![ELECTRON DIFFRACTION
• PM is perpendicular to AY and PN is perpendicular to
the diffracted beam.
• δ=AN-AM
• δ=APcos 𝜃 + ∅ − 90 - APcos 90 − ∅
• ∴ 𝐴𝑃 = 𝑟 sin 𝛼
• δ = 𝑟 sin 𝛼 cos 𝜃 + ∅ − 90 −rsin 𝛼 cos 90 − ∅
• 𝛿 = 𝑟 sin 𝛼 cos 𝜃 + ∅ − 90 − cos 90 − ∅
• 𝛿 = 𝑟 sin 𝛼[cos − 90 − 𝜃 + ∅ − cos 90 − ∅ ]
• Formula [ cos −𝜃 = cos 𝜃 ]
• 𝛿 = 𝑟 sin 𝛼 cos 90 − 𝜃 + ∅ − cos 90 − ∅
• Formula [cos 90 − 𝜃 = sin 𝜃 ]
• 𝛿 = 𝑟 sin 𝛼 [sin 𝜃 + ∅ − sin ∅)]
• sin 𝐶 − sin 𝐷 = 2[cos
𝐶+𝐷
2
× sin
𝐶−𝐷
2
]
𝜃+∅+∅ 𝜃+∅−∅
8
90-φ
θ
Θ-(90-φ)
A
φ P](https://image.slidesharecdn.com/random-170922020455/85/Electron-diffraction-for-m-sc-student-complete-unit-8-320.jpg)
.Electron diffraction for m.sc, student complete unit
- 1. ELECTRON DIFFRACTION SHYAM SUNDER PANDIYA M.Sc.(Chemistry) 1stsemester 2016 SHYAM SUNDER PANDIYA M.SC.(Chemistry) semester 1 1
- 2. CONTAIN 1. INTRODUCTION. 2. PRINCIPLE. 3. SCATTERING INTENSITY V/S SCATTING ANGLE. 4. WIERL EQUATION. 5. APPLICATIONS OF ELECTRON DIFFRACTION. 6. LEED & STRUCTURE OF SURFACES. 7. APPLICATIONS OF LEED. 2
- 3. ELECTRON DIFFRACTION 1) INTRODUCTION :- a)DIFFRACTION:-The process by which a beam of light or other system of wave spread out ad result of passing through a narrow aperture or across an edge. 3
- 4. ELECTRON DIFFRACTION • DE BROGLIE to conclude that Moving electron possess dual nature 1)wave 2)Partical λ=h/p λ=h/mv ……………………….(1) we know that K.E.=1/2(mv2) ……………..(2) & K.E.= Ve …………………(3) By equation (2) & (3) ½(mv2) = Ve mv2 = 2Ve v=2Ve/m v=(2Ve/m)1/2……………….(4) Put value of v in equation (1) λ= ℎ 𝑚 2𝑉𝑒 𝑚 1 / 2 λ= ℎ 2𝑉𝑒.𝑚 1 / 2 Put standard value of h,m,e & sol λ=12.25 / 𝑉 Ặ 4 wher e wave length h= Plank’s constant m= Mass of electron v= velocity V= Potential difference e= Charge on electron Standard value h= 6.602×10-34 JS m= 9.110×10-31 Kg e=
- 5. ELECTRON DIFFRACTOIN • 2)PRINCIPL:- • Electron can be accelerated to precisely controlled energy by applying a known potential difference. • when accelerated through 10 keV they acquire wave length 12pm which makes then suitable for molecule diffraction. • Electron diffraction study generally utilized with energies of the order of 40 keV . • Since electron are charged the are scattered strongly by their interaction with electron and nuclei of atom of the sample. • Hence they cannot be use for studying molecule in gaseous state held on surface and in thin films.(the application to surface which is called LOW ENERGY ELECTRON DIFFRACTION is a major use of the techniqe.) 5
- 6. ELECTRON DIFFRACTION • 3)SCATTERINGINTENSITY&SCATTERINGANGLE:- • Consider diatomic molecule AB to study electron diffraction theory. The atom A lies at the origin and B at a distance r away • The orientation of molecule AB is specified by angle α and φ. • The indecent electron beam enters parallel to Y-axis and diffraction occurs through an angle θ. 6 B rα P φ Z X Y A θ
- 7. ELECTRON DIFFRACTION • The interference between the wave scattered A and B depends on the difference between the length of the paths the traverse . • Draw from B a perpendicular BN on to diffraction direction and a perpendicular BM on to the undiffrected direction to calculate the path difference δ. • when M and N are in phase the path difference is δ=AN-AM 7 A B r P α φ θ N M
- 8. ELECTRON DIFFRACTION • PM is perpendicular to AY and PN is perpendicular to the diffracted beam. • δ=AN-AM • δ=APcos 𝜃 + ∅ − 90 - APcos 90 − ∅ • ∴ 𝐴𝑃 = 𝑟 sin 𝛼 • δ = 𝑟 sin 𝛼 cos 𝜃 + ∅ − 90 −rsin 𝛼 cos 90 − ∅ • 𝛿 = 𝑟 sin 𝛼 cos 𝜃 + ∅ − 90 − cos 90 − ∅ • 𝛿 = 𝑟 sin 𝛼[cos − 90 − 𝜃 + ∅ − cos 90 − ∅ ] • Formula [ cos −𝜃 = cos 𝜃 ] • 𝛿 = 𝑟 sin 𝛼 cos 90 − 𝜃 + ∅ − cos 90 − ∅ • Formula [cos 90 − 𝜃 = sin 𝜃 ] • 𝛿 = 𝑟 sin 𝛼 [sin 𝜃 + ∅ − sin ∅)] • sin 𝐶 − sin 𝐷 = 2[cos 𝐶+𝐷 2 × sin 𝐶−𝐷 2 ] 𝜃+∅+∅ 𝜃+∅−∅ 8 90-φ θ Θ-(90-φ) A φ P
- 9. ELECTRON DIFFRACTION • The difference in phase between to scattered wave is (2𝜋/λ)𝛿. • Assuming the atoms A & B identical the resultant amplitude at P is • A=Ḁ+Ḁe2𝜋𝑖𝛿/λ • A=Ḁ(1+e2𝜋𝑖𝛿/λ) • where Ḁ=atoms form factor for electron scattering(depands on the nuclear charge of the atom.) • The intensity of radiation is proportional to square of the amplitude . • I=A2 • I=A.Ǡ • I=Ḁ(1+e2𝜋𝑖𝛿/λ) . Ḁ(1+e-2𝜋𝑖𝛿/λ) • I= Ḁ2(1+e2𝜋𝑖𝛿/λ) .(1+e-2𝜋𝑖𝛿/λ) • Formula (1+𝑒 𝜃 )(1+𝑒−𝑖𝜃 ) = 2 1 + cos θ 9
- 10. ELECTRON DIFFRACTION • The differential element of solid is sin 𝛼 𝑑𝛼𝑑∅ and the total solid angle is 4𝜋 • 𝑡ℎ𝑢𝑠 𝑡ℎ𝑒 𝑎𝑣𝑒𝑟𝑒𝑔𝑒 𝑠𝑐𝑎𝑡𝑡𝑒𝑟𝑖𝑛𝑔 𝑖𝑛𝑡𝑒𝑛𝑠𝑖𝑡𝑦 𝑖𝑠 𝑔𝑖𝑣𝑒𝑛 • Iav ~ 4Ḁ2/4𝜋 0 2𝜋 0 𝜋 cos 2[2r𝜋/λsin 𝜃/2 sin 𝛼 cos ∅ + 10
- 11. ELECTRON DIFFRACTION • 4) WIERLEQUATION:- • when the molecule consist of a number of atom, we sum over the contribution from all pair and find that total intensity has an angular variation. • Given by equation: • I(θ)= 𝑖𝑗 𝑓𝑖 𝑓𝑗 sin 𝑠𝑅𝑖𝑗/s𝑅𝑖𝑗 • where s=4 𝜋 λ .sin 𝜃 2 11 where f= Electron scattering factor λ= wave length Scattering angle
- 12. ELECTRON DIFFRACTION • 5) APPLECATION OF ELECTRON DIFFRACTION :- i. Electron diffraction studies is useful for evaluating bond length and bond angle in simple gas phase molecule. ii. The accuracy of bond length obtained from electron diffraction studies is comparable to X-ray diffraction studies for simple gas phase molecules. iii. This shows that difficulties lie in the path of structure determination by electron diffraction . iv. Many molecular structure have been determined by this method. 12
- 13. ELECTRON DIFFRACTION Bond length and bond angle in some compounds. 13 Compound Bond Bond length in pm Geometry CCl4 Cl-Cl 285 Tetrahedral GeCl4 Ge-Cl 208 Tetrahedral TiCI4 Ti-Cl 218 Tetrahedral SF6 S-F 158 Octahedral Compound Bond Bond length in pm Bond angle C2H4 C-C 133 H-C-H 115.5o CH3Cl C-H 111 H-C-H 110o (CH3)3P C-P 185 C-P-C 98.8o Cl2O O-Cl Cl-O-Cl 111o
- 14. ELECTRON DIFFRACTION 1) LOW ENERGY ELECTRON DIFFRACTION (LEED) & STRUCTURE OF SURFACES :- • LEED is one of the most informative technique for determining the arrangement of atom close to the surface . • LEED generally electron diffraction but the sample is now the surface of a solid. • The use of low energy (10 to 200 eV) electrons corresponding to wave lengths in the range 100 to 400 pm . • The experimental arrangement used for LEED consists of i. Sample container ii. Electron gun iii. Grids iv. & phosphor screen 14
- 15. ELECTRON DIFFRACTION 15 ELECTRON GUN Phosphor screenGrids sample insulator Viewing port Apparatus used for LEED
- 16. ELECTRON DIFFRACTION • The LEED pattern portrays the two dimensional structure of surface. • Note:- i. nt angles to a plane of atom. LEED pattern is sharp if surface is well ordered for long distances compared with the wave length of incident electron. Generally , sharp patterns are obtained for surfaces ordered to depths of 20 nm or more . ii. Diffuse LEED pattern show the poorly ordered surface or presence of impurities. iii. The pattern is affected by the presence of terraces , steps and kinks in a surface. iv. The sample can be obtained by cleaning a crystal at differe 16
- 17. ELECTRON DIFFRACTION 7) APPLICATIONS OF LEED :- LEED is one of the most informative technique for Determining the arrangement of atoms close to the surface. LEED pattern may be used to assess the defect density . 17