Des surfaces aux joints de grains : la ségrégation dans tous ses états

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Des surfaces aux joints de grains : la ségrégation dans

tous ses états

Jérôme Creuze

To cite this version:

Jérôme Creuze. Des surfaces aux joints de grains : la ségrégation dans tous ses états. Analyse de données, Statistiques et Probabilités [physics.data-an]. Université Paris Sud - Paris XI, 2000. Français. �tel-00001572�

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ORSAY

N° D’ORDRE : 6278

UNIVERSITE DE PARIS-SUD

U.F.R. SCIENTIFIQUE D’ORSAY

THESE présentée pour obtenir

Le GRADE de DOCTEUR EN SCIENCES

DE L’UNIVERSITE PARIS XI ORSAY

Spécialité : métallurgie et matériaux PAR

Jérôme CREUZE

SUJET :

Des surfaces aux joints de grains :

la ségrégation dans tous ses états

Soutenue le 13 octobre 2000 devant la Commission d’examen

MM. Louisette Priester Présidente

François Ducastelle rapporteur

Joseph Morillo rapporteur

Jean Bernardini examinateur

Fabienne Berthier directeur de thèse

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Titre : Des surfaces aux joints de grains : la ségrégation dans tous ses états. Résumé :

Grand nombre des propriétés des alliages dépend de la structure et de la composition chimique des défauts. Dans ce contexte, nous avons étudié la ségrégation interfaciale d’un système présentant une forte démixtion en volume et une tendance à ségréger en surface (i.e. Cu/Ag), par simulations Monte Carlo avec déplacements et un modèle d’Ising effectif sur réseau rigide. Les interfaces considérées sont le joint de grains de flexion =5 +643,

k334l ainsi que les surfaces (001) et (310).

Les résultats obtenus en Monte Carlo pour le joint de grains montrent l’existence d’un composé ordonné bi-dimensionnel dans le plan du joint... dans un système à tendance à la démixtion ! Pour la surface (001), nous montrons l’apparition d’une surstructure cristallographique illustrant le couplage complexe entre ségrégation et modification structurale. L’analyse par le modèle sur réseau rigide nous a permis de déterminer les forces motrices de ségrégation intergranulaire et superficielle. Le couplage des deux méthodes a mis en évidence le rôle important de l’entropie vibrationnelle dans la ségrégation intergranulaire, alors qu’elle peut être négligée pour la ségrégation superficielle. L’évaluation deVvhjdoit tenir compte des couplages entre vibrateurs premiers voisins (le modèle d’Einstein ne pouvant donc être utilisé) et de la dilatation thermique différentielle à proximité du joint de grains.

Nous avons alors utilisé l’approche analytique pour déterminer les isothermes de ségrégation intergra-nulaire. Nous avons ainsi mis en évidence une transition de phase du premier ordre à caractère multicouche. Un comportement identique est obtenu pour la surface (310), les interactions inter-plan étant à l’origine de ces transi-tions.

Cet aspect multicouche de la ségrégation intergranulaire a été confirmé par des simulations Monte Carlo montrant de plus l’apparition d’un phénomène de mouillage, le joint de grains initial se scindant en deux interfaces séparées par une phase métastable.

Mots-clefs : Surface - Joint de grains - Ségrégation - Système Cu/Ag - Simulations Monte Carlo

- Modèle d’Ising - Entropie vibrationnelle.

———————————————————————————————————

Title : From surfaces to grain boundaries : the segregation in all its states. Abstract :

Number of alloys properties depends on the structure and the chemical composition of defects. In this context, we have studied interfacial segregation for a system presenting a strong tendency to bulk phase separate (e.g. Cu/Ag). This study has been performed by coupling Monte Carlo simulations with displacements and an effective Ising model. The considered interfaces are the =5 +643, k334l symmetrical tilt grain boundary as well as the (001) and (310) surfaces.

For the grain boundary, Monte Carlo simulations show the existence of a 2-D compound in the grain boundary plane for an alloy with a strong tendency to phase separation in the bulk! For the (001) surface, we show the appearance of a crystallographical superstructure illustrating the complex coupling between segregation and structural change. A detailed matching of the Monte Carlo results on the rigid lattice model allows us to determine the interfacial segregation driving forces. The coupling of both methods highlights a significant contribution of the vibrational entropy to intergranular segregation, whereas it can be neglected for superficial segregation. A satisfactory evaluation of this entropic term must take into account for the vibrational coupling between nearest neighbors (thus the Einstein model cannot be used) and the differential thermal expansion near the interface.

We then use the analytical approach to determine the segregation isotherms for the grain boundary. Thus, we show the existence of a first order multilayer phase transition. A rather similar behavior is obtained for the (310) surface, the interlayer interactions between open (310) planes being at the origin of these transitions both for the surface and the grain boundary.

This multilayer aspect of intergranular segregation is then confirmed by Monte Carlo simulations. Mo-reover, these simulations show a wetting phenomenon, the initial grain boundary being split up into two interfaces separated by a metastable monocrystalline phase.

Keywords : Surface - Grain boundary - Segregation - Cu/Ag system- Monte Carlo

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Maturité de l’homme : retrouver le sérieux qu’il mettait au jeu, étant enfant. Par-delà le bien et le mal, F. Nietzsche

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fodluyr|dqwh $

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Fkdslwuh 5

Prgëohv hw pìwkrghv vwdwlvwltxhv

dssoltxìv ã od vìjuìjdwlrq lqwhuidfldoh

Frpph qrxv o*dyrqv yx gdqv o*lqwurgxfwlrq/ od frqfhqwudwlrq suëv g*xq gìidxw +who tx*xqh vxuidfh rx xq mrlqw gh judlqv, gdqv xq dooldjh D3SES glëuh jìqìudohphqw gh fhooh gx yroxph1 Fh skìqrpëqh/ frqqx vrxv oh whuph gh vìjuìjdwlrq vxshuflhooh rx lqwhujudqx0 odluh/ d idlw o*remhw/ gx prlqv srxu ohv vxuidfhv/ gh qrpeuhxvhv ìwxghv wdqw h{sìulphqwdohv txh wkìrultxhv prqwudqw xqh judqgh ydulìwì gh frpsruwhphqw vxlydqw ohv dooldjhv ìwxglìv ÊW:<` 0 ^F<3` 0 ÎV<5` 0 Ê<7` 0 ^J<:` +skìqrpëqhv gh suì0suìflslwdwlrq/ dssdulwlrq gh frpsrvìv q*h{lvwdqw sdv hq yroxph111,1 Dq gh elhq frpsuhqguh ohv prwhxuv ìqhujìwltxhv slorwdqw fh skìqrpëqh/ lo hvw qìfhvvdluh gh oh gìfuluh ã o*ìfkhooh dwrpltxh1 Srxu fhod/ qrxv xwlolvrqv xq prgëoh dqdo|wltxh vxu uìvhdx uljlgh +Lvlqj Prgho rx L1P1, wudlwì gdqv o*ds0 sur{lpdwlrq gh fkdps pr|hq +Phdq Ilhog rx P1I1, grqw ohv judqghxuv ìqhujìwltxhv vrqw lvvxhv gh o*dssur{lpdwlrq dx vhfrqg prphqw ghv oldlvrqv iruwhv +Wljkw Elqglqj Vhfrqg Prphqw Dssur{lpdwlrq rx W1E1V1P1D1,1 Fhwwh gìpdufkh/ suìvhqwìh gdqv oh ¢514/ vhud frxsoìh ã ghv vlpxodwlrqv qxpìultxhv gh w|sh Prqwh Fduor dyhf gìsodfhphqwv/ suìvhqwìhv gdqv oh ¢5151 O*remhfwli hvw g*rewhqlu ghv lvrwkhuphv gh vìjuìjdwlrq/ uhsuìvhqwdqw o*ìyr0 oxwlrq ghv frqfhqwudwlrqv gdqv od uìjlrq gx gìidxw hq irqfwlrq gh od frqfhqwudwlrq gh yroxph/ ã xqh whpsìudwxuh grqqìh1 Vrxoljqrqv txh ohv sdudpëwuhv ìqhujìwltxhv lqwurgxlwv gdqv qrwuh prgëoh dqdo|wltxh vrqw rewhqxv ã o*dlgh gx píph prgëoh ìqhujìwltxh txh fhoxl xwlolvì gdqv ohv vlpxodwlrqv qxpìultxhv1 Fh prgëoh ìqhujìwltxh/ irqgì vxu o*dssur{lpdwlrq dx vhfrqg prphqw ghv oldlvrqv iruwhv/ d ìwì dmxvwì srxu uhsurgxluh ohv sulqflsdohv fdudfwì0 ulvwltxhv gx v|vwëph Fx0Dj +¢516,1 Hqq qrxv suìvhqwrqv gdqv oh ¢517 ohv lqwhuidfhv g*xq

(17)

srlqw gh yxh vwulfwhphqw jìrpìwultxh1

514 Prgëohv vxu uìvhdx uljlgh wudlwìv gdqv o*dssur{l0

pdwlrq gh fkdps pr|hq

Ohv suhplhuv wudydx{ frqfhuqdqw o*hqulfklvvhphqw gh od vxuidfh hq o*xq ghv frpsrvdqwv g*xq dooldjh vrqw gxv ã M1 Z1 Jleev ^J7;`/ txl hq irupxod od suhplëuh ghvfulswlrq wkìrultxh gdqv oh fdguh g*xqh dssurfkh wkhuprg|qdpltxh1 Oh gìyhorsshphqw gh fhwwh dssurfkh d grqqì olhx ã xqh prgìolvdwlrq vxu uìvhdx uljlgh txl dgrswh xqh ghvfulswlrq ìqhujìwltxh hpslultxh vrxv iruph g*lqwhudfwlrqv gh sdluh ^ZQ:7` 0 ^ZN::`/ frqqxh vrxv oh vljoh gh L1P1 +Lvlqj Prgho rx Prgëoh g*Lvlqj,1 Oh wudlwhphqw vwdwlvwltxh h{dfw gh fh prgëoh qh srxydqw íwuh rewhqx txh sdu vlpxodwlrqv qxpìultxhv gh w|sh Prqwh Fduor/ xqh dssur{lpdwlrq vwdwlvwltxh vrxyhqw idlwh hvw doruv o*dssur{lpdwlrq gh fkdps pr|hq ã xq vlwh rx pìwkrgh gh Eudjj0Zlooldpv ^EZ67` +¢51414,1 G*xq dxwuh f÷wì/ xqh ghx{lëph dssurfkh sulyloìjlh od ghvfulswlrq ìqhujìwltxh hq od gìulydqw gh od vwuxfwxuh ìohfwurqltxh dx gìwulphqw gh wrxw wudlwhphqw xowìulhxu gh sk|vltxh vwdwlvwltxh1 Fhwwh dssurfkh qh shuphw txh oh fdofxo ghv hqwkdoslhv gh vìjuìjdwlrq g*xq vroxwì lvroì +hqfruh dsshoì fdofxo g*lpsxuhwì rx gh gloxwlrq lqqlh, ^P;5` 0 ^UG;6` 0 ^GU;6` 0 ^P;8` 0 ^GV;:`1

Ghsxlv txhotxhv dqqìhv/ ghv prgìolvdwlrqv frxsodqw fhv ghx{ dssurfkhv rqw ìwì gìyh0 orssìhv1 O*xqh g*hqwuh hoohv/ frqqxh vrxv oh vljoh gh W1E1L1P +Wljkw0Elqglqj Lvlqj Prgho rx Prgëoh g*Lvlqj hq Oldlvrqv Iruwhv,/ d ìwì gìyhorssìh gdqv oh fdguh gh od vìjuìjd0 wlrq vxshuflhooh ^WOG;;` +¢51415,1 Od sulqflsdoh glìuhqfh hqwuh oh W1E1L1P1 hw oh prgëoh g*Lvlqj hpslultxh flwì suìfìghpphqw ^ZQ:7` 0 ^ZN::` uìvlgh gdqv od sulvh hq frpswh gh od vwuxfwxuh ìohfwurqltxh/ txl d shuplv g*dpìolruhu gh pdqlëuh vljqlfdwlyh od ghvfuls0 wlrq ìqhujìwltxh/ fhooh0fl vh phwwdqw doruv vrxv od iruph g*lqwhudfwlrqv gh sdluh hhfwlyhv1 Fhshqgdqw od gìwhuplqdwlrq gh fhv txdqwlwìv hq oldlvrqv iruwhv hvw orqjxh hw idvwlglhxvh/ píph vxu uìvhdx uljlgh1

Od ghvfulswlrq ìqhujìwltxh ghv ghx{ prgëohv suìfìghqwv +L1P1 hw W1E1L1P1, vrxuh gh od uhvwulfwlrq olìh dx uìvhdx uljlgh/ txl qh shuphw sdv od sulvh hq frpswh ghv uhod{dwlrqv gxhv vrlw ã od glìuhqfh gh wdlooh hqwuh ohv ghx{ frqvwlwxdqwv gh o*dooldjh/ vrlw ã od suì0 vhqfh g*xqh lqwhuidfh1 Srxu doohu dx0ghoã gh fhwwh olplwdwlrq/ ohv sdudpëwuhv ìqhujìwltxhv lqwurgxlwv gdqv oh prgëoh vxu uìvhdx uljlgh grlyhqw grqf frqwhqlu fhwwh lqirupdwlrq1 Od

(18)

Modèle énergétique empirique (E.)

Liaisons fortes (T.B.)

Approximation au second moment des

liaisons fortes (T.B.S.M.A.)

Modèle sur réseau rigide (I.M.) E.-I.M.-M.F. T.B.-I.M.-M.F. E.-I.M.-M.C. T.B.-I.M.-M.C. T.B.S.M.A.-I.M.-M.C. approximation de champ moyen (M.F.) traitement statistique exact (M.C.)

sans prise en compte des relaxations

sans prise en compte

des relaxations avec prise en compte des relaxations

T.B.S.M.A.-I.M.-M.F.

Iljxuh 504= Vfkìpd uìfdslwxodwli ghv glìuhqwv prgëohv suìvhqwìv gdqv ohtxho ohv sduwlhv ìqhujìwltxh +hq kdxw gx vfkìpd, hw vwdwlvwltxh +hq edv gx vfkìpd, vrqw glvwlqjxìhv1 O*ds0 surfkh txh qrxv xwlolvhurqv gdqv fh wudydlo hvw vxuoljqìh hq julv1

pìwkrgh txh qrxv dyrqv fkrlvlh frqvlvwh doruv ã xwlolvhu o*dssur{lpdwlrq dx vhfrqg pr0 phqw ghv oldlvrqv iruwhv/ ohv sdudpëwuhv ìqhujìwltxhv srxydqw íwuh gìwhuplqìv gh pdqlëuh uhodwlyhphqw vlpsoh hq whqdqw frpswh ghv uhod{dwlrqv +¢51416,1 Fh prgëoh shxw íwuh shuêx frpph xqh h{whqvlrq gx W1E1L1P1 hw vhud gìqrppì sdu od vxlwh W1E1V1P1D1 0 L1P1

Dq gh elhq phwwuh hq ìylghqfh ohv glìuhqfhv hvvhqwlhoohv gh fhv prgëohv/ qrxv suì0 vhqwrqv vxu od jxuh +504, xq vfkìpd uìfdslwxodwli vìsdudqw ohv sduwlhv ìqhujìwltxh hw vwdwlvwltxh1 Rq yrlw dlqvl txh oh prgëoh txh qrxv xwlolvrqv ghyudlw íwuh gìqrppì hq wrxwh uljxhxu W1E1V1P1D1 0 L1P1 0 P1I1 pdlv gdqv xq vrxfl gh olvlelolwì/ qrxv dyrqv suìiìuì rphwwuh od sduwlh gx vljoh frqfhuqdqw oh wudlwhphqw vwdwlvwltxh1 Gdqv od vxlwh gx pdqxv0 fulw/ o*dssur{lpdwlrq gh fkdps pr|hq vhud grqf v|vwìpdwltxhphqw vrxv0hqwhqgxh gdqv ohv glìuhqwv vljohv vh uìiìudqw dx{ prgëohv1

(19)

51414 Ghvfulswlrq ìqhujìwltxh hpslultxh

Vl o*rq frqvlgëuh txh o*ìqhujlh wrwdoh g*xq dooldjh D3SES shxw íwuh gìfrpsrvìh hq lq0 whudfwlrqv gh sdluh/ o*dooldjh shxw doruv íwuh gìfulw/ gdqv oh fdguh gx prgëoh g*Lvlqj/ sdu o*Kdplowrqlhq = MR ? ' ₂ [ c'c [ ?c6'? R ?R6"?6c +514, rü "

?6 hvw o*ìqhujlh g*lqwhudfwlrq hqwuh xq dwrph gh w|sh vxu oh vlwh ? hw xq dwrph gh w|sh vxu oh vlwh 6/ hw iR

?j hvw o*hqvhpeoh ghv idfwhxuv g*rffxsdwlrq gh vlwh who txh = R

?@/ vl oh vlwh ? hvw rffxsì sdu o*dwrph gh w|sh +@D/ E, R

?@f/ vlqrq1

Srxu xq dooldjh elqdluh D3SES vdqv gìidxw srqfwxho/ qrxv srxyrqv ìfuluh = R

?@0R?@R? hw o*ìtxdwlrq +514, vh udpëqh doruv ã =

M ' Mfn[ ? R? [ 6'? E?6 "?6 n [ ?c6'? R?R6"?6c +515, dyhf Mf ' ₂ [ ?c6'? " ?6c ?6 ' ₂"?6 "?6 hw "?6 ' ₂" ?6n "?6 2"?6 +516, O*dssur{lpdwlrq gh Eudjj0Zlooldpv +fkdps pr|hq ã xq vlwh, frqvlvwh ã qìjoljhu o*ruguh ã frxuwh glvwdqfh1 Dlqvl/ ohv rffxsdwlrqv pr|hqqhv ghv vlwhv ? hw 6 vrqw gìfrxsoìhv =

kR?R6l ' kR?l kR6l +517,

hw o*ìqhujlh lqwhuqh/ rewhqxh hq ìydoxdqw od pr|hqqh gh o*Kdplowrqlhq +515,/ v*ìfulw doruv =

kMl ' Mfn [

?c6'?

kR?l E?6 "?6 n [ ?c6'?

kR?l kR6l "?6 +518, Qrxv doorqv vxssrvhu sdu od vxlwh txh oh fulvwdo shxw íwuh gìfulw frpph xq hpslohphqw gh sodqv dwrpltxhv R sdudooëohv ã od vxuidfh +oh sodq gh vxuidfh fruuhvsrqgdqw ã o*lqglfh 3,/ vxssrvìv gh frpsrvlwlrq krprjëqh/ SR/ whooh txh kR?l@SR srxu wrxw ? dssduwhqdqw dx

(20)

sodq R1 Gh soxv/ vl o*rq qh frqvlgëuh txh ghv lqwhudfwlrqv olplwìhv dx{ suhplhuv yrlvlqv vxu uìvhdx uljlgh hw lqfkdqjìhv hq vxuidfh/ rq shxw srvhu =

"?6@" hw ?6@ vl ohv vlwhv ? hw 6 vrqw suhplhuv yrlvlqv/ "?6@?6@f vlqrq1

O*ìtxdwlrq +518, v*ìfulw doruv =

kMl ' Mfn E "[ R

R~RSRn "[ Rc^

R~R^SRS^c +519,

rü ~R^ hvw oh qrpeuh g*dwrphv gx sodq ^ suhplhuv yrlvlqv g*xq dwrph gx sodq R hw ~R

'S

^ ~R^

hvw od frruglqhqfh g*xq dwrph gx sodq R1 R hvw oh qrpeuh g*dwrphv sdu sodq txh qrxv vxssrvhurqv/ sdu od vxlwh/ frqvwdqw txho txh vrlw R = R@/ vdxi gdqv oh fdv g*xqh uhfrqvwuxfwlrq gh vxuidfh txl shxw hqwudñqhu xqh yduldwlrq gx qrpeuh gh vlwhv ã od vxuidfh +fi ¢71515,1

Hq qìjoljhdqw o*hqwurslh yleudwlrqqhooh g*h{fëv/ o*ìqhujlh oleuh/ gdqv o*hqvhpeoh judqg fdqrqltxh/ v*h{sulph doruv gh od pdqlëuh vxlydqwh ^GOW<3` =

8 ' kMl A 7[ R

SR{>c +51:,

A gìvljqdqw od whpsìudwxuh/ {>@>0> fruuhvsrqgdqw dx srwhqwlho fklpltxh g*dooldjh hw 7 ìwdqw o*hqwurslh gh frqjxudwlrq txl v*ìfulw gdqv o*dssur{lpdwlrq gh Eudjj0Zlooldpv ^GOW<3` =

7 ' & [ R

dSR*? SRn E SR *? E SRo c +51;, rü & hvw od frqvwdqwh gh Erow}pdqq1

Od plqlplvdwlrq gh o*ìqhujlh oleuh +Y8

YSR@f, frqgxlw doruv dx suro gh frqfhqwudwlrq iSRj

hq irqfwlrq gh S/ frqfhqwudwlrq hq dwrph E gx yroxph = SR SR ' S Si T {M_&ARre} c +51<, rü {Mre}

R hvw o*hqwkdoslh gh vìjuìjdwlrq gx sodq R txl uhsuìvhqwh oh elodq g*ìqhujlh plv hq mhx oruv gh o*ìfkdqjh =

R,@? Rn J,6e $ J,6en R,@? Rc +5143, 48

(21)

hq o*rffxuuhqfh/

{M_fre} ' ~_{E " n 2" d~ ESf}_{S n ~}_ES_2So _+5144, {Mre}

R ' 2" d~ ESR S n ~ESRnn SR3 2So ;R 9' fc

rü ~ hw ~ _{vrqw uhvshfwlyhphqw/ srxu xq vlwh gx sodq R/ ohv qrpeuhv gh suhplhuv yrlvlqv} vlwxìv gdqv oh sodq R hw gdqv ohv sodqv dgmdfhqwv dx sodq R1 Gdqv fh gìyhorsshphqw/ qrxv dyrqv frqvlgìuì xqh rulhqwdwlrq fulvwdoorjudskltxh whooh txh ohv suhplhuv yrlvlqv g*xq dwrph vlwxì gdqv oh sodq R vrqw wrxv vlwxìv gdqv oh sodq R hw ohv ghx{ suhplhuv sodqv dgmdfhqwv R0 hw R.1

O*hqwkdoslh gh vìjuìjdwlrq hq vxuidfh/ {M_fre}/ phw hq mhx ohv prwhxuv ìqhujìwltxhv vxlydqwv =

Od glìuhqfh ghv ìqhujlhv gh vxuidfh sdu dwrph ghv pìwdx{ sxuv/

{ ' ~₂ "_"_{' ~}_'_c _+5145, v*lo q*| d ghv oldlvrqv frxsìhv txh gdqv oh sodq gh vxuidfh1 Oh whuph ₀_{/ dsshoì} hhw gh whqvlrq vxshuflhooh/ hqwudñqh od vìjuìjdwlrq hq vxuidfh gh o*ìoìphqw gh soxv idleoh ìqhujlh gh vxuidfh1

2"@"_."_02"_{uhsuìvhqwh o*ìqhujlh plvh hq mhx oruv gx surfhvvxv gh irupdwlrq} g*xqh sdluh DD hw g*xqh sdluh EE ã sduwlu gh ghx{ sdluhv DE = 5DE$DD.EE1 Oh vljqh gh fhwwh txdqwlwì fdudfwìulvh od whqgdqfh ã o*ruguh +irupdwlrq gh sdluhv kìwìurdwrpltxhv/ ":f, rx od whqgdqfh ã od gìpl{wlrq +irupdwlrq gh sdluhv krprdwr0 pltxhv/ " f,1 Qrxv dsshorqv hhw g*dooldjh od sduwlh gh o*hqwkdoslh gh vìjuìjdwlrq sursruwlrqqhooh ã "1 Gdqv oh fdv g*xq dooldjh ã whqgdqfh ã o*ruguh +uhvs1 ã whqgdqfh ã od gìpl{wlrq,/ o*hhw g*dooldjh idyrulvh od vìjuìjdwlrq gx pdmrulwdluh +uhvs1 gx pl0 qrulwdluh, ^ZQ:7`1

Uhpdutxrqv txh {M_fre} shxw vh uììfuluh vrxv od iruph vxlydqwh =

{M_fre} ' {M_f6Roe|en {M?|eo@S|J?

f c +5146,

(22)

rü {M_f6Roe|e hvw o*hqwkdoslh gh vìjuìjdwlrq g*xq dwrph gh vroxwì E gdqv oh vroydqw D +SR hw S whqghqw yhuv f, hw {Mf?|eo@S|J? ylhqw gh o*lqwhudfwlrq hqwuh ohv dwrphv vìjuì0 jhdqwv = {M_f6Roe|e@0~_{E0" hw {M}?|eo@S|J?

f @2" d~ ESf0S .~ES02So1 Fhwwh gìfrpsrvl0 wlrq vh uìyëohud xwloh sdu od vxlwh/ gx idlw txh o*hqwkdoslh gh vìjuìjdwlrq g*lpsxuhwì shxw íwuh idflohphqw gìwhuplqìh sdu xq fdofxo vsìfltxh hq vlpxodwlrq qxpìultxh1

Qrwrqv hqq txh o*h{suhvvlrq gh o*hqwkdoslh gh vìjuìjdwlrq qh suhqg sdv hq frpswh od glìuhqfh gh wdlooh hqwuh ohv frqvwlwxdqwv gh o*dooldjh1 Gdqv ohv prgëohv skìqrpìqrorjltxhv/ fhw hhw gh wdlooh hvw sulv hq frpswh sdu o*dmrxw g*xqh frqwulexwlrq g*ruljlqh ìodvwltxh1 Hq xwlolvdqw o*ìodvwlflwì olqìdluh/ fh whuph hvw grqqì/ gdqv od olplwh lqqlphqw gloxìh/ sdu ^I87` 0 ^H89` 0 ^ZN::` =

m{Mre}

e,@r|m ' 2eZCooEo o

2

on eCo c +5147,

rü hvw oh prgxoh gh frpsuhvvlelolwì gx vroxwì +gh ud|rq dwrpltxh o, hw C hvw oh prgxoh gh flvdloohphqw gh od pdwulfh +gh ud|rq dwrpltxh o,1 Suìflvrqv txh/ gdqv fh w|sh g*dssurfkh/ o*hhw gh wdlooh frqgxlw wrxmrxuv ã od vìjuìjdwlrq gx vroxwì hq vxuidfh/ tx*lo vrlw soxv shwlw rx soxv jurv txh o*ìoìphqw gh od pdwulfh1

51415 Sulqflsdx{ uìvxowdwv gx prgëoh g*Lvlqj hq oldlvrqv iruwhv

Oh prgëoh ìqhujìwltxh suìvhqwì fl0ghvvxv vrxuh g*xq lqfrqyìqlhqw pdmhxu gdqv oh fdv ghv dooldjhv gh pìwdx{ gh wudqvlwlrq = o*ìqhujlh wrwdoh g*xq v|vwëph pìwdooltxh qh shxw sdv íwuh uhfrqvwuxlwh xqltxhphqw ã o*dlgh g*lqwhudfwlrqv gh sdluh ^I9<`1 Hq uhydqfkh/ I1 Gxfdvwhooh hw do1 rqw prqwuì/ gdqv oh fdguh gx Prgëoh gh Shuwxuedwlrq Jìqìudolvìh ^GJ:9` 0 ^GW;3` 0 ^EJ.;4` 0 ^G;<`/ txh od sduwlh gh o*ìqhujlh wrwdoh txl gìshqg gh od frqjxudwlrq gh o*dooldjh shxw v*ìfuluh vrxv iruph g*lqwhudfwlrqv gh sdluh hhfwlyhv gìulyìhv g*xq gìyhorsshphqw hq shuwxuedwlrq ã sduwlu gx plolhx pr|hq gìvrugrqqì1 O*h{whqvlrq gh fh prgëoh dx fdv ghv vxuidfhv d grqqì qdlvvdqfh dx W1E1L1P1 ^WOG;;` txl/ sduwdqw g*xq Kdplowrqlhq g*Lvlqj hhfwli Mess _R ? '[ ?c R ??n₂ [ c'c [ ?c6'? R ?R6T?6 +5148, rü

? hvw xq whuph gh fkdps gh orfdo uholì dx{ ìqhujlhv gh vxuidfh ghv pìwdx{ sxuv ^WOG;;` hw T

?6 hvw o*lqwhudfwlrq gh sdluh hhfwlyh hqwuh xq dwrph gh w|sh dx vlwh ? hw 4:

(23)

xq dwrph gh w|sh dx vlwh 6/ shuphw gh uììfuluh o*ìtxdwlrq +515, = Mess_{EiR?j '}[ ? R? # ess ? [ 6'? T?6 $ n [ ?c6'? R?R6T?6c +5149, dyhf ess ? ' ? ? n ₂ [ 6'? T ?6 T?6 +514:, hw T?6 ' ₂T ?6 n T?6 2T?6 +514;,

Hq qh frqvlgìudqw hqfruh txh ghv lqwhudfwlrqv gh sdluh hhfwlyhv T?6 olplwìhv dx{ suhplhuv yrlvlqv/ o*hqwkdoslh gh vìjuìjdwlrq vh phw doruv vrxv xqh iruph wuëv vlplodluh ã o*ìtxdwlrq +5144, = {M_fre} ' {ess_f n E~ n 2~_T_~Tff_{n ~}_Tf _+514<, n2~Tff_Sf_{T S}_{n ~}_Tf_S_{2T S} {Mre} R ' 2 ~ ETRR_S R T S n ~TRERnSRnn TRER3SR3 2T S ;R 9' fc dyhf {ess

R ' essR essJ,6e +5153,

Rxwuh vd wuëv iruwh dqdorjlh dyhf o*Kdplowrqlhq g*Lvlqj hpslultxh +515,/ oh W1E1L1P1 srvvëgh ohv sursulìwìv vxlydqwhv =

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Hqq/ lo idxw qrwhu txh od gìulydwlrq gx W1E1L1P1 qh suhqg sdv hq frpswh o*hhw gh wdlooh1 Srxu whqlu frpswh g*xqh ìyhqwxhooh glìuhqfh gh ud|rqv dwrpltxhv hqwuh ohv frqvwlwxdqwv gh o*dooldjh/ od vlpxodwlrq qxpìultxh/ frxsoìh ã xqh dssur{lpdwlrq vlpsoh ghv oldlvrqv iruwhv/ shuphw g*lvrohu od frqwulexwlrq gh o*hhw gh wdlooh/ {|@,,e

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Frpph gdqv o*dssurfkh hpslultxh/ o*hqwkdoslh gh vìjuìjdwlrq vh phw vrxv od iruph =

{M_fre} ' {M_f6Roe|en {M?|eo@S|J?

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(25)

51416 Sulvh hq frpswh ghv uhod{dwlrqv

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(27)

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Qrxv qrxv sursrvrqv gdqv fhwwh sduwlh gh suìvhqwhu ohv srlqwv hvvhqwlhov gx fdofxo ghv judqghxuv yleudwlrqqhoohv gdqv o*dssur{lpdwlrq kduprqltxh +hqwurslh hw gìsodfhphqwv txdgudwltxhv pr|hqv, ^PP.:4`/ ohv dvshfwv soxv whfkqltxhv ìwdqw udvvhpeoìv gdqv o*dq0 qh{h D1

Od vwuxfwxuh fulvwdoorjudskltxh ìwdqw uhod{ìh ã A @f N/ o*ìqhujlh srwhqwlhooh/ L/ hvw gìyhorssìh/ gdqv o*dssur{lpdwlrq kduprqltxh/ dx ghx{lëph ruguh sdu udssruw dx{ gìsod0 fhphqwv = L ' Lf_n 2 [ ?ck [ 6cq xf ?k6q?k6qc +515<,

rü Lf _{hvw o*ìqhujlh srwhqwlhooh gh od vwuxfwxuh uhod{ìh ã A@f N/ ?k} _{hvw oh gìsodfhphqw gh} o*dwrph ? gdqv od gluhfwlrq k@E%c + rx 5 hw xf _{hvw od pdwulfh ghv frqvwdqwhv gh irufh =}

xf

?k6q ' Y

2_Lf

Y?kY6q +5163,

O*ìqhujlh oleuh/ 8 / hvw rewhqxh ã sduwlu gh od ghqvlwì g*ìwdwv yleudwlrqqhov/ ?ED/ rü D 57

(30)

hvw od iuìtxhqfh/ sdu ^PP.:4` = 8 ' Lf _{n &A} ] D4@ f *? 2 t? D 2&A ?ED_Dc +5164,

rü ?ED_D hvw oh qrpeuh g*ìwdwv yleudwlrqqhov frpsulv hqwuh D hw D._D/ hw hvw od frqvwdqwh gh Sodqfn1 Udsshorqv txh ohv srvlwlrqv dwrpltxhv g*ìtxloleuh vrqw vxssrvìhv lqgìshq0 gdqwhv gh od whpsìudwxuh gdqv o*dssur{lpdwlrq kduprqltxh1 Sduwdqw gh +5164,/ o*hqwurslh gh yleudwlrq/ 7/ hw ohv gìsodfhphqwv txdgudwltxhv pr|hqv/ k2_{l/ srxu ghv dwrphv gh pdvvh} / vrqw grqqìv sdu ohv h{suhvvlrqv vxlydqwhv ^PP.:4` =

7 ' & ] _D_4@ f D 2&A UL| D 2&A *? 2 t? D 2&A ?ED_Dc +5165, 2 _' HZ2 ] _D_4@ f UL| D 2&A ?ED D _D +5166,

Od ghqvlwì g*ìwdwv yleudwlrqqhov hvw gìwhuplqìh sdu o*ìtxdwlrq gx prxyhphqw = ??k' 8?k ' _YYL ?k ' [ 6cq xf ?k6q6qc +5167,

rü ? hvw od pdvvh gh o*dwrph ?1 Fkhufkdqw ohv vroxwlrqv gh od iruph ?kE|@I_??ki TE2ZD| / +5167, ghylhqw =

D2_?k_'[ 6cq (f ?k6q6q +5168, (f ?k?q@ x f ?k6q

eZ2I_?₆ hvw od pdwulfh g|qdpltxh +66,/ vl hvw oh qrpeuh wrwdo

g*dwrphv1 Ohv gìwdlov whfkqltxhv gh o*rewhqwlrq gh od ghqvlwì g*ìwdwv yleudwlrqqhov sdu ohv pìwkrghv orfdohv vrqw grqqìv gdqv o*dqqh{h D1 Rq shxw fhshqgdqw idluh gëv ã suìvhqw ohv uhpdutxhv vxlydqwhv =

ohv lqwhuidfhv lqgxlvdqw ghv glvwruvlrqv hw ghv frxsxuhv gh oldlvrq/ hoohv hqwudñqhqw xqh prglfdwlrq ghv iuìtxhqfhv orfdohv gh yleudwlrq sdu o*lqwhupìgdluh ghv frqvwdqwhv gh irufh1 Gdqv xq pìwdo sxu/ xq vlwh hq whqvlrq +uhvs1 hq frpsuhvvlrq, gìsodfh oh vshfwuh gh yleudwlrq yhuv ohv edvvhv iuìtxhqfhv +uhvs1 ohv kdxwhv iuìtxhqfhv,1

Ohv glìuhqfhv gh ud|rqv hw gh pdvvhv dwrpltxhv ghv ghx{ frqvwlwxdqwv gh o*dooldjh lq xhqw dxvvl vxu oh vshfwuh gh yleudwlrq1 Sdu h{hpsoh/ od plvh hq vroxwlrq g*xq

(31)

dwrph gh vroxwì E soxv jurv hw soxv orxug txh ohv dwrphv D gh od pdwulfh hqwudñqh orfdohphqw xqh dxjphqwdwlrq gh od ghqvlwì ghv edvvhv iuìtxhqfhv +hhw gh pdvvh, hw ghv kdxwhv iuìtxhqfhv +hhw gh wdlooh,1

Dlqvl o*hqwurslh yleudwlrqqhooh gh vìjuìjdwlrq hvw wuëv vhqvleoh g*xqh sduw dx{ hhwv gh wdlooh hw gh pdvvh suryhqdqw ghv frqvwlwxdqwv gh o*dooldjh/ hw g*dxwuh sduw dx{ glvwruvlrqv hw frxsxuhv gh oldlvrq suìvhqwhv dx{ lqwhuidfhv1 Fhshqgdqw/ lo hvw lqwìuhvvdqw gh uhpdutxhu txh o*hqwurslh yleudwlrqqhooh gh vìjuìjdwlrq gdqv oh prgëoh g*Hlqvwhlq qh gìshqg sdv ghv pdvvhv ghv glìuhqwv frqvwlwxdqwv +fi dqqh{h D,1

Qrwrqv hqq txh od ghvfulswlrq gx fdofxo ghv judqghxuv yleudwlrqqhoohv d ìwì uìdolvìh mxvtx*ã suìvhqw gdqv o*dssur{lpdwlrq kduprqltxh/ l1h1 hq xwlolvdqw ohv srvlwlrqv dwrpltxhv g*ìtxloleuh ã A @f N1 Fhshqgdqw/ ohv srvlwlrqv pr|hqqhv shxyhqw íwuh prglìhv hq irqf0 wlrq gh od whpsìudwxuh/ dxvvl elhq gdqv oh yroxph +glodwdwlrq wkhupltxh yroxpltxh, tx*dx yrlvlqdjh g*xqh lqwhuidfh +glodwdwlrq wkhupltxh glìuhqwlhooh,1 Glìuhqwv w|shv g*dssur{l0 pdwlrq txdvl0kduprqltxh vrqw doruv vxvfhswleohv g*íwuh xwlolvìv vxlydqw od pdqlëuh grqw od uhod{dwlrq dwrpltxh hvw hhfwxìh ã whpsìudwxuh qlh1 Txhooh txh vrlw od pìwkrgh hp0 sor|ìh/ o*ìqhujlh srwhqwlhooh hvw wrxmrxuv gìyhorssìh dx ghx{lëph ruguh sdu udssruw dx{ srvlwlrqv dwrpltxhv/ vxssrvìhv íwuh ohv srvlwlrqv g*ìtxloleuh ^EN:7`1 Fhfl lpsoltxh txh oh suhplhu whuph gx gìyhorsshphqw/ olì dx{ irufhv h{hufìhv vxu ohv dwrphv/ hvw qxo1 Oh fdofxo oh soxv h{dfw hvw grqf fhoxl rewhqx oruvtxh o*rq frqvlgëuh ohv srvlwlrqv pr|hqqhv gìwhuplqìhv sdu vlpxodwlrqv Prqwh Fduor1 Fh fdofxo suhqg hq hhw hq frpswh od srvvleoh glìuhqfh gh glodwdwlrq wkhupltxh hq yroxph hw ã sur{lplwì g*xqh lqwhuidfh = f*hvw o*ds0 sur{lpdwlrq txdvl0kduprqltxh lqkrprjëqh +D1T1L1,1 Fhshqgdqw/ fhwwh dssurfkh qìfhvvlwh gh uìdolvhu ghv vlpxodwlrqv qxpìultxhv od uhqgdqw wuëv frþwhxvh hq whpsv gh fdofxo1 Rq shxw doruv od frpsduhu ã xqh dssur{lpdwlrq txdvl0kduprqltxh krprjëqh +D1T1K1,/ rü wrxwhv ohv glvwdqfhv lqwhudwrpltxhv vrqw glodwìhv hq dssoltxdqw oh frh!flhqw gh glodwdwlrq wkhupltxh olqìdluh gh yroxph ^UQ.<5`1

Gdqv oh suìvhqw wudydlo/ qrxv dmrxwhurqv dlqvl od frpsdudlvrq ghv glìuhqwhv dssur{l0 pdwlrqv +kduprqltxh/ txdvl0kduprqltxh krprjëqh hw txdvl0kduprqltxh lqkrprjëqh, ã fhooh ghv ghx{ whfkqltxhv gh fdofxo gx vshfwuh orfdo gh yleudwlrq +prgëoh g*Hlqvwhlq hw pìwkrgh gh uìfxuvlrq,1

(32)

515 Sulqflshv jìqìudx{ ghv vlpxodwlrqv qxpìultxhv

Od vlpxodwlrq qxpìultxh ã o*ìfkhooh dwrpltxh shuphw g*ìydoxhu ohv sursulìwìv sk|vltxhv g*xq v|vwëph gh sduwlfxohv hq lqwhudfwlrq1 Ohv ghx{ sulqflsdohv pìwkrghv vrqw od g|qd0 pltxh proìfxodluh hw od vlpxodwlrq Prqwh Fduor1 Fhv pìwkrghv/ sduirlv orxughv ã phwwuh hq rhxyuh hw uhodwlyhphqw frþwhxvhv hq whpsv gh fdofxo/ rqw o*dydqwdjh gh frqgxluh ã ghv uì0 vxowdwv h{dfwv gdqv oh fdguh g*xqh ghvfulswlrq grqqìh gx v|vwëph +qdwxuh hw sursulìwìv ghv sduwlfxohv/ prgëoh ìqhujìwltxh111,1 F*hvw srxutxrl rq sduoh vrxyhqw g*h{sìulhqfhv qxpì0 ultxhv/ dx{txhoohv shxyhqw íwuh frqiurqwìv ghv prgëohv soxv vlpsohv pdlv dssurfkìv/ whov txh oh W1E1V1P1D1 0 L1P1 txh qrxv yhqrqv gh suìvhqwhu1

Lo q*hqwuh sdv gdqv oh fdguh gh fhwwh ìwxgh gh gìwdloohu fhv whfkqltxhv/ dx{txhoohv xq wuëv judqg qrpeuh g*rxyudjhv rqw ìwì frqvdfuìv/ hw qrxv uhqyr|rqv oh ohfwhxu ã wurlv g*hqwuh hx{ srxu ohxu judqg lqwìuíw sudwltxh ^DW<7` 0 ^E<8` 0 ^IV<9`1 Gdqv fh txl vxlw/ qrxv doorqv grqqhu xqltxhphqw txhotxhv judqghv oljqhv frqfhuqdqw od plvh hq rhxyuh ghv pìwkrghv whoohv txh qrxv ohv dyrqv hpsor|ìhv1

Od g|qdpltxh proìfxodluh hw od vlpxodwlrq Prqwh Fduor vrqw irqgìhv vxu ghv sulqflshv glìuhqwv = od suhplëuh hvw xqh pìwkrgh gìwhuplqlvwh +l1h1 hooh gìfulw od wudmhfwrluh uìhooh ghv sduwlfxohv hq lqwìjudqw ohv ìtxdwlrqv gx prxyhphqw, doruv txh od vhfrqgh hvw xqh pìwkrgh vwrfkdvwltxh +l1h1 hooh gìfulw o*ìyroxwlrq gx v|vwëph gh pdqlëuh doìdwrluh,1 Hoohv frqgxlvhqw srxuwdqw wkìrultxhphqw dx{ píphv uìvxowdwv1 Fhshqgdqw/ xqh gh fhv pìwkrghv hvw jìqìudohphqw plhx{ dgdswìhv txh o*dxwuh ã o*ìwxgh g*xq sureoëph sduwlfxolhu1 Dxvvl/ srxu fh txl frqfhuqh od pdmhxuh sduwlh gh qrwuh wudydlo/ o*ìwxgh gh od vìjuìjdwlrq lqwhuid0 fldoh gdqv xq dooldjh D3SES/ od vlpxodwlrq Prqwh Fduor v*lpsrvh gh pdqlëuh ìylghqwh1 Hq hhw/ lo hvw lpsrvvleoh gh gìfuluh xq gìvruguh fklpltxh who txh o*hqulfklvvhphqw hq o*xq ghv frqvwlwxdqwv g*xqh sduwlh gh o*ìfkdqwloorq hq g|qdpltxh proìfxodluh1 Fhod ghpdqghudlw od glxvlrq g*xq judqg qrpeuh g*dwrphv vxu gh judqghv glvwdqfhv/ fh txl hvw luuìdolvdeoh hq xq whpsv udlvrqqdeoh1 Hq uhydqfkh/ od vlpxodwlrq Prqwh Fduor shuphw gh wudydloohu qd0 wxuhoohphqw gdqv o*hqvhpeoh judqg fdqrqltxh uìgxlw +rx svhxgr0judqg fdqrqltxh, grqw od sulqflsdoh fdudfwìulvwltxh hvw gh srxyrlu prglhu od frpsrvlwlrq g*xq dooldjh hq mrxdqw vxu od glìuhqfh gh srwhqwlho fklpltxh hqwuh ohv ghx{ frqvwlwxdqwv1 Qrxv xwlolvhurqv fhshqgdqw od g|qdpltxh proìfxodluh g*xqh idêrq xq shx sduwlfxolëuh gdqv oh exw gh plqlplvhu o*ì0 qhujlh lqwhuqh gx v|vwëph ã A @f N gdqv xqh frqjxudwlrq grqqìh/ whfkqltxh gìqrppìh g|qdpltxh proìfxodluh wuhpsìh1

(33)

Txhooh txh vrlw od pìwkrgh/ xqh judqghxu sk|vltxh ã odtxhooh hvw dvvrflìh o*revhu0 ydeoh '^_{c R}_{/ rü ^}_@E$_o

c $o2c c o$ hvw od frrugrqqìh gh srvlwlrq jìqìudolvìh hw R_@E$_{c 2}$₂_{c c}$_{od txdqwlwì gh prxyhphqw frqmxjxìh/ hvw ìydoxìh hq idl0} vdqw od pr|hqqh gh '^_{c R}_{vxu xq hvsdfh ìfkdqwloorq1 Fh ghuqlhu hvw o*hvsdfh gh wrxv} ohv ìwdwv hq Prqwh Fduor rx od wudmhfwrluh ghv sduwlfxohv hq g|qdpltxh proìfxodluh1 Hq wkhuprg|qdpltxh vwdwlvwltxh/ xqh ydohxu pr|hqqh/ glwh pr|hqqh g*hqvhpeoh/ v*ìfulw =

'^_{c R}_' A o'

^_{c R}_{i T}_qM_^_{c R}

A o i T dqM E^_{c R}_o +5169, Oh v|peroh Ao +wudfh, vljqlh txh o*rq vrpph vxu wrxv ohv ìwdwv dffhvvleohv gx v|vwëph hw q@42&A 1 Oh gìqrplqdwhxu hvw od irqfwlrq gh sduwlwlrq hw M^c R o*Kdplowrqlhq gx v|vwëph1 Xqh dxwuh ydohxu pr|hqqh/ glwh pr|hqqh whpsruhooh/ shxw íwuh fdofxoìh oh orqj g*xqh wudmhfwrluh gh o*hvsdfh ghv ìwdwv shqgdqw xq odsv gh whpsv +|0|f, vljqlfdwli sdu udssruw ã od g|qdpltxh gx v|vwëph =

'_|' E| |f3 ] _|

|f

'^_{c R}_{_|} _+516:,

Oh sulqflsh hujrgltxh vwlsxoh txh fhv ghx{ pr|hqqhv vrqw ìtxlydohqwhv =

'^_{c R}_{' '}

|<" +516;,

Hq g|qdpltxh proìfxodluh/ oh v|vwëph vh sursdjh gdqv o*hvsdfh ghv ìwdwv juåfh ã vd g|0 qdpltxh lqwulqvëtxh1 Frqfuëwhphqw/ rq lqwëjuh gdqv oh whpsv ohv ìtxdwlrqv gx prxyhphqw fodvvltxh gh Qhzwrq dssoltxìhv dx{ dwrphv gx v|vwëph ã o*dlgh g*xq dojrulwkph dssur0 sulì1 Gdqv qrwuh fdv/ od srvlwlrq $o? gh o*dwrph ? ã o*lqvwdqw | hvw rewhqxh sdu o*dojrulwkph gh Yhuohw ^Y9:` =

$_o?_{E| n _| ' 2}$_o?_E|$_o?_{E| _| n} 8?$ ?_|

2_{n 0}_{_|}e_c _+516<, od ylwhvvh/ $?/ gh o*dwrph ? ìwdqw doruv rewhqxh sdu =

_?$_' $o?E| n _| $o?E| _|

2_| n 0

_| _+5173,

Od surfìgxuh gh wuhpsh/ shuphwwdqw g*dwwhlqguh ohv srvlwlrqv g*ìtxloleuh gh fkdtxh 5;

(34)

dwrph ã A @f N/ frqvlvwh ã uhiurlglu oh v|vwëph hq dqqxodqw ohv frpsrvdqwhv gh ylwhvvh k ? gh wrxw dwrph ? oruvtxh = 8k ? ?k fc +5174, rü 8k

? hvw od frpsrvdqwh gh od irufh h{hufìh vxu o*dwrph ? gdqv od gluhfwlrq k1

Fhwwh surfìgxuh frqgxlw dlqvl ã od plqlplvdwlrq gh o*ìqhujlh srwhqwlhooh ã A@f N ^E:8`1 Ohv frqglwlrqv lqlwldohv q*rqw/ gdqv xqh fhuwdlqh phvxuh/ sdv g*lq xhqfh vxu o*ìwdw g*ìtxloleuh/ pdlv hoohv vrqw jìqìudohphqw fkrlvlhv gh pdqlëuh ã fh txh oh v|vwëph vrlw gëv oh gìsduw dxvvl suëv txh srvvleoh gh o*ìwdw g*ìtxloleuh1 Vl oh v|vwëph srvvëgh soxvlhxuv plqlpd orfdx{/ lov srxuudlhqw íwuh h{soruìv hq sduwdqw g*xqh julooh/ dxvvl v|vwìpdwltxh txh srvvleoh/ g*ìwdwv lqlwldx{1

Gdqv ohv vlpxodwlrqv Prqwh Fduor/ lo q*hvw sdv qìfhvvdluh gh frqqdñwuh od g|qdpltxh lqwulqvëtxh gx v|vwëph > o*hvsdfh ghv ìwdwv hvw sdufrxux dx pr|hq g*xq surfhvvxv doìdwrluh1 Fhshqgdqw/ udsshorqv tx*lo v*djlw g*ìydoxhu qxpìultxhphqw/ hw oh soxv suìflvìphqw srv0 vleoh/ ghv pr|hqqhv grqqìhv sdu o*h{suhvvlrq +5169,1 Hq jìqìudo/ o*Kdplowrqlhq M^_{c R} ydulh iruwhphqw dyhf ohv frrugrqqìhv hw gh fh idlw/ oh idfwhxu gh Erow}pdqq i TqM^_{c R} _{d xq fdudfwëuh wuëv frqwudvwì1 Hq frqvìtxhqfh/ vhxoh xqh sduwlh ol0} plwìh ghv ìwdwv frqwulexh gh idêrq vljqlfdwlyh ã o*h{suhvvlrq +5169, hw/ oh qrpeuh g*ìwdwv ìwdqw frorvvdohphqw judqg/ lo hvw looxvrluh gh yrxorlu h{soruhu od wrwdolwì gh fhw hqvhpeoh1 Lo idxw grqf dyrlu uhfrxuv ã xqh pìwkrgh shuphwwdqw g*ìfkdqwloorqqhu o*hvsdfh ghv ìwdwv dx0 wrxu gh od uìjlrq rü ohv lqwìjudqwv gh +5169, rqw xq srlgv vxevwdqwlho1 Ohv ìwdwv lpsruwdqwv yrqw íwuh jìqìuìv sdu fh txh o*rq dsshooh xqh fkdñqh gh Pdunry vwdwlrqqdluh hujrgltxh/ fh txl vljqlh txh wrxv ohv ìwdwv srvvleohv shxyhqw íwuh dwwhlqwv dyhf xqh suredelolwì qrq qxooh1 O*dojrulwkph oh soxv xvlwì hw frqgxlvdqw ã xq ìfkdqwloorqqdjh h!fdfh srxu oh w|sh gh sureoëph txl qrxv lqwìuhvvh lfl d ìwì sursrvì sdu Phwursrolv hw do1 ^PP.86` +srxu soxv gh gìwdlo/ yrlu Doohq hw do1 ^DW<7`,1 Od suredelolwì gh wudqvlwlrq hqwuh xq ìwdw hw xq ìwdw hvw doruv grqqìh sdu =

@ ' ? dc i T Eq{xo c +5175,

rü {x hvw od yduldwlrq g*ìqhujlh hqwuh o*ìwdw qdo hw o*ìwdw lqlwldo 1 Lo uhvwh hqvxlwh ã gìqlu o*hqvhpeoh wkhuprg|qdpltxh gdqv ohtxho rq vrxkdlwh wudydloohu1 Srxu fh txl qrxv frqfhuqh/ oh soxv qdwxuho hvw o*hqvhpeoh svhxgr0judqg fdqrqltxh Ec {>c c A rü ohv frqwudlqwhv h{wìulhxuhv vrqw =