Dielectric response of KCN crystal at ultra low frequencies

~

Solid State Communications, Printed in Great Britain.

Vol.58,No.8,

pp.519-522,

]986.

0038-I098/86 $3.00 + .00 Pergamon Journals Ltd.

DIELECTRIC RESPONSE OF KCN CRYSTAL AT ULTRA LOW FREQUENCIES

E.C. Ziemath and M.A. Aegerter Instituto de F~sica e Qu{mica de Sao Carlos, Universidade 13560 Sao Carlos (SP) Brasil

(Received

The dielectric measured

response

January

31

de Sao Paulo,

1986 by G.F. Bassani)

of pure KCN crystals

as a function of temperature

($', ~" and t g ~ ) has been

in the frequency range

10-2 Hz to

104 Hz. In t~e antiferroelectric phase the width of the loss peak are found practically independent of temperature (1.4 decades) and close to a DeDye behavlor; the relaxation time of the CN- dipoles is characterized by an Arrhenius

behavior

and U = 0,147 eV confirming tation of the dipoles.

O ~ = 'lYoeXp (U/KT) with

a classical

KCN crystallizes

from the

melt

in

reorien-

(ITC) 17, a pratically dc technique. In this communicatiou we present new data of the dielectric response of pure KCN single crystals measured in the frequency range

non

b) an electric dipole vector due to the asymetric head and tail charge distribution of the molecule.

NaCl structure 1'2. At high temperature sites have an octahedral pseudocubi¢

activated

with its surrouding. The average time between the reorientation of CN- ions in alkali cyanides has been expeperimentally measured over eleven decades of II-13 value using NMR technique , dielectric |4-17 . techniques in the frequency range 50 Hz to 100 KHz and ionic thermal conductivity

The study of the reorlentation and collective ordering behavior of linear diatomic ions in ionic solids is a field of great interest. Pure alkali cyanides (NaCN, KCN, RbCN and CsCN) are among the many components which have been extensively investigated both experimentally and theoretically. The anisotropic properties of the CN- molecular ion are of two types : a) an elastic dipole tensor due to the spherical shape of the molecular ion.

temperature

"t'~o= 7.26 x 10-]5s

10-2 to 40 Hz as well as data for higher fret8 quencies confirming the previous results. The new data fill partly the frequency range between ITC and earlier high frequency measurements.

the

anion symmetry

The dielectric response (6', 6 " and tg~) has been measured at high frequency with a commercial capacitance bridge (General Radio model 16|5-A). The response at low frequency was obtained with an equipment developed in our 19-20 laboratory . This equipment measures the current amplitude flowing through the sample

due to the fast reorientation of the CN-ions 3'4 As the temperature is lowered this compound exhibits at 168 K a structural phase transition of first order to a body centered orthorhombic 5,6 structure . The CN- axis align along the <110~ directions of the original cubic structure but the sense of the ions do not. This means that the electric quadrupolar moment orders but the electric dipole moment does not; the CNions are still rapidly orienting head and tail. The

I = I e j ( ~ t + @) and o the applied voltage V gital techniques; the matically scanned. The are given by

order is purely elastic 7. A second transition occurs at 83 K where the CN- ions become ordered 8-10

in an antiferroelectric manner In this phase the head to tail reorientations of the CN- ions are still present but occur at a much lower rate which gradually diminishes with the temperature until obtainning a full ordering at 0 K. The structure is primitive orthorhombic. Reorientation and ordering involve the rotation of the molecule within a rigid fixed lattice as well as sizeable deformations of the lattice due to strong anisotropic coupling of the CN-

~,

I o wC V O O

its phase difference with = V e~ t using modern di o frequency range is autodielectric parameters I 6"

cos~

tg ~ = where C

o sample C

V O O

sin~

6'

is the geometrical

S o o d The crystals have been

519

o ~C

capacitance

of the

= ~

grown

in our

labo-

520

Vol. 58, No. 8

DIELECTRIC RESPONSE OF KCN CRYSTAL AT ULTRA LOW FREQUENCIES

boratory by the Czochralsky technique using Merck pro analysis material. The samples (area 15 x I0 mm 2) have been cleaved or cut in thin slices and then finely polished until obtaining thicknesses of the order of d ~ 0,4 to 0~5 m~. Gold electrodes with guard rings have been evaporated on both faces. The sample holder was designed such that the crystal is standing almost free in the cell in order to avoid mecanical IB stresses . Miniature coaxial cable are soldered on the electrodes with silver paint. The measurements have been performed in a Supervaritemp Janis cryostat (helium gas cooling) where the crystal temperature is measured with a calibrated diode sensor and regulated to i 0~| K. Figure I shows the temperature behavior of the dielectric constant g' measured at 1 K H z (dotted line) and at lower frequencies: ~ 40~ 10, 1, 10-I and 10-2 Hz. All the data have been taken with decreasing temperatures. For T ( 250K

the curves appeared slightly shifted toward higher values of ~' as the frequencies decrease. The same behavior has been observed for pure KBr crystals; this peculiar behavior are thought to arise from electronic difficulties in the precise calibration of the electrometer 18-20 response as a function of the frequency The increase observed at low frequency for T • 250 K is however a real effect of polarization which becomes important at extremely low 21 frequencies already near room temperature The jump in ~' at the ferroelastic phase transition and which is not accompanied by a dielectric loss occurs always at the same temperature T = 168 K independently of the frequency of the applied field. It shows however a thermal hysteresis (not shown). Figure 2 shows in more details the behavior of ~' and tg ~ in the antiferroelectrlc phase as a function of temperature measured for different frequencies

'

I

'

I

i

7.O

E'

KCN dielectric

~

[

T

I

The

curves

~

KCN

constant

dielectric constont 52

A 4 0 . 6 9 0 1 HIll 0 t O , O I 6 0 HZ o I, O 0 0 6 H z v O, 1 0 0 4 Hz 0,0101 Hz

6,5

(10 -2 to 104 Hz).

A 40,6901 HI 0 10,0160 HI O I.O006Hz 0,1004 HZ I O.OlOt HIE

.~

s,O

4~S

l

4~

~

i.

I

tg 6

' 4

0,03

0,02

0,01 0 4 ,5 [ ....

I

0

I

~

I00

I

200

I

40

II

50

60

70

80

90

I00

II0

T(K)

$00

T(KJ FIG. FIG.

|

Temperature dependence of the tant ~' of pure KCN measured 10 Hz ( O ) , I ( ~ ) with our dotted curve, obtained at | 6015-A.

dielectric consat 40 Hz (g~),

Hz ( ~ ) , 10-I Hz ( V ) and 10-2 Hz low frequency equipment. The shows as reference, has been KHz with a commercial bridge Genrad

2

Temperature dependence of the dielectric constant 6' and tg~ of pure KCN in the antiferroelectric region measured at various frequencies f = 10-2 to f = 104 Hz. The curves have been slightly shiftedldownwards(see text). The dotted line is an extrapolation and represents the expected temperature variation of the dielectric constant at high frequencies ~ (see also fig.4).

Vol.

58,

No.

of g' have been slightly shifted downwards in order to practically coincide at T < 40 K. As the frequency diminishes we clearly observe a shift and a decrease of ~' and of the dielectric loss 6" towards lower temperatures showing that the dipole still reorient even at lower temperatures. The temperature dependence of the dielectric loss peak shift in frequency is shown in figure 3. The data have been obtained from the

compared with 1.144 decades for the Debye equation). This effect can be interpreted as being produced by a distribution of relaxation times such as the. Cole-Cole distribution proposed by Ortiz-Lopez 16. The area under the ~" curves in lOgl0t.o scale A (~') is directly related to the static susceptibility of the material ~s - ~-~o= 4~'~ s = ].466 A ( ~ " ) where

T (K)

~

1

~

s

and Et~ are respectively the dielectric

constant of the material measured at zero frequency ~ s = ~'(o) and at infinite frequency.

T

6 4

0

z

2

This area decreases with decreasing temperatures and corresponds to a diminution in the number of the mobile CN- dipoles as a consequence of the gradual formation of the antiferroelectric ordered state with frozen-in electric dipoles. The difference between the curves ~' (I0 -2 Hz) and &'(oo) (dotted line extrapolated in figure 2) is plotted in figure 4 with

0

-

i0 o AE'

i.., -? C .-I -4

/

-

_

iO-I

--

,

,

l

,

I0 "3 I0 -4

0.4

T~'

'

' - k f I 50

at high frequencies ( o ) (Genrad bridge) and low frequencies ( • ) . The ITC result ( • ) is taken from reference 17. The bars represent the uncertainties of the measurements. The 17 dotted line is the fit obtained by L~ty et al

maximum of the loss peaks. Also plotted in the figure is the result of the ionic thermal conductivity (ITC) technique obtained by OrtizLopez i6. The temperature dependence fectly fitted to an Arrhenius law ~=~oeXp

(U/ET) w i t h ~ O = 7.26 x

U = 0,147 eV in good agreement

I

60

0.2

a

70

I

80

m

90

I 0 I00 IlO

4

Temperature dependence of the difference between the dielectric constant 6' measured at -2 I0 ~z and at infinite frequency (dotted curve extrapolated of figure 2). For T > 55 K it represents the difference ~ E = k s- ~ = 1.466A(~") where A(~") is the integrated

loss area (dotted

line as measured by Ortiz-Lopez 16. The drop of E' observed for T < 55 K shows that the dipoles still not frozen-ln cannot respond to the low frequency applied

field (10 -2 Hz).

is perbehavior

I0-15 s

with

/

T (K) FIG.

= 7.26 x ]0-15s, U = 0,147 eV obtained

0.4

0.2

3

o

0.6

///

Arrhenius plot of the relaxation time of CNdipoles versus inverse temperatore~C"= r~oeXp(U/KT) with ~

I --I 1,0 "-- ---- -I A (~"l o.8-

17 /,,'

40 FIG.

l

Z"

iO-Z

-8 • / l ~ I l rI ~/' J m m I I = 12 14 16 18 20 2=2 T -o (10-3 K-If

,

0.6

-6

-I0

521

DIELECTRIC RESPONSE OF KCN CRYSTAL AT ULTRA LOW FREQUENCIES

8

and

the values

obtained by Luty et a117 (dotted line). The shape of the peaks are close to that predicted by the Debye equations. Their width at half maximum is pratically constant in the temperature range studied; it varies only from 1.36 decades at 68 K to 1.44decades at 53 K (to be

16 the results of Ortiz-Lopez for A ( ~ " ) . The agreement is found reasonable for T ~ 55 K and confirms the model of random internal field with a simple block function distribution of local electric fields P(EB) , symmetric with respect to E B = 0. Down to 55 K the curve ~' (10 -2

Hz)

is therefore a good approximation of the static value of the dielectric constant ~'(o). At

522

DIELECTRIC RESPONSE OF KCN CRYSTAL AT ULTRA LOW FREQUENCIES

T = 55 K most of the dipoles are frozen-in and the drop observed below this temperature reflects the fact that these dipoles still mobile cannot respond to the low frequency applied

Vol.

58,

Acknowledgement - We acknowledge the financial support from the Funda~ao de Amparo a Pesquisa do Estado de Sao Paulo (FAPESP) and the Financiadora de Estudos e Projetos (FINEP).

field (10 -2 Hz). I11':Fl': 11I':NCI,:S I. 2. 3. 4.

5. 6. 7. g. 9. IO. II. 12. 13. 14. 15. 16. 17. 18. 19. 2(}. 21.

No.

A • G(JOPER, NaLur(, I ( ) ] , 745 { 1 9 2 1 } , R .M. BOZ(JRTII, J o u r n a l of tim American Chemical Society _44 , 3 1 7 ( 1 9 2 2 ) . I) .L. PRICE, J.M. ROWE, J.J. RLIBII. E. PRINCI~,, I}.G. IIINKB and S. .qUSMAN, Journal (}f Chelnical Physics 5_6, 3697 (1972). J .M. ROWE, I).U. IIINKS, I).L. PRINCE, S. SUSMAN and J.J. RUSll, Journal of Chemical Physics 58 2039 (1973). II. . l . VEllWEEI, a n d J . M . B I J V O E T , Z e i t s c h r i f t f~ir K r i s t a l l o g r a f i e !5_{2, 201 ( 1 9 7 8 ) . 13'21Y, R u c u , , i l d,, TF;IV;HIX (h. C h i l u i e I)ay~;-I~;l:;II~{,Iv ] I I ~ () , (}I}8 ( I q ' } t)* ,I .M. 13IJV{}ET ;lll{I J . A . B • I~OIIA'H(, I'I'A" I)AVII}IIVITI:II, I''1;" SGAVAI/I)A I}O {:AIII'll) a n d F . I,i.l'l'Y, P h y s i c a l RCViL, U B 2q, 3586 (1984). D • FONTAINE, {'ompte.'4 R , , n d . s d~, I A { ; , h m " " { d e s S t i e n c ~ , s S e t B 2 8 1 , 443 { 1 9 7 9 ) . {}t: Ch{,mic;ll Phy:~ic~; {}6, ' ; g i l l { 1 9 / 1 ) . ,1 .hi. P.(}WI::~ . l . J . I,HI.{~II a n d I". PRINCE, . h } . r n a l 16, I(}] ( 1 9 7 / ) . ,I .M. R(IWI':, . 1 . 3 . I:IJSII, I'2. I'I(1NL:I': a n d N . J . t;lll.:,qSl.:l/, I " { . r r . , . l e c t r i c s R e v i e w B 3_{), 4 9 2 5 ( 1 9 8 4 ) and Pilvsic~l II . T . ST{}I(I;::4,~'i}.{'. A l l . ION a n d T . A . CASE, I ' h y s i c a l P . e v i e w I . e t . l : e r s z27, 2 6 8 ( 1 9 8 1 ) State C{mun,micaW• BU{.;tIHEIT, S. ELSCItNER, l l . D . MAIER, J . PETERSON a n d E. SCllNEIDER, S o l i d [ions 3 8 , (:,I}B ( 1 9 8 1 ) . f ; ; r P h y s i k B 5 2 , 37 ( 1 9 8 3 ) . S • EI.SCIITIER a n d ,l. PE'II'21tSI~N, ~ P i t . s c h r i f t _ (1976) Uniw~rsity of Utah (II.S.A.). N . l ) . . I I J I , I A [ I , P h . D. T h e s i s ! f 2 , 201 ( 1 9 7 7 ) . I~1.I}. .IIILIAN a n d F . LIJTY, l ; c r r o , , l t , c t r i c s of Iltah (II.S.A.). J • ORTIZ-I.III'I~Z, P h . D. ' l ' l H , s i s ( 1 9 8 3 ) I l n i v t , r s i t y Physical R{,vi,,w I , { ' l l u l - : ¢ ')(1, 12199 ( 1 9 < g 3 ) . F • I,ii'I'Y ,111{I ,]. (}ll'l'lZ-l,lll'l':Z, Insl itulo {h: I " i s i c a P { , h i [ m i c a d{: S~'io C a r l o s , Ilniv,,rsi1: . { ; . Z I I d ' I A ' I I I , H. So. Th.'~;i,<; ( 1 9 8 5 ) , {lade d e S£m I ' a u l u ( B r a s i l ) , lnstituCo de F[sica e Q u [ m i c a d e S~io { : a r l , , s , l l n i w , r s i d a J . F . SI,AETS. l ' h . D. ' l h e s i ~ ; ( 1 9 ] 9 } , {h' de S~,, I';ml,~ ( l ' , r a : ~ i l ) . lnstrmnents 1'2. C . ZII':HATII} ,J.F. gI,Al':l',% ,llld M . A . AL':GI';RTt':R} s u b m i t _ l { ' d t{} RPvi~:w o f S c i e n t i f i c (1986). and Chemistry of Solids _28, 6 5 7 ( 1 9 6 7 ) . J . l l . BI!AU?I(}NT a n d I ' . W . H . .}A(:{}BS, , l o u r n a l o f P h y s i c s

8