Dislocation structure at a f1210g=h1010i low-angle tilt grainboundary in LiNbO3

Atsutomo Nakamura • Eita Tochigi •

Jun-nosuke Nakamura • Ippei Kishida •

Yoshiyuki Yokogawa

Received: 8 September 2011 / Accepted: 22 February 2012 / Published online: 22 March 2012

� Springer Science+Business Media, LLC 2012

Abstract LiNbO3 is a ferroelectric material with a rhom-

bohedral R3c structure at room temperature. A LiNbO3

bicrystal with a f1210g=h1010i 1� low-angle tilt grain

boundary was successfully fabricated by diffusion bonding.

The resultant boundary was then investigated using high-

resolution TEM. The boundary composed a periodic array of

dislocations with b ¼ 1=3h1210i. They dissociated into two

partial dislocations by climb. A crystallographic consider-

ation suggests that the Burgers vectors of the partial dislo-

cations should be 1=3h0110i and 1=3h1100i, and a stacking

fault on f1210g is formed between the two partial disloca-

tions. From the separation distance of a partial dislocation

pair, a stacking fault energy on f1210g was estimated to be

0.25 J/m2 on the basis of isotropic elasticity theory.

Introduction

LiNbO3 is a widely used ferroelectric material with pyro-

electric, piezoelectric, electro-optic and photoelastic prop-

erties, and a high Curie point (*1200 �C) [1–3].

Ferroelectric materials have applications in constructing

various tools such as memory devices, actuators, surface

acoustic wave filters, heat sensors, and light wavelength

converters, owing to their characteristic properties.

Therefore, it is important to understand the mechanical,

electrical, and optical characteristics of ferroelectric

materials [4]. These characteristics are strongly related to

the structure of lattice defects in these materials.

The lattice defects of LiNbO3 have been studied for

several decades; the point defects [5–10] have received

attention because of their non-stoichiometry due to complex

oxides. On the other hand, it seems that the plane and line

defects of LiNbO3 receive less attention. It has been reported

that twinning deformation occurs on f1210g=h1011i[11–13] and that the basal glide system [0001] h1210iseems easier to activate than the prismatic glide system

f1210g=h1101i at high temperature [14]. The microscopic

structures of the twins and dislocations in LiNbO3 have not

been understood well because few studies have been con-

ducted using transmission electron microscopy (TEM).

In the present study, a LiNbO3 bicrystal with a

f1210g=h1010i low-angle tilt grain boundary was fabricated

by diffusion bonding of two single-crystals, to investigate the

boundary structure and characterize the microscopic structure

of a dislocation with b ¼ 1=3h1210i. Then the resultant

boundary was investigated using high-resolution TEM

(HRTEM) at room temperature, and its structure was exam-

ined from a crystallographic viewpoint. Here, the bicrystal

experiment using a low-angle grain boundary is powerful for

characterizing the dislocation structure because an ideal array

of dislocations is formed on the boundary [15–18].

A dislocation with b ¼ 1=3h1210i in LiNbO3 has a

minimum translation vector on the (0001) basal plane and

corresponds to the basal dislocation that brings about the

basal glide system ð0001Þh1210i. It is well known that a

basal dislocation with b ¼ 1=3h1210i in a-Al2O3 can dis-

sociate into two partial dislocations with the Burgers vec-

tors of 1=3h0110i and 1=3h1100i [19, 20], where a-Al2O3

A. Nakamura (&) � J. Nakamura � I. Kishida � Y. Yokogawa

Department of Mechanical & Physical Engineering,

Osaka City University, 3-3-138, Sugimoto, Sumiyoshi-ku,

Osaka 558-8585, Japan

e-mail: nakamura@imat.eng.osaka-cu.ac.jp

E. Tochigi

Institute of Engineering Innovation, The University of Tokyo,

2-11-16 Yayoi, Bunkyo-ku, Tokyo 113-8686, Japan

123

J Mater Sci (2012) 47:5086–5096

DOI 10.1007/s10853-012-6373-7

has a rhombohedral R3c structure, which is similar to the

R3c structure of LiNbO3 at room temperature. Thus, it is

worth paying attention to the structure of a dislocation with

b ¼ 1=3h1210i in LiNbO3. It should be noted that the core

structure of the boundary dislocations might differ from

that of the lattice dislocations owing to the proximity

between the neighboring boundary dislocations and the

diffusion bonding process in a bicrystal.

Crystal structure of LiNbO3

LiNbO3 has a rhombohedral R3c structure at room tem-

perature and R3c above its Curie point [1, 2]. Figure 1

shows a schematic illustration of the crystal structure in the

ferroelectric state at room temperature. Figure 1a–c show

the configuration of constituent ions along ½1210�; ½1010�,and [0001], respectively. Here oxygen ions were approxi-

mated to be in a hexagonal close packed (hcp) arrangement

for the ease of understanding the crystal structure. Note

that the actual sites of the oxygen ions are displaced

slightly on (0001) from the regular hcp arrangement. The

crystal structure can be thought of as having a hcp

arrangement of oxygen ions, where 2/3 of the octahedral

sites of oxygen ions are occupied by cations. As seen in

Fig. 1, LiNbO3 has a complicated crystal structure, which

may be an obstacle in understanding the structure of plane

and line defects.

Experimental procedure

A congruent LiNbO3 single-crystal grown by the Czo-

chralski method [21, 22] was used to fabricate a bicrystal

with a f1210g=h1010i low-angle tilt grain boundary.

Figure 2 shows a schematic illustration of the two pieces of

single-crystal plates before bonding and the fabricated bi-

crystal after bonding. The size of each single-crystal plate

was set as 10 9 10 9 1 mm3 to prepare a bicrystal with a

size of 10 9 10 9 2 mm3. The surfaces of the single-

crystal plates were successively polished using diamond

suspensions to achieve a mirror finish. The two single-

crystal plates were subsequently joined by diffusion

bonding in air at 800 �C for 10 h under an additional

pressure of 0.1 MPa. As shown in the figure, the ð1210Þsingle-crystal plate was bonded with the plate 1� off

from the exact ð1210Þ plane about the ½1010� axis, resulting

in the fabricated bicrystal with a 1� asymmetric

f1210g=h1010i tilt grain boundary. In this case, edge-type

dislocations with b = 1/3h1210i will primarily form on the

boundary [16, 23].

The directions of polarization in the two plates were set

up to be the same in the bonding process. LiNbO3 has

polarization only along \0001[ because it has the R3c

structure and the structure or character along the [0001]

direction differs from that along the opposite direction of

½0001�. Therefore, the temperature of 800 �C for bonding in

this study is selected to be sufficiently lower than the Curie

point of *1200 �C. Here, 800 �C (1073 K) corresponds to

about 0.7 times the melting point of 1253 �C (1526 K).

The polarization in the two plates will be conserved during

the bonding process.

Figure 3 shows optical photographs of the bicrystal

before and after diffusion bonding. The two plates exhibit

interference fringe on the interface, as seen in (a), because

the two plates have not yet been joined and have space

between them, while the fabricated bicrystal in (b) exhibits

little fringe and looks like a single-crystal. This indicates

that the two single-crystal plates were successfully joined

by diffusion bonding. The grain boundary of this fabricated

bicrystal was observed by TEM. The specimens for the

(a)

(c)

O ions

Li ions

Nb ions

vacant sites

[0001]

[121

0]

[1010]

[000

1]

[1010][1210]

pola

rizat

ion

1/3[1010]

1/3[

1210

]

(b)

[000

1]

[1010][1210]

1/3[1210][1010]

1/2[

0001

]

Fig. 1 Schematic illustration showing the crystal structure of

LiNbO3 at room temperature. The arrangement of ions along

½1210�; ½1010�, and [0001] are represented in (a–c), respectively.

Two kinds of stacking of O ions along [0001] are denoted by largeopen circles and large half-shaded circles. The vectors of

1=3½1210�; ½1010�, and [0001] correspond to the minimum translation

vectors along their directions of LiNbO3

J Mater Sci (2012) 47:5086–5096 5087

123

observation were prepared using a standard technique

involving mechanical grinding to a thickness of 0.1 mm,

attaching with a stainless-steel single-hole mesh for rein-

forcement, dimpling to a thickness of about 30 lm, and ion

beam milling to an electron transparency at about 4 kV.

TEM observation was conducted using a conventional

TEM (c-TEM; JEOL JEM-2100, 200 kV) and a high-res-

olution TEM (HRTEM; JEOL JEM-4010, 400 kV).

Results

Figure 4a shows a typical bright-field TEM image of the

grain boundary taken along ½1010�. In the case of a bright-

field image, as seen in the figure, the particle-like regions

of 100–200 nm with moire are distinctly observed at the

boundary, in addition to the boundary dislocations that

compensate the misorientation angle on this boundary.

Figure 4b shows a selected-area electron diffraction pattern

taken from a large region with a diameter of about 900 nm,

which includes the particle-like regions. The particle-like

regions with moire have the same crystal structure as the

bulk because the diffraction patterns are the same. The

regions with moire are considered to have little distortion

of the crystal lattice. This indicates that LiNbO3 may allow

a slight change in the lattice parameter locally, as expected

from its application as a piezoelectric material. Further

discussions about the particle-like regions with moire are

presented in the Appendix 1 so that we can focus on the

structure of boundary dislocations in the main text.

Figure 4c shows a TEM image of the boundary dislo-

cation array taken along ½1010� from the region with less

moire. This image is taken using a HRTEM technique,

although the magnification is not very high. The white

arrows in the figure indicate the position of the boundary

dislocations. The periodic spacing between two neighbor

dislocations is about 27 nm. Here the relation between the

spacing d and the misorientation angle in a low-angle tilt

grain boundary, h, is given by h = b/d, where b is the size

of the edge component of the Burgers vector of the

boundary dislocations, according to the Frank formula [24].

In this boundary, the minimum translation vector normal to

the (1210) boundary plane is 1=3½1210�, the size of which

corresponds to a representative lattice constant of LiNbO3,

that is, the Burgers vector of the boundary dislocations

should be 1=3½1210�. The calculated misorientation angle

is 1.1�.

Figure 5 shows a typical HRTEM image of a boundary

dislocation taken along ½1010�, which directly includes one

of the boundary dislocations. It should be noted that two

neighbor lattice discontinuities clearly appear in the mag-

nified HRTEM image, as indicated by the arrows. This

implies that a boundary dislocation dissociates into two

partial dislocations with a narrow separation distance.

Here, the periodicity of the bright points in the HRTEM

image corresponds to that of 1/3[0001] along [0001] and

1=6½1210� along ½1210�. See Appendix 2 for details on the

bright points on the HRTEM image of LiNbO3.

(a)

(b)

[0001]

[0001]

1o off from (1210)

(1210)

Fig. 2 Schematic illustration showing the shapes and crystallo-

graphic orientation relationship of the bicrystal before and after

diffusion bonding. a Two pieces of single-crystal plates for bonding.

b Fabricated bicrystal after bonding. The edge-type of a perfect

dislocation array is illustrated here, which can be formed ideally

(a) (b)

5 mm 5 mm

Fig. 3 Optical photographs of

the bicrystal before and after

diffusion bonding. a Double

single-crystal plates display

interference fringe on the

interface since the two plates are

not joined. b The fabricated

bicrystal displays little fringe

5088 J Mater Sci (2012) 47:5086–5096

123

Figure 6a shows the magnified HRTEM image from

Fig. 5 with the Burgers circuits around the two lattice

discontinuities. It can be clearly seen that the two lattice

discontinuities are the two dislocations with an edge

component of 1=6½1210�. Figure 6b shows an inverse Fast-

fourier-transferred (FFT) image reconstructed from a

mask-applied FFT image of the area shown in Fig. 6a. It is

found in Fig. 6b that the separation distance between the

two dislocations was 2.7 nm along [0001], while the two

are adjacently located along ½1210�. It can be said from

direct observation by HRTEM that a boundary dislocation

of b ¼ 1=3½1210� dissociates into two partial dislocations

with an edge component of 1=6½1210� by the narrow

separation distance along [0001]. It should be noted that

the separation distance of 2.7 nm appears to slightly vary

from one dislocation to another one.

Discussion

Structure of a dislocation of b ¼ 1=3½1210�

It is found experimentally that a dislocation of b ¼1=3½1210� in LiNbO3 dissociates into two partial disloca-

tions along [0001]. If a dislocation dissociates, a stacking

fault with the fault vector that corresponds to the Burgers

(c)

(1010)

1210g

200 nm

20 nm

[121

0]

[0001]

(b) ( Ι )

( ΙΙ )

( Ι )

( ΙΙ )

(a)

Fig. 4 Results of TEM observation of the grain boundary along

½1010�. a Bright-field image under a two-beam condition. b Selected-

area electron diffraction pattern taken from a large area, including the

particle-like regions in (a). I and II are magnified patterns to show

detail. c HRTEM image containing four boundary dislocations in the

region with less moire

J Mater Sci (2012) 47:5086–5096 5089

123

vector of a partial dislocation is formed between the partial

dislocations. Figure 7a, b show schematic illustrations of a

dissociated dislocation and a dissociated dislocation’s array

at the boundary, respectively. The stacking sequence of the

(1210) plane along [1210] in LiNbO3 is …abab…, as

shown in (a). Here, we note that the stacking fault plane of

(1210) is not on the (0001) basal plane. This means that a

dislocation dissociates by climb and not by glide. Although

climb requires point defect diffusion, this is easily possible

during diffusion bonding at elevated temperatures.

According to elasticity theory, the climb-dissociated con-

figuration is more stable than the glide-dissociated one.

Figure 7b explains the periodic formation of partial dislo-

cations caused by the dissociation of dislocations and

stacking faults between the partials. Here we discuss the

Burgers vectors of separated partial dislocations and the

structure of a stacking fault formed on (1210) between the

partials.

Figures 8 and 9 show schematic illustrations of the

cation and anion sublattices viewed along [0001]. The

stacking sequence along [1210] is also represented by aand b in these illustrations. For both sublattices, a perfect

stacking sequence is shown in (a), while the stacking

sequence, including the stacking faults on the (1210) plane

with shears of 1=2½1010�; 1=3½1010�, and 1=3½1010�, are in

(b–d), respectively. As shown in Fig. 6, a partial disloca-

tion has an edge component of 1=6½1210�. If it has only the

edge component, that is, if the Burgers vector is 1=6½1210�,the structure of the stacking fault between two partial

dislocations corresponds to the illustrations in Figs. 8b, 9b.

However, the structure in these figures gives rise to the

stacking fault of both the cation and anion sublattices of

[1210]

[1010]

[000

1]

3 nm

Fig. 5 Magnified HRTEM image including a boundary dislocation

along ½1010�

[1210]

[000

1]

(a) (b)

2 nm

2.7

nm

2 nm

Fig. 6 a Magnified HRTEM image of Fig. 5 with the Burgers

circuits around the two lattice discontinuities. b Inverse FFT image

reconstructed from a mask-applied FFT image of (a)

α1 α2 α3 α4 α5β1 β2 β3 β4 β5

(a) (b)

[1010]

[000

1]

crystal interface

stac

king

faul

ts

[1210]13

b

Fig. 7 Schematic illustration showing the structure of observed

dissociated dislocations. a Singular dissociated dislocation, which

corresponds to the observed dislocation in Fig. 5. The stacking

sequence of the ð1210Þ plane along ½1210� is represented by a and b.

A stacking fault is formed along the ð1210Þ plane between b2 and b3.

b Plural dissociated dislocation. Partial dislocations and stacking

faults are periodically formed on the boundary

5090 J Mater Sci (2012) 47:5086–5096

123

LiNbO3, since the 1=2½1010� shear does not coincide with a

translation vector of oxygen ions of 1=3h1010i or

1=3h0110i or 1=3h1100i on the [0001] plane. In contrast,

the structures in Fig. 8c, d show the stacking faults only for

the cation sublattices because their shear vectors corre-

spond to the translation vector of oxygen ions as shown in

Fig. 9c, d. In this case, the dislocation of b1 ¼ 1=3½0110� or

b1 ¼ 1=3½1100� has both the edge component of 1=6½1210�and the screw component of �1=6½1010�, and is therefore

possible to be a partial dislocation. The vectors of b1 and b2

are also shown in Fig. 8a. Thus, the three types of stacking

faults in (b–d) of Figs. 8, 9 are possible as the stacking

fault between the partial dislocations.

It is well known that a basal dislocation of b ¼1=3h1210i in a-Al2O3 often dissociates into two partial

dislocations with the Burgers vectors of 1=3h0110i and

1=3h1100i [19, 20]. The partial dislocation in a-Al2O3 has

a screw component of �1=6h1010i in addition to an edge

component of 1=6h1210i because a stacking fault in both

the cation and anion sublattices has much higher energy

than that in only the cation sublattice. This can be applied

to LiNbO3 with a similar crystal structure. It is suggested

that the dislocation of b ¼ 1=3½1210�] in LiNbO3 should

dissociate into the two partial dislocations of b1 ¼1=3½0110� and b2 ¼ 1=3½1100�.

As for the two types of stacking faults in (c) and (d) in

Fig. 8, the structure along ½1210� in (c) corresponds to that

along ½1210� in (d) as can be seen from b2 and b3. Thus, we

note that the structures of the two stacking faults have a

mirror symmetry relationship. The energy of these two

stacking faults should be the same. On the other hand, the

atomic arrangement around the core of a partial dislocation

may depend on the location of an extra half plane of the

core to the polarization direction along [0001]. That is, the

atomic structure at the core of a partial dislocation may be

dependent on the polarization direction. The influence of

polarization on the core structure, which is a specific issue

for ferroelectric materials, will be a subject for future

studies.

α1 α2 α3 α4 α5β1 β2 β3 β4

α1 α2 α4 α5

β1 β2 β3 β4α1 α2

α4 α5β1 β2

β3 β4

(a)

(d)

(b)[1

010]

[0001]

[1210]13

b

b2

b1 Li ionsNb ions vacant

sites

(c)

α1 α2 α4 α5β1 β2 β3 β4

Fig. 8 Schematic illustration showing the structure of the cation

sublattice viewed along [0001]. a Perfect stacking sequence. Stacking

sequences in b–d, show the cation arrangement, including stacking

faults on the ð1210Þ plane with the shears of 1=2½1010�; 1=3 ½1010�,and 1=3½1010�, respectively. The vectors of b1 and b2 are the Burgers

vectors of two partial dislocations, which are supposed to be formed

by the dissociation

O ions

(a) (b)

(d)(c)

[101

0]

[0001] [1210]

Fig. 9 Schematic illustration showing the structure of the anion

sublattice viewed along [0001]. a Perfect stacking sequence. Stacking

sequences in b–d, show the anion arrangement, including stacking

faults on the ð1210Þ plane with the shears of 1=2½1010�; 1=3 ½1010�,and 1=3½1010�, respectively. It should be noted that the stacking

sequences in (c) and (d) go back to a perfect stacking sequence

J Mater Sci (2012) 47:5086–5096 5091

123

Stacking fault energy and separation distance

A dislocation with b ¼ 1=3½1210� at the boundary dissoci-

ated into two partial dislocations with a separation distance

of 2.7 nm, forming a ð1210Þ stacking fault. The separation

distance is determined by a balance of two forces, the

repulsive elastic force between partial dislocations and the

attractive force due to the stacking fault energy, acting in the

dissociated dislocation. According to the Peach–Koehler’s

equation [25], the balance in the present dislocation can be

expressed by the following equation:

c ¼lb2

pð2þ mÞ8prð1� mÞ ; ð1Þ

where c is the stacking fault energy, l is the shear modulus

(66 GPa), m is the Poisson’s ratio (0.25), bp is the size of the

Burgers vectors of the partial dislocations with b1 ¼1=3½0110� and b2 ¼ 1=3½1100�, and r is the separation

distance. It should be taken into account that the separation

distance is affected by all the elastic repulsive forces, which

act on a partial dislocation from all other dislocations at the

boundary [15, 17, 23]. The balance between repulsive and

attractive forces in this boundary is given as

c ¼lb2

pð2þ mÞ8pð1� mÞd

X1

n¼0

1

nþ a� 1

nþ 1� a

� �; ð2Þ

where d is the periodic spacing between neighbor boundary

dislocations and a is the ratio of r to d. Here, a = 0.10 is

obtained owing to d = 27 nm and r = 2.7 nm. By substi-

tuting the values of d and a in Eq. 2, the energy of a (1210)

stacking fault is estimated to be about 0.25 J/m2. The elastic

constants used for the equations were derived from the former

studies [3, 26, 27]. The equations are based on a conventional

elastic theory for an isotropic elastic medium. Accordingly,

the evaluation using Eq. 2 may slightly lose accuracy because

of the specific crystal structure of LiNbO3 with polarization.

Here, the c11, c12, and c44 are reported to be 2.03 9 1011,

0.573 9 1011, and 0.595 9 1011 (N/m2), respectively [26].

The ratio of c44 to (c11 - c12)/2 is calculated to be 0.82. This

value indicates a degree of elastic anisotropy, which does not

seem large. Therefore, we could apply isotropic elasticity

theory. Note that, because of the extremely narrow separation

distance, the stacking fault between the partials may locally

have a different atomic arrangement from the ideal stacking

fault. This would lead to a slight error in the stacking fault

energy derived from the dissociated dislocation.

Conclusion

A LiNbO3 bicrystal with a f1210g=h1010i 1� low-angle tilt

grain boundary was fabricated by the diffusion bonding of

two single crystals with a controlling crystallographic ori-

entation relationship and polarization, to investigate the

structure of the resultant grain boundary and boundary

dislocations by TEM. The particle-like regions of 100–

200 nm with moire are distinctly observed at the fabricated

boundary, in addition to the boundary dislocations that

compensate the misorientation angle at the boundary.

HRTEM observation successfully found that the disloca-

tion with b ¼ 1=3h1210i dissociates into two partial dis-

locations along \ 0001 [ and with an adjacent location

along h1210i. This indicates that the dislocations dissociate

by climb, not by glide. It is suggested that the Burgers

vectors of the partial dislocations should be 1=3h0110i and

1=3h1100i. The stacking fault formed on f1210g by the

dissociation is thought to have either of the two types of

structures with mirror symmetry, which should be the same

in energy. By applying the separation distance in a partial

dislocation pair of 2.7 nm to the equation based on iso-

tropic elastic theory, the stacking fault energy on f1210g is

estimated to be about 0.25 J/m2.

Acknowledgements The authors wish to express their gratitude to

Prof. Y. Ikuhara and Prof. N. Shibata for fruitful discussion and

encouragement. They also thank Ms. N. Uchida for technical support

in TEM operation. Part of this work was supported by a Grant-in-Aid

on Priority Areas ‘‘Nano Materials Science for Atomic-scale Modi-

fication’’ (no. 19053001). The authors acknowledge the support of

National Center for Electron Microscopy, Lawrence Berkeley Labo-

ratory on the simulated HRTEM images, which is supported by the

U.S. Department of Energy under Contract # DE-AC02-05CH11231.

E. T. was supported by the JSPS postdoctoral fellowship for research

abroad.

Appendix 1: Particle-like regions with moire

at the boundary

Figure 10a shows a STEM bright-field image taken from

the boundary in the fabricated bicrystal. The particle-like

regions with moire were often observed at the boundary, as

can be seen in this figure. There may be some impurities in

the region with moire; therefore, a line analysis along the

dotted line in (a) and a spot analysis for the region with

moire were performed using an energy dispersive X-ray

spectrometer (EDS), as shown in Fig. 10b, c, respectively.

In (b), it was found that Nb and O ions are constantly

present in either region, with and without moire. Note that

Li ions cannot be detected because Li generates an X-ray

with energy that is too low for the EDS detector. It can be

also seen in (c) that only the Nb, O, Fe and Cr elements are

significantly detected in the region with moire. Here, small

amounts of Fe and Cr can be derived from the stainless-

steel single-hole mesh attached to the specimen, as

described in the experimental procedure. Their signals

5092 J Mater Sci (2012) 47:5086–5096

123

were detected from the bulk as well. In other words, par-

ticle-like regions with moire are not brought about by a

definite impurity.

Here we consider the observed spacing of the moire

fringes, which includes the information concerning a

degree of lattice distortion. In general, we observed moire

fringes in the following two cases. First, when two regions

with a rotation relationship (rotation moire) overlap along

the incident beam direction. Second, when two regions

with slightly different lattice spacing (translational moire)

overlap without rotation. Under the two-beam approxima-

tion in TEM, the rotational moire fringes are parallel to the

excited diffraction vector, whereas the translational moire

fringes are normal to the vector [28]. As observed in

Fig. 4a, the moire fringes are normal to the excited dif-

fraction vector. This means that the moire fringes observed

in this study are due to the overlap of two regions with

slightly different crystal lattice constants. In this case, the

spacing of the moire fringes in a bright-field image is

decided by the difference and an excited diffraction vector

[28]. It was estimated from the image of Fig. 4a and

Fig. 10a that the spacing of the moire fringes is about

16 nm along [1210]. The relation between the spacing dm

and the excited diffraction vector gð1210Þ is given as

jgð1210Þj � s = dm-1, where s is the displacement ratio of

the crystal lattice constant along [1210] to the bulk. Thus, s

was estimated to be about 0.016 for jgð1210Þj =

3.88 nm-1. This indicates that the region with moire has a

different crystal lattice constant of 1.6% from bulk.

The value of 1.6% seems to be large for a simple lattice

distortion. To account for this, the following two possi-

bilities are proposed. One is a break in stoichiometry

around the boundary. The ratio of constituent ions around

the boundary may have a deviation from the bulk because

LiNbO3 can be non-stoichiometric. The deviation of the

ratio affects the lattice parameter of LiNbO3; the deviation

might be a reason for the change of the crystal lattice

constant. However, the typical variation of lattice constants

due to the deviation is less than 0.2% [29]. The other

possibility is the presence of a space charge around the

boundary. Even if an electric field of 20 kV/mm is applied

to LiNbO3, however, the lattice strain by the piezoelectric

reaction does not reach 0.1% [3]. It seems that it is difficult

to explain the change of 1.6% by theories referring to the

bulk structure. Thus, it is suggested that localized regions

near the boundary may be distorted due to local and

extraordinary changes in stoichiometry or space charge.

Appendix 2: Bright points on the HRTEM image

of LiNbO3

Figure 11 shows the simulated HRTEM images of LiNbO3

bulk crystal observed along the [1010] zone axis obtained

with the MacTempas program [30]. An experimental

HRTEM image of the bulk crystal taken from Fig. 5 is also

shown at the upper right. The supercell in the simulation

was an orthorhombic structure containing 60 atoms

(5.418 9 8.992 9 13.86 A3), as shown in the insets of the

images, and the simulated images are described twice in

the supercell along the [1210] axis. The Debye–Waller

factors of Li, Nb, and O were set to 0.94, 0.50, and 0.43 A2,

respectively [1]. The simulation was performed within the

range of defocus from -50 to -10 nm and the sample

thickness was 9.8–32.1 nm. The Scherzer defocus of the

(a)

(b)

710 nm

Line analysis

[1210][000

1]

6.00.0 1.0 2.0 3.0 4.0 5.0 7.0

500

1000

(c)

Cou

nts

keV

Inte

nsity

Fig. 10 Results of STEM observation and analyses by EDS.

a STEM bright-field image of the boundary. b EDS line analysis

along the dotted line on (a). c EDS spot analysis derived from the

region with moire on (a)

J Mater Sci (2012) 47:5086–5096 5093

123

JEM-4010 is -34 nm. It is found that black contrasts

correspond to the atomic positions in the 9.8-nm-thick

images, whereas strong white contrasts correspond to the

oxygen columns in the 20.5–31.2-nm-thick images. The

contrasts of the 15.2-nm-thick images are more compli-

cated and thus difficult to associate with atomic positions.

In the experimental image, the three rows of white spots

along the [0001] direction correspond to alternate basal

planes (i.e., (0003) lattice planes), whereas the strong

contrasts of the simulated images correlate with the inter-

vals of successive basal planes (i.e., (0006) lattice planes).

Here, the contributions of the (0006) atomic planes to the

HRTEM image contrasts should be equivalent at the exact

[1010] incidence. It has been reported that the misalign-

ment of the electron beam and crystal orientation can cause

strong contrasts in the (0003) lattice planes in the HRTEM

imaging of a-Al2O3 along the [1010] direction [31]. That

is, the mismatch between the experimental and simulated

images in LiNbO3 could be due to misalignment effects in

the experimental HRTEM observation.

Figures 12a, b show simulated HRTEM images consid-

ering the misalignment up to 1.2 mrad with respect to the

[0001] and [1210] rotation axes, where the defocus value is

-30 nm in both cases and the sample thickness is 9.8 nm in

(a) and 20.5 nm in (b). In the case of 9.8-nm-thick images, the

simulated images are not sensitive to misalignment, whereas

the 20.5-nm-thick images significantly vary depending on

misalignment. The strong contrasts in the 20.5-nm-thick

images corresponding to the (0003) lattice planes are

enhanced by a misalignment of 0.6 or 1.2 mrad with respect to

the [0001] rotation axis. This feature is consistent with the

experimental image. In addition, the strong white spots in the

simulated images are present at the oxygen columns. There-

fore, the white spots in the experimental image probably

correspond to the oxygen columns that belong to the alternate

basal planes. However, the effects of the factors that have not

been experimentally identified still need to be investigated

further. Furthermore, quantitative measurements of defocus,

sample thickness, and misalignment are required to determine

the atomic positions from the experimental image.

Defocus / nm-50 -40 -30 -20 -10

Thi

ckne

ss /

nm9.

815

.220

.525

.931

.2

[000

1]

[1210] [1010]Li Nb O

(000

3)

(000

3)

exp.

Fig. 11 Simulated HRTEM

images of the LiNbO3 bulk

crystal. The defocus ranges

from -50 to -10 nm

(horizontal sets) and the sample

thickness is 9.8–32.1 nm

(vertical sets). The experimental

image is shown in the inset atthe upper right

5094 J Mater Sci (2012) 47:5086–5096

123

0

0

(000

3)

exp.

(000

3)

0.6 1.2

0.6

1.2

Misalignment respect to the [0001] rotation axis / mrad

Mis

alig

nmen

t res

pect

to th

e [1

210]

rota

tion

axis

/ m

rad

0 0.6 1.2

(000

3)

exp.

(000

3)

00.

61.

2

Mis

alig

nmen

t res

pect

to th

e [1

210]

rota

tion

axis

/ m

rad

Misalignment respect to the [0001] rotation axis / mrad

(a)

(b)

Fig. 12 Simulated HRTEM

images considering a

misalignment of up to 1.2 mrad.

The horizontal and vertical sets

correspond to misalignment

with respect to the [0001] and

½1210� axes, respectively:

a defocus of -30 nm and

sample thickness of 9.8 nm,

b defocus of -30 nm and

sample thickness of 20.5 nm

J Mater Sci (2012) 47:5086–5096 5095

123

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