XRD Crystallite Size Calculator (Scherrer Equation)

XRD Crystallite Size Calculator (Scherrer Equation)

Peak Position (2θ)

FWHM (2θ)

X-Ray Wavelength


Results
nm

Calculation Tutorial:

STEP1: Open the XRD graph of the material, which is obtained from the instrument. 2 Theta I n t e n s i t y 20 25 30 35 40 45 0 1000 2000 3000 4000 5000 STEP2: Now zoom on the area for which you want to calculate the crystallite size and note down the angle at which peak is shown and peak Full Width at Half Maximum (FWHM). Raw HTML 2 Theta I n t e n s i t y 20 25 30 35 40 45 0 1000 2000 3000 4000 5000 31.8 0.5 (FWHM) STEP3: Now enter the measured Peak Position (i.e. 31.8) and peak FWHM (i.e. 0.5) in desire columns of the calculator. You should get the calculated results of the crystallite size in the "Calculated Result" field.

NOTE: Default value of wavelength of LASER is set is 0.15418 (Cu K-alpha), which is mostly used in the instruments.

Theory Behind Calculations: X-Rays are having wavelength between 0.01nm to 10nm. Hence X-Rays can penetrate inside the crystal structure of any material very easily; and tells us the properties of material while coming out from that material. Which is why X-Ray spectroscopy is very useful technique for characterization of different types of materials. We can easily calculate the size of particles from Scherrer formula given:

Scherrer Formula:

Dp = (0.94 Χ λ) / (β Χ Cosθ)

Where, Dp = Average Crystallite size, β = Line broadening in radians, θ = Bragg angle, λ = X-Ray wavelength

NOTE: Please don't worry about the β(in radians), All the calculations are made such that you can enter β (i.e. Full Width at Half Maximum) value directly in degree as shown in "Calculation Tutorial"

Post a Comment

  1. K.M. Towe10 January 2017 at 22:58

    Step one: Prepare a suitable sample, one with an appropriate size range and prepared to avoid preferred orientation.

    ReplyDelete
  2. Ghaleb Al -Dahash11 January 2017 at 01:17

    It is very good web.

    ReplyDelete
  3. Mostafa6 March 2017 at 17:50

    This does not take into consideration instrumental widths right?

    ReplyDelete
  4. Sunitha16 April 2017 at 16:55

    How to do correction in fwhm values. While calculating fwhm for clays

    ReplyDelete
  5. Yoones9 June 2017 at 15:26

    Thank you very much. It is useful.

    ReplyDelete
  6. Mohamed Kordy21 December 2017 at 12:50

    it's good idea to help researchers

    ReplyDelete
  7. Sedrati Hichem29 May 2018 at 00:05

    THANK YOU..BUT K=0.94 IS FOR COPPER RADIATION
    I THINK YOU HAVE TO ADD OTHER CONSTANT LIKE K=0.89 FOR COBALT RADIATION..
    YOURS

    ReplyDelete
    Replies
    1. Anonymous23 July 2020 at 20:55

      The K is a material related, not source related, constant. Is true that they could give the option to give the K for your material, but is easy to fix dividing the outcome by 0.94 and multiplying for your desire K

      Delete
  8. Mustafa6 June 2018 at 22:00

    why The crystallite size of Ca-substituted in YBCO at Ba site samples was decreased for high concentration and increased for low concentration

    ReplyDelete
  9. Iroda Yuldashova21 June 2018 at 20:03

    Very good, but shape faktor for different crystals is vary.
    That has got a necessity for new section which can insert shape factor.

    ReplyDelete
  10. komal prasad malla23 July 2018 at 14:56

    Thank you so much it is a easier way to calculate particle size of nano materials.

    ReplyDelete
  11. LaquandaGissler14055@yahoo.com21 August 2018 at 15:39

    I agree with your details , fantastic post.

    ReplyDelete
  12. Mehwish25 August 2018 at 01:09

    what if we have multiple peaks as in the case of silver nanoparticles? which peak should we select?

    ReplyDelete
  13. Entidhar16 November 2018 at 23:35

    Thanks for this helpful site to find crystal size.

    ReplyDelete
  14. Harshwardhan Wadikar20 November 2018 at 11:38

    K depends on the crystal shape factor, K~0.9 for spherical crystallites.

    ReplyDelete
  15. Sugantha22 November 2018 at 23:06

    Very useful

    ReplyDelete
  16. Google21 December 2018 at 10:38

    One of our guests not long ago advised the following website.

    ReplyDelete
  17. How can I calculate FWHM12 February 2019 at 13:53

    Very useful.

    ReplyDelete
  18. Tesfay20 February 2019 at 17:57

    Thank you for easiness, but have considered the shape factor?
    With regard

    ReplyDelete
  19. Ashutosh Agarwal26 February 2019 at 08:25

    Different peaks in a XRD pattern gives different values of the particle size . How to evaluate the exact particle size then?

    ReplyDelete
  20. Habib Ur Rehman1 March 2019 at 22:51

    if we express theta values and FWHM in radians then crystallite size is different instead of express values in degrees?
    Why it is so?

    ReplyDelete
    Replies
    1. Anonymous20 June 2020 at 03:06

      Esto es porque los radianes solo están relacionados a una medida lineal -radio- (necesaria para conocer, por ejemplo, un parámetro de red), mientras que los grados se relacionan además con la inclinación de incidencia de los rayos X. Al expresar la FWHM en radianes, se esta realizando la conversión de unidades necesaria para concer la medida lineal del parámetro de red

      Delete
  21. Patipol20 March 2019 at 06:58

    Not wordy, nice explanation and easy to grasp so

    ReplyDelete
  22. Arthi2 April 2019 at 18:38

    Smart work..its very useful

    ReplyDelete
  23. Niyitanga Theophile12 April 2019 at 17:57

    This is really helpful. Thanks for saving our time!

    ReplyDelete
  24. Unknown22 May 2020 at 02:15

    do you includes contributions of instrumental error?

    ReplyDelete
  25. Unknown28 July 2020 at 20:50

    If both beta and theta in degree then which one have to convert in radians

    ReplyDelete

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