nt he y．I v a r i a t i onMSEo f４and８ mms c r i b i ngi ss imi l a ra td i f Ｇ f e r e n tp e akf l uxd e n s i t i e s,and１６ mms c r i b i nga c h i e v e s h i s ti nc r e a s e．Att hes amef l uxdens i t t i c ghe y,magne sh i e l d i nge f f i c i enc fC７１１s t e e li sg r e a t e rt hant ha t yo o f H６６８ s t e e l．I ti sa l so no t ed t ha t H６６８ s t e e l ２ Tanda t s t oppedi nc r e a s i nga t２ mm whenB ＜０ １ ０T,wh i chs i i f i e st ha t２mms c r i b i ngwi l lno ti n Ｇ gn
F i ４ MSEi nc r e a s er a t i o so fC７１１ ( a)andH６６８ ( b)s t e e l sa f t e rs c r i b i nga td i f f e r en tp e akf l uxd en s i t i e s g
I s sue７ Ef f e c to fBa l lSc r i b i ngon Magne t i cSh i e l d i ngEf f i c i encyo fGr a i n Ｇ o r i en t edS i l i c onS t e e l
duc eobv i ousMSEi nc r e a s e． ２ ５ Th i c kn e s sr e du c t i o na c h i e v e dt h r o u hb a l ls c r i b i n g g Th i ckne s si st hekeyf a c t o rf o r magne t i csh i e l Ｇ d i ng ma t e r i a l s．Theh i rt he MSEo ft he ma t e r i a l ghe i s,t het h i nne rt hemagne t i csh i e l d i ng ma t e r i a li sr e Ｇ i r edt oa ch i eveequa lmagne t i csh i e l d i nge f f e c t．A qu r educ t i oni nt h i ckne s so fma t e r i a l sc ou l dc on t r i bu t e t oani nc r e a s eo fus agee f f i c i enc a n dar e d u c t i o no f y ma s sands c a l eo fmagne t i csh i e l d i ngequ i t s．As pmen r e f l e c t i onsh i e l d i ngR i si ndependen to fp l a t et h i ckＧ , ne s s andi nne r mu l t i Ｇ r e f l e c t i onsh i e l d i ngi sneg l i Ｇ [ ] i b l ewhenA ≥１５dB２４ ,i ti sno t edf r om Eq ( ２) g A ( ６) t＝ １３１ ４３ fμσ
６８３
Th i c kn e s sr e i r e dt oab s o r t i ons h i e l d i ngo f５０dB qu p a f t e rd i f f e r e n ts c r i b i ngs a c i ngwa sc a l c u l a t e d,a ss hown p , i nF i ５．A f t e r s c r i b i n t h i c k n e s s r e d u c t i o no f g g C７１１s t e e li sappa r en ta tbo t hh i owf l uxden Ｇ ghandl s i t i e s．At１ ０T,t het h i c kn e s sc ou l db er e du c e df r om ３ １８ mm wi t hou ts c r i b i ng t o２ ４９ and２ ２０ mm wi t h４and１６ mms c r i b i ngr e spe c t i ve l h i ckＧ y．Thet ne s sr educ t i ono f H６６８s t e e lcou l dbed i v i dedi n t o twos e c t i ons． I nt hef i r s ts t age,t he r ei snoappa r en t ; t h i ckne s sr educ t i on wh i l et hep e akf l uxd e n s i t a l u e yv i sabove０ ３Tba l ls c r i b i ngt ake ss i i f i c an tr o l ei n gn r educ i ng p l a t et h i ckne s s．To a ch i eve abso r t i on p sh i e l d i ngo f５０dB,t het h i ckne s scou l dber educ ed f r om２ ２８mm wi t hou ts c r i b i nga t１ ０Tt o１ ９３and １ ７０ mm wi t hs c r i b i ngspa c i ngo f４and１６ mmr e s Ｇ
F i ５ Th i ckn e s s e so fC７１１ ( a)andH６６８ ( b)s t e e l swi t hab s o rp t i ons h i e l d i nge f f i c i enc f５０dBa t g yo d i f f e r en tp e akf l uxd en s i t i e s
c t i ve l pe y．
３ Conc l u s i on s ( １)Magne t i csh i e l d i nge f f i c i enc fC７１１s t e e l yo i s８ ２４dBa t１ ０Tbe f o r es c r i b i ng,wh i l ea f t e rs c r i Ｇ b i ng o f４and１６ mm t hee f f i c i enc e a che s１１ １６ yr and１３ ０３ dB r e spe c t i ve l i l e B ≥０ ３ T ba l l y．Wh s c r i b i ngg r adua l l nc r e a s e s magne t i csh i e l d i nge f f i Ｇ yi c i enc fH６６８s t e e l．Magne t i csh i e l d i nge f f i c i enc s yo yi １０ ９３dBa t１ ０T,wh i l ea f t e rs c r i b i ngo f４a nd１６mm t hee f f i c i e n c e a c h e s１２ ９７a nd１４ ８０dBr e s e c t i v e l yr p y． ( ２)Abs o r t i onsh i e l d i nge f f i c i enc r i a t i oni s p yva i den t i c a lt ot ha to ft o t a lma n e t i cs h i e l d i n e f f i c i e n c g g y． Thema i nd i f f e r enc ebe twe enC７１１and H６６８s t e e l s l i e si nr e f l e c t i onandi nne rmu l t i Ｇ r e f l e c t i onsh i e l d i ng． Be f o r es c r i b i ngsh i e l d i nge f f i c i enc fH６６８s t e e li s yo h i rt hant ha to fC７１１s t e e l,wh i l ea f t e rs c r i b i ng ghe bo t h abs o r t i on and sh i e l d i ng e f f i c i enc Ｇ p y gaps be twe enC７１１andH６６８s t e e lwe r eab r i dged． ( ３)Ast hes c r i b i ngspa c i ngi nc r e a s e smagne t i c
sh i e l d i nge f f i c i enc nc r e a s er a t i oo ft heC７１１s t e e l yi a s c ends,andt hei nc r e a s er a t i oi sabove１０％ ,f a l l i ng a f t e rr e a ch i ng pe ak po i n ta t０ ８－１ ０ T．Att he s amef l uxdens i t t i csh i e l d i nge f f i c i enc f y,magne yo C７１１i sg r e a t e rt hant ha to fH６６８s t e e l． ( ４)Toa ch i eveabso r t i onsh i e l d i ngo f５０dB, p l a t et h i c kn e s sc ou l db er e du c e df r om３ １８mm wi t hou t p s c r i b i ngt o２ ４９and２ ２０ mm wi t h４and１６ mm s c r i b i ngr e spe c t i ve l t１ ０T．Atl owe rf l uxd e n s i t ya y, t he r ei snoappa r en tt h i ckne s sr educ t i on;wh i l et he akf l uxdens i t sabove０ ３Tt hesh i e l d i nge f f e c t pe yi be come sappa r en t,andt het h i ckne s scou l d ber e Ｇ duc edf r om２ ２８mm wi t hou ts c r i b i nga t１ ０Tt o１ ９３ and１ ７０ mm wi t hs c r i b i ngspa c i ngo f４and１６ mm r e spe c t i ve l y．
Theau t ho r swou ldl i k et ot hankWo l s onCen t r e f rMagne t i c s,Cardiff Un i ve r s i t o rt he i rt e ch Ｇ yf fo no l ogi ca ls uppo r tt ot h i swo rk,andoneoft heau Ｇ t ho r si sgra t e u lf o ras cho l ar s h ipf r om t heCh i na f
６８４
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２１
Scho l ar s h ip Counc i l． Re f e r enc e s: [ １] MD．Wu l f,P．Wou t e r s,P． Se r an t,L．Dup r é,E．Ho f e r l i n, ge S． J a c obs,P．Ha r l e t,J．Magn．Magn．Ma t e r． ３１６ ( ２００７)e ９０８ Ｇ e ９１１． [ ２] S．Ko r og l u,P．Se r an t,N．Umurkan,S imu l．Mode l l．Pr a c t． ge ( ) Theo r ８ ２ ０ １ ０ ２ ０ ６ Ｇ ２ １６． y１ [ ３] C． J ohans en,Sc and． J．Wo rkEnv i r on．He a l t h３０ ( ２００４)s １,１ Ｇ ３０． [ ４] MH．Repa cho l i,B i oe l e c t r omagne t i c s１９ ( １９９８)１ Ｇ １９． [ ５] Z Y． Zhang,S．Ma t sumo t o,R．Te r an i sh i,T．Ki sh i,Phys i c s yo Pr o c ed i a２７ ( ２０１２)１８０ Ｇ １８３． [ ６] K．Kami a,B A．Wa r n e r,MJ．Mi c h a e l,Cr e n i c s４１ ( ２００１) y yo g ４０１ Ｇ ４０５． [ ７] S．Den i s ov,J．Di ckey,A．Dz i e r ba,W．Gohn,R．He i nz,D． Howe l l,M．Mi ke l s,D．O′Ne i l l,V． Samoy l enko,E． Sc o t t,P． Smi t h,S．Te i l． I ns t r um．Me t hodsPhys．Re s．Se c t．A ge,Nuc ５３３ ( ２００４)４６７ Ｇ ４７４． [ ８] S H．L im,HG．Kang,B S．Han,J J．Song, Ma t e r．Sc i． Eng．B１０２ ( ２００３)３４８ Ｇ ３５１． [ ９] T．Pr i c e,Sa f． Sc i． ４８ ( ２０１０)１４９８ Ｇ １５１５． [ １０] K．Nemo t o,M．Komo r i,Phys i c aC４７０ ( ２０１０)１７７７ Ｇ １７８１． [ １１] G．Gö c s e i,B．Néme t h,I．Ki s s,I．Be r t a,J．El e c t r o s t a t．７１ ( ２０１３)３９２ Ｇ ３９５． [ １２] WS．Kim,YB．Kim,MS．Kim,KT．Kim,Y．Chong,
P G．Pa rk,YG．Kim,J．Magn．Magn．Ma t e r．３１６ ( ２００７) e ８６２ Ｇ e ８６４． [ １３] T． Sa i t o,J．Magn．Magn．Ma t e r． ３２２ ( ２０１０)１５４０ Ｇ １５４３． [ １４] L．Go z z e l i no,A．Ago s t i no,R．Ge r ba l do,G．Gh i i Ｇ go,F．Lav ano,Supe r c ond． Sc i．Te chno l． ２５ ( ２０１２)１ Ｇ ５． [ １５] S Y．Le e,YS．L im,I H．Cho i,D I．Le e,S B．Kim,IEEE Tr ans．Magn． ４８ ( ２０１２)４５５０ Ｇ ４５５３． [ １６] C S．L i,H．Yang,YF．Wang,YM．Yu,J． I r on． S t e e lRe s． I n t． １７ ( ２０１０)No １２,４０ Ｇ ４６． [ １７] H．Wang,C S．L i,T． Zhu,B．Ca i,N．Mohamed,J．Ma t e r． Sc i．Te chno l． ２９ ( ２０１３)６７３ Ｇ ６７７． [ １８] C．Gheo r i e s,A．Don i I r on． S t e e lRe s． I n t． １６ ( ２００９) gh ga,J． No ４,７８ Ｇ ８３． [ １９] O．Bo t t aus c i o,M．Ch i amp i,D．Ch i a r abag l i o,M．Zuc c a,J． Magn．Magn．Ma t e r． ２１５ Ｇ ２１６ ( ２０００)１３０ Ｇ １３２． [ ２０] C S．L i,H．Yang,YF．Wang,YM．Yu,J． I r on． S t e e lRe s． I n t． １８ ( ２０１１)No ２,４０ Ｇ ４６． [ ２１] H．Wang,C S．L i,T．Zhu,N．Chukwuchekwa,B．Ca i,G． )２６ ( Huo,Ac t a Me t a l l． S i n．( Eng l．Le t t． ２０１３)６１８ Ｇ ６２２． [ ２２] D． Sne l l,P． Be ck l ey,J．Magn．Magn．Ma t e r． １３３ ( １９９４)１６７ Ｇ １６９． [ ２３] H．Wang,C S．L i,G．Huo,B．Ca i,N．Mohamed,J．Ha r b i n )２０ ( I ns t．Te chno l．( NewSe r． ２０１３)No ３,８１ Ｇ ８５． [ ２４] A． S c h e l kuno f f,E l e c t r oma e t i cWa v e s,DVonHo s t r a nd,Pr i c e Ｇ gn t on,１９４３． [ ２５] R B．Schu l z,VC．P l an t z,D R．Br ush,IEEE Tr ans．El e c Ｇ t r omagn．Compa t． ３０ ( １９８８)１８７ Ｇ ２０１．
JOURNALOFIRON ANDSTEELRESEARCH,INTERNATIONAL２ ０ １ ４,２ １( ７):６ ７ ９ Ｇ ６ ８ ４
Ef f e c to fBa l lS c r i b i ngon Ma t i cSh i e l d i ngEf f i c i e nc f gne yo Gr a i n Ｇ o r i e n t e dS i l i c onS t e e l Hao WANG１ , Chang Ｇ shengLI１ , Ru i Ｇb i n MEI２ , Gang HUO３
( １． S t a t eKeyLabo r a t o r fRo l l i ngandAu t oma t i on,No r t he a s t e r nUn i ve r s i t i aon i ng,Ch i na; yo y,Shenyang１１０８１９,L , , , , ２．No r t he a s t e r nUn i ve r s i t tQi nhuangdaoBr anch No r t he a s t e r nUn i ve r s i t nhuangdao０６６００４ Hebe i Ch i na; ya y Qi , , , , ) ３．Benx iS t e e lPo s c oCo l dS t r i l l i ngCo Lt d Benx i１１７０２１ L i aon i ng Ch i na pRo Ab s t r a c t:Magne t i csh i e l d i ngo fg r a i n Ｇ o r i en t eds i l i c ons t e e lwa si nve s t i t ed． Ba l ls c r i b i ngwi t hspa c i ngo f２t o１６mm ga wa spe r f o rmeda tpe akf l uxdens i t i e so f８ ０mTt o１ ３T．Magne t i csh i e l d i nge f f i c i encywa sc a l cu l a t ed, i nc l ud i ngab Ｇ s o r t i on,r e f l e c t i onandi nne rmu l t i Ｇ r e f l e c t i onsh i e l d i nge f f i c i enc i e s．Ma e t i cs h i e l d i nge f f i c i e n c n c r e a s er a t i o s p gn y (MSE)i a f t e rd i f f e r e n ts c r i b i ngs a c i ngwe r ec omp a r e d,andt h i ckne s sr e i r emen tt oa ch i e veabs o r t i onsh i e l d i ngo f５０dBwa s p qu p a l s oc a l cu l a t ed．Ther e su l t sshowt ha tmagne t i csh i e l d i nge f f i c i enc i e so fC７１１andH６６８s i l i c ons t e e l si nc r e a s eby４ ７９ and３ １５dBr e spe c t i ve l f t e rs c r i b i ngo f１６mm． Be f o r es c r i b i ng,sh i e l d i nge f f i c i encyo fH６６８s t e e lwa sh i rt han ya ghe t ha to fC７１１s t e e l,wh i l ea f t e rs c r i b i ng,bo t habs o r t i onandsh i e l d i nge f f i c i encygapswe r el a r l r i dgedbe twe en p ge yab C７１１and H６６８s t e e l s．P l a t et h i ckne s so fC７１１s t e e lc ou l db er e du c e df r om３ １８mm w i t hou ts c r i b i ngt o２ ２０mma f t e r s c r i b i ngo f１６ mm．The r ei snoappa r en tt h i ckne s sr educ t i ona tl owe rf l uxdens i t i e s;wh i l et hepe akf l uxdens i t s yi above０ ３T,t hesh i e l d i nge f f e c tbe c ome sappa r en t,andt het h i ckne s sc ou l dber educ edf r om２ ２８mm wi t hou ts c r i Ｇ b i ngt o１ ７０ mm wi t hs c r i b i ngspa c i ngo f１６ mm．Magne t i z i ngp r o c e s sandi t se f f e c tonva r i a t i ono fmagne t i csh i e l Ｇ d i ngwe r ea l s oana l z ed． y Ke r d s:magne t i csh i e l d i nge f f i c i ency;g r a i n Ｇ o r i en t eds i l i c ons t e e l;abs o r t i onsh i e l d i ng;r e f l e c t i onsh i e l d i ng;i n Ｇ p ywo ; ne rmu l t i Ｇ r e f l e c t i onsh i e l d i ng t h i ckne s sr educ t i on
Magne t i cf i e l dsmayc aus ec e r t a i nd i s t u rbanc et o a c cur a c fs ens i t i vee l e c t r on i cande l e c t r i c a lequ i Ｇ yo p , men t s． I nduc t i onhe a t i ngs t ems powe rd i s t r i bu Ｇ ys t i on,h i requ i t s,andi ndus t r i a lt r ans Ｇ ghpowe pmen f o rme rc en t e r sc anbeg i vena sexamp l e so fpo s s i b l y d i s t urb i ng magne t i cs ou r c e s,andt heexpo su r e sa t l owf r equenc i e smaya l s ol e adt oequ i tma l f unc Ｇ pmen [ ] t i on１－３ ． Somer e s e a r che r sc onc e rnedabou tt hepos Ｇ s i b l eh e a l t hh a z a r d sf o rhuma nb e i ng se xpo s e dt oe l e c t r i c [ ４,５] and magne t i cf i e l ds ．Magne t i csh i e l d i ngc anbe r equ i r eda l s ot oi nc r e a s et her obus t ne s so ft hes ens i Ｇ t i vee l e c t r on i cande l e c t r i c a lequ i m e n ta a i n s tt h e p g [ ] magne t i cf i e l d６－８ ．Th e r e f o r e,ma e t i cs h i e l d i ngha s gn be en wi de l l i edi n va r i ouss oph i s t i c a t ede i Ｇ y app qu p me n t sa nda l i a n c e s,s u c ha sma e t i cr e s on a n c eima Ｇ pp gn i ng (MRI)s c a n sa nd ma e t i c a l l e v i t a t e dt r a i n s,t o g gn yl
r o t e c thumanbe i ngsandma ch i necomponen t sf r om p [ ] t hei n f l uenc eo fmagne t i cf i e l ds９－１１ ． As h i e l d i ng ma t e r i a li sp l a c e di na ma e t i cf i e l d gn t r an s f e rs a c ei no r d e rt od imi n i s ho rb l o c kt hep r opaga Ｇ p t i ono fe l e c t r omagne t i c wave s,andsomer e s e a r ch wo rkha sbe enc a r r i edou tt oimp r ovet hesh i e l d i ng [ １２－１５] e f f i c i enc ．Duet oi t sapp r op r i a t e me chan i c a l y , r ope r t i e s l ow p r oduc t i on cos tand good e l e c t r i c p andmagne t i ci nduc t i onpe r f o rmanc e s,g r a i n Ｇ o r i en t ed s i l i cons t e e lbe come sapp r op r i a t emagne t i csh i e l d i ng [ ] ma t e r i a l１６－２０ ． Aba l ls c r i b i ngt e chn i oavo i dt her e Ｇ coa t i ng quet r ob l em wa s deve l oped by Eur ope an El e c t r i c a l p S t e e l s,andsomer e s e a r che shavebe enc a r r i edou t [ ２１, ２２] conc e rn i ngsuchat e chn i ． I nt h i spape r,ba l l que s c r i b i ng wa sapp l i edt oi nve s t i t ei t se f f e c tonmag Ｇ ga
Founda t i onI t em: I t em Spons o r edbyNa t i ona lNa t ur a lSc i enc eFounda t i ono fCh i na ( ５１１７４０５７,５１２７４０６２);Na t i ona lHi chno l ogyRe s e a r ch ghTe andDeve l opmen tPr og r amo fCh i na ( ２０１２AA０３A５０３) B i o r aphy: Hao WANG,Do c t o rCand i da t e; E Ｇma i l: nwuwanghao＠gma i l c om; Re c e i v e dDa t e: May２９,２０１３ g Co r r e s i ngAu t ho r:Chang Ｇ shengLI,Do c t o r,Pr o f e s s o r; E Ｇma i l:l i c s＠r a l neu edu cn pond
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２１
６８０
ne t i csh i e l d i nge f f i c i enc y．
１ Exp e r imen t a lMa t e r i a land Me t hod s Conven t i ona lg r a i n Ｇ o r i en t ed ( CGO)s i l i c ons t e e l she e t sandh i rme ab i l i t r a i n Ｇ o r i en t ed (HGO) ghpe yg s i l i cons t e e lshe e t swe r et e s t ed ma t e r i a l si nt h i spa Ｇ , r wh i ch we r enameda sC７１１and H６６８r e spe c Ｇ pe
t i ve l hechemi c a lcompos i t i oni sshowni n y,andt Tab l e１． Thes amp l e swe r e manu f a c t u r e da ss t and a r d Ep Ｇ , s t e i ns amp l e sa ndt h es amp l es i z ei s３ ５ ０mm×３ ０mm× ０ ３ mm．I n i t i a l magne t i cp r ope r t i e so f C７１１ and H６６８s t e e l sa t１ ０Ta r eshowni nTab l e２． Thet e s t e dma t e r i a l swe r es c r i b e dbys e l f Ｇ de s i gned
Tab l e１ Ch emi c a lc ompo s i t i ono fC７１１andH６６８t e s t e dma t e r i a l s ma s s％
Samp l e C７１１
H６６８
S i
３ ０５ ３ ０９
Mn
０ ０６５ ０ ０７２
C
０ ０３２ ０ ０５４
Cu
０ ０２８ ０ ０７５
S
０ ０２０ ０ ０１８
P
０ ０１２ ０ ０１５
Al
Fe
０ ００８
Ba l anc e
０ ０１０
Ba l anc e
Tab l e２ I n i t i a lma e t i cp r op e r t i e so fC７１１andH６６８s t e e l sa t１ ０T gn Samp l e C７１１
H６６８
/( /(Wkg－１) Coe I r onl o s s r c i vef o r c e Am－１) ０ ７１１ ０ ６６８
２８２ ９ ２８７ ６
Re l a t i vepe rme ab i l i t y
MBNrms１)/mV
２４７３ ７
０ ４４７
７９９ ４
０ ３９１
No t e:１)MBNrmsi st heave r agemagne t i cBa rkhaus enno i s e (MBN)amp l i t udei nt heMBNc l e． yc
ba l ls c r i b i ngi ns t rumen t．A s t anda r d Eps t e i ns t r i sg i venbySche l kuno f f２４ p wa ( １) f o rt e s t i ng wa sp l a c ed be twe en t he yoke s,and a Es＝A ＋R ＋B , st hep e n e t r a t i ono rab s o r t i onl o s si ndBi n Ｇ whe r e Ai f e edba ckc on t r o ls t em imp l emen t edi n LabVIEW p ys i d et heb a r r i e r;Ri st het o t a lr e f l e c t i onl o s si ndBf r om wa sus edt oc on t r o lt hef l uxdens i t oob t a i nr epe a t Ｇ s yt [ ] t hs u r f a c e so ft hes h i e l d,n e l e c t i ngt hee f f e c to fmu l Ｇ ab l eandc ompa r ab l e me a su r emen t s２３ ．The who l e bo g ; i l er e f l e c t i on si n s i d et heb a r r i e r andBi sapo s i t i v eo r me a su r emen twa sc onduc t edi na magne t i csh i e l d i ng t p e a t i v ec o r r e c t i ont e rmi ndu c e dbyt her e f l e c t i ngwa v e s r oomandt hec ompu t e rwa spu ti nano t he rr oomt o n g n s i d et hes h i e l d i ngb a r r i e r( mu l t i Ｇ r e f l e c t i on s)． avo i di n t e r f e r enc e．Ea chs t r i smagne t i s edunde r i p wa , s i nuso i da lf l ux dens i t he pe akf l ux dens i t ( y andt y A ＝１３１ ２) ４３ t fμσ wa sf r om８ ０ mTt o１ ３Ta tama e t i s i ngf r e e n c , ; gn qu y whe r e tr e f e r st op l a t et h i ckne s s fs t andsf o rf r e Ｇ o f５０ Hz．Ea ch me a su r emen to f magne t i cp r ope r t y quenc e f e r st or e l a t i vepe rme ab i l i t e Ｇ y;μ r y;andσ r wa smadet hr e et ime sandt henave r aged． Be f o r ee a ch p r e s en t sr e l a t i veconduc t i v i t y． æ ö me a su r emen te a ch s amp l e wa sd r awn ou tand de Ｇ ç fσ μ ÷ ３) ç l g５ ＋０ ３５４＋１ １７×１０－２ ３ ÷÷ ( ３５ ç magne t i z ed．The de t e c t i on po i n t sa r r angemen ti s R ＝２０ rσø è f μ showni nF i １． g whe r e,rr e f e r st od i s t anc ebe twe enmagne t i csour c e andmagne t i csh i e l d i ng ma t e r i a l,andf o rs imp l i c i t y, [ ]
F i １ Ma e t i cs h i e l d i ngandd e t e c t i onpo i n t sa r r ang emen t g gn
２ Re s u l t sandDi s c u s s i on ２ １ The o r e t i c a lba ckg r ound Magne t i csh i e l d i nge f f i c i enc ou l dbeeva l ua t ed yc wi t hEs,wh i chi sexp r e s s edi n de c i be l s( dB)．Es
r wa sf i xeda s１ m． I n magne t i cf i e l d,i nne rmu l t i Ｇ r e f l e c t i onB wa s [ ] de f i nedbySchu l ze ta l ２５ a sf o l l ows (/ ) B ＝２０ l １－１０－ A １０ ( cos ０ ２３０A －js i n０ ２３０A )] g[ ( ４) Fr om Eq ( ４),B wa sc a l cu l a t edaga i na st he f o l l owi ngequa t i on B ＝１０ l １＋１０－０２A －２×１０－０１Acos( ０ ２３０A )] g[ ( ５) ２ ２ To t a lma t i cs h i e l d i nge f f i c i enc r i a t i on gne yva Magne t i c sh i e l d i ng e f f i c i enc i e so f C７１１ and H６６８s t e e l si nc r e a s ef i r s tandde c r e a s ea th i rf l ux ghe , dens i t st hepe akf l uxdens i t s c ends a sshowni n ya ya F i ２,andt hei n c r e a s ei smo r eappa r en ti ns t e e lwi t h g
I s sue７ Ef f e c to fBa l lSc r i b i ngon Magne t i cSh i e l d i ngEf f i c i encyo fGr a i n Ｇ o r i en t edS i l i c onS t e e l
６８１
F i ２ Ma e t i cs h i e l d i nge f f i c i enc i e so fC７１１ ( a)andH６６８ ( b)s t e e l sa td i f f e r en tp e akf l uxd en s i t i e s g gn
l a r rs c r i b i ngspa c i ng．Thee f f e c to fba l ls c r i b i ngi s ge mo r eappa r en ti nC７１１s t e e l,andt hemagne t i csh i e l Ｇ d i nge f f i c i enc simp r oveda tbo t hl owe randh i r yi ghe akf l uxdens i t i e s．At１ ０ T,t he magne t i csh i e l Ｇ pe d i nge f f i c i enc s８ ２４dB wh i l ea f t e rs c r i b i ngo f４ yi and１６ mmt h ee f f i c i e n c e a c h e s１１ １６a nd１３ ０３dB yr r e spe c t i ve l r H６６８s t e e l,wh i l eB ＜０ ３ T ba l l y．Fo s c r i b i ngdoe sno ts howobv i ou se f f e c t,a ndwh i l eB ≥ ０ ３Tb a l ls c r i b i ngg r a du a l l n c r e a s e smagne t i csh i e l Ｇ yi d i nge f f i c i enc ０T,t hemagne t i csh i e l d i nge f Ｇ y．At１ f i c i enc s１０ ９３dBwh i l ea f t e rs c r i b i ngo f４a nd１６mm yi t hee f f i c i e n c e a c h e s１２ ９７a nd１４ ８０dBr e s e c t i v e l yr p y． Ast hes c r i b i ng spa c i ng i nc r e a s e s,pe ak magne t i c sh i e l d i nge f f i c i enc m o v e s t oh i h e r f l u xd e n s i t i e s ． y g Long i t ud i na landt r ans ve r s e pe rme ab i l i t i e so f s i l i cons t e e lva r r e a t l i chi sma i n l oi t s yg y,wh yduet s t r ongc r t a lmagne t i can i s o t r opy．Wh i l et he mag Ｇ ys ne t i z a t i ona l ongr o l l i ngd i r e c t i ona r r i ve sa ti t smax i Ｇ mumr e l a t i vepe rme ab i l i t i l l i ngo fmagne t i cf i e l d y,f l i ne sa ch i eve ss a t u r a t eds t a t uswhe r esh i e l d i ngene r Ｇ l s oh i t si t smax imum．Ast hepe akf l uxdens i t gya y r adua l l nc r e a s e s,r e l a t i vepe rme ab i l i t l ongo t hＧ g yi ya , e rd i r e c t i onssuc c e s s i ve l e a che s max imum wh i ch yr i nc r e a s e st he magne t i can i s o t r opy． I nc r e a s eo fc r Ｇ ys t a lmagne t i can i s o t r opywi l ll e adt of a l lo ft o t a lmag Ｇ ne t i c pe rme ab i l i t r i ng t he magne t i c sh i e l d i ng y．Du oc e s s,t he h i rt he r e l a t i ve pe rme ab i l i t f pr ghe yo r a i n Ｇ o r i en t eds i l i c ons t e e li s,t he mo r er ema rkab l e g t hesh i e l d i ng e f f e c ti s．S i nc et he magne t i cr e l a t i ve rme ab i l i t fg r a i n Ｇ o r i en t eds i l i c ons t e e li st hou Ｇ pe yo s andso ft ime sl a r e r t h a nt h ea i r r e l a t i v e e r m e a b i l Ｇ g p her e l uc t anc eo ft hec av i t s i t y( yi μshield ≫μair ),t muchl a r rt hant ha to fs i l i c ons t e e l( Rair≫Rshield), ge wh i l et heva s tma o r i t fmagne t i cf l uxi nt heou t e r j yo magne t i cf i e l dwi l lt r ave lt hr oughi nne rwa l lo fs i l i Ｇ cons t e e l,s ot he r ewi l lbel i t t l ef l uxdens i t nt he yi
c av i t Φshield≫Φair)．The r e f o r e,i nt hec av i t i e l Ｇ y( ysh dedbyf e r r omagne t i cma t e r i a lt he r ei sa lmos tnoex Ｇ , t e rna lmagne t i cf i e l d andt hr oughba l ls c r i b i ngt he magne t i cr e l a t i ve pe rme ab i l i t l dbe g r e a t l n Ｇ ycou yi c r e a s ed,wh i chwou l da ch i evesoundmagne t i csh i e l Ｇ d i nge f f e c t． ２ ３ Ma t i cs h i e l d i nge f f i c i enc e r a t i on gne ys pa As magne t i csh i e l d i ngcon t a i nst hr e es e c t i ons, abso r t i on,r e f l e c t i on,andmu l t i Ｇ r e f l e c t i onsh i e l d i ng p , e f f i c i enc i e swe r ec a l cu l a t edr e spe c t i ve l a s s h o w n i n y , F i ３． I ncompa r i sonwi t hF i ２ i ti sno t edt ha tab Ｇ g g so rp t i on sh i e l d i ng e f f i c i enc imi l a rt r ends y shows s wi t ht o t a lmagne t i csh i e l d i ngandcon t r i bu t e s mos t r to fsh i e l d i nge f f i c i enc pa y． At１ ０ T,t heabso r t i one f f i c i enc f C７１１ p yo s t e e li s４ ７２dBwh i l ea f t e rs c r i b i ngo f４and１６ mm t hee f f i c i enc e a che s６ ０３and６ ８３dBr e spe c t i ve l yr y． Fo rH６６８s t e e l,wh i l eB ＜０ ３Tba l ls c r i b i ngdoe s , no tshow obv i ouse f f e c t and wh i l eB ≥０ ３ T ba l l s c r i b i ngg r adua l l nc r e a s e s magne t i csh i e l d i nge f f i Ｇ yi c i enc ０ T,t he magne t i csh i e l d i nge f f i c i enc y．At１ y i s６ ３６dB wh i l ea f t e rs c r i b i ngo f４and１６ mmt he e f f i c i enc e a che s７ ５２and８ ５３dBr e spe c t i ve l yr y．At t hel owe rf l uxdens i t i e s,ade c r e a s ei nsh i e l d i nge f f i Ｇ c i enc a r s．Suchde c l i nei nsh i e l d i ng e f f i c i enc yappe y i nd i c a t e st ha ta tl owe rf l uxdens i t i e sr e f l e c t i onsh i e l Ｇ d i ngab i l i t spoo r． I ti sa l sono t edf r om F i ３( a) yi gs and３( b)t ha tt o t a lmagne t i csh i e l d i nge f f i c i enc r Ｇ yva i a t i oni si den t i c a lt ot ha to fabso r t i onsh i e l d i nge f f i Ｇ p c i enc ． R e f l e c t i o no fC ７ １ １s t e e l r e a c h e sl o w e s te f f i Ｇ y c i enc tabou t０ １Tandv a r i e sa a r e n t l st hef l ux ya pp ya dens i t nc r e a s e s．Re f l e c t i one f f i c i enc s４ ４８dBa t yi yi １ ０Twh i l ea f t e rs c r i b i ngo f４and１６mmt hee f f i c i e n c y r e a c he s５ ２５and６ ０１dBr e s e c t i v e l r ei sn e a r l p y．The y nor e f l e c t i oni nc r e a s eo fH６６８s t e e la tl owe rf l uxd e n Ｇ
６８２
J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２１
F i ３ Ab s o rp t i on,r e f l e c t i onandi nn e rmu l t i Ｇ r e f l e c t i ons h i e l d i nge f f i c i enc i e so fC７１１ ( a),( c),( e)and g ( ) ,( ) ,( ) H６６８ b d fs t e e l sa td i f f e r en tp e akf l uxd en s i t i e s
s i t i e s,andt her e f l e c t i one f f i c i e n c s４ ５５dBa t１ ０T yi wh i l ea f t e rs c r i b i ngo f４and１６ mm t hee f f i c i ency r e a che s５ ０７ and ５ ７５ dB r e spe c t i ve l nne r y．I mu l t i Ｇ r e f l e c t i ono fC７１１and H６６８s t e e l si nc r e a s e s sha r l i l eB ＜０ １ Tands l i l swh i l e p y wh ght ychange B ≥０１ T．Af t e rs c r i b i ngi nne rmu l t i Ｇ r e f l e c t i ono f C７１１ s t e e li nc r e a s e s appa r en t l i l et ha to f y, wh H６６８s t e e li nc r e a s e son l ６ T．Such y when B ≥０ va r i a t i onco i nc i de s we l lwi t ht her e l a t i onshowna s Eq ( ３)． Asc a nb es e e nf r om F i s ３( c)t o３( f),t hema i n g d i f f e r enc ebe twe enC７１１and H６６８s t e e l sl i e si nr e Ｇ f l e c t i onandi nne r mu l t i Ｇ r e f l e c t i onsh i e l d i ng．Be f o r e s c r i b i ngsh i e l d i nge f f i c i enc f H６６８s t e e li sh i r yo ghe t hant ha to fC７１１s t e e l,wh i l ea f t e rs c r i b i ngbo t hab Ｇ so r t i onandsh i e l d i ng e f f i c i enc r eab r i dged p ygapsa be twe enCGOandHGOs i l i c ons t e e l s．
２ ４ Ma t i cs h i e l d i nge f f i c i enc nc r e a s er a t i oc a l Ｇ gne yi cu l a t i on I no rde rt oh i l i tt hee f f e c to fba l ls c r i b i ng gh gh on magne t i cs h i e l d i nge f f i c i e n c i n c r e a s er a t i o s, y (MSE)
t hei nc r e a s er a t i oo fMSEont heba s i so fun Ｇ s c r i bed , s amp l e swa sc a l cu l a t ed a sshowni nF i ４．MSEi n Ｇ g c r e a s er a t i oo ft heC７１１s t e e la s c endsa st hes c r i b i ng spa c i ngi nc r e a s e s,andt hei nc r e a s er a t i oi sabove , １０％ f a l l i nga f t e rr e a c h i ngp e akpo i n ta t０ ８－１ ０ T． MSEo f H６６８s t e e lv a r i e s mo r ec omp l i c a t e d l nt he y．I v a r i a t i onMSEo f４and８ mms c r i b i ngi ss imi l a ra td i f Ｇ f e r e n tp e akf l uxd e n s i t i e s,and１６ mms c r i b i nga c h i e v e s h i s ti nc r e a s e．Att hes amef l uxdens i t t i c ghe y,magne sh i e l d i nge f f i c i enc fC７１１s t e e li sg r e a t e rt hant ha t yo o f H６６８ s t e e l．I ti sa l so no t ed t ha t H６６８ s t e e l ２ Tanda t s t oppedi nc r e a s i nga t２ mm whenB ＜０ １ ０T,wh i chs i i f i e st ha t２mms c r i b i ngwi l lno ti n Ｇ gn
F i ４ MSEi nc r e a s er a t i o so fC７１１ ( a)andH６６８ ( b)s t e e l sa f t e rs c r i b i nga td i f f e r en tp e akf l uxd en s i t i e s g
I s sue７ Ef f e c to fBa l lSc r i b i ngon Magne t i cSh i e l d i ngEf f i c i encyo fGr a i n Ｇ o r i en t edS i l i c onS t e e l
duc eobv i ousMSEi nc r e a s e． ２ ５ Th i c kn e s sr e du c t i o na c h i e v e dt h r o u hb a l ls c r i b i n g g Th i ckne s si st hekeyf a c t o rf o r magne t i csh i e l Ｇ d i ng ma t e r i a l s．Theh i rt he MSEo ft he ma t e r i a l ghe i s,t het h i nne rt hemagne t i csh i e l d i ng ma t e r i a li sr e Ｇ i r edt oa ch i eveequa lmagne t i csh i e l d i nge f f e c t．A qu r educ t i oni nt h i ckne s so fma t e r i a l sc ou l dc on t r i bu t e t oani nc r e a s eo fus agee f f i c i enc a n dar e d u c t i o no f y ma s sands c a l eo fmagne t i csh i e l d i ngequ i t s．As pmen r e f l e c t i onsh i e l d i ngR i si ndependen to fp l a t et h i ckＧ , ne s s andi nne r mu l t i Ｇ r e f l e c t i onsh i e l d i ngi sneg l i Ｇ [ ] i b l ewhenA ≥１５dB２４ ,i ti sno t edf r om Eq ( ２) g A ( ６) t＝ １３１ ４３ fμσ
６８３
Th i c kn e s sr e i r e dt oab s o r t i ons h i e l d i ngo f５０dB qu p a f t e rd i f f e r e n ts c r i b i ngs a c i ngwa sc a l c u l a t e d,a ss hown p , i nF i ５．A f t e r s c r i b i n t h i c k n e s s r e d u c t i o no f g g C７１１s t e e li sappa r en ta tbo t hh i owf l uxden Ｇ ghandl s i t i e s．At１ ０T,t het h i c kn e s sc ou l db er e du c e df r om ３ １８ mm wi t hou ts c r i b i ng t o２ ４９ and２ ２０ mm wi t h４and１６ mms c r i b i ngr e spe c t i ve l h i ckＧ y．Thet ne s sr educ t i ono f H６６８s t e e lcou l dbed i v i dedi n t o twos e c t i ons． I nt hef i r s ts t age,t he r ei snoappa r en t ; t h i ckne s sr educ t i on wh i l et hep e akf l uxd e n s i t a l u e yv i sabove０ ３Tba l ls c r i b i ngt ake ss i i f i c an tr o l ei n gn r educ i ng p l a t et h i ckne s s．To a ch i eve abso r t i on p sh i e l d i ngo f５０dB,t het h i ckne s scou l dber educ ed f r om２ ２８mm wi t hou ts c r i b i nga t１ ０Tt o１ ９３and １ ７０ mm wi t hs c r i b i ngspa c i ngo f４and１６ mmr e s Ｇ
F i ５ Th i ckn e s s e so fC７１１ ( a)andH６６８ ( b)s t e e l swi t hab s o rp t i ons h i e l d i nge f f i c i enc f５０dBa t g yo d i f f e r en tp e akf l uxd en s i t i e s
c t i ve l pe y．
３ Conc l u s i on s ( １)Magne t i csh i e l d i nge f f i c i enc fC７１１s t e e l yo i s８ ２４dBa t１ ０Tbe f o r es c r i b i ng,wh i l ea f t e rs c r i Ｇ b i ng o f４and１６ mm t hee f f i c i enc e a che s１１ １６ yr and１３ ０３ dB r e spe c t i ve l i l e B ≥０ ３ T ba l l y．Wh s c r i b i ngg r adua l l nc r e a s e s magne t i csh i e l d i nge f f i Ｇ yi c i enc fH６６８s t e e l．Magne t i csh i e l d i nge f f i c i enc s yo yi １０ ９３dBa t１ ０T,wh i l ea f t e rs c r i b i ngo f４a nd１６mm t hee f f i c i e n c e a c h e s１２ ９７a nd１４ ８０dBr e s e c t i v e l yr p y． ( ２)Abs o r t i onsh i e l d i nge f f i c i enc r i a t i oni s p yva i den t i c a lt ot ha to ft o t a lma n e t i cs h i e l d i n e f f i c i e n c g g y． Thema i nd i f f e r enc ebe twe enC７１１and H６６８s t e e l s l i e si nr e f l e c t i onandi nne rmu l t i Ｇ r e f l e c t i onsh i e l d i ng． Be f o r es c r i b i ngsh i e l d i nge f f i c i enc fH６６８s t e e li s yo h i rt hant ha to fC７１１s t e e l,wh i l ea f t e rs c r i b i ng ghe bo t h abs o r t i on and sh i e l d i ng e f f i c i enc Ｇ p y gaps be twe enC７１１andH６６８s t e e lwe r eab r i dged． ( ３)Ast hes c r i b i ngspa c i ngi nc r e a s e smagne t i c
sh i e l d i nge f f i c i enc nc r e a s er a t i oo ft heC７１１s t e e l yi a s c ends,andt hei nc r e a s er a t i oi sabove１０％ ,f a l l i ng a f t e rr e a ch i ng pe ak po i n ta t０ ８－１ ０ T．Att he s amef l uxdens i t t i csh i e l d i nge f f i c i enc f y,magne yo C７１１i sg r e a t e rt hant ha to fH６６８s t e e l． ( ４)Toa ch i eveabso r t i onsh i e l d i ngo f５０dB, p l a t et h i c kn e s sc ou l db er e du c e df r om３ １８mm wi t hou t p s c r i b i ngt o２ ４９and２ ２０ mm wi t h４and１６ mm s c r i b i ngr e spe c t i ve l t１ ０T．Atl owe rf l uxd e n s i t ya y, t he r ei snoappa r en tt h i ckne s sr educ t i on;wh i l et he akf l uxdens i t sabove０ ３Tt hesh i e l d i nge f f e c t pe yi be come sappa r en t,andt het h i ckne s scou l d ber e Ｇ duc edf r om２ ２８mm wi t hou ts c r i b i nga t１ ０Tt o１ ９３ and１ ７０ mm wi t hs c r i b i ngspa c i ngo f４and１６ mm r e spe c t i ve l y．
Theau t ho r swou ldl i k et ot hankWo l s onCen t r e f rMagne t i c s,Cardiff Un i ve r s i t o rt he i rt e ch Ｇ yf fo no l ogi ca ls uppo r tt ot h i swo rk,andoneoft heau Ｇ t ho r si sgra t e u lf o ras cho l ar s h ipf r om t heCh i na f
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J ou r na lo fI r onandS t e e lRe s e a r ch,I n t e r na t i ona l Vo l ２１
Scho l ar s h ip Counc i l． Re f e r enc e s: [ １] MD．Wu l f,P．Wou t e r s,P． Se r an t,L．Dup r é,E．Ho f e r l i n, ge S． J a c obs,P．Ha r l e t,J．Magn．Magn．Ma t e r． ３１６ ( ２００７)e ９０８ Ｇ e ９１１． [ ２] S．Ko r og l u,P．Se r an t,N．Umurkan,S imu l．Mode l l．Pr a c t． ge ( ) Theo r ８ ２ ０ １ ０ ２ ０ ６ Ｇ ２ １６． y１ [ ３] C． J ohans en,Sc and． J．Wo rkEnv i r on．He a l t h３０ ( ２００４)s １,１ Ｇ ３０． [ ４] MH．Repa cho l i,B i oe l e c t r omagne t i c s１９ ( １９９８)１ Ｇ １９． [ ５] Z Y． Zhang,S．Ma t sumo t o,R．Te r an i sh i,T．Ki sh i,Phys i c s yo Pr o c ed i a２７ ( ２０１２)１８０ Ｇ １８３． [ ６] K．Kami a,B A．Wa r n e r,MJ．Mi c h a e l,Cr e n i c s４１ ( ２００１) y yo g ４０１ Ｇ ４０５． [ ７] S．Den i s ov,J．Di ckey,A．Dz i e r ba,W．Gohn,R．He i nz,D． Howe l l,M．Mi ke l s,D．O′Ne i l l,V． Samoy l enko,E． Sc o t t,P． Smi t h,S．Te i l． I ns t r um．Me t hodsPhys．Re s．Se c t．A ge,Nuc ５３３ ( ２００４)４６７ Ｇ ４７４． [ ８] S H．L im,HG．Kang,B S．Han,J J．Song, Ma t e r．Sc i． Eng．B１０２ ( ２００３)３４８ Ｇ ３５１． [ ９] T．Pr i c e,Sa f． Sc i． ４８ ( ２０１０)１４９８ Ｇ １５１５． [ １０] K．Nemo t o,M．Komo r i,Phys i c aC４７０ ( ２０１０)１７７７ Ｇ １７８１． [ １１] G．Gö c s e i,B．Néme t h,I．Ki s s,I．Be r t a,J．El e c t r o s t a t．７１ ( ２０１３)３９２ Ｇ ３９５． [ １２] WS．Kim,YB．Kim,MS．Kim,KT．Kim,Y．Chong,
P G．Pa rk,YG．Kim,J．Magn．Magn．Ma t e r．３１６ ( ２００７) e ８６２ Ｇ e ８６４． [ １３] T． Sa i t o,J．Magn．Magn．Ma t e r． ３２２ ( ２０１０)１５４０ Ｇ １５４３． [ １４] L．Go z z e l i no,A．Ago s t i no,R．Ge r ba l do,G．Gh i i Ｇ go,F．Lav ano,Supe r c ond． Sc i．Te chno l． ２５ ( ２０１２)１ Ｇ ５． [ １５] S Y．Le e,YS．L im,I H．Cho i,D I．Le e,S B．Kim,IEEE Tr ans．Magn． ４８ ( ２０１２)４５５０ Ｇ ４５５３． [ １６] C S．L i,H．Yang,YF．Wang,YM．Yu,J． I r on． S t e e lRe s． I n t． １７ ( ２０１０)No １２,４０ Ｇ ４６． [ １７] H．Wang,C S．L i,T． Zhu,B．Ca i,N．Mohamed,J．Ma t e r． Sc i．Te chno l． ２９ ( ２０１３)６７３ Ｇ ６７７． [ １８] C．Gheo r i e s,A．Don i I r on． S t e e lRe s． I n t． １６ ( ２００９) gh ga,J． No ４,７８ Ｇ ８３． [ １９] O．Bo t t aus c i o,M．Ch i amp i,D．Ch i a r abag l i o,M．Zuc c a,J． Magn．Magn．Ma t e r． ２１５ Ｇ ２１６ ( ２０００)１３０ Ｇ １３２． [ ２０] C S．L i,H．Yang,YF．Wang,YM．Yu,J． I r on． S t e e lRe s． I n t． １８ ( ２０１１)No ２,４０ Ｇ ４６． [ ２１] H．Wang,C S．L i,T．Zhu,N．Chukwuchekwa,B．Ca i,G． )２６ ( Huo,Ac t a Me t a l l． S i n．( Eng l．Le t t． ２０１３)６１８ Ｇ ６２２． [ ２２] D． Sne l l,P． Be ck l ey,J．Magn．Magn．Ma t e r． １３３ ( １９９４)１６７ Ｇ １６９． [ ２３] H．Wang,C S．L i,G．Huo,B．Ca i,N．Mohamed,J．Ha r b i n )２０ ( I ns t．Te chno l．( NewSe r． ２０１３)No ３,８１ Ｇ ８５． [ ２４] A． S c h e l kuno f f,E l e c t r oma e t i cWa v e s,DVonHo s t r a nd,Pr i c e Ｇ gn t on,１９４３． [ ２５] R B．Schu l z,VC．P l an t z,D R．Br ush,IEEE Tr ans．El e c Ｇ t r omagn．Compa t． ３０ ( １９８８)１８７ Ｇ ２０１．