Structural Biology Methods
Fall 2024
Lecture #2
nl = 2d sinq
Bragg’s law:
There is NO PHASE DIFFERENCE if the path differences are equal to
whole number multiplies of wavelength
w
sinq = w/d
2w = nl
There is no path and PHASE DIFFERENCE
when rays reflect from a plane
nl = 2d sinq
Bragg’s law:
There is NO PHASE DIFFERENCE if the path differences are equal to
whole number multiplies of wavelength
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
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
=
=
X-rays scatter from electrons in all directions
Primary beam
Secondary beams
X-ray scattering from several electrons
Primary beam
When do electrons scatter “in phase” so that waves add
constructively?
X-rays scatter from electrons in all directions
Primary beam
Secondary beams
Dot product
System of two electrons
-s0
Scattering by an atom
Scattering by an atom depends on 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