Temperature dependence of dielectric constant and loss tangent in methyl ammonium aluminium alum

Transcription

1 Id Jourl of Pure & Appled Physcs ol. 5, Mrch 06, pp Temperture depedece of delectrc costt d loss tget methyl mmoum lumum lum Arvd Kumr Rwt* & Trlo Chdr Updhyy Deprtmet of Physcs, HNB Grhwl Uversty, rgr 6 7, Id Receved eptember 05; revsed December 05; ccepted 0 Jury 06 A model of pseudosp-lttce coupled mode for methyl mmoum lumum lum (MAD) hs bee modfed to clude cubc d qurtc phoo hrmoc terctos. Wth the help of double-tme temperture depedet Gree s fucto method d modfed Hmlto, epressos for soft mode frequecy, delectrc costt d loss tget hve bee evluted. By fttg model vlues of physcl quttes the theoretcl epressos, temperture depedece of soft mode frequecy, delectrc costt d loss tget hve bee obted d compred wth epermetl results of Pepsy et l. 5, whch show good greemet. Keywords: Delectrc costt, Pseudosp-phoo tercto, Ahrmoc terctos Itroducto Ferroelectrc mterls fd potetl pplctos techology due to ther peculr propertes. They re used memory devces, frred detectors, optcl modultors, lrge cpctors etc. Methyl mmoum lumum lum (MAD), (CH NH )Al(O ).H O s ferroelectrc below 77 K. I hgh temperture phse, the CH NH groups re foud to be symmetrclly oreted so tht they re dstgushble from ech other. But lowtemperture phse, CH NH groups re seprtely rrged whch loo le dumbbell. I hgh temperture phse, CH NH groups re oreted dsordered fsho, s f ther verge oretto loos sphercl, whle below T c the ordered stte, they te o prtculr oretto d become dstgushble d symmetrc. The orderg of methyl group MAD gves rse to order-dsorder type of phse trsto. Derby hs crred out crystl growth study of methyl mmoum lumum lum. Weber hs crred out studes of methyl mmoum lumum lum. Bouelbe d Mhr 5 hve doe Rm spectroscopc studes methyl mmoum lumum lum. chdev et l. 6 hve doe crystl growth studes o methyl mmoum lumum lum. Zg et l. 7 hve crred out epermetl determto of hysteress curve for ths lum. Bsr et l. 8 hve studed electrcl coductvty of lums. gh et l. 9 hve doe sythess d chrcterzto *Correspodg uthor (E-ml: rvdsgf@gml.com) studes o lums. et l. 0 hve studed physcl propertes of polymer med lums. Ghem et l. hve studed epermetlly the effect of dopg dfferet polymers o these lums. Prevously Chudhury et l. hve studed ferroelectrc trsto methyl mmoum lumum lum usg pseudosp-lttce coupled mode model wth fourth order phoo hrmoc tercto term. They hve ot cosdered thrd-order phoo hrmoc tercto term. They hve decoupled correltos t erly stge d some mportt terctos hve dsppered from ther results. I the preset wor, the pseudosp-lttce coupled mode model log wth thrd d fourth-order phoo hrmoc terctos terms, hs bee cosdered. We shll decouple the correltos t proper stge. I MAD lum, sce there s o sotope effect hece the term B (whch hs bee cosdered by erler reserchers ) mes lmost o cotrbuto to the system d so we hve ot cluded ths term our model of MAD (s suggested by Chule et l. lso). By usg modfed model d double-tme therml Gree s fucto method, epressos for wdth, shft, reormlzed soft mode frequecy, trsto temperture, delectrc costt d loss tget hve bee obted. By fttg model vlues of vrous quttes derved formule, ther therml vrtos hve bee clculted. The theoretclly clculted vlues for soft mode frequecy hve bee compred wth correlted vlues of soft mode frequecy obted from epermetl

2 8 INDIAN J PURE & APPL PHY, OL 5, MARCH 06 results of delectrc costt for MAD crystl reported by Pepsy et l. 5 Theoretcl results for delectrc costt d loss tget for MAD crystl hve bee compred wth epermetlly reported results of Pepsy et l. 5 Model Hmlto For methyl mmoum lum, t s cocluded from eutro dffrcto epermet tht the symmetrc dstrbuto of the H bods roud the sulphte groups mght be cuse of the ferroelectrc trsto. Cocetrtg our tteto o the proto sub-system ssocted wth the ctve os, the smplest form of modfed model Hmlto s epressed s: H J ( Α Α Β Β ),, Α Α Α,, Α Α Α Α. Z Z, z Α () I Eq. (), the lst two terms hve bee dded by us. (α=, y, z) s the α th compoet of the pseudosp, s proto tuelg frequecy, J s sp sp tercto costt. A d B re posto d mometum opertors, s hrmoc phoo frequecy, () d () re thrd- d fourth order tomc force costts. Gree s Fucto, hft d Wdth Followg Zubrev, the Gree s fucto s cosdered s : z ; z G t t t t z z = t t t ; t, () Dfferettg Gree s fucto Eq. () two tmes wth respect to tmes t d t, respectvely, Fourer trsformg d wrtg Dyso s equto form oe obts: G d δ, π P y Ft, t P Ft ;F t π... (),... (), (5) wth z z z z F t ; F t J ; ; z ; z z ;z A ; A. (6) Eq. (6) cots hgher order Gree s fuctos whch re evluted fter decouplg them by usg decouplg scheme AB; CD AB CD AC BD AD BC. mpler Gree s fuctos re evluted usg zerothorder ppromto,.e., eglectg hgher order Gree s fuctos them. I ths wy, F( t); F( t ) s evluted. Its rel prt s clled shft () d mgry prt s clled wdth (). Hece, Eq. () becomes δ G. (7) π ˆ Δ, (8) + b bc, (9) = J z,... (0) b =, () c = J,... () shft Δ d Γ() b c Δ d wdth Γ re obted s: b K δ, Γ c N () π δ δ δ δ. () I Eqs () d (), d re modfed phoo frequecy d phoo wdth, respectvely. These pper the evluto of phoo Gree s fucto A ; A whch s obted s:

3 RAWAT & UPADHYAY: METHYL AMMONIUM ALUMINIUM ALUM 85 A ; A (5) ( ) I Eq. (5) s obted s :.... (6) () s obted s : Γ 9π,, δ + δ +8 π,,, δ δ I Eq. (6), ( ) ppers whch s obted s : Δ 8P +8P, (7) + hgher terms.... (8) I Eq. (8), P stds for prcpl prt. Modfed oft Mode Frequecy Accordg to Cochr the ferroelectrc trsto cert crystls results from freezg of orml mode frequecy t trsto temperture. The epresso for ths frequecy c be esly obted from Eq. (8). Puttg vlue of Δ Eq. (8) d smplfyg, oe obts: ˆ 8. (9) The trsto temperture T C c be evluted by puttg the codto tht phse trsto occurs whe T pproches, T C,.e., whe becomes zero. From Eq. (9), oe obts d b bc = 0, =J Z = 0 t T C so b bc = 0, c = X d th( ) T B C Z X J t T C. Hece, we obt th( ) whch gves trsto temperture B T C J T C s: Tc, (0) B th J J J.... () Equtos (9-) show tht modfed soft mode frequecy ˆ s fucto of tuelg frequecy s well s modfed phoo hrmoc frequecy. The trsto temperture Tc s fucto of tuelg frequecy, sp-lttce tercto costt s well s modfed phoo frequecy. The phoo frequecy depeds upo phoo hrmoc terctos terms. 5 Delectrc Costt d Loss tget Followg Zubrev, the electrcl susceptblty χ s epressed s: χ lm πχnμ G 0 X. () The delectrc costt s relted to susceptblty χ s πχ.... () I ferroelectrc crystls, lwys, >> therefore πχ... () Hece, oe obts usg Eqs. (), () d Gree s fucto Eq. (7), the epresso for delectrc costt s: X 8πNμ ˆ Γ (5)

4 86 INDIAN J PURE & APPL PHY, OL 5, MARCH 06 Fg. Temperture depedece of soft mode frequecy ˆ - (cm ) of MAD lum ( Preset results; epermetlly correlted results of Pepesy et l. 5 ) I delectrc d ferroelectrc mterls, some power s lost the form of het, clled delectrc tget loss. Ths s rto of rel d mgry prts of delectrc costt. From Eq. (5), oe obts t ˆ (6) From Eqs (5) d (6), oe observes tht delectrc costt d loss tget deped o modfed soft mode frequecy. Hece, these deped upo tuelg frequecy s well s hrmoc terctos terms. 6. Results d Dscusso For clculto of the model vlues, the physcl quttes pperg epressos, derved for methyl mmoum lumum lum,.e., = 0.7, T C =77 K, J = cm -, = cm -, N = 0.50, µ0 8 cgs =.5, = 5 cm -, C = 50 K, J = cm -, A 0 7 (erg.k - ) = 7.66, hve bee used. Temperture vrtos of shft, wdth, soft mode frequecy, delectrc costt d loss tget hve bee clculted. The theoretcl vrtos of soft mode frequecy wth temperture re compred wth vlues obted by correltg the epermetl dt o delectrc costt mesuremets reported by Pepsy et l. 5 for MAD crystl. The vrtos of delectrc costt d loss tget hve bee compred wth epermetl results of Pepsy et l. 5 Preset results gree wth epermetl results of these reserchers (Fgs. -). Fg. Temperture depedece of delectrc costt ε of MAD lum ( Preset results; Epermetl results of Pepesy et l. 5 ) Fg. Temperture depedece of tget loss (δ) of MAD lum( Preset results; Epermetl results of Pepesy et l. 5 ) 7. Coclusos Preset study shows tht the pseudosp-lttce coupled mode model log wth thrd-d fourthorder phoo hrmoc tercto terms epls well the temperture depedece of delectrc d ferroelectrc propertes of methyl mmoum lumum lum. The phoo hrmoc terms reormlze the soft mode frequecy. The modfed soft mode frequecy clerly epls the ture of phse trsto t 77 K MAD lum. If shft, wdth, d thrd order hrmoc tercto terms re eglected from preset clcultos, preset results t oce reduce to results of Chudhury et l. These reserchers hve decoupled the correltos the erly stge d hve

5 RAWAT & UPADHYAY: METHYL AMMONIUM ALUMINIUM ALUM 87 ot cosdered the thrd-order phoo hrmoc terms. Therefore, they could ot obt better d covcg results to epl ferroelectrc trsto MAD lum. I the preset wor, the correltos hve bee solved by decouplg them t proper stge. Hece, ll the mportt terctos could be coted the epressos. Therefore, preset results re much better d covcg, whch gree wth epermetl results of Pepsy et l 5. Acowledgemet Authors re grteful to Emet Physcst Prof B emwl (Former HOD) for hs vluble suggestos d to Prof C Bhtt (HOD), Prof N Neg (Hmchl Prdesh Uversty, hml), Prof y Gupt (Delh Uversty, Delh), Prof K K erm (A U, Fzbd), Prof R P Grol, Prof U C Nth, Prof G C Josh d Dr Msh Uyl for ther d ecourgemets, Oe of uthors (AKR) s thful to Dr K P emwl who tught hm computer progrmme (umercl clcultos). Refereces Pht C, Petford-Lg A K, Belegg M & Gref M De, Phys Rev B, 89 (0). Chudhury K R, Nth D, Beree & Chudhur B K, Phys Rev B, 6 (98) 676. Derby J J, th It ummer chool o Crystl Growth (ICG- ), Dl Ch, (00). Weber, Zets fur Krstll, 9 (00) Boelbee M & Mhr T, It J pectrosc, (0) uchdev A, gh R, gh P K & Bhttchry B, Mter Techol, (0) Zhg W, Zhug Che L, Xog R G, Nmur T & Hug D, J Al Chem oc, (009) Bsr M A, Iqbl Z, Rhm K, Rhm H & Ez M F, J Appl Res Techol, (0) gh P K, Bhttchry B, chdev A & gh R, Mter Techol, 7 (0) q G, Ayesh A, Zhlf A, Mrtuscell E & Zgost R, Polym Test, (00) 79. Ghem H M E, q u, d M & Abdul Jwd, J Mod Phys, (0) 55. Chudhury K R, Nth D, Beree & Chudhur B K, Phys Rev B, 6 (98) 67. Chule W, Z Q & Jgbo Z, Ferroelectrcs, 77 (988). Zubrev D N, ov Phys Usp, (960) 0. 5 Pepsy R, Jo F & hre, Phys Rev, 0 (956) 8.