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# Slide share version historical background of diffractometer

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# Slide share version historical background of diffractometer

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### Slide share version historical background of diffractometer

1. 1. Diffractometer Presented by Sehrish Inam Advanced Experimental Techniques In Physics Course Incharge: Ghulam Mustafa Khan NED university of Engineering and Technology
2. 2. Table of contents O Historical background O Diffractometer and error correction O Worked example for error correction O Conclusion
3. 3. Historical Background of Diffractometer
4. 4. DEBYE SCHERRER Powder camera • Powder x-ray diffraction in accordance with Braggs law to produce one diffracted beam • It shows diffraction lines and holes for incident and transmitted beam • A very small amount of powdered material is sealed into the fine capillary • The specimen placed and aligned to be the centre of camera through collimator
5. 5. DEBYE SCHERRER Method O Method of studying the structure of finely crystalline substance using x-ray diffraction O Narrow parallel beam monochromatic x-rays upon falling onto crystalline samples O And reflected by the crystallite that make up the sample O Produce no of coaxial that having one common axis O Diffracting cone
6. 6. THE SCHERRER EQUATION O D=K*λ/BCosϴ We use this formula to fine diameter D = diameter of the crystallite forming film λ=wavelength B=FWHM full width half maximum ϴ=is the Braggs angle
7. 7. Fundamental principal of x-ray powder diffraction(XRD) O X-ray diffraction is based on constructive interference of monochromatic x-rays and crystalline sample O X-ray generated by cathode ray tube ,filtered generated monochromatic x-ray O Correct orientation of crystal ,Braggs angle satisfy Braggs equation
8. 8. DEBYE SCHERRER CAMERA
9. 9. Error in the measurement of theta • Film shrinkage • Incorrect camera radius • Off -centering of specimen • Absorption in specimen • Divergence of the beam
10. 10. How error can be corrected? O By applying extrapolation function for achieving high precision O Nelson-Riley function It has greater range of linearity, Only few angle present More precision then bradley-function O At larger angle error will be minimize
11. 11. Advantages of DBSC Camera •Simplest camera type ,simple to use •Need very little sample are at low cost •Film is reasonably good storage medium •Does not required expansive medium
12. 12. Diffractometer Errors and correction Presented by Sehrish Inam
13. 13. Diffractometer
14. 14. Diffractometer Advantages O To obtain an x-ray diffraction pattern. O The data can be stored on floppy disks and easily retrieved. O Produce high-quality versions of the diffraction patterns using, for example, laser printers. O Data can also be directly processed by using computer software to obtain information about the structure, lattice parameters, lattice strain, crystallite size of the specimen.
15. 15. Diffractometer Errors 1. Misalignment of the instrument. 2. Use of a flat specimen 3. Absorption in the specimen
16. 16. Diffractometer Errors 4. Displacement of the specimen from the diffractometer is largest single source of error and causes an error in d given by
17. 17. Diffractometer Errors 5.Vertical divergence of the incident beam. This error is minimized, with loss of intensity, by decreasing the vertical opening of the receiving slit.
18. 18. Diffractometer Reduction of Error Extrapolate the lattice parameter against Cos2ϴ/Sinϴ for displacement of the specimen from the diffractometer and against cos2ϴ for the error of flat specimen and absorption in the specimen.
19. 19. Diffractometer Reduction of Error OWhen a peak is resolved into α1 and α2 ,will have two lattice parameter points for each hkl value. OThe resolution of the peak into α1 and α2 components can be achieved by simply enlarging the 2ϴ scale.
20. 20. Diffractometer Increment in Number of Diffraction Peaks ODecreasing the wavelength of the radiation used OUsing both the K α1 and K α2 components, the angular separation between α1 and α2 increases with increasing value of ϴ. O Modern diffractometers use monochromators that are aligned to diffract only the Kα component.
21. 21. Diffractometer OThe presence of Kβ peaks in a pattern can usually be revealed by calculation, since if a certain set of planes reflect Kβ radiation at an angle ϴ they must also reflect Kα radiation at an angle ϴβ they must also reflect Kα radiation at an angle ϴα and one angle may be calculated from the other from the relation
22. 22. Diffractometer Owhere λ2 kα/ λ2 kβ has the value 1.226 for Cu K radiation. ODraw straight line by using the least- squares method. OThe random errors involved in measuring the peak positions are responsible for the deviation of the various points from the extrapolation line.
23. 23. Analytical method
24. 24. Random errors are chance errors, such as those involved in measuring the position of the diffraction peak. These errors may be positive or negative, and they do not vary in a regular manner with some particular parameter, say the Bragg angle θ. ANALYTICAL METHOD: An analytical method that minimizes the random errors in a reproducible and objective manner has been proposed by Cohen. and it can be used to calculate the lattice parameters precisely for cubic and noncubic systems. We know that 𝜆 = 2𝑑 𝑠𝑖𝑛𝜃 Squaring the Bragg equation and taking logarithms, we get log 𝑠𝑖𝑛2 𝜃 = log 𝜆2 4 − 2 log 𝑑
25. 25. Differentiate above equation. Δ𝑠𝑖𝑛2 𝜃 𝑠𝑖𝑛2 𝜃 = −2 Δ𝑑 𝑑 if we assume that the combined systematic errors take the form Δ𝑑 𝑑 = 𝐾𝑐𝑜𝑠2 𝜃 By combining above two equations, we get Δ𝑠𝑖𝑛2 𝜃 = −2𝐾𝑐𝑜𝑠2 𝜃𝑠𝑖𝑛2 𝜃 Δ𝑠𝑖𝑛2 𝜃 = 𝐷𝑠𝑖𝑛22𝜃 where D is a new constant. (This equation is valid only when the 𝑐𝑜𝑠2 𝜃 extrapolation function is valid). The true value of 𝑠𝑖𝑛2 𝜃 for any diffraction peak is 𝑠𝑖𝑛2 𝜃 𝑡𝑟𝑢𝑒 = 𝜆2 4𝑎02 (ℎ2 + 𝑘2 + 𝑙2)
26. 26. where ao is the true value of the lattice parameter we wish to obtain. But 𝑠𝑖𝑛2 𝜃 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 − 𝑠𝑖𝑛2 𝜃 𝑡𝑟𝑢𝑒 = Δ𝑠𝑖𝑛2 𝜃 𝑠𝑖𝑛2 𝜃 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 − 𝜆2 4𝑎02 ℎ2 + 𝑘2 + 𝑙2 = 𝐷𝑠𝑖𝑛2 2𝜃 𝑠𝑖𝑛2 𝜃 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 = Aα + 𝐶𝛿 The parameter D is called the "drift" constant, and is a fixed quantity for any diffraction pattern but differs from one pattern to another. Best precision is achieved when the value of D is as small as possible. According to the theory of least squares, the best values of the coefficients A and C are those for which the sum of the squares of the random observational errors is a minimum; i.e. 𝑒2 = 𝑎 𝑚𝑖𝑛𝑖𝑚𝑢𝑚 = [Aα + 𝐶𝛿 − 𝑠𝑖𝑛2 𝜃 𝑜𝑏𝑠𝑒𝑟𝑣𝑒𝑑 ]2
27. 27. A pair of normal equations can be obtained by differentiating above equation with respect to A and C and equating them to zero. Thus, 𝛼 𝑠𝑖𝑛2 𝜃 = 𝐴 𝛼2 + 𝑐 𝛼𝛿 𝛿 𝑠𝑖𝑛2 𝜃 = 𝐴 𝛼𝛿 + 𝑐 𝛿2 By solving these equations we determine A, and from this value of A the true lattice parameter 𝑎0 can be determined.

### Hinweis der Redaktion

• DEBYE SCHERRE CAMERA