P. Goodman and A. F. Moodie, -beam wave functions in electron scattering by the multi-slice method, Acta Crystallographica Section A, vol.30, issue.2, p.280, 1974.
DOI : 10.1107/S056773947400057X

URL : https://hal.archives-ouvertes.fr/in2p3-00706858

D. Van-dyck, The path integral formalism as a new description for the diffraction of high-energy electrons in crystals, physica status solidi (b), vol.30, issue.1, pp.321-336, 1975.
DOI : 10.1002/pssb.2220720135

D. Van-dyck, Fast computational procedures for the simulation of structure images in complex or disordered crystals: a new approach, Journal of Microscopy, vol.52, issue.1, pp.141-152, 1980.
DOI : 10.1111/j.1365-2818.1980.tb04084.x

D. Gratias and R. Portier, Time-like perturbation method in high-energy electron diffraction, Acta Crystallographica Section A Foundations of Crystallography, vol.39, issue.4, pp.576-584, 1983.
DOI : 10.1107/S0108767383001105

D. Van-dyck, Real space treatment of electron diffraction in crystals, 1987.

D. Van-dyck, In Microscopia elettronica in trasmissione e tecniche di analisi di superfici nelle scienza dei materialli, Parte B : Microscopia elletronica in trasmissione, 1989.

D. Van-dyck, In Electron microscopy in material science, page 193, 1992.

S. Amelinckx, D. Van-dyck, C. J. Humphreys, and E. Bithell, Voir aussi dans le même livre la contribution de, Electron diffraction techniques, 1993.

Z. L. Wang, Elastic and Inelastic Scattering in Electron Diffraction and Imaging, 1995.
DOI : 10.1007/978-1-4899-1579-5

J. M. Cowley, Diffraction Physics, 1981.

K. Kambe, G. Lehmpfuhl, and F. Fujimoto, Interpretation of electron channeling by the dynamic theory of electron diffraction, Z. Naturforsch, vol.29, p.1034, 1974.

F. Fujimoto, Periodicity of crystal structure images in electron microscopy with crystal thickness, Physica Status Solidi (a), vol.1, issue.1, p.99, 1978.
DOI : 10.1002/pssa.2210450110

B. F. Buxton, J. E. Loveluck, and J. W. Steeds, Bloch waves and their corresponding atomic and molecular orbitals in high energy electron diffraction, Philosophical Magazine A, vol.73, issue.3, pp.259-278, 1978.
DOI : 10.1080/01418617808239233

K. Kambe, Visualization of bloch waves of high energy electrons in high resolution electron microscopy, Ultramicroscopy, vol.10, issue.3, pp.223-228, 1982.
DOI : 10.1016/0304-3991(82)90042-0

D. Van-dyck, J. Danckaert, W. Coene, E. Selderslaghs, and D. Broddin, The atomic column approximation in dynamical electron diffraction calculation, Computer simulation of electron microscope diffraction and images, page 107. édité par W. Krakow et M. O'Keefe (The Mineral, Metals and Materials Society, 1989.

J. M. Cowley and A. F. Moodie, The scattering of electrons by atoms and crystals. I. A new theoretical approach, Acta Crystallographica, vol.10, issue.10, p.609, 1957.
DOI : 10.1107/S0365110X57002194

K. Ishizuka and N. Uyeda, A new theoretical and practical approach to the multislice method, Acta Crystallographica Section A, vol.33, issue.5, pp.740-749, 1977.
DOI : 10.1107/S0567739477001879

K. Ishizuka, Multislice formula for inclined illumination, Acta Crystallographica Section A, vol.38, issue.6, pp.773-779, 1982.
DOI : 10.1107/S0567739482001594

D. Van-dyck, High-Speed computation techniques for the simulation of high resolution electron micrographs, Journal of Microscopy, pp.31-42, 1982.

D. Van-dyck and W. Coene, The real space method for dynamical electron diffraction calculations in high resolution electron microscopy, Ultramicroscopy, vol.15, issue.1-2, pp.29-40, 1984.
DOI : 10.1016/0304-3991(84)90072-X

W. Coene and D. Van-dyck, The real space method for dynamical electron diffraction calculations in high resolution electron microscopy, Ultramicroscopy, vol.15, issue.1-2, pp.41-50287, 1984.
DOI : 10.1016/0304-3991(84)90073-1

A. F. De-jong, W. Coene, and D. Van-dyck, On the phase-object function, used in dynamical electron diffraction calculations, Ultramicroscopy, vol.23, issue.1, pp.3-16, 1987.
DOI : 10.1016/0304-3991(87)90222-1

A. J. Metherell, Diffraction of electrons by perfect crystals, In Electron Microscopy in Material Science, 1975.

F. N. Chukhovskii and V. L. Vergasov, Physical and mathematical foundations of multiwave electron diffraction, Acta Crystallographica Section A Foundations of Crystallography, vol.46, issue.3, pp.153-165, 1990.
DOI : 10.1107/S010876738900735X

P. G. Self, M. A. O-'keefe, P. R. Buseck, and A. E. Spargo, Practical computation of amplitudes and phases in electron diffraction, Ultramicroscopy, vol.11, issue.1, pp.35-52, 1983.
DOI : 10.1016/0304-3991(83)90053-0

P. A. Stadelmann, EMS - a software package for electron diffraction analysis and HREM image simulation in materials science, Ultramicroscopy, vol.21, issue.2, p.131, 1987.
DOI : 10.1016/0304-3991(87)90080-5

F. Ducastelle, Order and Phase Stability in Alloys, 1991.
DOI : 10.1007/978-3-642-84968-8_14

A. Howie-amelinckx, R. Gevers, and G. , The theory of high energy electron diffraction, Modern Diffraction and Imaging Techniques in Material Science, 1970.

P. A. Dirac, The Principles of Quantum Mechanics Première édition 1930, quatrième édition (révisée), 1967.

K. Fujiwara, Relativistic Dynamical Theory of Electron Diffraction, Journal of the Physical Society of Japan, vol.16, issue.11, p.2226, 1961.
DOI : 10.1143/JPSJ.16.2226

K. Watanabe, Y. Kikuchi, K. Hiratsuka, and H. Yamagushi, -beam dynamical calculations, Acta Crystallographica Section A Foundations of Crystallography, vol.46, issue.2, pp.94-98, 1990.
DOI : 10.1107/S0108767389010135

URL : https://hal.archives-ouvertes.fr/in2p3-00310862

A. Messiah, Mécanique quantique, 1959.

I. Leonard and . Schiff, quantum mechanics. McGraw-Hill International Edition, 1968.

C. Tannoudji, Mécanique quantique, 1975.

P. A. Doyle and P. S. Turner, Relativistic Hartree???Fock X-ray and electron scattering factors, Acta Crystallographica Section A, vol.24, issue.3, p.390, 1968.
DOI : 10.1107/S0567739468000756

G. H. Smith and R. E. Burge, The analytical representation of atomic scattering amplitudes for electrons, Acta Crystallographica, vol.15, issue.3, p.182, 1962.
DOI : 10.1107/S0365110X62000481

M. Op-de-beeck, Direct Structure Reconstruction in High Resolution Transmission Electron Microscopy, 1994.

W. Neil, N. Ascroft, and . David-mermin, Solid State Physics, 1976.

J. M. Ziman, Theory of Solids, 1972.

A. Walter and . Harrison, Solid State Theory, 1979.

A. Weickenmeier and H. Kohl, Computation of absorptive form factors for high-energy electron diffraction, Acta Crystallographica Section A Foundations of Crystallography, vol.47, issue.5, pp.590-597, 1991.
DOI : 10.1107/S0108767391004804

M. Cornier-quiquandon, Théorie dynamique de la diffraction des électrons rapides par les cristaux et quasi-cristaux, 1988.

J. W. Steeds, P. M. Jones, J. E. Loveluck, and K. Cooke, The dependence of zone axis patterns on string integrals or the number of bound states in high energy electron diffraction, Philosophical Magazine, vol.1, issue.2, pp.309-322, 1977.
DOI : 10.1080/14786437508228097

J. F. Cornwell, Group Theory and Electronic Energy Bands in Solids, 1969.

A. W. Joshi, Elements of Group Theory for Physicists, 1982.

A. Nikiforov and V. Ouvarov, Eléments de la théorie des fonctions spéciales, Editions Mir, 1976.

G. Caloz, Equations différentielles ordinaires et aux dérivées partielles : théorie et méthodes numériques Notes de cours éditées par G, 1987.

D. Gratias, M. Cornier, and R. Portier, Symmetries and beam reduction in the matrix formulation of the dynamical theory of fast electrons, Acta Crystallographica Section A Foundations of Crystallography, vol.44, issue.6, pp.789-798, 1988.
DOI : 10.1107/S0108767388003721

P. L. Fejes, S. Ijima, and J. M. Cowley, Periodicity in thickness of electron-microscope crystal-lattice images, Acta Crystallographica Section A, vol.29, issue.6, p.710, 1973.
DOI : 10.1107/S0567739473001737

J. Thibault, Haute Résolution en microscopie électronique : visualisation des structures cristallines, Thèse de doctorat de l'université scientifique et médicale de Grenoble, 1977.

J. L. Rouvière, Structure atomique des joints de grains de flexion d'axe < 001 > dans le Silicium et le Germanium, Thèse de doctorat de l'université Joseph Fourier-Grenoble I, 1977.

P. Schwander, C. Kisielowski, M. Seibt, F. H. Baumann, Y. Kim et al., Mapping projected potential, interfacial roughness, and composition in general crystalline solids by quantitative transmission electron microscopy, Physical Review Letters, vol.71, issue.25, p.4150, 1993.
DOI : 10.1103/PhysRevLett.71.4150

C. Kisielowski, P. Schwander, F. H. Baumann, M. Seibt, Y. Kim et al., An approach to quantitative high-resolution transmission electron microscopy of crystalline materials, Ultramicroscopy, vol.58, issue.2, 1995.
DOI : 10.1016/0304-3991(94)00202-X

C. Herring, A New Method for Calculating Wave Functions in Crystals, Physical Review, vol.57, issue.12, p.1169, 1940.
DOI : 10.1103/PhysRev.57.1169

A. Walter and . Harrison, Electronic Structure and the Properties of Solids, 1988.

C. Barreteau and F. Ducastelle, The orthogonalized plane-wave method applied to the calculation of dynamical effects in electron diffraction, Ultramicroscopy, vol.57, issue.1, pp.11-15, 1995.
DOI : 10.1016/0304-3991(94)00168-M

S. Tochilin and M. J. Whelan, Combined basis algorithm for HREM wave field calculations, Ultramicroscopy, vol.50, issue.3, pp.313-320, 1993.
DOI : 10.1016/0304-3991(93)90199-8

W. H. Press, B. Flannery, S. A. Teukolsky, and W. T. Vetterling, Numerical Recipies, the art of Scientific Computing, 1986.

A. Ourmazd, F. H. Baumann, M. Bode, and Y. Kim, Quantitative chemical lattice imaging: theory and practice, Ultramicroscopy, vol.34, issue.4, pp.237-255, 1990.
DOI : 10.1016/0304-3991(90)90018-H

A. F. De-jong and D. Van-dyck, Composition determination from HREM images of substitutional alloys, Ultramicroscopy, vol.33, issue.4, pp.269-279, 1990.
DOI : 10.1016/0304-3991(90)90044-M

C. Barreteau and F. Ducastelle, Quantitative Transmission Electron Microscopy in Substitutionally Disordered Alloys, Physical Review Letters, vol.75, issue.2, pp.284-287, 1995.
DOI : 10.1103/PhysRevLett.75.284

W. Coene, D. Van-dyck, J. Van-landuyt, and S. Amelinckx, High-resolution structure imaging of partially disordered atomic columns in binary alloy systems, Philosophical Magazine Part B, vol.32, issue.4, pp.415-427, 1987.
DOI : 10.1016/0304-3991(82)90047-X

P. De-meulenaere, D. Van-dyck, G. Van-tandeloo, and J. Van-landuyt, Dynamical electron diffraction in substitutionally disordered column structures, Ultramicroscopy, vol.60, issue.1, 1995.
DOI : 10.1016/0304-3991(95)00040-8

R. Kubo, Generalized Cumulant Expansion Method, Journal of the Physical Society of Japan, vol.17, issue.7, p.1100, 1962.
DOI : 10.1143/JPSJ.17.1100

A. Ourmazd, D. Taylor, J. Cunningham, and C. W. Tu, Chemical Mapping of Semiconductor Interfaces at Near-Atomic Resolution, Physical Review Letters, vol.62, issue.8, p.933, 1989.
DOI : 10.1103/PhysRevLett.62.933

J. M. Pénisson, Detection of substitutional atoms in a ????? phase by high-resolution electron microscopy, Ultramicroscopy, vol.51, issue.1-4, pp.264-269, 1993.
DOI : 10.1016/0304-3991(93)90152-N

D. Shindo and M. Hirabayashi, Dynamical diffraction effects on high-resolution electron microscopy of ordered alloys, Acta Crystallographica Section A Foundations of Crystallography, vol.44, issue.6, pp.954-960, 1988.
DOI : 10.1107/S0108767388007408

J. Gjønnes, The influence of Bragg scattering on inelastic and other forms of diffuse scattering of electrons, Acta Crystallographica, vol.20, issue.2, pp.240-249, 1966.
DOI : 10.1107/S0365110X66000471

J. M. Cowley and A. P. Pogany, Diffuse scattering in electron diffraction patterns. I. General theory and computational methods, Acta Crystallographica Section A: Crystal Physics, Diffraction, Theoretical and General Crystallography, vol.24, issue.1, pp.109-116, 1968.
DOI : 10.1107/S0567739468000148

R. Caudron, M. Sarfati, M. Barrachin, A. Finel, F. Ducastelle et al., In situ diffuse scattering of neutrons in alloys and application to phase diagram determination, J. Phys, vol.2, pp.1145-1171, 1992.
URL : https://hal.archives-ouvertes.fr/jpa-00246594

J. M. Pénisson, M. Bode, F. H. Baumann, and A. Ourmazd, Chemical lattice imaging of a Ni-based superalloy, Philosophical Magazine Letters, vol.8, issue.5, pp.269-276, 1991.
DOI : 10.1063/1.97840

C. Barreteau, A. Loiseau, C. Ricolleau, and F. Ducastelle, Weak beam study of antiphase boundaries in Fe-27%Al as a function of temperature, Le Journal de Physique IV, vol.04, issue.C3, pp.65-73, 1994.
DOI : 10.1051/jp4:1994309

URL : https://hal.archives-ouvertes.fr/jpa-00252506

B. Jouffrey and M. Karlík, First attempt towards the direct determination of the Guinier-Preston zones (GP1) copper content in Al-1.7 at % Cu alloy, Microscopy Microanalysis Microstructures, vol.3, issue.2-3, pp.243-257, 1992.
DOI : 10.1051/mmm:0199200302-3024300

J. Dieudonné, Calcul Infinitésimal, 1980.

F. William and . Ames, Numerical Methods for Partial Differential Equations, 1977.