Standard Indexed Topographs

Multi-polytypic silicon carbide crystals display syntactic coalescence: that is the growth of one polytype layer on top of another with exact atomic register across the common boundary (0001-plane).  Consequently edge-topographs display a complex superposition of Laue-type diffraction patterns but with one simplifying feature: that each polytype sub-pattern is identically oriented.  A computer program Indexing Topographs (INDTOP)/White Radiation Indexing of Synchrotron Topographs (WRIST) was developed by Barnes and Fisher (1984),to aid in the interpretation of the x-ray data collected on the station 7.6 camera. A typical output data file is shown in table 1.  for the 6H polytype (listing d-spacings, wavelength and hkl values for the spatial x, y coordinates), further simulations have been made for the other common low period 4H and 15R Polytypes.

Table 1 Typical output from the INDTOP/WRIST computer program for the 6H Polytype. The input data corresponds to the geometry depicted in Figure edge geometry. The x and y coordinates have been interchanged from the raw data, so that a simulation plot resembles the orientation of the photographic plate as it is inspected under the optical microscopes. This alignment of the crystal c-axis (vertical) is more convenient for measurement work.

 

h

k

l

d spacing

Wavelength (Å)

X (mm)

Y (mm)

5

1

-6

0.470303

0.593289

20.3402

-13.1136

5

1

-4

0.474946

0.605061

19.20381

-8.709709

5

1

-2

0.477798

0.612351

18.52604

-4.34511

5

1

2

0.478519

0.614201

18.35708

4.34511

5

1

4

0.474946

0.605061

19.20381

8.709709

5

1

6

0.470303

0.593289

20.3402

13.1136

4

1

-12

0.527887

0.639749

26.55657

-33.48882

4

1

0

0.581687

0.77684

14.53884

-0.000008

4

1

12

0.527887

0.639749

26.55657

33.48882

3

1

-8

0.688261

0.904521

17.16334

-28.91549

3

1

-6

0.709259

0.960554

13.5366

-21.42508

3

1

-4

0.725491

1.005025

10.99916

-14.16139

3

1

-2

0.735783

1.03374

9.497404

-7.044593

3

1

2

0.735783

1.03374

9.497405

7.044611

3

1

4

0.725491

1.005025

10.99917

14.16141

h

k

l

d spacing

Wavelength (Å)

X (mm)

Y (mm)

3

1

6

0.709259

0.960554

13.5366

21.4251

3

1

8

0.688261

0.904521

17.16336

28.91551

5

2

-12

0.404161

0.560686

11.00758

-25.52613

5

2

0

0.426842

0.625381

5.075073

-0.000009

5

2

12

0.404161

0.560686

11.00758

25.52613

2

1

-6

0.935163

1.331941

7.949534

-31.64137

2

1

-5

0.95596

1.390783

5.414524

-26.13851

2

1

-4

0.973349

1.442937

3.372984

-20.76308

2

1

-3

0.987862

1.486288

1.804955

-15.48721

2

1

-2

0.998635

1.518882

0.69439

-10.28466

2

1

-1

1.00527

1.539134

0.03378

-5.130356

2

1

0

1.007512

1.546005

-0.186078

-0.000009

2

1

1

1.00527

1.539134

0.03378

5.130356

2

1

2

0.998635

1.518882

0.69439

10.28466

2

1

3

0.987862

1.486288

1.804955

15.48721

2

1

4

0.973349

1.442937

3.372984

20.76308

2

1

5

0.95596

1.390783

5.414524

26.13851

2

1

6

0.935163

1.331941

7.949534

31.64137

3

2

-8

0.581687

0.899917

-2.566175

-27.20436

3

2

-6

0.594198

0.939044

-4.864161

-20.23641

3

2

-4

0.603645

0.969142

-6.482687

-13.41259

3

2

-2

0.609535

0.988145

-7.444825

-6.6803

3

2

2

0.609535

0.988145

-7.444825

6.6803

3

2

4

0.603645

0.969142

-6.482687

13.41259

3

2

6

0.594198

0.939044

-4.864161

20.23641

3

2

8

0.581687

0.899917

-2.566175

27.20436

4

3

-8

0.426842

0.691654

-8.503587

-20.00656

4

3

-6

0.431712

0.707528

-9.667182

-14.94144

4

3

-4

0.435295

0.71932

-10.49231

-9.930951

4

3

-2

0.437488

0.726586

-10.98501

-4.956511

4

3

2

0.437488

0.726586

-10.98501

4.956511

4

3

4

0.435295

0.71932

-10.49231

9.930951

4

3

6

0.431712

0.707528

-9.667182

14.94144

4

3

8

0.426842

0.691654

-8.503587

20.00656

 

The coordinates (x, y) of the principal hkl reflections tabulated in Table 1. have been plotted in Figure 1. For comparison the simulation has been indexed alongside a full plate topograph of the 6H polytype in Figure 1. Similar results have been obtained for the 4H and 15R polytypes and the full plate topograph and indexed reflections for these are shown in Figure 4H/15R Index. These form the basis of all assignment work in this project, having identified the three most common polytypes from their edge signatures it is an easy matter to determine their contribution to complex multipolytypic topographs. These invariably contain reflections from two or more of the low period (6H, 15R and 4H) polytypes displaced spatially along the diffraction row.