Bakshim, P S

Goyal, S C

Shanker, Jai

IACS Institutional Repository

9 1 8 H. S. Sahota and Raj Mittal■RtofebenoesAmlrpjisfhofr W , HubborH F , ScbilliiiKfl K D &. Slary F 19(i9 Niicl. Phijs. A137, 093 Biagarcl K M . Oleseii K & Ofltoigard P 1002 A^nrl. Phys. 33, 126.Biegarcl K. M , Nielsen b. J., Staboll E & Oslorgard 1\ 1905 Nucl. Phys. 71, 192.Hraboe V , Mul.v L lSs Vobodry iA] 1971 Bull Aca. UBSP, Phys 35, 1424.Jlanvish S M., Sa oiis.soii I. G\, LinclHlcog J , Solbed H & Joimson N. 0. 1974 Nittl Phys.A236, 340.Ellis Y. A. 1976 Nncl Data ,Sheets H, 347,Ewbaiik W. B 1900 Nnct Data, Bl, 2, 23.Hager P R. ii, Seltzer E C. 196R Nurl Data A4, 1.Hagoi R. S. & Seltzer E. C. 1909 N atl Data AC, 1Honnan A VV., Heigb\^ay H & MaeAHhiu J D, 1070 CV/a J. Phys 48,1040. baughorr ir. lOO? Vhys Jtco. 159, 103.‘bI’otoi-Bon K , Tniinpy G & Ostorgard P lf)07 Phi/s Lett 20, 527.Subba Uan K , Jli , SndfniUar K , Premohaiid K . Narusimbam K. L & Lakfllnuinarayanaii Y.1973 A’ncl. Phys. and Solid Stale Phys Symp (India). Subba Tvari K . Ila 1*. Sudhalar K , Ib'emeband K , Narasimbam K. Ji iSt Luksbrninarayaimti V.1974 Xiicl Jdn/s and Solid State Phys Sytnp. (Lidia), 17B, 3.6. Widomaiin F Si Sebille 1*. 1060 Port. Phys 4, 215,Jmlian J. Phys 50, OlH-921 (1976)Crystalline behaviour o f  the e le ctron ic  polarizabilities and sizes o f  ions in silver and thallous halides.J a i  S h a n k e r . 8 C. OoYAL AND P. S, B a k h s i i i  Deparhmmt of Phy,'^ icN, .4gra College, ytj;? «-282002 {Received 20 Jawuary 197(), revised 30 March 197G)Tlio oj'ystals of wilvor and ihallons halides havi‘ atiracted thi‘ attention of numer­ous jiivestigations (Mayer 1933, Lynch 1967, .Bcttger k  Cleddes 1967, Jai Shankcr 1973) hocause of their eomplicaticd nature of tlie chemical lionding between the ions. Tlu‘ present of d-(dect]’oiis in Ag''" and T1+ ions causes the deviations Irom ilie pui-ely ionic bonding. The evaluation of polarizabilities in siliror and thallous halides is usefid foi* understanding the dioloetrio behaviour of these crystals. Fn the present study wc evaluate the (dectrouii! polarizatbilitics and sizes of ions in these crystals by taking into account the effect of Madelung potential as suggested by Ruffa (1968) and the polarizability-radius cube relation (Jai Shanker et al 1973). The method of calculation v'lll not bo discussed in detail here as it has already boon presented iu an earlier paper (Jai Shanker & Verma 1975),Polarizabilities and sizes o f ions in Jialides 9 1 9Tho cryatallhw) state polarizability (ac) ol an ion is related to its free stale value (^/) l>y tlic expressionOCf ( H f - r ^  )■ • (i)where /?/ is tlu‘, energy paranietor corjespoiidiiig t,o fie<^  s1<al(' introdueod 1>y Itiitta and Vm is the Madolung potential existing at the ion site. It should, oL‘ eourse, be j(‘nuunheied that Vm is not tlie only contrilmlmg potential and tor th( (lumpleteness of the JoimalLsin one should also aeeount- 1‘er oilier iidiuact- ing terms like short range rejiulsive potentials Ho^ \ever, it is a]ijia]iait. Iroin the work ot Mayer (1933) that the magnitude ol repulsive ])uteiitr.d is nnieh ymalli'r than that of l'/|j ’^ rhciefoie, assuming V]\j to be a ilomuumt eoiitiibul ion to the crystal potent ial we obtain approximate values oi (etc) hii eatious from ec(. (1) taking O/from Paulmg (1927) The values ol ofc thus obtained (table 1), loi Agi' and TJ' ions in their halides, are utilised to ealeiilate the sizes (r^ ) ol tli(‘So ions cor espcuuLing to erystallme state using t lu^  polanzability-radius cube (iX-r^) relation (Jai iShank<‘r rl al 1973) Aceordiiig tc, a- r'* relation om^  can wiil.ea/ r f ( )^The values of {xdxf) a.re dneetly ileducible liom (H| (1) The ionic radii deteimined by l^ aiiling (1990) are fiee stall*, ladii tor the reasons discussed by Tosi (1904). It IS also evident lioiii an analysis ol the eleetrimie chaigi* distiibn- t ioiis eoiTcspoiiding 1.0 free ion wave lunetions recently jxTformod by Deb (rhoslr (197r>) that lAiiilmg’s radii arii iiear-ly (upial to tliosc m free state. Thus Upsiiig the values of fiom Paidnig and (cCf/a/^ ) Irom eep (1) ue Iumt ealoulated rc from orp (2) foi' Ag' and Th'" ions in their lialidcsThe ciystalliue state iiolarizabilitios of anions, how'cver, cannot, bi' estimated from eq. (1). This is diir to the fact. that, for anions the situation is somew-hat. different heeansc tlie escitatioii levels eontribute suh,stantially to the anion polarizability in tho crystal. Tn order to circumvent the dilliCLilty we follow a different procedure to extimate the amon polarizabilities. Tiist., we dotennine the ciystalliue state radii (rg) of anions from the expi'rJniental int.i'iionic sopaia- tions (Mayor 1933) by subtracting the aiipropriate cat ion ladius e\"aluated irom eqs. (1) and (2). The values of Vc Tor halogen ions, thus obtained, have been utilised to estimate for these ions Irom oq. (2) using tho values of ctj and from Pauling (1927, 1900).The results obtained have boon listed in (table 2) alongwith tho input para- ' meters (JS7/ and Vm)’ 1^1 informative t,o observe from table 1 that the electronic polarizability and rad'us of Ag"*’ or TD ion show a smooth trend of variation fromfl20 Jai Shanker, S. C. Goyal and P. S. BakkshiA chlorjilo t-o ilu‘ voriGHpondin  ^ lodidt  ^ uyatnl TJiiw trend oJ vuT'iaiioii i« aimilar to tljut predicted Low^ndes t't Martin (19(i9) i'or tlio effective ionic chargea m .silver and Ibalions lialides in  fact the vaiuitions of polarizability, radins and the olleclive chaigo of the ion from crystal to ery.stal aie lelated with the character of bonding between the ions (Liicovsky at al 1971).Ill table 2 vre p/cscnl a compari.son ol the calculated ciystalline state poLirizabilities (Ai'-eragi; values) Avitli the cm responding values dei’ivcd by Tc.ssman at al (1953) lioin ex]>erimental ndraction data, on ciystals (given within paian- tho.se,s) For tlu* sake ol contrast, we have also cited the ]k lai izabilitie.'.^  o fficeions in table 2. It is mtiTCsting to remark Iroiu table 2 that the polarizabilities c^alculatcd in the jiK'si'iit study agi'cc w'lth tlu) exiiernnental values Aialliin nearly except, for I ion and differ iiom the free state polarizabilities in a inaimcj suggesting the loosiuiiiig of cations and tightening ol anions in the tTy.stallino state T)i(‘ loosening and tighlming effects were long ago predicted by Fajans I't. .loos (I92J) and v\''ei(i sub.scipKuitly eonliriiied by T*etra(‘heii at al (1950) For iodide ion, A\e liave obtaimul .suhstiantially lov\ ei values of eh'ctroiiie polaiizabiliry and ionic radius, parl.icnlaily in Agi eiysial Tins prediction iicifds liirthei attention. It is noteworthy to mention that Agl difh'is in the following ie,specl.s from the ot.her eryslals nndor study . (i) it ciysiallizes in the zinc—blonde stnic- t.nre and lienee the numbei' ol nearest noiglibouis is reduced to 4 in contrast to NaOl (CsCJ) st.juctiuo A\'here the coordination number is (5 (8). it  can be uudci stood tbat tlu^  reduction in Uie imudier of nearest, neighbours is diieetly lesjion.sible foi tlio lower v'alues of eJeiitroiiK; polarizability and loi'ic radins in Agl crystal, (ii) It is appaient from the theory ol clieiiiical bonding (Pliillip.s 1970) fbat Agl is a eiystal with signilicani, covalenl ehaiacter. The. cfh'ct ol Ifus eovalency on tJie lonie radii has been analysed in detail by A'aii Vecliteii & Phillips (1970) and their analysis also sugge,sts that the ionic radins and electronic polariza­bility of ion should be nmcJi smaller in Agi eiy.stal tlian in bighly ionic aciystals.Table I. TJie values of input xJ«J’ameters (>>/ and V f^ in eV), (;al- culated crystalline electronic xiolariza-bilities {a-c in A-*) and ciystalline radii (?c m A)Ef Vm ac^ a>c- •Ic-AgOl 5‘A 99 8.9S 2.-18 2.87 1.10 1 07AgBi C3.99 8 03 2.44 3.09 1.09 1.79Agi G3.99 8.30 2.41 3 71 1.08 1.73TlCl 49.9J 7.C2 4.80 2.07 1 70 1.6.3TJPr •19.91 7.28 4.80 3.45 1.09 1.75'I’ll 49.91 C 92 4 73 5.17 1.68 1.94Table 2. Average values of crystalline electronic polarizabilities (in of ions.Polarizabilities and sizes o f  ions in  halides 921Ag+ T1+ Cl- Br- I-Calculated 2 44 4.70 2.77 3.57 4,44Experimental 2.40 6 20 2 96 4.16 6.43Free State 1.72 3.50 3.66 4.77 7.10RbefbencesHotigor G. L, cfc Geddes A. L. 1967 J. Gh&m. Phya. 46, 3000,Dob S. K. & Ghosh A. K. 1975 Indian J. Phya, 49. 628. fc’ajans K. & Joos G. 1924 Z. Phyaik 23, 1.Jai Shanker 1973 It^dian J. Pure & Phya. 11. 381.Jai Shankor, Kumar N. «S& Verma M. P. 1073 Indian J. Pure & Appl. Phya* 11, 644. Jai Shanker & Vorma, N. P. 1976 Phya. Rev. B12. 3449.Lowndes R. P. & Martin D. H. 1969 Proc. Roy. Soc. A308, 473.Lucovsky G., Martin R. M. & Burstoin E. 1971 Phya. Rev. B4, 1367.Lynch D. W. 1967 J. Phya. Chem. Solids 28, 1941.Mayor J. E. 1933 J. Chem* Phya. 1, 327.Pauling L. 1927 Proc. Roy. Soc. A114, 181.Pauling L. 1960 The Nature of Chemical Bond (Cornell University Press, Ithaca). Petrashen M I., Avaronkov L. V. & Kristofel N. N. 1060 Opt. Spectroae  ^N .Y. 9, 276, Phillips J. C. 1970 Rev, Mod. Phya. 42, 317.Ruffa A. R. 1963 Phya. Rev. 130, 1412.Tessmun J. R., Kahn A, H. Shocliloy W. 1963 Phya. Rev. 92, 800.Tosi M. P. 1964 Solid iStatc Physics 16, 1.Van Vechton J. A. & Phillips J. C. 1970 Phya. Rdev. B2, 2160.Petrashen M. 1., Avaronkov L. V. & Kristofol N. N. 1960 Opt. Spectroae, N .Y. 9, 276. Phillips J. C. 1970 Rev. Mod. Phya. 42, 317- Ruffa A. R. 1963 Phya Rev. 130, 1412.Tossman J. R., Kahn A. H. & Shockley W. 1963 Phya. Rev, 92, 800.Tosi M. P. 1964 Solid State Phyaica 16, 1.Van Veohten J. A, & Phillips J. C. 1970 Phya. Rev. B2, 2160.

Crystalline Behaviour of the Electronic Polarlzabilities and Sizes of Ions in Silver and Thallous Halides

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Crystalline Behaviour of the Electronic Polarlzabilities and Sizes of Ions in Silver and Thallous Halides

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