Effect of Electric Field on Ferroelectric and Dielectric Properties in Rochelle Salt Crystal

Size: px

Start display at page:

Download "Effect of Electric Field on Ferroelectric and Dielectric Properties in Rochelle Salt Crystal"

Oscar Webb
5 years ago
Views:

1 DOI:0.7598/cs07.65 Chemcal cece Trasacos IN: REERCH RTICLE Effec of Elecrc Feld o Ferroelecrc ad Delecrc Properes Rochelle al Crysal KLIK PRD EMWL ad TRILOK CHNDR UPDHYY Physcs Deparme H.N.B. Garhwal Uversy Ceral Uversy ragar Garhwal Uarahad- 67 Ida alaprasadsemwal@gmal.com Receved 0 December 06 / cceped 5 Jauary 07 bsrac: The model of wo-sublace pseudosp lace coupled mode for Rochelle sal has bee modfed by addg hrd ad fourh-order phoo aharmoc eraco erms ad elecrc feld erm. By usg double-me emperaure depede Gree's fuco mehod epressos for shf wdh sof mode frequecy delecrc cosa ad loss age were obaed for Rochelle sal crysal. By fg model values of physcal quaes emperaure depedece of sof mode frequecy delecrc cosa ad loss age have bee calculaed for dffere felds for Rochelle sal. Theorecal resuls agree wh he epermeal resuls of ohers. Keywords: Ferroelecrcs Gree s fuco of mode harmoc eraco Iroduco Poassum sodum arrae NaKC H O 6 H O or Rochelle sal R s he maeral whch ferroelecrcy was dscovered earles. Large crysals of Rochelle sal are easy o grow. lhough s he earles ferroelecrc maeral bu s sll he subec of esve sudy due o s wo rasos. I s ferroelecrc bewee 55 K o 97 K showg mooclc srucure ferroelecrc phase. O duerao he raso emperaures shf o 5 K ad 06 K respecvely. The Theores of ferroelecrc properes of Rochelle sal were aed by Muller. Maso assumed ha he dsplaceme of he proo s he O-H O 0 hydroge bod s he ferroelecrc dpole ad was able o oba wo cure pos agreeme wh observao. Chaudhur e al. have used wo-sublace-pseudosp-lace coupled mode model alog wh a fourh order phoo aharmoc erm. However hey decoupled he correlaos a a early sage ad egleced hrd-order aharmoc eraco erm. They herefore could o oba beer ad covcg resuls. Hla e al. hoa e al. 5 Noda e al. 6 Kua e al. 7 have epermeally suded delecrc ad oher properes of Rochelle sal crysal. I he prese wor a eeral elecrc feld erm hrd-order phoo aharmoc eraco erm ad fourh-order phoo aharmoc eraco erm have bee added he wo-sublace pseudosp-lace coupled mode model. By applyg double me hermal Gree s fuco mehod 8 epressos for shf wdh reormaled

2 Chem c Tras sof mode frequecy delecrc cosa ad loss age have bee evaluaed. By usg model values of varous physcal quaes gve by Chaudhur e al. emperaure ad feld depedeces of sof mode frequecy delecrc cosa ad loss age have bee calculaed. The heorecal resuls have bee compared wh epermeal daa of ady ad Joes 9 for Rochelle sal. Model Hamloa For Rochelle sal he eeded wo-sublace pseudosp-lace coupled mode model alog wh hrd-ad fourh-order phoo aharmoc eraco erms s epressed as H Ω J [ K µ E B B Where Ω s proo uellg frequecy ad are compoes of pseudosp varables J s echage eraco cosa bewee sp of same laces K s echage eraco cosa bewee sps of eghbourg laces s sp-lace eraco cosa µ s dpole mome of O-H O bod ad B are poso ad momeum operaors s harmoc phoo frequecy ad are hrd-ad fourh-order aomc force cosas 0. Gree s fuco We cosder he Gree's fuco GF G ; θ ; Dffereag Eq. wh respec o me ad ' wo mes each usg Hamloa Fourer rasformg ad wrg o Dyso's equao form we oba G Where Ω Ω π[ Ω a ' b bc P ' a [ J K E µ 5 b Ω 6 ad c[ [ s s 7

3 68 Chem c Tras Now P coas hgher order Gree s fucos abcd ab cd ac bd ad bc 8 The smpler Gree s fucos are solved eroh-order appromao.e. hgher order Gree s fucos are egleced. hf Wdh ad Ferroelecrc mode frequecy The P s resolved o s real ad magary pars gve Eq. fally becomes Ω π [ Ω Ω { } G. The Gree s fuco wh 0 Ω a Ω Ω Ω N a µ E a Ω Ω 9 ad 5 [ πa Ω Ω ΩΩ N a [ Ω Ω ΩΩ πµ E a [ Ω Ω 6 7 ΩΩ 8 9

4 Chem c Tras I Eqs ad 8 s reormaled phoo frequecy ad s phoo wdh. These are obaed by solvg phoo Gree s fuco ; ' ' G. 8 Re P P 8P { hgher erms 0 ad [ { [ } { [ 8 9 X X π π

5 70 Chem c Tras ad T Now Gree s fuco 9 becomes Ω G π [ Ω Ω Wh Ω Ω Ω olvg Eq self cossely oe ges [ Ω ± Ω 8 Ω Ω 5 Delecrc cosa ad loss age The respose of a crysal o elecromagec feld s epressed by elecrcal suscepbly gve by lm χ πnµ G 0 6 Where N s umber of dpoles havg dpole mome µ he sample. The delecrc cosa s relaed o suscepbly as πχ 7 We have from Eqs 6 7 ad sce [ ferroelecrcs. 8πNµ Ω [ Ω Ω Eq. 8 shows ha delecrc cosa eplcly depeds upo elecrc feld hrough Ω.The dsspao of power delecrcs s epressed as age losss gve by Im agary Ω a Re al Ω Eq. 9 shows ha loss age eplcly depeds upo elecrc feld sce boh Ω ad coa elecrc feld erms. Numercal calculaos By usg model values gve Table he emperaure ad feld depedeces of shf wdh sof mode frequecy ad delecrc cosa ad loss have bee calculaed Fgure & ad compared wh epermeal resuls of ady ad Joes 9. Table. Model values of physcs parameers for Rochelle sal crysal J K Ω η cm - cm - T c K T c K cm - cm - cm - cm - cm - g 0 7 erg/k

6 Chem c Tras of mode frequecy cm - Temperaure K Fgure. Calculaed emperaure depedece of sof mode frequecy of R wh comparso of epermeal daa Fgure. Calculaed emperaure depedece of delecrc cosa of R wh comparso of epermeal daa Resuls ad Dscusso Earler researchers have o cosdered hrd order phoo aharmoc eraco erm. They decoupled he correlao a a early sage due o whch some mpora eracos dsappeared from her epressos. I ca be see from our epressos ha our frequecy Ω s he same as he al frequecy of Chaudhur e al. However our sof mode frequecy Ωˆ coas era erms. The sof mode frequecy of Chaudhur e al. Temperaure K coas erms le. Bu our sof mode frequecy Ωˆ coas era erm ad

7 7 Chem c Tras These era erms are erm gve. These erms dffereae our epressos wh he epressos gve he wor of Chaudhur e al. The cluso of hrd-order phoo aharmoc eraco erms s que mpora sce s cluso gves correc epermeal emperaure depedece of ferroelecrc ad delecrc properes of Rochelle sal crysal. The phoo aharmoc eracos modfy he sof mode frequecy hrough sp-lace eraco. The sof mode frequecy creases whle boh delecrc cosa ad loss age decrease wh he crease he elecrc feld sregh. Ths fdg s foud o be agreeme wh he epermeal observaos. Cocluso The wo sublace-pseudosp-lace coupled mode model alog wh hrd ad fourh order phoo aharmoc eraco erms eplas well he emperaure depedece of sof mode frequecy delecrc cosa ad loss age Rochelle sal he presece of elecrc feld. Theorecal resuls agree well wh epermeal resuls of ady ad Joes 9. coweledgeme uhors are graeful o Eme Physcs Prof. B emwal E HOD Physcs for hs valuable suggesos. They are also haful o Prof U C NahaHOD Paur campus Prof R P Garolaformer HOD ragar campus Prof C BhaHOD Physcs Prof K D Puroh Prof ay Gupa DelhUv. Prof K TrpahPuab Uv. ad o Mrs Deepal Mrs ubhu Mss achal Mr. Prabha Khadur ad Dr. Deepa Josh for her valuable ecouragemes. Refereces. Mular K Helv Phys ca Maso W P Phys Rev Chaudhur B K a TGagul ad Chhura H Phys oc Jp Hla J Kulda J Kamba ad Peel I Phys Rev B ; DOI:0.0/PhysRevB hoa Y hmu K Noa R Ferroelecrcs ; DOI:0.080/ NodaN Noa R ad hso Y Phys Rev B ; DOI:0.0/PhysRevB Kua T Kawabe R Yamaa T ad Naaar N J Korea Phys oc Zubarev D N ov Phys sp ; DOI:0.070/PU960v000- BEH ady F ad Joes R Phys Rev ; DOI:0.0/PhysRev Upadhyay T C ad emwal B Ida J Pure ppl Phys Upadhyay T C Ida J Pure ppl Phys

(1) Cov(, ) E[( E( ))( E( ))]

(1) Cov(, ) E[( E( ))( E( ))] Impac of Auocorrelao o OLS Esmaes ECON 3033/Evas Cosder a smple bvarae me-seres model of he form: y 0 x The four key assumpos abou ε hs model are ) E(ε ) = E[ε x ]=0 ) Var(ε ) =Var(ε x ) = ) Cov(ε, ε )