Small-angle scattering of X-rays

Prog. Crystal Growth and Cheract. 19~, Vol. 18, pp. 1-19 0146-3535/89 $0.00 + .50 Printed in Greet Britain. All rights reserved Copyright ~) 1989 Pergamon Press plc

SMALL-ANGLE SCATTERING OF X-RAYS

H. B. Stuhrmann*

GKSS Forschungszentrum, Abtei lung Makromolekulare Struktruforschung, D-2054 Geesthact, F.R.G.

1. INTRODUCTION

There are two l ines of small-angle scattering of X-rays which play an increasingly important ro le: time resolved methods and anomalous scattering. Both techniques re ly on the high b r i l - liance of synchrotron radiation and both are applied to materials sciences and l i f e sciences. This developement has led to new kind of instrumentation and data-aquisition. Soft X-rays not only allow a higher resolution of momentum transfer but also o f fe r the use of anomalous scattering near the K absorption edges of l ight elements, e.g. sul fur, phosphorus and eventually s i l icon. Some results w i l l be presented at the end of this chapter. There are simi lar deve- iopements in neutron scattering, which w i l l be contrasted to the poss ib i l i t i es offered by synchrotron radiat ion. There has also been considerable progress in data analysis, e.g. a new method of separation of Bessel functions proposed by Svergun w i l l be discussed.

2. INSTRUMENTS

Di f f rac t ion is a process controlled by a recprocal law: The scattering angle is the smallert the larger the dimensions of the scattering object ape in comparison to the wavelength. Colloidal structures with character ist ic dimensions of some 180 A irradiated by X-rays of 1.5 wavelength w i l l give r ise to scattering into a cone with about 0.1 + opening angle. The direct ional spread of the incident beam must be considerably smaller than that which can be achieved with common devices (powder camera, rotat ion camera, etc ). The design of an appropriate camera is essential foe the experimental detection of any X-ray small angle scattering. Collimation of a su f f i c i en t l y narrow beam penetrating the sample is a basic prerequisite for recording at very low angles.

2.1. Collimators and monochromators

The easiest way is to combine two narrow pinhole diaphragms in a l ine. Foe reasons of inten- s i t y , however, l ine shaped primary beams <i.e. with a band-like cross section) have been preferred in nearly a l l f i e lds of X-ray small-angle scattering research [1] . ]he wavelength of 1.54 ~ (Cu - K~ radiat ion) is used most frequently.

Small-angle scattering experiments using X-Pay synchrotron radiation have to take into account the unique features of th is radiat ion source. The spectrum of synchrotron radiation does not show any discrete l ines as does the spectrum from X-ray tubes, but i t is continuous. I t exhi- b i ts high br i l l iance, d i rec t iona l i t y and polarisation in a wide range of wavelengths extending from the v is ib le region to hard X-rays. Synchrotron radiation is emitted in the plane defined by the closed path of the electrons circulat ing at a speed very close to that of l ight . The off-plane radiation yanishes within small fract ions of 1 + [2 ] [3 ] . The res t r i c t ion of the emitted l ight into the orb i t f a c i l i t a t e s the construction of X-Pay scattering instruments considerably. The continuous spectrum introduces a new element into the design of d i f f r ac to - meters, as very e f f i c i e n t monochromators become necessary.

2 H.B. Stuhrmann

X-ray small-angle instruments using synchrotron radiation look quite d i f ferent from common laboratory instruments. They always use crystal monochromators at least and their resolution re l i es on rather long distances between collimators. The instruments are larger. Very often much e f f o r t is put into a focussing system. The following arrangements are presently in use:

a. Bent crystal monochromator. The beam is deflected by the angle 2 0 in the horizontal plane yielding the uavelengths

n ~k = 2 d sin e ( 1 )

The 111 plane of germanium (2d = 6.53 A) or s i l icon (2d = b.32 ~) is often used as the 222 re f lec t ion is forbidden. The monochromatic beam is convergent result ing in a l ine at the focus of the bent crystal . This simple set up can be used as the incident ~hite spectrum does not provide wavelengths of the th i rd and higher order harmonics [43,

b. Bent mirror - bent monochromator. Grazing incidence of the beam on the horizontal mirror cuts o f f the short uavelength part of the X-ray spectrum. With quartz the range of wavelenghts being ref lected star ts roughly from

~ ( ~ = 0.38 e (mrad) ( 2 )

Using a bent mirror the premonochromated beam cross section converges towards a horizontal l ine. The selection of a narrow wavelength band is achieved as described under a. The X-ray photon f lux in the point l ike focus ( typ ica l l y of the order of 6.5 x 0.5 mm) can amount to about 1011 photons/second. This set up is used for time-resolved measurements [4] ,

F

Fig. 1. Schematic diagram of the double focussing camera X13 of the EMBL Outstation at DESY Hamburg. Synchrotron radiation (SR) is focussed in the ver t i ca l plane by eight plane quartz mirrors (= Sv 20 cm length each) at 20 m distance from the source point. A bent, tr iangular crustal monochromator (length : 6 cm) focusses the beam in the horizontal plane onto the sample at F. The focal distance can be varied from 3 to 6 m ( i .e . the end of the optical bench) by a bending force at P and be realigning the mirrors. The convergence angle of the beam is larger than the divergence of the beam accepted by the optical components. The size of the beam is typ ica l ly less than 1 mm 2 This kind of X-ray instrument is used now at many synchrotron radiation laboratories.

c. Bent mirror - double crystal monochromator. This system provides rapid tunab i l i t y to a desired uavelength [5 ] [6]° The mirror acts as described in b, The paral le l faces of the two crystals sh i f t the beam in the ver t i ca l plane. This may be corrected for by independent rotat ion and displacement of the axis of the second crystal [7] . - A very a t t rac t ive

Small-angle sca~ering

a l t e r n a t i v e i s t o use a t o r o i d a l m i r r o r uhich c o n c e n t r a t e s the i n c i d e n t beam i n t o a p o i n t l i k e f o c a l spot [ 8 ] . I t i s used f o r resonant X-Pay d i f f r a c t i o n .

e-

1 2 3 1+ 1 2 3 ~

Sp

$F :

9m

D3 D1

+--20cm--+

D2

SQ

I Z 3

5 m

I J

I 2 '

~ r ~ ' ~

I1

2,3m

Fig. 2. Double mirror - single crystal optics for soft X-rays (d). SF = gold coated double focussing mirror. SQ = plane quartz mirror. One half of i t is coated ui th gold (SG). MI, M2~ M3 are the crgstal monochromators which can be used a l te rna t i ve ly . P = sample exchanger. 11~ 12 = ionization chambers. DI~ D2, D3 are position sensit ive area counters. The upper inserts show the actual synchrotron radiat ion spectrum. The Iouer inserts show the d i f f rac t ion pattern of bacteriorhodopsin as i t would appear on the three detectors using 5 ~ photons. This instrument is ins ta l led at beam A1 of HASYLAB.

d. Double mirror - single crystal monochromator. This system (at DESY) provides rapid tunab i l i t y over a s t i l l uider range of wavelengths than described in c. With ~ = 7 mrad the f i r s t gold coated mirror re f lec ts wavelengths from about 1.2 A onuards. The tuo halves of the second mirror surface have very d i f fe ren t electron densities due to gold and quartz. The r e f l e c t i v i t y of the la t te r s tar ts at uavelengths around 3 A. Lateral displacement of th is mirror u i l l tay lor the spectrum to the needs of monochromatisation bw the single crystal monochromator over a uide range of wavelengths extending from 1.2 to about 8 ~. As the r e f l e c t i v i t y of crystals decreases s ign i f i can t l y (about 0.15 at ~-= 6 A from 111 re f lec t ion of 6e [11]) only one crystal is used. This means that the scattering instrument has to be turned around the axis of the crystal monochromator. The rotat ion in the ver t i ca l plane is preferred in order to avoid losses due to the polar isat ian of synchrotron radiat ion from a bending magnet section of the electron storage ring [10] . This instrument extends the use of resonant X-ra~ scattering experiments to the near soft X-ray spectrum (Fig. 3).

4 H.B, Stuhrmann

/'

pI I I

o"

~x J .L. ,, ~... ,~B ' 1 ~::: Ei]r /"'U

~'~ /:"Pb r - - " ~

6 90"

T

Xe

Fig. 3. The wavelength range of the diffractometer at beam l ine A1 of HASYLA~. Using the 111 plane of a germanium single crystal ~avelengths up to 6.4 A can be reached by rotating the crystal by e = 80 ° and the camera b~ 2 e = Ib0 °. Thus the K absorption edges down to phosphorus

(Z = 15), the L 3 absorption edges down to Yttrium (Z = 39) and the M 5 absorption edges down to iridium (Z = 783 can be used. - Replacing germanium cr~stal by indium antimonide as monochromator extends the wavelength range to 7.3 A including the K absorption edges of s i l icon (Z = 14) as well [9] .

2.2. Sable environme_nnt_

Liquid samples are usuallw kept in thinwalled glass cap i l la r ies of appropriate diameter. The optimal sample thickness of aqueous solutions irradiated with 1.5 A X-rays is 1 mm. I t depends strongly on the wavelength. With 3 ~ X-rays the thickness has to be adjusted to 1 / 23 = 1/8 mm and at 6 ~ i t further decreases to 1 / (8 * 8) = 1/64 = 0.016 mm. Glass cap i l la r ies then are no longer useful. They have to be replaced by plast ic windows with a few pm thickness.

As the beam path in small angle instruments may have a length of several metres, absorption by a i r ~ i l l reduce the intensity considerably. 1 m a i r absorbes X-rays to nearly the same extent as 1 mm water. Then only 1/e = 36 % of 1.5 A X-rays are transmitted. Soft X-rays are strongly absorbed in a i r . The penetration depth of 6 ~ X-rays in a i r is onl~ 16 mm.

I t is for th is reason why the X-ray beam path has to be f i l l e d with helium or evacuated. Evacuation reduces the scattering from gas. X-ray small angle instruments are either put into a large vacuum vessel (camera) or they are made of a series of evacuated tubes with very thin windows at the entrance and ex i t of the beam. Large windows for the connection to area detectors are either made of beryllium or more recently by a thin p last ic f o i l supported by a steel grid [7 ] .

Small-angle scattering 5

2.3. Detectors

X-rags are detected bB xenon f i l l e d proportional counters in most cases. In the last 15 gears position sensit ive counters have come into use [11]. The spatial resolution of l inear position sensit ive counters may reach 0.05 mm. Two dimensional multiwire proportional counters (MWPC) with a sensit ive area of 200 x 200 em usually resolve 2mm in x and y direction [7] . The detector is based on the delay l ine method [12] [13] [14]. When an X-ray photon traverses the gas of the detector chamber i t loses energy due to ionisation of gas molecules. In a Xe-CO_ mixture th is is i electron-hole pair fop about 27 eV of energB loss. BB means of thin ano~ wires at high voltage (+4kV) one produces a region of high e lec t r i c f i e l d in the gas. In the proximity of the wire the charges are amplified ( x 10.000) in an avalanche l ike fashion. On the cathode sides in front and behind the anode wire plane, one makes these charges propagate along the delaB l ine. The differences in time of a r r i va l at the respective ends of the delaB l ine corresponds to the position at which the photon arrived. The area detectors we use are equipped with 300 nsec total delag which means that about 3 105 positional determinations/see can be performed uith less than 20% coincidence or dead time loss.

The detector associated electronics have to d ig i t i ze the differences in time of a r r i va l at the ends of the deaIB l ine. Classical methods have re l ied on time-to-pulse-height conversion followed bB pulse height anaIBsis. A considerable improvement in speed was achieved by direct time d ig i t i za t ion [15]. The sBstem is capable of handling about 3 105 events/sec.

Further increase in speed of data taking is expected bB segmentation of detectors each detector having i t s own read out sBstem. A l inear position sensitve detector developed recently at EMBL consists of 12B anode wires each of them acting as individual counter. The integral count rate is 10 HHz of s t a t i s t i c a l events. - A simi lar developement has been started for area counters. The new diffractometer for X-Pay resonance scattering in HASYLAB is equipped with three area counters (Fig.2). This sBstem can handle nearlg a mi l l ion s ta t i s t i ca l events per second [9] .

High spatial resolution of about 0.1 mm on a smaller area of 80 mm diameter is achieved by a vidicon camera (e.g. from Westinghouse) [16]. The X-rams are converted to electrons on a screen (10 pm thick lamer of 6dosoO:T b or 30 ~m ZnS(Ag) from Proxitronic, GermanB) Ioacated on the surface of a 7 mm thick ~n~ 80 mm wide f iber optics plate (6al i leo, USA). The charge pattern is created on the s i l i con target of the Vidicon and is read out in the fast scan standard technique (25 frames per second). - This sBstem is verg convenient for handling verb high count rates of 108 or so. For low intensitB applications~ which is the case in small-angle scattering studies, the charge mag be integrated on the target for up to 999 frames before i t is read out. The signal to noise ra t io is of c r i t i c a l importance for such applications. The noise mainIB results from the dark current and can be reduced by cooling the target.

The present modern position sensit ive counters in general cope uith the scattering intensitB produced at the present sBnchrotron radiation sources. As an increase of the br i l l iance of sBnchrotron radiat ion bB 1000 to 10 000 is expected with planned electron storage rings considerable e f f o r t has to go into the developement of area detectors and their read out sBstems.

2.4. Data aquisit ion

In a typical experiment we want to record the scattering pattern as function of

- time - eavelength

in time-resolved experiments or as a function of in resonant X-rag scattering experiments

In addition we have to monitor

- the physical or chemical state of the sample in time resolved experiments or - the absorption of the sample in resonant scattering.

Time resolved experiments ape mostly done with l inear position sensit ive counters. Scattering patterns <256 channels) are recorded as a function of time (25b time frames of programmable length) together eith the chemical state of the sample. In the case of microtubuli assembly [17] the parameters are temperature and the time at which assembly is init iated~ either bY temperature jump or rapid mixing. One of the major d i f f i c u l t i e s in this experiment is the sheer volume of information one has to col lect for a proper characterisation of the sample. With 256 detector channels and 16 cal ibrat ion channels one experiment contains up to 25a x <256 + 16) =

6 H.B. Stuhrmann

~9.632 data items (16 b i t each), and several dozen experiments can be performed during one 8 h sh i f t of each beam time. The present system at the EMBL Oustation at Hamburg can cope mith this data at a rate of about i MHz, and time framing being chosen betmeen lysec and 90 min. [14].

Resonant X-ray scattering is usually recorded at 5 to 30 d i f ferent wavelengths near an X-ray absorption edge. Using three position sensit ive area counters shomn in Fig 2. 65.536 data items represent one scattering pattern. One scan typ ica l ly produces 20 x bS.53b = 1.310.720 data items in about one hour. On-line data reduction then becomes necessary.

2.5 Time resolved scatter ing.

In principle the chemical reactions to be studied by time resolved X-ray scattering could be induced by any of the classical perturbation methods, such as temperature jump, rapid mixing, or pressure jump, etc. [18]. One severe constraint is that the glass or saphire windoms used for optical detection methods are opaque for X-rays. Thus one has to replace them by thin sheets of mica, Lindemann glass, or beryllium. This maw lead to transient changes in e f fect ive cel l thickness mhich can obscure the signals arising from the chemical reaction. The problem is noticeable in mixing devices and makes pressure jump experiments very d i f f i c u l t .

For temperature jumps or scans the specimens are contained in a thermostated cel l with mica mindows mhich are su f f i c i en t l y transparent to X-rags (30 - 50 ~m). The cel l is constructed in a hollom copper block, through mhich one drives either very cold (-20°C), cold (0°C), warm (37*C) or hot (70*C) mater or mater glycerol mixtures. With a combination of fast valves and electronic servoloops one can change and s tab i l i ze the temperature with time constants of about 1 - 2 sec This set up has been developped at the EMiL Outstation Hamburg for the investigation of microtubuli assembly [14].

For higher temperatures up to 300°C a modified device is used. The block is heated by heating cartridges, simi lar to those used in soldering irons. The sol id sample is wrapped in thin Al f o i l s and clamped to a brass support which f i t s into the copper block. The sample is driven by a remotely operated pneumatic piston into the preheated copper block. Thermal eqil ibrium is reached at 200 °C in about 100 sec. This unit is being used for the investigation of phase transi t ions in polymers in the synchrotron radiation laboratory, HASYLAB at DESY [15]. A modified sample holder for the study of melting and crystal l izaton experiments is used at Novosibirsk [19].

Relaxation experiments in the second and certainl~ in the subsecond range have to be repeated many times in order to obtain the time dependence of the scattering pattern with reasonable accuracy. Rapid mixing experiments for the study of the recombination of isolated ~ - and B-chains of hemoglobin needed 200 shots in order to fo l lo~ the increase of small-angle scattering du to the hemoglobin formed [20]. The time constants involved are of the order of some ten seconds. The mixing chamber for X-ray scattering experiments has been developed by M. Moody [21]. More e f f i c i e n t mixing devices have been bu i l t recently by R. Rigler [22].

3. SOLUTION SCATTERING

There are several reviews on the subject of solution scattering theory [23] [24] [25] [26]. and the use of synchrotron radiation in biology [27]. The approach to the elucidation of structure and function of mocromolecular systems by small-angle scattering is complementary. Time resolved scattering experiments look at structural changes, assembly and dissociation processes. Resonance scattering is a physical method of selective 's ta in ing ' of a macromolecule for the pourpose of molecular structure research. Suppose an assembly of atoms which defines a macromolecular structure o(r):

m

Time resolved scattering experiments w i l l look at changes of the atomic co-ordinates ~" ~hereas in X-ray resonant scattering experiments i t is the atomic form factor f ~hich is of interest. The changes in a scattering pattern is more readily amenable to a detai~ed analysis i f the perturbation concerns re la t i ve l y small parts of a macromolecule. This approach not only helps to elucidate the pathwa~ of assembly and conformational changes of macromolecules but i t is also the strategg of structure research. F i rs t ~e shall look at the scattering process of individual atoms ~hich leads us to the description of X-ray anomalous scattering. A comparison with spin dependent neutron scattering mi l l be given.


3.1. Scatterin9 of a single atom

When the wavelength of the incident X-ray beam is close to the absorption edge of an atom, the atomic scattering factor becomes complex to a greater extent

f ( ~ ) = fo + f ' ( ~ ) + i f " ( ~ ) ( 4 )

f~ is the short wavelength l im i t of the scattering amplitude. Following the t rad i t ion of X-ray dYffraction f is given in electrons, e.g. f~(o) of iron is 26. The scattering length of one electron is 2.8 10-'~mm. f ' and f" exhibi~ a wavelength dependence or dispersion. The absorption edge for X-raus represents the threshold frequency above which an inner electron can be ejected into the continuum. The resonance absorption also known as photoelectric absorption is an ine last ic channel. The opt ical theorem for X-rays then is

e ~ photoelectr ic = 2 ~ ~ f " (o) ( 5 )

Since 6 . . . . . , . . . . . . exists only on the short wavelength region of the absorption edge, so also does f " ~ u ~ L ~ e r s i o n of f"(O) is f u l l y control led b~ ~hotoe lec t r ic " For the K edge, photoelectr ic is represented f a i l r l y well by the empirical formula

6 photoelectr ic ( Od~ 13~ = ~ j photoelectric ((xJK) ( b )

Since for photons k = U:/c, f " (~) should vary with the frequency roughly as 1 / ~ F i g . 4 shows that the dispersion of f"(O) is s l i gh t l y more complicated as ion i - zation of p and d electrons w i l l give r ise to addit ional abrupt changes of f .

L, L. ,

10 8 6 lC',,

' ' J i ' ' ' ' ' ' 1 , v

I,.l l . . . . ,=JJ , ~ i J

121 o2 l ~ 1 Z ..'3

Fig. 4. D~spersion of the imaginary part f " of the atomic foPm factor of uranium, f" <in units of electrons) reaches nearl~ two th i rd of the non-resonant atomic form factor f = 92. The schemati~ representation has been taken from The Internat ional Tables of Crystallc~aphy IV. The dispersion of f " shows strong peaks at

the M v and M. absorp- t ion edge [28~.

2O

In fact the schematic representration of the absorption edge in Fi9.4 has to be replaced by a mope structured dispersion pPofiles at higher frequency resolut ion, as is shown in Fig.5.

8 H.B. Stuhrmann

{,

°1 60

50

30

10

{o

L., L,, L,

I

4~ i I I

t~ t.6 /,5

Fig. 5. Dispersion of f + f ' of europium in Ec~(PhAcAc) at the three absorption edges af ter af ter Lye, Phi l l ips, Kaplan, Doniach and Hodgson [29]. The f ' values were calculated by using the Kramers - Kronig re lat ion (E~. 10). The absolute scale (in electrons) re l ies on values of f" and f ' which were taken from The In- ternational Tables of Crystallography IV.

The absorption coef f ic ient ~ (in mm -1 and density 1Mg/m 3 is

2 ~ ~ e ~ 337 ~ f. = ~ f" = ~ ( 7 ) /v~ nnc~ /v~

(N L = b.02 1023 , M = atomic weight, e2/mc 2 = 2.8 10 -12 mm) From the numerous empirical formulae used for the Computation of X-ray absorption coeff ic ients we just mention

= 0.016 >3 Z3.94/M ( 8a ) = 0.000529 ~k. 3 Z4"3/M ( 8b )

Z is the atomic number. On passing the X-ray K-absorption edge from lower to higher frequencies the absorption coef f ic ient ~ w i l l increase by the factor 63.868 / Z0.6207. Since the spatial d istr ibut ion of the core electrons is confined to a very small volume near the nucleus, f" (and f ' ) show a re la t i ve l~ weak dependence on the scattering angle. Onl~ few experiments have been done to confirm theoretical predictions, e.g. on Barium [30] with MoK ° radiation where

f " ( ~ ) = 2.40(5) - 0.59(11) sin2e / ~ 2

The physical process of resonance neutron scattering is through the formation of a 'compound nucleus'. 113Cd, 149Sm and 157Gd belong to the small class of nuclei which exhibi t a resonance in r 113 114 • the the mal energu region. In the case of Cd the compound nucleus Cd w i l l either eject a neutron in an (n,n) process or emit ~ -rays in an (n,~-) process the la t te r being in- e last ic . Unlike in X-ray anomalous dispersion, in the present case both the e last ic (n,n) and inelast ic (n, ~ ) processes contribute to b'(O) :

(n,n) + ~ (n,E) = 2 ~ f"(O) ( 9 )

The measurement of the tota l cross section determines completely the dispersion of f " . - The


dispersion of the real part is not independent of that of f " t for there exists a general relationship between them known as the Hramers- Kronig relat ion:

~:' u..F T " ( o o ' ) 2,

Thus a knowledge of f ' ( ) over a suf f ic ient ly wide frequency region permits the evaluation of f ' ( ). With X-rays the frequency interval of strong anomalous dispersion mad be verb narrow. Then Eq.(10) simplif ies to

4~

~- "~Ir(u'>+~ d& ( 11 ) 4

f ' ( u O ) = - "~1 , . , E,

where ~ is of the order 0.01 . ~--~

The dispersion of the resonant nuclear scattering amplitudes compares to those encountered at the L 3 absorption edges of rare earth ions. There are however important differences between these two kinds of resonance phenomena, une of them is that that resonant thermal neutron scattering extends over a rather wide sPectral range, whereas the region of strong anomalous dispersion is limited to the close v i c in i t y at X-ray absorption edges. In fact, the interval l of dispersion may be so small that the angular distr ibution of X-raw reflections hardly changes in an resonance scattering experiment, ~hmreas neutron di f f ract ion patterns ~ i l ] move considerably in the detection plane on passing through the resonance. Resonant neutron scattering experiments may require isotopic enrichment of the nucleus in question~ as the natural abundance of the resonant isotopes mentioned above hardly exceeds 15% .

The interplay of f ' and f" becomes clearer when the amplitude f is represented in the plane of complex numbers (Argand diagram ). As is shown in Fig.(6) f of iron in f e r r i t i n , an iron storing protein, follows two third of a circular l ine at wavelengths near i t s K absorption edge at ~. = 1.743 ~ [31] . In the case of nuclear resonance a nearlw closed circle ~ould be observed. Anomalous X-ray scattering at the L 3 edges of rare earth atoms verb often sho~s a strongly enhanced Peak at the absorption edge ~ielding an Argand diagram verb similar to nuclear resonance. The strong variation of the resonant amplitude of these elements has gained considerable importance in X-ray resonant di f f ract ion [29] [32].

t E

x,,.- 1. 3 -o.o,

~-X~ / ........ 0

i J ~ °- ~1¢, s ..-"

-0,01 0 ' I ' t 8

1

4-- ~Ok)

- Io -8 -6 | | . • . ,

t f"

Fig. 6. Construction of the Argand diagram from the dispersion of f ' and f ' . f ' is taken from the dispersion of apparent radius of gy- ration~ Rv of f e r r i t i n f" is Proportional to the absorption of the f e r r i t i n solution at the K absorption edge of iron a t e = 1.743 ~. [33].

ImCO--B

10 H . B . S t u h r m a n n

3.2. Spin dependent neutron scattering.

The interaction between an atom and a thermal neutron may be expressed by a scattering amplitude operator which contains three main terms [34]

A = b + 2 A ~±.'~ + 2 3 7. ~ ( 12 )

The f i r s t and the th i rd term take into account the interaction between the neutron and the atomic nucleus. The f i r s t one, b is the isotopic nuclear scattering amplitude. The th i rd expresses the interaction between the neutron carrying a spin ~, and the nucleus , carrying a spin I.

The well-known second term corresponds to the dipolar interaction between the electronic moment of the atom, and the magnetic moment of the neutron with i t s spin s. M'i magnetic

denotes the component of the magnetization normal to the scattering vector q. The scattering length of an unpaired electron with spin s in paral le l arrangement to the neutron spin is

b = b ~ S = 0.28 10 -12 1.97 1/2 = 0.27 10 -12 cm ( 13 )

where l~ is the magnetic moment of the neutron expressed in nuclear magnetons and S the spin quantum number of the electron. This formula is also a good approximation for the evaluation of b of the many - electron systems of the t ransi t ion elements. The value of b w i l l then be d i f fe rent for d i f fe rent valence states of an atom such as Fe ~'+ and Fe ~+ , for which the S values are 2 and 5/2 respectively. Eq. (13) can be rewrit ten as

b= ~ 2S ( 14 )

containing the factor 2S for an atom in which the orb i ta l momentum is completelu quenched, is equal to the magnetic moment expressed in Bohr magnetons. With the rare earth ions the spin orb i t coupling of the atomic electrons has to be considered as well [35]. Some of these ions exhibit very high magnetic moments. As the ~ave functions of the atomic electrons can be calculated to reasonable precision , the X-ray and magnetic neutron scattering amplitudes of dipolar interaction type can be predicted on theoretical grounds.

Coming back to the f i r s t and the th i rd term in Eq.12 le t us reca l l , that they may be expressed as a function of b c÷~ and b c-) . These are the nuclear scattering amplitudes corresponding to the scattering processes in which I and s couple in the channels I + 1/2 and I - 1/2 respectivelu. One has

c~'*~) b~*~ I b ~'-~ b ~''~- b c-; b = and B = ( 15 )

~I +4 2~]~ +,I

The so called spin dependent scattering length B enters into the scattering amplitude in an interesting way. To show this we consider a very simple case, a crystal bu i l t up of identical atoms of only one nuclear species with non-zero nuclear spin, without any electronic moment, th is crystal having only one atom per unit ce l l . Then there w i l l be coherent scattering

= -B--B

IFl I b ~ + ]B ~ I ~ P~ + 2 b B I P'n ( 16 )

and incoherent scattering

~ = B~ I ( I + I ) - Bi I i P :L- B~ I -~.~ ( 17 ) inc

where P and n describe the spin of the nuclei and neutrons respectively. Depending on the d i f ferent combinations of nuclear and neutron polarization , the following cases emerge [34]

Polar i zat ion coherent incoherent nuclear neutron scattering scattering

0 • / n b ~ B $ I ( I + I ) P 0 b:~+ B~I~P ~ BZl( l+l) - BzI2"P ~ P n b~'+ B2"I~"P z 2b ~ ~'~ B : ~ I ( I + l ) - ]B~'I':'P ~'- I~'I ~.n"

We notice that the three terms of coherent scattering can be determined separately just by choosing various combinations of nuclear and neutron polarization. This is a unique feature which is not encountered with other techniques of contrast var iat ion.

In the case of hydrogen (proton spin I = 1/2) we have

Smal l -angle scattering 11

-.i~. b(-) -tZ b (+) = + 1.085 10 cm = - 4 . 7 4 10 cm ( 18 )

and therefore

-tZ -b?- b = - 0 , 3 7 5 10 cm ]3 = + 2 . 9 2 10 cm ( 19 )

Today, intense beams of polarized n~utrons can be produced [36] . With col l inear or ientat ion of nuclear and neutron spin ue have P.R = P with ( - i < P < 1 )

Polar izat ion coherent nuclear neutron scattering

0 0 b ~" P 0 b~+ - ~ B P P n = I ( b + --~' BP ) ~

The e f fec t ive coherent scattering length of the protons then is

b = ( -0.375 + 1.46 P ) 10 -12 cm

incoherent scatter ing

3 ( P - - ~ P )

( 2 0 )

We note that there is no incoherent scattering i f the proton and neutron spins have equal direct ions of polar izat ion. This is not the case with ant ipara l le l spin or ientat ion , where ue have strong incoherent scatter ing.

3.3. Scatterinq by oriented macromolecules

The description of of resonance scattering s tar ts from an assembly of M atoms eQtJlof them having f ixed coordinates ~n with respect to an or ig in. Out of these a smaller number N of atoms is supposed to have a strong resonance scattering. The structure ~ (~) is then represented by

~ ( ~ ) = ~ f ~ (~ - ~n ) + ( f ' + i f ' ) ~ ~ (~ - ~n ) ( 21 ) n=~ 0 M=4 e U(7) + ( f ' + i f " ) V(~)

I t has been assumed that a l l strongly resonant scatters have the same dispersion i .e . thew represent the same chemical element and they are assumed to have the same chemical environment. With U(~) and V(~') as the real and imaginary part of ~ (~) respectively, we obtain the scatterin9 amplitude of the structure ~(~) as

F(h) ~ ~ [ U(~) + iU(~)] e i~''~ d3~ ( 22 )

ehere-~ is the scattering vector and h = lh'l = 4 ~ ( s i n 0) /4 . The mul t ip l icat ion of F(~) with i t s complex conjugate

F * ( ~ ) ~ ~ [ U(~) - i U ( ~ ) ] e - i ~ ' ~ d3 r ( 23 )

Bields the scattering in tens i ty S(E)

s(~) = A(~') A*(~') = ~ [ U ( ; ) + i V ( ~ ) ] [ U ( P ) - i V ( ~ ' ) ] e i ~ ( ' ~ - ; ' ) d3 r d3r ' ( 24 ) = S E [ U ( 7 ) U ( P ) + v G ) v ( ~ ' ) ] cos [~" (F - ; ' ) ] d3r d3r '

+ E ~ [ U ( F ) V ( P ) - V G ) U ( ; ' ) ~ sin [T; (7 - F ' ) ~ dar ~ r '

Separatin9 the resonant real part we obtain

S(h ) = ~ ~ u ( ~ ) u ( F ' ) c o s [ ~ (~ - ~ ' ) ] d3 r d3 r ' ( 25 ) + 2 f ' ~ ~ u ( ; ) v ( 7 ' ) cos[h" (7 - ; ' ) ] d3 r d3 r '

+ ( f , 2 + f . 2 ) ~ f v ( 7 ) v ( 7 ' ) c o s [ E (7 - F ' ) ] d3r d3~ ' + f " 13 [ u ( ; ) v ( ; ' ) - v ( ; ) u ( 7 ' ) ] s i n [ ~ ( 7 - ' ~ ' ) ] d3 r d3r '

= Su(E ) + f , Suv(E) + ( f , 2 + f . 2 ) Sv (~ ) + f . ~(-~)

The overal l e f fec t of resonant scattering is to cause the break down of Fr iedel 's law so that the Bi jvoet pairs of Peflections S(h) and S(-~) are unequal (see e.g. [37] ). The difference

S(h) - S(- 'h) = 2 f" (~(~) ( 26 )

12 H.B. Stuhrmann

is used to determine the absolute configuration [38].

We now compare the resul t of resonant scattering with the corresponding formalism of neutron scattering. I f X ( 0 < X < I ) is the degree of isotopic of an element then X in

w i l l influence neutron scattering in the following wa~:

s<~) = Su<~> + XSuv(~ + x ~ s v ( ~ ( ~ a )

Nuclear spin dependent neutron scattering is described by

S(~) = Su(~) + ~ .~ Suv(~) + p2 Sv(~ ) ( 29 )

Assuming completel~ polarised neutrons ( compare Eq. 2~) the two preceding equations become more simi lar.

In Eq. 29 i t has been assumed that there is only one kind of nuclear spins which is going to be polarised, e.g. the proton spins. In practice, labels r ich in protons are embedded in a deuterated matrix. I t is therefore desirable and achievable to have proton spins and deuteron spins polarised se lect ive ly . Then Eq. 29 is va l id . I f both hydrogen isotopes are polarised the experiment w i l l ~ield the sum of the contr ibutions of polarised proton spins and deuteron spins to neutron scatter ing.

3.4 Scatterin~ by free molecules.

A f i r s t step towards the consideration of free, randoml~ oriented molecules (or microcrystals ) is the superposition of S(h) with S(-~). Onl~ the cosine terms in Eq.(25) ape conserved. Introducing the wavelength dependence of f ' and f " exp l i c i t e l y , we obtain by integration of S(~) over the sol id angle J-L [33] .

l(h, ~) = ~ S(h, ~) d~ ( 30 = ~ ~ u(~) u(F') sin h l ~ - ~ ' f / t F - ~ + I d 3 r d3r '

+ 2 f ' (X ) ~ ~ u ( r ) v ( r ' ) s in hl~ - ~ ' ( / I F - ~ ' l d3r d3r ' + [ f ' 2 ( k ) + f " 2 ( X ) ] ~ ~ v ( r ) v ( r ' ) s in h l F - F'I / t ~ - ; ' l d 3 r d3r '

= Iu(h) + f ' ( Y ) Iuv(h) + [ f , 2 ( k ) + f " 2 ( X ) ] Sv(h)

Macromolecules in solution as descibed by Eq.(2B) give r ise to three basic scattering functions. I . ( h ) is the off-resonance scatter ing, I v originates from the structure of the resonant scatterers alone, and I v(h) is a cross term, containing the influence of both u(r) and v ( r ) as the i r convolution. I~ many cases the resonant scattering terms in Eq.(30) may be much smaller than lu(h) . The quadratic term in Eq.(30) then can be neglected and we obtain

I ( h , ~ ) = Iu(h) + f ' ( ~ ) luv(h) ( 31

This equation stresses the dominant role of f ' in resonant scattering of noncrystal l ine structures. As can be deduced from Fig.(3) resonant scattering in th is case w i l l be observed In the very close v i c i n i t y of the absorption edge. This is quite d i f fe rent from d i f f rac t ion by non-centrosymmetric uni t cel ls where the f " dispersion according to Eq.(25) allows resonance scattering measurements even at much shorter wavelengths than that of the absorption edge [39]. The tunab i l i t y of synchrotron radiat ion to the narrow regions of strong dispersions of f ' near the absorption edge for the f i r s t time created the necessary conditions for successful measurements of resonance scattering from disordered systems which is basical ly linked to f ' ( ~ ) Iuv(h).

The analysis of the resonant solution scattering data demands a d i f fe rent representation of the Debye equation (33). I f the macromolecular structure would have a spherical appearance, then the formalism of isomorphous replacement in single crystal d i f f rac t ion outl ined in the preceding section would appl~. This is not surprising as the rotat ion of a spherical structure could not be noticed anyhow. In more complicated, asymmetric macromolecular structures i t is the spherical average of the structure which can be subjected to the phase analysis described above. As th is statement is less t r i v i a l , we shall extend the description of a macromolecular structure beyond i t s spherical average by introducing an expansion of ~ (F) as a series of spherical harmonics Ylm ( uJ )


~ ( ; ) = ~E m: ~ ~ Im( r ) Ylm(~ ) ( 32 )

where 91m(r) S~(;) " = Ylm( uJ ) d~

oO is a uni t vector in physical space The amplitude F(~) again is represented as a sum of par t ia l waves :

F(~) -->_ ~ (h) Ylm(~Z) ( 33 )

where the radia l functions are uniquely related by Hankel transformations

q'~-i 1 ~ ~ l m l r ) J l l h r ) r 2 dr ( 34 I Flm(h) = i

~)lm (r> = / ] ~ ( - i ) l ~ Flm(h) J l ( h r ) h 2 dh ( 35 ) h=O

On averaging F(h) F*(h) with respect to a l l o r ien ta t ions ( J ~ ) in rec iprocal (or momentum ) space ue obtain

I (h) = 2 IT 2 ~ Flm(h) Flmlh) ( 36 ) ~-=o =-(

This is the form of a scalar product which can be wr i t ten as I = ~ F I F > . Each multipole ~1.(r) YI.(~O ) has i t s own scattering function I Flm(h)l 2. In ~ar t icu lar , the scattering of the average structure appears as the monopole scatterlng (F__(h)l • Thls representatlon of the scattering from randomly oriented par t ic les gains considerable importance, as i t opens a general way of separating the various multipole contr ibutions to I (h ) . In fact Svergun, Feigin and Schedrin have proposed an algorithm which allows to dist inguish between groups of multipoles with the same index 1. [40]

"t~=-t ~ ~lmlr) Vlm(b°) ~- . . . . . . . -> ~= -~ I Flmlh) IZ ( 37 ) This means that there is a ua~ to separate the monopole scattering ( l = (D) from the scatter ing of the three dipoles p ~ p., Pz ( l = 1; m = -1,8,1 ) and the f i ve quadrupole functions (1 = 2; m = -2,-1,0,1~2 ) and"incFeaslnglB bigger groups of higher multipoles . To merge th is mathematical analusis of I (h) with the method of resonance scattering we modifu Eq.(32)

~(~) = ~o ~ [Ulmle) + I f ' + i f ' ) V lm l r ) ] Y lm(~) ( 38 )

Flh) = ~ [Almlh) + I f ' + i f " ) I~lmlh)] Ylm(.~-) ( 39 )

The dispersion of l (h) then writes

I (h) = ~ rn=-t ~ Almlh) + f '[Almlh)Blmlhl+Blmlh)Almlh)] + (f ,2+f.21 Blmlh) ( 40 )

More e x p l i c i t e l y and omitting (h) we obtain

I (h) = AooAo ° + 2 f ' Aoc~o o ( f ,2+ f ,2 ) ]BooBo°

i l oA lo + 2 f ' AloBlo ( f ,2+f ,21 ILoB I 1_1A1_1 + f ' (A1_1B1_1+B1_1A1_1) • (f:~2+ff:22! _~1-1~1-1 11 Al l + f ' (A l l B I I + B I I A l l ) + ( f ~ ~ I I 011

+ 2f ' A20020 .2 cr~o

+ ( f ,~ - f ) ~^_.B2_ 1 o -1 + f ' (A2-1]~2-1+B2-1A2-1) + ( f ,2+ f .2 )B2,1B~, .A21 6"21 + f ' (A21 B21 + B21 A21)

+ f ' (A22 B22 + B22 A22) ( f 22 B22

more blocks with 21 + 1 l ines ma~ follow ( 41 )

The strategw of data analysis is now at hand. Contrast var ia t ion determines the colums of Eq.41 whereas groups of ro~s of 21-1 terms can be ident i f ied ~i th the Svergun method r40].

For I=1 the monopole structure can be determined completely i f B (h) is known. In fact , the oo

phase problem of F reduces to the determination of the sign of Foo . This is usually not too d i f f i c u l t a t ~ k for B o~ as plausible arguments can be made concerning the corresponding radia l mass d is t r ibu t ion Voo(r ) of the resonant label atoms. Once the signs of

14 H.B. Stuhrmann

the sinusoidal function B (h) are known for each peak, the phases of Aoo(h) can be determined direct ly by using°~he cross term.

I f the structure is elongated the quadrupole terms (d-functions) have to be considered. Out of the f ive terms three can be elimated by rotation of the structure by the Eulerian angles oC, and~ . Thus we are le f t with [41]

I2 (h) = A21(h) A21(h) + A22(h) A22(h) ( 42 ) I2 u (h) A21(h) B21(h) + A22(h) B22(h) ( /+3 ) I2v~h) B21(h) B21(h) + 322(h) B22(h) ( 44 )

I2 denotes the basic scattering functions for 1=2. I t is also assumed that the complex radial functions have been converted to real functions A2 and B2 by appropriate linear combinations of the A_ and B -. Again i t is assumed that the spatial distr ibution of the resonant atoms is siepl~menough2~o guess the signs of B21(h) and B2?(h) . Then A21(h) and A29(h) can be found by the following geome~r;cal cons~ructioh which has To be made for each h-Int~rval l . In the A21

; q A 2 ~ - T ~ l a ; e w E ~ 4 2 e r ~ : ; e p : n t s ~ ~i2rcl ~ U~iaCh s isSliu;tioe~;eoC~e~hbUe~ ~tr~ghtyliu::n:efa~ned by • • 2 2 " , - , "

approximation of the radial functions by rather few members of a series of polynomials a correlation between the solution in various h-intervals can be achieved. Laguerre polynomials are of particular interest because of their simple transformation properties [41].

The evalution of the three At_ leads to a construction in three-dimensionals space. The solutions are found as the inter§Wction l ine of a plane with the surface of a sphere. With increasing index 1 of the multipoles the correlation between the resonant structure and the whole structure through the basic scattering function I (h) usually gets weaker and ~eaker.

As an important result of this jo in t use of resona~ scattering and advanced multipole analysis we note that a part ial structure ~ u ] . ( r ) y1 . (~ ) can be sp l i t into i ts constituents b~ the introduction of the known resonant l ~ e l structures v1_(r) Y~m(~). In the case of the quadrupole structure, one obtains the relat ive orientation of t~e mai~ axes between the resonant structure and the total molecule. I f a different resonant structure can be used, more information can be obtained, as the non-resonant structure gets convoluted with an other reference structure as a probe. This procedure might gain considerable importance in ribosome structure work [42].

Very often i t is not possible to obtain a l l basic scattering functions with the same accuracy. In resonant scattering we are often l e f t uith the cross term I (h) only This is s t i l l quite

UV . "

an acceptable situation, i f the resolution to a monopole approx~matlon of the structure is required, as Aoo(h ) and Boo(h) may be determined completely from the two remaining functions I. (h) and I,,v(h). Hoeever a straight-forward method for the evaluation of higher multipoles in t~e sense o¥ the above calculation then cannot be used an~ more.

4. RECENT ADVANCES IN CONTRAST VARIATION

Neutron di f f ract ion in H?O/D?o mixtures is probably the most often used technique of contrast variation. The excbangebf tSe mother liquor of protein crystals or of solutions does not present any problems in general. In a similar wag heavy metal atoms are introduced, part icular ly into protein crystals, uithout any apparent change of the molecular structure. Here, the success is less certain. Both methods are presently extended by - anomalous scattering of native labels, e.g. sulfur and phosphorus, and in - nuclear spin dependent coherent neutron scattering

The use of native labels avoids the d i f f i c u l t task of finding isomorphous derivatives. Sulfur is present in the amino acids methionin and cystein. The lat ter very often form disulf ide bridges between adjacent protein chains. I t is an important constituent of rubber and i t is also found in fossile fuels and many minerals. Phosphorus is present in ribonucleic acids and in polar head groups of membranes.

The isotopic exchange of hydrogen in subcellular structures has made considerable progress [42]. Labels of nearly any size can be introduced to any si te of a large biological structure. This is the preparative basis for the use of nuclear spin dependent neutron scattering.

4.1 Anomalous s c a t t e r i n g o_f. lsulfu~

The use of 5 ~ X- rays near the K abso rp t i on edge o f s u l f u r has to overcome s e v e r a l t e c h n i c a l d i f f i cu l t i es uhich are due to the strong absorption by nearly any kind of matter. Biological


samples have to very thin. The optimal thickness is about 30 pm. The detector s t i l l has to be e f f i c i e n t and the monochromator system should transmit only the fundamental wavelength (n = 1 in Eq. 1). Using synchrotron radiat ion the qual i ty of the premonochromator as shown in Fig.2 is of utmost importance. In view of these problems a f i r s t t ry has been made with two-dimensional bacteriorhodopsin crystals. The uni t cel l dimensions of the hexagonal arrangment of th is membrane protein ape 63 ~. A sample of appropriate thickness is easi ly prepared by sedimentation of the small membrane sheets onto the surface of a thin p last ic f o i l . As the ~ater content of the sample is very low i t can be introduced into the vacuum of the instrument (Fig.3) wihout major damage to the crystals. The choice of a c rys ta l l ine structure of fers several advantages : - the eventual contamination of the monochromatic beam by higher order

wavelenghts ( ~ / n , n = 3141... with Ge(111)) would lead to addit ional d i f f rac t ion rings.

- the spat ial resolution of the position sensit ive area counters can be characterised mope readi ly .

- and f ina l ly1 the successful experiment should reveal the spat ial d is t r ibu t ion of the ? sul fur atoms among the 9 hel ical rods of th is membrane protein. This s t ructura l information would help to f ind the N- and C- terminal of the the protein chain.

The performance of the instrument at the beam l ine A1 of HASYLAB was quite sa t i fac tory . Apart from the expected energy resolution of 1 eV (Fig. 7) at the K absorption edge of su l fur , E = 2470 eV, the main resul ts were: - the contamination by th i rd order harmonics is small. I t does not af fect the

d i f f rac t ion pattern of the 5 ~ photons. - the multiwire proporional counter f i l l e d with At/CO 2 (7/3) is s t i l l

act ive. The spat ial resolution is about 4 mm ( 2mm at >~= 1.5 ~). The count Pate was rather low: several thousand counts per second were measured. This is due to various p last ic windows which add up to 100 pm thickness. The d i f f rac t i on pattern of bacteriorhodopsin was measured at two wavelengths where the change of X-Pay absorption by sul fur (Fig.7) is strong and hence a large difference in f ' can be expected (compare Fig. 6).

Fig. 7. The X-ray absorption spectrum of su l fur near the K edge at ~ = 5.E18 ~ or at E = 247B eV. The f u l l points indicate the two ~avelenghts ~hich were used by Munk et a l . [43] .

Anomalous scattering of sul fur was found in the 111 re f lec t ion of the hexagonal bacteriorhodopsin l a t t i ce [43 ] - The contr ibution of anomalous scattering to the in tens i ty of the other re f lec t ions f a l l s into the error bars of the present data (Fig. 8).

16 H.B. Stuhrmann

13

Q

12., 2,,1

• t | ~ .

c A

Fig. 8. First measurement of the anomalous scattering of sulfur near the K absorption edge of sulfur [43].

a. X-ray di f f ract ion of bacteriorhodopsin at ~ = S A .

b. Anomalous X-ray di f f ract ion obtained as difference between measurements at t~o wavelengths indicated in Fig. 7

c. Difference between the intensity profi les taken at the same wavelength.

4.2. Polarised neutron scattering bu d~namic p o l a r i s e d . _ ~ t s

This technique has seen a renaissance in small-angle neutron scattering in 1985. Polarised targets as used in high energy physics experiments may be of considerable interest in biological structure research [44]. So far this promising technique has been facing

d i f f i cu l t i es in getting reasonable polarisation of target nuclei. Intense beams of polarised neutrons became available with the developement of 'super mirrors' [36] around 1980. We report on some experisents uhich sere carried out at the research reactor of 6KSS, Gemsthacht in collaboration with ILL, Grenoble and CERN, 6eneva.

According to Eq. 29 the basic scattering functions of spin contrast variation are obtained by polarising polarised neutron scattering from a polarised sample. Using the 'super mirrors' of O. Sch&rpf the polarisation i f the thermal neutron beam is nearly unity [36]. The polarisation direction of the neutron beam is easily inverted by a f l a t coil spin f l ipper. Measurements of the neutron scattering pattern from a polarised target at opposite neutron spin direction ~ields Suv(h ) as a difference pattern.

Among the nuclear spins those of the protons are most easily polarised. Nevertheless, the proton spin polarisation reaches P(H) = 0.2"3 % only in a f ie ld of 2.5 Tesla at T = 1K in about one hour. The time to reach more favorable equi l ibr ia at Ickier temperatures increases dramatically to days and weeks. Proton spins are most easily aligned by dynamic nuclear polarisation (DNP). DNP is achieved by irradiating the sample ~ith 4 mm microwaves at helium bath tmmpmratures at g.3 K in a magnetic f ie ld of 2.5 T in the presence of an organic radical (e.g. Cr(V)) [44]. The polarisation of the protons is measured bY continuous-wave nuclear magnetic resonance (NHR), calibrated by measurements of the NMR signal in thermal equilibrium ~ith the helium bath around 1K.


r(Q

l e

oe no•

® ~ , ~ ® ® ~ o.os o.4

Q (A")

Fig. 9. Polarised neutron scattering by bovine serum albumin at P(H) = 0.63. Changing the polarisation direction of the neutron spins into the opposite direction leads to a big change of small- angle scattering E45].

The proton spins of biological matt•molecules in a deuterated solvent can be nearly as easilg polarised as the best frozen spin target materials in high energy physics research. Lysozyme in a mixture of D?O and deuterated 1,2-propandediol reached a polarisation of 77 % after two hours microuave irradiat ion at T = 0.3 K. Fig. 9 shous neutron small angle scattering of bovine serum albumin at P(H) = a3 % at opposite spin directions of the incident neutron beam. The uncorrected data (no background subtraction) shou a drastic change of small angle scattering by a factor four.

Several proteins, tRNA and ribosomes have been investigated in the same uay. At T = 0.4 to 0.5 K proton polarisations around 50 % uere achieved. Higher nuclear polarisations are expected at lower temeperatures.

Spin contrast variation u i l l probably bear i ts f ru i t s in in situ structure determinations. 3y this ue mean that only a part of the matt•molecular structure has the hydrogen isotope 1H uhereas the larger remainder is completely deuterated. This techniqe of specific isotopic labelling is nou uell established uith ribosomes and other subcellular particles which allou i_D y i t r o recombination of the constituents [42].

The construction of the diffract•meter for the use of soft X-rays at HASYLAB and the polarised target project at GKSS are supported by the Bundesministerium for Forschung und Tschnologie (Grant No. 05 353 FAI and 03-I-21Eg5).

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Small-angle scattering of X-rays