Giant room temperature compression and bending in ferroelectric oxide pillars

Plastic deformation in ceramic materials is normally only observed in nanometre-sized samples. However, we have observed high levels of plasticity (>50% plastic strain) and excellent elasticity (6% elastic strain) in perovskite oxide Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3, under compression along <100>pc pillars up to 2.1 μm in diameter. The extent of this deformation is much higher than has previously been reported for ceramic materials, and the sample size at which plasticity is observed is almost an order of magnitude larger. Bending tests also revealed over 8% flexural strain. Plastic deformation occurred by slip along {110} <1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\bar{1}$$\end{document}1¯0 > . Calculations indicate that the resulting strain gradients will give rise to giant flexoelectric polarization. First principles models predict that a high concentration of oxygen vacancies weaken the covalent/ionic bonds, giving rise to the unexpected plasticity. Mechanical testing on oxygen vacancies-rich Mn-doped Pb(In1/2Nb1/2)O3-Pb(Mg1/3Nb2/3)O3-PbTiO3 confirmed this prediction. These findings will facilitate the design of plastic ceramic materials and the development of flexoelectric-based nano-electromechanical systems.


This PDF file includes:
1.
Experimental set up of compression, tensile and bending tests;

3.
Compression test results of PIN-PMN-PT pillars with diameters ranging from 130 nm ~ 270 nm, with a loading direction of [010]pc; 4.
Compression test results of SrTiO3 (STO) single crystal pillars with diameter ranging from 150 nm to 260 nm, and loaded along [010]; 5.
Tensile test results of PIN-PMN-PT with loading direction along [010]pc; 9.
Theoretical microstructural model contains multiple mini-interfaces in the PIN-PMN-PT sample; 13.
Oxygen vacancies in PIN-PMN-PT;
Electronic structure: bonding analysis using charge density plots; 16.

Compression test results of PIN-PMN-PT pillars with diameters ranging from 130 nm ~ 270 nm, with a loading direction of [010]pc: Supplementary Fig. Engineering stressstrain curves obtained during in-situ compression of pillars with diameters ranging from 130 nm ~ 270 nm, and corresponding TEM images of pillars after compression tests.
In image e, A and B are TEM images showing the pillar before and after the compression test. Dislocations are evident in A as indicated by a red arrow. All stressstrain curves and images are typical of plastic deformation.

Compression test results of SrTiO3 (STO) single crystal pillars with diameter ranging
from 150 nm to 260 nm, and loaded along [010]: STO pillars were fabricated with 150 nm to 260 nm diameters using the same method as PIN-

Inconsistent plasticity in large PIN-PMN-PT pillars:
In Fig. 1i j, red crosses represent pillars that underwent brittle fracture while black diamonds (open and solid) indicate plastically deformed pillars. In Fig. 1i, it is evident that all pillars with diameters less than 600 nm show excellent plasticity while those with diameters greater than 700 nm show inconsistent plasticitywith some pillars plastically deformed and others not. The fracture strains range from 2.4% ~ 6.2%, comparable to those of elastic strain of 1.3% ~ 6.0% in the plastically deformed pillars (the fracture strain and elastic strain are measured from SEM images of pillars before compression and before fracture / initiation of plastic deformation).
There are a few possible explanations for this phemonemon: Firstly, pre-existing dislocation sources or dislocations. It is widely accepted that plastic deformation in metals depends highly on the pre-existing dislocation sources. 3,4 Here, the Secondly, slight pillar misalignment may facilitate deformation. A perfect alignment along [010]pc means that three slip planes have an equal critical resolved shear stress (CRSS), meaning that multiple slip systems are likely to be operations. Interactions between dislocations on different slip planes may result in crack generation like that observed in Supplementary Fig. 7a and Supplementary Fig. 10.
There are other possible reasons for the inconsistent plasticity instability observed in pillars with diameter greater than 700 nm: (a) For large pillars, stress concentration tends to occur during loading, especially if the front end of the pillar and the diamond punch do not fit exactly; (b) Surface effect. Some nanowires show plasticity due to their extremely small size 5 , in which surface plays a significant role in determining its performance. In the PIN-MN-PT pillars with diameter greater than 700 nm, the surface effect is significantly reduced, and it is more likely a bulk material in behavior; (c) In pillars with diameter larger than 700 nm, more slip systems are able to to initiate, resulting in multiple slip bands or dislocation interactions, which easily result in local work hardening and fracture.

Bending test results of PIN-PMN-PT along [010]pc:
Flexural strain is calculated using following equation: where b (0.67 μm) and x (1.51 μm) are width and maximum deflection of the cantilever beam, while l (4.32 μm) is the distance between loading point and the base of the cantilever beam.
Elastic strain and plastic strain are calculated using the reversible deflection (1.25 μm) and residual deflection (0.26 μm) respectively. Uniform distribution of these elements is evident.

Three sets of tetragonal subunits.
The perovskite PT-PIN-PMN crystal structure is complex. For instance, even for pure PMN, there is a degree of disordering of Mg 2+ and Nb 5+ ions at the B site 6

Theoretical microstructural model contains multiple mini-interfaces in the PIN-PMN-PT sample:
When the three materials (namely PT, PIN and PMN) are mixed at high temperature, the three unit-cells are assumed to retain their chemical identities by considering the electron counting rule such that to maintain the local charge neutrality. Immediately, this leads to a conclusion that the mixing of these three sets of subunits will generate multiple mini-interfaces. Such a scenario is supported by our experimental atomic scale EDS mapping, as shown in Supplementary Fig. 16.
We performed a thorough study on a large number of possible interface structures.  It is found that the configurational ordering is found important; for instance, PT-PIN-PMN-B is higher in energy that PT-PIN-PMN by 0.64 eV.
To evaluate the likelihood of interfaces, we calculated the interface formation energies E f , defined as: where E is the total energy.

Oxygen vacancies in PIN-PMN-PT:
It is well established that charged vacancies, both oxygen vacancy (VO) and lead vacancy (VPb), are the common point defects in PbTiO3 and similar oxides 10,11 . Here we studied the incorporation of one oxygen vacancy in the identified energetically favorable interfaces. For each interface with one vacancy, we conducted a complete search by calculating different vacancy sites. The relaxed atomic structures are shown in Supplementary Fig. 20.   Supplementary Fig. 20. Calculated atomic structure of the interfaces containing O vacancy.
To evaluate the effect of interfaces on the presence of oxygen vacancies, we calculated the VO formation energy in bulk (PT, PIN and PMN) phases and their interfaces. To make these values comparable, we deliberately used small supercells (10 -30 atoms) for the bulk phases. However, it is known that a charged vacancies calculation requires corrections to artificial Coulomb interaction, and hence a large supercell. Therefore, in this study, we only focus on neutral vacancies. To evaluate the relative stability of vacancies, we calculated the formation energy by assuming the Pb and O atom reservoirs are bulk Pb and O2 12 . The calculated neutral VO and VPb formation energy in bulk phases and interfaces are shown in Supplementary Fig. 21.
Significantly, the calculated VO formation energy values in the PIN-PMN-PT interfaces are significantly lower than those in the bulk phases, by ~ 1.5 -2 eV per VO. In sharp contrast, the VPb formation energy values in the interfaces are similar or higher than those in the bulk phases.
Thus, our DFT results suggest that, energetically, the presence of interfaces promotes the formation of VO but not VPb.
Using Boltzmann distribution 13 , the equilibrium oxygen vacancy concentration ratio in interface versus in bulk is: where ΔE corresponds to the formation energy difference in bulk and in interface, namely ~1.5 -2 eV, k is the Boltzmann constant and T is the temperature. At T = 300 K, the estimated C ratio is ~ e 60 -e 80 ! While this value from the simple model may have been severely overestimated considering that (1) the practical process is far from the equilibrium condition, (2) the expected large error-bar of the calculated formation values of neutral vacancies. Nevertheless, our theoretical results clearly demonstrate that in the PT-PIN-PMN sample, the O vacancy concentration is much higher than in the corresponding bulk phases. It is also interesting to notice that for the most configurations shown in Supplementary Fig. 20

Mechanical properties from first principles:
The mechanical properties can be estimated by elastic moduli such as bulk modulus (B) and shear modulus (G). In particular, the Pugh ratio B/G is conveniently used as an indicator for determining whether a material is ductile or brittle. If the ratio is larger than