Structural coherence and ferroelectricity decay in submicron- and nano-sized perovskites V. Petkov, 1, * V. Buscaglia, 2,† M. T. Buscaglia, 2 Z. Zhao, 3 and Y. Ren 4 1 Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, USA 2 Institute for Energetics and Interphases, CNR, Via De Marini 6, I-16149 Genoa, Italy 3 Institute of Inorganic Chemistry, University of Stockholm, S10691 Stockholm, Sweden 4 Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA Received 2 March 2008; revised manuscript received 5 June 2008; published 11 August 2008 Understanding the loss of ferroelectricity in submicron- and nano-sized perovskites is an issue that has been debated for decades. Here we report results from a high-energy x-ray diffraction XRD study on a prime example of the perovskite’s family, BaTiO 3 ceramics with a grain size ranging from 1200 to 5 nm. We find that the loss of ferroelectricity in submicron- and nano-sized BaTiO 3 has an intrinsic origin related to the increased atomic positional disorder in spatially confined physical systems. Our results imply that no particular critical size at which ferroelectricity in BaTiO 3 , in particular, and perovskites, in general, is completely lost exists. Rather it weakens exponentially with the decreasing of their physical size. Smart technological solutions are needed to bring it back. DOI: 10.1103/PhysRevB.78.054107 PACS numbers: 61.43.-j, 81.07.Bc I. INTRODUCTION Ferroelectric materials of the perovskite family ABO 3 , where A =Ba, Sr, and Pb, and B =Ti and Zr, are extensively used in electronic industry for fabrication of multilayer ca- pacitors, piezoelectric transducers, pyroelectric elements, and ferroelectric memories. 1,2 With these technologies moving quickly toward smaller scales, electronic devices are already shrunk to nanometer sizes. Unfortunately, such a reduction in the physical size of perovskite ferroelectrics results in a dramatic deterioration of one of their most useful properties, in particular a dramatic reduction in the spontaneous polarization. 3 In bulk ceramics a progressive suppression of the spontaneous polarization and a reduction in the dielectric constant are observed when the grain size is reduced already below 1 m. 4,5 The suppression seems to be full when the grain size gets down to 30 nm since ferroelectric hysteresis loops no longer show evidence of domain switching even when electric fields of 60 kV/cm are applied. 6 High-quality epitaxial ABO 3 films have been reported to exhibit a similar behavior retaining ferroelectricity down to a thickness of a few nanometers only. 7,8 Several studies aimed at understand- ing the observed ferroelectricity “size” effect have been con- ducted. Classical, phenomenological thermodynamic theory studies Landau-Ginzburg-Devonshire approach concluded that the effect may be viewed as a phase transition from a ferroelectric to a paraelectric state taking place at a critical system size of a few to a few tens of nanometers. 9 Another point of view asserts the presence of a thin layer, referred to as “dead,” lacking in or with a greatly reduced spontaneous polarization and low dielectric constant at the grain bound- aries of bulk ceramics and the electrode/ferroelectric inter- face in supported thin films/capacitors. 4,10,11 The layer has been explained in terms of a depolarization field arising from the inhomogeneity of charge distribution at the surface/ interface discontinuity. 12 The likely presence of structural imperfections such as oxygen vacancies, dislocations, disor- der, etc. at the film interfaces and/or grain boundaries has been widely discussed as well. 11–13 However, the loss of fer- roelectricity in both thin perovskite films and bulk ceramics has also been found to be accompanied by a profound hard- ening of the so-called soft phonon mode. 12–14 Phonon modes are the elementary vibrations of crystalline lattices, implying that not just the increased surface in submicron- and nano- sized perovskites but the way atoms interact inside them may be at the root of the unwanted ferroelectricity loss. Here we explore this aspect of the size effect using high-energy x-ray diffraction XRD and atomic pair distribution function PDF analysis. The approach has already proven to be very successful in studying the atomic arrangement inside materi- als of very limited structural coherence, including nanosized crystals. 15 We concentrated on a prime example of the per- ovskite ferroelectrics family, BaTiO 3 . We found that the de- terioration of spontaneous polarization in submicron- and nano-sized BaTiO 3 is indeed a typical decay of a bulk mate- rial’s property due to a gradual weakening of the longer- range interatomic correlations that are necessary for that property to exist. The weakening may be understood easily if considered in terms of the famous “uncertainty principle”; in this case it is a gradual increase in the root-mean-square rms fluctuations of atomic positions taking place when the size of physical systems is reduced gradually down to the nanometer scale. In other words, we found that the deterio- ration of spontaneous polarization in submicron- and nano- sized perovskites has an intrinsic origin related to the spatial confinement of the system. II. EXPERIMENT RATIONALE AND RESULTS At high temperature, BaTiO 3 has a centrosymmetric cubic structure and is paraelectric. Between room temperature and 393 K, known as the ferroelectric Curie temperature, the material possesses a tetragonal-type structure, below 278 K the structure is orthorhombic, and below 183 K— rhombohedral. 16 Fragments of the cubic and the technologi- cally important tetragonal phases of BaTiO 3 are presented in Fig. 1. The structural pattern is characteristic for all ABO 3 perovskites. It features a three-dimensional 3D network of PHYSICAL REVIEW B 78, 054107 2008 1098-0121/2008/785/0541077 ©2008 The American Physical Society 054107-1