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XX--ray opticsray opticsXX--ray opticsray opticsCrystal opticsCrystal opticsCrystal opticsCrystal optics
Jürgen HärtwigJürgen HärtwigJürgen Härtwig
ESRF X-ray Optics Group, Crystal Laboratory
Jürgen Härtwig
ESRF X-ray Optics Group, Crystal Laboratory
XX--ray Optics Groupray Optics Group
OOGGXXXX--ray Optics Groupray Optics Group
OOGGXXOOGGXXESRF
What was already presented (among others)?
Physics of the electron beam source (Boaz Nash)
Ph i f X di ti d ti d t t (M l Physics of X-ray radiation production and transport (Manuel Sánchez del Río)
Multilayers in synchrotron optics (Christian Morawe)
Energy resolving detectors for X-ray spectroscopy (John Morse)
So we continue today with the X-ray opticsSo we continue today with the X ray optics
OutlineOutline
1. Introduction
2. Monochromators
3 S ti f t i l fl ti3. Some properties of asymmetrical reflections
4. Shortly about high energy resolution
5. Crystal quality and how to measure it
(6 Plane or divergent monochromatic or (6. Plane or divergent, monochromatic or polychromatic waves in our experiments?)
1. Introduction1. Introduction1. Introduction1. IntroductionSome questions I plan to discuss and maybe to answer:Which kind of monochromators are used? How may I change the energy
l ti b di b di i ?resolution, beam divergence, beam dimension?
May the Bragg diffraction geometry have an influence on the coherence?
R l f i d l i I fl t l Role of source size and angular source size. Influence on transversal coherence, resolution etc. ?
Are “Imaging quality” “focusing properties” “coherence preservation” Are Imaging quality , focusing properties , coherence preservation related?
What is a “highly perfect” crystal? What are the lowest strains that we can measure?
Is there a “highly parallel (monochromatic)” beam? Is there a “nanometric parallel” beam?parallel beam?
We need to define what a “plane” or a “monochromatic” wave could be in the real experimental life. How may we approximate them?p y pp
etc.
Optical system / experimental set-up:Optical system / experimental set up:Source optical elements sample optical elements detector
The task of the optics:To transform the beam to obtain the best matching with the o transform the beam to obta n the best match ng w th the experiment; not loosing the good properties of the beam after its creation.
It acts on:- shapeshape- wavelength/energy- divergence- polarisation- coherence
“No optics is the best optics”!?
Y b t Yes, but …In principle possible - all in vacuum, working
with non-modified “white” or “pink” beam.
However, not very useful. We may need e.g.
monochromatisation, focussing, ... .
A whole zoo of optical elements
• slits, pinholes• filters, windows• mirrors (reflectivity based)• beam splitter monochromators (crystals)
h / ll / l ( l• monochromators/collimators/analysers (crystals,multi-layers – often also called “mirrors”)
h l ( h d l i ) ( l )• phase plates (phase retarder, polarizer) (crystals)• lenses, zone plates
bi d l t (ML ti B F l l )• combined elements (ML gratings, Bragg-Fresnel-lenses)• etc.
Mirrors and monochromators, collimators, analysers flat, but also bent for collimation, focussing, image f at, ut a so nt for co mat on, focuss ng, mag
magnification, ...
Main physical effects used in X-ray optics were discovered inthe first years starting from the discovery of X rays bythe first years starting from the discovery of X-rays byC. W. Röntgen:
absorption (Röntgen 1895/96 filters)absorption (Röntgen 1895/96 filters)Bragg-diffraction (Laue 1912 monochromators, etc.)specular reflection (Compton 1922 mirrors)refraction (Larsson, Siegbahn, Waller 1924 later lenses)
P ti f d bl d t l tProperties of double and many-crystal set-ups:Jesse W. M. DuMond, Physical Review, 52, 872-885 (1937)DuMond graphs dispersive and non dispersive set ups DuMond graphs, dispersive and non-dispersive set-ups, channel cut crystals (later invented as “Bonse-Hart-camera”), four crystal spectrometer (later invented as “Barthels four crystal spectrometer (later invented as Barthels monochromator”), etc.
B d lBut - many newer developments
Quite a lot of literatureQ
Overviews:
Tadashi Matsushita, X-ray Monochromators, in Handbook on Synchrotron Radiation, Vol. 1, ed. E. E. Koch, North-Holland P bli hi C 1983Publishing Company, 1983
Dennis M. Mills, X-Ray Optics for Third-Generation Synchrotron Radiation Sources, in Third-Generation Hard X-ray Sources, ed. Dennis M. Mills, John Wiley & Sons Inc., New York, 2002,
Short remark concerning beam dimensionsShort remark concerning beam dimensionsShort remark concerning beam dimensionsShort remark concerning beam dimensions
Few years ago – micro-beams were modern,
now – nano-beams are in voguenow nano beams are in vogue.
But - we need all kind of beams:
large beams (decimetre sized) g ( )and small ones (nanometre sized),
“parallel” divergent and focussed beamsparallel , divergent and focussed beams.
Beam dimensions – example: paleontologyp p gy
Examples from Paul Tafforeau
Nearly 4 orders of magnitude in dimension
Without scanning
Without magnificationWithout magnification
Multi scale experiments!
Further large scale objects: the monochromator crystals
For their tests we like to use:wide beams if possible at least 10 x 45 mm2 (V x H)wide beams, if possible at least 10 x 45 mm2 (V x H),with a “good” spatial resolution ~ 1 μm
The above field of view and resolution needs sensors with:10,000 x 45,000 pixels, this is 450 Mega pixels
Not yet on the market (?)Not yet on the market (?)
but also by: filters + 2. Monochromators2. Monochromators100
E = 8 keV
100
E = 8 keV
source spectrum + scintillator screen
response spectrum (P l T ff /ID19)
10-2
10-1
forbidden area 10-2
10-1
forbidden area
(Paul Tafforeau/ID19)
10-3
10-2
d re
flect
ivity
R = 1
ors)
10-3
10-2
d re
flect
ivity
R = 1
ors)
10-4
10
Inte
grat
ed
High-ZLow-Zn
ML
's
d M
L's
Ge111
(Mir
ro
10-4
10
Inte
grat
ed
High-ZLow-Zn
ML
's
d M
L's
Ge111
(Mir
ro
10-5 Crystals
ML's
h-re
solu
tion
epth
-gra
dedSi
111
10-5 Crystals
ML's
h-re
solu
tion
epth
-gra
dedSi
111C*
111
10-6
10-6 10-5 10-4 10-3 10-2 10-1 100hi
gh de
Be110
10-6
10-6 10-5 10-4 10-3 10-2 10-1 100hi
gh de
Be110
Ch. Morawe
E/EHigh resolution 10-8 and below
Bragg diffracting X-ray optical elements like
M f t d f di l ti f t l
gg g y pmonochromators, analysers, etc.
Manufactured from dislocation free crystals.Mostly used: Si, Ge, C* (locally dislocation free diamond).
We mainly use silicon.
They must be tailored into monochromators etc.
Orientation cutting lapping polishing and etchingOrientation, cutting, lapping, polishing and etching.
Strain free crystal preparation.
Accurate and stable mounting.
Adequate cooling schemeAdequate cooling scheme.
Crystal laboratory:Crystal laboratory:
Manufacturing of nearly all perfect Si (and few Ge) crystal Si (and few Ge) crystal monochromators & analysers, etcfor all ESRF beam lines, CRG b li d t l beamlines and external laboratories.Silicon pieces are made from float Silicon pieces are made from float zone silicon ingots with 100 mm diameter (Wacker).More than 1.5 tons of silicon single crystal material has been processed in more than twenty yearsin more than twenty years.
Example manufacturing crystal monochromators and analysersmonochromators and analysers
Which types of monochromators are used?yp
Single crystal monochromators -beam splitter monochromators
white beam white beam white beam
monochr. beam 2monochr. beam 1
Double crystal monochromators
white beammonochr. beam
Reflection (Bragg) and t nsmissi n (L ) transmission (Laue) geometry used
Single crystal monochromators -beam splitter monochromators
white beam white beam white beam
monochr. beam 2monochr. beam 1
Double crystal monochromators
Reflection (Bragg) and t nsmissi n (L )
white beam monochr. beam
transmission (Laue) geometry used
Few theory and definitionsFew theory and definitions
Reflectivity (and transmissivity) curve of a crystalplane RTheory
Plane & monochromaticincoming wave,
plane monochromatic
waveDarwin width
R
R+T+A=1
incoming wave,varying the angle of incidence
counting the diffracted photons
width
Rocking curveReal situation - experimentConvolution (autocorrelation) of
R T A 1
any wavereflectivity (or transmissivity) curve
with other reflectivity curves,or/and wavelength (energy) g ( gy)
distribution,or/and divergence distribution
(instruments/apparatus function)( pp f )
Numerical example (using XOP):d bl h di i ( )
Numerical example (using XOP):d bl h di i ( )double monochromator non-dispersive (+,-)double crystal set-up in Bragg casedouble monochromator non-dispersive (+,-)double crystal set-up in Bragg case
two 111-Si reflections
wh 0 8
1,0
two Si 111 crystals
0 8
1.0
Darwin curveSi 111, 60keV, 10mm thick plateSi 111, 60keV, 5cm thick plate
gg
wh
wh
0,4
0,6
0,8
refle
ctiv
ity
0.4
0.6
0.8
refle
ctiv
ity
emat
ical
Bra
gpo
siti
on
0
-1,0 -0,5 0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,50,0
0,2
-1.0 -0.5 0.0 0.5 1.0 1.5 2.0 2.50.0
0.2 kine
angle - B (arc seconds)angle - B (arc seconds)
However, in operation known since: C. G. Darwin, However, in operation – mostly fixed angleThe theory of X-ray reflection,
Phil. Mag. 27, 315, 675 (1914)
Reflectivity curves, with stronger absorptionReflectivity curves, with stronger absorptiony g py g p
Prins-Darwin or reflectivity curveSi 111, 8keV, 5cm thick plate
0 8
1,0 Si 111, 8keV, 5cm thick plate
w
0,6
0,8tiv
itywh
0,4refle
ct
0,0
0,2
-5 0 5 10 15 20,
angle - B (arc seconds)
How to measure it? Not so easy! See later.
Double crystal monochromatorsDouble crystal monochromators
Incident and exit beams have the same directionhave the same direction
In working position: RR()
fixed angle (mostly);
multiplication of two R
2
multiplication of two reflectivity curves
Two variantswo var ants
Fixed exit monochromator- more than one movement
necessary
Two variantswo var ants
Fixed exit monochromator- more than one movement
necessary
Two variantswo var ants
Fixed exit monochromator- more than one movement
necessary
Channel-cut monochromator- NOT fixed exitNOT fixed exit- naturally aligned- weak link plus piezo
movement for detuning etc.
Two variantswo var ants
Fixed exit monochromator- more than one movement
necessary
Channel-cut monochromator- NOT fixed exitNOT fixed exit- naturally aligned- weak link plus piezo
movement for detuning etc.
Two variantswo var ants
Fixed exit monochromator- more than one movement
necessary
Channel-cut monochromator- NOT fixed exitNOT fixed exit- naturally aligned- weak link plus piezo
movement for detuning etc.
“Generic” cryo enically Generic” cryogenically cooled channel-cut double
crystal monochromator
Pusher
y
no fixed exit
high heat load applications Pusher mechanism
Steel flexure
high heat-load applications
Channel-cut crystal
Crystal assembly (simplified for visibility)
Possible problem – “higher harmonics”p g2dnh’,nk’,nl’ sinB = nif (h,k,l)=(nh’,nk’,nl’)
Si (2n,2n,0), = 1.6Å, = 0.8Å, etc.
Refraction correction (middle of the reflection domain):
BhB0 sin,sin
h0
20
0 12sinV2
Fr
Refraction correction (middle of the reflection domain):
0Buc 2sinV2
R d ti f hi h h m i s (if mi s m b s d)Reduction of higher harmonics (if no mirrors may be used)monochromator detuning
d d At detuned position(slightly misaligned)
S ll b d i Smaller band in angle and energy
Synchrotron optics: Multilayer high flux monochromators• Two bounce optics• 100x larger bandwidth compared with Si(111)• Harmonics suppression due to refraction and filling factor
Ch. Morawe – SPring-8 11.09.07
How may I change the beam dimension,y gthe beam divergence, th l ti ?the energy resolution?
3. Some properties of asymmetrical 3. Some properties of asymmetrical flfl
3. Some properties of asymmetrical 3. Some properties of asymmetrical flfl
p p yp p yreflectionsreflections
p p yp p yreflectionsreflections
Up to now we looked at symmetrical cases of Up to now we looked at symmetrical cases of Bragg diffraction
symmetrical Bragg case
(reflection case)
symmetrical Laue case
(transmission case)
– angle between lattice planes and surface
(reflection case) (transmission case)
With asymmetric reflections - possibilities to change y p gthe beam width and the divergence
for a single crystal reflection
Lin0K
whin
in
hK
Lout
whout
Of course, the same works also other way around.
So we have possibilities to act on the beam dimension (expansion, compression), as well as on
h b d ( ll l )the beam divergence (smaller, larger)
LouthK
whout
out
0K
Lin
whin
But all is related and things have their price
L 0Kwh
in
Lin 0K
hK
Loutwh
out
0B)i ()sin(b
Asymmetry factor:
hB )sin(
w out = |b| w inThis example: >0, |b|<1: whout = |b| wh
in
Relation to symmetrical reflections
pLin > Lout and wh
in < whout
w in L = w out L = constant reflectionswh
in = |b|-1/2 whsym
whout = |b|1/2 wh
sym
wh Lin = wh Lout = constant
right asymmetry (<0) – less divergence possible to obtain h | | hg p
Some “philosophy”p p yWith flat crystals we may change the divergence.We may decrease (or increase) it. Not “more parallel”, y ( ) p ,but less divergent! This is collimation*). Focussing needs convergent beams. We can not focus
i h fl l i l i l I k i h b with flat crystals in a classical way. It works with bent crystals. Often other X-ray optical elements are more efficient for this (future lectures?!)
*) The word "collimate" comes from the Latin verb collimare,
efficient for this (future lectures?!).
The word collimate comes from the Latin verb collimare, which originated in a misreading of collineare, "to direct in a straight line". (Wikipedia)
BUT BUT …wh
in Lin = whout Lout = constant
This is too simple, hand-waving “derivation”. We need an additional dimension for the h phase space.
Besides size and anglel l h ( ) i d dalso wavelength (or energy) is needed
L t t t f th b iLet us start from the basics
0 = B + - in K
0 B in
h = B - + out
0Kh
t
From electrodynamics (and dynamical diffraction theory)
n
BB
dynamical diffraction theory) we know that: 0K
hK
0h
hKK 0h
For the wave vectors outside the crystal:0h
But for the tangential components - continuity:
tt0ht hKK
And remember, wave vectors depend on wavelength: )(fK , p g )(
For small in, out and K we obtain (for Bragg and Laue case!):
K
Ksin
)cos()cos(sinsin||
B
BBin
B
Bout
The divergence in and polychromaticity K/K of the incomingbeam contribute to the divergence out of the outgoing beam
BB
beam contribute to the divergence out of the outgoing beam
An increased divergence out of the outgoing beam (with respect t th t if th i i b ) s: to that if the incoming beam) means: the source is virtually closer, or the source size is virtually larger, or the angular source size is virtually larger.
Special case 1
Monochromatic divergent incoming radiation
arg r, or th angu ar sourc s z s rtua y arg r.
Monochromatic, divergent incoming radiation
K = 0, in 0 out = |b| in
t ior whout = |b| wh
in
Special case 2
P l h ti ll l i i di tiPolychromatic, parallel incoming radiation
K 0, in = 0 K)cos()cos( BB
K)sin( Bout
Remember, “our” beams often are rather close
2.1. out = 0 if cos(B - ) = cos(B + ) if (sym. Bragg case!)
to plane waves, but rather polychromatic
Only in the symmetric Bragg case the beam divergenceis conserved for a polychromatic beam!!!Only in that case coherence is conserved!!!Only in that case coherence is conserved!!!Only in that case focussing is not perturbed!Only in that case highest geometrical resolution possible!
2.2 out 0 for all other cases
A divergent, polychromatic beam is transformed in a d l h b !even more divergent, polychromatic beam!
Source size and angular source size are crucial Source size and angular source size are crucial parameters with respect to the character of the wave “seen” by the sample.
angular source size ( = s/p)p
not source divergence!!ps δ
The angular source size is important for further physical properties:physical properties:
the geometrical resolution for imaging,the transversal coherence lengththe transversal coherence length,the demagnification limit of a “lens”.
Image blurring due to non-zero source size
angular source size: δ = s/p
qps δ
geometrical resolution: ρ = q s/p = q δ
s δqp
s δ
Spatial coherenceSpatial coherenceTransversal coherence length: lT = ½ λ p/s = ½ λ/δ
Magnification, demagnification, focussing properties/quality
G t i l d ifi ti Diff ti li it d f iGeometrical demagnification,source size limit:
/ δ
Diffraction limited focusing:ρDL = 1.22 λ / sinα
s ρ
ρG = q s/p = q δ
s ρ
p q(graph: J Susini)(graph: J. Susini)
4 Shortly about high energy resolution4 Shortly about high energy resolution4 Shortly about high energy resolution4 Shortly about high energy resolution4. Shortly about high energy resolution4. Shortly about high energy resolution4. Shortly about high energy resolution4. Shortly about high energy resolution
One way: One way: Sophisticated many crystal set-ups.
Example ID18:A two-step collimation with low-index
l ll asymmetric reflections followed by a two-step angular analysis with high-index asymmetric reflections reflections.
Idea: M.Yabashi, K.Tamasaku, S.Kikuta, and T.Ishikawa, Review of Scientific Instruments, 72, 4080 (2001).
ID18 ESRFID18 ESRF Alexander Chumakov ID18/ESRF
High resolution optics for Nuclear Resonance Scattering“0.5 meV” monochromator (∆E/E ≈ 3.5·10-8)
(theoretically expected performance)
High-resolution optics for Nuclear Resonance Scattering
(theoretically expected performance)
31
divergence: 65 nano-radacceptance: 130 nano-rad
vertical size: 0.6 mmdivergence: 2 radvertical size: 0.6 mm
31 mm
23
divergence: 2 rad divergence: 2 rad
14
1st crystal: Si(400)B = 18.469º
t |b| 0 18
2nd crystal: Si(400)B = 18.469º
t |b| 0 18
3rd crystal: Si(12 2 2)B = 77.533º
t |b| 9 8
4th crystal: Si(12 2 2)B = 77.533º
t |b| 3 2asymmetry: |b| = 0.18in = 5.4ºout = 31.6ºangular acceptances:in = 20 rad
asymmetry: |b| = 0.18in = 5.4ºout = 31.6ºangular acceptances:in = 20 rad
asymmetry: |b| = 9.8in = 27.6ºout = 2.7ºangular acceptances:in = 0.72 rad
asymmetry: |b| = 3.2in = 35.4ºout = 10.4ºangular acceptances:in = 1.3 radin
out = 3.6 radfootprint: 6.4 mm
in out = 3.6 radfootprint: 33 mm
in out =7 radfootprint: 41 mm
in out = 4 radfootprint: 3.3 mm
Other possibility – back scattering geometry(Bragg angle close to 90 deg)
with high order reflections (large h k l)
= 2dhkl sinB ∆ = ∆ · 2dhkl cosB
∆ ∆E/E ∆ /∆= ∆E/E = ∆/tanB
) f 10 8 d b) d [ t () 0]
Silicon @ 20KeV, h=k=l=13, (E/E) ~10-8E ≈ 0.5 meV,
a) → a few 10-8 rad b) → deg [cotg() → 0]
@ , , ( ) ,
ID16, ID28 Sample
analyserp
Detectormonochromatorsource
5. How high crystal quality and how to 5. How high crystal quality and how to
5. How high crystal quality and how to 5. How high crystal quality and how to
g y q yg y q ymeasure it?measure it?
g y q yg y q ymeasure it?measure it?
Crystal quality - limit in high energy resolution, …(?)
I fl h ti i lit Influence on coherence preservation, image quality, focussing efficiency, ...
∆d/d= 5x10-9
Crystal interferometers
Diamonds at the ESRFDiamonds at the ESRFFrom the very beginning of the ESRF used as h l t d h tphase plates and monochromators.
Now locally dislocation- and stacking fault free Now locally dislocation and stacking fault free material available.
Which is the level of local residual strains?
Future MX BL ID30A (MASSIVE)
~100 μm215 2 100 μm~15 μm2
56
X-ray diffraction topographyWhite beam topograph
in transmission
(work with Fabio Masiello)
110-oriented plate
supplier: Paul ppBalog/Element Six
Dislocation free areas of 11 3 mmDislocation free areas of 6x4mm2 and more!!!
Locally crystal quality close to that of silicon
11.3 mm
Locally crystal quality close to that of silicon, quantitatively confirmed by double crystal topography
But are we able to measure weak strains quantitatively?
Quantitative analysis strain analysis110-oriented crystal plate
effective misorientation map
Q y y
effective misorientation map basing on one topograph
20keV Si [880] C* [660] 20keV, Si [880] C [660], detection limit: δθ > 8·10-9
The effective misorientation is The effective misorientation is of the order of 4 × 10−8 for a
region of interest of0 5 × 0 5 mm2 and × 10-80.5 × 0.5 mm2 and
1 × 10−7 in a region of1 × 1 mm2
Sample is slightly bent due to the non-homogeneous
dislocation distribution!dislocation distribution!work with Fabio Masiello
6. Plane or divergent, monochromatic or l h ti
6. Plane or divergent, monochromatic or l h ti polychromatic wavespolychromatic waves
Two basic questions:What are “plane” or “divergent” waves?
Wh “ h i ” “ l h i ” “ hi ”
w qu
What are “monochromatic”, “polychromatic”, “white”beams/waves?
For our monochromator and/or single crystalline sample!
Reminder of basic physics:Reminder of basic physics:Plane wave – infinite extend, wave front is plane, one wave vector perpendicular to it, delta-function in k-space.Monochromatic wave – wave train of infinite length, infinitely sharp spectral line, delta-function in ω-space.They do not exist in nature!!!They do not exist in nature!!!
The full width at half maximum of the reflectivity curve,y ,
good reference for our sample, monochromator, ... , to define the character of a wavedefine the character of a wave
R()FWHM in the angular space:
P h h h 2
R()
wh
g p
whh h
B
h
2 0
sin
FWHM in the wavelength space: R()
wh
w wh h B cot
Example of a typical crystal/monochromator reflection:
silicon, 111 reflection, Bragg case, thick crystal
energy wh wh
/energy wh wh /
8 keV 7.6 arcsec 1.5·10-4
20 keV 2 9 arcsec 1 5 10-420 keV 2.9 arcsec 1.5·10-4
Those are to be compared with source properties:
wave length spread of the source ()wave length spread of the source ()
angular source size ( = s/p)ps
not source divergence!!ps δ
relative wave length spread of the source (E/E)
FWHM in the wavelength space hw<<
“ h ” “monochromatic” wave
angular source size = s/p
<< FWHM in the angular space hw
“plane” wave
Practical examples:
relative wave length or energy spread of the source
source
source
Si 111 double mono 2·10-4
energy
8 keV
wh/
1.5·10-4
laboratory (e.g. CuK1) 3·10-4
white beam 1···10
20 keV 1.5·10-4
SR–white beams: >>> wh
really polychromatic
”monochromatic” beam (SR or laboratory): <?> wh
often not monochromatic(for all reflections narrower than the 1.5·10-4 for silicon 111)
special effort is necessary to approximate “monochromaticity”p y pp y
Practical examples:
angular source size ( = s/p)
source source size s source dist D δsource source size s source dist. D δ
class. lab tube 400 µm 0.4 m 1·10-3 3.5 arcmin
f t b 5 1 1 10 5 1
energy
8 keV
wh
7 6 arcsecµ-focus tube 5 µm 1 m 1·10-5 1 arcsec
SR 100 µm 150 m 6.7·10-7 0.14 arcsec
7
8 keV
20 keV
7.6 arcsec
2.9 arcsec
SR 50 µm 75 m 6.7·10-7 0.14 arcsec
laboratory: >< wh divergent & quasi plane waves possible
SR - ESRF: < wh quasi plane wave (mostly)
Source divergences > angular source sices
E F h q p (m y)
g g
For your curiosity:y yFirst published (direct) measurements of
fl i i fl i i reflectivity curvesreflectivity curves,(Not rocking curves! Those were measured earlier),g
the ones that we are able to calculate since Darwin’s first dynamical theory published in 1914, was in???
1962
first dynamical theory published in 1914, was in???
nearly 50 years after Darwin’s results!!!nearly 50 years after Darwin s results!!!
C. G. Darwin, The theory of X-ray reflection, Phil. Mag. 27, 315, 675 (1914)Charles Galton Darwin (1887-1962) grandson of Charles Darwin
How can we measure a reflectivity How can we measure a reflectivity curve???
Not trivial. One needs two ingredients.
1. Narrow instruments function
in angular space – asymmetrical reflectionsg p ymm f
in wavelength space – high-resolution mono.
2. Crystals of good quality. They became available with development
of electronics, later micro-electronics and opto-electronics
Double (or triple) crystal monochromator collimator Double (or triple) crystal monochromator-collimator with one asymmetrical Bragg reflection
1st experimental reflection curves
=-4.48
=0
=4.48
111-reflections of Ge, different asymmetriesy
CuK1-radiation, triple crystal set-up, silicon double monochromator
R. Bubáková, Czech. J. Phys. B12, 776 (1962), J y , ( )
B th th p b bl fi st p blish d By the way – the probably first published measurements in a double crystal set-up with an asymmetric monochromator/collimator crystal asymmetric monochromator/collimator crystal were about X-ray diffraction topography in 1952.
W. L. Bond J. Andrews, Structural Imperfections in Quartz Crystals, p yAm. Mineral. 37, 622-632 (1952)
This technique was later developed further to the “Plane” Wave Topography,
t d t t t l ll t i fi ldto detect extremely small strain fieldsin nearly perfect crystals.
Thank you for your Thank you for your tt ti !attention!
