MAGENTIC PROPERTIES OF MATERIALS

MAGENTIC PROPERTIES OF MATERIALS Dia, Para and Frro magntism, Qualitativ planation basd on lctron structur, Curi and Curi-Wiss law (qualitativ). all Effct, prssion for carrir concntration. Basd on th bhavior of th matrials in an applid magntic fild, th ar classifid in to thr major groups. Th ar (1) Diamagntic, () Paramagntic and (3) Frromagntic, Antifrromagntic and Frri-magntic substancs. Th origin of ths magntic proprtis dpnds on th intrnal structur of th atom and thir arrangmnt in a crstal lattic. Th discovr of magntic proprtis of lctric currnt has rvolutionid th undrstanding of th bhavior of atoms in an applid magntic fild. Th magntic proprt of an matrial is a rsult of th bhavior of lctrons in an atom individuall and collctivl. Intnsit of magntiation: Th vctor sum of th magntic momnts of all th atoms containd in unit volum is known as intnsit of magntiation. An lctron rvolving in an orbit is quivalnt to a currnt loop and hnc it producs a magntic fild along th ais or prpndicular to th orbit. Sinc th ara of th orbit is ngligibl small [as compard to prcivabl distancs] magntic fild producd du to a circulating currnt in an atom is quivalnt to th fild of a magntic dipol of dipol momnt p m. In th absnc of trnal magntic fild, individual atomic magntic dipols orint randoml du to thrmal agitation and hnc th matrial as a whol ma possss ro magntic momnt and has no magntiation. On th othr hand in prsnc of an trnal fild, th individual atomic magntic dipols orint in th dirction of th trnal fild rsulting in a rsultant magntiation. If P mi magntic momnt of th i th atom and if thr ar N numbr of atoms pr unit volum, thn th intnsit of magntiation is givn b, M Lim V N 1 P - - - - - (1) mi V i1 Th intnsit of magntiation M is dirctl proportional to th magntiing fild and hnc, w can writ, M Or M - - - () In quation (), is a constant for a matrial known as magntic suscptibilit of th matrial. Th magntic suscptibilit of a matrial is dfind as th magntiation pr unit applid fild. Th valu of is ngativ for diamagntic substancs, slightl positiv for paramagntic matrials and has a vr high valu [about 1 6 tims that for a paramagntic matrials]. Diamagntism: Michal Farada discovrd this phnomnon in 1846 in Bismuth. Whn a sampl of Bismuth was takn nar th pols of a magnt, it rplld from th magnt. namd such substancs diamagntic and th phnomnon rsponsibl for such rpulsion is known as diamagntism. Eampls: Mrcur, Gold and Coppr ar othr ampls of diamagntic matrials. In th cas of diamagntic substancs and it is indpndnt of th tmpratur and magntic fild. In ths matrials, du to th application of magntic fild, orbital motion of lctrons is affctd and a magntic momnt is inducd in a dirction opposit to th applid magntic fild. Thus M has a dirction opposit to and hnc givs a ngativ valu for. Paramagntism: Th matrials attractd towards th rgion of strongr magntic fild ar calld paramagntic matrials and th proprt rsponsibl for such a bhaniour is calld Paramagntism. Paramagntic matrials hav suscptibilit slightl gratr than ro and it is dpndnt on th tmpratur in accordanc with Curi law givn b, C - - - (3) T In quation (3), C is known as Curi constant. Eampls: Aluminium, Ogn and Platinum ar paramagntic matrials. Paramagntism occurs in matrials with atoms or molculs of thos matrials possssing a prmannt magntic dipol momnt. In th absnc of trnal magntic fild, th atomic magntic dipols MBR, Vrashaiva Collg, Bllar Pag 1

point in random dirction, so that th rsultant magntiation of th substanc is ro. Th random orintation is a rsult of thrmal agitation within th substanc. Whn an trnal magntic fild is applid, th atomic magntic dipols tnd to orint thmslvs paralll to th fild rsulting in a positiv contribution to th magntic suscptibilit. At low tmpratur, th thrmal agitation rsponsibl for random orintation rducs and hnc a larg proportion of magntic dipols orint in th fild dirction. This rsults in an incras in th valu of magntiation for a givn fild. Thus for ordinar filds, 1. For a larg fild, at low tmpratur, th magntiation is no longr proportional to th applid fild, but, tnds to b a constant valu. This saturation ffct is producd whn all th atomic magntic dipols ar alignd paralll to th fild and hnc th magntiation rachs a maimum valu. As a rsult suscptibilit bcoms vr larg transforming th paramagntic matrial in to a frromagntic matrial. This occurs at a particular tmpratur known as Curi tmpratur. Frromagntism: Matrials possssing a strong magntiation in prsnc of an trnal magntic fild ar calld Frromagntic matrials and th phnomnon rsponsibl for such high magntiation is calld frromagntism. Th valu of is about 1 6 tims that of paramagntic matrials. Eampls: Iron, Nickl and Cobalt ar frromagntic matrials. In ths matrials as tmpratur incrass, dcrass and abov Curi tmpratur, th frromagntic matrial transforms in to paramagntic matrial. Distinction btwn dia, para & frromagntic matrials: No. Diamagntic matrial Paramagntic matrial Frromagntic matrial 1 A diamagntic rod suspndd in a uniform magntic fild sts its longst ais prpndicular to fild. In a non uniform magntic fild, ths matrials mov from strongr to wakr fild. 3 A diamagntic liquid in a U shapd tub subjctd to magntic fild is dprssd in th limb 4 Ths matrials do not prmit th magntic lins of induction to pass through thm. A paramagntic rod suspndd in a uniform magntic fild sts its longst ais paralll to fild. In a non uniform magntic fild, ths matrials mov from wakr to strongr fild. A paramagntic liquid in a U shapd tub subjctd to magntic fild is lvatd in th limb Ths matrials prmit th magntic lins of induction to pass through thm. T A frromagntic rod suspndd in a uniform magntic fild sts its longst ais paralll to fild. In a non uniform magntic fild, ths matrials mov from wakr to strongr fild. A paramagntic liquid in a U shapd tub subjctd to magntic fild is lvatd in th limb Ths matrials radil prmit th magntic lins of induction to pass through thm. 5 μr < 1 and χ < μr > 1 and χ > μr >> 1 and χ > > 6 Substanc loss its magntiation as soon as th magntiing fild is rmovd. Substanc loss its magntiation as soon as th magntiing fild is rmovd. Substanc rtains its magntiation as soon as th magntiing fild is rmovd. 7 Eampls: Bismuth, antimon, coppr, gold, quart, mrcur, watr, alcohol, air, hdrogn tc. 8 Diamagntic suscptibilit is indpndnt of fild and tmpratur. Eampls: Aluminum, platinum, chromium, mangans, coppr sulphat, ogn tc. Paramagntic suscptibilit is dpndnt on th strngth of th fild and also on th tmpratur. Blow curi tmpratur it transforms in to frromagntic matrial. Eampls: Iron, cobalt, nickl and numbr of allos. Frromagntic suscptibilit is dpndnt on th strngth of th fild and also on th tmpratur. Abov curi tmpratur it transforms in to paramagntic matrial. Langvin thor of Diamagntism: Considr an lctron of mass m rotating about th nuclus [charg Z] in a circular orbit of radius r. Lt w b th angular vlocit of th lctron. Th forc acting on th lctron is givn b Z Z F m r 3 4 r 4 mr MBR, Vrashaiva Collg, Bllar Pag

Z - - - (1) 3 4 mr Th magntic momnt associatd with an lctronic orbit is givn b, m currnt ara of th loop r r Lt a magntic fild B is applid prpndicular to th orbit and into th pag. Du to this an additional forc FL calld Lornt forc acts on th lctron givn b, F L v B B r - - - () Th condition for stabl quilibrium is givn b, Z Z mr m r B r B r mr B r 3 4r 4mr B B Dividing b mr, w gt, (3) m m B Solving th quadratic quation, w gt, m B m 4 B m B - - - (4) m Nglcting B B compard to, w gt, - - - (5) m m Thus th angular frqunc of th lctron in its orbit changs with th application of an trnal magntic fild. Thrfor, th rsult of stablishing a fild of flu dnsit B is to st up a prcssional motion of th lctron orbit with an angular vlocit B. This is known as Larmor thorm. m B Thus th chang in frqunc of rvolution of th lctron = m B n - - - (6) 4m Th corrsponding chang in magntic momnt of th lctron is givn b, B B r m currnt ara ( charg frqunc) ara r 4 m - - - (7) 4m On summing ovr all th lctrons in th atom, th inducd momnt pr atom bcoms B r m atom 4m If thr ar N atoms pr unit volum, thn th magntiation M is givn b, N B r M Nmatom - - - (8) 4m All th lctron orbits ar not orintd normal to th fild. nc r in quation should b rplacd b th avrag of th squar of th projction of th orbit radii for various lctrons in a plan prpndicular to B. nc r should b rplacd b r Z. Thrfor, 3 NZ B r NZ r M - - - (9) 6m 6m Whr, μ is th prmabilit of th matrial. Th volum suscptibilit of th matrial is givn b, NZ r NZ M NZ r - - - (1) 6m 6m 6m Equation (1) shows that magntic suscptibilit is indpndnt of both th fild strngth and tmpratur. This is in good agrmnt with Curi s primntal rsults. r MBR, Vrashaiva Collg, Bllar Pag 3

Langvin thor of Paramagntism: Langvin assumd that ach atom has a prmannt magntic momnt m. Th onl forc acting on th atom is that du to th trnal magntic fild B. Thn th magntic potntial nrg of th atomic dipol is givn b, U mb cos According to classical statistics, th numbr of atoms having potntial nrg U is givn b, ` U ` mb cos n K p K p kt kt Th numbr of atoms having potntial nrg btwn U and U + du inclind at an angl btwn & ( d ) is givn b, ` mb cos mb mb cos dn K p sin d C sin d kt kt kt mb Whr k is Boltmann constant and T is th absolut tmpratur. Putting, w gt, kt cos dn C sin d - - - (1) Th total numbr of atomic magnts in unit volum of th paramagntic matrial is givn b, Put cos. Thn sin d d. cos n dn C sin d - - - () 1 1 1 n C d C d C C 1 1 n C - - - (3) Th componnt of ach dipol momnt paralll to B is m cos θ. Th total magntic momnt of all th n atoms containd in unit volum of th gas is th magntiation M. It is givn b, cos M m cos dn m cos C sin d - - - (4) Put cos, thn sin d d. With this w can writ quation (4) as follows. M 1 1 m C 1 mn 1 1 M mn mn coth Or, M mn L - - - (5) d Cm Evaluating this intgral and substituting th valu of C from quation (3), w gt, M 1 1 n m 1 mn d d 1 1 1 Whr, L coth is calld Langvin function. Cas (i): At low tmpratur [or larg magntic fild] L(α) 1. nc M = mn. So th saturation is rachd and all th atomic dipols ar paralll to th fild B. d 1 Th variation of M with α is shown MBR, Vrashaiva Collg, Bllar Pag 4

1 mb Cas (ii): Undr normal condition α is vr small. Thn L coth 3kT mb nm B nm M mn 3kT 3kT 3kT Thus th magntic suscptibilit is givn b, M n m C (6) 3kT T Whr C = μnm /3k is calld Curi constant. Failur of Langvin thor: (i) Langvin thor fails to plain mor complicatd dpndnc of suscptibilit on tmpratur hibitd b svral paramagntic substancs such as highl comprssd and coold gass, vr concntratd solutions of salts. (ii) Langvin thor could not account for th intimat rlation btwn para and frromagntism. Wiss modification of Langvin thor: Langvin thor applis strictl to gass, whr th molculs ar sufficintl far apart so that th mutual intractions btwn molculs ar ngligibl. In liquids and solids intraction btwn molculs is larg rsulting in a dviation from Curi law. Wiss modifid th thor and drivd a modifid quation for suscptibilit of paramagntic matrials in th following form: C (7) T In quation (7), θ is known as Curi tmpratur and is charactristics of th substanc. Equation (7) holds onl at tmpraturs T > θ. At T = θ, th transition from paramagntic to frromagntic matrial taks plac. At T < θ substanc bhavs lik frromagntic substanc and at T > θ, th matrial bcom paramagntic substanc. all Effct and Eprssion for carrir concntration: Whn a magntic fild is applid prpndicular to a currnt carring conductor, a voltag is dvlopd across th spcimn in a dirction prpndicular to both th dirction of currnt and th dirction of applid magntic fild. This phnomnon is calld all Effct and th voltag dvlopd across th spcimn is calld all Voltag. Eprssion for all voltag and all cofficint: Lt a slab of a conductor is subjctd to an trnal lctric fild E along -ais and a magntic fild along X -ais. As a rsult of lctric fild, a currnt dnsit flow in th dirction of an lctron of charg Z X will E X. Sinc th currnt is carrid b (- ), th magntic fild rts a. v Z forc on th lctron givn b This magntic forc on th lctron causs it to drift in downward dirction and as a rsult lowr surfac of th conducting slab collcts a nt ngativ charg and th uppr surfac collcts a nt positiv charg. Th collction of positiv and ngativ charg at opposit nds of th slab rsults in an lctric fild E Y, known as all lctric fild. Th hall lctric fild opposs th furthr transvrs drift of lctrons. Finall, quilibrium is rachd whn th magntic forc on th lctron is qual and opposit to th forc on th lctron du to th all fild. Now, th forc on th lctron du to hall fild E. This is along positiv -ais. Th forc du to magntic fild v. This is along ngativ -ais. In stad stat, nt forc on th lctron is ro. MBR, Vrashaiva Collg, Bllar Pag 5

F E v E v - - - (1) Equation (1) is th quation for all fild. Lt n b th fr lctron dnsit, thn th currnt dnsit is givn b, n v v - - - () n From quations (1) & (), w gt, E R n - - - (3) n In quation (3), R 1 is calld th all cofficint for th matrial of th slab. Th ngativ valu n of R indicats that th currnt carrirs ar lctrons. If th charg carrirs ar hols, R is positiv. Th valu of R can b dtrmind primntall b masuring all voltagv E d, whr d is th thicknss of th slab [= sparation of positiv & ngativ chargs] and b masuring th valu of. Rlation btwn all cofficint [ R ] and mobilit [μ]: Th mobilit [μ] is dfind as th vlocit acquird b th currnt carring particl pr unit v lctric fild. Thus,. E v - - - (4) E Substituting for v in quation (1), w gt, E E - - - (5) Comparing quations (3) and (5), w gt, E R E 1 R - - - (6) Whr, is th lctrical conductivit of th mtal slab. Thus, R E Eprssion for carrir concntration: From quation (3), w can writ, E n Thrfor, carrir concntration is givn b, n E Z - - - (8) - - - (7) Also from th quation for all cofficint, R 1 n W can writ, 1 n (9) R Knowing all cofficint and its sign, it is possibl to stimat th carrir concntration and th natur of charg carrir. Eprimntal dtrmination of all Cofficint: Eprimntal arrangmnt to stud all ffct is as shown in th following figur. A thin mtal strip, svral mm wid and svral cm long is connctd to a Battr, milli-ammtr, plug k and rhostat in sris and th strip is arrangd along ais. A magntic fild Z is applid along dirction. Two potntial lads ar attachd to th facs A and B and ar connctd to a snsitiv calibratd potntiomtr to masur th dvlopd all voltag V. MBR, Vrashaiva Collg, Bllar Pag 6

A suitabl currnt is passd through th mtal strip and magntic fild is applid along ais. all voltag is dvlopd along th ais. Th dvlopd all voltag is masurd using a potntiomtr. Th primnt is rpatd for diffrnt currnts in th strip. Th valu of all cofficint is calculatd as follows. all fild is givn b, E R - - - (1) Z Also, currnt dnsit & Elctric fild E ar givn b, I V & E b d d Substituting ths valus in quation (1), w gt, V R I Z V b R - - - () d b d I Knowing th valus of b, V, I & Z, th all cofficint is calculatd using quation (). Applications: all Effct masurmnts provid th following information about th solids: 1. Th sign of th charg carrirs [lctron or hol] can b dtrmind.. Th carrir concntration [numbr of charg carrirs pr unit volum] is dtrmind. 3. Th mobilit of charg carrirs is masurd dirctl. 4. W can dcid whthr a matrial is a mtal, smiconductor or insulator. 5. Knowing th all cofficint of a matrial and b masuring th all voltag it is possibl to know th unknown magntic fild. 1 Mark qustions: 1. What is th caus of magntism possssd b matrial bodis?. What is a diamagntic matrial? 3. What is a paramagntic matrial? 4. What is a frromagntic matrial? 5. Who discovrd diamagntism? 6. Dfin intnsit of magntiation. 7. Dfin magntic suscptibilit. 8. Dfin curi law. 9. At what tmpratur th matrial transforms from paramagntic to frromagntic substanc? 1. What is th ffct of application of magntic fild to a diamagntic matrial? 11. What is th ffct of non uniform magntic fild on dia/para/frromagntic matrial? 1. What is all Effct? 13. Writ th prssion for all Cofficint. MBR, Vrashaiva Collg, Bllar Pag 7 Z

14. Writ th prssion for carrir concntration. 15. What is mobilit of a charg carrir? 16. Writ th rlation btwn all cofficint and mobilit. 5/1 Marks qustions: 1. Distinguish btwn dia, para and frromagntic matrials.. Writ a not on th magntiation of magntic matrial. 3. Discuss Langvin thor of diamagntism./show that th diamagntic suscptibilit is indpndnt of fild strngth and tmpratur. 4. Discuss Langvin thor of Paramagntism/ Show that th paramagntic suscptibilit is invrsl proportional to absolut tmpratur. 5. What is all Effct? Driv an prssion for all voltag and all cofficint. 6. Eplain all ffct and driv th rlation btwn al cofficint and mobilit of a charg carrir. 7. Eplain all ffct and driv an prssion for carrir concntration. 8. Eplain how all cofficint is primntall dtrmind. MBR, Vrashaiva Collg, Bllar Pag 8