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JAST 2012 March;3(1):128-134.
Published online 2012 March 20.   doi:http://dx.doi.org/10.5355/JAST.2012.128
Copyright ⓒ 2010 Journal of Analytical Science & Technology
Application of FFT Data from HREM images to Electron crystallography
Sang-Gil Lee1, Youn-Joong Kim1,2, Seung-Jo Yoo1, Seok-Hoon Lee1, Jin-Gyu Kim1*
1Division of Electron Microscopic Research, Korea Basic Science Institute, 169-148 Gwahangno, Yuseong-gu, Daejeon 305-806, Republic of Korea
2Graduate School of Analytical Science and Technology, Chungnam National University, 79 Daehangro, Yuseong-gu, Daejeon, 305-764, Republic of Korea
Corresponding Author: Jin-Gyu Kim ,Tel: +82-42-865-3961, Fax: +82-42-865-3939, Email: jjintta@kbsi.re.kr
ABSTRACT
We succesfully determined the 3D crystal structure of inorganic nano-crystalline material using fast fourier transform (FFT) data from high-resolution electron microscopy (HREM) images. For extracting the reliable structure information from nano-crystalline materials by HREM imaging, it is essential to minimize the dynamical scattering effects happend from interactions bewteen electrons and matters. To alleviate this restriction, we tried to solve the crystal structure by employing high voltage electron microscope (HVEM) which has excellent tilting capability, atomic resolution as well as higher penetration power. First, the allowed sample thickness for CaMoO4 crystal was evaluated by examining the existence of forbidden reflections in FFT data of HREM images obtained at various sample thickness. The kinematical scattering conditions were satisfied up to a sample thickness of about 28.2 nm. Next, we tried to extract the crystallographic data and determine the atomic structure of CaMoO4 crystal by FFT analysis of HREM images obtained from 15 different zone axes. Consequently, its cell parameters and space group were a = 5.24(3) Å, c = 11.50(8) Å and I41/a (#88), respectively. These values were coincided with X-ray crystallography results within 0.002 ~ 0.080 Å. Finally, the atomic structure could be determined with an accuracy of 0.16 Å.
Keywords: High voltage electron microscope, Fast fourier transform, Electron crystallography, High-resolution electron microscopy, CaMoO4
Introduction
The determination of crystal structures at the atomic scale is a fundamental step to understand the properties of materials. X-ray crystallography is commonly employed for the determination of crystal structures. However, X-ray crystallography is insufficient method to investigate individual crystals in nano size because X-rays interact weakly with matter. On the other hand, electron crystallograpy can be applied to 3D structure determination of nano-crystalline materials because electrons more strongly interact with matter than X-rays. Generally, there are two methods for structural determination of nano-crystalline materials by electron crystallography: HREM image analysis [1-3] and QED (quantitative electron diffraction) analysis [4-7]. For obtaining the basic crystallographic information of nano-crystalline materials, it is easy and convenient to apply ED (electron diffraction) analysis because ED analysis has an advantage to solve the crystal structure without sample damage by electron dose, compared to HREM imaging. However, ED analysis has a problem of dynamical scattering phenomenon because ED data is often collected from larger sample area included severe thickness variation. To overcome this problem, HREM imaging could be applied because data can be obtained from smaller sample area. Moreover, FFT data of HREM images obtained at near atomic resolution has the structural information similar to ED patterns although its data resolution is lower than that of the ED pattern. In addition, the phase information of crystal structures which can not be extracted in ED patterns can be determined and corrected by applying the CIP (crystallographic image processing) method [1,8].
Herein, we reported the usefulness of HVEM application to alleviate the sample thickness restriction for reliable structure analysis and structure determination of CaMoO4 crystal using FFT analysis of HREM images.
Materials and Methods
The sample used in this study is inorganic single crystal, CaMoO4, grown by the Czochralski method. CaMoO4 crystal structure has tetragonal system (I41/a) and its cell parameters is a = 5.2384 Å and c =11.425 Å.
Two type samples were prepared by using ion-milling and crushing. They were used to evaluate the thickness limitation to avoid the dynamical scattering effects and 3D structure analysis using FFT analysis of HREM images, respectively.
HVEM (JEM-ARM 1300S, 1,250kV) was employed to evaluate its usefulness for structure analysis of CaMoO4 crystal. All HREM images were zero-loss filtered with an energy-filtering system using HV-GIF (Gatan Inc.). Instrumental conditions, such as specimen thickness, focus conditions and tilting, were strictly controlled [9,10]. Each EELS (electron energy loss spectroscopy) spectrum was obtained with same instrumental conditions: dispersion of 0.2 eV; a entrance aperture of 2 mm; a collection angle of 3.4 mrad. The mean free path of CaMoO4 crystal was determined to ~201.0 nm at 1,250 kV.
Magnification calibration was preformed by standard sample using Digital Micrograph (Gatan Inc.). Intensities of all reflections for each FFT data from HREM images were extracted by the program ELD [11]. The program TRICE was used to reconstruct the 3D reciprocal space from each HREM tilt series and calculate the cell parameters [12]. The extraction of phase and amplitude information for all HREM images was carried out by applying the CIP method with the program CRISP [1]. 2D information (phase and amplitude) of FFT data was scaled and merged into 3D information by the program TRIPLE referring the common reflections [13]. Final 3D potential maps were constructed using the program eMap [14].
Results and Discussion
Evaluation of allowed sample thickness
To evaluate the allowed sample thickness for kinematical scattering conditions, HREM images and EELS spectrums were acquired from 10 different positions selected from thin to thick area in a sample (Fig.1). Log-ratio calculation for EELS spectrums [15] was applied in order to estimate the sample thickness for each positions and the estimated sample thicknesses for each positions are listed in Table 1.
HREM images of CaMoO4 crystal and their corresponding FFT data are shown in (Fig.2). The first row is HREM images for [100] and [110] direction and the inset numbers indicate the sample positions in (Fig.1). The (002) reflections marked with yellow circle in each FFT data indicate the forbidden reflection depended on the crystal symmetry when it is considering the kinematical scattering conditions of CaMoO4 crystal. Thus, the (002) reflection should be absent in order to satisfy the kinematical scattering conditions. Through FFT analysis of HREM images, it was revealed that the weak intensity of the (002) reflection was producted in the [100] HREM image obtained from sample position #4 and the [110] HREM image obtained at sample position #5. These results indicate that the thicknesses of two sample positions are the critical sample thickness to satify the kinematical scattering conditions. By comparing the estimated results of sample thickness, the kinematical HREM images at the [100] and [110] zone axes could be obtained at the thickness below 25.6 nm and 28.2 nm, respectively.
Therefore, it was demonstrated that the kinematical scattering conditions could be satisfied up to a sample thickness of about 28.2 nm when the structure analysis was carried out using HVEM. Also, this effect of higher accelerating voltage is similar to the previous experimental report and the theoretical calculation [16,17].

FFT analysis of HREM images
A tilt series of HREM images taken along the [110] zone axis and their FFT data were shown in (Fig.3). For obtaining the basic crystallographic information of CaMoO4 crystal, three tilt series of HREM images were taken from 15 different zone axes.
The determining procedures of the cell parameters from tilt series of FFT data were shown in (Fig.4). In order to determine the cell parameters from unknown crystal structure using tilt series, each FFT data was indexed in 2D reciprocal space ((Fig.4)(a)). Thereafter, its reflection data was extracted by the program ELD (Fig. 4(b)). All reflection data in 2D reciprocal space were merged by referring to angular relation between each zone axes using the program TRICE ((Fig.4)(c)). The cell parameters were calculated from 3D reconstruction data in reciprocal space. The calculated cell parameters are summarized in Table 2. Final cell parameters of CaMoO4 were calculated by averaging three different cell parameters of each tilt series. Under consideration the measurement errors by the goniometer unstability, magnification calibration and quality of FFT data, it could be finally determined that its cell parameters and crystal system were a = 5.24(3) Å, c = 11.50(8) Å and tetragonal system. These values coincided with the X-ray crystallography results within 0.002 ~ 0.080 Å.
After determining the cell parameters, the examination of reflection conditions from four major zone axes ([001], [100], [110] and [111]) was carried out to determine the 3D symmetry information (Fig.5). First, we checked whether the kinematical scattering conditions of HREM images were satisfied or not. Then, the reflection conditions determined from FFT data of four HREM images are following: hkl → h+k+l=2n; hk0→h, k=2n; 0kl→k+l=2n; h00→h=2n; 0k0→k=2n; 00l→l=4n; hhl→l=2n; hh0→h=2n. By comparison of these reflection conditions with all 68 tetragonal space groups, the space group of CaMoO4 crystal was determined to I41/a (#88).
To reconstruct the 3D potential map from 15 different HREM images, the amplitudes of all 2D reflections were extracted from FFT data of HREM images and these were merged by the program TRIPLE. As a result, 92 independent reflections were extracted. The phases of all reflections were determined by applying the 3D symmetry. Phase values for all reflections were set to 0° or 180° owing to its centrosymmetric space group. The 3D potential map with these 92 reflections was constructed using the program eMap. As a result, the potential difference between the heavy and light atoms is very large as shown in Fig. 6. Considering this factor, 12 atomic positions in the unit cell were determined by applying the suitable threshold value of 0.432 (Table 3). All atomic coordinates were reassigned into equivalent positions by symmetry relationship, which resulted in the averaged atomic positions of the Ca, Mo and O atoms: 0.0006(6), 0.7416(6), 0.6250(11); 0.0006(6), 0.2416(6), 0.1250(11) and 0.1536(12), 0.4964(36), 0.1971(11), respectively (Table 4).
was relatively large. The atomic coordinates of the Mo and Ca atoms were nearly identical to the X-ray results because their atomic coordinates could be regarded to special positions under consideration of Wyckoff positions of the space group. The atomic coordinates determined by HREM image analysis were consistent within 0.16 Å, compared to X-ray crystallography data for the same sample (Table 4).
In this study, we evaluated usefulness of HVEM for reducing the dynamical scattering effects. To avoid the dynamical scattering effects, HVEM gives us the effective and practical advantage for sample thickness restriction (~28 nm) compared to mid-voltage TEM (<10 nm). Also, it was possible to solve the crystal structure by FFT anlysis of the HREM images. Finally, it is expected that FFT analysis of HREM images by using HVEM gives a new solution for 3D structure determination of nano-crystalline materials due to its higher resolution, higher penetration and favorable kinematical scattering conditions.
Acknowledgement
This work was supported by a grant (T3221B) from Korea Basic Science Institute to J.–G. Kim and by New & Renewable Energy R&D program(20113020030020) under the Ministry of Knowledge Economy, Republic of Korea.
FIGURES
Fig.1 Fig.1
TEM image of CaMoO4 crystal for thickness estimation (a) and their corresponding EELS spectrums (b).
Fig.2 Fig.2
HREM images of CaMoO4 crystal and their FFT data.
Fig.3 Fig.3
A tilt series of HREM images taken along the [110] zone axis and their FFT data.
Fig.4 Fig.4
The determining procedures of the cell parameters from tilt series of HREM image. (a) 2D indexing of FFT data, (b) Extracting of reflection data, (c) 3D reconstruction map of all FFT data in reciprocal space.
Fig.5 Fig.5
Extraction of reflection conditions from four major zone axes to determine the 3D symmetry.
Fig.6 Fig.6
The 3D potential map reconstructed with 92 reflections. (a) shows an structure drawing of CaMoO4 crystal with the atomic labeling scheme based on XRD analysis. (b)~(d) show 2D potential maps of [100], [010] and [001] direction, respectively.
TABLES
Fig.1 Table.1
The results of thickenss estimation from different sample positions.
Fig.2 Table.2
Cell parameters of CaMoO4 determined by FFT analysis of three tilt series HREM images.
Fig.3 Table.3
12 atomic positions extracted from 3D potential map.
Fig.4 Table.4
Comparison of atomic coordinates of CaMoO4 crystal structure determined by electron and X-ray crystallography.
 
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