Lesson 9

Publishing XRD Results

Nicola Döbelin(‘s humble opinions…)

RMS Foundation, Bettlach, Switzerland

…totally irrelevant to the rest of the world

June 07 – 09, 2017, Oslo, N

Relevant Topics

2

- Quality of Rietveld refinement results

- Graphs

- «Experimental» section

Quality: Accurate + Precise

3

https://phidgets.wordpress.com

Quality of Rietveld Refined Data

4

- Often no complementary analytical

technique 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 quantification

organized by RMS Foundation / Nicola Döbelin

in 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

Qu

an

tity

[%

]

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 / configurations

analyzed the same powder

n=5

Results returned from one lab/instrument:

A:I A:II A:IIIA:IV B:I B:II B:IIIB: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 M:I M:II

70

71

72

73

74

*

**

*

*

**

**

**

**

**

**

**

HA

Phase Q

uantity

[re

l. w

t-%

]

Laboratory:Configuration

Weight FractionG:\Auftr_Proj\S-Auftraege\2016\S16_0004 XRD Freiberg\Abbildungen\S12_0008-Mean-Values.opj

*

Accuracy of Rietveld Refined Data

7

* p < 0.05

** p < 0.01

RK

ND

Döbelin, N. "Interlaboratory study on the quantification of calcium phosphate

phases by Rietveld refinement." Powder Diffraction, 2015 30(3): 231-241.

Precise Results ≠ Accurate Results

Validation of β-TCP + HAp Quantification at RMS

8

0 20 40 60 80 100

0

20

40

60

80

100

HA

p R

efin

ed

(w

t-%

)

HAp Nominal (wt-%)

100 80 60 40 20 0

-TCP Nominal (wt-%)

Reference mixtures

Hydroxyapatite + β-TCP (Whitlockite)

Measured and refined multiple times

Quality of Rietveld Refined Data

9

0 20 40 60 80 100

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5 Systematic Error

Random Error

Expanded Uncertainty (k=2)

Ab

so

lute

Qu

an

tity

[w

t-%

]

Nominal HA Phase Quantity [wt-%]

Quality of Rietveld Refined Data

10

0 20 40 60 80 100

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5 Micro-Absorption Error

Noise Floor

Systematic Error

Random Error

Expanded Uncertainty (k=2)

Ab

so

lute

Qu

an

tity

[w

t-%

]

Nominal HA Phase Quantity [wt-%]

Uncertainty of Phase Quantifications

Quantification of trace amounts:

Depends on signal-to-noise ratio

Largely unaffected by micro-absorption

Quantification of main phases:

Affected by micro-absorption, requires

particles < 5 μm

Largely unaffected by S/N ratio

11

0 20 40 60 80 100

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5 Micro-Absorption Error

Noise Floor

Systematic Error

Random Error

Expanded Uncertainty (k=2)

Ab

so

lute

Qu

an

tity

[w

t-%

]

Nominal HA Phase Quantity [wt-%]

0 20 40 60 80 100

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5 Micro-Absorption Error

Noise Floor

Systematic Error

Random Error

Expanded Uncertainty (k=2)

Ab

so

lute

Qu

an

tity

[w

t-%

]

Nominal HA Phase Quantity [wt-%]

Detection Limits

12

Possible Definition of Detection Limit (LOD):

𝑃ℎ𝑎𝑠𝑒 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 < 2 ∙ 𝜎

Possible Definition of Quantification Limit (LOQ):

𝑃ℎ𝑎𝑠𝑒 𝑄𝑢𝑎𝑛𝑡𝑖𝑡𝑦 < 4 ∙ 𝜎

0

4σ

2σ

LOQ

LOD

LOD / LOQ Warning in Profex

13

BGMN ESDs are

very realistic!

Guidelines for Reporting Phase Quantities

14

For error bars use 3 · ESD (or 2.77 · ESD) 3 · ESD = 99.7% repeatability limit, normal distribution

(2.77 · ESD = 95% repeatability limit, t distribution [1])

Report Values < LOQ as «< 4 · ESD» Report 0.76 ± 0.23 as «< 0.92»

Report Values < LOD as «not detected» Report 0.21 ± 0.11 as «not detected»

[1] ASTM E177-13: «Standard Practice for Use of the

Terms Precision and Bias in ASTM Test Methods».

10 15 20 25 30 35 40 45 50 55

Inte

nsity (

a.u

.)

Diffraction Angle (°2)

10 15 20 25 30 35 40 45 50 55

Inte

nsity (

a.u

.)

Diffraction Angle (°2)

Methods

… phase quantities

were calculated

from XRD data…

Graphs: XRD / Rietveld are «visual» methods

15

Is the data good

enough?

Your friendly reviewer

Graphs: XRD / Rietveld are «visual» methods

16

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]

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0

500

1000

1500

Iobs

Icalc

Idiff

Background

Inte

nsity [co

un

ts]

Angle [°2theta]

Graphs: XRD / Rietveld are «visual» methods

17

10 20 30 40 50 60

0

500

1000

1500

Iobs

Icalc

Idiff

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Inte

nsity [co

un

ts]

Angle [°2theta]

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500

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Iobs

Icalc

Idiff

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nsity [co

un

ts]

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Iobs

Icalc

Idiff

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nsity [co

un

ts]

Angle [°2theta]

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Iobs

Icalc

Idiff

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nsity [co

un

ts]

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500

1000

1500

Iobs

Icalc

Idiff

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Inte

nsity [co

un

ts]

Angle [°2theta]

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0

500

1000

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Iobs

Icalc

Idiff

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nsity [co

un

ts]

Angle [°2theta]

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Iobs

Icalc

Idiff

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nsity [co

un

ts]

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0

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1000

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Iobs

Icalc

Idiff

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nsity [co

un

ts]

Angle [°2theta]

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0

500

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Iobs

Icalc

Idiff

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nsity [co

un

ts]

Angle [°2theta]

10 20 30 40 50 60

0

500

1000

1500

Iobs

Icalc

Idiff

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nsity [co

un

ts]

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10 20 30 40 50 60

0

500

1000

1500

Iobs

Icalc

Idiff

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nsity [co

un

ts]

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Iobs

Icalc

Idiff

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nsity [co

un

ts]

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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

18

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 (°2)

500 °C

HA-TCP-TCP

10 20 30 40 50 60

0

500

1000

1500

Iobs

Icalc

Idiff

Background

Inte

nsity [co

un

ts]

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 (°2)

500 °C

HA-TCP-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 [

counts

]

Angle [°2theta]

Show more graphs if the

manuscript improves

«Materials and Methods» Section

19

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

20

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

21

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

22

«Materials and Methods» Section

23

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

24

Refinement strategy

«Materials and Methods» Section

25

Special calculations

Summary: DOs and DON’Ts in Manuscripts

26

Do:

- Show your raw data (stacked plots)

- Show one full refinement

- Give details according to the relevance

of XRD data for the manuscript

Don’t:

- Spam the manuscript with refinement plots

- Publish results from non-standard samples

- Publish results from poor refinements!!!