Chapter 6

Ultrasonic investigations of elastic properties and phase transition in

LiKo,9Nao,1S04, crystal

771i.v (.'iicip/cr nii//i~ie.s ihe phase transition study of Li KO 9 Nu 1 SO4 cq~.rial

hy using ultr~iconic PEO technique. The present irivestigutior? 11'0s curried

oril io see the e f i c t of doping the crystal u ~ i t h sodiun? oil the ten?peralure

vrrriuiion of el~tstic constants and also to see whether this doj~ing hiis trny

coririectio~i 1t.ii11 pliuse trcinsition. DSC ~i~easurerneiils (I?? this ci.y.clcr/ tire

~ ~ ~ . e . w ~ ~ t e t l . El~rctic properties of the doped cry.stci1 are siudied,for the first

ii~rie. .411 the l i ve elastic constants have been ~neosured There ex-ists cr

controver.sy re~cirding the symmetry o f the crystal while groil~th is per:fi,rrned

iii 35°C' n,itIi ei/uiriioleculor ,fraction of Li2S04H20, K2SOj and RINZ~COJ

l.'~-i~rri the /,r.e.~i,iii s t~ idy the riiisco~~cq,tio~i clboi.it the structure (! / ' /he og~s tn l

1 i~ i . s I I L ' C I I i . ~ ~ . \ ~ i l ~ ~ e ~ I . I S ' ~ ~ ~ : f u ~ e plots ~f phrrse l ~ c l o c i t ~ ~ . .sloivric.s.s, Yoiirig'.v

riii1d~i1ii.s tinci lineur conlpressibiliiy have been niade and it revealed the

~ i r i i ~ ~ t r ~ j ? ) ~ in cIcr.slic properties.

Ultrasonic investigations of elastic properties and phase transition in

Li Ko.9Nao.,S04 crystal

6.1 Introduction

I~.ithiurn potassium sulphate (LKS) is a very extensively studied

crystal. I t exl~ibits a series of phase transitions from 20 K to 998 K [6.l] . Tile

iniportancc 01' this crystal is that it shows pyroclcctric and fcrroelcctrics

hcliavior 16.21, clectro optic effect 16.31, large ni~mber of phase transitions,

lid obsel.vatio~~ of incom~nensurate lattice phase in certain temperature

regions. Phasc transition occurs at high temperature, first from paraphase to a

slaw with conrmensurate and then with incorn~llensurate nlodulation [6.4]. In

this state LKS is simultaneously ferroelastic and superionic. A variety of

experinlcntal techniques such as Raman scattering [6.5], Dielectric study

[6.6], Ferroelcctric [6.7], Piezoelectric property studies[6.8], X-ray analysis

[6.91, '1'herm;il analysis [6.10], Neutron scattering [6.1 11, Brillouin scattering

[6.12] and Ultrasonic study [6.13] have been used to investigate the physical

properties. The elastic properties of LKS have been studied previously by

using Briilouin scattering [6.14] and ultrasonic techniques [6.15]. Elastic

propcrtics of' l,KS are also investigated earlier by resonance technique and

torsion pendulum method [6.16] whereas very few studies are reported in the

literature about the physical properties of Sodium doped Lithium Potassiuni

Sulphate.

Lithium sodium potassium sulphate, Li2NaK(S04)2, (LSKS) was

synthesized by Kitahatna and Frech [6.17] by slow evaporation technique at

80 "C by cquiniolecular fraction of Li2S04H20, K2S04 and Na2S04. Liang el ol.

[6.18], Ramhurnar el 01. [6.19] and Reddy et L I ~ [6.20] have reported tlic

sy~~thcsis and growth of the same orthorhombic crystal at 35°C. They havc

studied the ionic conduciivity and optical properties of Cu and Ni doped

crystal. But I'i~iienta el (11.. [6.21] have reported that the crystal grown at

3SL'C with equimolecular fraction of Li2S04H20, &SO4, Na2S04 is an

hexagonal crystal with composition Li Ko.<Va 0 . 1 S04. The crystal, Li KO9

Na 0 , SO4, comes under the space group c261, [P63 / 1111. The lattice

parameters [6.21] are a = b = 5.1421 A, c = 8.602 A which gives VIZ =

98.48 ,& .For the sake of comparison, the cell parameters of LiKS04 are a = b

= 5.1452 A,c=8.6343 A which give V/Z = 98.98 A. The cell dimensions

together with space group possibilities indicate the predominance of LiKS04

in the mixed conipound Li Ko9Na 0 , S0.r [6.21]. The nielting point of this

crystal is 650°C and this is also inter~nediatc between 1,KS and LSS.

Pimenta el al. [6.21] studied the electrical conductivity in order to

investigate the nlechanisn~ of ionic conduciion at the high temperature phase

transition in these compounds. They ooserved that the mixed crystal

undergoes phase transition at about 472'C accompanied by a change in the

electrical conductivity by a factor 50. It is interesting to note that these

values are intermediate between the transition temperature of LKS and LSS.

The value of electrical conductivity was reported to be in between that of

LiKS04 and LiNaS04.

The activation energy 16.211 calculated from temperature variation of

ionic conductivity was found to be intermediate between that of LKS and

LSS. It is proposed that the rotation of tke sulphate ions enhances the ionic

mobility in this family of compounds tllrough a 'paddle wheel' mechanism

Therefore the height of a potential barrier over which the ions must jump is

expected to decrease with increasing sullate ion orientational disorder. The

discontinuity in the evolution of the a2tivation energy above the phase

transition, which occurs approximately at the super ionic transition and

melting point of the pure compound LC,S, can also be related to an extra

enhancement of sulphate ion orientational disorder.

( ' l ~ r o . ~ o ~ ~ i c i,wes~~,quiio,,s ~ / ' E / o s / i c p r o p e ~ ~ / i c ~ . ~ ~ o I L / , I / ~ [ I s ~ I / . ~ J O S J I I O , I i,i I . ! K, , ,, ;Vo ,, , .SO, C,;IKS/[I/ p~ ~-

21 I

1)rozclowki el 01. [6.14] have rcportcd a pliasc transition at 333 K for

I.KS from 131-illouin scattering techniques. They have reported that elastic

constants Czz. C33 and C(j6 undergo anomalous changes at this temperature.

Later Brillouin scattering by Pilnenta [6.21] could not detect such an

anomaly. But Wan-Ji-fang et al. [6.22] from their ultrasonic study reported

that there is abrupt change for C j j at 333 K. The thernial expansion study by

Sharma et ul. / 6.231 on this crystal also reported a dip at 333 K in the thermal

expansion coefficient curve. But ultrasonic study by Godfrey ct 01. j6.151

could not detect this phase transition. At this juncture present study

iiivestigates controversial phase transition at 333K due to the effect of doping

with impurity like sodium.

Further. in this chapter the elastic study of sodium doped LKS (Li KO 9

N a ,, I SOJ ) crystal is reported. The aim of this investigation is to examine

\vhat type 01' crystal is found at 3j°C with equimolecular fraction of

l,izS04HzO, KzS04 and NazS04 since there is a controversy regarding the

type of c~ystal found while growth is performed at 3 joC. This examination

can also be perfonned using the measurement of interfacial angles, XRD

and density. I'hese measurement's will give information about the type of

c~ystal growii at 35°C. So far, no information is found in the literature about

r i~c elastic properties of Li K o . 9 N ~ . I So4 crystal. All the five Elastic stiffness

constants, Coinpliance constants and Poisson's ratios of the crystal have

bccn evalua~ctl for the first time and also primed surface plots of Phase

\.eiocity. Young's modulus, linear compressibility, and Slowness in the a-b

~ ~ n d a-c planes have been reported.

6. 2 Experimental techniques

6. 2.1 Sample preparation

Large single crystals of Li Ko.9 N Q . ~ SO4 of size ( 30x25~16) n1m3

linvc been grown from saturated aqueous solution by slow evaporation

technique at 323K for 60 days. Similar crystals werc also grown at 308K and

318K. Tlic solution has been prepared by equimolccular 1.1-nctio~i of

Li lSo~H20. KzS04 and Na2S04. The details of slow evaporation technique

have been described in Scction 2.2. The XllD of the crystal grown and the

photographs of the crystals are as shown in Figures (6.1 and 6.2). The

presence of rnetallic element and their percentage composition have been

examined using AAS (Atomic Absorption S ~ectroscopy) and flame test.

6.2.2 X-ray Diffraction spectrum

The crystal structure of Li Kos Na 0 I So4 has been examined by

Powder X -ray Diffraction and reported [Figure.6.1]. This is cornpared with

the reported spectrums [6.36 and 6.3:'] of hexagonal LiKS04 and

orthorhornbic LSKS.

Figure 6.1. X-ray diffraction spectrum of sodiun doped lithium potassium Sulphate

6.2. 3 Me:isul-crnent of interfacial anglcs

Table 6.1 Coinparison of computed interfacial angles of 1.i Ko9 Na ,,, Sod. (323K grown) with measured value

[ I Interfacial angles betwecti tlli=I

A stet-cographic projection of the natural hccs of tile crystal was

computed itsing the lattice parameter obtained by Pimenta c/ (11. [6.21]. The

interiiicial atigics of natural faces of the presently grown crystal are

compared with the computed value of the interfacial angles. Thus the natural

c a c ~ s . - . of tile sample have been identified by thc technique discussed in

Section 2.2.3. The morphology of the crystal is as shown in (Figure 6.3).

'I'hc crystal has been grown at different temperatures. i.e., at 308, 313, and

323 K. In all the three cases the interfacial angles are same. i.e. no structural

ch;inge was oliscrved

Crystal faces

I ~

0 0 i - O l i

0 0 i - i O i

-~

O O i - . I O i

1: 00i-i li

010-1 10

; 0 i O - i i 0

The density of the material is measured using Archimedes' principle

by litlciit~g tile loss ol'weight in the liquid carbon tctracliloridc. The density

oi'(;(~'I.I is 1.67~;tnlcc. 'I'he density is measured to be 2.464gmicc.

faces

Cotnputed

149.85

149.85

149.85

149.85

60

60

-

Measured

I 50

150 -

150 -

150

60

60

Figure 6.2 Photograph of Sodium doped Lithum Potassium Sulphate

. .. . . C . . . ' . ,

..A&; &, ;, 7 - J

I. .P .

Figufe 6.3 Morphology of Sodium doped Lithum Potassium Sulphate

U/#rawnic investigation Q f Wnclic properties dphm 1rrursi:ilion in

Li & . p ~ a a r SO, crysral

FQure. 6.4 (8) Stereographic projections of duped LKS about a-axis

Figure. 6. B(b) Stereographic pm&dona of s&nS doped LKS about c-axis

I3ulk s;iniplcs have been cut using a slow speed diamond \\'heel saw

so as to havc liropagation direction along a- and c-axes. The mis-orientation

is less than I" . f h e thickness of the sample crystal is in the range 0.8-1.5 cm.

.l'lie samples arc well polished by Cerium oxide powder. This enables one to

gct proper boilcling of transducer.

6.2.5 Ultrasonic velocity and elastic constants measurement

The elcments of determinantal equation are defined by elastic

constants and the direction cosines of the direction of propagation. The

velocity of ulrrasonic waves may be determined by nicasuring round trip

t i i l~e of plane i~ltrasonic longitudinal and transverse waves in the specimen

usiug X -ant1 Y-Cut transducer. The measurement was done with Pulse

Echo Overlap technique (PEO) [6.27]. Details of iueasuring the elastic

consta~it of I lcxagonal crystals have been discussed in Section 1.3.5.

I lexagonal crystal has five-second order elastic stiffi~ess constants.

6.3 Results and Discussions

6.3.1 Structure of grown crystal

Single crystals of LiKo.gNao.1 So4 have been grown by slow

evaporation of saturated aqueous solution containing equimolecular fraction

of I,izSOsIi20. K2S04 and Na2S04 at 35'C. Earlier workers 16.18 - 6.201

conducted thcir work on growth using the samc reactants at 35°C and the

crystal grown was reported to be Lithium sodiun~ potassiuiu sulphate.

Li2NaK(S04)Z. However the powder X ray diffraction pattern (Figure 6.1) of

the presently grown crystal was compared with JCPDS file [6.38] of Liz Na

K (SO4) 2 anti that of LiKS04 [6.37] The observed intensity peaks are not

matching wit11 the spectrum of LizNaK (S04) 2 (6.38). However. ~ i ~ o s t of the

iiltensity peaks arc closely matching with intensity peaks of LiKS04(6.37).

i l ~ e additional peaks in the spectrutn of Li Ko.g Na I SO4 are possibly due to

the slight structural distortion resulting f r ~ ) n ~ the Na doping. Again, the

presence of metallic element sodium and its percentage composition have been

confirmed using AAS (Atomic Absorption Spectroscopy) and flame test.

In addition, the density measureme ~t on Li KO 9 Na o I So4 (2.469

gmlcc) shows that the value is in between those of LiKS04 (2.396 gn~lcc)

and Lithium Sodium Sulphate (2.599gmlc(:) and not of Liz Na K (S04) 2

(LSKS) (2.2 gmlcc). Fro111 the density measurement i t is found that Li Ko9

Na 0 I SO4 is a different crystal. The interfacial angles of grown crystal are

measured with an accurate contact goniometer and compared with computed

values, (Table 6.1) which indicated that the symmetry of the grown crystal is

hexagonal. Hence from the above findings it is found that the presently

grown crystal is LiKo.9Nao.l SO4 as found b) Pimenta et.al [6.21].

Hexagonal crystal has five second order elastic constants whereas

orthorhombic crystals are having nine. IJltrasonic velocities have been

measured i l l [loo], [010] and [OOl] directions. It is noticed that velocity

along [loo], and [010] have the same valu-s and hence the crystal has only

five elastic constants. Hexagonal crystal has the following five second order

elastic stiffness constants C I I = C22, ~ 3 3 , C41 = CSS, C66 and C, , = Czj (Table

6.2).The diagonal elastic constants CI C3,, Cqq and C66 have direct 2 relationship with the suitable ultrasonic r o d e velocity given by C,, = pv .

Relationships between elastic constants for relevant ultrasonic wave velocity

for the Hexagonal system are discussed in Section 1.2.4 [6.8,6.9] The off

diagonal constant C13 is estimated by measuring the velocity in [101]

direction and the corresponding equation i:; given by

2 2 2 C I3 =fa , ={&[(s2Cll +c C,, -pv, )(I C4, + + C ' C ~ ~ -pv,')] C S

where s = sin 8 c = cos 0 where v is the velocity of propagation

of respective mode; where 0=28' from ;I-c plane. p = 2.464gmicc. C I ~ =

C I ) - ~ C ~ ~ = 37.06GPa.

t i / / ~ ~ ~ r . \ o ~ ~ t < , ~ 1 1 1 ~ ~ ~ ~ ~ , ~ ~ ~ / ~ 0 ~ 1 , ~ EIo.~ric proper~ies o,~dp/jose r rc ,~~s i l io ,~ ill L , K,, , \< , , , , so, , ,,..%/,,/

-p-- . 21s

Considering all experimental uncertainties, the absolute accuracy of

elastic constant value is estimated to be better than 0.2% for diagonal elastic

constants and 1 % for off diagonal elastic constants. In all the vclocity

mcasuremcnts. the correct overlap identification and bond correction havc

been applied. O f the 9 propagation modes, velocity measurements of 5 mode

arc sullicicnt lo evaluate all the 5 second order elastic constants with cross

cliccks possiblc on some of the values such as

For the I lexagonal system, there are five elastic constants CI I = C22.

C:;,, C,.) = C S 5 Cb6 and C , , = C2). The constant C,2 can be calculated from

Cb(,. Starting with the well-known Christoffel equation, one can deduce the

relationship between the elastic constants. These relationsl1ips and velocity

of propagation of various ultrasonic modes measured along selected

directions in the crystal is listed in the Table 6. 2. The McSkimin At

Criterion [6.29-311 has been applied to correct for the phase lag introduced

by the bonding medium on the RF echoes. Taking into account the

uiicertai~ities in riieasuring the length and various other experimental

limitations. an absolute accuracy better than 0.3% has been obtained in the

vclocity iiieasurcments. These measurements enable one to nieasure five

elastic coilstants. From the above results it is proved that crystal synthesized

with equirnolecular fraction of Li2S04.Hz0, Na2S04 grown at 35'C is

Hexagonal. having the chemical formula LiKo9Nao.l SO4, and not

Orthorhombic Na K(S04)2 as reported by Liang et ul. [6.18]. The second

order elastic stil't'ness constants and the corresponding compliance constants and

Poisson's ratios are calculated from mode velocities tabulated in Table 6.3.

Table 6.2. Velocities of ultrasonic modes in Li Kn 9 Nu n.,SO, at 300K. L, T and QL represent longitudinal, transverse and quasi-longitudinal modes respectively. The relations between mode velocities and elastic constants are also given.

constant relation

c,,= cz2 = pv, ?

V, = 24771 2

C:: = pv., -

[OOlI I 1 001

V 6 = 2 8 5 6 + 3 c44 = Css = PV,

Table 6.3 Elastic stiffness constants, Compliance constants and Poisson's ratios of Li Ko,g Nu 0 .1 SO4 at 300K

/ SIN0 I Elastic stiffness constant (GPn)

Poisson's ratio

The elastic constants of Li KO9 Na 0.1S04 and LiKS04 are compared

in Table 6.4. The elastic constants have sut~stantial difference. The difference

in density and velocity of ultrasonic Naves through these samples are

responsible for this difference. Elastic st~ffness constants C I ~ (23%), Cl3

(16%) and C ,, (16%) have exhibited large deviation than constants C 33 (4%)

, Csj(9.8%) and C66(1 1.3%).

I I I

S,1=0 .21 1 C,, =C,,= 68.86 * 0.14

6 . 3. 2 Tempc~.:lture Variation of Elastic Constarlts

U i i r ~ ~ + o ~ ~ , c i j ) ! L . \ I J , ,>fto,i.\ ,!/ 1 ~ i ~ ~ ~ r i c ~ 1 ~ ~ ~ p ~ ~ 1 ; e . s ~11id.111;ase ~ ~ [ I I ? . S ~ ~ I ( J I I 1 1 )

1 , \ , 5 , ' \ \ i l ! l 225 ~- .- -~ - - - - .- - -

Table 6 4 Coiirparrson of elastic stiffness constants of Li h'a v h'tr IJ 1 SO4 and Litillurn Potassium sulphate (LKS)

-

Elastic stiffiicss constant Elast~c slifl~iless constant

I Doped LKS (Gpa) LKS (GPa)

i 68.86 -t 0.14 57.24

l'he te~nperature variation of the velocity of longitudinal and shear

- -- ! 1 c;; I I Cdd- Crs

I-- I Chh 1~- - -

Ci? ! ~ _ _ - ! Cli L- -. -

waves propagating along the various directions in the crystal has been

determined in the range 300 K-375 K by keeping the sample in a temperature

controlled chamber. The change in velocity with temperature has bee11

64.89 i 0.13

23.4% 0.046

15.94 i0 .03

37.061 0.7

19.251 0.4

n~casured by carefully adjusting the CW oscillator frequency, keeping the

sclected 11F cchoes in the phase matched condition. The rate of temperature

change in all the measurements is in the range of 1 K per minute. In the

present study the temperature variation of 4 elastic constants C I I . C;;, Cu.

mti Ci,,, h;lve been made. Investigation beyond 375 K was not possible

bccausc o l ho~idi~ig problems. The thermal expansion has bcei~ neglected

\\bile measuring thc variation of ultrasonic wave velocities with temperature.

67.45

21.51

14.29

28.66 -

22.37

1600 23.1 300 310 320 3 30 340 350

Temperature: ( K )

F~gure 6.5 Variat~on of C,, and C,, with temperature of Li KO 9Na 0 1 SO,

Figure 6.6 Variation of C,, and Cll w~th terlperature of Li KO 9 Nu n 1 ,SO4.

'l'l~c t c ~ ~ > l ~ c r a t ~ ~ ~ - e variation of elastic constants C I 1 , C]], C44 and C(,(, in

the tempcratul-e range 300 K-375K is carried out. It can be shown fiorn the

Figures [6.5. 6.61 that a number of constants are showing anomalous

behaviour i l l tllc rcgion 313K-345K. The 111ost pronounced anomaly is

sho\\,n by C66. I t shows a dip at 320K, a peak at 325K and small dip at 330K.

l'he constant 1:44 shows minor anomalies in the range 3.15K-32SK. The

constant 633 shows anomalies in the range 310K-325K. C I I does not have

significant anoinalies in the temperature range.

Present DSC (Figure 6.7) shows no anomalies in the temperature

ra~igc. 'l'liis may be due to the fact that the thermal changes associatcd in this

weak anomaly is not appreciable, while ultrasonic technique is able to detect

such 1tli110r ;111ol11alics. Lack of correlation between the anomalies in dif'ierent

elastic constalits as temperature is varied shows the absence of a definite

phase lransitioll in the crystal in this telnperature range. Early repo~ted 16.14,

6.181 controvcrsial anomaly at 333K ( 6 0 ' ~ ) for the undoped crystal

(LiKS04) is not found in this doped crystal. But when compared to the

undoped ciystal this crystal shows several minor ano~nalies in the range

3 l.3K-340K. I'his leads to the conclusion that weak phase transition

anomalies are noticeable if it is doped with suitable material.

6.3.3 Phase Transition study by Differential Scanning Calorimetry

~fherin~rl changes of Li Ko.9 Na 0.1 S04 crystal have been observed in

thc rangc 3 0 L 1 ~ ' - l ~ ~ n ~ at a slow heating rate of l"/min. The DSC scan is as

sl~o\vn in I'ig111.e [6.7]. Even though there is a broad dip centered around

35OK ( 7 7 ' ~ ) . i t is not a strong evidence for a phase transition.

0.C'JS. 1 A a: 40 03 w l r n

1 -""

Temperature('^)

Figure 6 .7 . DSC scan of Li KO 9 Nu 0 .1 SO4 crystal

6.3.4 Surface Plots of I'hase velocity, Slowness, Young's modulus, a n d Linear compressibility

The anisotropy of elastic wave propagation in this crystal can be

made clear by drawing [lie phase velocity surface plots in the a-b and a-c

planes by following a well known procedure [6.32,6.34]. Figures 6.8 [a, b] show

the phase velocity surface in the respective planes; the ultrasonic mode

corresponds to quasi-longitudinal [QL] mode with higher velocity of propagation.

The other two modes are pure shear [PSI and q-mi - shear [QS]

Phase velocity-XY Plane 1358 9

I "I * + + I I --I

Phase velocity (I/=)

F~gure 6 8 (a) Sudace Plots of Phase velocity along the XY Plane

Figure 6 8 (b) Surface Plots of Phase velocity along the XZ Plane

Phase velocity-XZ Plane 5300 1 +.+.++'U+.+.+. I I --

- .+ * +'+, QL ++ +-

f %+p 00

.+ +. ," 2650 - f

0

4

* f '? - - t t

c.

0 0 0 - m

+ + 0

f + 2 -2610 - +, + 4 +.

i - n. +. i

Y .+ ,+ +.

530G 5300 -2650 0 2650 5300

Phase velocity (I/=)

Slosness-:CY Plane

Slowness (s/l)

Figure6.9 (a) Surface plots of slowness along the XY plane

Slowness-XZ Plane

- I \ Y1 - YI Y1 D a b 0 i m

Figure 6.9(b) Surface plots of slcwness along the XZ plane

Young's Hodulus

Young's Hodulus

Figure 6.10 Surface Plots of Young's moduii in the XY and XZ Planes

8 %

$ 4 . 4 3 I

Linear Compressibility

... , , - , , . ,+. I+..

Y f XY -- . t t XZ ++

+, + +. .4

Linear compressibility

Figure 6. I I Surface Plots of Linear compressibility in the XY and XZ planes

a %-+L &++\

VI *++ ++ +.

m

A greater insight into the elastic anisotropy of a crystal is obtained by

plotting the inverse phase velocity (slowness) surfaces [6.32]. Slowness

s u ~ . ~ ~ c c also p~ovidcs a better pictorial representation of elastic anisotropy in

d 2 0 m -4.5

+, +' +

5t +.

P f

a ctystal. 'Thc surface plots for Li Kou Na 1 SO4 crystal are plotted in

Figure.(6.9 a -6.9 b) Thc velocity surface ,lots alone cannot completely

describe the anisotropy of the elastic propenies of a crystal.

Young's ~iiodulus surface plots are ve.y important in this regard. The

Young's modulus [6.32], I::, in the direction c f unit vector ni for a Hexagonal

crystal is given by

The cross sectionjof Young's moduli surfaces of Li Ko9 Na o I So4 plotted

in the a-b and a-c planes are shown in Figure 6.10.

The linear colnpressibility of a Hexagonal crystal [6.32,6.33] in matrix for111

can be written as

B = [ S I I + S I ~ + S I I I - [ S I I + S I ~ - S I J - S331 w2 (6.4)

The linear colnpressibility of Li Keg Na 1 SO4 crystal in the a-b and a-c

planes has been plottcd. The plots are as sh,wn in Figure 6. 1 1

The Poisson's ratios [6.33.6.34] have been evaluated and the corresponding

equations are derived

v31 = -633 " 1 1 = 4 3 , IS11

The volume colnpressibility Silkk is an invaricmt parameter for a crystal. For a

hexagonal crystal, in matrix notation, it is gi~ren by [6.32]

where S,,'s are the correspo~iding compliant: constants. Hence bulk modulus

of the crystal is given by K = l/Siikk (6.7)

Volu~iie co~uprcssibility and Bulk ~iiodulus of 1.i &gNa o I SO4 are evaluated as

0.323 x (10."') N " I ~ ' and 30.959 GPa respectively

I'his study undoubtedly proved that crystal synthesized with

ccli~iinolccular Liaction of LizS04Hz0, K2S04 and Na2S04 grown at 3 jnC is

L,iKi, ,,Nail I S O ; with hexagonal symmetry and not Liz Na K(S04)? as reported e. '11 .I' ler [(,.I 8-bZO].

kicxagonal crystal has five second order elastic constants, whereas

ortliorhombic crystals are having nine. For this doped crystal there are only

f i ~ c clastic constants. For the Hexagonal system, the independent second

order elastic constants C I I ~ = C22; C33, C44 = Cjj, C66 and C I ~ = C23. The

collstant C l z can be calculated from C66. All the elastic stiffness constants,

compliance constants, Poisson's ratio's, Bulk modulus, Volu~ne

co~npressibility and the surface plots in a-b, a-c planes of phase velocity,

slo~vness, Young's n~odulus and linear con~pressibility for the sodium doped

LiKS04 (Li K,,,) Na o . ~ SO4), crystal are reported for the first time.

l'hc silspected phase transition [6.14] at 333 K is examined by

sl~~dyiiig tile temperature variation of elastic constants C I 1 , C33, c4.1 and C b b in

thc tcmpcrature range 300K-375 K. The constants (244, ( 2 3 and (266 exhibited

weak anoixx\lies in the range 313K-345K. The most pronounczd anomaly is

shown by Ch(,. l'his leads to the conclusion that elastic anomalies of LiKS04

can be enhanced if it is doped with Na. Present DSC studies on this material

at ;i very slow lheating rate 1°/min. do not exhibit any appreciable change in

the Ileal flow.

References

6.1 A.J.Oliveira, F.A.Gerrnano, J .M . Filho, F.E.A.Melo and .I.E.Morei~.a : Phys. [lev. B, 38, 12633 (1988) /Phase transiriom? in LiKSO, below rooiii / ~ i l l [ J ~ ~ < l l l ~ ~ ~

6.2 H.Kabclka and G.K!rchler : Ferroelectrics, 88, 93 ( I988)/ E/u.ststic .st!flirc.s.r conslii~it L I I I ( / eluststi~. relanutiom7 arounr' /Ire finrsl lolo teiiiperurlir.e ,')ilosc frui?si~jomr in LiKSO,.

6.3 S.F~rjimoto, N.Yasuda and H.Hibino : Appl.Phys., I S , L135(1985) /i're.>.ri~~,e und Teii~perutr~re depndence of the elec'ro-optic coe$cirm~t in LKS

6.4 Y.Y.Li : Solid State Comm., 51,355(1584)

6.5. M.L.Bansal, S.K.Deb, V.C.Sahiniand .ind A.P.Roy : Phys. Rev. B, 30. 7307(1984)/ Orientcr1io17alphase transiiion in LiKSO,.

6.6 S.Fujirnoto, N.Yasclda and H.Hibin,, : Appl. Phys., 18, 1871(1985) 1 Pressure and Temnperature dependertce of rhe dielectric properties ofLKS

6.7 S.Fujirlloto, N.Yasuda and H.Hibino : Appl.Phys.,lll, L35 ( 1 984)lFerroelectrici~ in Limo,..

6.8 B.Mroz, T.Krajewski, T.Breczewsci, W.Choinka and D.Sematowicz : Ferroelectrics, 42 7 1 (1982) / Anomalous changes it? the piezoelectric rri~d elastic properties oj LKS crystal.

6.9 P.E.Tornaszewski zrrld K.Lukaszewic;. : Phy. Status Solidi A, 71, K53 (1982)

6.10 P.E.Tomaszewski a n d K.Lukaszewicz Phase Transition., 4 , 37 (1983)

6.1 1 . L.Abello, K.Chhor and C.Pommier : J . Chem. Therrnodyn., 17,1023 (1985) /Tl1rrmi1o~ly17a117ic srrrdies on the succe~sive phase I ~ L I I ? S ~ / ~ O I ~ in LKS o/ loll' te~itprrrrlure.

6.12. Tu An, Liu Jing-ging,Gu Ben-yuan, Mo Yu-jun, Yang tlua-guang and Wang Yarl-yun : Solid State Comm., 161, I , (1987) IRrillouim? slurly qfph~i.\e trutisition in LKS in the low tem~ipertrtz re range.

6.13 E.V.Charnaya, B.F.L3orisov, A.K.Radjabov and ?'.K~.ajewski : Solid Stale Colnri~., 85, 443 (1993) /Sound velociry hys~erisis hi the high /eiii]~erritiire inco~~?imrensurule phcrse range of LKS.

6.14 M.Di.ozdowski, F.I loluj and M.Czajl<owski : Solid-State Comm., 45, 1005 (1983) IBrillorrir~ lih.111 scatlerir~g in LiKSO,.

6.15. L.Godli.cy and J . P l i i l i p : Solid State COIII I I , . ( U K ) , 97, 635-638 (1996) /U/tr~i.srsnnic ineosui.orieril of the elastic com~.s~ant of LKS hctii,eeii 300 rind 3 70K.

l J / l ! ~ o . ~ ~ ~ ~ ~ ! c ~ ~ I v ~ s I ~ , ~ ~ ~ I I o ~ ~ s o/Eluslicprc~perlie.s o i ~ d / ~ / i ~ ~ . i e 11~(11i.~ilior~ ~ I I

Ll K , , \ ' t i ,, : S O , < ,7..s1ul ~- 235

6.16 M.A. I'ilrrenta, Y.Luspin, P.Echegut and G.1-laui-et : Solid State Comm., 59. 48 1 ( 1986) I Brillouir~ lighl .scutIeriiip ill LKS hei~1zeer7 20 rind 80°C.

6.17 K.Kitalia~na and R.Frech : J.Chem.Phy., 82, 2, 720-25 (1985) 1 Xunrur7 Scatteri~ig oftriple cation salt Li2NaK (SO,) I

6 , I S J.K.l.iailg, X.J.Xu and Z.Chai : J . Solid State Chemistry, 76,270-275 (1988) I Tlie Piiiise diagruni of the systeru LiNaS0,- LiICSO, and cq,s~uilogr~iphic / J I I ~ O I I W / ~ ~ ~ . S and ionic cond~c/ iv i ty ofLi:NnK (SO,) ,

9 I1.R.K~ilrrar and B.C.V.Reddy : Acta Physica Polonica A , 87, 6 , 1023- 20( 1995)./Ah.sorl1tio1i Speclr~on of Ni (/Il ioris ~1o.11cd ill lillriiiirr poIiis.si~rir~ .soiiiii~ii O I I J J I I N I C .siriple c~ys la l .

6.20. U.C.V.l<cddy : Crys. Res. Tech., 28, 4, 535-538(1993) I Ol~lical ubso,;r)tiorr s/x!ciriiiir of CII ' ions doped in lilhiui~i ~~o/a . ss iu~u sodiw17 srrlp17ure single cl:l~.\l<il

6.2 1 . M.A.l'i~iienta, S.L.A.Vieira, F.O.V.Letelier, N.L.Speziali and M.S.Dantas : Solid-5i:ite comm., 82, 10, 755-757 (1992) 1 lorlic Cor~ducl i i~i l j~ ill LiK,, 9,\'iio lSO, single crystals.

6.72. Wa~ig-1.;-Fang and Hang Dao-fan : Chin. Phy. Letters 2, 201 (1985). Tl7e c/irr,-ac~~~~i.slic of ahrupt change on elastic co11.sirri7i C.;? of LKS ot 60°C.

6.23 D.P.Shar~na : Pramana, 13, 223 (1979) Tl~eri~rol e.~parisio17 m l d u rie~i~p/ru.se tr.rn1.sitii117 in Pyroelectric LKS.

6.34. M.J.Hecg and A.Hurd : Acta Cryst. C, 43,161-62(1987)/Tlie structure o f 'Triple ciition salt L i~NuKfSO, )~

6 . 2 5 L G o d l i c y and J . P l i i l i p : J. Appl. Phys., 75 , 5 , 2393-2397 (1994)l Eio.slic cori.sloi~~.s m ~ d high te~nperafure m i o ~ ~ ~ u i i e s neai. 123K in Lill~iurr~ / ~ ~ ~ i / ~ ~ ~ i : o i ~ i r o ~ r .si~/plia~e

6 . 2 6 A . Smahi~la : Phys. Rev., 99, 1747 (1955)

6 27 .I i.M;i\ .Ir : IIIE. Natl. Conv. Rec., 6 part2, I34 (1958)

6.28 l1.P.Papadakis in 'Physical Acoustics' Vol. XI1 Eds. W.P.Musorr arid R.N.Tiliir.stor~ (Academic Press New York 1976) p.227

6.29 I~I.J.McSkimin ; Acou. Soc. Am., 33, 12 (1961)

6.30 tl.J.McSkimin and P.Andreatch : Acou. S o c Alil., 34, 609 (1962)

6.31 II.J.McSki~nin iri 'Physical Acoustics' Volliirre I, Port A. Ed [i'.I'.12.f~i.soii (Acade~riic Press New York 1964) p.271

6 .32 M.1.1'. bl~isgrave : Crysla/ Aco~r.slic.s, 1111r0d~i~Ii(~ri lo . ~ I L I L / ~ of ~ I L I s ~ ~ L . 1o~i~~C.s iirril ~ , ihr . ( i / io~~ irr c~ys~c i l s : Holden-Day 1970

6.33 S.F.Nye : P1y.sicalproperties of cryst~rls,(Oxford u11ive1-sity press, London 1957)

6.34 A.V.Alex and J.Philip : Material Science and Engineering B, 90, 241-245 (2000)/Elasticproj~erlies of Di-arnmonium hydrogen citrate sbigle crystcr1.s: An sltrasonic study

6.35 L. Godfrey and J.Philip : Acou. Letters ,l9, 1,l 1-14(1995)1A N~rtnr~.icir/ techr7ic~~tefor bond correctiorz in ultrasonic r~~easrrrerr?ort.

6.36 M.S. Heeg and A.Hurd : Acta. Cryst. 17, 43,161-162(1987)/Structzrre of tire triple cation salt Lil Na K(S04)z

6.37. JCPDS file no. o f (I,iKSOa): 81004 1

6.38, JCPDS tile no o f LilNa K (SO-/)* : 77>473