Ghosh, U S

English

IACS Institutional Repository

13A SHORT NOTE ON THE ORTHO-RHOMBIC POTENTIAL IN TERMS OF LIGAND MOMENTS AND THEIR DISTANCES IN AN OCTAHEDRAL COMPLEX(n  S. ftHOSH 'l)KrAltTMBNT OK MaOHETISM, UnDJAN AlSHOOIATION FOll THE CULTIVATION Of St'lJ'lNIJE.JADAVPUii, Calcutta-32{RccnvQ<} Ju ly  22, 19C3) \Tliooretical luvosiigatioii on tlio magnelK! and optical hcliavioiir of some iron group salts considers the ciystallinc electric field as having an ortho-rliombh' symmetry. The expression foi’ potential near the central ion of an octahedral eompl(‘X is iisiially obtained by expanding ihe ])otential in tenns of spherical harmo­nics since it satisfies Laplace’s ecpiation A'*^ V -  0 . Considering that the s;\mimetry , of the field is ortlio-rhombic and that the eleistrons of interest belong to the 8d shell in iron group salts, the expression for potential is gnnm by (Bose d «/, 1963).-  • • (1 )The form of the potential function must remain unchanged even if ive take a purely ionic model of ihe octahedral complex, but the above expression does not explicitly contain the distamies of the c,o-ordinating ligands from the central ion and their dipole moments, the only thing that can be said is that the co-ofli- cients 1), A, B,oc and are related ivith them. Polder (1942) derived an expres- .sion for potential in tenns of these ijuantitics considering only a tetragonal dis­tortion of the complex. An expression for ortho-rhombic potential and hence the co-effieients D, A B, ol and /i m terms of dipole moments and distances of the ligands might be helpful in some investigations and with a view to this such an expression has been derivedThe type of octahedral complex that Avill be considered here has the para­magnetic ion at the centre which is the origin of our co-ordinate system and dipoles of moment fiy, /V3 at (±n , 0 , 0 ), (0 , ±h , 0 ), and (0 , 0 , respectively. The548Letter to the Editor 549iiegatJVL' ('iicIh L)f lJiC‘ clipolers nre pfuiituig inwHrdn and their axes are <-o]neiding witli tile CD-ordinate axesPotentiaJ at a point (:i:, y, z) near the origin due to the pair of dipoli's( 0 , 0 ) /ti(u -x)_ _  f j  j  .id _  7 5 ^ l^a'^  (i^  -1 ff*’ ud 4 2  J(retaining terms upto tlie lourtli ]iower as ean be seen from eijuation (1 ), higlier [)oa er terms need not be considered in iron groii]))( )^iisidering all the tliree ]iairs of di])oles. tlie total potential at (.r. y, z) is( f hw  ^ ¥ 4 III"1754/^Vi\ ff«1 i 'V j 1 -> 3  \ ' ¥ 1ir) J  x %  1 \2 \ a^  ^ ^  ¥ IThe lirst term leprcsenting potential at t.io iigion is constant and is generally leit out ol consideration. Remembering that .id |-i!/“ ]'2“ reariangingthe Kmiaimng terms the expression can be jnit into tlu' form given in (upiation ( 1 ) as follows/ _  Q r/^2 I iW"i /^^ i 1,^2 1 3[/^3 I . .. 2/ia 1  ^F/ii ,25 r 4./li 4/r. /Igl / 4 I .,4_a^4\_L [/i? _  /^ sl 4^25 r //] yigl 4 , 25 r y^ i I _  ^ 3 1 4^ ... xh^rd j " 2 Lh« edj- I Z'*! „  '“'si v/2z2 i 2La« c« J^ " ” ■ ^550 Letter to the EditorTl)e form oi' Uiiw expression is identical with that given m equation (1 ); the co­efficients D, A, B, a and /i are thus expressed in terms of /z^ , and, a, h, c as follows .D . f  V i  I _ _  H4 I   ^ />«^ — S I _2 /Zj 1’ c f  \_  3 [ /*a I ^  _  /^^ -a 1L J\\OL- — \4 L ?)« r» I/y ^  25 r //j^  _  /^ al' 4 [a^ c«lTf we put« ^  h — c and =  /A3, we get A — B — a — /? — 0 and the expres­sion (2 ) reduces to the wellknown result for cubic potential as expected in case of a regular octahedron i.e.V — ( ^ + y '^ z '- l r * )In case of tetragonal distortion along s—axis of the octaliedron a ~  h r/z c and — //a y  /Z.J. we get A - B,oi — ft and the expression (2 ) reduces toF  =4 La® c®J 'Expression (3) can be shown to be equal to3  -  ^ i] -  f  [ ^  +  r*)... (3)Letter to the Editor 551This expression exactly agrees with Polder's result lor potential under tetra­gonal distortion of the octahedron. Numerical calculations of the coefficients in the ortliorhomhic case are presently in progress.The author is grateful to Prof. A. Bose, D.Sc., F.N L, for liis guidance and Jielpful criticism of the workR E F E R E N C E SHoHO A. and ChatterjeL'i R, 19GH, Pioo, Phys. Soc , B2, 28. Polder, 1942, Physicn 9, 709.

A Short Note on the Ortho-Rhombic Potential in Terms of Ligand Moments and their Distances in an Octahedral Complex

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A Short Note on the Ortho-Rhombic Potential in Terms of Ligand Moments and their Distances in an Octahedral Complex

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