Module 2 : Heterogeneous catalysis

Lecture 12 : Catalyst characterization -XRD analysis

 

Examples

1.  XRD pattern of oxide supports

Titania and zirconia are used as catalyst support or as active catalyst itself. They can be identified from their XRD pattern by comparison with the standard files. For any unknown sample the peaks are identified by comparison with the standard data. For oxides calcined at 400-500°C, the typical XRD profiles of titania and tetragonal zirconia are shown in Fig 3.

Fig. 3. XRD profiles for titania and zirconia prepared by precipitation method

Solved problem

1.  A cubic crystal was placed in an x-ray diffractometer using incoming x-rays with a wavelength λ=0 .154 nm. The various peak intensities recorded at different 2θ values are given in following table.

Determine the followings

  1. Calculate the crystal size ( Given, k=0.9; β = 0.0098)
  2. Calculate the value for the lattice constant (Assume first order diffraction with n = 1.)

Solution

  1. The crystal size can be calculated using the peak corresponding to 2θ = 40.3 having highest peak intensity.

    Hence, k = 0.9 ; β = 0.0098; λ=0.154 nm; θ=20.15, the crystal size L can determined using the Scherrer equation as follows


  2. The plane spacing of cubic crystal is related to the lattice parameter (a) by the following equation.


    [1]
                                                                                   

From Braggs Law,

 

or

or

nλ = 2d sin θ [2]

n2λ2 = 4d2 sin2θ

[2]

 

[3]

From [1] and [3] Combining ,

                                                                            

Using the peak corresponding to 2θ = 40.3 having highest peak intensity with [hkl] value of [110] the lattice constant ‘a ' for cubic crystal can be calculated as follows.

Or

Or, a = 0.342 nm

 

Book reference

 

•  Sam Zhang, Lin Li, Ashok Kumar, Materials Characterization Techniques, CRC Press, 2009

•  Y. Leng, Materials Characterization: Introduction to microscopic and spectroscopic methods, John Wiley & Sons, 2008

•  Edited by R.E. Dinnerbier and S. L. J. Billinge, Powder Diffraction :Theory and Practice , RSC Publishing, 2008

•  J. M. Thomas & W. J. Thomas, Principles and Practice of Heterogeneous Catalysi, VCH, 1997