Advanced=20 Simulation of

PolyCrystalline=20 Electron Diffraction Pattern

(PCED2.0)

User=92s=20 manual

X.Z.=20 LI

Nebraska=20 Center for Materials and Nanoscience, University of=20 Nebraska

(June,=20 2009)

Table of Contents

1.=20 Introduction. 3

2. = Theory=20 background. 4

2.1 = Blackman=92s=20 theory on intensity of polycrystalline electron = diffraction. 4

2.2=20 Pseudo-Voigt function for peak profile. 5

2.3 = March=20 Model for polycrystalline texture. 5

3. = Graphic=20 user interface of PCED2.0. 7

3.1 = Main=20 interface. 7

3.2 = Menu and=20 toolbar. 9

4. = Usage of=20 PCED2.0. 11

4. 1 = Prepare=20 new data file. 12

4.2=20 Simulation. 12

4.3 = Save and=20 print 13

5. = Special=20 topics on PCED2.0. 14

5.1 = Partial=20 occupancy factor and isotropic temperature factor. 14

5.2 = Load and=20 center EDP.. 14

5.3 = Peak=20 profile, incident beam and texture. 14

5.4 = Indexing=20 and parameter table. 16

5.5 = Determine=20 weight ratio of two-phase system.. 16

5.6 = Grain size=20 and the FWHM of diffraction ring. 16

6. = Example:=20 PCED analysis of thin films of FePt L1₀phase. 17

6.1 = Example 1.=20 FePt film with thickness 20 nm.. 18

6.2 = Example 2.=20 EePt film with thickness 4 nm.. 18

6.3 = Example.=20 FePt film with thickness 12 nm.. 19

7.=20 Reference. 21

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1.=20 Introduction

For=20 polycrystalline or powder TEM specimens, electron diffraction ring = patterns are=20 extensively used for phase identification, in which the diffraction = pattern of a=20 known phase acts as a fingerprint.

Since=20 electron diffraction from polycrystalline specimens is analogous to = X-ray=20 diffraction from powders, computer programs designed for powder X-ray=20 diffraction may be used to analyze polycrystalline electron diffraction = patterns=20 for phase identification. Electron diffraction ring pattern needs to be=20 transformed into the form of integral intensity as a function of = scattering=20 angle for comparison with a powder X-ray diffractogram. The other = approach is to=20 use computer programs that implement the formula for electron = diffraction=20 intensity to analyze raw or processed polycrystalline electron = diffraction=20 patterns. Integrated electron diffraction software packages often = provide a=20 module for simulating polycrystalline electron diffraction pattern, but = rarely=20 do they include features for direct comparison with experimental data = for phase=20 identification. A specially designed computer program is needed to = provide a=20 fast and accurate method for accomplishing this task. This is the = motivation to=20 develop the first version of PolyCrystalline=20 Electron Diffraction (JECP/PCED, Li 2004).

PCED2.0 is an=20 upgraded version of previous JECP/PCED. New features include (i) = Blackman=92s=20 theory, an integral two-beam dynamical theory, for intensity = calculation, (ii)=20 Match model for out-of-plane and in-plane texture, (iii) pseudo-Voigt = function=20 for peak profile of diffraction ring and (iv) improvement on diffraction = pattern=20 indexing and matching to experimental pattern.

The = GUI of=20 PCED2.0 includes (i) a main frame with a panel is used to show the = simulated=20 pattern or to match to the preloaded experimental diffraction pattern; = (ii)=20 input parameters for calculation can be initialized with separated = dialogs;=20 (iii) input structure data file can be prepared using a designed = interface; (iv)=20 two phases can be loaded and calculated simultaneously to simulate the=20 diffraction diagram of two phase systems or for directly comparison of = the two=20 phases.

PCED2.0 is=20 written and complied in Java 6.0. Further code optimization (including=20 obfuscation) is carried out on the compiled class files. A=20 registration =93key=94 code is needed to unlock the program (PCED2.0f) = for loading=20 new input data files. = Without the=20 key the program is locked up in demo mode, which working only on default = input=20 files (Al and Mg).

2.=20 Background

Kinematic theory=20 of electron diffraction is described in details in any texture book on = this=20 topic (e.g. Peng et al = 2004). The=20 electron atom scatter factor can be derived from X-ray atom scatter = factor using=20 Mott-Bethe relationship or directly obtained from parameterized table of = electron atom scatter factor (Peng et=20 al. 1996). Here we use the second method.

Following the=20 electron diffraction geometry, the radius of the diffraction ring, R, can be related to the = length of the=20 reciprocal vector g(hkl) as

(1)

where = L is the camera length, g=3D|g(hkl)| and K is the wave vector of = incident=20 electron beam, K =3D |K|.

2.1=20 Blackman=92s theory on intensity of polycrystalline electron=20 diffraction

Blackman=92s=20 theory (Blackman 1939) for polycrystalline electron diffraction = intensity is=20 based on Bloch wave dynamic theory initially formulated by Bethe and the = formulas are given as integral intensity of two-beam dynamic = diffraction.=20 According to the book by Peng et al.=20 (2004), = Blackman=92s theory for=20 polycrystalline electron diffraction intensity is an advanced theory on = this=20 topic although the theory was published decades ago. Readers should = refer to the=20 original paper for details derivation of the formulas. Some important = formulas=20 are listed here.

The = dynamical=20 structure factor is given

(2)

where = m is electron mass, e is electron charge, h is Planck constant, V_g is Fourier coefficient of = crystal=20 potential.

The = wave vector=20 in vacuum is given

(3)

here E is accelerated voltage of = electron=20 microscope.

The = wave vector=20 inside crystal is corrected with mean inner = potential

(4)

The = diffraction=20 intensity formulas can be given below in an integrated form considering = there=20 are angle distribution between the incident beam and the zone axis of = the=20 polycrystalline grains,

(5)

Where = is intensity of the incident = beam,=20 is dynamical structure factor, = is wave vector and = the zero-order Bessel function=20 and,

(6)

Here is K normal component and = = ( is K component in the zero-order = Laue=20 zone).

The = final=20 intensity is an averaged integral intensity over , = considering=20 the angle between incident beam and the surface normal in a range from = to .

2.2=20 Pseudo-Voigt function for peak profile=20

Although Voigt=20 (V) function, as convolution of a Gaussian (G) and a Lorentzian (L) = functions,=20 is regarded as the most suitable function to describe the profile of the = cross-section of the diffraction rings, but it is rather complex. = Pseudo-Voigt=20 (pV) function is usually good enough substation for the job. = pseudo-Voigt=20 function is a linear combination of Gaussian and Lorentzian function, as = following (Li, 2007),

(7)

(8)

(9)

Here h = is peak=20 height, x₀ is peak position, FWHM is full width at half = maximum.=20 Figure 1 shows the comparison of profiles of Gaussian and Lorentzian=20 functions.

2.3=20 March Model for polycrystalline texture=20

For = powder=20 samples, axially symmetric platy or capillary specimens, composed of = effectively=20 disk- or rod-shaped crystallites, can form textures due to the shape of=20 crystallites. For thin film samples, polycrystalline microstructures = with=20 out-of-plane or in-plane preferred orientations often occur during the = film=20 growth. The diffracted intensities from preferred orientation can be = corrected=20 or measured with a single pole-density profile. The March model is used = as for=20 correcting the powder X-ray diffraction with texture, which is simple = but=20 effective method for both of out-of-plane (platy) and in-plate (rode)=20 textures.

Figure 1. Comparison of = profiles of=20 Gaussian and Lorentzian functions.

The = formals were=20 firstly given for X-ray powder diffraction, which is reformulated for = the=20 diffraction geometry in polycrystalline electron diffraction considering = the=20 diffraction geometry of polycrystalline electron diffraction. Figure 2 = show=20 example curves of the March functions used in X-ray powder diffraction=20 (Bragg-Brentano geometry) and in polycrystalline electron diffraction = for platy=20 (out-of-plane) texture. Referring to the figure 1 in the paper by = Dollase=20 (1986), the density of preferred zone axis for polycrystalline electron=20 diffraction can be formulated as following.

For = out-of-plane=20 texture,

(10)

For = in-plane=20 texture,

(11)

If the = axial=20 pole-density profile, is = known,=20 may be obtained by numerical = integration=20 making use of the relation among coordinates: .

The = intensity of=20 polycrystalline electron diffraction including texture can be expressed = as,=20

(12)

where = s is the=20 scale factor, P_g(a_i) is = the density=20 of g(hkl) poles at the scattering vectors and a_i=20refers = to the=20 angle between G(HKL) and the ith=20 member of the symmetry-equivalent set of m diffraction planes. The = preferred=20 orientation plane itself is a member of some set of symmetry-equivalent = planes.=20 If the dominant morphological feature of the crystallites is re-indexed = as some=20 other member of this set, the individual values of a_i in = above will=20 be permuted but the sum of terms remains the same. The sum can be = considered as=20 a generalized multiplicity term.

Figure 2. = Example=20 curves of the March functions used in X-ray powder diffraction = (Bragg-Brentano=20 geometry) and in polycrystalline electron diffraction for platy = (out-of-plane)=20 texture. Angle away from the preferred orientation is in abscissa and = the=20 density (or weight) in ordinate. =

3.=20 Graphic user interface of PCED2.0

3.1=20 Main interface

The = main=20 interface of PCED2.0 is shown in Figs. 3 and 4, which includes a menu = and a=20 toolbar to take input parameters and a frame to show the output of the=20 simulation. The usage of PCED2.0 for simulation needs to load structure = data and=20 to set up input parameters, then simply click Run button in Calculation dialog (shown = later). The=20 usage of PCED2.0 for phase identification needs to load experimental = diffraction=20 pattern first and then to match to the calculated patterns by chosen = structure=20 data and input parameters. Two structure data can load at the same time = for=20 comparison or for simulation of a two-phase system. =

Figure 2. Snap-shot of the = main=20 interfaces of PCED2.0, a simulation of polycrystalline electron = diffraction in a=20 two-phase system, Al and Mg.

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Figure 3. Snap-shot of the = main=20 interfaces of PCED2.0, a phase identification using calculated = polycrystalline=20 electron diffraction pattern. Experimental PCED pattern is Al.

3.2=20 Menu and toolbar

Menu = and toolbar=20 can be used to pop up dialog interfaces for data loading or parameters = reading=20 or changing. Although = menu give=20 more text description and organized in groups while toolbar in graphics = and=20 easily to access, most functions of menu and toolbar are same. However, = there=20 are some functions are only provided either in menu or in toolbar.=20

File=20 menu = provides an=20 interface for preparing the input structure data, saving the hkl = intensity list=20 (and other info can be saved as option), and print to printer or to a = PDF file=20 when a PDF print driver was installed.

EDP=20 menu = provides an=20 interface to load experimental polycrystalline electron pattern in jpg = (or jpeg)=20 format. The loaded pattern can be centered by drag-and-drop with = referring to a=20 set of preset circles when the checkbox of Center (image) is selected. = Clear in=20 EDP can be used to remove the pattern. Drag-and-drop: selecting a = point in=20 image by mouse, press down left button of mouse, drop to the selected = point, for=20 example, the center of panel, and release the left button of the mouse. = When the=20 position of the image is set up, uncheck the Center (image)=20 box;

Simulation menu=20 provides a=20 submenu for the choice of theory and several dialogs for specific = parameters in=20 simulation. Two theories are used for calculation of electron = diffraction=20 intensity. Kinematical theory is selected by default and the second = choice is=20 Blackman=92s theory, which is integral two-beam dynamic theory. = Intensities=20 calculated by Blackman=92s theory are more accurate than those = calculated by=20 kinematical theory, but the calculation of dynamic theory will take = longer time.=20

Option = menu=20 provides a=20 freedom of customizing the appearance of simulated pattern, for = examples, the=20 color of the diffraction peak and ring, the curve or solid profile, = number of=20 reference circles, and the selection in the hkl-inten list=20 file.

Toolbar=20 provides a=20 second way to conveniently access the dialogs described above. The = functions of=20 the toolbar are indicated by the icon and tooltip text. Only most = frequently=20 used menus and submenus are listed in Toolbar.

The = key field=20 and the lock icon are new items here. A registration =93key=94 code is = needed unlock=20 the full version PCED2.0f, which works on normal=20 input files or = the limited=20 version PCED2.0i, which works on=20 the input files with one-way hash code. = Without the=20 =93key=94 code, the program is locked up in demo mode, which working = only on default=20 input files (Al and Mg).

4.=20 Usage of PCED2.0

To=20 run PCED2.0, just type: java = =96jar=20 (-Xmx512m) PCED2.0.jar in command line or double click the icon of = PCED2.0.jar. =96Xmx512m is an = option to=20 set the memory of Java virtual machine up to 512 MB. An interface of the = program=20 similar to Figure 3 will show up. To type in the =93key=94 code in the = key field of=20 the tool bar will unlock PCED2.0f or PCED2.0i. Otherwise, the program = will work=20 on the default structure data in demo mode.

In the = following, we show step by step from preparing structure data file, = common=20 routine usage for simulation, and to the last steps of saving and = printing the=20 results. More details on specific topics are left to next section.=20

Figure 4. Snap-shot of the = preparation=20 of input structure data file.

4.=20 1 Prepare new data file

Structure data=20 file can be prepared using the PCED=20 Phase Input File dialog in Figure = 5=20 or using a text editor to modify other structure data file. The = dialog=20 provides a certain level of assistant for user and also makes sure to = meet the=20 requirement of the format of the file.

=B7 =20 Description=20 field can be filled in a name of the phase.

=B7 =20 Bravais lattice=20 can be selected a list. Lattice types are provided for each crystal = system.=20

=B7 =20 Lattice=20 parameters are preset according to Bravais = lattice.

=B7 =20 Space = group=20 number is limited to possible group according to Bravais=20 lattice.

=B7 =20 Fill = the info of=20 each atom in and then add to the atom list. For modifying or removing = the list,=20 user should select the atom row in the list and click the Remove=20 button.

=B7 =20 Notes = field can=20 be used for the purpose for simulation or = reference.

To = save the data=20 structure click the Save = button or=20 to make new one click the New=20 button.

4.2=20 Simulation

Kinematical=20 theory is used as a default selection in the simulation since it is fast = and=20 less input parameters are required. Integral dynamical two-beam theory=20 (Blackman=92s theory) can be turned on using Theory submenu in Simulation menu. =

Basic = parameters=20 for calculation and adjustment of diffraction pattern can be filled in = or=20 changed in Calculation = dialog in=20 figure 6. To generate new diffraction pattern needs click Run button. The pattern is=20 automatically updated corresponding to the change of other parameters.=20

Mass=20 ratio = defines=20 relative mass of the two phases with the fields of phase1 and phase2 are = checked,.

G-spacing zoom = and Intensity scale, simulated = the camera=20 length and the exposure time in experiment, which are used to make a = better=20 appearance of the calculated pattern.

Diffraction=20 diagram can be viewed as peak and profile separately or=20 together.

Diffraction=20 ring can = be viewed=20 as either a ring to match experiment pattern or only top half in order = to=20 clearly show index without intervening, or without ring at=20 all.

The = appearance=20 of diffraction ring is also controlled by peak height itself (intensity threshold) and peak = height=20 comparing to neighbor points (intensity=20 sensitivity). =20

Figure 5. Snap-shot of the = calculation=20 dialog.

4.3=20 Save and print

Calculated=20 diffraction data can be saved into a file using Save in File menu, in which it = includes hkl=20 and intensity (per unit-length) together with the parameters used in the = simulation as default option. More info, such as, length of reciprocal = vector=20 (g), crystalline plane spacing (d), intensity (per unit angle), can be = chosen to=20 be saved by using selection in = hkl-inten dialog in option menu. =20

Simulated=20 electron diffraction pattern together with the experimental pattern if = preloaded=20 can be sent to print directly using Print in File menu or save into a PDF = file if a=20 PDF printer driver was installed.

5.=20 Special topics on PCED2.0

5.1=20 Partial occupancy factor and isotropic temperature = factor

Some=20 atom coordinates may be not in full occupancy in a crystalline = structure. In=20 this case, the occupancy factor (default value 1.0) should be changed to = the=20 values according to the crystalline structure in preparation of the = structure=20 data file for polycrystalline electron diffraction simulation.=20

Partial=20 occupancy factor can also be used to simulate a certain level of = chemical order=20 in structure. For example, the chemical ordered FePt L1₀ = phase, see=20 section 6. In this case, different type of atoms may be assigned to the = same=20 atomic coordinates with different occupancy according to the chemical = ratio, but=20 the sum of the occupancy factors of the two atoms is = 1.0.

Isotropic=20 temperature factor is used here to simulate the effect of lattice = vibration=20 (Debye model). Although isotropic temperature factor is a rough model, = it can be=20 used simulate the decrease of the diffraction intensity with the = variation of=20 the |g| value, the higher the value of |g| the more decrease of the = diffraction=20 intensity.

5.2=20 Load and center EDP=20

For = phase=20 identification, an experimental polycrystalline electron diffraction = pattern is=20 needed to loaded up and compare with simulated patterns, which were = calculated=20 from the related phase files. The experimental pattern should be in jpg = (or=20 jpeg) format and is better prepared into square shape with pattern in = the=20 center. The experimental pattern can be load using Load in EDP menu and then center by = using Center in EDP menu. Once Center is clicked, five = concentric=20 circles will appear in the main panel. =20 Select the center of the pattern using mouse and hold on the left = button=20 of mouse, the pattern can be dragged and drop into the center of the = panel.=20 Click the Center in EDP = menu the=20 pattern is locked up in the position and concentric circles disappear. = More=20 adjustment in small step may be needed to find the accurate position. = Number of=20 concentric circles can be changed using Number of Reference Circle in = Option = menu.

5.3=20 Peak profile, incident beam and texture

Profile of the=20 cross-section of diffraction ring is referred as peak profile, which can = be=20 simulated using a pseudo-Voigt function, together with grain size = (diameter) and=20 constant K. The ratio of Gaussian and Lorentzian functions in = pseudo-Voigt=20 function can be adjusted using Peak=20 Profile in Simulation = menu=20 (default value is 0.5). The grain size (diameter) and constant K can be = adjusted=20 using Average Grain Size = dialog in=20 Simulation=20 menu.

Incident beam in=20 polycrystalline electron crystalline is very strong comparing to the = diffraction=20 ring, it may submerge the relative week rings near the incident beam. = Incident=20 beam can be

Figure 6. Snap-shot of the = EDP pattern=20 centered by the drag-and-drop action.

included in the=20 simulated pattern by check on the Included box in Peak Profile dialog and = adjust the=20 shape by changing the corresponding values of height and=20 fwhm.

Peak = and profile=20 can be selected individually and the style of profile can be chosen = between=20 solid or curve.

In texture dialog, axis of = texture and=20 March parameter (default value 1.0 for full random case) can be input = for=20 simulation. These values can be setup separately for phase1 and phase2.=20

March = parameter=20 (r) is suitable for describing the slight deviation of the randomness of = polycrystalline/or powder sample, thus the higher the value the better=20 approaching the randomness. =20

To = describe the=20 status of preferring orientation, it is suggested to used reversed March = parameter r=92 =3D 1.0 - r. Thus, full randomness r=92 =3D 0, the higher = the prefer=20 orientation, the higher the value of r=92 and for the perfect prefer = orientation=20 r=92 =3D 1.0.

5.4=20 Indexing and parameter table

There = are cases=20 that diffraction peak are quite dense, the index labels may be = overlapped when=20 they are shown by the side of the diffraction diagram, especially for = the=20 diffraction diagram of two-phase system.

To = avoid the=20 situation, PCED2.0 is allowed to select location of index label and to = spread=20 them when necessary. In index=20 dialog, top point can be viewed when the check box of Guide line is selected and = moved around=20 by arrow keys when the corresponding radio button is selected (no = further mouse=20 click for the moment). Base = line can=20 be viewed when the check box of Link=20 line is selected and moved up/down by arrow keys when the = corresponding=20 radio button is selected (no further mouse click for the=20 moment).

For = convenience=20 to track down the parameters used in the simulation, a Parameter Table can be pop up = using Parameter Table in Simulation menu, which lists = the=20 important parameters of phase1 and phase 2.

5.5=20 Determine weight ratio of two-phase system

The = PCED2.0=20 program provides a way to simulate of the composite diagram of two-phase = system=20 with given weight ratio. The formula used in the program is to convert = the=20 weight ratio into the numbers of unit-cell in diffraction using atomic = weight=20 per unit-cell for each phase for simplicity. Experimentally determining = weight=20 ration of two-phase system should be calibrated by using a standard = sample with=20 known weight ratio.

5.6=20 Grain size and the FWHM of diffraction ring

The = PCED2.0=20 program provides a way to simulate of the FWHM of diffraction ring for = given=20 average grain diameter and K factor. The values of FWHM for each ring in = calculated diagram are consistent to the same pseudo-Voigt function used = in the=20 simulation. The diffraction rings in experimental pattern are often = composed of=20 separately individual spots from grains with different grain size, the = peak=20 profiles are obtained by using data sum up around each ring. In such = case, the=20 peaks may need to be fitting to different pseudo-Voigt function for each = ring.=20 The grain size is not related to the peak profiles of polycrystalline = electron=20 diffraction ring pattern in a simple way. The grain size should be = measured by=20 using bright field or dark field imaging method.

6.=20 Example: PCED analysis of thin films of FePt L1₀₌₂₀phase

In = order to=20 increase the areal density of magnetic recording media, grain sizes of = the=20 magnetic films must be reduced. A high-anisotropy material is thus = essential for=20 the new media to retain thermal stability. The high anisotropy energy of = FePt=20 L1₀ phase makes FePt alloy system one of the most promising = materials=20 candidates. As-deposited FePt films normally consist of the disordered = fcc=20 phase, which is a magnetically soft phase, and can be transformed into = the=20 L1₀ phase upon annealing treatment. The chemical order of the = L1₀ phase depends on the composition and the heat treatment = condition=20 of the film.

For = data-storage=20 applications, it is desirable that the [001] axis of the L1₀ = phase is=20 perpendicular to the film plane since the [001] axis of the = L1₀ phase=20 is a magnetic easy axis. Hence, the films in a (001) texture have an = advantage=20 over randomly or other (e.g. (111)) oriented films. One way to achieve = the (001)=20 texture has been developed by depositing multilayer of Fe and Pt film = and=20 annealing at elevated temperature. The formation of the (001) texture = for=20 various ranges of film thicknesses were studied by selected-area = electron=20 diffraction (SAED), examples are discussed here to show the application = of=20 PCED2.0. Different schemes for comparison of experimental and simulated = patterns=20 are used in each example as demonstration.

Figure=20 7. SAED pattern of the FePt L10 phase in = film with=20 thickness of 20 nm annealed at 600 =B0C for 30 second and calculated = pattern for=20 phase identification.

6.1=20 Example 1. FePt film with thickness 20 nm=20

Figure = 8 shows=20 the SAED pattern of FePt film with thickness of 20 nm annealed at 600 = =B0C for 30=20 second and calculated pattern of the FePt L1₀ phase in for = phase=20 identification. The ring radiuses and corresponding intensities in the=20 calculated pattern in Figure 8 are considered matching well with = experimental=20 pattern, on the other hand, the ring radiuses and corresponding = intensities in=20 the calculated pattern with FePt random fcc structure (not shown here) = are not=20 matching with experimental pattern. Thus the phase is confirmed to be = the=20 chemical ordered FePt L1₀ phase. It also indicates that the = random=20 distribution of grains in the film in comparison to Figure 9 in example=20 2.

Figure 8. SAED pattern of the = FePt L10=20 phase in a film with thickness of 4 nm annealed at 600 =B0C for 30 = second and=20 calculated pattern with (001) texture.

6.2=20 Example 2. EePt film with thickness 4 nm

Figure = 9 shows=20 the SAED pattern of the FePt L1₀ phase in a film with = thickness of 4=20 nm annealed at 600 =B0C for 30 second and calculated pattern of the FePt = L1₀ phase with (001) texture for phase identification. Radius = distribution of the diffraction patterns in Figure 9 is the same as those in Figure 8, however, = the=20 intensity distribution of the diffraction patterns are dramatically = different,=20 which means a texture exists in Figure 9, as confirmed in the calculated = pattern=20 with (001) texture.

Now we = estimate=20 the (001) texture of the film with thickness of 4 nm = semi-quantitatively. Figure=20 10 is digital processed diagram of Figure 9 using a program QPCED (Li, = 2007). By=20 using March parameters of 0.45 and a given chemical order (Pt sites with = 80%Pt+20%Fe; Fe sites with 80%Fe+20%Pt), a calculated diagram in Figure = 11 is=20 best matching with Figure 10 is obtained. As discussed in section 5.3, = if we use=20 revised March (0.0 for full random and 1.0 for perfect texture), the = texture can=20 be described as 55% of the (001) texture.

Figure 9. Digital processed = diagram of=20 experimental electron diffraction pattern in Figure 9.

Figure 10. Simulated = diffraction=20 diagram fitting to the Figure 10 with aim to reveal the degrees of = chemical=20 order and (001) texture of film with thickness of 4nm.

6.3=20 Example. FePt film with thickness 12 nm

Figure = 12 shows=20 the SAED pattern of FePt film with 12 nm of repeated bilayer FePt and = 1nm Pt top=20 layer in deposition followed by annealing at 600 =B0C for 30 second and = simulated=20 pattern. The profile of digital diffraction pattern was loaded in the = PCED2.0=20 and to compare the simulation pattern directly, which was calculated = using March=20 parameters of 0.17 and a given chemical order (Pt sites with = 80%Pt+20%Fe; Fe=20 sites with 80%Fe+20%Pt). Thus the texture can be described as 83% of the = (001)=20 texture.

Figure 12. = Simulated=20 diffraction diagram fitting to an experimental PCED profile aim to = reveal the=20 degrees of chemical order and (001) texture of the FePt film, which was=20 deposited as thickness of 12nm of repeated FePt bilayer and 1 nm of Pt = top layer=20 followed by annealing at 600 =B0C for 30 second.

7.=20 Reference

Blackman,=20 M., On the Intensities of Electron Diffraction Rings. Proceedings of the = Royal=20 Society of London, Series A, Mathematical and Physical Sciences, 173 = (1939)=20 68-82. =

Dollase=20 W.A., Correction of Intensities for Preferred Orientation in Powder=20 Diffractometry: Application of the March Model. J. Appl. Cryst. 19 = (1986)=20 367-272.

Li,=20 X.Z., JECP/PCED=97a=20 computer program for simulation of polycrystalline electron diffraction = pattern=20 and phase identification. Ultramicroscopy 99 (2004)=20 257-261.

Li,=20 X.Z., Quantitative Analysis of Polycrystalline Electron Diffraction = Patterns,=20 Microanalysis and Microscopy = 2007.

Peng=20 L.-M., Dudarev S. L. and Whelan M. J.,=20 High=20 Energy Electron Diffraction and Microscopy, Oxford=20 University Press (01/01/2004).

Peng=20 L.-M., Ren G., Dudarev S.L. and Whelan, M.J., Robust Parameterization of = Elastic=20 and Absorptive Electron Atomic Scattering Factors, Acta Cryst. A52 = (1996)=20 257-276.