Download presentation

Presentation is loading. Please wait.

1
**Followed by a few examples of**

X-ray Diffraction The Basics Followed by a few examples of Data Analysis by Wesley Tennyson NanoLab/NSF NUE/Bumm

2
**X-ray Diffraction Bragg’s Law Lattice Constants Laue Conditions**

θ - 2θ Scan Scherrer’s Formula Data Analysis Examples NanoLab/NSF NUE/Bumm

3
Bragg’s Law nλ = 2 d sin θ Constructive interference only occurs for certain θ’s correlating to a (hkl) plane, specifically when the path difference is equal to n wavelengths.

4
**the diffraction condition is met**

Bragg condition’s The diffraction condition can be written in vector form 2k∙G + G2 = 0 k - is the incident wave vector k’ - is the reflected wave vector G - is a reciprocal lattice vector such that where G = ∆k = k - k’ the diffraction condition is met NanoLab/NSF NUE/Bumm

5
**Lattice Constants The distance between planes of atoms is**

d(hkl) = 2π / |G| Since G can be written as G = 2π/a (h*b1+ k*b2 +l*b3) Substitute in G d(hkl) = a / (h2 + k2 + l2)(1/2) Or a = d * (h2 + k2 + l2)(1/2) a is the spacing between nearest neighbors NanoLab/NSF NUE/Bumm

6
**Laue Conditions a1∙∆k = 2πυ1 a2∙∆k = 2πυ2 a3∙∆k = 2πυ3**

Each of the above describes a cone in reciprocal space about the lattice vectors a1, a2, and a3. the υi are integers When a reciprocal lattice point intersects this cone the diffraction condition is met, this is generally called the Ewald sphere. NanoLab/NSF NUE/Bumm

7
Summary of Bragg & Laue When a diffraction condition is met there can be a reflected X-ray Extra atoms in the basis can suppress reflections Three variables λ, θ, and d λ is known θ is measured in the experiment (2θ) d is calculated From the planes (hkl) a is calculated NanoLab/NSF NUE/Bumm

8
θ - 2θ Scan The θ - 2θ scan maintains these angles with the sample, detector and X-ray source Normal to surface Only planes of atoms that share this normal will be seen in the θ - 2θ Scan NanoLab/NSF NUE/Bumm

9
**Angle of incidence (θi) = Angle of reflection (θr)**

θ - 2θ Scan The incident X-rays may reflect in many directions but will only be measured at one location so we will require that: Angle of incidence (θi) = Angle of reflection (θr) This is done by moving the detector twice as fast in θ as the source. So, only where θi = θr is the intensity of the reflect wave (counts of photons) measured. NanoLab/NSF NUE/Bumm

10
θ - 2θ Scan NanoLab/NSF NUE/Bumm

11
**Smaller Crystals Produce Broader XRD Peaks**

12
**Scherrer’s Formula t = thickness of crystallite**

K = constant dependent on crystallite shape (0.89) l = x-ray wavelength B = FWHM (full width at half max) or integral breadth qB = Bragg Angle

13
**Scherrer’s Formula What is B? B = (2θ High) – (2θ Low)**

B is the difference in angles at half max Peak 2θ low 2θ high Noise

14
**When to Use Scherrer’s Formula**

Crystallite size <1000 Å Peak broadening by other factors Causes of broadening Size Strain Instrument If breadth consistent for each peak then assured broadening due to crystallite size K depends on definition of t and B Within 20%-30% accuracy at best Sherrer’s Formula References Corman, D. Scherrer’s Formula: Using XRD to Determine Average Diameter of Nanocrystals.

15
**Data Analysis Plot the data (2θ vs. Counts)**

Determine the Bragg Angles for the peaks Calculate d and a for each peak Apply Scherrer’s Formula to the peaks

16
Bragg Example

17
**Bragg Example d = λ / (2 Sin θB) λ = 1.54 Ǻ**

= 2.35 Ǻ Simple Right!

18
Scherrer’s Example

19
**Scherrer’s Example t = 0.89*λ / (B Cos θB) λ = 1.54 Ǻ = 1200 Ǻ**

Simple Right!

Similar presentations

Presentation is loading. Please wait....

OK

Don’t Ever Give Up!.

Don’t Ever Give Up!.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on united nations organization Ppt on media research group Ppt on juvenile rheumatoid arthritis Ppt on different occupations in the medical field A ppt on computer networking Ppt on central administrative tribunal new delhi Ppt on amplitude modulation and demodulation Ppt on content addressable memory test Ppt on recent natural disasters in india Ppt on conservation of environment quotes