Selected Area Electron Diffraction Analysis Essay

SAED3b

Simulation and Analysis

of Electron Diffraction Pattern

(SAED3d)

X.Z. Li

From SAED2s to SAED3d:

Main upgrades include dynamical diffraction calculation (Bloch wave method) and image processing (resize and rotation), acceptance of jpeg and tiff format, font size for index, and redesign of some dialogue panels.

(Renewed manual of SAED3d is included in the saed3d_exe .7z file in download page)

Table of Contents

  1. Introduction
  2. Theory Background
  3. Graphic user interface of SAED3
  4. Usage of SAED3
  5. Special topics on SAED3
  6. Examples
  7. Related programs: JECP/SVAT, JECP/SAKI, SPICA and ProJECT/PCED3
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/PCED3 is for selected-area electron diffraction patterns of polycrystalline samples. ProJECT/SAED3 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 SAED3c, as the successor of the previous JECP/ED and SAED2s.

Features in SAED3 include (i) interactive simulation of electron diffraction pattern from single crystal grains, (ii) kinematical diffraction theory  and dynamical diffraction theory (Bloch wave theory) for intensity calculation, (iii) processing multiple phases and (iv) improvement on diffraction pattern indexing and matching to experimental pattern.

The GUI of SAED3 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.

SAED3 is written and complied in Java 8.0. Further code optimization (including obfuscation) is carried out for the compiled class files. A license file is needed to unlock the program (saed3d.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.

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2. Theory background

2.1 Electron diffraction geometry and intensity

The kinematical and dynamical theories of high-energy electron diffraction have been well documented in the textbooks (e.g. Peng et al., 2004, other book) and literatures (e.g., Metherell, 1975).

The electron atom scatter factor can be derived from X-ray atom scatter factor using Mott-Bethe relationship or directly obtained from parameterized table of electron atom scatter factor (Peng et al. 1996). Here we use the second method.

Following the electron diffraction geometry, the reciprocal length (R) of a reflection in a diffraction pattern can be related to the length of the reciprocal vector g(hkl) as:

where L is the camera length, g=|g(hkl)| and K is the wave vector of incident electron beam, K = |K|.

For high-energy electron diffraction, the radius of the Ewald sphere is fairly large, thus electron diffraction pattern of the thin sample reveals the two dimensional distribution of reciprocal lattice points.

Electron diffraction intensity in kinematical theory is given by:

Here Fg is the so called structure factor.

Dynamical electron diffraction intensity can be calculated using Bloch wave method or multislice method. Readers should check the formulas in the original documents. 

2.2 Electron diffraction of twins and coexisted multiple phases

Based upon their diffraction patterns, twinned crystals may be grouped into three general categories. Non-merohedral twins have two or more crystalline domains with reciprocal lattices that either do not overlap or only partially overlapped. In contrast, Merohedral twins have domains with diffraction patterns that are completely overlapped. For merohedral twins, the symmetry operations relating the twinned domains are a part of the Laue group of the sample, but are not a part of the space group.Pseudo-merohedral also have domains with completely overlapped diffraction patterns, but the symmetry operation relating the domains is not a part of the Laue group of the sample. 

Two phases or more may coexist with a fixed orientation relationship in a complex alloy system. Electron diffraction analysis can be used to determine the orientation relationship. Precipitates may have a fixed orientation with matrix. In order to study of the precipitates it usually to tilt the matrix in order to get a particular orientation of the precipitates since the precipitates are small particles. 

For twins and multiple coexisted phases, the simulation of the electron diffraction pattern requires to be calculated based on multiple structures in one frame. SAED3 is designed to calculate the patterns from multiple structures one by one and easily adjusted any of the patterns to simulate the patterns from twins and from multiple structures coexisted with fixed orientation.

2.3 Determination of a zone axis and indexing

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. 

SAED3 provides a tool to measure the lengths of two basic reciprocal vectors and the angles between them on a diffraction pattern (8bit tiff and jepg image). Calibration of the scale factor can be carried out using the scale bar in the same pattern. 

The lengths of the two basic reciprocal vectors are matched to all possible (hkl) with a given tolerance and then the angle is checked, one of the zone axes with least mismatch values is listed out and a possible zone axes can be saved to a file.

Since only the tolerance of reciprocal lengths is defined in the Find Zone Axis dialog, the angle is checked by the reciprocal length of the third edge in the triangle formed by the two basic reciprocal vectors. 

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3. Graphic user interface of SAED3

3.1 Main interface

The main interface of SAED3 is shown in Fig. 1, which includes a menu and a toolbar for setting and input, and a frame to show the output of the simulation. The usage of SAED3 for simulation needs to load structure data and to set up input parameters, then simply click Calculate button in Calculation control panel. The usage of SAED3 for zone axis search or phase identification needs to load experimental diffraction pattern first and then to find zone axis and then to match to the calculated patterns by chosen structure data and input parameters. Multiple structure data can load at the same time for comparison or for simulation of various twins and coexisted structures with fixed orientation. 

3.2 Menu and toolbar

Menu and toolbar can be used to pop up dialog windows for loading data or changing parameters. Menu gives more text description and organized in groups while toolbar shows in graphics and easily to access. Although most functions of menu and toolbar are same, however, there are some functions are only provided either in menu or toolbar. 

Structure menu provides an interface for creating the new structure data, loading the input structure (the same structure can reload for twins), and clearing all the loaded structures except the default (Al) structure.

Experiment menu provides an interface for loading experimental electron diffraction pattern (EDP) in jpg (or jpeg) format. The loaded pattern can be set to an inverse contrast, and centered by drag-and-drop with referring to a set of preset circles when the Center icon is selected. EDP can be clear out or reloaded. Drag-and-drop: selecting a point in image by mouse, press down left button of mouse, drop to the selected point, for example, the center of panel, and release the left button of the mouse. When the position of the image is set up, deselected the Center icon; Find [uvw] provides a dialog window for calibrating the matching-factor, which is a combination of camera constant and the dot per inch (dpi) of the image (digital diffraction pattern), finding the basic reciprocal vectors of the EDP and finding the [uvw]. A zone axis with the least mismatching residue is shown and detail info on a list of all possible zone axes can be saved to a text file.

Simulation menu provides a submenu for the choice of theories. The default choice is the kinematical diffraction theory. The high voltage of the microscope and the maximum of index number for calculation can be set up.

Pattern menu provides a dialog window for adjusting the pattern zoom and intensity scale, which simulate the camera length and exposure time and a dialog window for selecting the label of diffraction spots (reflections). The intensity of EDP can also be displayed in logarithmic scale for comparing EDP on negative film.

Option menu provides a freedom of customizing the appearance of SAED3 (look and feel skin) and assistant tools, e.g., a number of reference circles, least radius for diffraction spot with very weak intensity and the selection of standard materials for calibration of matching factor.

Output menu can be used to save the simulated patterns as output files in .jpg or .tif format and to send the simulated patterns directly to printer.

System menu can be used to find the current drive and the serial number (SN), which is required for license files and exit (shutdown) SAED3.

About menu shows information about Landyne: computer software and its production of JECP and ProJECT. 

Toolbar provides a quick way to access conveniently the functions described above. The functions of the toolbar are shown by both the icon image and tooltip text. Only most frequently used menus and submenus are listed in the Toolbar. A lock icon is unlocked when valid license file is the same fold. Without license file, SAED3 can be evaluated in trial model, which is full functional working on structural data with one-way hash code. Contact to Landyne for purchasing the license file or codes.

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4. Usage of SAED3

To run SAED3, using Landyne launcher or double click SAED3d.exe.  The main frame and the control interface of the program similar to Figs. 1 and 3 will show up. 

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. 

4.1 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 SAED3 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.

  • Description field can be filled in a name of the phase.
  • Bravais lattice can be selected a list. Lattice types are provided for each crystal system.
  • Lattice parameters are preset according to Bravais lattice.
  • Space group number is limited to possible group according to Bravais lattice.
  • Fill the info of each atom in and then add to the atom list. For modifying or removing the list, user should select the atom row in the list and click the Remove button.
  • Notes field can be used for the purpose for simulation or reference.

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

4.2 Simulation

Kinematical theory is used as a default selection in the simulation. Bloch wave theory can be applied to crystals with small or middle size unit-cells. 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.

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.

4.3 Determination of zone axis and indexing

SAED3c 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. Experimental diffraction pattern can be loaded, resized/rotated and  centered. Gray contrast can be converted if needed. Figure 4 shows the [uvw] finder dialog window.

Step 1. Update the match factor. Use Scale marker to calibrate scale of simulated pattern to match with experimental one (or a single diffraction spot/ring). 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/A).
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. The tolerance value is defined as the maximum of percent errors: Ve = experimental value and Vk = known value,

Percent error = (Ve - Vk)/ Vk x 100%.

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. 
Step 5. The list of all possible zone axes within the tolerance can be saved to an ASCII text file. In the file, the zone axes, the measured g1 and g2 and angle, and their percent errors are listed.

 

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5. Special topics on SAED3

5.1 Partial occupancy factor and isotropic temperature factor

Some atom coordinates may be not in full occupancy in a crystalline structure. In this case, the occupancy factor (default value 1.0) should be changed to the values according to the crystalline structure in preparation of the structure data file for electron diffraction simulation. 

Partial occupancy factor can also be used to simulate a certain level of chemical order in structure. For example, the chemical ordered FePt L1o phase, see section 6. In this case, different type of atoms may be assigned to the same atomic coordinates with different occupancy according to the chemical ratio, but the sum of the occupancy factors of the two atoms is 1.0.

Isotropic temperature factor is used here to simulate the effect of lattice vibration (Debye model). Although isotropic temperature factor is a rough model, it can be used simulate the decrease of the diffraction intensity with the variation of the |g| value, the higher the value of |g| the more decrease of the diffraction intensity.

5.2 Load and center EDP

Experimental electron diffraction pattern can be loaded up and centered for analysis and compare with simulated patterns. The experimental pattern should be in jpg (or jpeg) format and is better prepared into square shape with pattern in the center. The experimental pattern can be load using Load in Experiment menu and then center by using Center in Experiment menu. Once Center is clicked, five concentric circles will appear in the main panel. Select the center of the pattern using mouse and hold on the left button of mouse, the pattern can be dragged and drop into the center of the panel. Click the Center in Experiment menu the pattern is locked up in the position and concentric circles disappear. More adjustment in small step may be needed to find the accurate position. Number of concentric circles can be changed using Number of Reference Circle in Option menu.

5.3 Determination of weight ratio of multiple phase system

The SAED3c program provides a way to roughly estimate the weight ratio of a composite diffraction pattern of multiple phases. Adjust the mass proportion mp(i) of each phase to match the relative intensities of its diffraction pattern to experimental patterns, then the final mass ratio of phase i is:

5.4 Simulation of twins and coexisted multiple phase

Electron diffraction patterns of twins can be simulated using SAED3. In order to generate twining diffraction patterns, the same structure data is needed to be loaded multiple times according to the number of twin components. In reciprocal space the twin patterns may be generated by rotation, mirror or inverse operations. For rotation twin, the twinning component can be rotated in calculation control panel. For reflection twin, the twining component can be reflected at horizontal mirror and then rotated to the requested angle. For inversion twin, the twin component can calculated using zone axes of [uvw] and [-u,-v,-w].

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6. Examples

6.1 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 = 0.43240 and c = 0.5501 nm; Pt2Bi3: a = 0.413 and c = 0.558 nm) whereas the three polymorphs of PtBi2 crystallize in the AuSn2 type Orthorhombic (α-PtBi2: a = 0.6732, b = 0.6794 and c = 1.3346 nm), FeS2 cubic pyrite (β-PtBi2: a = 0.6701 nm), and trigonal (γ-PtBi2: a = 0.657, and c = 0.6.16 nm) crystal structures, respectively. 

PtBi and PtBi2 films were synthesized on glass and thermally oxidized silicon substrates by e-beam evaporation and annealing. TEM analysis shows that the films prepared by post-deposition annealing of 300 _C and 400 _C are mostly polymorphic PtBi2 with small trace of PtBi. Although TEM analysis shows a signature of β-phase PtBi2, the γ-phase is the dominant phase in these samples. Both the PtBi and PtBi2 samples are textured but the γ-PtBi2films are highly c-axis oriented where the c-axis is perpendicular to the film plane. Figure 7. shows (a) experimental electron diffraction pattern of Pt-Bi thin film, which consists of the twin of γ-PtBi2 and coexisted hexagonal PtBi phase, (b) the simulated EDP in comparison with (c) simulated EDP with single phase of γ-PtBi2. The orientation relationship between the ?-PtBi2 and the PtBi phases is [001] of the γ-PtBi2 //[001] of the PtBi and (100) of the γ-PtBi2 //(110) of the PtBi. Figure 8. shows (a, c) experimental electron diffraction patterns of Pt-Bi thin film, which consists of β-PtBi2 and α-PtBi2, (b, d) the simulated EDP. 

6.2 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 _m 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.

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.

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7. Related programs: JECP/SVAT, SPICA and PCED3

All programs in JECP and ProJECT are using the input structure data in the same format. A few of them are listed here, which can be used in combination with ProJECT/SAED3. Users may check the program specification or user manual for each programs in detail.

7.1 JECP/SVAT

The need of a structural viewer/an analytical tool, using the same input data format as the JECP and ProJECT software, becomes obvious with the growth of the JECP and proJECT programs and users. There exist many programs for structural design and/or display in various levels developed by individual, research group or software company. Some of them are expensive software with multi-purpose and advanced graphics, which may not be suitable for beginners. Others are simply programs for building/displaying crystal structures. The motivation for the development of JECP/SVAT is to provide a structure viewer and also working as a analytical tool.

7.2 JECP/SAKI

JECP/SAKI is designed for simulation and analysis of Kikuchi and double diffraction patterns. JECP/SAKI can be viewed as an extension of SAED2s. Kikuchi lines are useful for precise determination of the specimen orientation in a TEM. JECP/SAKI provides flexible labels of the indices for SAED spots and Kikuchi lines. Double diffraction, where an electron diffracted twice before leaving the specimen, requires that that beam from the first diffraction serve as the incident beam for a second diffracton. JECP/SAKI simulate the occurrence of forbidden diffraction due to double diffraction effect.

7.3. SPICA

SPICA is the next version of early JECP/SP, which was designed for stereographic projection with an application for specimen orientation adjustment using TEM holders. SPICA inherits JECP/SP functions and extends to many new functions for crystallographic analysis with a more user-friendly GUI design. SPICA provides the all necessary functions of stereographic projection for regular application of single phase, which provides automatic plotting of stereographic standard projections of crystals of arbitrary lattice parameters, with any wanted centeral pole. Poles of crystal directions and planes can be plotted alternatively. Interactive plotting of single poles is also provided. Trace curve and Kikuchi/pseudo-Kossel, EDSD pattern can be displayed. It also allows to generate and to overlay two stereograhic projections of two phases, which can be two phases with fixed crystallographic relationship or the same phase for the different properties in stereograms. Just as the JECP/SP, it can be used to predicate the tilt/rotation angle of the TEM holder for zone axes, thus to minimize the difficulties for highly beam-sensitive, and/or small-grain-size specimens with known structures using either a double-tilt or a rotation holder.

7.4 ProJECT/PCED3

PCED3 is an upgraded version of previous JECP/PCED. New features include:

  1. Blackman's theory, an integral two-beam dynamical theory, for intensity calculation,
  2. Match model for out-of-plane and in-plane texture,
  3. pseudo-Voigt function for peak profile of diffraction ring and
  4. improvement on diffraction pattern indexing and matching to experimental pattern.

The GUI of PCED3 includes:

  1. a main frame with a panel is used to show the simulated pattern or to match to the preloaded experimental diffraction pattern;
  2. input parameters for calculation can be initialized with separated dialogs;
  3. input structure data file can be prepared using a designed interface;
  4. two phases can be loaded and calculated simultaneously to simulate the diffraction diagram of two phase systems or for directly comparison of the two phases.

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