Simulation and Analysis of Electron Diffraction Pattern


X.Z. Li

1. Introduction

Selected area electron diffraction analysis has been extensively used in materials science for phase identification, interpretation of twins and coexisted multiple phases and so forth. Simulation of electron diffraction pattern plays an important role to interpret experimental results. Electron diffraction patterns from a single crystal grain and from a polycrystalline sample are common in essence but different in many aspects, so we treat the two cases separately for advanced simulation and analysis of electron diffraction patterns. ProJECT/PCED2 is for selected-area electron diffraction patterns of polycrystalline samples. ProJECT/SAED2.0 is for selected-area electron diffraction patterns of single crystal samples.

Current available software for simulation of electron diffraction is mostly designed for a single phase only. For advanced simulation and analysis of electron diffraction patterns, the functionalities in such a software is not enough, for examples, in the analyses of twining, coexisted multiple phases with fixed orientation, and for the comparison of two similar diffraction patterns from different phases. In addition, a practical task in electron diffraction analysis is to find the zone axis of the diffraction pattern and indexing, such an analysis can be used for phase identification, the orientation of a crystal grain, and so forth. With the motivation to fulfill the need, we have developed SAED2.0, as the successor of the previous JECP/ED.

Features in SAED2.0 include (i) interactive simulation of electron diffraction pattern from single crystal grains, (ii) kinematical diffraction theory (dynamical diffraction theory is not included in current version) for intensity calculation, (iii) processing multiple phases and (iv) improvement on diffraction pattern indexing and matching to experimental pattern.

Figure 1. Snap-shot of the SAED2.0, a simulation of electron diffraction pattern of MnAl3, an approximant of MnAl decagonal quasicrsystalline phase.

The GUI of SAED2.0 includes
(i) a main frame with a panel is used to show the simulated pattern or to match to the preloaded experimental diffraction pattern;
(ii) input parameters for calculation can be initialized with an operational panel and several dialog windows;
(iii) input structure data file can be easily prepared using computer assistant;
(iv) multiple phases can be loaded and calculated simultaneously to simulate the diffraction patterns for twins, coexisted phases with fixed orientation and comparison of the similar patterns from different phase.

SAED2.0 is written and complied in Java 6.0. Further code optimization (including obfuscation) is carried out for the compiled class files. A license file is needed to unlock the program (saed2.jar) for loading input data files. Without the license file the program is locked up in trial mode, which works with input files with code numbers. License can be purchased from LANDYNE/computer software. First time users may send their input data in to get the code number.

2. Usage of SAED2.0

To run SAED2.0, just double click the icon of SAED2.jar or type: java -jar (-Xmx512m) SAED2.jar in command line. -Xmx512m is an option to locate the memory of Java virtual machine up to 512 MB.

In the following, we show step by step from preparing structure data file, common routine usage for simulation, and to the last steps of saving and printing the results. More details on specific topics are left to next section.

Figure 2. Snap-shot of the preparation of input structure data file.

2. 1 Prepare new data file

Structure data file can be prepared using the Create an input file dialog window in Figure 3 or using a text editor to modify other SAED2.0 structure data file. The dialog window provides a certain level of assistant for user and also makes sure to meet the requirement of the format of the file.

To save the data structure click the Save button or to make new one click the New button.

2.2 Simulation

Kinematical theory is used as a default selection in the simulation. Bloch wave or multislice theories are available in later version (after v2.5). Basic parameters for calculation, e.g., high voltage, pattern zoom and intensity scale can be adjusted in Simulation menu.

A structure data for calculation should be selected in a list of loaded structure data. After choosing thickness, zone axis, tilt angles, to generate new diffraction pattern needs simply click Calculate button. The pattern can be adjusted by changing other parameters.

Mass proportion defines the same unit weight for all loaded structure as default value. Mass proportion is meaningful only when two or more structural data are calculated at a composite diffraction pattern.

Orientation and mirror operation are used to orient the simulated pattern to match the experimental pattern and to generate various twins.

Figure 3. Snap-shot of the calculation dialog window of SAED2.0.

Diffraction Pattern can be viewed with four predefined spot shape and in various color. Pattern (ZOLZ and FOLZ) can be displayed or hidden. Index and intensity can be labeled for basic reciprocal vectors and for diffraction spots selected by the intensity level. Basic vectors and Laue center can be displayed and hidden.

2.3 Determination of zone axis and indexing

SAED2.0 can be used to determine the zone axis of an experimental diffraction pattern if it belongs one of the known structures which were loaded into the structure list (see example 2. below). Experimental diffraction pattern (about 600 dot x 600 dot in jpg format) can be loaded and centered by drag and drop operation. Gray contrast can be converted if needed.

Step 1. Update the match factor. Any experimental diffraction with known structure and zone axis can be used for the same purpose. If a standard electron diffraction pattern of polycrystalline materials, e.g, Al or Au or any sample vailable was used for the calibration, th e matching factor can be updated by matching simulated fcc polycrystalline diffraction pattern to the experimental pattern. The match factor can be saved so it doesn't need to be calibrated all time as soon as the same experimental conditions were used.

Step 2. Find the basic reciprocal vectors g1 and g2, the length can be labeled in (1/┼), which can be used for refinement using JECP/LPR (see later).

Step 3. Define the tolerance value (default as 5%) and find the possible zone axis. The one with least mismatching residue is shown and the all list can be saved to a text file.

Step 4. The zone axis is obtained by matching reciprocal length and angle between them. The zone axis should be confirmed by comparing a simulated pattern to the experimental one.

3. Examples

3.1 Pt-Bi thin film

There has been considerable interest in understanding various properties of Pt-Bi based compounds because of their high activity as fuel-cell anode catalysts for formic acid (HCOOH) or methanol (CH3OH) oxidation. Although Pt is regarded as one of the most efficient catalyst materials, the main problem with this conventional catalyst is that it is readily poisoned by carbon monoxide (CO) that is produced as a side product of the reaction. The CO poisoning reduces the catalytic activity and cell efficiency because it tends to remain strongly bound to the electrode surface. However, some recent reports show that the use of ordered intermetallic compound such as BiPt as an electrode material exhibits an improved cell efficiency with a dramatic reduction in the CO adsorption.

The three common intermetallic compounds based on Pt and Bi are PtBi, PtBi2 and Pt2Bi3. Equiatomic PtBi phase is at the low temperature side of the phase diagram and may be off-stoichiometric towards Pt-rich side. PtBi2 has four polymorphs namely α-PtBi2(oP24), β-PtBi2(cP12), γ-PtBi2(hP9) and δ-PtBi2 (oP6) from low to high temperature in equilibrium phase diagram. PtBi and Pt2Bi3 adopt the hexagonal NiAs structure (PtBi: a = 4.3240 and c = 5.501 ┼; Pt2Bi3: a = 4.13 and c = 5.58 ┼) whereas the three polymorphs of PtBi2 crystallize in the AuSn2 type Orthorhombic (α-PtBi2: a = 6.732, b = 6.794 and c = 13.346 ┼), FeS2 cubic pyrite (β-PtBi2: a = 6.701 ┼), and trigonal (γ-PtBi2: a = 6.57, and c = 6.16 ┼) crystal structures, respectively.

Figure 4. (a, c) experimental electron diffraction patterns of Pt-Bi thin film, which consists of ⓰-PtBi2 and ⓯-PtBi2, (b, d) the simulated EDP.

PtBi and PtBi2 films were synthesized on glass and thermally oxidized silicon substrates by e-beam evaporation and annealing. Figure 4. shows (a, c) experimental electron diffraction patterns of Pt-Bi thin film, which consists of ⓰-PtBi2 and ⓯-PtBi2, (b, d) the simulated EDP.

3.2 Cu2S nanofiber

Hierarchical nanostructures are increasingly attractive for application in optics, electronics, sensing, and so forth. Specifically, core-branch heterostructures (i.e., branches of nanowires or nanorod on central nanowire or nanofiber core), having core and branches composed of different materials, allow targeted properties of the nanowires and the base, offer high surface-to-volume ratio and nanowire-to-base ratio, and bring promise of novel functional membranes.

In our recent work, a novel hierarchical architecture, inorganic Cu2S nanowires standing on organic polyacrylonitrile (PAN) nanofiber, has been produced by combining the electrospinning technique and room-temperature gas-solid diffusion-assisted chemical growth. The produced nanowires are 1.5~1.8 Ám long with uniform diameter of about 80 nm (Figure 9a). The experimental EDPs of the single nanowires matches monoclinic Cu2S crystal phase and indicates that the nanowires growth direction is perpendicular to the (2,0,-4) crystal plane, i.e. parallel to the c axis of the monocrystal (Figure 9b, 9c). The growth of the nanowires seems to be preceded the formation of Cu2S sheath on the surface of the nanofibers.

Figure. 5. TEM images of the hierarchical structure (a). Experimental EDPs of the Cu2S nanowires (b), arrows show the nanowire growth direction and corresponding simulated patterns of monoclinic Cu2S crystal structure (c).

The basic reciprocal vectors for the experimental EDP are measured, as shown in Figure 10. The calibrated matching factor and basic reciprocal vectors for the experimental EDP are listed in Figure 11. The tolerance is chosen as 5%. The most possible zone axis is found to be [2 1 1] and there are 7 possible zone axes, which can be saved to a file. The simulated pattern of [2 1 1] zone axis matches well with the experimental EDP, thus the zone axis and index of the EDP are determined.

Figure. 6. Measurement of basic reciprocal vectors in the experimental EDP of Cu2S nanofiber.

Figure 7. Matching factor and g lengths and angles of the basic reciprocal vectors. The possible zone axis is found to be [2 1 1] with a tolerance of 5%.

Figure. 8. Simulated EDP of Cu2S with zone axis [2 1 1].