Full length article Quantitative measurements of grain boundary excess volume from HAADF-STEM micrographs Yulia Buranova a , Harald R € osner a, * , Sergiy V. Divinski a , Robert Imlau b , Gerhard Wilde a a Institut für Materialphysik, Westf€ alische Wilhelms-Universit€ at Münster, Wilhelm-Klemm-Str.10, D-48149 Münster, Germany b FEI Company, Achtseweg Noord 5, 5600 KA Eindhoven, The Netherlands article info Article history: Received 9 November 2015 Received in revised form 14 January 2016 Accepted 16 January 2016 Available online 28 January 2016 Keywords: Grain boundaries (GBs) Excess volume Transmission electron microscopy (TEM) High angle annular dark field (HAADF) Electron energy loss spectroscopy (EELS) abstract A novel approach for quantitative measurements of grain boundary (GB) excess volume has been developed using correlative analytical transmission electron microscopy (TEM) and successfully demonstrated for several simulated symmetrical [100] tilt GB configurations as well as for the experi- mental case of an Al bicrystal containing a near S13 GB with an additional twist component. The reli- ability and precision of this new approach is analyzed and the limitations are discussed. © 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. 1. Introduction Grain boundaries (GBs) with their specific atomic structure have a significant impact on a wide range of physical properties (me- chanical, electrical or diffusional) of polycrystalline materials. GBs are typically classified with respect to the misorientation angle, q, of the abutting grains; that is, (i) low-angle boundaries with q  15  and (ii) high-angle boundaries with q > 15  [1]. Low-angle GBs are composed of dislocations. The above mentioned critical value for q ¼ 15  corresponds to the largest angle for which the dislocation- based model applies [2]. Read and Shockley [3] have developed such a model describing the accommodation of the misorientation between the abutting grains by arrangements of edge dislocations. One of the fundamental parameters for the characterization of GBs is their volume expansion ε GB , i.e. the amount of excess volume in the GB [4]. It has been shown that the GB excess volume is corre- lated with the GB energy [5,6] and has thus an influence on transport and thermodynamic properties of GBs such as diffusion and/or segregation [7]. The GB excess volume (per unit area A) of low-angle GBs can be described according to Wolf [5,8] as: ε GB ≡ dV ðqÞ A ¼ sin q½dV c  dV s lnðsin qÞ=jbj (1) where dV C is the excess core volume per unit length of a dislocation, dV S is the related strain-field contribution (per unit length), q is the misorientation angle between the grains and b is the Burgers vector. For FCC materials low-angle GBs with misorientation angles q < 15  are composed of dislocations with Burgers vectors b ¼ [100]. Accordingly, low-angle GBs with misorientation angles around 90  are composed of dislocations with Burgers vectors of the type b ¼½ [110] [3,9]. High-angle GBs are typically characterized by periodic structure units [10] using structural unit cells that differ from crystal unit cells. The excess volume of high-angle GBs can be derived from the basics of thermodynamics, see e.g. Ref. [4]. Bishop and Chalmers [11] determined the excess volume of high-angle GBs, V F , as a parameter expressing the change in volume of a polycrystalline material together with the change of GB area (A) at constant tem- perature (T), pressure (P), number of atoms (n i ) and composition (x). The equilibrium state can be described as: V F ¼  vV vA  T;P;n i ;x nm 3 per nm 2 (2) Atomistic calculations for gold and copper crystals using the * Corresponding author. E-mail address: rosner@uni-muenster.de (H. R€ osner). Contents lists available at ScienceDirect Acta Materialia journal homepage: www.elsevier.com/locate/actamat http://dx.doi.org/10.1016/j.actamat.2016.01.033 1359-6454/© 2016 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Acta Materialia 106 (2016) 367e373