Reet at 14:51, 22 May 2026

2026-05-22T14:51:01Z

← Older revision		Revision as of 16:51, 22 May 2026
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	λ is a wavelength of X-ray radiation (λ Cu-K<sub>α1</sub> = 1.540562 Å, and in case both Cu-K<sub>α1</sub> and Cu-K<sub>α2</sub> are present λ Cu-K<sub>α1,2</sub> = 1.541871 Å) <br>		λ is a wavelength of X-ray radiation (λ Cu-K<sub>α1</sub> = 1.540562 Å, and in case both Cu-K<sub>α1</sub> and Cu-K<sub>α2</sub> are present λ Cu-K<sub>α1,2</sub> = 1.541871 Å) <br>
	θ is Bragg angle <br>		θ is Bragg angle <br>
	β<sub>sample</sub> is a peak broadening. The technical point should be noted that ~~intergal~~ breadth and/or FWHM have to be inserted in radians.<br>		β<sub>sample</sub> is a peak broadening. The technical point should be noted that integral breadth and/or FWHM have to be inserted in radians.<br>

	<br clear="all" />		<br clear="all" />

Reet at 14:47, 22 May 2026

2026-05-22T14:47:30Z

← Older revision		Revision as of 16:47, 22 May 2026
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	This page describes values of Instrumental broadening in [[Specific_Process_Knowledge/Characterization/XRD/Process_Info#2θ_scan._Graizing_Incident_X-ray_Diffraction_(GiXRD)\|GiXRD measurements]], and can be used as a reference for peak broadening in 2θ - scans. ~~Most~~ four common slit configuration cases are chosen.		This page describes values of Instrumental broadening in [[Specific_Process_Knowledge/Characterization/XRD/Process_Info#2θ_scan._Graizing_Incident_X-ray_Diffraction_(GiXRD)\|GiXRD measurements]], and can be used as a reference for peak broadening in 2θ - scans. The four most common slit configuration cases are chosen.
	The instrumental broadening has been measured by using standard Si powder sample.		The instrumental broadening has been measured by using standard Si powder sample.

Eves at 16:40, 9 November 2023

2023-11-09T16:40:50Z

← Older revision		Revision as of 18:40, 9 November 2023
Line 7:		Line 7:


	This page describes values of Instrumental broadening in GiXRD measurements, and can be used as a reference for peak broadening in 2θ - scans. Most four common slit configuration cases are chosen.		This page describes values of Instrumental broadening in [[Specific_Process_Knowledge/Characterization/XRD/Process_Info#2θ_scan._Graizing_Incident_X-ray_Diffraction_(GiXRD)\|GiXRD measurements]], and can be used as a reference for peak broadening in 2θ - scans. Most four common slit configuration cases are chosen.
	The instrumental broadening has been measured by using standard Si powder sample.		The instrumental broadening has been measured by using standard Si powder sample.

Eves at 12:13, 9 November 2023

2023-11-09T12:13:49Z

← Older revision		Revision as of 14:13, 9 November 2023
Line 1:		Line 1:
			'''Feedback to this page''': '''[mailto:labadviser@nanolab.dtu.dk?Subject=Feed%20back%20from%20page%20http://labadviser.nanolab.dtu.dk/index.php?title=Specific_Process_Knowledge/Characterization/XRD/XRD_SmartLab/Instrumental_broading_in_GiXRD&action=submit click here]'''


			<i>This page is written by <b>Evgeniy Shkondin @DTU Nanolab</b> if nothing else is stated. <br>
			All images and photos on this page belongs to <b>DTU Nanolab</b>.<br>
			The fabrication and characterization described below were conducted in <b>2023 by Evgeniy Shkondin, DTU Nanolab</b>.<br></i>


	This page describes values of Instrumental broadening in GiXRD measurements, and can be used as a reference for peak broadening in 2θ - scans. Most four common slit configuration cases are chosen.		This page describes values of Instrumental broadening in GiXRD measurements, and can be used as a reference for peak broadening in 2θ - scans. Most four common slit configuration cases are chosen.
	The instrumental broadening has been measured by using standard Si powder sample.		The instrumental broadening has been measured by using standard Si powder sample.

Eves: Created page with "This page describes values of Instrumental broadening in GiXRD measurements, and can be used as a reference for peak broadening in 2θ - scans. Most four common slit configuration cases are chosen. The instrumental broadening has been measured by using standard Si powder sample. Scherrer formula: $D=\frac{K\cdot\lambda}{\beta_{sample}\cdot cos\theta}$ where: K is Scherrer constant (typically close to unity K=0.9-1)
λ is a wavelength of X-ray radiatio..."

2023-11-09T12:12:28Z

Created page with "This page describes values of Instrumental broadening in GiXRD measurements, and can be used as a reference for peak broadening in 2θ - scans. Most four common slit configuration cases are chosen. The instrumental broadening has been measured by using standard Si powder sample. Scherrer formula: <math>D=\frac{K\cdot\lambda}{\beta_{sample}\cdot cos\theta}</math> where: K is Scherrer constant (typically close to unity K=0.9-1) λ is a wavelength of X-ray radiatio..."

New page

This page describes values of Instrumental broadening in GiXRD measurements, and can be used as a reference for peak broadening in 2θ - scans. Most four common slit configuration cases are chosen.
The instrumental broadening has been measured by using standard Si powder sample.

Scherrer formula:

<math>D=\frac{K\cdot\lambda}{\beta_{sample}\cdot cos\theta}</math>

where:
K is Scherrer constant (typically close to unity K=0.9-1) 
λ is a wavelength of X-ray radiation (λ Cu-Kα1 = 1.540562 Å, and in case both Cu-Kα1 and Cu-Kα2 are present λ Cu-Kα1,2 = 1.541871 Å) 
θ is Bragg angle 
βsample is a peak broadening. The technical point should be noted that intergal breadth and/or FWHM have to be inserted in radians. 

 

<math>\beta_{sample}=\beta_{measure}-\beta_{instrumental}</math> in the case where the peaks obey Lorentzian (or Cauchy) distribution profile. 

<math>\beta_{sample}^2=\beta_{measure}^2-\beta_{instrumental}^2</math> in the case of Gaussian distribution profile. 

Experimental results implied crystallite size to cause a Cauchy-type broadening while strain broadening was associated with a Gauss profile. Real measurement contains contributions of both Lorentzian (Cauchy) and Gaussian distributions.

=Full scans=

<gallery caption="2θ scans of Si reference sample." widths="1200px" heights="500px" perrow="1">
image:eves_GiXRD_Si_reference_instrumental_brodening_spectra_20220319.png|Measured Si powder reference sample with different incident slit (IS) and incident angle ω values.
</gallery>

<gallery caption="Broadening functions." widths="800px" heights="500px" perrow="2">
image:eves_GiXRD_Si_reference_instrumental_brodening_FWHM_20220319.png|Calculated FWHM as a function of 2θ.
image:eves_GiXRD_Si_reference_instrumental_brodening_int_br_20220319.png|Calculated Integral breadth as a function of 2θ.
</gallery>

= case1 =

IS=0.5 mm and ω=2°

{| border="2" cellspacing="0" cellpadding="9"

!colspan="1" border="none" style="background:silver; color:black;" align="center"|Peak number
|style="background:silver; color:black"|2θ (°)
|style="background:silver; color:black"|FWHM (°)
|style="background:silver; color:black"|FWHM (rad)
|style="background:silver; color:black"|Integral breadth (°)
|style="background:silver; color:black"|Integral breadth (rad)

|-
!style="background:WhiteSmoke; color:black;" align="center" |1
|style="background:WhiteSmoke; color:black" align="center"|28.4077
|style="background:WhiteSmoke; color:black" align="center"|0.2923
|style="background:WhiteSmoke; color:black" align="center"|0.0051
|style="background:WhiteSmoke; color:black" align="center"|0.3232
|style="background:WhiteSmoke; color:black" align="center"|0.0056

|-
!style="background:WhiteSmoke; color:black;" align="center" |2
|style="background:WhiteSmoke; color:black" align="center"|47.2895
|style="background:WhiteSmoke; color:black" align="center"|0.3109
|style="background:WhiteSmoke; color:black" align="center"|0.0054
|style="background:WhiteSmoke; color:black" align="center"|0.3395
|style="background:WhiteSmoke; color:black" align="center"|0.0059

|-
!style="background:WhiteSmoke; color:black;" align="center" |3
|style="background:WhiteSmoke; color:black" align="center"|56.1274
|style="background:WhiteSmoke; color:black" align="center"|0.3004
|style="background:WhiteSmoke; color:black" align="center"|0.0052
|style="background:WhiteSmoke; color:black" align="center"|0.3368
|style="background:WhiteSmoke; color:black" align="center"|0.0059

|-
!style="background:WhiteSmoke; color:black;" align="center" |4
|style="background:WhiteSmoke; color:black" align="center"|69.1426
|style="background:WhiteSmoke; color:black" align="center"|0.3082
|style="background:WhiteSmoke; color:black" align="center"|0.0054
|style="background:WhiteSmoke; color:black" align="center"|0.3325
|style="background:WhiteSmoke; color:black" align="center"|0.0058

|-
!style="background:WhiteSmoke; color:black;" align="center" |5
|style="background:WhiteSmoke; color:black" align="center"|76.3659
|style="background:WhiteSmoke; color:black" align="center"|0.2585
|style="background:WhiteSmoke; color:black" align="center"|0.0045
|style="background:WhiteSmoke; color:black" align="center"|0.2936
|style="background:WhiteSmoke; color:black" align="center"|0.0051

|-
!style="background:WhiteSmoke; color:black;" align="center" |6
|style="background:WhiteSmoke; color:black" align="center"|88.0122
|style="background:WhiteSmoke; color:black" align="center"|0.3174
|style="background:WhiteSmoke; color:black" align="center"|0.0055
|style="background:WhiteSmoke; color:black" align="center"|0.3609
|style="background:WhiteSmoke; color:black" align="center"|0.0063

|-
!style="background:WhiteSmoke; color:black;" align="center" |7
|style="background:WhiteSmoke; color:black" align="center"|94.9581
|style="background:WhiteSmoke; color:black" align="center"|0.3126
|style="background:WhiteSmoke; color:black" align="center"|0.0055
|style="background:WhiteSmoke; color:black" align="center"|0.3434
|style="background:WhiteSmoke; color:black" align="center"|0.0060

|-
!style="background:WhiteSmoke; color:black;" align="center" |8
|style="background:WhiteSmoke; color:black" align="center"|106.7351
|style="background:WhiteSmoke; color:black" align="center"|0.3317
|style="background:WhiteSmoke; color:black" align="center"|0.0058
|style="background:WhiteSmoke; color:black" align="center"|0.3637
|style="background:WhiteSmoke; color:black" align="center"|0.0063

|-
|}

= case2 =

IS=0.5 mm and ω=1°

{| border="2" cellspacing="0" cellpadding="9"

!colspan="1" border="none" style="background:silver; color:black;" align="center"|Peak number
|style="background:silver; color:black"|2θ (°)
|style="background:silver; color:black"|FWHM (°)
|style="background:silver; color:black"|FWHM (rad)
|style="background:silver; color:black"|Integral breadth (°)
|style="background:silver; color:black"|Integral breadth (rad)

|-
!style="background:WhiteSmoke; color:black;" align="center" |1
|style="background:WhiteSmoke; color:black" align="center"|28.4185
|style="background:WhiteSmoke; color:black" align="center"|0.2961
|style="background:WhiteSmoke; color:black" align="center"|0.0052
|style="background:WhiteSmoke; color:black" align="center"|0.3246
|style="background:WhiteSmoke; color:black" align="center"|0.0057

|-
!style="background:WhiteSmoke; color:black;" align="center" |2
|style="background:WhiteSmoke; color:black" align="center"|47.2935
|style="background:WhiteSmoke; color:black" align="center"|0.2961
|style="background:WhiteSmoke; color:black" align="center"|0.0052
|style="background:WhiteSmoke; color:black" align="center"|0.3214
|style="background:WhiteSmoke; color:black" align="center"|0.0056

|-
!style="background:WhiteSmoke; color:black;" align="center" |3
|style="background:WhiteSmoke; color:black" align="center"|56.1085
|style="background:WhiteSmoke; color:black" align="center"|0.2881
|style="background:WhiteSmoke; color:black" align="center"|0.0050
|style="background:WhiteSmoke; color:black" align="center"|0.3206
|style="background:WhiteSmoke; color:black" align="center"|0.0056

|-
!style="background:WhiteSmoke; color:black;" align="center" |4
|style="background:WhiteSmoke; color:black" align="center"|69.1297
|style="background:WhiteSmoke; color:black" align="center"|0.3009
|style="background:WhiteSmoke; color:black" align="center"|0.0053
|style="background:WhiteSmoke; color:black" align="center"|0.3203
|style="background:WhiteSmoke; color:black" align="center"|0.0056

|-
!style="background:WhiteSmoke; color:black;" align="center" |5
|style="background:WhiteSmoke; color:black" align="center"|76.3485
|style="background:WhiteSmoke; color:black" align="center"|0.3110
|style="background:WhiteSmoke; color:black" align="center"|0.0054
|style="background:WhiteSmoke; color:black" align="center"|0.3525
|style="background:WhiteSmoke; color:black" align="center"|0.0062

|-
!style="background:WhiteSmoke; color:black;" align="center" |6
|style="background:WhiteSmoke; color:black" align="center"|88.0310
|style="background:WhiteSmoke; color:black" align="center"|0.2972
|style="background:WhiteSmoke; color:black" align="center"|0.0052
|style="background:WhiteSmoke; color:black" align="center"|0.3234
|style="background:WhiteSmoke; color:black" align="center"|0.0056

|-
!style="background:WhiteSmoke; color:black;" align="center" |7
|style="background:WhiteSmoke; color:black" align="center"|94.9806
|style="background:WhiteSmoke; color:black" align="center"|0.2872
|style="background:WhiteSmoke; color:black" align="center"|0.0050
|style="background:WhiteSmoke; color:black" align="center"|0.3114
|style="background:WhiteSmoke; color:black" align="center"|0.0054

|-
!style="background:WhiteSmoke; color:black;" align="center" |8
|style="background:WhiteSmoke; color:black" align="center"|106.7100
|style="background:WhiteSmoke; color:black" align="center"|0.2838
|style="background:WhiteSmoke; color:black" align="center"|0.0050
|style="background:WhiteSmoke; color:black" align="center"|0.3024
|style="background:WhiteSmoke; color:black" align="center"|0.0053

|-
|}

= case3 =

IS=1 mm and ω=2°

{| border="2" cellspacing="0" cellpadding="9"

!colspan="1" border="none" style="background:silver; color:black;" align="center"|Peak number
|style="background:silver; color:black"|2θ (°)
|style="background:silver; color:black"|FWHM (°)
|style="background:silver; color:black"|FWHM (rad)
|style="background:silver; color:black"|Integral breadth (°)
|style="background:silver; color:black"|Integral breadth (rad)

|-
!style="background:WhiteSmoke; color:black;" align="center" |1
|style="background:WhiteSmoke; color:black" align="center"|28.3469
|style="background:WhiteSmoke; color:black" align="center"|0.3041
|style="background:WhiteSmoke; color:black" align="center"|0.0053
|style="background:WhiteSmoke; color:black" align="center"|0.3237
|style="background:WhiteSmoke; color:black" align="center"|0.0056

|-
!style="background:WhiteSmoke; color:black;" align="center" |2
|style="background:WhiteSmoke; color:black" align="center"|47.2945
|style="background:WhiteSmoke; color:black" align="center"|0.3009
|style="background:WhiteSmoke; color:black" align="center"|0.0053
|style="background:WhiteSmoke; color:black" align="center"|0.3242
|style="background:WhiteSmoke; color:black" align="center"|0.0057

|-
!style="background:WhiteSmoke; color:black;" align="center" |3
|style="background:WhiteSmoke; color:black" align="center"|56.1208
|style="background:WhiteSmoke; color:black" align="center"|0.3064
|style="background:WhiteSmoke; color:black" align="center"|0.0053
|style="background:WhiteSmoke; color:black" align="center"|0.3322
|style="background:WhiteSmoke; color:black" align="center"|0.0058

|-
!style="background:WhiteSmoke; color:black;" align="center" |4
|style="background:WhiteSmoke; color:black" align="center"|69.1388
|style="background:WhiteSmoke; color:black" align="center"|0.3363
|style="background:WhiteSmoke; color:black" align="center"|0.0059
|style="background:WhiteSmoke; color:black" align="center"|0.3598
|style="background:WhiteSmoke; color:black" align="center"|0.0063
|-
!style="background:WhiteSmoke; color:black;" align="center" |5
|style="background:WhiteSmoke; color:black" align="center"|76.3682
|style="background:WhiteSmoke; color:black" align="center"|0.2689
|style="background:WhiteSmoke; color:black" align="center"|0.0047
|style="background:WhiteSmoke; color:black" align="center"|0.3100
|style="background:WhiteSmoke; color:black" align="center"|0.0054

|-
!style="background:WhiteSmoke; color:black;" align="center" |6
|style="background:WhiteSmoke; color:black" align="center"|88.0168
|style="background:WhiteSmoke; color:black" align="center"|0.3443
|style="background:WhiteSmoke; color:black" align="center"|0.0060
|style="background:WhiteSmoke; color:black" align="center"|0.3811
|style="background:WhiteSmoke; color:black" align="center"|0.0067

|-
!style="background:WhiteSmoke; color:black;" align="center" |7
|style="background:WhiteSmoke; color:black" align="center"|94.9673
|style="background:WhiteSmoke; color:black" align="center"|0.3018
|style="background:WhiteSmoke; color:black" align="center"|0.0053
|style="background:WhiteSmoke; color:black" align="center"|0.3289
|style="background:WhiteSmoke; color:black" align="center"|0.0057

|-
!style="background:WhiteSmoke; color:black;" align="center" |8
|style="background:WhiteSmoke; color:black" align="center"|106.7248
|style="background:WhiteSmoke; color:black" align="center"|0.3344
|style="background:WhiteSmoke; color:black" align="center"|0.0058
|style="background:WhiteSmoke; color:black" align="center"|0.3655
|style="background:WhiteSmoke; color:black" align="center"|0.0064

|-
|}

= case4 =

IS=1 mm and ω=1°

{| border="2" cellspacing="0" cellpadding="9"

!colspan="1" border="none" style="background:silver; color:black;" align="center"|Peak number
|style="background:silver; color:black"|2θ (°)
|style="background:silver; color:black"|FWHM (°)
|style="background:silver; color:black"|FWHM (rad)
|style="background:silver; color:black"|Integral breadth (°)
|style="background:silver; color:black"|Integral breadth (rad)

|-
!style="background:WhiteSmoke; color:black;" align="center" |1
|style="background:WhiteSmoke; color:black" align="center"|28.4186
|style="background:WhiteSmoke; color:black" align="center"|0.2981
|style="background:WhiteSmoke; color:black" align="center"|0.0052
|style="background:WhiteSmoke; color:black" align="center"|0.3187
|style="background:WhiteSmoke; color:black" align="center"|0.0056

|-
!style="background:WhiteSmoke; color:black;" align="center" |2
|style="background:WhiteSmoke; color:black" align="center"|47.2990
|style="background:WhiteSmoke; color:black" align="center"|0.2998
|style="background:WhiteSmoke; color:black" align="center"|0.0052
|style="background:WhiteSmoke; color:black" align="center"|0.3192
|style="background:WhiteSmoke; color:black" align="center"|0.0056

|-
!style="background:WhiteSmoke; color:black;" align="center" |3
|style="background:WhiteSmoke; color:black" align="center"|56.0990
|style="background:WhiteSmoke; color:black" align="center"|0.2991
|style="background:WhiteSmoke; color:black" align="center"|0.0052
|style="background:WhiteSmoke; color:black" align="center"|0.3418
|style="background:WhiteSmoke; color:black" align="center"|0.0060

|-
!style="background:WhiteSmoke; color:black;" align="center" |4
|style="background:WhiteSmoke; color:black" align="center"|69.1210
|style="background:WhiteSmoke; color:black" align="center"|0.2992
|style="background:WhiteSmoke; color:black" align="center"|0.0052
|style="background:WhiteSmoke; color:black" align="center"|0.3318
|style="background:WhiteSmoke; color:black" align="center"|0.0058
|-
!style="background:WhiteSmoke; color:black;" align="center" |5
|style="background:WhiteSmoke; color:black" align="center"|76.3549
|style="background:WhiteSmoke; color:black" align="center"|0.3070
|style="background:WhiteSmoke; color:black" align="center"|0.0054
|style="background:WhiteSmoke; color:black" align="center"|0.3386
|style="background:WhiteSmoke; color:black" align="center"|0.0059

|-
!style="background:WhiteSmoke; color:black;" align="center" |6
|style="background:WhiteSmoke; color:black" align="center"|88.0328
|style="background:WhiteSmoke; color:black" align="center"|0.3053
|style="background:WhiteSmoke; color:black" align="center"|0.0053
|style="background:WhiteSmoke; color:black" align="center"|0.3437
|style="background:WhiteSmoke; color:black" align="center"|0.0060

|-
!style="background:WhiteSmoke; color:black;" align="center" |7
|style="background:WhiteSmoke; color:black" align="center"|94.9712
|style="background:WhiteSmoke; color:black" align="center"|0.2838
|style="background:WhiteSmoke; color:black" align="center"|0.0050
|style="background:WhiteSmoke; color:black" align="center"|0.3127
|style="background:WhiteSmoke; color:black" align="center"|0.0055

|-
!style="background:WhiteSmoke; color:black;" align="center" |8
|style="background:WhiteSmoke; color:black" align="center"|106.7197
|style="background:WhiteSmoke; color:black" align="center"|0.2799
|style="background:WhiteSmoke; color:black" align="center"|0.0049
|style="background:WhiteSmoke; color:black" align="center"|0.2980
|style="background:WhiteSmoke; color:black" align="center"|0.0052

|-
|}

Specific Process Knowledge/Characterization/XRD/XRD SmartLab/Instrumental broading in GiXRD - Revision history

Reet at 14:51, 22 May 2026

Reet at 14:47, 22 May 2026

Eves at 16:40, 9 November 2023

Eves at 12:13, 9 November 2023