Moscow packages of structure programs

The software for the electron diffractometry and structure calculations

Anatoly Avilov, Alexey Kuligin, Alex Dudka,

Valery Andrianov, Stavros Nicolopoulos

Institute of Crystallography of Russian Academy of sciences

contents

• Software for the electron diffractometry (EDSA)

• Software for the structure calculations (ASTRA)

• Software for the structure calculations (AREN)

EDSA - software for the electron diffractometry. Alexey Kuligin

1 – electron diffractometer,

2 – electron microscope,

3 – imaging plate,

4 – polycrystalline sample,

5 – textured sample,

6 – mosaic monocrystalline sample,

7 – ent of the atomic structure,

8 – LSQ – method,

9 – direct methods,

10 – refinement of parame-ters of chemical bonding,

11 – Fourier maps

Scheme of the electron diffractometer

Possibility of the software:

• Measurements of the intensity in «accumulation mode» (with given accuracy) and in «constant time mode», quasi-monitoring in the process of measurement

• Statistical treatment of measurements• Indexing of the all type of DPs - (polycrystals, textures,

mosaic monocrystals) - with accounting for the curvature of the Ewald sphere

• Subtraction of the background• Analysis of the peak forms, positions of the maxima and of

the «center of mass», integration• Eddition of the measurement results for the structure

calculations• Structure calculations

Program for measurements of DP’s

Statistical treatment of experimental intensities

accumulation mode for measurements, statistical treatment and «control point» - 1-2% statistical accuracy

Our aim:

• The precise structure investigations :

- quantitative analysis of the ESP and

chemical bonding

- fine structure determinations (hydrogen position,

occupancies etc.)

- examination of the thermal atomic vibrations

• It is necessary to measure reflection intensiteis with maximal accuracy

Measurement of intensity• Best accuracy (1- 2 %) - «accumulation mode»

• Two stage of measurements:

1. Fast scanning : big step and small accumulation

- determination of the reflections positions

- indexing and calculation of the positions of other

reflections

- marking of the areas of the reflections for the precise

measurement

2. Slow scanning with the small step and big statistics of

all marked reflections

How measurements are made..

Example of measurements: mosaic monocrystalline film - CaF2 [ (001) - plane]

• One of the results of two-dim. scanning of all pattern. Sample is slightly inclined around hh0-axis. The statistical accuracy- 1%

• time of measurement is about 1 hour

• background is subtracted

1. Fast scanning

• Two areas were choosed for fast scanning: circle and sector

• Red colore is the places with approx. «zero» intensity

1. Fast scanning - indexing

Program

calculates

positions

of all

reflections

1. Fast scanning - marking of the areas for the precise measurements

2. Slow scanning of marked areas

The results of measurements are fixed as table with all information: Ihkl, hkl, positions of peaks etc.

N. X0_DP Y0_DP X0_FI Y0_FI ALL real sum X0_DP Y0_DP X0_FI Y0_FI Imax CM_X0_DP CM_Y0_DP CM_X0_FI CM_Y0_FI ! h k l

1. 1328 576 0 140 317 317 189 120 -424 151 15 10 120.04 -428.70 150.99 14.41 ! 4 8 0 2. 1328 912 0 182 318 314 109 -200 -448 191 12 3 -160.29 -459.30 186.04 10.59 ! 6 8 0 3. 1312 224 2 96 318 318 286 448 -424 110 15 12 455.19 -425.20 109.10 14.85 ! 2 8 0 4. 1304 -320 3 28 322 322 137 1096 - 408 29 17 5 1154.51 -423.36 21.69 15.08 ! -2 8 0 5. 1296 -40 4 63 321 321 195 776 -416 69 16 8 798.73 -412.14 66.16 16.48 ! 0 8 0 6. 1040 952 36 187 323 323 216 -216 -144 193 50 6 -196.11 -143.22 190.51 50.10 ! 6 6 0 7. 1024 592 38 142 318 318 460 112 -120 152 53 15 123.86 -134.89 150.52 51.14 ! 4 6 0 8. 1008 248 40 99 321 321 1450 440 -112 111 54 73 446.12 -115.21 110.23 53.60 ! 2 6 0 9. 992 -320 42 28 320 320 388 1088 -96 30 56 34 1107.15 -106.78 27.61 54.65 ! -2 6 010. 984 -32 43 64 322 322 1301 768 -112 70 54 29 797.23 -117.98 66.35 53.25 ! 0 6 011. 736 976 74 190 319 319 533 -224 168 194 89 19 -213.36 152.26 192.67 87.03 ! 6 4 012. 728 624 75 146 322 322 1879 104 184 153 91 70 119.38 168.32 151.08 89.04 ! 4 4 013. 712 264 77 101 316 316 5041 432 192 112 92 236 439.56 174.81 111.06 89.85 ! 2 4 014. 696 -320 79 28 321 321 607 1072 208 32 94 33 1122.16 180.97 25.73 90.62 ! -2 4 015. 680 -24 81 65 321 321 1049 752 192 72 92 59 770.10 185.32 69.74 91.16 ! 0 4 016. 432 1008 112 194 322 322 503 -232 480 195 128 24 -222.06 468.83 193.76 126.60 ! 6 2 017. 424 656 113 150 317 317 3 018 88 480 155 128 148 105.63 475.53 152.80 127.44 ! 4 2 018. 416 296 114 105 323 323 8536 416 488 114 129 440 434.53 485.45 111.68 128.68 ! 2 2 019. 400 -336 116 26 322 322 1612 1080 520 31 133 302 1077.06 507.62 31.37 131.45 ! -2 2 020. 376 -16 119 66 321 321 17174 744 512 73 132 1263 752.10 499.23 71.99 130.40 ! 0 2 021. 104 720 153 158 322 322 1599 88 792 155 167 67 86.53 778.02 155.18 165.25 ! 4 0 022. 104 992 153 192 322 322 1016 -240 784 196 166 30 -211.31 767.59 192.41 163.95 ! 6 0 023. 96 352 154 112 320 320 8954 400 800 116 168 554 426.90 793.67 112.64 167.21 ! 2 0 024. 80 -392 156 19 322 322 3514 1056 824 34 171 558 1063.09 815.88 33.11 169.98 ! -2 0 025. 64 0 158 68 197 197 139003 728 808 75 169 22520 740.79 805.78 73.40 168.72 ! 0 0 026. -192 960 190 188 318 318 220 -256 1096 198 205 16 -232.69 1076.91 195.09 202.61 ! 6 -2 027. -200 328 191 109 322 322 1022 400 1096 116 205 197 417.28 1103.66 113.84 205.96 ! 2 -2 028. -200 640 191 148 321 321 1061 72 1104 157 206 119 85.30 1075.84 155.34 202.48 ! 4 -2 029. -224 -336 194 26 319 319 3635 1048 1128 35 209 280 1057.96 1120.91 33.75 208.11 ! -2 -2 030. -232 64 195 76 321 321 10880 728 1120 75 208 1003 730.46 1113.15 74.69 207.14 ! 0 -2 0

ASTRA- system of programs for the precise structure investigation

Alexander Dudka

• The system is intended for the refinement of the crystal structure models on the data: electron diffraction, X-ray and neutron diffraction

• Main distinctive characterstics of ASTRA

1. Using of the methods inter-experimental minimization (IEM), in particular, combined treatment of set of experimental data, obtained in different conditions

2. Effective algorithm of nonlinear minimization

3. Detailed structure model includes additional parameters of

the experimental devices and constants of crystals

4. The system was projected for the continuous modernization

Inter-experimental minimization

1. Necessary to have a repeated experiments : different irradiation or different samples, to know exactly - what part of the model will be responsible for the alterations (e.g. with T0 - Debay-Waller factor)

2. The model of the differences (part of all structure model) from different experim. sets should be built up. Only condition - other parameters must coincide

3. To reduce of the same name experimental data to one scale - to get a «cross-set»

4. To refine residuary model parameters using a «cross set»

5. To repeat if it is necessary the process of refinement from the position 2, etc.

Minimized functional:

- is traditional member for LSQ (stabilizes the refinement process)

- is responsible for the distinctions between of the same name data

cross- cross-functional is responsible for the refinement on the

averaged data

, , - Lagrange-factors, N - number of equiv.refl., w’-weight-

correction, norm- scaling, cross- averaging on N data, Kw-interexp. scale-factor

cross

2

11

2

11 1

2

12

1 basecalchkl

normcrosshkl

n

hkl hkl

hklN

m

normmobsh

mw

normcrosshkl

n

hkl hkl

hklN

m

n

hkl

basemcalchkl

normmobshklhkl II

w

wIKI

w

wIIw

N

crosscrosscross

The defects of usual LSQ

• The defects becomes apparent in the:

- Correlation between parameters of refinement

- Correct work is possible only with the of equal accuracy data.

- Insufficient adequacy of the theoretical model • Hence :

- Ambiguity of the solution - a number of the models with small distinctions have very close minimal R-factors

- LSQ is very small sensitive to the systematical errors

For the reduction of the correlation:

• Inter-experimental comparison can be made by:

- IEM in general form: of the same name reflections from different set of data are compared

- Anysotropic IEM: comparison of the equivalent reflection from one set serves for the more exact determination of the parameters of anysotropic effects

- IEM on the subsets of data: comparison at the angle of scattering; comparison between occasional subsets of the data formed from one set ; comparison of the profiles of reflections for the excluding of the input of TDS etc...

Another method of the decreasing of the influence of the correlations is realized in the adapted nonlinear

algorithm of minimization with using normalization on the Lavrent’ev, Levenburg, Markvardt -

«nonlinear LSQ»

• Due to this two problems are solved:

- the choice of the direction of the searching of minimum of the functional

- negative influence of the correlations is decreased

The organization of the work of ASTRA

• IBM PC , not lower MS WINDOWS - 98

• On-line storage - not lower 10 Mb

• Kompiler – Borland Delphi v.7.0 и Compaq Visual Fortran v.6.

• ASTRA is the system of programs (exe и dll modules), controled by interfaces

• Main interface - universal program interface UPI (analog guid of MS WINDOWS) - allows to edit and to transmit information to working programs, to look results...

The manager information are constructed as hierarhical one

• Useful information appear on the right panel UPI after

choise of the requisite task or the chapter of task

The bigest tasks (profile analysis, refinement of model) have a specialized interfaces for the input control data and for the looking of the results (in grafical form). Lower - the specialized interface for the electron diffraction structure analysis of CaF2

Usual LSQ refinement for Al2BeO4:Cr3+

• The results of two refinement (for two experiments) are contrary one to another - the curve is not stright line

• Eobs- discrepancies of refinement, Ecalc- calculated discrepancies

Nonlinear minimization

• The results of two refinements (two experiments) are good corresponent each to other

• Eobs- discrepancies of the refinement coincide with theory

• by repetition the experiments the besector should be obtained

The search of the minimum in the hard cases. Standart (linear) LSQ don’t stop on the inclined part (it means ambiguity of the dicision in the case of the correlation between parameters). This construction allows one to find valid decision.)

Difference Fourier synthesis for the electrostatic potential for CaF2

Three- dimensional map of the potential CaF2

Three-dimensional Fourier syntheis of ESP in three-dimensional representation