
swatantra electron maathruka

soolid-stettu physixil, oru loha kharapadaarthathile charge kaariyarukalude swabhaavathinulla oru kwaandam mechanical modalaan free electron model. 1927ll pradhaanamaayum classical drude modaline kwaandam mechanical fermi-dirac staattistiksumaayi samyojippicha arnold somerfeldaanu ithu vikasippichath, athinaal ithu drude-somerfeld model ennum ariyappedunnu.
athinte laalithyam kanakkiledukkumbol, niravadhi pareekshanathmaka prathibhasangal vishadeekarikkunnathil ithu athishayakaramaamvidham vijayichu, prathyekichu
swatantra electron model kadinamaaya modalumaayi bandhapetta pala poruthakkedukalum pariharikkukayum lohangalude mattu niravadhi gunangalekkurichu ulkkaazhcha nalkukayum cheythu. ionukalkku eathaandu oru pankumillaattha oru kwaandam electron vaathakam kondaanu lohangal nirmmichirikkunnathe swatantra electron maathruka kanakkakkunnu. kshaaratthilum lohangalilum prayogikkumbol eee maathruka valare pravachanatheethamaayirikkum.
ashayangalum anumaanangalum.
swatantra electron maathrkayil naalu pradhana anumanangal kanakkiledukkunnu
oro electrone oorjjavum aakkam thammilulla athath chathura bandhamullah swatantra kanikayaayi kanakkakkaan kazhiyunnathinaal aadyathe rund anumanangalil ninnaan modalinte peru vannath.
swatantra electron maathrkayil kristtal laattis vyakthamaayi kanakkiledukkunnillenum oru varshathinusesham (1928) blochinte sidhaantham oru kwaandam-mechanical nyaayeekaranam nalkki oru anboundu electron vaakvam free electronaayi oru periodic pottensialil neengunnu, electron maas "mii" oru phalapradamaaya maas "emm *" aayi maarunnu, athu "mii" yill ninnu ganyamaayi vyathichalichekkaam (electron holukalude chaalakatthe vivarikkan negatteevu phalapradamaaya maas polum upayogikkaam). swatantra electron maathrkayil aadyam kanakkiledukkaatha baand ghadana kanakkukoottalukalil ninnu phalapradamaaya pindangal uruthirinjedukkaam.
kadinamaaya maathrkayil ninnu.
chila samavaakyangal kanangalude sthithivivarakkanakku vitharanathe aashrayikkaathathinaal pala bhauthika gunangalum kadinamaaya maathrkayil ninnu nerittu pinthudarunnu. oru anuyojyamaaya vaathakathinte classical vegatha vitharanam allengil oru fermi vaathakathinte vegatha vitharanam edukkunnathu electronukalude vegathayumaayi bandhapetta phalangale maathrame maattunnulloo.
pradhaanamaayum, swatantra electron modalum drude modalum oom niyamathinu ore dissy electrical conductivity "σ" pravachikkunnu, athaayath
formula 4 ennathu vaidyuthadhaarayude saandrata, formula 5 ennathu baahya vaidyutha mandalam, formula 6 ennathu electronic saandrata (electronukalude ennam/vooliyam), formula 1 ennathu sharashari swatantra samayavum formula 8 ennathu electron vaidyutha chaarjumaan.
free electron modalinu keezhil drudinu keezhil athepadi nilanilkkunna mattu alavukal essy sexeptibility, plasma freekwansi, magnetoresistans, haal efakttumaayi bandhapetta haal coffificient ennivayaanu.
oru electron vaathakathinte savisheshathakal.
swatantra electron modalinte pala gunangalum fermi vaathakavumaayi bandhapetta samavakyangalil ninnu nerittu pinthudarunnu, kaaranam swatantra electron ekadesha kanakk parasparapravarthanarahithamaaya electronukalude oru koottatthilekku nayikkunnu. trimana electron vaathakathin namukk fermi oorjjathe ingane nirvachikkaam
ivide formula _ 10 ennathu reduced plank konsttant aanu. poojya thapanilayil ettavum uyarnna oorjja electroninte oorjjathe fermi oorjjam nirvachikkunnu. lohangale sambandhichidatholam fermi oorjjam free electron baand minimum oorjjathinu mukalilulla electronvolttukalude yoonittukalude kramathilaanu.
samsthaanangalude saandrata.
parasparapravarthanamillaatha oru electron vaathakathinte avasthakalude 3d saandrata (oorjja avasthakalude ennam, oru voliyathinu oorjjam) nalkunnathu
ivide soothravaakyam _ 12 ennathu oru electroninte oorjjamaanu. eee soothravaakyam spin degeneracy kanakkiledukkunnu, pakshe kandakshan baandinte adibhaagam kaaranam saadhyamaaya oorjja maattam pariganikkunnilla. 2d-ll avasthakalude saandrata sthiravum 1d-ll electron oorjjathinte varggamoolathinu vipareeta anupaathathilumaanu.
fermi level.
oru kharapadaarthathile electronukalude kemikkal pottensial formula _ 13 fermi level ennum ariyappedunnu, anubandha fermi oorjjam pole, palappozhum formula _ 14 ennu soochippikkunnu. uyarnna thapanilayil fermi level (formula _ 15) kanakkakkaan somerfeld vipuleekaranam upayogikkaam
ivide formula 17 thaapanilayaan, nammal formula 18 neey fermi thaapanilayayi nirvachikkunnu (formula 19 boltsman sthiraankamaanu). oru lohathinu fermi thaapanila saadhaaranayaayi ekadesham 105 keey aayathinal aswasthathayundaakkunna sameepanam nyaayeekarikkappedunnu, athinaal muriyile thapanilayil allengil kuranja fermi oorjja soothravaakyavum kemikkal pottensial soothravaakyavum praayogikamaayi thulyamaanu.
lohangalude compressibilityum degeneracy mardhavum.
oru yoonit voliyathinte motham oorjjam (soothravaakyam _ 22 ll) sisttathinte ghatta idathil samyojippichum kanakkakkaam, namukk labikkum.
ithu thapanilaye aasrayikkunnilla. oru anuyojyamaaya vaathakathinte oro electroninteyum oorjjavumaayi thaarathamyam cheyyuka formula _ 24, poojya thapanilayil poojyamaanu. oru anuyojyamaaya vaathakathin electron vaathakathin thulyamaaya oorjjam undaakanamenkil, thaapanila fermi thaapanilayude kramathilaayirikkanam. thermodynamicamaayi, electron vaathakathinte eee oorjjam poojya thaapanila marddavumaayi poruthappedunnu
ivide formula _ 26 voliyavum formula _ 27 motham oorjjavumaanu, thapanilayilum raasa pottensial sthiraankathilum nadathunna derivative. eee marddathe electron degeneracy marddam ennu vilikkunnu, ithu electronukalude vikarshanathil ninno chalanatthil ninno varunathalla, marichu randil kooduthal electronukalkku (spinninte rund moolyangal kaaranam) ore oorjja nila kaivashappeduthaan kazhiyillenna niyanthranatthil ninnaan varunnath. eee marddam lohathinte compressibility allengil bulk modulasine nirvachikkunnu.
eee padaprayogam kshara lohangalkkum nooble lohangalkkumulla bulk modulasinu sariyaaya alavukolukal nalkunnu, ithu eee marddam lohathinullile mattu efakttukaleppole pradhaanamaanennu kaanikkunnu. mattu lohangalkk kristalin ghadana kanakkiledukkendathundu.
kanthika prathikaranam.
booar-vaan leuven sidhaantham anusarichu, thermodynamic santhulithaavasthayilulla oru classical systethinu kanthika prathikaranam undaakilla. oru microscopic sidhaanthathinte adisthaanathil dravyathinte kanthika gunangal poornnamaayum kwaandam mechanicalaanu. oru electron vaathakathin, motham kanthika prathikaranam paragnetic aanu, athinte kanthika samvedanakshamatha nalkunnathu 
ivide soothravaakyam _ 30 ennathu vaakvam permittivityum soothravaakyam _ 31 ennathu booar maagnettanum aanu. eee moolyam rund sambhaavanakalude malsarathil ninnaan undaakunnatha kaanthikakshethrathinte saannidhyathil electronukalude bhramanapatha chalanatthil ninnu varunna oru diamagnetic sambhavana (lando diagnetism ennariyappedunnu), oru paragnetic sambhavana (poolii paragnettism). randaamathe sambhavana diamagnetic sambhavanayekkaal moonniratti valuthaanu, ithu electron spinil ninnaan varunnath, ithu rund vyathiriktha moolyangal edukkaan kazhiyunna oru aantharika kwaandam digri oof freedam aanu, ithu electron magnetic momentumaayi bandhappettirikkunnu.
drudinte maathrkayile thiruthalukal.
taapa sheshi.
kwaandam mekkaaniksinte varavinu munbulla kharaavastha bhauthikashaasthrathile oru thuranna prashnam lohangalude taapa sheshi manassilakkuka ennathaayirunnu. mikka kharapadaarthangalkkum valia thapanilayil ekadesham 32 enna soothravaakyam nalkunna dulong-pitt niyamam nalkunna sthiramaaya volumetric taapa sheshi undaayirunnuvenkilum, kuranja thapanilayil athinte swabhaavam shariyaayi pravachichu. nalla chaalakangalaya lohangalude kaaryatthil, electronukal taapa seshiyum sambhavana cheiyumennu pratheekshichirunnu.
oru anuyojyamaaya vaathakathe adisthaanamaakkiyulla drudinte model upayogikkunna classical kanakkukoottal, nalkunna volumetric taapa sheshi nalkunnu
anganeyaanengil, oru lohathinte taapa sheshi dulong-pitt niyamam prakaram labhikkunnathinte 1.5 aayirikkanam.
ennirunnaalum, lohangalude taapa seshiyil ithrayum valia adhika sambhavana orikkalum alakkapettilla, ithu mukalilulla vaadathekkurichu samshayangal uyarthunnu. somerfeldinte vipuleekaranam upayogikkunnathiloode oraalkk parimithamaaya thapanilayil oorjja saandrathayude thiruthalukal nedaanum oru electron vaathakathinte volumetric taapa sheshi nedaanum kazhiyum, ithu nalkunnu
ivide formula _ 35-nte munghadakam formula _ 36-ll kaanapedunna 3-2-nekkaal valare cheruthaanu, ooshmaavil 100 madangu cheruthaanu, kuranja formula _ 37-ll valare cheruthaanu.
vyakthamayum, electronic sambhavana maathram dulong-pitt niyamam pravachikkunnilla, athaayath.iii. uyarnna thapanilayil oru lohathinte taapa sheshi ippozhum sthiramaanenna nireekshanam. kristtal laattisinte vibrationukalude sambhavana cherkkunnathiloode eee ardhathil swatantra electron model mechappeduthaam. rund prashasthamaaya kwaandam thiruthalukalil ainsteen soolid modalum kooduthal parishkaricha debby modalum ulppedunnu. randaamathethu cherthukondu, kuranja thapanilayil oru lohathinte volumetric taapa sheshi kooduthal krithyamaayi eee roopathil ezhuthaam, 
ivide formula 39 umm formula 40 umm metteeriyalumaayi bandhapetta sthiraankangalaanu. leanier padam electronic sambhavanayil ninnaan varunnath, cubic padam debby modalil ninnaan varunnath. uyarnna thapanilayil eee padaprayogam shariyalla, electronic taapa sheshi avaganikkappedaam, lohathinte motham taapa sheshi dulong-pitt niyamam nalkunna sthirathayilekku neengunnu.
swatantra paatha ennaanu ardham.
vishrama samaya ekadesha kanakk illaathe, electronukalkku avayude chalanathe vyathichalippikkan oru kaaranavumillenn shradhikkuka, kaaranam edapedalukalonnumilla, athinaal sharashari swatantra paatha ananthamaayirikkanam. electronukalude sharashari swatantra paatha metteeriyalile ionukal thammilulla doorathodu aduthaanennu drude model kanakkakki, electronukalude defusive chalanam ayonukalumaayulla koottiyidi moolamaanennu munbathe nigamanathe soochippikkunnu. swatantra electron modelle sharashari swatantra pathakal pakaram formula _ 41 (ivide formula _ 42 fermi vegathayaanu) nalkukayum noorukanakkinu aangstromkalude kramathilaayirikkukayum cheiyunnu, saadhyamaaya eathoru classical kanakkukoottalinekkaalum oru kramatthilenkilum valuppamenkilum. sharashari swatantra paatha electron-ayoon koottiyidikku kaaranamakunnathalla, marichu lohathile vaikalyangalum maalinyangalum moolamo allengil taapa ettakkurachilukal moolamo metteeriyalile apoornathakalumaayi bandhappettirikkunnu.
taapa chaalakathayum thaapavaidyuthiyum.
drudinte model swatantra electron modalinte vaidyutha chaalakathaykk samanamaaya moolyam pravachikkumbol, modalukal alpam vyathyasthamaaya taapa chalakatha pravachikkunnu.
taapa seshiye aashrayichirikkunna sharashari swatantra paathaykkum (soothravaakyam _ 44 electronukalude sharashari (chathuram) vegathayo swatantra electron modalinte kaaryatthil fermi vegathayo aanu) taapa seshiye aashrayichirikkunna swatantra kanangalkk 43 enna soothravaakyam nalkunnu. ithu soochippikkunnathu taapa, vaidyutha chalakatha thammilulla anupatham wideman-france niyamamaan nalkunnathu ennaanu.
ivide formula _ 46 ennathu laurence nambaraanu,
swatantra electron model formulayude alanna moolyamaaya _ 48 v2/k2-nodu aduthaanu, athesamayam kadinamaaya pravachanam moolyathinte pakuthiyolam oof aanu, ithu valia vyathyaasamalla. drude modelle lorenz samkhyayekkurichulla adutha pravachanam electroninte classical gathikorjjam kwaandam pathippinekkaal 100 cheruthaanu, ithu classical taapa sheshiyude valia moolyam nikathunnu.
ennirunnaalum, drudinte mooad seabeck coffificientinte (thermopower) thettaaya kramam pravachikkunnu, ithu oru sample formula udaneelam thaapanila gradient prayogikkunnathiloode oru pottensial vyathyaasathinte ulppaadanavumaayi bandhappettirikkunnu. eee coffificient formula _ 50 aayi kaanikkam, ithu taapa sheshiykk aanupaathikamaanu, athinaal drude model swatantra electron modalinte moolyathekkaal nooriratti valuppamulla oru sthiraangam pravachikkunnu. randaamathethu thapanilayil rekheeyamaaya gunakamaayi labikkukayum muriyile thapanilayil kurachu pathinaayirakkanakkin microvy/keey kramatthil kooduthal krithyamaaya moolyangal nalkukayum cheiyunnu.
krithyathayillaaymakalum vipuleekaranangalum.
swatantra electron maathruka pareekshanathmaka nireekshanatthiloode vairudhyamulla niravadhi aparyapthathakal avatharippikkunnu. chila krithyathayillaaymakal njangal chuvade pattikappeduthunnu
mattu aparyapthathakal intermediat thapanilayil wideman-france niyamathilum opttikkal spectrathile lohangalude aavruthi-aashrithathvathilum undu.
boltsman transport samavaakyangalilekko kubo formulayilekko aakarshikkunnathiloode relaxation-time ekadesha kanakk mriduvaakkunnathiloode vaidyutha chaalakathaykkum wideman-france niyamathinum kooduthal krithyamaaya moolyangal nedaanaakum.
exchange interaakshan eee maathrkayil ninnu poornnamaayum ozhivaakkappettirikkunnu, athinte ulppeduthal ferromagnettism polulla mattu kanthika prathikaranangalilekku nayichekkaam.
eathaandu swatantra electron model ennariyappedunna baand ghadana modalinte adisthaanam roopappeduthunna shoonyamaaya laattis ekadesha kanakk anumaanikkunnathiloode swatantra electron modalinte udanadi thudarcha nedaanaakum.
electronukal thammilulla vikarshaneeyamaaya edapedalukal cherkkunnath ivide avatharippicha chithratthil valia mattamonnum varuthilla. vikarshaneeyamaaya edapedalukalkku keezhilulla oru fermi vaathakathe lohathinte gunangalil cheruthaayi maattam varuthunna thulyamaaya kwasi paarttikkilukalude vaathakamaayi kaanaan kazhiyumennu leve laandau kaanichu. lando maathruka ippol fermi liqvid sidhaantham ennariyappedunnu. edapedalukal aakarshakamaakaavunna soopparkandaktivitti polulla kooduthal videsha prathibhaasangalkk kooduthal parishkritha sidhaantham aavasyamaanu.

