Elastic properties of KCN x Cl 1-x

Transcription

1 OPTOELECONICS AND ADVANCED MATERIALS RAPID COMMUNICATIONS Vol. 3, No. 5, May 9, p Elasti poptis of KCN x Cl -x P. SINGH *, N. K. GAUR Dpatmnt of Physis, Baatullah Univsity, Bhopal, 6 6 India In th psnt pap w hav applid an Extndd Th-Body Fo Shll Modl (ETSM) to invstigat th lasti poptis of mixd alali yanid-alali halid ystal KCN xcl -x fo x=.,.56,. at diffnt tmpatu. This modl inluds th fft of oupling btwn th tanslational and otational motion of yanid moluls. Th stati sha lasti onstant obtaind by us shows an anamolous bhaviou as a funtion of tmpatu and followd th sam tnd as obsvd xpimntally. W hav also potd th and of KCN xcl -x mixd ystal. (Rivd Apil, 9; aptd May 5, 9) Kywods: Elasti Constants, Cohsiv ngy, Elasti onstants, Elasti softning, Mixd ystals, Tanslational-otational oupling. Intodution Mixd ystals of th typ A(CN) x X -x, wh A is an alali mtal ion (K, Rb, Na t.) and X is a halogn ion (B o Cl) hav bn a subjt of xtnsiv sah duing nt yas. Th KCN x Cl -x mixd ystals off a usful systm fo undstanding th impotan of th tanslational-otational oupling in ointationally disodd ystal. Th oupling has tund out to b sponsibl fo impotant ffts in ths ointationally disodd ystals. In mixd ystals, it is possibl to vay th impat of tanslational otational oupling by hanging th substitutional disod []. It influns th lasti as wll as th phonon poptis at finit wav vto, whih may lad to an ointational glass stat o vn to latti instability [, 3]. In patiula, CN - ointational mods a stongly oupld with tansvs aousti (TA) latti tanslational mods and th sha lasti onstant softns dastially []. Elasti onstants of ystals and thi tmpatu dpndn a of intst in thmslvs as wll as thy povid muh insight into th int-atomi fos of solids [5]. Th apid das of in pu KCN has bn shown to ais fom a stong oupling btwn th ointation of CN - ion and TA phonon of th ystal [6]. Th sha lasti onstant fo pu ystal is small and vais apidly with th tmpatu whas it boms mo intsting to study th fft of tmpatu on th lasti soft mod of th plad ion [7]. Sval thotial modls hav bn poposd to dsib th ointational oding in mixd ystals [8-] but a ompltly satisfatoy dsiption is still not availabl. W hav dvlopd an Extndd Th-Body Fo Shll Modl (ETSM) by inluding th fft of oupling btwn th tanslational and otational mods of CN - moluls [, 3]. This modl has sussfully bn applid to study th stati, dynami, dilti, optial and anhamoni poptis of pu ioni ystals. In th psnt wo, w xtnd th appliation of th ETSM to alulat th sond od lasti onstant (SOECs), thid od lasti onstant (TOECs) and thi pssu divativs fo mixd KCN x Cl -x (x=.,.56,.) at K T 3K. An invstigation of ths high od lasti onstants and thi pssu divativs povids usful infomation about thi int-atomi fos and anhamoni poptis.. Essntial fomalism Th intation potntial usd to div th famwo of th psnt ETSM an b xpssd as[-6] φ = d 6 Z Z ( ) f () 8 b β φ xp ρ wh th fist two tms psnt th long ang Coloumb and Th Body Intation [3]; th thid and fouth tms a th van d Waals(vdW) intation du to dipol-dipol(d-d) and dipol-quadapol(d-q) attations, th fifth tm psnts th Hafmist Flyga [] typ shot- ang ovlap pulsion xtndd up to sond nighbou ions, β a th Pauling offiint [5, 6]; ρ and b a th ang and hadnss modl paamts, sptivly as dfind ali [7-9] and th bul modulus dφ( ) d = = d φ( ) B = 9K d = () (3)

2 5 P. Singh, N. K. Gau φ is th ontibution du to oupling ffts [] Wh is th nast nighbou (nn) spation and o is th quilibium nn spaation. K as th ystal stutu onstant (=. fo NaCl stutu). Th oupling fft has bn tan though lasti onstant. Th tmpatu dpndnt Sond Od Elasti =.5Tbβ T C 3A f ( )] [.5B f ( ).5B () Constants (SOECs) a dtmind with th hlp of following quations: =.388Tβ BT [ A.388B.888B () 9.3 f ( )] δ =.9T βbt [.9B (5).B 9.3 f ( )] δ.b ] δ =.9TβB T A A A [.9B wh Tβ BT = [.65ε { ε f ( )} B B ] and A, A, B, B a th shot ang fo paamts; f ( ) and f ( ) a th TBI paamts. Th paamt f ( ) and its divativs a alulatd fom th nowldg of lasti onstants and th lation f = f xp (- / ρ). Th SOECs a obtaind fom quation () to (6) inopoatd by oupling. Th oupling onstants a givn by, δ (6) 8 = Aff ( T ) (7) χ δ = Aff χ( T ) (8) δ = Bff ( T ) (9) χ wh A R, B R a th shot ang pulsion and A Q, B Q a th quadupol ontibutions to th tanslational otational oupling and χ ij (T) is th otational susptibility []. Th tmpatu dpndnt TOECs a obtaind as = 3.37TbβT [ 3.3B 3.8B C A C 3A B f ( )] () 66 C 3 = 6.5Tbβ T [.5B.5B () 3A B f ( )] 5.56 f ( )] =.33Tbβ T [.33( B B ) (3) f ( )] =.33Tbβ T [.33( B B ) () =.33Tbβ T [.33( B B )] (5) wh all th paamts a sam as dfind ali. Using ths quations, w hav alulatd lasti onstants (SOECs and TOECs) and pssu divativs at x =.,.56,. fo th tmpatu ang K T 3K. 3. Rsult and disussion Using th input data fo pu KCN and KCl [-3] w hav obtaind th mixd valus at diffnt omposition by applying Vgads law [] to alulat int-atomi spaation( ) fo x =.,.56,. at diffnt tmpatus [5] and listd thm in Tabl. Tabl. Input data fo KCN x Cl -x mixd ystals. Poptis KCN. Cl.59 KCN.56 Cl. KCN. Cl. (Å) ( dyn/m ) ( dyn/m ) ( dyn/m ) α ( Å) α ( Å) Th valus of vdw and oupling offiint a usd fom ou ali paps [7-9]. Th oupling offiints a inopoatd in lasti onstant on th lins of Sahu and Mahanti [], this tas pop aount of th Cauhy dispany whih is vy lag in KCN x Cl- -x. Ths valus w futh usd to alulat th modl paamts ρ, b and f(). Th valus of modl paamts ρ, b and f() along with osponding int atomi spaation a givn in Tabl.

3 Elasti poptis of KCN x Cl -x 53 Tabl. Modl Paamts fo KCN x Cl -x at diffnt omposition and tmpatu. Conntat Modl paamts at 3 K ion (x) (Å) B ρ (Å) f () ( g) W hav alulatd th SOECs (, and ) fo x=.,.56,. at K T 3K and dpitd thm in Fig., and 3 sptivly. Fig. and th inas in tmpatu fo all th omposition x=.,.56 and. and bhaviou of ths two onstants hang whn omposition of yanid ion dass mo and shows quasilina bhaviou. Ou valus of and at x= i. pu KCN a los to th availabl xpimntal valus []. Th SOECs and at x=. and.56 ould not b ompad du to la of xpimntal data on thm. H, it is intsting to not that das shaply at high onntation of CN - fo th low tmpatu ang whih indiat th hang towads instability. ( dyn/m ) 3 x=.56 x=. x= Tmpatu(K) Fig.. Vaiation of psnt sond od lasti onstant with tmpatu fo KCN x Cl -x at x=.,.56 and. a shown by ( ), ( ) and ( ) sptivly. Th solid tiangl ( ) psnts th xpimntal data [] at xw=.. ( dyn/m ) ( dyn/m ) Tmpatu(K) x=. x=.56 x=. Fig.. Vaiation of psnt sond od lasti onstant with tmpatu fo KCN x Cl -x at x=.,.56 and. a shown by ( ), ( ) and ( ) sptivly. Th solid tiangl ( ) psnts th xpimntal data [] at x= Tmpatu(K) x=. x=.56 x=. Fig. 3. Vaiation of psnt sond od lasti onstant with tmpatu fo KCN x Cl -x at x=.,.56 and. a shown by ( ), ( ) and ( ) and xpimntal data [8 ] shown by il ( ), squa ( ) and tiangl ( ) fo x=.,.56 and. sptivly. Tabl 3. Valus of TOECs ( dyn/m ) of KCN x Cl -x as a funtion of tmpatu at x=.,.56 and.. T(K) 6 x=. x=.56 x=. x=. x=.56 x=. x=. x=.56 x= (Expt.) (-.9) (-.) (-.6)

4 5 P. Singh, N. K. Gau Tabl 3. (Continuation). T(K) 3 56 x=. x=.56 x=. x=. x=.56 x=. x=. x=.56 x= (Expt.) (.) (.3) (.3) Expt.-[8-3] Th sha lasti onstant ( ) plays signifiant ol in xplaining th anomalous bhaviou of mixd ystals KCN x Cl -x at patiula tmpatu and onntation. Fig. 3 shows th dviation fom th staight lin fo KCN x Cl -x, this dviation might b du to th diffn of ioni adii of CN - (Cl - ). In addition, it is intsting to not that shows softning at low tmpatu sid. This softning might b du to th fftiv ombining of CN - ions and tmpatu dpndn of flts olltiv bhaviou of th oupld impuity. Th nti ang of tmpatu invstigatd maths vy wll with th tnd shown by Galand t. al [6]. W onlud that ovall agmnt btwn th xpimntal and ou thotial valus of, and a faily good. W hav alulatd th TOECs fo mixd KCN x Cl -x at diffnt tmpatu and onntation pobably fo th fist tim. Th TOECs obtaind at onntation x=.,.56,. in th tmpatu ang K T 3K a listd in Tabl 3. It is found that with th das in tmpatu all th TOECs (i.. C, C,, C 6,C 3, C and C 56 ) inass. This vaiation may b du to th das in int-atomi spaation with tmpatu. It is found that at oom tmpatu, th thmal ffts a impotant and thi ontibution to SOECs and TOECs a signifiant [7, 8]. Th vaiation of TOECs fo both th ompositions (x=.,.56) follow th sam tnd whil at x=. th valus of TOECs a bing slightly high. Thfo, it an b said that TOECs is mo of tmpatu dpndnt ath than omposition dpndnt fo atlast in th tmpatu ang of psnt study. W hav also alulatd th pssu divativs of SOECs and TOECs listd at T=3K in Tabl. Ou sults on pssu divativs of lasti modulii a found in good agmnt with th xpimntal data [9, 3] xpt d /dp. Tabl. Valus of pssu divativs of SOECs and TOECs of KCN x Cl -x at 3K fo x=.,.56 and.. Poptis At 3K x=. x=.56 x=. d / dp (.6) xpt. ds /dp (5.9) xpt. d / dp (-.) xpt. d /dp d /dp d 3 /dp d /dp d 66 /dp d 56 / dp H, it is intsting to not that th Cauhy lation, whih a blivd to b almost fulfilld with alali halids a svly violatd by th yanids in SOECs. Th lation is = in SOECs; th tansvs onstant - is muh lag than i. th Cauhy lation in th sns >> bhav in tain spt li fluid [9], wh = and is almost zo. Thfo, this is not unxptd, as ETSM famwo is apabl to aount fo th fft of Cauhy violation (lasti poptis) and oupling fo th lasti, thmal and ohsiv poptis of psnt systm KCN x Cl -x.

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