Supplemental Material for Monoclinic Nanodomains in Morphotropic Phase
Boundary Pb(Mg1/3Nb2/3)O3 - PbTiO3
Y. Sato1, T. Hirayama2, and Y. Ikuhara1-3,
1
Institute of Engineering Innovation, The University of Tokyo, 2-11-16, Yayoi, Bunkyo, Tokyo,
113-8656, Japan.
2
Nanostructures Research Laboratory, Japan Fine Ceramics Center, 2-4-1, Mutsuno, Atsuta, Nagoya,
456-8687, Japan.
3
World Premier International Research Center, Advanced Institute for Materials Research, Tohoku
University, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan.
Materials and Methods:
PMN-xPT (nominal composition: x ~ 0.30 ± 0.01, the average value measured by energy-dispersive
X-ray spectroscopy in scanning transmission electron microscope: x ~ 0.33) single crystal as used in
our previous studiesS1-S3 is studied in this paper. Thin foil for transmission electron microscopy
(TEM) observation was prepared with the conventional procedures including mechanical grinding
and argon ion-beam milling for obtaining electron transparency. Ion beam energy for the milling was
4 keV until a hole was made and ~ 1 keV for the final milling to remove the damaged layer. After
this process, the foil was heated at 200 ºC for 30 min. to ensure unpoled state of the specimen. TEM
observation was carried out with JEM-2010HC (JEOL Ltd.) electron microscope at the acceleration
voltage of 200 kV. Electron incident axis to the specimen was parallel to [ 1 1 0] , while it was
sometimes slightly inclined. Dark-field (DF) TEM images were taken at approximate two-beam
conditions. When recording selected area diffraction pattern (SADP), parallel illumination of the
electron beam was used. Area of interest was chosen by inserting selected area aperture with the
diameter of ~ 500 nm or ~ 2 m. SADPs and TEM images were recorded onto photographic films.
The negative films were scanned by a high-resolution flatbed scanner (Epson GP-X970). TEM
images and the SADPs were recorded as 16-bit grayscale images.
Since previous studies have pointed out that the splitting of SADP in MPB PMN-PT is too small to
be observedS4, we started this study with checking if the splitting can be obtained or not. In order to
improve the reciprocal space resolution of the SADP, we paid particular attentions to the following.
First, the nominal camera length was increased up to 1,200 or 1,500 mm. Next, the 000 spot was
moved to the edge of the film. These two things make the 000 spot and the spot of interest further
apart while they can still be simultaneously recorded in a single film (Fig. S1(a)). Finally, the film
was scanned at greater resolution as high as 9,600 spi (~ 2.6 x 2.6 m2 per a pixel), which is enabled
by modern scanners. As a result, the spot splitting has been unambiguously observed from the region
including two NDs (Fig. S1(b)).
For quantitative analysis of the split spot, peak fitting with two-dimensional Gaussian functions was
carried out. The Gaussian function for the peak number i has the form of:
 1  x  x 2 1  y  y 2 

ci   
ci  ,
Zi ( x, y )  Ai  exp  



2  wi 
2  wi  



where Z i ( x, y ) is the peak intensity as a function of x and y, Ai and wi are the peak height and
the width, and ( xci , yci ) represents the peak center.
Valuables ( Ai , xci , and yci ) were iteratively optimized for some chosen values of wi so that  2
be minimized.  2 is defined as:
2
n

    Zi ( x, y)  Z 0   Z e ( x, y)2 ,
i 1

2
where Z 0 and Ze ( x, y) represent the background and the experimental intensities, and the total peak
number is n. The fitting was carried out using our homemade program.
FIG. S1 SADP obtained under the present experimental condition. (a) Whole view of the SADP
recorded in a film. It was taken with the 000 spot shifted upward and the nominal camera length of
1,200 mm. Electron incident axis is parallel to [ 1 1 0] . (b) Enlargement of the 2 2 3 spot, where the
splitting is unambiguously observed as indicated by arrows. The negative film was scanned at the
9,600 spi resolution.
G-dependence of ND contrast:
Trace of nanoscale DWs (NDWs, Fig. S2(a)) is parallel to (1 1 1) in the MD A and (1 1 1) in the
MD B. It is also found that the ND contrast strongly depends on the g-vector used in recording DF
TEM imagesS1,S5. ND contrast appears both in the MDs A and B for the g  002 image (Fig. S2(b)),
while only in the MD A for the g  1 1 1 image (Fig. S2(c)), and only in the MD B for the
g  1 1 1 image (Fig. S2(d)).
FIG. S2 G-dependent ND contrast in MPB PMN-PT. (a) Schematic illustration of nanodomains
(NDs a ~ d). (b) G = 002, (c) g  1 1 1 , and (d) g  1 1 1 DF TEM images. Colored lines indicate
the NDWs appearing as strong contrast.
SADP from the MD A (the NDs a and b) and its relation to ND contrast
In the SADP taken from the MD A (Fig. S3(a)), the 3 33 (Fig. S3(b)) and the 005 (Fig. S3(c))
spots are split. Approximate match between the experimental (Fig. S3(d)) and the fitted (Fig. S3(e))
intensities was obtained with the Gaussian peak fitting. This is supported by the residual matrix (Fig.
S3(f)), where the absolute value is smaller than 30 % in most of the area. The spots have two
different d spacings by 0.13 %, rotated by 0.10 º each other. Similarly, the 005 spot has two different
d spacings by 0.20 % without relative rotation (Figs. S3 (g)-(i)).
Splitting of the 3 33 spot indicates that the 1 11 spot is not common to the NDs a and b.
Similarly, the 002 spot is not common to the NDs a and b. These results explain the appearance of
NDW contrast in DF TEM images (Figs. S2(b) and (c)). Since the 002 spots for the NDs a and b are
not common, the NDs a and b can have different contrast in the g = 002 image (Fig. S2(b)). Similar
domain contrast mechanism was also reported for the (110) 90º domain in BaTiO3 (Ref. S6). The
same discussion holds for the g  1 1 1 DF image case (Fig. S2(c)).
SADP from the MD B (the NDs c and d) and its relation to NDW contrast
In the case of the MD B (Fig. S4(a)), similar result is obtained. The 3 3 3 (Fig. S4(b)) and the
004 (Fig. S4(c)) spots are split. Again, the Gaussian peak fitting shows approximate match with the
absolute value of the residuals smaller than 30 % (Figs. S4 (d)-(i)). It is found that the two 3 3 3
spots have identical d spacing but different  by 0.10 º. On the other hand, the 004 spot have two
different d spacings by 0.29 % but no difference in . Also, the splitting of the 3 3 3 and the 004
account for the ND contrast in the g = 002 and g  1 1 1 DF TEM images (Figs. S2(b) and (d)). ND
contrast mechanism in the MD A is therefore quite analogous to that in the MD B, implying that the
MDs A and B are of the same crystal phase.
FIG. S3. SADP from the MD A and the peak analysis. (a) Selected area for the MD A (NDs a and b).
Enlargement of the (b) 3 33 and the (c) 005 spots. Peak fitting analysis for the 3 33 spot (d-f). (d)
The experimental and (e) the fitted intensities, and (f) the residual matrix. Peak fitting analysis for
the 005 spot (g-i). (g) The experimental and (h) the fitted intensities, and (i) the residual matrix.
FIG. S4. SADP from the MD B and the peak analysis. (a) Selected area for the MD B (NDs c and d).
Enlargement of the (b) 3 3 3 and the (c) 004 spots. Peak fitting analysis for the 3 3 3 spot (d-f).
(d) The experimental and (e) the fitted intensities, and (f) the residual matrix. Peak fitting analysis for
the 004 spot (g-i). (g) The experimental and (h) the fitted intensities, and (i) the residual matrix.
SDAP from both the MDs A and B (the NDs a ~ d)
In the SADP taken from both the MDs A and B (Fig. S5), multiple spots are split (Fig. S6). In
particular, the 221 , 220 , 22 1 , and 3 3 0 spots (Fig. S7) have quite similar splitting patterns. This
allows us to assign four spots in the 220 spot as in Fig. S7. Thus, with this assignment, the 220
spot was analyzed (Fig. S8 (a)-(d)). Four individual peaks are obtained as in Figs. S8 (e)-(h). It is
found that r for #1, #2, and #3 differ by -0.12 %, +0.24 %, and -0.29 %, respectively from that for #4.
Corresponding values for a reported m(Pm) phaseS7 is -0.04 %, +0.25 %, -0.16 % as compared to the
reference one (0 %).  for #1, #2, and #3 differ from that for #4 by +0.30º, +0.22º, and +0.07º,
respectively.
FIG. S5. SADP taken from both the MDs A and B.
FIG. S6. Enlargement of the spots as indexed in Fig. S5.
FIG. S6. (continued).
FIG. S7. Splitting pattern of the 220 and a few neighboring spots. (a) Enlargement of the 221 ,
2 20 , 22 1 , and 3 3 0 spots, and (b) the splitting patterns for the respective cases.
FIG. S8. Peak fitting analysis of the 220 spot obtained from both the MDs A and B. (a) The
experimental and (b) the fitted intensities for the 220 spot. (c) Assigned peaks as indicated in Fig.
S7. (d) The residual matrix. Fitted peaks (e) #1, (f) #2, (g) #3, and (h) #4, respectively.
Orientation of permissible DWs in monoclinic (Pm) phase
Bokov and Ye reported the possible domain configuration and DW orientation in m (Pm) phaseS8.
They reported Wf-type DWs and S–type DWs for ferroelastic (as well as ferroelectric) DWs. Out of
these two types, Wf DWs are inconsistent with the NDWs observed in the present study. Although Wf
DWs should be parallel to one of {100} or {110}, the trace of the present NDWs is ( 1 1 1 ) and (1 1 1) .
On the other hand, there are three types of S DWs. S1 and S2 DWs are uncharged while S3 DWs are
basically charged. Since charged DW is considered unstable, S3 DW is not discussed here.
Orientation of the S1 and S2 DWs depends on the crystal lattice constants. Discussion in Ref. S8
using the value provided by Ref. S9 suggests that the S1 DWs has the orientation very close to {111},
and the orientation of S2 DWs should be close to {221}. NDWs observed in the present study, which
have ( 1 1 1 ) and ( 1 11) traces, are therefore considered to be S1 DWs.
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