Supplementary Infermation
Significant Increase of Curie Temperature in Nano-scale BaTiO3
Yueliang Li,1 Zhenyu Liao,1 Fang Fang,1 Xiaohui Wang,2 Longtu Li,2 and Jing Zhu*,1
1
Beijing National Center for Electron Microscopy, School of Materials Science and Engineering,
State Key Laboratory of New Ceramics and Fine Processing, Laboratory of Advanced Materials
(MOE), Tsinghua University, Beijing 100084, China
2
State Key Laboratory of New Ceramics and Fine Processing, School of Materials Science and
Engineering, Tsinghua University, Beijing 100084, China
* Electronic mail: [email protected]
1. Distribution Maps of D-value between the Lengths of the Two Basis Vectors

a

and b
In order to draw out the distribution maps of possible phases related with symmetry,
distribution maps of D-value between the lengths of the two basis vectors

a

and b
(obtained according to the accurately measured coordinate of each atomic column in
the experimental images, denoted in Fig. 1(a-c)) and those of D-value between the
 
angles of < a , b > and 90° (60° for <111> zone axis) were to be drawn out first. Fig.
S1(a-c) show the distribution maps of D-value between the lengths of the two basis


vectors ( a - b
for <100> and <111> zone axis, while
 
2a -b
for <110> zone axis)
corresponding to Fig. 1(a-c) respectively. Unit cells with small D-value locate in cool
areas while those with big D-value locate in warm areas. Warm areas appear more in
the shell of particles according to Fig. S1.
nm
nm |a - b|
nm
nm
|1.4a - b|
nm
nm
nm
|a - b|
nm
（a）
nm
（b）
（c）
Fig. S1. Distribution maps of D-value between the lengths of the two basis vectors
corresponding to Fig. 1(a-c) respectively.
 
2. Distribution Maps of D-value between the Angles of < a , b > and 90° (60° for
<111> Zone Axis)
 
Fig. S2(a-c) show the distribution maps of D-value between the angles of < a , b >
and 90° (60° for <111> zone axis) corresponding to Fig. 1(a-c) respectively. Unit cells
with small D-value locate in cool areas while those with big D-value locate in warm
areas. Warm areas appear more in the shell of particles according to Fig. S2.
nm
|< a, b > - 90°|
°
nm
|< a, b > - 90°|
nm
（a）
°
nm
|< a, b > - 60°|
nm
°
nm
（b）
（c）
 
Fig. S2. Distribution maps of D-value between the angles of < a , b > and 90° (60° for <111>
zone axis) corresponding to Fig. 1(a-c) respectively.
3. Identification of Possible Phases Based on the Two D-values
To identify possible phases based on the two D-values, we first list out all ideal Dvalues of each phase structure for each zone axis, as shown in Table. S1.
Table. S1. All ideal D-values (e.g. the D-value between the lengths of the two basis vectors is 0
if a = b) of each phase structure for each zone axis.
C
<001> zone axis
<110> zone axis
<111> zone axis
a = b, < a, b > = 90°
b = 1.4a, < a, b > = 90°
a = b, < a, b > = 60°
b ≠ 1.4a, < a, b > = 90°
a ≠ b, < a, b > ≠ 60°
67%：a ≠ b, < a, b > = 90°
67%：b ≠ 1.4a, < a, b > ≠ 90°
67%：a ≠ b, < a, b > ≠ 60°
33%：a = b, < a, b > ≠ 90°
33%：b ≠ 1.4a, < a, b > = 90°
33%：a = b, < a, b > ≠ 60°
67%：a ≠ b, < a, b > = 90°
T
33%：a = b, < a, b > = 90°
O
50%：a ≠ b, < a, b > ≠ 60°
50%：b ≠ 1.4a, < a, b > ≠ 90°
R
a = b, < a, b > ≠ 90°
25%：a = b, < a, b > ≠ 60°
50%：b ≠ 1.4a, < a, b > = 90°
25%：a = b, < a, b > = 60°
To explain Table. S1, we take the T phase and <001> zone axis as an example. For
the T phase, the lattice constant satisfies the condition a = b ≠ c. Therefore in the (100)
and (010) projected 2D plane the two basis vectors satisfy the condition a ≠ b and < a,
b > = 90°, while in the (001) projected 2D plane the two basis vectors satisfy a = b and
< a, b > = 90°. The possibility of the two conditions is 67% and 33% respectively for
<001> zone axis.
Based on Table. S1, possible phase structures and corresponding possibility can
be listed out for each basis vector condition for each zone axis, as shown in Table. S2.
According to Table. S2, the distribution maps of possible phases related with symmetry
(Fig. 1(d-f), Fig. 2 and Fig. 3) were drawn out combined with the two kinds of D-value
distribution maps (Fig. S1 and Fig. S2).
Table. S2. Possible phase structures and corresponding possibility for each basis vector
condition for each zone axis.
<001> zone axis
<110> zone axis
<111> zone axis
C(75%) or T(25%)
C(100%)
C(80%) or R(20%)
a = (1.4)b, < a, b > =
90(60)°
a ≠ (1.4)b, < a, b > =
T(55%) or O(18%)
T(50%) or O(50%)
90(60)°
unknown
or R(27%)
a = (1.4)b, < a, b > ≠
O(25%) or R(75%)
unknown
O(57%) or R(43%)
unknown
O(57%) or R(43%)
90(60)°
a ≠ (1.4)b, < a, b > ≠
T(46%) or O(31%)
90(60)°
or R(23%)
4. Error Estimation
As the error of atomic column position measurement is about 5 pm [1], the errors
of the two D-values for each zone axis were estimated, as shown in Table. S3. Taking
<001> zone axis as an example, if the measured D-value between the lengths of the two
basis vectors is smaller than 10 pm, we consider that the lengths of the two basis vectors
satisfy a = b.
Table. S3. The estimated errors of the two D-values for each zone axis.
<001> zone axis
<110> zone axis
<111> zone axis
Error of D-value between the lengths of the two basis vectors 10 pm 12 pm 9 pm
Error of D-value between the angle and 90(60) °
1.5°
1.8°
1.5°
Reference
[1]
C.-L. Jia, S.-B. Mi, K. Urban, I. Vrejoiu, M. Alexe, and D. Hesse, Nat. Mater. 7, 57
(2008).