Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

  • Primer
  • Published:

X-ray diffraction under grazing incidence conditions

Nature Reviews Methods Primers volume 4, Article number: 15 (2024) Cite this article

Subjects

Abstract

Material properties frequently relate to structures at or near surfaces, particularly in thin films. As a result, it is essential to understand these structures at the molecular and atomistic levels. The most accurate and widely used techniques for characterizing crystallographic order are based on X-ray diffraction. When dealing with thin films or interfaces, standard approaches, such as single crystal or powder diffraction, are not suitable. However, X-ray diffraction under grazing incidence conditions can provide the required information. In this Primer, grazing incidence X-ray diffraction (GIXD) is comprehensively introduced, starting from basic considerations on X-ray diffraction at crystals with reduced dimensionality and the optical properties of X-rays, followed by a more in-depth description of an experimental performance, including X-ray sources, goniometers and detectors. Experimental errors, limitations and reproducibility are discussed. Various applications, from highly ordered inorganic single crystal surfaces to weakly ordered polymer thin films, are presented to illustrate the potential of GIXD. Data visualizations, representations and evaluation strategies are summarized, based on the example of anthracene thin films. The Primer compiles information relevant to perform high-quality GIXD experiments, evaluate data and interpret results, to extend knowledge about X-ray diffraction from surfaces, interfaces and thin films.

This is a preview of subscription content, access via your institution

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: Real space crystal lattices and their reciprocal space representations.
Fig. 2: Optical properties of the primary X-ray beam.
Fig. 3: Experimental set-ups of a grazing incidence X-ray diffraction experiment.
Fig. 4: Types of thin film samples and exemplary results on anthracene.
Fig. 5: Strain effects at perovskites.
Fig. 6: Crystal truncation rods and Bragg rods.
Fig. 7: Reproducibility and limitations.

Similar content being viewed by others

Data availability

Original data and meta data on the grazing incidence X-ray diffraction (GIXD) studies of anthracene thin films are available via the repository of the Graz University of Technology at https://doi.org/10.3217/8rxt9-jy433.

References

  1. Bennett, D. W. in Understanding Single-Crystal X-Ray Crystallography 497–672 (Wiley-VCH, 2010).

  2. Clegg, W. et al. (eds) Crystal Structure Analysis: Principles and Practice (Oxford Univ. Press, 2009).

  3. David W. I. F., Shankland K., McCusker L. B. & Bärlocher C. (eds) Structure Determination from Powder Diffraction Data (Oxford Univ. Press, 2006).

  4. Bracco G. & Holst B. (eds) Surface Science Techniques (Springer, 2013).

  5. Meyer, E., Bennewitz, R. & Hug, H. J. in Scanning Probe Microscopy (eds Becker, K. H. et al.) 13–46 (Springer Nature, 2021).

  6. Daillant, J. & Giabud, A. (eds) X-Ray and Neutron Reflectivity (Springer, 2009).

  7. Als-Nielsen, J. & McMorrow, D. in Elements of Modern X-ray Physics (Wiley, 2001). This book gives a comprehensive overview on X-ray techniques under specific consideration of surface diffraction of X-rays.

  8. Levine, J. R., Cohen, J. B., Chung, Y. W. & Georgopoulos, P. Grazing-incidence small-angle X-ray scattering: new tool for studying thin film growth. J. Appl. Cryst. 22, 528–532 (1989).

    Article  ADS  CAS  Google Scholar 

  9. Renaud, G., Lazzari, R. & Leroy, F. Probing surface and interface morphology with grazing incidence small angle X-ray scattering. Surf. Sci. Rep. 64, 255–380 (2009).

    Article  ADS  CAS  Google Scholar 

  10. Hexemer, A. & Müller-Buschbaum, P. Advanced grazing-incidence techniques for modern soft-matter materials analysis. IUCrJ 2, 106–125 (2015).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  11. Marra, W. C., Eisenberger, P. & Cho, A. Y. X‐ray total‐external‐reflection–Bragg diffraction: a structural study of the GaAs–Al interface. J. Appl. Phys. 50, 6927–6933 (1979).

    Article  ADS  CAS  Google Scholar 

  12. Eisenberger, P. & Marra, W. C. X-ray diffraction study of the Ge(001) reconstructed surface. Phys. Rev. Lett. 46, 1081–1084 (1981).

    Article  ADS  CAS  Google Scholar 

  13. Pietsch, U., Holy, V. & Baumbach, T. in High-Resolution X-Ray Scattering: From Thin Films to Lateral Nanostructures 143–278 (Springer Science & Business Media, 2004).

  14. Pietsch, U. Investigations of semiconductor surfaces and interfaces by X-ray grazing incidence diffraction. Curr. Sci. 78, 1484–1495 (2000).

    CAS  Google Scholar 

  15. Stangl, J., Holý, V. & Bauer, G. Structural properties of self-organized semiconductor nanostructures. Rev. Mod. Phys. 76, 725–783 (2004).

    Article  ADS  CAS  Google Scholar 

  16. Chabinyc, M. L. X‐ray scattering from films of semiconducting polymers. Polym. Rev. 48, 463–492 (2008).

    Article  CAS  Google Scholar 

  17. Pron, A., Gawrys, P., Zagorska, M., Djurado, D. & Demadrille, R. Electroactive materials for organic electronics: preparation strategies, structural aspects and characterization techniques. Chem. Soc. Rev. 39, 2577–2632 (2010).

    Article  CAS  PubMed  Google Scholar 

  18. Fenter, P., Schreiber, F., Zhou, L., Eisenberger, P. & Forrest, S. R. In situ studies of morphology, strain, and growth modes of a molecular organic thin film. Phys. Rev. B 56, 3046–3053 (1997).

    Article  ADS  CAS  Google Scholar 

  19. Banerjee, R., Kowarik, S. & Schreiber, F. in Advanced Characterization of Nanostructured Materials: Probing the Structure and Dynamics with Synchrotron X-rays and Neutrons (eds Sinha, S. K., Sanyal, M. K. & Loong, C. K.) 49–95 (World Scientific, 2021).

  20. Jackson, J. D. in Classical Electrodynamics 488–491 (Wiley, 1962).

  21. Sivia, D. S. in Elementary Scattering Theory: For X-ray and Neutron Users (ed. Adlung, S.) 21–22 (Oxford Univ. Press, 2011).

  22. Kittel, C. in Introduction to Solid State Physics (ed. Johnson, S.) 29 (Wiley, 2004).

  23. Shmueli, U. (ed.) International Tables for Crystallography, Volume B: Reciprocal Space (Kluwer Academic, 2006).

  24. Thomas, J. I. Multiple slit interference: a hyperbola based analysis. Eur. J. Phys. 42, 055304 (2021).

    Article  Google Scholar 

  25. Smilgies, D.-M. Scherrer grain-size analysis adapted to grazing-incidence scattering with area detectors. J. Appl. Cryst. 42, 1030–1034 (2009). This paper introduces the analysis of peak widths in terms of crystal size analysis.

    Article  ADS  CAS  Google Scholar 

  26. Miller, A. M. et al. Extracting information from X-ray diffraction patterns containing Laue oscillations. Z. Naturforschung B 77, 313–322 (2022).

    Article  CAS  Google Scholar 

  27. Robinson, I. K. & Tweet, D. J. Surface X-ray diffraction. Rep. Prog. Phys. 55, 599 (1992). This review is an easy to read, comprehensive introduction to GIXD.

    Article  ADS  CAS  Google Scholar 

  28. Disa, A. S., Walker, F. J. & Ahn, C. H. High-resolution crystal truncation rod scattering: application to ultrathin layers and buried interfaces. Adv. Mater. Interfaces 7, 1901772 (2020). This review article presents an introduction to CTRs and summarizes the achievements.

    Article  Google Scholar 

  29. Savikhin, V. et al. GIWAXS-SIIRkit: scattering intensity, indexing and refraction calculation toolkit for grazing-incidence wide-angle X-ray scattering of organic materials. J. Appl. Cryst. 53, 1108–1129 (2020).

    Article  ADS  CAS  Google Scholar 

  30. Creagh, D. C. & Hubbell, J. H. in International Tables for Crystallography, Volume C: Mathematical, Physical and Chemical Tables (eds Wilson, A. J. C. & Prince, E.) 220–236 (Kluwer Academic, 1999).

  31. Henke, B. L., Gullikson, E. M. & Davis, J. C. X-ray interactions: photoabsorption, scattering, transmission, and reflection at E = 50–30,000 eV, Z = 1–92. At. Data Nucl. Data Tables 54, 181–342 (1993).

    Article  ADS  CAS  Google Scholar 

  32. Toney, M. F. & Brennan, S. Observation of the effect of refraction on X rays diffracted in a grazing-incidence asymmetric Bragg geometry. Phys. Rev. B 39, 7963–7966 (1989).

    Article  ADS  CAS  Google Scholar 

  33. Stepanov, S. A. et al. Dynamical X-ray diffraction of multilayers and superlattices: recursion matrix extension to grazing angles. Phys. Rev. B 57, 4829–4841 (1998).

    Article  ADS  CAS  Google Scholar 

  34. Dosch, H. Evanescent absorption in kinematic surface Bragg diffraction. Phys. Rev. B 35, 2137–2143 (1987).

    Article  ADS  CAS  Google Scholar 

  35. Vineyard, G. H. Grazing-incidence diffraction and the distorted-wave approximation for the study of surfaces. Phys. Rev. B 26, 4146–4159 (1982).

    Article  ADS  CAS  Google Scholar 

  36. Yoneda, Y. Anomalous surface reflection of X rays. Phys. Rev. 131, 2010–2013 (1963).

    Article  ADS  Google Scholar 

  37. Dosch, H. in Critical Phenomena at Surfaces and Interfaces: Evanescent X-Ray and Neutron Scattering (ed. Höhler, G.) 6–31 (Springer, 1992).

  38. Resel, R. et al. Multiple scattering in grazing-incidence X-ray diffraction: impact on lattice-constant determination in thin films. J. Synchrotron Rad. 23, 729–734 (2016).

    Article  CAS  Google Scholar 

  39. Feidenhans’l, R. Surface structure determination by X-ray diffraction. Surf. Sci. Rep. 10, 105–188 (1989).

    Article  ADS  Google Scholar 

  40. Reichert, H., Eng, P. J., Dosch, H. & Robinson, I. K. Thermodynamics of surface segregation profiles at Cu3Au(001) resolved by X-ray scattering. Phys. Rev. Lett. 74, 2006–2009 (1995).

    Article  ADS  CAS  PubMed  Google Scholar 

  41. Renaud, G., Robach, O. & Barbier, A. What can we learn on the structure and morphology of metal oxide/metal interfaces by measurement of X-ray crystal truncation rods in situ, during growth. Faraday Discuss. 114, 157–172 (1999).

    Article  ADS  CAS  Google Scholar 

  42. Als-Nielsen, J. et al. Principles and applications of grazing incidence X-ray and neutron scattering from ordered molecular monolayers at the air–water interface. Phys. Rep. 246, 251–313 (1994).

    Article  ADS  CAS  Google Scholar 

  43. Kaganer, V. M., Möhwald, H. & Dutta, P. Structure and phase transitions in Langmuir monolayers. Rev. Mod. Phys. 71, 779–819 (1999). This review gives an introduction to the field of 2D crystals at surfaces.

    Article  ADS  CAS  Google Scholar 

  44. Flesch, H.-G. et al. Microstructure and phase behavior of a quinquethiophene-based self-assembled monolayer as a function of temperature. J. Phys. Chem. C. 115, 22925–22930 (2011).

    Article  CAS  Google Scholar 

  45. Steele, J. A. et al. How to GIWAXS: grazing incidence wide angle X-ray scattering applied to metal halide perovskite thin films. Adv. Energy Mater. 13, 2300760 (2023). This recent review gives a comprehensive introduction to GIXD investigations for thin films with uniplanar texture.

    Article  CAS  Google Scholar 

  46. Mahmood, A. & Wang, J.-L. A review of grazing incidence small- and wide-angle X-ray scattering techniques for exploring the film morphology of organic solar cells. Sol. RRL 4, 2000337 (2020).

    Article  CAS  Google Scholar 

  47. Simbrunner, J. et al. Correlation between two- and three-dimensional crystallographic lattices for epitaxial analysis. II. Experimental results. Acta Cryst. A 78, 272–282 (2022).

    Article  CAS  Google Scholar 

  48. Colombi, P. et al. Glancing-incidence X-ray diffraction for depth profiling of polycrystalline layers. J. Appl. Cryst. 39, 176–179 (2006).

    Article  ADS  CAS  Google Scholar 

  49. Robinson, I. K., Waskiewicz, W. K., Tung, R. T. & Bohr, J. Ordering at Si(111)/a-Si and Si(111)/SiO2 interfaces. Phys. Rev. Lett. 57, 2714–2717 (1986).

    Article  ADS  CAS  PubMed  Google Scholar 

  50. Rivnay, J., Mannsfeld, S. C. B., Miller, C. E., Salleo, A. & Toney, M. F. Quantitative determination of organic semiconductor microstructure from the molecular to device scale. Chem. Rev. 112, 5488–5519 (2012).

    Article  CAS  PubMed  Google Scholar 

  51. Yoneda, Y. et al. Structural characterization of BaTiO3 thin films grown by molecular beam epitaxy. J. Appl. Phys. 83, 2458–2461 (1998).

    Article  ADS  CAS  Google Scholar 

  52. Hestroffer, K. et al. In situ study of self-assembled GaN nanowires nucleation on Si(111) by plasma-assisted molecular beam epitaxy. Appl. Phys. Lett. 100, 212107 (2012).

    Article  ADS  Google Scholar 

  53. Lee, S. H. et al. Oxidation state and surface reconstruction of Cu under CO2 reduction conditions from in situ X-ray characterization. J. Am. Chem. Soc. 143, 588–592 (2021).

    Article  CAS  PubMed  Google Scholar 

  54. Martin, D. J. et al. Reversible restructuring of supported Au nanoparticles during butadiene hydrogenation revealed by operando GISAXS/GIWAXS. Chem. Commun. 53, 5159–5162 (2017).

    Article  Google Scholar 

  55. Neuschitzer, M. et al. Grazing-incidence in-plane X-ray diffraction on ultra-thin organic films using standard laboratory equipment. J. Appl. Cryst. 45, 367–370 (2012).

    Article  ADS  CAS  Google Scholar 

  56. Vegso, K. et al. A wide-angle X-ray scattering laboratory setup for tracking phase changes of thin films in a chemical vapor deposition chamber. Rev. Sci. Instrum. 93, 113909 (2022).

    Article  ADS  CAS  PubMed  Google Scholar 

  57. Fischer, J. C. et al. GIWAXS characterization of metal–organic framework thin films and heterostructures: quantifying structure and orientation. Adv. Mater. Interfaces 10, 2202259 (2023).

    Article  CAS  Google Scholar 

  58. Smieska, L. et al. The functional materials beamline at CHESS. Synchrotron Radiat. N. 36, 4–11 (2023).

    Article  ADS  Google Scholar 

  59. Fontaine, P., Ciatto, G., Aubert, N. & Goldmann, M. Soft interfaces and resonant investigation on undulator source: a surface X-ray scattering beamline to study organic molecular films at the SOLEIL synchrotron. Sci. Adv. Mater. 6, 2312–2316 (2014).

    Article  CAS  Google Scholar 

  60. Takahara, A. et al. Advanced soft material beamline consortium at SPring-8 (FSBL). Synchrotron Radiat. N. 27, 19–23 (2014).

    Article  ADS  Google Scholar 

  61. Ogawa, H. et al. Experimental station for multiscale surface structural analyses of soft-material films at SPring-8 via a GISWAX/GIXD/XR-integrated system. Polym. J. 45, 109–116 (2013).

    Article  CAS  Google Scholar 

  62. Seeck, O. H. et al. The high-resolution diffraction beamline P08 at PETRA III. J. Synchrotron Rad. 19, 30–38 (2012). This work gives a detailed description of a high-resolution GIXD set-up installed at a synchrotron source.

    Article  CAS  Google Scholar 

  63. Smilgies, D.-M., Boudet, N., Struth, B. & Konovalov, O. Troika II: a versatile beamline for the study of liquid and solid interfaces. J. Synchrotron Rad. 12, 329–339 (2005).

    Article  CAS  Google Scholar 

  64. Bera, M. et al. Opportunities of soft materials research at advanced photon source. Synchrotron Radiat. N. 36, 12–23 (2023).

    Article  ADS  Google Scholar 

  65. Barbour, A. et al. X-ray scattering for soft matter research at NSLS-II. Synchrotron Radiat. N. 36, 24–30 (2023).

    Article  ADS  Google Scholar 

  66. Arnold, T. et al. Implementation of a beam deflection system for studies of liquid interfaces on beamline I07 at Diamond. J. Synchrotron Rad. 19, 408–416 (2012).

    Article  CAS  Google Scholar 

  67. Anton Paar GmbH. DHS1100: a new high-temperature attachment for materials science in the whole orientation space. J. Appl. Cryst. 40, 202–202 (2007).

    Article  ADS  Google Scholar 

  68. Cantelli, V. et al. The in situ growth of nanostructures on surfaces (INS) endstation of the ESRF BM32 beamline: a combined UHV–CVD and MBE reactor for in situ X-ray scattering investigations of growing nanoparticles and semiconductor nanowires. J. Synchrotron Rad. 22, 688–700 (2015).

    Article  CAS  Google Scholar 

  69. Ritley, K. A., Krause, B., Schreiber, F. & Dosch, H. A portable ultrahigh vacuum organic molecular beam deposition system for in situ X-ray diffraction measurements. Rev. Sci. Instrum. 72, 1453–1457 (2001).

    Article  ADS  CAS  Google Scholar 

  70. Kowarik, S. Thin film growth studies using time-resolved X-ray scattering. J. Phys. Condens. Matter 29, 043003 (2016). This review gives an introduction to thin film growth studies.

    Article  ADS  PubMed  Google Scholar 

  71. Kneschaurek, E. et al. Compact sample environment for in situ X-ray scattering during spin-coating. Rev. Sci. Instrum. 94, 063901 (2023).

    Article  ADS  CAS  PubMed  Google Scholar 

  72. Ruge, M., Golks, F., Zegenhagen, J., Magnussen, O. M. & Stettner, J. In operando GISAXS studies of mound coarsening in electrochemical homoepitaxy. Phys. Rev. Lett. 112, 055503 (2014).

    Article  ADS  PubMed  Google Scholar 

  73. Festersen, S. et al. Nucleation and growth of PbBrF crystals at the liquid mercury–electrolyte interface studied by operando X-ray scattering. Langmuir 36, 10905–10915 (2020).

    Article  CAS  PubMed  Google Scholar 

  74. Ankner, J. F., Majkrzak, C. F. & Satija, S. K. Neutron reflectivity and grazing angle diffraction. J. Res. Natl Inst. Stand. Technol. 98, 47–58 (1993).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  75. Kyrey, T. et al. Grazing incidence small-angle neutron scattering: background determination and optimization for soft matter samples. Appl. Sci. 11, 3085 (2021).

    Article  CAS  Google Scholar 

  76. Mahan, J. E., Geib, K. M., Robinson, G. Y. & Long, R. G. A review of the geometrical fundamentals of reflection high‐energy electron diffraction with application to silicon surfaces. J. Vac. Sci. Technol. A 8, 3692–3700 (1990).

    Article  CAS  Google Scholar 

  77. Ichimiya, A. & Cohen, P. I. in Reflection High-Energy Electron Diffraction 12–16 (Cambridge Univ. Press, 2004).

  78. Hafez, M. A., Zayed, M. K. & Elsayed-Ali, H. E. Review: geometric interpretation of reflection and transmission RHEED patterns. Micron 159, 103286 (2022).

    Article  CAS  PubMed  Google Scholar 

  79. Fumagalli, E. et al. Grazing-incidence X-ray diffraction study of rubrene epitaxial thin films. J. Synchrotron Rad. 19, 682–687 (2012).

    Article  CAS  Google Scholar 

  80. Renaud, G., Villette, B. & Guénard, P. Apparatus for 3D surface X-ray scattering during in situ molecular beam deposition. Nucl. Instrum. Methods Phys. Res. B 95, 422–430 (1995).

    Article  ADS  CAS  Google Scholar 

  81. Nicklin, C., Arnold, T., Rawle, J. & Warne, A. Diamond beamline I07: a beamline for surface and interface diffraction. J. Synchrotron Rad. 23, 1245–1253 (2016).

    Article  CAS  Google Scholar 

  82. Sakata, O. et al. Beamline for surface and interface structures at SPring-8. Surf. Rev. Lett. 10, 543–547 (2003).

    Article  ADS  CAS  Google Scholar 

  83. Yang, T.-Y. et al. Introduction of the X-ray diffraction beamline of SSRF. Nucl. Sci. Tech. 26, 5–9 (2015).

    Google Scholar 

  84. Patterson, B. D. et al. The materials science beamline at the Swiss Light Source: design and realization. Nucl. Instrum. Methods Phys. Res. A 540, 42–67 (2005).

    Article  ADS  CAS  Google Scholar 

  85. Patterson, B. D. et al. The materials science beamline at the Swiss Light Source. Nucl. Instrum. Methods Phys. Res. B 238, 224–228 (2005).

    Article  ADS  CAS  Google Scholar 

  86. Hexemer, A. et al. A SAXS/WAXS/GISAXS beamline with multilayer monochromator. J. Phys.: Conf. Ser. 247, 012007 (2010).

    Google Scholar 

  87. Schlepütz, C. M. et al. Improved data acquisition in grazing-incidence X-ray scattering experiments using a pixel detector. Acta Cryst. A 61, 418–425 (2005).

    Article  Google Scholar 

  88. Kowarik, S. et al. A novel 3D printed radial collimator for X-ray diffraction. Rev. Sci. Instrum. 90, 035102 (2019).

    Article  ADS  CAS  PubMed  Google Scholar 

  89. Metzger, T. H., Luidl, C., Pietsch, U. & Vierl, U. Novel versatile X-ray reflectometer for angle and energy dispersive characterization of liquid and solid surfaces and interfaces. Nucl. Instrum. Methods Phys. Res. A 350, 398–405 (1994).

    Article  ADS  CAS  Google Scholar 

  90. Kowarik, S. et al. Energy-dispersive X-ray reflectivity and GID for real-time growth studies of pentacene thin films. Thin Solid. Films 515, 5606–5610 (2007).

    Article  ADS  CAS  Google Scholar 

  91. Wakabayashi, Y., Shirasawa, T., Voegeli, W. & Takahashi, T. Observation of structure of surfaces and interfaces by synchrotron X-ray diffraction: atomic-scale imaging and time-resolved measurements. J. Phys. Soc. Jpn. 87, 061010 (2018).

    Article  ADS  Google Scholar 

  92. Schlepütz, C. M., Mariager, S. O., Pauli, S. A., Feidenhans’l, R. & Willmott, P. R. Angle calculations for a (2+3)-type diffractometer: focus on area detectors. J. Appl. Cryst. 44, 73–83 (2011).

    Article  ADS  Google Scholar 

  93. Schwartzkopf, M. et al. Role of sputter deposition rate in tailoring nanogranular gold structures on polymer surfaces. ACS Appl. Mater. Interfaces 9, 5629–5637 (2017).

    Article  CAS  PubMed  Google Scholar 

  94. Bertram, F., Deiter, C., Pflaum, K. & Seeck, O. H. A compact high vacuum heating chamber for in-situ X-ray scattering studies. Rev. Sci. Instrum. 83, 083904 (2012).

    Article  ADS  CAS  PubMed  Google Scholar 

  95. Kotnik, P. et al. DHS1100—a new high temperature attachment for 4-circle X-ray goniometers. Acta Cryst. A 62, 158 (2006).

    Article  Google Scholar 

  96. Holzer, V. et al. Impact of sample misalignment on grazing incidence X-ray diffraction patterns and the resulting unit cell determination. Rev. Sci. Instrum. 93, 063906–063906 (2022). This paper gives the influence of sample misalignment to the diffraction pattern and introduces a procedure for sample alignment.

    Article  ADS  CAS  PubMed  Google Scholar 

  97. Chantler, C. T., Rae, N. A. & Tran, C. Q. Accurate determination and correction of the lattice parameter of LaB6 (standard reference material 660) relative to that of Si(640b). J. Appl. Cryst. 40, 232–240 (2007).

    Article  ADS  CAS  Google Scholar 

  98. Blanton, T. N., Barnes, C. L. & Lelental, M. Preparation of silver behenate coatings to provide low- to mid-angle diffraction calibration. J. Appl. Cryst. 33, 172–173 (2000).

    Article  ADS  CAS  Google Scholar 

  99. Kintzel, E. J. Jr. et al. Investigation of the morphology of the initial growth of the aromatic molecule p-quaterphenyl on NaCl(001). J. Vac. Sci. Technol. A 19, 1270–1276 (2001).

    Article  CAS  Google Scholar 

  100. Roe, R. J. & Krigbaum, W. R. Description of crystallite orientation in polycrystalline materials having fiber texture. J. Chem. Phys. 40, 2608–2615 (1964).

    Article  ADS  CAS  Google Scholar 

  101. Heffelfinger, C. J. & Burton, R. L. X-ray determination of the crystallite orientation distributions of polyethylene terephthalate films. J. Polym. Sci. 47, 289–306 (1960).

    Article  ADS  CAS  Google Scholar 

  102. Mahieu, S., Ghekiere, P., Depla, D. & De Gryse, R. Biaxial alignment in sputter deposited thin films. Thin Solid Films 515, 1229–1249 (2006).

    Article  ADS  CAS  Google Scholar 

  103. Hammersley, A. P. FIT2D: a multi-purpose data reduction, analysis and visualization program. J. Appl. Cryst. 49, 646–652 (2016).

    Article  ADS  CAS  Google Scholar 

  104. Schneider, C. A., Rasband, W. S. & Eliceiri, K. W. NIH image to ImageJ: 25 years of image analysis. Nat. Methods 9, 671–675 (2012).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  105. Yang, L. Using an in-vacuum CCD detector for simultaneous small- and wide-angle scattering at beamline X9. J. Synchrotron Rad. 20, 211–218 (2013).

    Article  CAS  Google Scholar 

  106. Kriegner, D., Wintersberger, E. & Stangl, J. xrayutilities: a versatile tool for reciprocal space conversion of scattering data recorded with linear and area detectors. J. Appl. Cryst. 46, 1162–1170 (2013).

    Article  ADS  CAS  Google Scholar 

  107. Jiang, Z. GIXSGUI: a MATLAB toolbox for grazing-incidence X-ray scattering data visualization and reduction, and indexing of buried three-dimensional periodic nanostructured films. J. Appl. Cryst. 48, 917–926 (2015).

    Article  ADS  CAS  Google Scholar 

  108. Schrode, B. et al. GIDVis: a comprehensive software tool for geometry-independent grazing-incidence X-ray diffraction data analysis and pole-figure calculations. J. Appl. Cryst. 52, 683–689 (2019).

    Article  ADS  CAS  Google Scholar 

  109. Klug, H. P. & Alexander, L. E. in X-Ray Diffraction Procedures: For Polycrystalline and Amorphous Materials 618–754 (Wiley, 1974).

  110. Birkholz, M. in Thin Film Analysis by X-Ray Scattering 85–296 (Wiley-VCH, 2005). This book summarizes the X-ray techniques for the crystallographic characterization of thin films.

  111. Mason, R. The crystallography of anthracene at 95°K and 290°K. Acta Cryst. 17, 547–555 (1964).

    Article  CAS  Google Scholar 

  112. Baker, J. L. et al. Quantification of thin film cristallographic orientation using X-ray diffraction with an area detector. Langmuir 26, 9146–9151 (2010).

    Article  CAS  PubMed  Google Scholar 

  113. Schulz, L. G. A direct method of determining preferred orientation of a flat reflection sample using a Geiger counter X‐ray spectrometer. J. Appl. Phys. 20, 1030–1033 (1949).

    Article  ADS  Google Scholar 

  114. Alexander, L. E. in X-ray Diffraction Methods in Polymer Science 209–215 (Robert E. Krieger, 1979).

  115. Resel, R. et al. Wide-range three-dimensional reciprocal-space mapping: a novel approach applied to organic monodomain thin films. J. Appl. Cryst. 40, 580–582 (2007).

    Article  ADS  CAS  Google Scholar 

  116. Takagi, Y. & Kimura, M. Generalized grazing-incidence-angle X-ray diffraction (G-GIXD) using image plates. J. Synchrotron Rad. 5, 488–490 (1998).

    Article  CAS  Google Scholar 

  117. Simbrunner, J. et al. Indexing of grazing-incidence X-ray diffraction patterns: the case of fibre-textured thin films. Acta Cryst. A 74, 373–387 (2018).

    Article  MathSciNet  CAS  Google Scholar 

  118. Tate, M. P. et al. Simulation and interpretation of 2D diffraction patterns from self-assembled nanostructured films at arbitrary angles of incidence: from grazing incidence (above the critical angle) to transmission perpendicular to the substrate. J. Phys. Chem. B 110, 9882–9892 (2006).

    Article  CAS  PubMed  Google Scholar 

  119. Smilgies, D.-M. & Blasini, D. R. Indexation scheme for oriented molecular thin films studied with grazing-incidence reciprocal-space mapping. J. Appl. Cryst. 40, 716–718 (2007).

    Article  ADS  CAS  Google Scholar 

  120. Hinderhofer, A. et al. Machine learning for scattering data: strategies, perspectives and applications to surface scattering. J. Appl. Cryst. 56, 3–11 (2023).

    Article  ADS  CAS  Google Scholar 

  121. Breiby, D. W., Bunk, O., Andreasen, J. W., Lemke, H. T. & Nielsen, M. M. Simulating X-ray diffraction of textured films. J. Appl. Cryst. 41, 262–271 (2008).

    Article  ADS  CAS  Google Scholar 

  122. Hailey, A. K., Hiszpanski, A. M., Smilgies, D.-M. & Loo, Y.-L. The Diffraction Pattern Calculator (DPC) toolkit: a user-friendly approach to unit-cell lattice parameter identification of two-dimensional grazing-incidence wide-angle X-ray scattering data. J. Appl. Cryst. 47, 2090–2099 (2014).

    Article  ADS  CAS  Google Scholar 

  123. Kainz, M. P. et al. GIDInd: an automated indexing software for grazing-incidence X-ray diffraction data. J. Appl. Cryst. 54, 1256–1267 (2021).

    Article  ADS  CAS  Google Scholar 

  124. Talnack, F. et al. Thermal behavior and polymorphism of 2,9-didecyldinaphtho[2,3-b:2′,3′-f]thieno[3,2-b]thiophene thin films.Mol. Syst. Des. Eng. 7, 507–519 (2022).

    Article  CAS  Google Scholar 

  125. Smilgies, D. M. Geometry-independent intensity correction factors for grazing-incidence diffraction. Rev. Sci. Instrum. 73, 1706–1710 (2002).

    Article  ADS  CAS  Google Scholar 

  126. Kahn, R. et al. Macromolecular crystallography with synchrotron radiation: photographic data collection and polarization correction. J. Appl. Cryst. 15, 330–337 (1982).

    Article  ADS  CAS  Google Scholar 

  127. Moser, A. Crystal Structure Solution Based on Grazing Incidence X-Ray Diffraction. Thesis, Graz University of Technology (2012).

  128. Salzmann, I. & Resel, R. STEREOPOLE: software for the analysis of X-ray diffraction pole figures with IDL. J. Appl. Cryst. 37, 1029–1033 (2004).

    Article  ADS  CAS  Google Scholar 

  129. Pawlik, K. Determination of the orientation distribution function from pole figures in arbitrarily defined cells. Phys. Status Solidi 134, 477–483 (1986).

    Article  Google Scholar 

  130. Oehzelt, M. et al. Organic heteroepitaxy: p-sexiphenyl on uniaxially oriented α-sexithiophene. Adv. Mater. 18, 2466–2470 (2006).

    Article  CAS  Google Scholar 

  131. Scardi, P. et al. Size–strain separation in diffraction line profile analysis. J. Appl. Cryst. 51, 831–843 (2018).

    Article  ADS  CAS  Google Scholar 

  132. Nath, D., Singh, F. & Das, R. X-ray diffraction analysis by Williamson–Hall, Halder–Wagner and size–strain plot methods of CdSe nanoparticles—a comparative study. Mater. Chem. Phys. 239, 122021 (2020).

    Article  CAS  Google Scholar 

  133. Cantin, S., Pignat, J., Daillant, J., Perrot, F. & Konovalov, O. Grazing incidence X-ray diffraction determination of the structure of two-dimensional organic-inorganic crystals at the water surface. Soft Matter 6, 1923–1932 (2010).

    Article  ADS  CAS  Google Scholar 

  134. Braun, D. E. et al. Surface induced phenytoin polymorph. 1. Full structure solution by combining grazing incidence X-ray diffraction and crystal structure prediction. Cryst. Growth Des. 19, 6058–6066 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  135. Hao, Y. et al. From 2D to 3D: bridging self-assembled monolayers to a substrate-induced polymorph in a molecular semiconductor. Chem. Mater. 34, 2238–2248 (2022).

    Article  CAS  Google Scholar 

  136. Sakata, O. & Nakamura, M. in Surface Science Techniques (eds Bracco, G. & Holst, B.) 165–191 (Springer, 2013).

  137. Simbrunner, J., Salzmann, I. & Resel, R. Indexing of grazing-incidence X-ray diffraction patterns. Crystallogr. Rev. 29, 19–37 (2023).

    Article  Google Scholar 

  138. Kim, G.-H. et al. High thermal conductivity in amorphous polymer blends by engineered interchain interactions. Nat. Mater. 14, 295–300 (2015).

    Article  ADS  CAS  PubMed  Google Scholar 

  139. Proffit, D. E. et al. Thermal stability of amorphous Zn–In–Sn–O films. J. Electroceram. 34, 167–174 (2015).

    Article  CAS  Google Scholar 

  140. Ferrer, P., Rubio-Zuazo, J., Heyman, C., Esteban-Betegón, F. & Castro, G. R. Multi-use high/low-temperature and pressure compatible portable chamber for in situ grazing-incidence X-ray scattering studies. J. Synchrotron Rad. 20, 474–481 (2013).

    Article  CAS  Google Scholar 

  141. Burkle, D. et al. Development of an electrochemically integrated SR-GIXRD flow cell to study FeCO3 formation kinetics. Rev. Sci. Instrum. 87, 105125 (2016).

    Article  ADS  CAS  PubMed  Google Scholar 

  142. Scherzer, M. et al. Electrochemical surface oxidation of copper studied by in situ grazing incidence X-ray diffraction. J. Phys. Chem. C. 123, 13253–13262 (2019).

    Article  ADS  CAS  Google Scholar 

  143. Lee, M. Y. et al. Regular H-bonding-containing polymers with stretchability up to 100% external strain for self-healable plastic transistors. Chem. Mater. 32, 1914–1924 (2020).

    Article  ADS  CAS  Google Scholar 

  144. Zhu, W. et al. Kinetically controlled growth of sub-millimeter 2D Cs2SnI6 nanosheets at the liquid–liquid interface. Small 17, 2006279 (2021).

    Article  CAS  Google Scholar 

  145. Greco, A. et al. Kinetics of ion-exchange reactions in hybrid organic–inorganic perovskite thin films studied by in situ real-time X-ray scattering. J. Phys. Chem. Lett. 9, 6750–6754 (2018).

    Article  CAS  PubMed  Google Scholar 

  146. Ranacher, C. et al. Layered nanostructures in proton conductive polymers obtained by initiated chemical vapor deposition. Macromolecules 48, 6177–6185 (2015).

    Article  ADS  CAS  Google Scholar 

  147. Perrotta, A., Christian, P., Jones, A. O. F., Muralter, F. & Coclite, A. M. Growth regimes of poly(perfluorodecyl acrylate) thin films by initiated chemical vapor deposition. Macromolecules 51, 5694–5703 (2018).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  148. Cohin, Y. et al. Growth of vertical GaAs nanowires on an amorphous substrate via a fiber-textured Si platform. Nano Lett. 13, 2743–2747 (2013).

    Article  ADS  CAS  PubMed  Google Scholar 

  149. Huss-Hansen, M. K. et al. Structural stability of naphthyl end-capped oligothiophenes in organic field-effect transistors measured by grazing-incidence X-ray diffraction in operando. Org. Electron. 49, 375–381 (2017).

    Article  CAS  Google Scholar 

  150. Paulsen, B. D. et al. Time-resolved structural kinetics of an organic mixed ionic–electronic conductor. Adv. Mater. 32, 2003404 (2020).

    Article  CAS  Google Scholar 

  151. Qiao, Y. et al. Mechanistic insights into aldehyde production from electrochemical CO2 reduction on CuAg alloy via operando X-ray measurements. ACS Catal. 13, 9379–9391 (2023).

    Article  CAS  Google Scholar 

  152. Qin, M., Chan, P. F. & Lu, X. A systematic review of metal halide perovskite crystallization and film formation mechanism unveiled by in situ GIWAXS. Adv. Mater. 33, 2105290 (2021).

    Article  CAS  Google Scholar 

  153. Tan, W. L. & McNeill, C. R. X-ray diffraction of photovoltaic perovskites: principles and applications. Appl. Phys. Rev. 9, 021310 (2022).

    Article  ADS  CAS  Google Scholar 

  154. Steele, J. A. et al. Thermal unequilibrium of strained black CsPbI3 thin films. Science 365, 679–684 (2019). 

    Article  ADS  CAS  PubMed  Google Scholar 

  155. Marronnier, A. et al. Anharmonicity and disorder in the black phases of cesium lead iodide used for stable inorganic perovskite solar cells. ACS Nano 12, 3477–3486 (2018).

    Article  CAS  PubMed  Google Scholar 

  156. Tsai, H. et al. Light-induced lattice expansion leads to high-efficiency perovskite solar cells. Science 360, 67–70 (2018). 

    Article  ADS  CAS  PubMed  Google Scholar 

  157. Treacy, J. P. W. et al. Structure of a superhydrophilic surface: wet chemically prepared rutile-TiO2(110)(1 × 1). J. Phys. Chem. C. 123, 8463–8468 (2019).

    Article  CAS  Google Scholar 

  158. Hussain, H. et al. Water-induced reversal of the TiO2(011)-(2 × 1) surface reconstruction: observed with in situ surface X-ray diffraction. J. Phys. Chem. C. 123, 13545–13550 (2019).

    Article  CAS  Google Scholar 

  159. Nadeem, I. M. et al. Water dissociates at the aqueous interface with reduced anatase TiO2(101). J. Phys. Chem. Lett. 9, 3131–3136 (2018).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  160. Springell, R. et al. Water corrosion of spent nuclear fuel: radiolysis driven dissolution at the UO2/water interface. Faraday Discuss. 180, 301–311 (2015).

    Article  ADS  CAS  PubMed  Google Scholar 

  161. Merte, L. R. et al. Structure of the SnO2(110)-(4 × 1) surface. Phys. Rev. Lett. 119, 096102 (2017).

    Article  ADS  PubMed  Google Scholar 

  162. Novák, J. et al. Crystal growth of para-sexiphenyl on clean and oxygen reconstructed Cu(110) surfaces. Phys. Chem. Chem. Phys. 13, 14675–14684 (2011).

    Article  PubMed  Google Scholar 

  163. Jones, A. O. F., Chattopadhyay, B., Geerts, Y. H. & Resel, R. Substrate-induced and thin-film phases: polymorphism of organic materials on surfaces. Adv. Funct. Mater. 26, 2233–2255 (2016).

    Article  CAS  Google Scholar 

  164. Davies, D. W. et al. Radically tunable n-type organic semiconductor via polymorph control. Chem. Mater. 33, 2466–2477 (2021).

    Article  CAS  Google Scholar 

  165. Davies, D. W. et al. Unraveling two distinct polymorph transition mechanisms in one n-type single crystal for dynamic electronics. Nat. Commun. 14, 1304 (2023).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  166. Wu, W.-R. et al. Competition between fullerene aggregation and poly(3-hexylthiophene) crystallization upon annealing of bulk heterojunction solar cells. ACS Nano 5, 6233–6243 (2011).

    Article  CAS  PubMed  Google Scholar 

  167. Huang, Y.-C. et al. Insight into evolution, processing and performance of multi-length-scale structures in planar heterojunction perovskite solar cells. Sci. Rep. 5, 13657 (2015).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  168. Weidman, M. C., Smilgies, D.-M. & Tisdale, W. A. Kinetics of the self-assembly of nanocrystal superlattices measured by real-time in situ X-ray scattering. Nat. Mater. 15, 775–781 (2016).

    Article  ADS  CAS  PubMed  Google Scholar 

  169. Hodas, M. et al. Real-time monitoring of growth and orientational alignment of pentacene on epitaxial graphene for organic electronics. ACS Appl. Nano Mater. 1, 2819–2826 (2018).

    Article  CAS  Google Scholar 

  170. Vakalopoulou, E. et al. Metal sulfide thin films with tunable nanoporosity for photocatalytic applications. ACS Appl. Nano Mater. 5, 1508–1520 (2022).

    Article  CAS  Google Scholar 

  171. Predecki, P., Zhu, X. & Ballard, B. Proposed methods for depth profiling of residual stresses using grazing incidence X-ray diffraction (GIXD). Adv. X-Ray Anal. 36, 237–245 (1992).

    Google Scholar 

  172. Angerer, P. & Strobl, S. Equi-penetration grazing incidence X-ray diffraction method: stress depth profiling of ground silicon nitride. Acta Mater. 77, 370–378 (2014).

    Article  ADS  CAS  Google Scholar 

  173. Wang, H. et al. Interfacial residual stress relaxation in perovskite solar cells with improved stability. Adv. Mater. 31, 1904408 (2019).

    Article  CAS  Google Scholar 

  174. Yazdanmehr, A. & Jahed, H. On the surface residual stress measurement in magnesium alloys using X-ray diffraction. Materials 13, 5190 (2020).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  175. Dippel, A.-C. et al. Local atomic structure of thin and ultrathin films via rapid high-energy X-ray total scattering at grazing incidence. IUCrJ 6, 290–298 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  176. Tsai, E. H. R., Xia, Y., Fukuto, M., Loo, Y.-L. & Li, R. Grazing-incidence X-ray diffraction tomography for characterizing organic thin films. J. Appl. Cryst. 54, 1327–1339 (2021). This paper introduces a method to obtain spatial resolved crystallographic information from GIXD performed in a tomographic mode.

    Article  ADS  CAS  Google Scholar 

  177. Smilgies, D.-M., Koker, M. K. A., Li, R., Shaw, L. & Bao, Z. Grazing-incidence texture tomography and diffuse reflectivity tomography of an organic semiconductor device array. Chem. Methods 2, e202200016 (2022).

    Article  CAS  Google Scholar 

  178. Miao, J., Ishikawa, T., Robinson, I. K. & Murnane, M. M. Beyond crystallography: diffractive imaging using coherent X-ray light sources. Science 348, 530–535 (2015).

    Article  ADS  MathSciNet  CAS  PubMed  Google Scholar 

  179. Sandy, A. R., Zhang, Q. & Lurio, L. B. Hard X-ray photon correlation spectroscopy methods for materials studies. Annu. Rev. Mater. Res. 48, 167–190 (2018).

    Article  CAS  Google Scholar 

  180. Kowarik, S. et al. Real-time X-ray diffraction measurements of structural dynamics and polymorphism in diindenoperylene growth. Appl. Phys. A 95, 233–239 (2009).

    Article  ADS  CAS  Google Scholar 

  181. Simbrunner, J. et al. Indexing grazing-incidence X-ray diffraction patterns of thin films: lattices of higher symmetry. J. Appl. Cryst. 52, 428–439 (2019).

    Article  ADS  CAS  Google Scholar 

  182. Unterumsberger, R. et al. A round robin test for total reflection X-ray fluorescence analysis using preselected and well characterized samples. J. Anal. At. Spectrom. 36, 1933–1945 (2021).

    Article  CAS  Google Scholar 

  183. Colombi, P. et al. Reproducibility in X-ray reflectometry: results from the first world-wide round-robin experiment. J. Appl. Cryst. 41, 143–152 (2008).

    Article  ADS  CAS  Google Scholar 

  184. Schiefer, S., Huth, M., Dobrinevski, A. & Nickel, B. Determination of the crystal structure of substrate-induced pentacene polymorphs in fiber structured thin films. J. Am. Chem. Soc. 129, 10316–10317 (2007).

    Article  CAS  PubMed  Google Scholar 

  185. Yoshida, H., Inaba, K. & Sato, N. X-ray diffraction reciprocal space mapping study of the thin film phase of pentacene. Appl. Phys. Lett. 90, 181930 (2007).

    Article  ADS  Google Scholar 

  186. Nabok, D. et al. Crystal and electronic structures of pentacene thin films from grazing-incidence X-ray diffraction and first-principles calculations. Phys. Rev. B 76, 235322 (2007).

    Article  ADS  Google Scholar 

  187. Gründer, Y., Stettner, J. & Magnussen, O. M. Review—in-situ surface X-ray diffraction studies of copper electrodes: atomic-scale interface structure and growth behavior. J. Electrochem. Soc. 166, D3049 (2018).

    Article  Google Scholar 

  188. Holton, J. M. A beginner’s guide to radiation damage. J. Synchrotron Rad. 16, 133–142 (2009).

    Article  CAS  Google Scholar 

  189. Meents, A., Gutmann, S., Wagner, A. & Schulze-Briese, C. Origin and temperature dependence of radiation damage in biological samples at cryogenic temperatures. Proc. Natl Acad. Sci. USA 107, 1094–1099 (2010).

    Article  ADS  CAS  PubMed  Google Scholar 

  190. Davies, R. J., Burghammer, M. & Riekel, C. Micro-Raman spectroscopy as an in situ tool for probing radiation damage during microdiffraction experiments in soft condensed matter. Macromolecules 41, 7251–7253 (2008).

    Article  ADS  CAS  Google Scholar 

  191. Antonio, E. N. & Toney, M. F. Why it is important to determine and report the impact of probe radiation. Joule 6, 723–725 (2022).

    Article  Google Scholar 

  192. Li, M. et al. Evidence of morphological change in sulfur cathodes upon irradiation by synchrotron X-rays. ACS Energy Lett. 7, 577–582 (2022).

    Article  ADS  CAS  Google Scholar 

  193. Meents, A., Dittrich, B. & Gutmann, S. A new aspect of specific radiation damage: hydrogen abstraction from organic molecules. J. Synchrotron Rad. 16, 183–190 (2009).

    Article  CAS  Google Scholar 

  194. Neuhold, A. et al. X-ray radiation damage of organic semiconductor thin films during grazing incidence diffraction experiments. Nucl. Instrum. Methods Phys. Res. B 284, 64–68 (2012).

    Article  ADS  CAS  Google Scholar 

  195. Stenger, P. C. et al. X-ray diffraction and reflectivity validation of the depletion attraction in the competitive adsorption of lung surfactant and albumin. Biophys. J. 97, 777–786 (2009).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  196. Warkentin, M. & Thorne, R. E. Glass transition in thaumatin crystals revealed through temperature-dependent radiation-sensitivity measurements. Acta Cryst. D. 66, 1092–1100 (2010).

    Article  CAS  Google Scholar 

  197. Kaduk, J. A. et al. Powder diffraction. Nat. Rev. Methods Primers 1, 1–22 (2021).

    ADS  Google Scholar 

  198. Yang, H. et al. Conducting AFM and 2D GIXD studies on pentacene thin films. J. Am. Chem. Soc. 127, 11542–11543 (2005).

    Article  CAS  PubMed  Google Scholar 

  199. Pachmajer, S., Werzer, O., Mennucci, C., Buatier de Mongeot, F. & Resel, R. Biaxial growth of pentacene on rippled silica surfaces studied by rotating grazing incidence X-ray diffraction. J. Cryst. Growth 519, 69–76 (2019).

    Article  ADS  CAS  Google Scholar 

  200. Tolan, M. X-Ray Scattering from Soft-Matter Thin Films 148 (Springer, 1999). This book introduces X-ray reflectivity, which is often used as a supplementary X-ray technique to characterize surfaces, interfaces and thin films.

  201. Swain, M. C. & Cole, J. M. ChemDataExtractor: a toolkit for automated extraction of chemical information from the scientific literature. J. Chem. Inf. Model. 56, 1894–1904 (2016).

    Article  CAS  PubMed  Google Scholar 

  202. Olivetti, E. A. et al. Data-driven materials research enabled by natural language processing and information extraction. Appl. Phys. Rev. 7, 041317 (2020).

    Article  ADS  CAS  Google Scholar 

  203. Steadman, P. & Fan, R. in Hyperspectral Imaging—A Perspective on Recent Advances and Applications (ed. Huang, J. Y.) (IntechOpen, 2022).

  204. Chamard, V. et al. Anomalous diffraction in grazing incidence to study the strain induced by GaN quantum dots stacked in an AlN multilayer. Nucl. Instrum. Methods Phys. Res. B 200, 95–99 (2003).

    Article  ADS  CAS  Google Scholar 

  205. Eriksson, M., van der Veen, J. F. & Quitmann, C. Diffraction-limited storage rings—a window to the science of tomorrow. J. Synchrotron Rad. 21, 837–842 (2014).

    Article  CAS  Google Scholar 

  206. Raimondi, P. & Liuzzo, S. M. Toward a diffraction limited light source. Phys. Rev. Accel. Beams 26, 021601 (2023).

    Article  ADS  Google Scholar 

  207. Estandarte, A. K. C. et al. Bragg coherent diffraction imaging of iron diffusion into gold nanocrystals. N. J. Phys. 20, 113026 (2018).

    Article  CAS  Google Scholar 

  208. Sinha, S. K., Jiang, Z. & Lurio, L. B. X-ray photon correlation spectroscopy studies of surfaces and thin films. Adv. Mater. 26, 7764–7785 (2014).

    Article  CAS  PubMed  Google Scholar 

  209. Dallari, F. et al. Analysis strategies for MHz XPCS at the European XFEL. Appl. Sci. 11, 8037 (2021).

    Article  CAS  Google Scholar 

  210. Stangl, J., Mocuta, C., Chamard, V. & Carbone, D. in Nanobeam X-Ray Scattering: Probing Matter at the Nanoscale 89–154 (Wiley-VCH, 2013).

  211. Könnecke, M. et al. The NeXus data format. J. Appl. Cryst. 48, 301–305 (2015).

    Article  ADS  Google Scholar 

  212. Zielinski, P. et al. Probing exfoliated graphene layers and their lithiation with microfocused X-rays. Nano Lett. 19, 3634–3640 (2019).

    Article  ADS  CAS  PubMed  PubMed Central  Google Scholar 

  213. Sonntag, J. et al. Excellent electronic transport in heterostructures of graphene and monoisotopic boron-nitride grown at atmospheric pressure. 2D Mater. 7, 031009 (2020).

    Article  CAS  Google Scholar 

  214. Joshi, G. R. et al. In situ grazing incidence X-ray diffraction of sweet corrosion scaling on carbon steel. Presented at the CORROSION 2015, Dallas, Texas (2015).

  215. Pramana, S. S. et al. Understanding surface structure and chemistry of single crystal lanthanum aluminate. Sci. Rep. 7, 43721 (2017).

    Article  ADS  PubMed  PubMed Central  Google Scholar 

  216. Alhazmi, N., Pineda, E., Rawle, J., Howse, J. R. & Dunbar, A. D. F. Perovskite crystallization dynamics during spin-casting: an in situ wide-angle X-ray scattering study. ACS Appl. Energy Mater. 3, 6155–6164 (2020).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  217. Nicklin, C. et al. MINERVA: a facility to study microstructure and interface evolution in realtime under vacuum. Rev. Sci. Instrum. 88, 103901 (2017).

    Article  ADS  PubMed  Google Scholar 

Download references

Acknowledgements

The authors thank beamline XRD1, synchrotron Elettra and Trieste for providing beamtime to perform grazing incidence X-ray diffraction (GIXD) measurements to show different types of anthracene thin films. Argonne National Laboratory’s work was supported by the US Department of Energy, Office of Science, under contract DE-AC02-06CH11357.

Author information

Authors and Affiliations

  1. Department MATERIALS, Joanneum Research Forschungsgesellschaft mbH, Weiz, Austria

    Oliver Werzer

  2. Department of Physical Chemistry, Institute of Chemistry, University of Graz, Graz, Austria

    Stefan Kowarik

  3. Institute of Solid State Physics, Graz University of Technology, Graz, Austria

    Fabian Gasser & Roland Resel

  4. X-Ray Science Division, Argonne National Laboratory, Argonne, IL, USA

    Zhang Jiang & Joseph Strzalka

  5. Diamond Light Source, Harwell Science and Innovation Campus, Didcot, UK

    Christopher Nicklin

Authors
  1. Oliver Werzer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stefan Kowarik
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fabian Gasser
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Zhang Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Joseph Strzalka
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Christopher Nicklin
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Roland Resel
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Introduction (R.R.); Experimentation (S.K.); Results (O.W. and F.G.); Applications (Z.J. and J.S.); Reproducibility and data deposition (R.R.); Limitations and optimizations (C.N.); Outlook (C.N.); overview of the Primer (all authors).

Corresponding author

Correspondence to Roland Resel.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Reviews Methods Primers thanks Marianna Marciszko and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Glossary

2D powder

(Two-dimensional powder). Crystallites with a defined crystallographic plane parallel to the substrate surface but without any azimuthal or in-plane alignment.

Angle of grazing incidence

(αi). The angle of the primary X-ray beam relative to the sample surface is defined as the angle of incidence.

Biaxial texture

Crystallographic texture where the crystallites are preferably aligned along two different axes, for example, one perpendicular to the surface and one along a defined surface azimuth.

Bragg rods

The crystallographic lattice of two-dimensional crystals is represented by Bragg rods in the reciprocal space.

Critical angle of total external reflection

(αc). At angles of grazing incidence below αc, the primary X-ray beam is totally reflected from an ideally flat substrate surface.

Crystallographic texture

The distribution of crystallites within a sample in respect to their orientation relative to the sample coordinate system.

Crystal truncation rod

(CTR). Cleaving of a crystal results in a crystalline lattice with a missing half. The presence of lattice points on one side and missing lattice points on the other side results in CTRs in reciprocal space.

Macrostrain

External stress causes strain of the crystal lattice detectable by peak shifts.

Microstrain

Structural defects of crystalline lattices cause internal strain, which is associated with peak broadening.

Mosaicity

Average deviation of crystal alignments (or crystal orientations) from a given sample direction.

Penetration depth

(Λ). Total reflection of the primary X-ray beam at the sample surface reduces the penetration into a sample surface to characteristic values in the nanometre range. When the angle of grazing incidence αi is greater than the critical angle of total external reflection αc, penetration is determined by the linear absorption coefficient µ of the sample material.

Powder plot

Integration of the measured intensity across the scattering vector \(\vec{q}\), representing a diffraction pattern of randomly distributed crystallites.

Refraction correction

Only the z part of the scattering vector has to be corrected according to refraction effects; largest corrections are present at αf and/or αi ≈ αc, where αf is the angle between the reflected X-ray beam and the sample surface, αi is the angle of grazing incidence and αc is the critical angle of total external reflection.

Scattering angles

Angles between the primary X-ray beam and the diffracted beam.

Scattering vector

The scattering vector \(\vec{q}\) is the difference between the wavevectors of the primary and the scattered X-ray beam.

Slit interference function

General diffraction condition for gratings with a limited number of repeating units.

Wave vector

The wave vector \(\vec{k}\) gives the direction of the X-ray beam; the length of the vector is related to the wavelength λ (or energy E) of the radiation.

X-ray diffraction

Superposition of coherently (and elastically) scattered X-ray waves according to their phase difference resulting from path length differences between the different scattering centres.

Yoneda peak

The scattered intensity is enhanced when the angle between the reflected X-ray beam and sample surface is close to the critical angle of total external reflection αc.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Werzer, O., Kowarik, S., Gasser, F. et al. X-ray diffraction under grazing incidence conditions. Nat Rev Methods Primers 4, 15 (2024). https://doi.org/10.1038/s43586-024-00293-8

Download citation

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s43586-024-00293-8

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing