anomalous diffraction project status update 1-22-09

$: Anomalous Diffraction Project Status Update 1-22-09$
Anomalous Diffraction Project

Status Update1-22-09

Completed So Far

• Incorporating Daniel Haskel’s solid-state effects into the model

• Incorporating experimental uncertainties into the data and fits

• Inverting the ratios taken, so I fit S1/F instead of F/S1• Creating and testing a full model of the Bragg

reflections and slit function• Systematically fitting the data, varying the Debye-

Waller factor

Solid State Effects

-10

-9

-8

-7

-6

-5

-4

11.311.211.111.010.9x103

Ge_f1 GeTheo_f1

6

5

4

3

2

1

11.311.211.111.010.9x103

Ge_f2 GeTheo_f2

-12

-10

-8

-6

-4

680067006600650064006300

Mn_f1 MnTheo_f1 MnExp_f1

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

680067006600650064006300

Mn_f2 MnTheo_f2 MnExp_f2

4

3

2

1

79007800770076007500

Co_f2 CoTheo_f2 CoExp_f2

-9

-8

-7

-6

-5

-4

-3

79007800770076007500

Co_f1 CoTheo_f1 CoExp_f1

So far, I’ve used only the theoretical scattering factors because of the absence of measured factors for Ge.

Uncertainties• Since we originally took the data with DAFS in mind, the

uncertainty from the amplitudes are fairly low• The larger source of uncertainty comes from the L-scan

intensities, which were used to scale all the amplitudes– the superlattice peaks were relatively weak and a peak shape

suffered– Could have been avoided if I wasn’t trying to get more

compositions than I had time for• Of note is that some data sets lack the (111) amplitude

data.– Again, could have been avoided if I hadn’t tried to get too many

compositions (took lots of data at the Fundamental)

Inverting the Data

• Since one reason for fitting intensity ratios rather than intensity is to ‘normalize’ to the fundamental, Yong suggested fitting S1/F and S2/F rather than the reverse.

• As expected, this did not noticeably affect the fits or results.

Slit Function Correction

• Several models were attempted taking various short-cuts and making various assumptions

• None gave a correction even close to that of the Full Model:– 3D Lorentian Bragg Reflection– 2D Slit Window in 3-space, sectioning the Ewald

Sphere– Correct reflection widths confirmed by comparing

modeled scans to various data sets (see next slides)

Deteco

r

L-direction

Ewald Sphere

BraggReflection

q

ki

kf

Another BraggReflection

kf

Blending Lab with Reciprocal Space

Whatever intersects the Ewald sphere in reciprocal

space will become scattered photons in lab space.

Sample

Slits

• This is only a 2D representation. • The Bragg reflection is really a

3D volume and the Ewald sphere is a surface.

• The slits limit the amount of the Ewald sphere for the detector to see.

L-direction

Ewald Sphere

Slits limit how much solid angle of the Ewald Sphere the detector can see.

The diffractometer manipulates the Ewald Sphere so that it travels through the Bragg reflection along L.

BraggReflection

Illustrating an L-Scan

The Model• Right: A 2D representation of the

final Lorentian used for all three reflections and four compositions

• Below: an example of the modeled slit window and the intensity it captured from the Ewald Sphere. This was summed as one data point in a diffractometer scan such as an L-scan.

0.10

0.08

0.06

0.04

0.02

0.00

-0.0

2-0

.04

-0.0

6-0

.08

-0.1

0 -40 -20 0 20 40x10-3

-0.5

0.0

0.5

V P

os [m

m]

-2.0 -1.0 0.0 1.0 2.0Horizontal Position [mm]

15

10

5

x10-3

Confirming Model Accuracy• With known slit sizes, all

I had to do was model the three reflection widths.

• I had all three directions (L, In-Plane, and Phi) scanned for the Fundamental and the (111)-type to test the model

• One set of widths clearly work for all three directions, both reflections and most compositions.

• L-scan’s tails are off due to interface fringes -1.0 -0.5 0.0 0.5 1.0

Phi [Deg]

160

140

120

100

80

60

40

20

Inte

nsity

[arb

. uni

ts] Ge30

Ge35 Ge40 Ge45 Model

1.03rlu1.021.011.000.990.980.97K [rlu]

160

140

120

100

80

60

40

20

Inte

nsity

[arb

. uni

ts]

Data (offset) Model

4.2rlu4.14.03.93.8L [rlu]

160

140

120

100

80

60

40

20

Inte

nsity

[arb

. uni

ts]

Data (offset) Model

Comparison(014) Scans

at E=10.58 keV(1,5)mm Slits

pNames pw

Amp 1

H-FWHM 0.005

H-Pos 1

K-FWHM 0.005

K-Pos 0

L-FWHM 0.055

L-Pos 4

-1.0 -0.5 0.0 0.5 1.0Phi [Deg]

250

200

150

100

50

0In

tens

ity [a

rb. u

nits

]

1.03rlu1.021.011.000.990.980.97K [rlu]

250

200

150

100

50

0

Inte

nsity

[arb

. uni

ts]

1.15rlu1.101.051.000.950.900.85L [rlu]

250

200

150

100

50

0

Inte

nsity

[arb

. uni

ts]

Ge30 Ge35 Ge40 Ge45 Model

Comparison(011) Scans

Final CorrectionThe same model also worked for a data series with varying slit sizes.

40

30

20

10

0

NaI

[103 ]

4.1rlu4.03.93.83.7 L [rlu]

250

200

150

100

50

0

Modeled Intensity [arb. units]

4.14.03.93.8 L [rlu]

S#1414 in 's137a' Det Slits (2x5mm)

S#1415 in 's137a' Det Slits (1x5mm)

S#1416 in 's137a' Det Slits (0.5x5mm)

Model Slit=(2x5) Model Slit=(1x5) Model Slit=(0.5x5)

0.1

2

3

4

5678

1

Rat

io

4.1rlu4.03.93.83.7 L [rlu]

4.14.03.93.8 L [rlu]

Data Model M/L M/L S/L S/L S/M/ S/M

1.8

1.7

1.6

1.5

S2/

F In

tens

ity R

atio

1211109876Energy [keV]

Gauss L Lorentz L fit_F2int

values ± stdevK0=0.32873 ± 0.00445K1=0.27133 ± 0.00154K2=-0.01697 ± 0.000174K3=0.00042096 ± 6.45e-006

1.30

1.28

1.26

1.24

1.22

1.20

1.18

S1/

F In

tens

ity R

atio


Gauss L Lorentz L fit_F1int

values ± stdevK0=0.63427 ± 0.00474K1=0.14546 ± 0.00164K2=-0.011079 ± 0.000186K3=0.00030874 ± 6.87e-006

6000

5000

4000

3000

Inte

grat

ed In

tens

ity [a

rb]


Fint S1int S2int

Right: The final Corrections used in the anomalous diffraction fits.

Systematic Fitting• The Debye-Waller factor measured (including the

latest Slit correction) gave a value of σ=0.13 → Imeasured = I0 exp(- σqi

2), where i represents different reflections

• This value is still probably not accurate because σ is actually different for different directions

• The measured value allows a range, which are systematically set and fit.

• The proper value is determined based on the fit outputting the measured composition.

Fits with All Corrections but Sold State

• Next slide shows results from these fits• We desire for an acceptable fit:

– low nchisq value (first param)– Co-Mn ratio near 2 (panel 2, blue)– Ge comp near 30, 35, 40 and 45 respectively

(panel 2, red)– Co-Mn swapping = 0 (panel 3, red)

35

30

25

20

Ge

in B

-Site

s

0.400.300.200.10Debye-Waller Factor

30

25

20

15

10

5

0G

e in C-S

ites Corr30_bG Corr30_cG

1.0

0.8

0.6

0.4

0.2

0.0

B-S

ite V

acan

cies


6.0

5.5

5.0

4.5

4.0

3.5

C-S

ite Vacancies

Corr30_bV Corr30_cV

10

8

6

4

2

0% C

M a

nd G

C S

wap

ping


22

20

18

16

14

% M

n-Ge S

wapping

Corr30_CM Corr30_GC Corr30_MG

44

40

36

32

% G

e


2.6

2.5

2.4

2.3

2.2

Co-M

n Ratio

Corr30_GeComp Corr30_CMcomp

4.4

4.2

4.0

3.8

3.6

3.4

Nch

isq


12

10

8

6

Nch

isq


40

38

36

34

32

% G

e0.400.300.200.10

Debye-Waller Factor

4.0

3.5

3.0

2.5

Co-M

n Ratio


12

8

4

0

% C

M a

nd G

C S

wap

ping


35

30

25

20

15

% M

n-Ge S

wapping


1.0

0.8

0.6

0.4

0.2

0.0

B-S

ite V

acan

cies


7.0

6.5

6.0

5.5

5.0

4.54.0

C-S

ite Vacancies

Corr35_bV Corr35_cV

60

50

40

30

20

Ge

in B

-Site

s


12

8

4

0

Ge in C

-Sites

Corr35_bG Corr35_cG

All Corrections but Solid StateGe=30% Data Set


8

7

6

5

Nch

isq


48

46

44

42

40

38

% G

e


10

8

6

4

Co-M

n Ratio


12

8

4

0% C

M a

nd G

C S

wap

ping


20

15

10

5

0

% M

n-Ge S

wapping


1.0

0.8

0.6

0.4

0.2

0.0

B-S

ite V

acan

cies


11

10

9

8

7

6

C-S

ite Vacancies

Corr45_bV Corr45_cV

80

70

60

50

40

Ge

in B

-Site

s


15

10

5

0

Ge in C

-Sites

Corr45_bG Corr45_cG

5.45.2

5.0

4.8

4.6

4.4

4.2

Nch

isq


46

44

42

40

38

36

34

% G

e


3.0

2.8

2.6

2.4

Co-M

n Ratio Corr40_GeComp

Corr40_CMcomp

10

8

6

4

2

0% C

M a

nd G

C S

wap

ping


24

23

22

21

20

19

% M

n-Ge S

wapping


1.0

0.8

0.6

0.4

0.2

0.0

B-S

ite V

acan

cies


9

8

7

6

5

C-S

ite Vacancies

Corr40_bV Corr40_cV

44

40

36

32

Ge

in B

-Site

s


25

20

15

10

5

0

Ge in C

-Sites

Corr40_bG Corr40_cG



Compositions Fi

t Par

amet

ers

Adding Solid State Effects

• Problem: I don’t get compositions that are correct for the Ge-level

• It seems as though the spike in the Ge scattering factor is the cause as residuals go down everywhere else when adding solid state effects.

80.001

2

4

6

80.01

2

4

6

8

S1/

F In

tens

ity R

atio

11.611.511.411.311.211.111.0Energy [keV]

4.0

3.8

3.6

3.4

3.2

Nch

isq


30

29

28

27

% G

e


2.25

2.20

2.15

2.10

Co-M

n Ratio

SS30_GeComp SS30_CMcomp

25

20

15

10

5

0% C

M a

nd G

C S

wap

ping


26

24

22

20

% M

n-Ge S

wapping

SS30_CM SS30_GC SS30_MG

1.0

0.8

0.6

0.4

0.2

0.0

B-S

ite V

acan

cies


7

6

5

4

C-S

ite Vacancies

SS30_bV SS30_cV

16

12

8Ge

in B

-Site

s


2.0

1.5

1.0

0.5

0.0G

e in C-S

ites

SS30_bG SS30_cG

With Solid State CorrectionsGe=30% Data Set

12

10

8

6

Nch

isq


36

34

32

30

28

26%

Ge


3.0

2.8

2.6

2.4

2.2

2.0

Co-M

n Ratio


20

15

10

5

0% C

M a

nd G

C S

wap

ping


40

35

30

25

20

% M

n-Ge S

wapping


1.0

0.8

0.6

0.4

0.2

0.0

B-S

ite V

acan

cies


8

7

6

5

C-S

ite Vacancies

SS35_bV SS35_cV

40

30

20

10

0

Ge

in B

-Site

s


2.0

1.5

1.0

0.5

0.0

Ge in C

-Sites

SS35_bG SS35_cG


5.0

4.8

4.6

4.4

4.2

4.0

Nch

isq


33

32

31

30

29

28

% G

e


2.40

2.35

2.30

2.25

2.20

2.15

Co-M

n Ratio


25

20

15

10

5

0% C

M a

nd G

C S

wap

ping


31

30

29

28

27

% M

n-Ge S

wapping


1.0

0.8

0.6

0.4

0.2

0.0

B-S

ite V

acan

cies


10

9

8

7

6

5

C-S

ite Vacancies SS40_bV

SS40_cV

25

20

15

10

Ge

in B

-Site

s


2.0

1.5

1.0

0.5

0.0

Ge in C

-Sites

SS40_bG SS40_cG


8

7

6

5

Nch

isq


40

36

32

% G

e


4.5

4.0

3.5

3.0

2.5

Co-M

n Ratio


20

15

10

5

0% C

M a

nd G

C S

wap

ping


30

25

20

15

10

% M

n-Ge S

wapping


1.0

0.8

0.6

0.4

0.2

0.0

B-S

ite V

acan

cies


12

11

10

9

8

7

6

C-S

ite Vacancies

SS45_bV SS45_cV

60

50

40

30

20

Ge

in B

-Site

s


2.0

1.5

1.0

0.5

0.0

Ge in C

-Sites

SS45_bG SS45_cG


Compositions Fi

t Par

amet

ers

Chosen Fits (no SS): Ge30 Data

0.01

0.1

1

10R

esid

uals

1110987Energy [keV]

0.001

0.01

0.1

S1/

F In

tens

ity R

atio

Data: Final30Fit: Corr30Model GeShift: -0.006Nchisq: 3.492Comp: [48.2, 21.1, 30.7]

0.01

0.1

1

10

Res

idua

ls

1110987Energy [keV]

0.001

0.01

0.1

S2/

F In

tens

ity R

atio

NamesParams uParams

DW 0.10 0.00

CM 0.00 0.55

MG 22.41 0.23

GC 0.52 0.58

aV 0.00 0.00

bV 0.00 0.04

cV 5.94 0.04

bG 18.18 0.78

cG 0.72 0.88

0.001

2

4

6

0.01

2

4

6

S1/

F In

tens

ity R

atio

11.611.511.411.311.211.111.0Energy [keV]

2

4

6

0.001

2

4

6

0.01

2

S2/

F In

tens

ity R

atio

11.611.511.411.311.211.111.0Energy [keV]


0.01

0.1

1

10R

esid

uals

1110987Energy [keV]

0.001

0.01

0.1

1

S1/

F In

tens

ity R

atio


0.01

0.1

1

10

Res

idua

ls

1110987Energy [keV]

10-4

10-3

10-2

S2/

F In

tens

ity R

atio

NamesParams uParams

DW 0.22 0.00

CM 0.00 0.73

MG 42.96 0.82

GC 0.00 1.02

aV 0.00 0.00

bV 0.23 0.18

cV 5.72 0.09

bG 24.17 1.34

cG 8.84 0.79

0.001

2

4

6

0.01

2

4

6

0.1

S1/

F In

tens

ity R

atio

11.611.511.411.311.211.111.0Energy [keV]

6

10-4

2

4

6

10-3

2

4

S2/

F In

tens

ity R

atio

11.611.511.411.311.211.111.0Energy [keV]


0.01

0.1

1

10R

esid

uals

1110987Energy [keV]

0.001

0.01

0.1

1

S1/

F In

tens

ity R

atio


0.01

0.1

1

10

Res

idua

ls

1110987Energy [keV]

10-4

10-3

10-2

S2/

F In

tens

ity R

atio

NamesParams uParams

DW 0.18 0.00

CM 0.00 0.44

MG 22.67 0.21

GC 2.17 0.49

aV 0.00 0.00

bV 0.00 0.03

cV 7.12 0.03

bG 37.24 0.65

cG 14.17 0.74

0.001

2

4

6

0.01

2

4

6

0.1

S1/

F In

tens

ity R

atio

11.611.511.411.311.211.111.0Energy [keV]

6

10-4

2

4

6

10-3

2

4

S2/

F In

tens

ity R

atio

11.611.511.411.311.211.111.0Energy [keV]


0.01

0.1

1

10R

esid

uals

1110987Energy [keV]

0.001

0.01

0.1

1

S1/

F In

tens

ity R

atio


0.01

0.1

1

10

Res

idua

ls

1110987Energy [keV]

10-4

10-3

10-2

S2/

F In

tens

ity R

atio

NamesParams uParams

DW 0.22 0.00

CM 0.00 0.47

MG 21.00 0.26

GC 0.54 0.64

aV 0.00 0.00

bV 0.00 0.17

cV 8.18 0.08

bG 48.76 0.83

cG 12.70 0.63

0.001

2

4

6

0.01

2

4

6

0.1

S1/

F In

tens

ity R

atio

11.611.511.411.311.211.111.0Energy [keV]

6

10-4

2

4

6

10-3

2

4

S2/

F In

tens

ity R

atio

11.611.511.411.311.211.111.0Energy [keV]

anomalous diffraction project status update 1-22-09

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