1
Structural Biology
Methods
Fall 2020
Lecture #2
Electromagnetic wave
Electricfieldstrength
Distance
E – electric field strength
t – time
z – position
A – amplitude
λ – wavelength
2π – to convert relative
distance to angles
Electricfieldstrength
Distance
E (t=0; z) = A cos (2p z/l)
Electric field strength
Magneticfieldstrength
M (t=0; z) = A sin (2p z/l)
E (t=0; z) = A cos (2p z/l)
F F = A cos(2p z/l) + i A sin(2p z/l)
F = A cosa + i A sina
F = A exp(ia)
a
A
Real axis
Imaginaryaxis
A - wave amplitude
a - wave phase angle
F
A
Wave as a vector
F = A cosa + i A sina
F = A exp(ia)
A
E
λZ
z
=
=
X-rays scatter from electrons in all
directions
Primary beam
Secondary beams
X-ray scattering from several electrons
Primary beam
A
E
λZ
z
When do electrons scatter
“in phase” – waves add
constructively?
There is no path and PHASE
DIFFERENCE when rays reflect
from a plane
A
E
λZ
z
nl = 2d sinq
Bragg’s law:
There is NO PHASE DIFFERENCE if the path
differences are equal to whole number multiplies of
wavelength (l)
w
sinq = w/d
2w = nl
nl = 2d sinq
Bragg’s law:
sinq = w/d
2w = nl
There is NO PHASE DIFFERENCE if the path
differences are equal to prime number multiplies of
wavelength (l)
w
X-rays scatter from electrons in all
directions
Primary beam
Secondary beams
System of two electrons
Dot product
System of two electrons
S
-s0
Scattering by an atom
Scattering by an atom depends of the
length of |S| (resolution)
Scattering by a unit cell
Scattering by a crystal
Diffraction Conditions
Bragg planes are identical to lattice planes
=>
Reciprocal lattice and Ewald construction
Expected end of lecture #2
Wave as a vector
F=Acosa+iAsina
F=Aexp(ia)
a
A
Real axis
Imaginaryaxis
A- wave amplitude
a- wave phase
A
E
λZ
z
F
A
Phase problem
αα
α
F = A cosa + i A sina
F = A exp(ia)
a
A
Real axis
Imaginaryaxis
A - wave amplitude
a - wave phase angle
A
E
λZ
z
F
A
Wave as a vector
Wave description
E(t=0; z) = A cos (2πz/λ)
E – electric field strength
t – time
z – position
A – amplitude
λ – wavelength
2π – conversion to angles
ν – frequency
c – speed of light
ω – angular velocity
ν = c/λ ω=2πν