ANNEXE IV

FONCTION DE TOURNARIE

La fonction de Tournarie $T(x)$ est définie ci-dessous pour $0 < x < 1$
$(T(x) = T(1-x))$ (d'après la Thèse de TOURNARIE, Paris, 1959) :

<figure><img src="image_44.png" /></figure>

<table><thead><tr><th>40 x</th><th>T(x)</th><th>40 x</th><th>T(x)</th></tr></thead><tbody><tr><td>0</td><td>1</td><td></td><td></td></tr><tr><td>1</td><td>0,999999</td><td>11</td><td>0,902570</td></tr><tr><td>2</td><td>0,999982</td><td>12</td><td>0,869477</td></tr><tr><td>3</td><td>0,999802</td><td>13</td><td>0,834400</td></tr><tr><td>4</td><td>0,998935</td><td>14</td><td>0,791630</td></tr><tr><td>5</td><td>0,996528</td><td>15</td><td>0,746528</td></tr><tr><td>6</td><td>0,991527</td><td>16</td><td>0,689910</td></tr><tr><td>7</td><td>0,982960</td><td>17</td><td>0,649790</td></tr><tr><td>8</td><td>0,970900</td><td>18</td><td>0,599980</td></tr><tr><td>9</td><td>0,953040</td><td>19</td><td>0,560780</td></tr><tr><td>10</td><td>0,930555</td><td>20</td><td>0,500000</td></tr></tbody></table>
<figure><img src="image_45.png" /></figure>
BIBLIOGRAPHIE

Pages

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      <td>J. KRUGER, G.G. LONG, M. KURIYAMA, I. GOLDMAN<br>"Ex-situ and in-situ sample and detector chambers for the study of passive films using surface EXAFS"<br>"Passivity of Metals and Semiconductors", M. Froment Ed., p.163, Elsevier, Amsterdam (1983).</td>
      <td>21,86,87</td>
    </tr>
    <tr>
      <td>[101]</td>
      <td>L. BOSIO, R. CORTES, A. DEFRAIN, M. FROMENT<br>"EXAFS from measurements of X-ray reflectivity on passivated electrodes"<br>J. Electroanal. Chem., <u>180</u>, 265 (1984).</td>
      <td>21,87</td>
    </tr>
    <tr>
      <td>[102]</td>
      <td>A.M. PRITECHARD, C.M. DOBSON<br>"Mössbauer spectra of passivated iron surfaces"<br>Chem. Phys. Lett., <u>23</u>, 514 (1973).</td>
      <td>21,24</td>
    </tr>
    <tr>
      <td>[103]</td>
      <td>G.W. SIMMONS, E. KELLERMAN, H. LEIDHEISER Jr<br>"In-situ studies of the passivation and anodic oxidation of cobalt by emission Mössbauer spectroscopy : I. Theoretical background, experimental methods, and experimental results for borate solution (pH 8.5)"<br>J. Electrochem. Soc., <u>123</u>, 1276 (1977).</td>
      <td>21,24</td>
    </tr>
  </tbody>
</table>
[104] W.E.O'GRADY
"Mössbauer study of the passive oxide film on iron"
J. Electrochem. Soc., 127, 555 (1980). 21,24,27,84

[105] M. MEISEL, H.J. CUTTEMANN, P. GUTLICH
"The influence of phosphoric acid on steel and its
corrosion products: A Mössbauer spectroscopic approach"
Corros. Sci., 23, 1373 (1983). 21,24

[106] L. TRANSTAD
"The investigation of thin surface films on metals by
means of reflected polarized light"
Trans. Faraday Soc., 29, 502 (1933). 20

[107] B.D. CAHAN, W.J. HORKANS, E. YEAGER
"Modulation ellipsometry and its application to the
study of the electrode-electrolyte interface"
Surf. Sci., 37, 559 (1973). 22

[108] W.J. HORKANS, B.D. CAHAN, E. YEAGER
"Electrode potential scanning ellipsometric spectroscopy.
Study of the formation of anodic oxide film on
noble metals"
Surf. Sci., 46, 1 (1974). 22

[109] B.D. CAHAN
"Implication of three parameter solutions to the three
layer models"
Surf. Sci., 56, 354 (1976). 22

[110] J.L. ORD, D.J. DESMET
"Correlation between ellipsometric and electrical
measurements on passive iron"
J. Electrochem. Soc., 113, 1259 (1966). 22

[111] J. KRUGER, J.P. CALVERT
"Ellipsometric-potentiostatic studies of iron
passivity - I. Anodic film growth in slightly basic
solution"
J. Electrochem. Soc., 114, 43 (1967). 22

[112] R.D. ARMSTRONG
"The dissolution-precipitation model of passivation"
J. Electroanal. Chem., 28, 221 (1970). 25

[113] R. CALSON, M. FROMENT
"Sur l'identification des substances formées au cours
de la polarisation anodique du nickel"
C.R. Acad. Sci. Paris, 268, 1197 (1969). 26

[114] G. BLONDEAU, M. FROELICHER, M. FROMENT, A. HUGOT-LE GOFF
"Etude des propriétés de films anodiques poreux de
type NiOxSy"
Phys. Stat. Sol. (a), 26, 181 (1974). 26
[115] R.L. COWAN, R.W. STAEHLE
"The thermodynamics and electrode kinetic behavior of nickel in acid solution in the temperature range 25° to 300°C"
J. Electrochem. Soc., 118, 557 (1971). 26

[116] C.L. FOLEY, J. KRUGER, C.J. BECHTOLD
"Electron diffraction studies of active, passive and transpassive oxides films on iron"
J. Electrochem. Soc., 114, 994 (1967). 26

[117] J.W. SCHULTZE
"Electron transfer reactions on passive films"
"Passivity of Metals", R.P. Frankenthal and J. Kruger
Eds., p.82, The Electrochem. Soc. Inc., N.J. (1978). 26

[118] K. KURODA, B.D. CAHAN, Gh. NAZRI, E. YEAGER, T.E. MITCHELL
"Electron diffraction study of the passive film on iron"
J. Electrochem. Soc., 129, 2163 (1982). 26

[119] M.C. BLOOM, L. GOLDENBERG
"γ-Fe₂O₃ and the passivity of iron"
Corros. Sci., 5, 623 (1965). 26

[120] G. OKAMOTO, T. SHIBATA
"Stability of passive stainless steel in relation to the potential of passivation treatment"
Corros. Sci., 10, 371 (1970). 27,108,109

[121] H.G. FELLER, H.J. RATZER-SCHEIBE, W. WENDT
"Anodic dissolution of Ni in 1N H₂SO₄ studied by dynamic impedance measurements"
Electrochim. Acta, 17, 187 (1972). 27,46

[122] J. NEWMAN
"Current distribution on a rotating disk below the limiting current"
J. Electrochem. Soc., 113, 1235 (1966). 30

[123] G.G. SUSBIELLES, P. DELAHAY
"Relaxation of electrode processes with simultaneous consideration of double-layer charging and faradaic current. Part II"
J. Electroanal. Chem., 17, 289 (1968). 30

[124] J.V. WHITE
"The representation of non linear systems by exhaustive linearization"
Proc. IEEE, 59, 98 (1971). 31
<table>
  <tbody>
    <tr>
      <td>[125]</td>
      <td>M. KEDDAM, H. TAKENOUTI, N. YU<br>"Influence of cristallographic orientation on kinetics of transpassive dissolution of Ni in sulfate acid media"<br>166th Meeting of the Electrochemical Society of America: New Orleans, Extended Abstracts, Vol.84-2, p.264 (1984).</td>
      <td>36</td>
    </tr>
    <tr>
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      <td>C.J. MAUVAIS, R.M. LATANISION, A.W. RUFF Jr<br>"On the anisotropy observed during the passivation of nickel monocrystals"<br>J. Electrochem. Soc., 117, 902 (1970).</td>
      <td>36</td>
    </tr>
    <tr>
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      <td>M. KEDDAM, H. TAKENOUTI, N. YU<br>"Transpassive dissolution of Ni in acidic sulfate media : A kinetic model"<br>J. Electrochem. Soc., 132, 2561 (1985).</td>
      <td>38,81,84</td>
    </tr>
    <tr>
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      <td>N. SATO, G. OKAMOTO<br>"Kinetics of the anodic dissolution of nickel in sulfuric acid solutions"<br>J. Electrochem. Soc., 111, 897 (1964).</td>
      <td>38</td>
    </tr>
    <tr>
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      <td>I. EPELBOIN, C. GABRIELLI, M. KEDDAM, H. TAKENOUTI<br>"The study of the passivation process by the electrode impedance analysis"<br>"Comprehensive Treatise of Electrochemistry", J.O'M. Bockris, B.E. Conway, E. Yeager and R.E. White Eds., p.151, Plenum, N.Y. (1981).</td>
      <td>41,47</td>
    </tr>
    <tr>
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      <td>C. GABRIELLI<br>"Identification of Electrochemical Processes by Frequency Response Analysis"<br>Solartron Instruments (1984).</td>
      <td>47</td>
    </tr>
    <tr>
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      <td>I. EPELBOIN, M. KEDDAM<br>"Faradaic Impedances : diffusion impedance and reaction impedance"<br>J. Electrochem. Soc., 117, 1052 (1970).</td>
      <td>47</td>
    </tr>
    <tr>
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      <td>I. EPELBOIN, M. KSOURI, R. WIART<br>"Kinetics of zinc electrocrystallization with the deposit morphology"<br>Faraday Disc. Chem. Soc., 12, 115 (1978).</td>
      <td>46,47</td>
    </tr>
    <tr>
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      <td>M. KEDDAM, O.R. MATTOS, H. TAKENOUTI<br>"Reaction model for iron dissolution studied by electrode impedance. II. Determination of the reaction model"<br>J. Electrochem. Soc., 128, 266 (1981).</td>
      <td>46,47,49</td>
    </tr>
    <tr>
      <td>[134]</td>
      <td>C.V. RAMAN<br>"A new radiation"<br>Indian J. Phys., 2, 387 (1928).</td>
      <td>70</td>
    </tr>
  </tbody>
</table>
[135] C. LANDSBERG, L. MANDELSTAM
"Eine neue Erscheinung bei der Lichtjerstenuung in krystalten"
Naturwiss, 16, 557 (1928). 70

[136] D.L. JEANMAIRE, R.P. VAN DUYNE
"Surface Raman spectroelectrochemistry. Part I : Heterocyclic, aromatic and aliphatic amines adsorbed on the anodized silver electrode"
J. Electroanal. Chem., 84, 1 (1977). 71

[137] N.G. ALBRECHT, J.A. CREIGHTON
"Anomalously intense Raman spectra of pyridine at a silver electrode"
J. Am. Chem. Soc., 99, 5215 (1977). 71

[138] E.B. WILSON Jr, J.C. DECIUS, P.C. CROSS
"Molecular Vibration"
Mc Graw Hill, N.Y. (1955). 73

[139] P. DELICHERE, A. HUGOT-LE GOFF, N. YU
"Identification by in-situ Raman spectroscopy of the films grown during the polarization of nickel in sulfuric solutions"
J. Electrochem. Soc., 133, 2106 (1986). 76

[140] K. CARR, S. XU, C.A. MELENDRES
"Laser Raman spectroelectrochemical studies on the corrosion and passivation behavior of nickel in aqueous solutions"
Extended Abstracts, I.S.E. 36th Meeting, Salamanca (Spain) (1985). 81

[141] H.P. BOEHM
"Acidic and basic properties of hydroxylated metal oxide surfaces"
Disc. Faraday Soc., 52, 264 (1971). 83

[142] K. CARR, S. BAER, C.A. MELENDRES
"On the composition of anodic corrosion films on nickel in the region of secondary passivity"
Corros. Sci., 42, 307 (1986). 84

[143] E.A. STERN
"Extended X-ray absorption fine structure (EXAFS) and its application to surface structure"
J. Vac. Sci. Technol., 14, 461 (1977). 86

[144] J. STOHR, L. JOHANNSON, L. LINDAU, P. PIANETTA
"Extended X-ray absorption fine structure studies of low-Z atoms in solid and on surface : Studies of $Si_3N_4$, $SiO_2$ and oxygen on Si (111)"
Phys. Rev. B, 20, 664 (1979). 86
<table>
  <tbody>
    <tr>
      <td>[145]</td>
      <td>G. MARTENS, P. RABE, G. TOLKIEHN, A. WERNER<br>"EXAFS in photoelectron yield spectra at K edge of Cu,<br>Ni and Ge"<br>Phys. Stat. Sol. (a), 55, 105 (1979).</td>
      <td>86</td>
    </tr>
    <tr>
      <td>[146]</td>
      <td>P.H. CITRIN, P. EISENBERGER, R.C. HEWITT<br>"Extended X-ray absorption of surface atoms on single-crystal substrates: Iodine absorbed on Ag(111)"<br>Phys. Rev. Lett., 41, 309 (1978).</td>
      <td>86</td>
    </tr>
    <tr>
      <td>[147]</td>
      <td>J.A. DEL CUETO, N.J. SHEVSHIK<br>"EXAFS of ultra thin layers of Cu"<br>J. Phys. C, Solid State Phys., 11, L833 (1978).</td>
      <td>86</td>
    </tr>
    <tr>
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      <td>R. BARCHERVITZ, M. CREMONESE-VISICATO, G. ONDRI<br>"X-ray photoabsorption of solids by specular reflection"<br>J. Phys. C, 11, 4439 (1978).</td>
      <td>86</td>
    </tr>
    <tr>
      <td>[149]</td>
      <td>R. FOX, S.J. GURMAN<br>"EXAFS and surface EXAFS from measurement of X-ray reflection"<br>J. Phys. C, 13, L249 (1980).</td>
      <td>86</td>
    </tr>
    <tr>
      <td>[150]</td>
      <td>G. MARTENS, P. RABE<br>"The extended X-ray absorption fine structure in the reflectivity at the K edge of Cu"<br>J. Phys. C, 14, 1523 (1981).</td>
      <td>86</td>
    </tr>
    <tr>
      <td>[151]</td>
      <td>L.BOSIO, R.CORTES, A.DEFRAIN, M.FROMENT, A.M.LEBRUN<br>"EXAFS as probe of the passive film structure"<br>"Passivity of Metals and Semiconductors", M. Froment<br>Ed., p.131, Elsevier, Amsterdam (1984).</td>
      <td>86</td>
    </tr>
    <tr>
      <td>[152a]</td>
      <td>R. DEL KRONIG<br>"Zur Theorie der Feinstrukture in den Röntgen Absorptionssepektien"<br>Z. Phys., 70, 317 (1931).</td>
      <td>88</td>
    </tr>
    <tr>
      <td>[152b]</td>
      <td>R. DEL KRONIG<br>"Zur Theorie der Feinstrukture in den Röntgen Absorptionssepektien. II"<br>Z. Phys., 15, 191 (1932).</td>
      <td>88</td>
    </tr>
    <tr>
      <td>[153a]</td>
      <td>E.A. STERN<br>"Theory of the extended X-ray absorption fine structure"<br>Phys. Rev. B, 10, 3027 (1974).</td>
      <td>88</td>
    </tr>
    <tr>
      <td>[153b]</td>
      <td>F.W. LYTHE, D.E. SAYERS, E.A. STERN<br>"Extended X-ray absorption fine structure technique. II. Experimental practice and selected results"<br>Phys. Rev. B, 11, 4825 (1975).</td>
      <td>88</td>
    </tr>
  </tbody>
</table>
<table>
  <tbody>
    <tr>
      <td>[153c]</td>
      <td>E.A. STERN, D.E. SAYERS, F.W. LYTHE<br>"Extended X-ray absorption fine structure technique.<br>III. Determination of physical parameters"<br>Phys. Rev. B, 11, 4836 (1975).</td>
      <td>88</td>
    </tr>
    <tr>
      <td>[154]</td>
      <td>P. EISENBERGER, G.S. BROWN<br>"The study of disordered systems by EXAFS : Limitations"<br>Solid. State Comm., 29, 481 (1979).</td>
      <td>88</td>
    </tr>
    <tr>
      <td>[155]</td>
      <td>P.H. CITRIN, P. EISENBERGER, B.M. KINCAID<br>"Transferability at phase shifts in extended X-ray<br>absorption fine structure"<br>Phys. Rev. Lett., 36, 1346 (1976).</td>
      <td>90, 101</td>
    </tr>
    <tr>
      <td>[156]</td>
      <td>B.K. TEO, P.A. LEE, A.L. SIMONS, P. EISENBERGER,<br>B.M. KINCAID<br>"Approximation, parameterization and chemical<br>transferability of amplitude functions"<br>J. Am. Chem. Soc., 99, 3854 (1977).</td>
      <td>90, 101</td>
    </tr>
    <tr>
      <td>[157]</td>
      <td>B.K. TEO, P.A. LEE<br>"Ab initio calculation of amplitude and phase function<br>for extended X-ray absorption fine structure spectroscopy"<br>J. Am. Chem. Soc., 101, 2815 (1979).</td>
      <td>90</td>
    </tr>
    <tr>
      <td>[158]</td>
      <td>G. MARTENS, P. RABE<br>"EXAFS studies on superficial regions by means of<br>total reflection"<br>Phys. Stat. Sol. (a), 58, 415 (1980).</td>
      <td>91</td>
    </tr>
    <tr>
      <td>[159]</td>
      <td>J.G. PARRATT<br>"Surface studies of solids by total reflection of<br>X-ray"<br>Phys. Rev., 95, 359 (1954).</td>
      <td>91, 93</td>
    </tr>
    <tr>
      <td>[160]</td>
      <td>WINICK and DONIACH, Eds.<br>"Synchrotron Radiation Research"<br>Plenum, N.Y. (1980).</td>
      <td>96</td>
    </tr>
    <tr>
      <td>[161]</td>
      <td>J.GOULON, M.LEMONNER, R.CORTES, A.RETOURNARD, D.RAOUX<br>"Development of a new energy scanned (4-20keV) EXAFS<br>II spectrometer at LURE"<br>Nucl. Instr. Method, 208, 625 (1983).</td>
      <td>96</td>
    </tr>
    <tr>
      <td>[162]</td>
      <td>P.A. LEE, P.H. CITRIN, P. EISENBERGER, B.M. KINCAID<br>"Extended X-ray absorption fine structure - its<br>strengths and limitations as a structural tool"<br>Rev. Mod. Phys., 53, 769 (1981).</td>
      <td>99</td>
    </tr>
    <tr>
      <td>[163]</td>
      <td>J.B.A.D. VAN ZON, D.C. KONINGSBERGER,<br>H.F.J. VAN'T BLICK, D.E. SAYERS<br>"An EXAFS study of the structure of metal-support<br>interface in highly dispersed Rh/Al<sub>2</sub>O<sub>3</sub> catalysis"<br>J. Chem. Phys., 82, 5742 (1985).</td>
      <td>99</td>
    </tr>
  </tbody>
</table>
[164] P.A. LEE, G. BENI
"A new method for the calculation of atoms phase shifts: Application to extended X-ray absorption fine structure (EXAFS) in molecules and crystals"
Phys. Rev. B, 15, 2862 (1977). 99

[165] D. RAOUX, J. PETIAU, P. BONDOT, G. CALAS, A. FONTAINE, P. LAGARDE, P. LEVITZ, G. LOUPIAS, A. SADOC
"L'EXAFS appliqué aux déterminations structurales de milieux désordonnés"
Revue Phys. Appl., 15, 1079 (1980). 103

[166] B. LENGELER, R. ZELLER
"X-ray absorption near edge structure of nickel hydride"
Solid State Comm., 51, 889 (1984). 105

[167] M. CRESPIN, P. LEVITZ, L. GATINEAU
"Reduced forms of LaNi<sub>3</sub> Perovskite. Part I. Evidence for new phases: La<sub>2</sub>Ni<sub>2</sub>O<sub>5</sub> and LaNi<sub>2</sub>"
J. Chem. Soc. Faraday Trans., 2, 1181 (1983). 105

[168] B. LENGELER
"Applications of X-ray absorption spectroscopy in materials science : status and new trends"
Z. Phys. B, 61, 421 (1985). 105

[169] A.J.C. WILSON, Ed.
"Structure Reports"
N.V.A. OOSTHOEK'S SUUITGEVERS MIT UTRECHT, Vol.13 (1950). 107

[170] Y. FARGE
"Le rayonnement synchrotron et ses applications diverses en physique, chimie et biologie"
J. de Physique, 36, C7-17 (1975). 107

[171] G. BLONDEAU, M. FROELICHER, M. FROMENT, A. HUGOT-LE GOFF
C. VIGNAUD
"Disappearance of nickel passivity through the introduction of foreign elements in the oxide cristallographic lattice"
"Passivity of Metals", R.P. Frankenthal and J. Kruger Eds., p.844, The Electrochem. Soc. Inc., N.J. (1978). 108

[172] L. BOSIO, R. CORTES, P. DELICHERE, M. FROMENT, A. HUGOT-LE GOFF, N. YU
"Identification of thin films grown on nickel polarized in sulfuric solutions"
Comm. 37th Meeting of I.S.E., Vilnius (URSS) (1986). 103
<figure><img src="image_46.png" /></figure>