X- X- -ray optics -ray optics ray optics ray optics Crystal - - PowerPoint PPT Presentation

X-

• ray optics

ray optics X-

• ray optics

ray optics

Crystal optics Crystal optics Crystal optics Crystal optics

Jürgen Härtwig Jürgen Härtwig Jürgen Härtwig

ESRF X-ray Optics Group, Crystal Laboratory

Jürgen Härtwig

ESRF X-ray Optics Group, Crystal Laboratory

• ray Optics Group

O O G

G X X

• ray Optics Group

O O G

G X X O

O G

G X X

ESRF

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 optics So we continue today with the X ray optics

Outline Outline

• 1. Introduction
• 2. Monochromators

3 S ti f t i l fl ti

• 3. 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. Introduction
• 1. Introduction
• 1. Introduction
• 1. Introduction

Some 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

• 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:

• shape

shape

• 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 in the first years starting from the discovery of X rays by the first years starting from the discovery of X-rays by

• C. 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 t Properties 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 l But - many newer developments

Quite a lot of literature Q

Overviews: Tadashi Matsushita, X-ray Monochromators, in Handbook on Synchrotron Radiation, Vol. 1, ed. E. E. Koch, North-Holland P bli hi C 1983 Publishing 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 dimensions Short remark concerning beam dimensions Short remark concerning beam dimensions Short remark concerning beam dimensions

Few years ago – micro-beams were modern, now – nano-beams are in vogue now 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 beams parallel , divergent and focussed beams.

Beam dimensions – example: paleontology p p gy

Examples from Paul Tafforeau

Nearly 4 orders of magnitude in dimension Without scanning Without magnification Without 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. Monochromators
• 2. Monochromators

100 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 reflectivity

R = 1

• rs)

10-3 10-2

d reflectivity

R = 1

• rs)

10-4 10

Integrated

High-Z Low-Z n ML's d ML's

Ge111

(Mirro 10-4 10

Integrated

High-Z Low-Z n ML's d ML's

Ge111

(Mirro 10-5 Crystals ML's h-resolution epth-graded

Si111

10-5 Crystals ML's h-resolution epth-graded

Si111

C*

111

10-6 10-6 10-5 10-4 10-3 10-2 10-1 100 high de

Be110

10-6 10-6 10-5 10-4 10-3 10-2 10-1 100 high de

Be110

• Ch. Morawe

 

E/E

High 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 p monochromators, 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 etching Orientation, cutting, lapping, polishing and etching. Strain free crystal preparation. Accurate and stable mounting. Adequate cooling scheme Adequate cooling scheme.

Crystal laboratory: Crystal laboratory:

Manufacturing of nearly all perfect Si (and few Ge) crystal Si (and few Ge) crystal monochromators & analysers, etc for 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 years in more than twenty years. Example manufacturing crystal monochromators and analysers monochromators and analysers

Which types of monochromators are used? yp

Single crystal monochromators - beam splitter monochromators

white beam white beam white beam

• monochr. beam 2
• monochr. beam 1

Double crystal monochromators

white beam

• monochr. 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 2
• monochr. beam 1

Double crystal monochromators Reflection (Bragg) and t nsmissi n (L )

white beam

• monochr. beam

transmission (Laue) geometry used

Few theory and definitions Few theory and definitions

Reflectivity (and transmissivity) curve of a crystal

plane R

Theory Plane & monochromatic

incoming wave,

plane monochromatic wave

Darwin width

R

R+T+A=1

incoming wave, varying the angle of incidence counting the diffracted photons



width

Rocking curve

Real situation - experiment

Convolution (autocorrelation) of

R T A 1

 

any wave

reflectivity (or transmissivity) curve with other reflectivity curves,

• r/and wavelength (energy)

g ( gy) distribution,

• r/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 case double 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 curve Si 111, 60keV, 10mm thick plate

Si 111, 60keV, 5cm thick plate

gg

wh



wh 

0,4 0,6 0,8 reflectivity 0.4 0.6 0.8 reflectivity

ematical Brag position

0

• 1,0 -0,5

0,0 0,5 1,0 1,5 2,0 2,5 3,0 3,5 4,0 4,5 0,0 0,2

• 1.0
• 0.5

0.0 0.5 1.0 1.5 2.0 2.5 0.0 0.2

kine

angle  - B (arc seconds) angle  - B (arc seconds)

However, in operation

known since:

• C. G. Darwin,

However, in operation – mostly fixed angle

The theory of X-ray reflection,

• Phil. Mag. 27, 315, 675 (1914)

Reflectivity curves, with stronger absorption Reflectivity curves, with stronger absorption y g p y g p

Prins-Darwin or reflectivity curve Si 111, 8keV, 5cm thick plate 0 8 1,0 Si 111, 8keV, 5cm thick plate

w   

0,6 0,8 tivity

wh

 

0,4 reflect 0,0 0,2

• 5

5 10 15 20 , angle  - B (arc seconds)

How to measure it? Not so easy! See later.

Double crystal monochromators Double crystal monochromators

Incident and exit beams have the same direction have the same direction In working position:

R

R()

fixed angle (mostly); multiplication of two

R

2

multiplication of two reflectivity curves



Two variants wo var ants

Fixed exit monochromator

• more than one movement

necessary

Two variants wo var ants

Fixed exit monochromator

• more than one movement

necessary

Two variants wo var ants

Fixed exit monochromator

• more than one movement

necessary Channel-cut monochromator

• NOT fixed exit

NOT fixed exit

• naturally aligned
• weak link plus piezo

movement for detuning etc.

Two variants wo var ants

Fixed exit monochromator

• more than one movement

necessary Channel-cut monochromator

• NOT fixed exit

NOT fixed exit

• naturally aligned
• weak link plus piezo

movement for detuning etc.

Two variants wo var ants

Fixed exit monochromator

• more than one movement

necessary Channel-cut monochromator

• NOT fixed exit

NOT 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 g 2dnh’,nk’,nl’ sinB = n

if (h,k,l)=(nh’,nk’,nl’)

Si (2n,2n,0),  = 1.6Å,  = 0.8Å, etc. Refraction correction (middle of the reflection domain):

   

B h B

sin , sin                           

h 2

1 2 sin V 2 F r Refraction correction (middle of the reflection domain):     

B uc

2 sin V 2

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 g the beam divergence, th l ti ? the energy resolution?

• 3. Some properties of asymmetrical
• 3. Some properties of asymmetrical

fl fl

• 3. Some properties of asymmetrical
• 3. Some properties of asymmetrical

fl fl p p y p p y reflections reflections p p y p p y reflections reflections

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 g the beam width and the divergence for a single crystal reflection Lin

K 

wh

in in

h

K 

Lout wh

• ut



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) Lout

h

K 

wh

• ut
• ut

K 

Lin wh

in



But all is related and things have their price

L

K 

wh

in

Lin

K

h

K 

Lout wh

• ut

B

) i ( ) sin( b        Asymmetry factor: 

h B

) sin(     w out = |b| w in This example: >0, |b|<1: wh

• ut = |b| wh

in

Relation to symmetrical reflections p Lin > Lout and wh

in < wh

• ut

w in L = w out L = constant reflections wh

in = |b|-1/2 wh sym

wh

• ut = |b|1/2 wh

sym

wh Lin = wh Lout = constant right asymmetry (<0) – less divergence possible to obtain

h

| |

h

g p

Some “philosophy” p p y

With 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 = wh

• ut Lout = constant

This is too simple, hand-waving “derivation”. We need an additional dimension for the h phase space. Besides size and angle l l h ( ) i d d also wavelength (or energy) is needed L t t t f th b i Let us start from the basics

0 = B +  - in

K 

B     in h = B -  +  out 

K h  t 

From electrodynamics (and dynamical diffraction theory)

n 

B B

dynamical diffraction theory) we know that:

K 

h

K 

0 h

h K K

h

    

For the wave vectors outside the crystal:

h

But for the tangential components - continuity:

  

t t ht

h K K  

And remember, wave vectors depend on wavelength:

) ( f K  

, p g

) (

For small in, out and K we obtain (for Bragg and Laue case!):

     

K K sin ) cos( ) cos( sin sin | |

B B B in B B

• ut

                       The divergence in and polychromaticity K/K of the incoming beam contribute to the divergence out of the outgoing beam

   

B B

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 i

• r

wh

• ut = |b| wh

in

Special case 2 P l h ti ll l i i di ti Polychromatic, parallel incoming radiation K  0, in = 0 K ) cos( ) cos(

B B

           K ) sin(

B

• ut

      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 divergence is 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!!

p s

δ

The angular source size is important for further physical properties: physical properties: the geometrical resolution for imaging, the transversal coherence length the transversal coherence length, the demagnification limit of a “lens”.

Image blurring due to non-zero source size angular source size: δ = s/p

q p s 

δ

geometrical resolution: ρ = q s/p = q δ

s 

δ

q p s 

δ

Spatial coherence Spatial coherence Transversal 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 i Geometrical 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

(g raph: J Susini) (g raph: J. Susini)

4 Shortly about high energy resolution 4 Shortly about high energy resolution 4 Shortly about high energy resolution 4 Shortly about high energy resolution

• 4. Shortly about high energy resolution
• 4. Shortly about high energy resolution
• 4. Shortly about high energy resolution
• 4. 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 ESRF ID18 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-rad acceptance: 130 nano-rad vertical size: 0.6 mm divergence: 2 rad vertical size: 0.6 mm 31 mm

2 3

divergence: 2 rad divergence: 2 rad

1 4

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 2 asymmetry: |b| = 0.18 in = 5.4º out = 31.6º angular acceptances: in = 20 rad asymmetry: |b| = 0.18 in = 5.4º out = 31.6º angular acceptances: in = 20 rad asymmetry: |b| = 9.8 in = 27.6º out = 2.7º angular acceptances: in = 0.72 rad asymmetry: |b| = 3.2 in = 35.4º out = 10.4º angular acceptances: in = 1.3 rad

in

 out = 3.6 rad footprint: 6.4 mm

in

 out = 3.6 rad footprint: 33 mm

in

 out =7 rad footprint: 41 mm

in

 out = 4 rad footprint: 3.3 mm

Other possibility – back scattering geometry

(Bragg angle close to 90 deg)

with high order reflections (large h k l)  = 2dhkl sinB ∆ = ∆  · 2dhkl cosB ∆ ∆E/E ∆ / ∆= ∆E/E = ∆/tanB )  f 10 8 d b)  d [ t () 0] Silicon @ 20KeV, h=k=l=13, (E/E) ~10-8E ≈ 0.5 meV, a)  → a few 10-8 rad b) → deg [cotg() → 0] @ , , ( )  , ID16, ID28

Sample analyser p Detector monochromator source

• 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 y g y q y measure it? measure it? g y q y g y q y measure 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 ESRF Diamonds at the ESRF

From the very beginning of the ESRF used as h l t d h t phase 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 μm2 15

2

100 μm ~15 μm2

56

X-ray diffraction topography

White beam topograph in transmission (work with Fabio Masiello) 110-oriented plate supplier: Paul pp Balog/Element Six Dislocation free areas of 11 3 mm Dislocation 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 analysis

110-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

• f the order of 4 × 10−8 for a

region of interest of 0 5 × 0 5 mm2 and

× 10-8

0.5 × 0.5 mm2 and 1 × 10−7 in a region of 1 × 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 waves polychromatic 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 wave define the character of a wave

R()

FWHM in the angular space:

P

h h h 

2   

R()

wh



g p

wh

h h B h 

  2     sin



FWHM in the wavelength space:

R()





wh



w w

h 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 10-4 20 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)

p s

not source divergence!!

p s

δ

relative wave length spread of the source (E/E) FWHM in the wavelength space

 h

w

<<

“ h ” “monochromatic” wave

angular source size  = s/p

<<

FWHM in the angular space

 h

w

“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. CuK1) 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 δ source 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 arcsec

µ-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 y

First published (direct) measurements of

fl i i fl i i reflectivity curves reflectivity 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 reflections g p ymm f in wavelength space – high-resolution mono.

• 2. Crystals of good quality.

They became available with development

• f electronics, later micro-electronics and
• pto-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 asymmetries y CuK1-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 y

• Am. 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 ld to detect extremely small strain fields in nearly perfect crystals.

Thank you for your Thank you for your tt ti ! attention!