Effect of solute segregation on the strength of nanocrystalline alloys: Inverse Hall–Petch relation T.D. Shen a, * , R.B. Schwarz a , S. Feng a , J.G. Swadener a , J.Y. Huang b , M. Tang a , Jianzhong Zhang c , S.C. Vogel c , Yusheng Zhao c a Materials Science and Technology Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA b Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM 87185, USA c LANSCE Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Received 19 April 2007; received in revised form 9 May 2007; accepted 10 May 2007 Available online 28 June 2007 Abstract We have used a high-energy ball mill to prepare single-phased nanocrystalline Fe, Fe 90 Ni 10 , Fe 85 Al 4 Si 11 , Ni 99 Fe 1 and Ni 90 Fe 10 pow- ders. We then increased their grain sizes by annealing. We found that a low-temperature anneal (T < 0.4 T m ) softens the elemental nano- crystalline Fe but hardens both the body-centered cubic iron- and face-centered cubic nickel-based solid solutions, leading in these alloys to an inverse Hall–Petch relationship. We explain this abnormal Hall–Petch effect in terms of solute segregation to the grain boundaries of the nanocrystalline alloys. Our analysis can also explain the inverse Hall–Petch relationship found in previous studies during the ther- mal anneal of ball-milled nanocrystalline Fe (containing 1.5 at.% impurities) and electrodeposited nanocrystalline Ni (containing 1.0 at.% impurities). Published by Elsevier Ltd on behalf of Acta Materialia Inc. Keywords: Inverse Hall–Petch effect; Nanocrystalline; Mechanical property; Hardening by annealing; Grain boundary segregation 1. Introduction It is often observed that the strength P of a polycrystal- line material increases with decreasing grain size D accord- ing to the Hall–Petch relation: P ¼ P 0 þ kD 1=2 ; ð1Þ where P 0 and k are material constants. This Hall–Petch relation has been explained by several models, such as the pile-up of dislocations ahead of grain boundaries [1,2], the grain boundary acting as a source of dislocations [3], and the influence of grain size on the dislocation density (under the assumption that dislocation density is inversely proportional to grain size) [4,5]. The Hall–Petch relation is obeyed fairly well in crystal- line materials with grain sizes ranging from tens of nano- meters to microns. It often fails, however, in alloys with grain sizes in the range 3–20 nm. Most nanocrystalline materials that do not obey the Hall–Petch relation were first prepared as the smallest grain size possible (e.g. using techniques such as high-energy ball milling, electrodeposit- ion or gas condensation) and then annealed (at increasingly higher temperatures) to increase their grain size. In materi- als prepared this way, the strength increased with increas- ing grain size and thus these materials were said to obey an inverse (or abnormal) Hall–Petch relationship [6–16]. The inverse Hall–Petch effect has been attributed to factors such as: (i) a decrease in dislocation line tension with decreasing grain size [17]; (ii) the difficulty of generating dislocation pile-ups within grains having sizes less than a critical value [18]; (iii) a contribution to plasticity from grain-boundary diffusion creep [19–21], grain-boundary sliding [22,23] or grain-boundary shear [24]; (iv) an overall softening with decreasing grain size due to the increase in the density of triple junctions [25,26] or grain boundaries 1359-6454/$30.00 Published by Elsevier Ltd on behalf of Acta Materialia Inc. doi:10.1016/j.actamat.2007.05.018 * Corresponding author. Tel.: +1 505 665 1171; fax: +1 505 667 8021. E-mail address: tdshen@lanl.gov (T.D. Shen). www.elsevier.com/locate/actamat Acta Materialia 55 (2007) 5007–5013