Gupta, V P

Shanker, Jai

Sharma, O P

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J6 2 A .  T a w f iking Hold. The wtrongth of polarisatjon increaHed with impi'essing stress resulting in a higher net polarization at tlic surface of the sample.The stress dependence of the generated charges is linear because the charges appearing on the electrode Hurfac(\s maintain an electric field in the same direction as the original i^oling field. This field encourage the domains to be reoriented after releasing the static stress.Tlio non-linear behaviour of the stress dependence of the electric field is due to piezoelectrically generated electric field tend to maintain in the opposite direc­tion to the original poling field and domain reorientation occurs even less readily under open circuit than short circuit conditions. It is obvious that the behaviour of the piezoelectric effect in polarized sod. ben. ac. is similar to that of the sod. acctylacetonatc Tlie increase of conduction through the sample with raising temperature (figure 3) caused the decrease of the piezoelectric response due to disturbance of the dipole orientation.At 70° C the polarisation disappeared and the material became unpiezoeloctric duo to partial chemical transformation that took place in the material.R eferencesTawlik A. 1976 Imhan J. Phys. 49, 3S6.Inihan J. Phya. 52A, 182-186 (1976)Analysis of the strain derivative of the Szigeti effective charge parameter in alkali halides,1at Suanker, V. V. Gupta* and 0 . P. Sharma Department of Physics, Agra College, A(7m-282002[Received 25 July 1977)The concept of effective ionic charge introduced by Szigeti (1949,1960) has been widely used in the studies of dielectric and lattice dynamical behaviour of ionic crystals. An excellent discussion of the Szigeti effective charge parameter eg* for alkali halides has boon made by Lowndes k  Martin (1969). Studios based on the various theoretical models (Dick & Overhauser 1968, Hardy 1962, Mitskevitch 1964) have revealed that the deviation of e^ * from the nominal charge can be inter­preted as a measure of ionic distortions in crystals. The amount of overlap and♦ Department of Physios, Govt. P-G. College, Morena, M.P,distortion of ions in crystals under tho effect oi' pi’csBure should increase as thedem*volume is decreased This expectation should lead to the jiositive values of .However, the predictions made by Jones (1967) and Barron & Batana (1969) are not Consistent with this criterion These investigators have obtained negativedvdecreases when the crystal is compressed. This anomaly has also been discussed by Fontanclla el al (1972) and Hardj  ^ & Karo (1973) leaving the question uu- ansAvored In particular, it should bo mentioned that Hardy l^', Karo (1973) have used an expression for the strain derivative of high frequency dielectric constani (eq. 3.21 in their paper) whih is not in agreement with experimental data on photoelasticity (Sharma at al 1976).Szigeti effective charge parameter in alkali halides 183According to Szigeti (1950) wo have the relation_  477 (e « + 2 )V 2Oo ( l )where and are the low frequency (static) and high frequency (electronic) dielectric constants respectively, fi is the joducod mass per ion jiair, wto the transverse optic mode frequency and V the volnme ])cr ion pair. Differentiation of eq. (1) Avith respect to volume yieldsV  d v ” ) 1 + « F 5 ; , 1  ■ ' ( w - )• I_____2((.n -c.) \ dV I ( 2)(to-eatAvhero the transverse optic mode Glruneisen parameter is givmi byExpressions identical to eq (2) have been used by Jones (1967), Barron & BatanaF lde,*\(1969) and Fontanella el al (1972) to estimate the values ol j . However,tho experimental data used by those investigators were not good partiularly for Yto (having an uncertainty of about 30%). Very recently Lowndes & Rastogi (1976) have measured for many alkali halideii*, which are quite accurate andcan be used Avith confidence to derive (2) which may lead to somedecisive conclusion. We have evaluated (^) alkalihalides with NaCl structure. Those are listed in table-1 alongwith the input184 J a i S h ankar, V . P . G u p ta  an d  0 .  P . Sharm adata Wo liavo been oareful inHolecting tJio most leccnt and reliable experimental data on t-lie dielectric constants and their strain derivatives (table 1). Values ol V I deg* \e * \ d v )  from the recent data used in the present study differ ai)pre-ciably from those estjjiiated by Jones (1967) and by Barron & Batana (1969). It is remarkable to note from table-1 that j arc positive lor all the crystalsunder' consideration. This implies that the overlaj) and distortion of ions increase when the crystal is compressed, a physically plausible jircdiction. The anomaly observed by Barron k Batana (1969) and furthei' discussed by Fonianella H al (1972) thus seems to be removedBarron and Batana have suggested a yn'oretical method based on the defor­mation dipole model (DDM) of Hardy (1960) and Mitskcvitch (1964) Following DDM one can express the deviation of the effectivii cdiarge from its nominal valuc ase g * — e =  2//t'(r)-l 4m(»)A Table 1(4)r / <Jc, * ' c** \d\ '.Jj-yylalya>0JjowiuioriandRaHir) !^(1976)r„LuwiuluhandMartin(1969)* ODLowndusandMarini(1969)) ( » Expori- niontal valuns (eq, 2)Deforma­tion Dipole model (cq, 6).LiF 2-:{5 8.50 i 93 - 0  37« 30 OO** 0-55 0-56NaP 2-08 4 73 1-76 -0-33'^ 12-70«> 0-69 0 50NaUi 2 60 6-le 2*36 -0 -74 “ ] 160'^ 0 62 0 96NaBr 2-37 6-78 2-64 -0-99 '' lO-OO** 103 1-07KCl 2'2S 1-49 2-20 -0-680 9-1P 0-52 0 82KBr 206 152 2 39 -1 0 8 0 8-92" 1-04 109Kl 2-20 1 68 2-68 - 1  40« 0 68rf O'58 1 29RbCI 210 4-53 2-20 - 1  01“ 8-22d 0 57 0‘81KbBi 2-39 4-51 ^2-36 ~1'24“ 7-37‘< 0-40 0-96KbI 2 09 4-66 2-61 -1-41“ 0 73 1-27(a) Van Vnehten J. A. 1969 Phys R e v . 182, 891(t) Jfoiiianella J. Andeon C & Schuele D. 1972 Phys. Ecu B6, 682.(c) Srinivaaan R. & Sririiviiaan K  1973 Phys Stat. Sol. (b) 57, 757.(d) Mahmud K. K. Kamath K. V. & Sooifo B. K. P. 1971 Phil. Mag, 23, 656.Szigeti effective charge parameter in alkali halides 185where m ix )  is the deformation dipole moment due to an ion pair and m '{ r )  is its derivative with respect to ionic separation r. It has been suggested (LoAvndes & Martyin 1970) that m {r )  varies exponentially with rw(r) =  Woexp(—r/p) ... (5)where p is the Born repulsive hardness parameter. Eqs (4) and (5) gives- , 7 ^ 1  ( ; ? - ■ )V / deg* \Values  ^y  j calculated from eq. (6) are compared in table 1 with the cor­responding values derived from the experimental data,Finally, it should be mentioned that Lawaetz (1971) has investigated a rela­tionship between e^ * and the Phillips electronegativity parameter Cwhore fiojp is known as the plasma energy and varies as Volume derivativeof eq (7) yields(8)halides ^  0 and hence ( ^ 7  ) ~  'Van Vochton (1969) has discussed at length that for highly ionic solids like alkali0 \dVI ~  c * \ d V ithat this prediction holds well for most of the crystals under study.Financial assistance received from the UGC, India is gratefully acknowledged. Thanks are duo to Professor M. P. Verma, Head of Physics Department Agra College Agra for providing the facilities.R e f e r e n c e sBarron 'J\ H K & Batana A 1969 Phil, Mag, 20, 619.Dick B. G. & Overhauser A W. 1968 Phys, Rev, 112, 90,Fonbatiolla .J. Andeon C. & Schiiolo D. 1972 Phya. Rev. B6, 582.Hardy J. B. 1900 Phil, Mag. 6, 27.Hardy R. J. & Karo A, M. 1973 Phya, Rev. B7, 4690.JoncB B. W 1967 PInl. Mag. 16, 1085.Lawaotz 1*. 1971 Phya. Rev, Lett. 26, 697.Lowndea R. & Martin D. H. 1909 Proc. Roy. Soc, A308, 473.Lowndoa R. P. & Raatogi A. 1976 Phy^. Rev, B14, 3698.Miatkevitch V. V. 1964 Soviet Phyaioa Solid State 5, 2668.Szigoti B. 1049 Trana. Faraday Soc. 45, 156.Szigeti B. 1949 Trana. Faraday Soc. 45, 155.Szigeti B. 1960 Proc. Roy. Soc. A204, 51.Shorma H. P. Jai Shankur & Verma M. P. 1976 Phil. Mag. 34, 163,Van Veohten J, A. 1969 Phya. Rev. 132, 891,13

Analysis of the Strain Derivative of the Szigeti Effective Charge Parameter in Alkali Halides

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Analysis of the Strain Derivative of the Szigeti Effective Charge Parameter in Alkali Halides

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