### Abstract

Measurements of residual stresses in textured thin films have always been problematic. In this article, a new experimental method using grazing-incidence X-ray diffraction is presented with its principles based upon the conventional sin
^{2}
ψ method. Instead of using the Bragg-Brentano (B-B) or Seemann-Bohlin geometry, the proposed method utilizes an asymmetrical diffraction geometry for which the X-ray beam is incident at a grazing angle γ to the sample surface, while the angle ψ is the tilt angle of the sample surface as defined by the conventional sin
^{2}
ψ method. Basic equations involved in the X-ray residual stress analysis are described, along with exemplified experimental data. Analysis shows that, for an isotropic medium, strain measured using this grazing-incidence geometry assumes a linear relationship with the geometrical parameter cos
^{2}
α sin
^{2}
ψ, where the angle α is a constant and is defined as the Bragg angle at ψ = 0°, θ
_{o}
, minus the grazing incidence angle γ, i.e. α = θ
_{o}
-γ. The grazing-incidence diffraction geometry effectively increases the irradiation volume from a thin-film specimen, thereby giving rise to higher intensity for high-angle Bragg peaks than the conventional B-B geometry. The proposed analysis has another advantage, in that the inhomogeneous sample casts little effect on the residual stress results when compared to the traditional sin
^{2}
ψ method.

Original language | English |
---|---|

Pages (from-to) | 73-78 |

Number of pages | 6 |

Journal | Thin Solid Films |

Volume | 418 |

Issue number | 2 |

DOIs | |

State | Published - 15 Oct 2002 |

### Keywords

- cos α sin ψ method
- Residual stress
- Textured thin film

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## Cite this

*Thin Solid Films*,

*418*(2), 73-78. https://doi.org/10.1016/S0040-6090(02)00680-6