Gilra, N K

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Screw dipole of infinitesirnal width 207positioiifcj of the energy levels and the observed baud positions. We have boon able assign all the observed bauds except tliose starred. Those bands do not fall with in framework of th(^  ligud Ihdd model. Similar bands are also obserx ed in other Mii^  ^ spectra and they are ascribed to the vibrouie transjtions. That these may bo spin doublet states can be ruled t>uli from thc^  fact that thosev have comparable intensity whoroas the intensity of tlu* sextet in iho doublet transit ion is expected to be very small as these are doubly spiii-forbiddt‘iL.Incorporation of tlu^  tetiagonal hold is ejiouglx to explain all tlu^  tcatam^ s of the observed l>ands. Splitting of all cubic fiidd states can be ol>served except that of the first excited stat e Tliis is a vejy broad band and the split ting isnot resolved.In conclusion the spectra of rhodoixite shows the presence of the tetragonal crystal field at the site of the metal ion v\hieh corroborates the structuralevidence of near octahedral euviromiiont of Mn“' ion in rhodonik*.Refehenoesl)i3LM W. A., HoAvin H. A. cV ZiiMHHian J .  1902 Hoch Formiiuj Minerals, LongmtLiiM, Groon Go. Limited (London)l)(jHai V. i*.. Do DjIuj, iVj ( Jtmkravui’l y A. IS. 1970 hid. J .  Fhys. (To bo publishod).(in tlik i J . S,, L901 Thnoii/ of Ttitn'^ihon Metal lonit, CJtimbridgo TJiiivorsily PresH, London. LiiksUimu) S. V. .1. .t Itoddy L. J . I97:t Phyaica 66, OUL Low W , Kosongartoii G. J!rG4 J .  MoL Sped, 12, 314.Mtniiiiiig r. Cl. 190S Oanad. MvnertU 9, 34 8.Mohr-a A. & VoiikatosAvarln P. 1907 J .  (Jheni. Phya. 47, 23,34.Pappalai-do It. 19.59 J .  Chnn. Pky.s. 31, 1050.Slov(3iison J3. 19(>0 f^hys. Ren. 152, 531.Siouh J W. 1959 J .  Phvm. Phys. 31, 709.Siigano S.. Taiiabo 'S' & Ivaniiniiiia II. 1970 Malt^p Ida of TretaaiHou Atdal Iona tn Oryatala, Aoadomic Press, Now York.Vala M. T., Ballhauson C. J„ Dmglo H. & Holt S. L. 1972 Mol Phya, 31, 217,Washinuya 8. & Dondaira K. 1907 J .  Phya. Soc. Ja p a n  23, 1.Wyckoff 11. W. G. 1968 Crystal Slructurca Vol. 4, IntoracionoG PubliBhors.Indian  J .  Phya. 61A, 207-211 (1977)Screw dipole of infinitesimal widthN. K. GilraDepartment of Physicfi, University of Science ami Technology,Kumasi, Ghana{Received 3 September 1976)In recent yoais, it has been shown that unlike screw dislocations could not pass each other due to the formation of uuiltijioles if it is assumed that they are cons­trained not to cross slip by invoking a high frictional force on tlu^  cross slip plane.208 N. K . G ilraHorc' th(^  st-jGHH Held ol’ a werovv clipoJe of infinitesimal width is analysed and its «*lasti(‘ iitioraotinn with, dislocations is disciissod.Sadauajjda. and Marciidtow'ski (L972, 1973) have showm the uuhko scre^ v dislocation form muliipoh s^ if they arc constrained ind to cross slip. We consider [icie a such [ivniight inhniu* scr(*\^  dipole of inlinitcsima] wadtli a lying along the axis with a.j. - f and Uy - It as slnnvu in tigare 1. F(H’ conveniouc(' the notation tor edgf' dislocation has h(u>n us(al. Th('. stress held of the dipole is given as.1 vStraij l^it Bcrow dialocalion dipoUi and i(h intorticlioii with a dislootttiuiia,, = f .. . (1wheia^  cr'Vfy^ are the known stress components of a st-raight scroAv dislocation lying along the z axis.For an isotropic mediump'and_ (y'^-x^)^-2xy h. . .  (2)... (3)whoro — , /< is tho Hhear modulus, h is ll»o Burpers vector of the screwdislocation and pThe. stable equilibrium j)osit-ions of the dipole correspond to h —Lot us consider the inlcratdion of thci dipolo wa'th screw diBloeaiioii, the Burgers vector of wLieh has the eompouentsS b/ — cos a, cos — 6* cos y.The dislocation line is given by .r — .r„ ]-/ cos a, y ™ y^ +^l cos /J. z ~ cosy ... (4)wliere .r^ , t/o* P h^it on the dislocation lino and / is a parameter.Screw dipole of infinitesimal width 209Tht' coinpoJiGuts of the i'orce /  on a unit eloment oi' the screw dislocation are computed from the Poach-Koehler formula (3) and are given as/x =  6*[(cos‘'*//—cos-y)trj,z-l-cos a cos/ytr j^JJ y  —  l)<[(co8 cos- a)cr ,^—cos a cos llrry-\fg — 1)S cos y((Tyz cos a—(Tj.; cos /i) ... (5)where tho stress componouts of the dipole must ))(' tn-keii ai points (4).For a screw disolcation, parallel to the dipolt'/x =-  (fi)/= = «Tho dcpeudouco o f/^  on x  for screw dislocation moving in the slip iilane ()j ^  —  const) for A — f_  hm . (l-C'*-2/.)2/„-= (I-NT. . .  (7 )Fig 2 Force/x e*> umt olomeiit of u screw dislocation jiacrallol to tho tiipolo os a lunctiou of its position x in the glide piano (y ~  yo)where = xjy  ^ is shown in Figure 2. The dependence ofh>Dhy/  (V+«i*r'.. (8)\vJi(jio — [//xq, I'Yom o(|s (7) and (8), it is obvious tliat f j l  — ^ JV 2/o“ /Ib^ hiiKh !  [ ■> ) vary in tlio sajin" manner Avith i and rcs|i<x;tiveJy.b'or tlj(j screw rlisloeatiojj peipcuidicular to the dipol(‘ (cosy — 0, com (] = sin a)Jx cr^ 2 jJ y -  -?/''[ws-ao-*2+Sz -  0at the points x — |-/ cos cl, y — I sin a, — 0b\)i‘ CL — 7t/2, and k — iji particularbWh2 10  N. K . G ilraL  - ... (10),t ’lg .‘t on unit nlomoiii nt fi arrow dialocaiioii normal t») tho clopolovv^ hure t.2 — \ U\). The tsourse ot'/j, is shoAvn iji figure Jl.Now wo consider the interaction oftlio dipole with edge dislocation, tho Burgers vector b^ of Avhieh has the components b ~  con a\ by^ ~  b^ cos/J' and b-^  — /V^ c^osy'. The dislocation line is given by eq (4). For an edge disloca-  ^‘o»x, the folloAving relat ioncos a cos a' +cos // cos /J' +cos y cos y' — 0 ... (11)Screxo dipole of infinitesimal width 211exists.The components of the foi co / on a unit olemenl ol’ th(' edge dislocntion nro computed from the Peach Koehler’s formula (3) and arc given asfx “  P a (7^ --|-(e()s cos/i*' —cos y cos y')cryz\f y  -  6 [^(cos y cos y'— cos a  cos o c ' ) n r ^ . z - <‘os a  cos p ’  c r y . ]  ... (12)/z — cos y'fcoB cos /yo-.,.,]where the stress components oi' the dipole niiisl lu^  tnlum at points (t). For an edge dislocat.ion parallel to the dipoles(I:i)t’or an edge dislocat ion perpendicular tothc dipole (cos y ^ 0, cos p ~ sin a) with Burgers vector in the x—y plainsn,„)fy — eos- arr,,2-  a,,,- ) (14)h  =  '»at t he points :r — .^ o+? cos a, // - I sin oc,r^  — 0For -  /■ L> ’ Jjhf^ Dh IH J(Iwhere — IThe curve botAveen/J [ \ aiid will he same as Uie ciirv''c slvovnm Figure 2.These results can be taken for’ a long range approximat ion of a dipole^  of finite widt h and are useful Avhen considering the interact ion of a dipole Avith ot her defects AAdio distance from the dipole is large* compared Avitli tlu^  dipole Avidtli.The author is tliaiikful to J’rofessor P, A. Dziwoniooli for the constant cii- coiiragement during this work.ReferencesK roupa F  1902 f h e rh  J  Phys,  B12 101Saclanamla. Iv & Marcialcowski IVl J 1073.7  AppI Phyti 43,30,1  Sadaiianrla A' it Marcinkowski M .1 1973 71/f^ r Sri Pnrjr 1 1 ,0 1Woort inan J & Woottman H 1064 E l n n r i i l n r y  Th’slocatio)i Theory {Thn ^hxr^hWsm (Joinpany London)01

Screw Dipole of Infinitesimal Width

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Screw Dipole of Infinitesimal Width

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