Lesson 10

Publishing XRD Results

Nicola Döbelin(‘s humble opinions…)

RMS Foundation, Bettlach, Switzerland

…totally irrelevant to the rest of the world

January 14 – 16, 2015, Bern, Switzerland

Relevant Topics

2

- Accuracy of Rietveld refinement results

- Graphs

- «Experimental» section

Accuracy of Rietveld Refined Data

3

Standard procedure:

- Do multiple measurements

- Calculate mean and standard deviation

How good is your analysis?

Is there a systematic error / bias? Caused by:

- Your instrument configuration

- Your sample preparation

- Your refinement strategy

Much trickier question:

Accuracy of Rietveld Refined Data

4

- Often no complementary analyticaltechnique available

- Hardly any reference materials available

- Refinement: Highly operator dependent

XRD / Rietveld refinements are very difficult to validate:

One option: Participate in round robins

� Compare your results with other labs

Round robin on CaP phase quantificationorganized by RMS Foundation / Nicola Döbelinin 2012/2013

Accuracy of Rietveld Refined Data

5

Round Robin Reference Sample:

- Simple 2 phase system: HA + β-TCP

- Very homogeneous distribution

- No texture

- No micro-absorption

- Highly crystalline

- Mean cryst size ~200 nm

0.01 0.1 1 10 100

0

2

4

6

8

10

Qua

ntity

[%

]

Particle Diameter [µm]

Volume

Number

0.01 0.1 1 10 100

0

2

4

6

8

10

Qua

ntity

[%

]

Particle Diameter [µm]

Volume

Number

� Nearly «Best Case» Scenario

Accuracy of Rietveld Refined Data

6

Sample β-TCP [wt-%] HA [wt-%]

1 28.01 71.99

2 28.22 71.78

3 28.49 71.51

4 28.29 71.71

5 28.20 71.80

Mean (Std. Dev) 28.24 (0.17) 71.76 (0.17)

Round Robin

12 Labs with 26 different instruments / configurationsanalyzed the same powder

n=5

Accuracy of Rietveld Refined Data

7

A:I A:II A:IIIA:IV B:I B:II B:III B:IV C:I C:II D:I E:I E:II F:I G:I G:II H:I H:II H:III I:I I:II J:I J:II J:III K:I L:I

70

71

72

73

74

**

*

*

**

**

**

**

**

**

**

HA

Phase Q

uantity

[re

l. w

t-%

]

Laboratory:Configuration

*

* p < 0.05** p < 0.01

71.97 (0.54)

Accuracy of Rietveld Refined Data

8

Results for this scenario* (Round Robin 2-phase sample):

* only for this scenario!

Repeatability:

- Same Lab

- Same Instrument

- Same Configuration

- Same Operator

- Same Refinement Software

- Same Refinement Strategy

� σQuantification = 0.29 wt-%

Reproducibility:

- Different Lab

- Different Instrument

- Different Configuration

- Different Operator

- Different Refinement Software

- Different Refinement Strategy

� σQuantification = 0.60 wt-%

σ will increase for more complex samples

Accuracy of Rietveld Refined Data

9

Parameter �� ��� �� �� � �

Weigth Fraction β-TCP [wt-%] 28.03 0.54 0.29 0.60 0.81 1.67

Weigth Fraction HA [wt-%] 71.97 0.54 0.29 0.60 0.81 1.67

Unit Cell Length β-TCP a [nm] 1.04099 0.00027 0.00005 0.00027 0.00015 0.00077

Unit Cell Length β-TCP c [nm] 3.73561 0.00102 0.00024 0.00104 0.00066 0.00292

Unit Cell Length HA a [nm] 0.94221 0.00026 0.00005 0.00026 0.00013 0.00073

Unit Cell Length HA c [nm] 0.68845 0.00019 0.00003 0.00019 0.00009 0.00054

Crystallite Size β-TCP [nm] 212.87 110.30 31.04 113.74 86.91 318.48

Crystallite Size HA <001> [nm] 106.99 16.67 6.69 17.72 18.74 49.60

Crystallite Size HA <100> [nm] 92.69 14.38 4.54 14.95 12.72 41.85

�̿: Average of Cell Averages̅: Standard deviation of Cell Averages�: Repeatability standard deviation : Reproducibility standard deviation�: 95% repeatability limit�: 95% reproducibility limit

Precision statistics according to ASTM E691 - 13

Accuracy of Rietveld Refined Data

10

[1] Doebelin, N. «Interlatoratory study on the quantification of calcium phosphate phases by Rietveld refinement», in preparation.

[2] Stutzman, P. «Powder diffraction analysis of hydraulic cements: ASTM Rietveld round-robin results on precision.» Powder Diffraction, 2005, 20(2): 97-100.

sr = Repeatability Standard Deviation (same lab / instrument / config / operator / software / refinement strategy)

Sr = Reproducibility Standard Deviation (different lab / instrument / config / operator / software / refinement strategy)

The round robin has demonstrated:

- Small standard deviation ≠ accurate results

- Most labs obtain biased results(from insignificant to highly significant bias)

- Rule of thumb: [1] and [2] show that for phase quantificationsSr ≈ 2 · sr

In a nut shell:

Accuracy of Rietveld Refined Data

11

General consensus in the Rietveld Community:For n=1: Forget about the decimals!

Publish as:

HA: > 99 wt-%

betaTCP: < 1 %

- Do multiple measurements and report Std. Dev. σ(ignore bias)

- Do multiple measurements and report [1]:Repeatability r = 2.77 · sr(more realistic error bars)

- Do a full test validation to calculate accurate and realistic σ(extremely difficult and time consuming)

3 options to report refined phase quantities in publications:

Probably the

most feasible

Probably the

most feasible

Probably the

most feasible

[1] ASTM E177-13: «Standard Practice for Use of theTerms Precision and Bias in ASTM Test Methods».

10 15 20 25 30 35 40 45 50 55

Inte

nsity (

a.u

.)

Diffraction Angle (°2θ)

10 15 20 25 30 35 40 45 50 55

Inte

nsity (

a.u

.)

Diffraction Angle (°2θ)

Methods

… phase quantities

were calculated

from XRD data…

Graphs: XRD / Rietveld are «visual» methods

12

Is the data

good

enough?

Your friendly reviewer

Graphs: XRD / Rietveld are «visual» methods

13

Methods

… XRD data was

analyzed by

Rietveld

refinement…

How good

was the

refinement?

10 20 30 40 50 60

-1000

-500

0

500

1000

1500

2000 Iobs

Icalc

Idiff

Background

Inte

nsity [co

un

ts]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs

Icalc

Idiff

Background

Inte

nsity [co

un

ts]

Angle [°2theta]

Graphs: XRD / Rietveld are «visual» methods

14

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc Idiff

Background

Inte

nsity

[cou

nts

]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc Idiff

Background

Inte

nsity

[cou

nts

]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc

Idiff Background

Inte

nsi

ty [

coun

ts]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc

Idiff Background

Inte

nsi

ty [

coun

ts]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc

Idiff Background

Inte

nsi

ty [

coun

ts]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc

Idiff Background

Inte

nsi

ty [

coun

ts]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc Idiff

Background

Inte

nsity

[cou

nts

]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc Idiff

Background

Inte

nsity

[cou

nts

]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc

Idiff Background

Inte

nsi

ty [

coun

ts]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc

Idiff Background

Inte

nsi

ty [

coun

ts]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc

Idiff Background

Inte

nsi

ty [

coun

ts]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc

Idiff Background

Inte

nsi

ty [

coun

ts]

Angle [°2theta]

Recommendation:

- Show all your raw data(documents your data quality)

- Show 1 full refinement(documents your refinement quality)

- All the information is in the raw data

- Only additional information in refinement plots (Icalc, Idiff, Bkgr):

«The refinement was done right»

Graphs: XRD / Rietveld are «visual» methods

15

10 15 20 25 30 35 40 45 50 55

25 °C

1000 °C

950 °C

900 °C

850 °C

800 °C

750 °C

700 °C

650 °C

600 °C

550 °C

525 °C

575 °C

25 °C

Inte

nsity (

a.u

.)

Diffraction Angle (°2θ)

500 °C

HAα-TCPβ-TCP

10 15 20 25 30 35 40 45 50 55

25 °C

1000 °C

950 °C

900 °C

850 °C

800 °C

750 °C

700 °C

650 °C

600 °C

550 °C

525 °C

575 °C

25 °C

Inte

nsity (

a.u

.)

Diffraction Angle (°2θ)

500 °C

HAα-TCPβ-TCP

10 20 30 40 50 60

0

500

1000

1500

Iobs Icalc

Idiff Background

Inte

nsity [

co

unts

]

Angle [°2theta]

10 15 20 25 30 35 40 45 50 55

25 °C

1000 °C

950 °C

900 °C

850 °C

800 °C

750 °C

700 °C

650 °C

600 °C

550 °C

525 °C

575 °C

25 °C

Inte

nsity (

a.u

.)

Diffraction Angle (°2θ)

500 °C

HAα-TCP

β-TCP

30 31 32 33 34 35 36

0

500

1000

1500

Iobs Icalc Idiff Background

b-TCP HA

Inte

nsity [co

un

ts]

Angle [°2theta]

Combine your raw patterns

30 31 32 33 34 35 36

0

500

1000

1500

Iobs

Icalc

Idiff

Background

b-TCP

HA

Inte

nsity [

co

un

ts]

Angle [°2theta]

30 31 32 33 34 35 36

0

500

1000

1500

Iobs

Icalc

Idiff

Background

b-TCP

HA

Inte

nsity [

co

un

ts]

Angle [°2theta]

Show more graphs if themanuscript improves

«Materials and Methods» Section

16

Used for phase identification

Match the level of detail to the relevance of XRD for the study

- Basic intrument parameters:

- Instrument / Manufacturer

- Scan range (start, end, step size)

- References to PDF / ICDD / COD phase

entries

«Materials and Methods» Section

17

10 20 30 40 50 60

0

500

1000

1500

Iobs

Icalc

Idiff

Background

Inte

nsity [co

un

ts]

Angle [°2theta]

«Materials and Methods» Section

18

Used for phase quantification

- Detailed intrument parameters:

- Instrument / manufacturer

- Scan range (start, end, step size [°2θ])

- Radiation, filter / monochromator, divergence slit

- References to sources of crystal structures

- Rietveld software (program name, version, reference)

«Materials and Methods» Section

19

«Materials and Methods» Section

20

Used for advanced refinements(structural parameters, amorphous fractions, crystallite size analysis, texture analysis etc.)

- Detailed intrument parameters:

- Instrument / manufacturer

- Scan range (start, end, step size [°2θ])

- Radiation, filter / monochromator, divergence slit

- … (detector, masks, ASS, Soller slits, generator settings…)

- References to sources of crystal structures

- Rietveld software (program name, version, reference)

- Refinement strategy

- Any non-standard calculations, sample preparations, measurement conditions,

etc…

«Materials and Methods» Section

21

Refinement strategy

«Materials and Methods» Section

22

Special calculations

Summary: DOs and DON’Ts in Manuscripts

23

Do:

- Show your raw data (stacked plots)

- Show one full refinement

- Give details according to the relevanceof XRD data for the manuscript

Don’t:

- Spam the manuscript with refinement plots

- Publish results from non-standard samples

- Publish results from poor refinements!!!