GISAXS and GIWAXS update 7/2024 Detlef-M. Smilgies Chance favors the prepared mind. (Louis Pasteur)

Overview

Scattering geometry

In order to make x-ray scattering surface sensitive, a grazing incidence angle a is chosen between about half the critical angle a_c and several times the critical angles of the film material. The actual choice depends on the system to be studied. For free-standing quantum dots, an incident angle below a_c may be chosen to make the scattering exclusively surface-sensitive [Smilgies7]. Largest scattering cross sections are achieved when the incident angle is inbetween the critical angles of the film and the substrate, however, multiple scattering effects have to be taken into account to properly model the data. If the incident angle is somewhat above the critical angle of the substrate, dynamic scattering effect are much reduced, and often the data can be modeled well within the quasi-kinematic approximation introduced by [Naudon]. In each of the latter two cases, a full penetration of the sample for several 100 nm is ensured.

The area detector records the scattering intensity of scattered rays over a range of exit angles b and scattering angles y in the surface plane. A beam stop has to be set up to block spill-over direct beam as well as the reflected beam and the intense diffuse scattering in the scattering plane. The scattering geometry is thus relatively simple, and lends itself to study samples in in-situ environments [Renaud, Smilgies]. As the scattering intensity in the forward direction is high, real-time studies have become feasible [Renaud, Dourdain, Kim,  Smilgies2, Papadakis2, Paik, Zhang2]. With modern pixel array detectors, one-shot movies of sample kinetics with 100 frames per second [Smilgies6] or better have become feasible.

In the scattering plane the GISAXS intensity distribution corresponds to a detector scan in Diffuse Reflectivity [Sinha]. The intensity distribution parallel to the surface plane corresponds to a line cut through the corresponding transmission SAXS pattern. The full GISAXS intensity map can be theoretically described within the framework of the Distorted-Wave Born-Approximation [Sinha, Rauscher, Lazzari, Lee1, Busch3, Tate, Stein].

GIWAXS is a related scattering technique probing atomic and molecular distances in crystal lattices. It is closely related to Grazing Incidence Diffraction, however, typically area detectors are used as in GISAXS. GIWAXS is typically used to probe the morphology of conjugated molecules and polymers[ Sirringhaus, Breiby, Chabinyc, He, Huang, Osaka]. Combined GISAXS and GIWAXS studies reveal the orientational order of crystalline blocks in polymers [Busch5, Sasaki, Darko] and orientational order of nonspherical nanocrystals on their superlattice sites [Bian, Choi, Choi2].

Structure factor - lateral and normal density correlations

GISAXS provides information both about lateral and normal ordering at a surface or inside a thin film. This shall be illustrated with the archetypical case of lamellar films formed by symmetric polystyrene - polybutadiene block copolymers (PS-b-PB). In a block copolymer two immiscible polymer chains are coupled by a chemical bond. If both chains occupy equal volumes, a lamellar phase is formed. In a thin film, i.e. if the thickness of the film is on the order of the lamellar period, the presence of two interfaces, air-film and film substrate, may induce preferential order in the film as compared to the bulk polymer which forms a 3D powder of micron-sized lamellar domains:

If interfacial energies are the dominant factor, i.e. if one of the block strongly favors the interface, parallel lamellae are formed. If the interfacial energies of the blocks are similar, interfacial entropy will determine the orientation of the blocks. In particular, chain stretching in the vicinity of the bond between the immiscible polymer chains yields a perpendicular orientation of the lamellae, while the chain end effect favors a parallel orientation [Pickett]. As the entropic effects scale with the chain lengths, a thin film morphology change as a function of chain length is possible. This has been indeed observed for PS-b-PB, where parallel lamellae are observed for short chains and perpendicular lamellae for long chains [Papadakis]

What kind of scattering will result from these two extreme cases ?
 

If one of the blocks strongly favors one of the two interfaces, or even both, the lamellae will be parallel to the substrate. The classic example is PS-b-PMMA on a Si wafer covered with the native oxide [Anastasiadis]. The signature of parallel lamellae in GISAXS are stripes of intensity at regular spacings along the qz direction. In Langmuir-Blodgett films, such stripes in the diffuse reflectivity are referred to as Bragg sheets. The schematic shows the diffuse scattering only (the intense specular reflection from the surface is omitted).  Strictly speaking, the sketched pattern is obtained within the validity of the Born-Approximation, i.e. if the incident angles and scattering angles are well above the critical angles of film and substrate. For incident angles between the critical angles of film and substrate, scattering patterns may be more complicated, which can be explained within the framework of DBWA theory [Busch3] The obvious method of choice for this system is specular reflectivity [Anastasiadis]. The modulation in the electron density by the alternating blocks gives rise to extended Kiessug fringes [Kiessig 1932]. Interestingly reflectivity and GISAXS are complementary in this case: for near-perfect ordereing, lamellar Brage peaks are observed in XR while the GISAXS pattern appears featureless, as the diffuse Bragg sheets are hidden behind the beamstop. If lamellae are more disordered and display wavy interfaces, XR may only show the Kiessig fringes corresponding to the average thickness of the polymer film, while GISAXS reveals diffuse Bragg sheets close to the beamstop. For such a measurement it is essential to use a scattering angle between the critical angles of substrate and film and cover both the specular and diffuse reflectivity in the incident plane with a rod-like beamstop [Smilgies, Busch4].

If both blocks have similar interface energies, chain stretching at the interface comes into play. Chain stretching occurs at the link between the immiscible blocks of the polymer. A nematic ordering of this stretched part parallel to the interface may become favorable giving rise to the formation of perpendicular lamellae. As both interactions scale differently with the degree of polymerization [Pickett, Potemkin], there can be a transition from parallel lamellae to vertical lamellae, as we have found for PS-b-PB [Busch]. The signature of perpendicular lamellae are correlation peaks parallel to the interface, with a rod-like shape normal to the surface, similar to the scattering rods in Grazing-Incidence Diffraction of amphiphilic molecules at the air-water interface [Als-Nielsen].

 

Note that perpendicular lamellae still have the freedom to change direction parallel to the surface plane - in fact AFM pictures [Busch, Busch2] show that meandering lamellae are formed (aka "fingerprint patterns"). Such a system constitutes a 2D powder, similar to monolayers at the air-water interface [Als-Nielsen]. Another way of describing thin film samples is that they have uniaxial alignment. Closely related to such scattering patterns is fiber diffraction, and sometimes such images are also refered to as having "fiber texture" [Breiby]. A fiber is the dual system to a thin film, however, it should be kept in mind that fiber diffration is a transmission experiment and well described within the kinematic approximation, while GISAXS works in reflection geometry, and reflection-refraction effects have to be included for a proper interpretation of the scattering patterns.
 

AFM image of a diblock copolymer film displaying vertical lamellae [Busch2]

GISAXS from the polymer film shown on the left. [Smilgies]

The scattering from such a lamellar system with a period of about 75 nm is strong and the ordering kinetics sufficiently slow, so that in-situ time-resolved measurements of the swelling of the film in solvent vapor on a timescale of tens of seconds were possible [Smilgies].

Not always does the kinetics of the film formation result in a single morphology. This is particularly important in a system like PS-b-PB [Busch, Papadakis, Busch3, Busch4, Potemkin], where the morphology changes from parallel lamellae to perpendicular lamellae gradually as a function of chain length. At intermediate chain lengths there is only a small preference of one morphology over the other, i.e. the driving force is weak, and the system is hence slow to reach equilibrium. In this case a coexistence of different structures is observed.

PS-PB sample V5 with a chain length in the intermediate regime.
A mixture of  parallel, perpendicular, and unoriented lamellae
is observed. [Busch4, Smilgies11]

The situation can be even more complex in thick films where the film thickness is considerable larger than the lamellar period.
 

In thick films on the order of microns the ordering induced at the interfaces may not prevail throughout the film, and the interior of the film may assume the 3D powder bulk structure. Rings or partial rings in the intensity maps can indicate anything from complete disorder of the lamellar domains to partial ordering, e.g. lamellae with a finite distribution of tilt angles with respect to the interface. But the story does not end here: For films thicker than the lamellar prevailence length, top and bottom interface are decoupled. Interfacial ordering is still in effect, however, can be different at the air-film and the film-substrate interfaces. So it is possible to have parallel lamellae at one interface and perpendicular lamellae at the other, as dictated by the interplay of interfacial enthalpy and entropy. Such a behavior has been reported in the closely related cylindrical morphology wich can also display a parallel or perpendicular preferential orientation of the cylindrical domains at the interfaces [Singh].

Block copolymer morphologies

GISAXS from block copolymer based nanocomposites:
(a) standing hollow cylinders [Li-M]  (b) monolayer of hollow spheres [Du]
(c) lying semicylinders [Pelletier]  (d) titania gyroid nanoscaffold [Crossland]

Apart from the lamellar structures discussed in the previous section, there is a number of other well-known block copolymer structures Again the question arises how these structures are effected by  interfacial effects in thin films. A number of studies has been devoted to this problem:  Du et al. characterized and modelled a monolayer of spherical voids in a matrix [Du] using the IsGISAXS code by [Lazzari] and applying Babinet's theorem. [Xu] and [Li-M] characterized standing hexagonal cylinders. The Ree group investigated lying hexagonally-packed cylinders, hexagonal perforated layers, and gyroid phases [Lee1, Park-I] and modeled the scattering for the cylinder phase within DWBA. In addition they characterized and modelled a film with randomly distributed spherical pores [Lee2].  The Hillhouse and Wiesner groups independently analyzed the gyroid phase [Tate, Urade], [Crossland] as templates for inorganc nanoporous scaffolds. Ed Kramer's group  performed a comprehensive study of thin film ordered spherical phases, from hexagonally packed monolayers to several tens of monolayers that form bcc-packed spheres with a (110) orientation, as expected from the bulk equilibrium phase [Stein]. More recently [Zhang-Q] and collaborators described how to form single gyroid superlattices, Hence most of the regular bulk phases have been characterized, as they occur in thin film morphology, and preferential alignment with regard to the substrate surface could always be achieved. [Ree] has recently provided a comprehensive review on the multitude of scattering patterns observed in block copolymer thin films. 

Early studies of the effect of solvent vapor on the block copolymer thin film morphology were performed by [Smilgies] and [Xu]. In their study of silica surfactant mesophases the kinetics of the formation of various morphologies was studied by [Gibaud] and coworkers. [Wolff] studied the absorption of spherical micelles from the liquid onto a silicon substrate with grazing-incidence neutron scattering . Jin Wang, Sunil Sinha, and collaborators have shown, how nanoparticles trapped between two polymer surfaces diffuse laterally using resonance-enhanced GISAXS [Narayanan]. The Korgel group showed that monodisperse CuS nanodisks can form ordered columnar arrays on drop casting [Saunders]. Many more papers on nanoparticle self-assembly into two and three dimensional superlattices have been published recently, for example [Alexandrovic, Bian, Campolongo, Choi, Dunphy, Goodfellow, Hanrath, Heitsch, Smith, Zhang]

Hierarchical order in block copolymers with liquid-crystalline side-chains

Hierarchical order in a block copolymer. The cylindrical domains are formed by the short polystyrene block, while the matrix is formed
by a polymer block with liquid crystalline side chains. The GISAXS image in the center panel shows the hexagonally packed cylinders at q_par=0.025 invA.
The smectic ordering of the mesogen side chains shows up as the intense reflection at q_perp=0.15 invA. Finally the GIWAXS image in the right panel shows
the side chain packing and tilt demonstrating that the surface-near mesogens form a smectic-C structure.[Busch5].

Hierarchical ordering has been reported by [Busch5] where a block copolymer in the cylindrical phase and with liquid crystalline side chains in the majority block showed ordering on the mesocopic scale (30 nm), the scale of the scale of the smectic layers (3 nm), and the molecular scale of the alkyl chain packing (0.5 nm). [Sasaki] studied thermal treatment of polyethylene films in-situ with simultaneous small- and wide-angle scattering. Simultaneous small and wide angle scattering was also the key to unravel the intricate relation of superlattice symmetry and on-site orientation of individual particles in PbS and PbSe nanocrystal assemblies [Bian, Choi, Choi2].

Preferential lateral ordering and patterning

All examples discussed so far were 2D powders, i.e. had a well-aligned axis perpendicular to the substrate and rotational averaging with respect to the surface normal, resulting in a rotationally homogeneous scattering intensity with respect to the azimuth angle f. However, by patterning the substrate, further ordering may be imposed on the film, and structures may show a preferential lateral orientation with respect to the substrate as seen in polymer blends, where the surface had been prepared by alternating hydrophobic and hydrophilic stripes [Böltau].

Basic scattering angles for a GISAXS experiment. If the structure is anisotropic in the film plane,
the GISAXS intensity map will depend on the sample azimuth f.

Similarly, regular patterns can be prepared in photoresists by lithographic techniques representing artificial lamellar systems. In these cases the GISAXS intensity distribution depends now also on the azimuth angle f of the substrate. The Kowalewski group has developed the method of zone casting, which makes the preparation of laterally oriented block copolymer domains possible, and after calcination, the creation of oriented carbon nanogratings [Tang]. Nanogratings can also be prepared by using oriented block copolymer films as templates for reactive ion etching [Park-M], as shown in the example below. A quantitative description of such in-plane texture for the use with area detectors has been suggested by [Breiby] et al.

Form factor

Another type of scattering is observed for nano-objects with a narrow size distribution and well-defined shape. Here the form factor dominates the scattering, in particular, if the nano-objects are randomly placed on the surface. Examples are monodisperse voids in a silica film on a wafer surface [Du], molecular sieves based on standing block copolymer cylinders with the cylinder material removed [Li] as well as quantum dot arrays [Metzger]. Below the calculated scattering intensity from a dilute layer of oblate elliptical nanoparticles on a wafer surface is shown in the quasikinematic approximation (left panel).
 
 

elliptical nanoparticles: dilute layer

oblate elliptical nanoparticles: dense layer with in-plane correlations

The characteristic form factor oscillations are clearly to be seen in the parallel and the perpendicular direction. When the exit angle of the scattered beam is close to the critical angle, signal enhancement due to the Vineyard effect [Vineyard] occurs, resulting in a bright band of intensity at the critical angle. This is also referred to as the Yoneda peak [Yoneda]. Below the critical angle the scattering intensity falls quadratically off to zero. For thin films the Yoneda band extends between the critical angles of the film and the substrate, in particular if the former is smaller than the latter, as often encountered in organic thin films.

For a dense layer of nano-objects, particles have more or less well-defined nearest-neighbor distances. This density correlation gives rise to a structure factor with characteristic modulations parallel to the surface, but constant in the perpendicular direction (right panel).  The characteristic intensity streaks are related to the scattering rods in Grazing-Incidence Diffraction [Als-Nielsen], and are modulated by the form factor.

 

structure factor S(qy)     form factor F(qy,qz) (log scale)   Vineyard factor T(qz)

Contributions to a GISAXS intensity map in the quasikinematic approximation.

GISAXS image from a Langmuir-Blodgett film of FePt nanocrystals (left) and simulation within the quasi-kinematic approximation (right). [Heitsch].

Uniformly orientated nanopaticles

The highest degree of information on nanoparticles is obtained, if these have not only uniform shape, but also uniform orientation. The classic example are pyramid-shaped quantum dots on single crystalline surfaces [Metzger]. In the latter case the scattering intensity of a line scan taken parallel to the surface depends on the relative orientation of the pyramids to the beam as given by the azimuth angle f of the sample. Another spectacular example of very highly oriented monodisperse nanoparticles are the in-situ growth studies by Renaud et al. in an all-vacuum, windowless small-angle scattering set-up [Renaud]. [Tang] created carbon nanogratings based on zone casting of a lamellar block copolymer which resulted in the formation of perpendicular lamellae both to the substrate and the casting direction. Subsequent pyrolysis  removed one block and converted the other to carbon.
 
 

Dynamic scattering effects

Block copolymer film featuring standing cylinders.The bright bands between the critical angles of the film and the substrate
are waveguide resonances in the outgoing wavefunction. The region between the critical angles is also known as
the Yoneda band. The number of resonances sustained  is related to the film thickness and the difference
between the critical angles [Smilgies7, Smilgies11].

Full scattering simulations

Indexation of complex scattering patterns

Self-organized nanoparticles synthesized by solution chemistry have attained better and better quality and monodispersity. Some spectacular results have been achieved for monolayers deposited on the air-water interface [Schultz] and on solid substrates  [Alexandrovic, Jiang, Heitsch]. Moreover, highly ordered and oriented unary [Saunders, Dunphy, Hanrath, Zhang] and binary [Smith] superlattices have be obtained. A key for these latter studies was careful tuning of deposition technique and annealing conditions. Indexation schemes for such complex patterns have been described by [Breiby, Smilgies3, Tate].

Other 3D nanostructures than nanoparticle assemblies and block copolymers have been studied with GISAXS as well: Nanotube forests can be grown using metal nanoparticles as nuclei and have been analyzed with GISAXS [Sendja]. Complex 3D nanostructured materials recently studied with GISAXS are block-copolymer templated nanoporous materials [Urade, Crossland] which are of interest for organic solar cells, catalyst scaffolds, and molecular sieves. Such structures a based on bicontinous phases such as the double gyroid and give rise to complex spot patterns.

Grazing-Incidence Wide-Angle Scattering (GIWAXS)

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Indexation of pyrene grown from solution onto a glass surface. The polymorph could be identified  as bulk polymorph I
with the (001) plane growing parallel to the surface [Smilgies12]. The image was obtained at former G2 station
using grazing-incidence reciprocal space mapping on a psi-circle diffractometer with a linear diode array detector [Smilgies3].

Combined GISAXS and GIWAXS

Bain transition in PbS nanocrystal superlattices as a function of drying dynamics. Structures covering the whole Bain path fcc > bct > bcc can be obtained by tweaking the drying kinetics. As structures approach bcc, nanocrystals display increasing relative orientation on their superlattice sites.

Orientational ordering of nanocrystals in oriented FCC(111) and BCC(110) superlattices [Choi]. In the FCC lattice nanocrystals behave like spheres and have random orientation on their lattice sites. In the BCC lattice formed by PbS nanocrystals with reduced ligand density GIWAXS data of the PbS atomic lattice reveals that particles are highly oriented.

Microstructure characterization

• the radial widths of the spots
• within the Scherrer equation information on the average grain size of ordered material can be obtained, provided a careful determination of the resolution is done [Smilgies4].
• if the spot width increases with q (after a proper resolution correction !), further information about the type of disorder in the system can be obtained [Rivnay]

Effect of gemometric smearing illustrated for a pentacene thin film.
Note the increase in spot elongation as the scattering angle increases [Smilgies9].
Sample width 25 mm, detector distance 100 mm.

• the angular width of the spots
• the angular width of the spots or arcs in the GISAXS image is related to the degree of orientation of lamellae, cylinders, or lattices with regard to the substrate surface [Huang]. Orientation distribution functions for the so-called mosaicity can be extracted from the images following [Breiby] or [Baker2], for instance see [Darko] or [Baker]. 
• azimuthal scans reveal whether there is in-plane texture of the deposits [Tang, Breiby, Park-S]. Such studies are of particluar interest, if the deposition process or substrate modification break the isotropy of the substrate.
• in some cases orientational thin film polymorphs occur, when structures crystallize with two or more preferred planes parallel to the interface. In thin films, competing structures can be formed at the air-film and film-substrate interfaces [Choi2].
  
• the complete orientational effects can be described with the Orientation Distribution Function (ODF).
• the visibility of higher order diffraction rings is not a quality indicator per se. In grazing incidence sacttering mosaicity plays a main role how many diffraction orders are visible [Smilgies9]
  

Spatially resolved studies

• [Roth] and [Muller-B] demonstrated that GISAXS studies can be performed with a spatial resolution down to a 5 microns. They studied the ordering in concentration gradients of self-organized gold clusters deposited on a polymer film.
• [Campolongo] devised a "lab-on-a-drop" experiment, to study the equilibrium configuration of Gibbs layers of DNA-coated gold nanoparticles. In this experiment the temperature, the nanoparticle concentration, the buffer salt concentration, and vapor pressure inside the sample cell are well defined. The Gibbs layer on the surface of the drop is in contact with a reservoir of nanoparticles and buffer salt in the interior of the drop. Vapor pressure is controlled by adding identical buffer solution to a reservoir below the drop. After a brief equilibration period the shape and size of the drop is stable. The sample cell consists mainly of aluminum and provides a homogeneous temperatures around the drop. Thus a small drop can be kept stable and fully equilibrated for hours. Finally, the particles in the Gibbs layer are free to move laterally due to the liquid substrate. They do not experience sticking or strain due to drying forces as in nanoparticles on a solid substrate. Hence these Gibbs layers constitute an ideally equilibrated system allowing detailed study of DNA-mediated particle interactions. In order to accomodate the curved surface of the drop, the usual GISAXS scattering geometry had to be modified. It was found that by keeping the x-ray beam parallel to the substrate ("parSAXS"), the apex of the drop could be studied with GISAXS, while the interior of the drop could be studied with transmission SAXS.
• [Li-R] used a 10 micron x-ray beam to study the microstructure of thin films of conjugated molecules in organic field-effect transistor structure with gate channels of 10-100 microns width. They found that the morphology on the gold source and drain electrodes is maintained on the silicon oxide gate electrode for tens of microns. However in wider channels a second orientational polymorph develops, that correlates with a much reduced mobility. Coating the device structure with a self-assembled monolayer helped to reduce the formation of the parasitic polymorph.
• [Böttiger] prepared a library of P3HT-PCBM bulk heterostructure film with varying composition by slot-die coating. They could read out the microstructure using a band transprt system with a barcode reader to identify individual composition. Such combinatorical studies show great promise for fine-tuning a large range of deposition parameters efficiently.
• [Smilgies6,Giri] demonstrated that the onset of crystallization of conjugated molecules can be studied in the meniscus region during shear coating with 15 micron spatial resolution and 10 msec time resolution.
• [Jacobs] performed detailed studies of laser spike annealed traces in a block copolymer film using microGISAXS with a resolution of 15 microns

Scanning a droplet of a solution of DNA-coated gold nanoparticles revealed formation of an ordered Gibbs layer at the apex of the drop [Campolongo].
The x-ray beam was parallel to the substrate (parSAXS).

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Combining GIXS and tomography

Grazing-incidence scattering tomography of gold contacts for OFETs at 20 micron pixel size [Smilgies13].

The techniques described above require suitable samples for essentially 1D scanning due to the large footprint of the beam on the sample. A different approach to image patterned films has been taken by [Kuhlmann], [Innis-S], and [Ogawa, Ogawa2, Ogawa3] by combining GISAXS and tomography. In this case the sample is scanned through a small x-ray beam. The scan is repeated for many angles around the surface normal, and specific areas of intensity in the scattering images are used to reconstruct the distribution of material on the surface. In this case the long footprint of the grazing-incidence beam becomes an asset for the 2D reconstruction [Smilgies13]. Beamline stability and precise alignment to keep the incident angle constant during the azimuthal rotation as well as the large number of scattering images are the major challenges of the technique. Using the GIWAXS intensities, [Tsai] reconstructed the grain structure of an organic semiconductor film. [Smilgies13] and coworkers found that the structure of an organic transistor array could be imaged at 20 micron resolution using the texture reflection for the organic semiconductor and the diffuse reflectivity for the gold contacts.

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In-situ and real-time studies

Instabilities during swelling of block copolymer lamellae [Papadakis2].	Kirkwood-Alder transition in dropcast PtCu nanoctahedra during drying under controlled vapor pressure [Zhang2].
Crystallization of nanocubes with competing structures at the substrate-solution interface and the air-solution interface [Choi2].	Self-organized Oswald ripening of 2nm gold nanocrystals during heating. Binary superlattices of large fused particles and the original small particles are formed [Goodfellow].
TIPS-Pn crystallization during blade coating [Smilgies6]	Spotlight on in-situ GIWAXS studies: coating of perovskite films [Barrit]

Block copolymers:

• [Papadakis]  identified the lowering of the glass transition and the order-disorder transition during solvent vapor precessing of block copolymers as determining factors whether a given polymer film can be vapor-annealed. They found that the degree of swelling or the solvent volume fraction in the block copolymer film should be chosen to lower the glass temperature as much as possible, while preventing the system to cross the order-disorder transition [Di]. The seemingly simple lamellar structures in block copolymers turned out to show the most complex ordering behavior. The origin of thsis behavior lies in the highly connected topology which requires a major break-up and large mass transport, in order to reach a new equilibrium configuration [Papadakis2].
  
• [Paik] found that block copolymer film morphology can be changed by swelling with a highly selective solvent. Using fast drying, this non-equilibrium structure can be quenched with a small vertical distortion due to drying. Treating such films with a non-selective solvent transformed the films back to their equilibrium configuration at high swelling ratio. This processing cycle could be repeated several times.
• [Zhang-J] observed the formation of a disordered PB top layer during swelling of vertical PS-PB block polymer lamellae in solvent vapor, and the formation of protrusions during successive controlled drying.
• [Chavis] found a full range of block copolymer nanostructures be annealing a block copolymer varying the mixsture solvents which were selective to one of the blocks. In addition a transition from BCC(110) to SC(100) was observed for the shorter one of two studied polymers.
  
• [Gu] observed the formation of a skin layer forming regular square pore lattice in PI-PS-P2VP triblock copolymers after in-situ doctor blading.
• [Posselt] and collaborators compiled a major review on real-time in-situ scattering studies of solvent vapor annealing.
  
• Recently a powerful new modelling method, dispersive particle dynamic (DPD), was developed in Igor Potemkin's group at moscow State University [Rudov] as well as the groups of Juan de Pablo and Glen Frederikson. First direct comparisons between experiment and theory look very promising [Berezkin]. This can potentially lead to design block copolymers for specific purposes and predict the best annealing route.
• While most solvent vapor annealing temperatures were performed at ambient temperature, [Berezkin2] and collaborators developed a set-up for solvothermal vapor annealing at elevated temperatures.

Solvent vapor annealing of a symmetric PSPB block copolymer after spin coating. The initially perpendicular lamellae transform into parallel lamellae upon swelleing in toluene vapor. At a swelling ratio above 60% the parallel lamellae dissolve. After the film is quenched, only poorly formed parallel lamellae are formed. Some vertical lamellae remain throughout the anneal. [Smilgies2].

Nanoparticles:

• [Hanrath] found that evaporation kinetics has a profound effect on the degree of order and the degree of orientation attained in nanocrystal superlattices. By optimizing deposition conditions via slow drying of vapor annealing close to perfect FCC(111) and BCC(110) lattices could be obtained. Moreover, the exact packing of such objects was found to be dependent on nanocrystal shape [Bian] and the nanocrystal ligand density [Choi]. Using a combination of GISAXS and GIWAXS, first well-oriented superlattices were prepared and then the degree of orientation of individual nanocrystals on their lattice sites was probed. While nanocrystals should an uniform distribution in FCC(111), as to be expected for isotropic nanoparticle interaction, nanoparticles forming BCC(110) lattices were highly oriented. Lattices with an intermediate degree of on-site orientation were found to be tetragonal, covering the well-know Bain path between FCC and BCC. While BCC superlattices had been observed before, this work provided the first proof of the important on non-isotropic interactions in a BCC lattice.
  
• [Zhang2] observed a Kirkwood-Alder transition during the self-assembly of PtCu nanoctahedra to oriented BCC superlattices on a silicon wafer.
  
• [Senesi] engineered DNA-coated gold and silver nanoparticles in a way that they can do a strict layer-by-layer deposition of particles onto a gold film functionalized with complementary DNA.
• [Choi2] found competing structures of PbS nanocubes at the substrate solution (simple cubic 001) and the solution-air (rhombohedral 111) interfaces.
• [Goodfellow] observed complex fusion processes in gold nanoparticle superlattices upon heating that gave rise to ordered structures typically observed in binary superlattices.
• [Yu] found increased ordering upon heating in superlattices of small gold nanocrystals.
  
• [Ocier] observed reorganization of CdSe-CdS nanorods during solvent vapor uptake simultaneously with GISAXS, GIWAXS, and optical spectroscopy.
  
• [Weidman] obtained detailed simultaneous GISAXS/GIWAXS images on the Bain transition in PbS superlattices during controled drying. The Bain transition is driven by the densification of the deposit as the superlattice dries. The FCC to BCC transition is accompanied by a rotation of the superlattice grains from FCC(111) to BCC(110).
• [Perlich] studied the formation of nanocrystal monolayers during dip coating.
• [Smilgies8] and Hanrath wrote an invited minireview on in-situ and real-time studies of nanocrystal self-assembly.
• [Patel] et al. studied the compression of nanocrystal monolayers in a small Langmuir trough with a barrier at D1.
  

Organic electronics:

• [Sanyal] studied the drying kinetics of P3HT-PCBM bulk heterojunctions after doctor blading.
  
• [Smilgies6] found that the crystallization of conjugated molecules at the edge of the meniscus can be studied with 15 micron spatial resolution and down to 10 msec time resolution during solution shearing.
  
• In-situ real-time studies of spin coating were performed by [Chou] and [Perez].
• [Wan] found intermediate phases in the crystallization of the small-molecule semiconductor C8-BTBT after hollow-pen writing.
• [Pozdin] observed thermal reorganization processes in a semiconducting conjugated polymer under inert atmosphere.
• The upcoming materials for solar cells in recent years have been hybrid organinc-inorganic perovskites, such as methylammonium lead iodide with photon conversion efficiencies over 20%, i.e. on par with amorphous silicon. Thermal annealing at 100degC of spincoated solutions yield high-performance films [Moore]. [Foley] could show that highly oriented films could be obtained by using proper chemical additives. Other important in-situ results were the formation of 2D perovskites with well-defined orientation [Chen] which show higher stability in heat and humidity at a lower performance [Zhang-X]. An alternative to the usual 2-step process of spin coating and then thermal annealing was recently found in 1-step blade coating at elevated temperature  and efficiencies of over 17% were obtained [Zhong][Li-J]. An overview of the real-time in-situ experiments of the KAUST-China-CHESS collaboration was recently given [Barrit]. A major challenge with lead iodide-based perovskites remains their poor stability at elevated temperatures and in humidity. First ways of overcoming this issue by using mixed 2D and 3D perovskites have been demonstrated by [Niu].
  

These discoveries were facilitated by the ability to study nanostructured materials in a well-controlled in-situ sample environment and in real time. It is to be expected that the GISAXS and GIWAXS techniques will unfold their full potential here.

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Coherence Effects

Soft  and Tender X-ray Scattering

Summary and Outlook

Mesoscopic systems can display a large variety of ordering properties. Each of these has a well-defined signature in its GISAXS and/or GIWAXS intensity pattern.  Moreover, due to the penetration power of x-rays, not only surface structures, but also the internal structure of thin films and buried interfaces can be studied without any need of elaborate sample preparation, as needed for instance for cross-section transmission electron microscopy.

Hard x-rays can penetrate air, vapor, and small amounts of liquid allowing samples to be studied in-situ [Smilgies]. The GISAXS and GIWAXS scattering geometries  are straightforward and, in many cases, without the need for scanning, making GISAXS and GIWAXS very attractive to combine even with elaborate in-situ chambers [Renaud]. GISAXS scattering intensities are high compared to grazing incidence diffraction, and in combination with the essentially static scattering geometry, make GISAXS an ideal technique to combine with real-time measurements. Typical CCD cameras acquire at 1 frame per 10 sec down to 1 frame per sec; commercially available pixel array detector can acquire data up to 100 frames per second.  While swelling kinetics in block copolymers happens on the time scale of minutes, and thus CCD cameras are already well matched for the study of polymer kinetics, conjugated  molecules crystallize from solution on a msec time scale. As area detectors are evolving, the msec time scale has become readily accessible with the Pilatus pixel array detector family, opening a new window in the self-organization kinetics of nanostructured materials. And the next generation of detectors capable of submillisecond resolution movies are becoming commenrcially available. However, let's keep in mind that each nanoscale system has its own timescale and radiation damage threshold, so the experimenter's challenge is still to find the best combination of single frame exposure and frame rate.

All of these features make GISAXS and GIWAXS versatile tools to study shape and density correlations in nanoscopic systems in situ and in real time and thus follow the kinetics of the self-assembly pathways.

Links

Some dear memories

When my interest in GISAXS started around 1998, the technique was almost unknown in the soft matter community, except for the pioneeing work of Peter Mueller-Buschbaum and his gang on correlated roughness in homopolymer thin films. As it happened, after one of their visits to my beamline at ESRF, a friend from my time in Denmark, Christine Papadakis, showed me one of her AFM images of her block copolymer samples, and I was hooked - how cool would it be, to do grazing-incidence diffraction (my original playground) on a sample with a period of 1000 Angstroems instead of just atomic length scales? Other colleagues and users at ESRF, Hartmut Metzger, Gilles Renaud, and Dominique Thiaudiere, had gotten spectacular results from inorganic systems at the same time, but  soft materials remained largely by the wayside. Shortly afterwards, in 2000, I moved to CHESS and had the opportunity to work with a 2D detector at D-line - my first crude GISAXS set-up already revealed  the most intriguing and beautiful scattering images - see the image from Perter Busch's sample V5 above. I am grateful to CHESS director extraordinaire Sol Gruner for giving me the opportunity to explore an obscure technique that I saw a lot of potential in. Many thanks also to my partners in crime, Christine Papadakis, Peter Busch and Dorthe Posselt as well as Chris Ober and Uli Wiesner and their students with whom I started highly successful collaborations on structure and the self-assembly kinetics in block-copolymer thin films. Rui Zhang and Tomek Kowalewski challenged me to get a GIWAXS set-up working for their studies of P3HT and bulk heterojunctions - this resulted in one of my best cited papers and many others. Then I had the opportunity to make the full circle back to my original background in hard materials, when the first nanocrystals arrived at D-line, and I had the opportunity to play with crystallization on the 2-10 nm scale with the groups of Brian Korgel, Tobias Hanrath, James Fang, Will Tisdale and Marie-Paule Pileni gaining amazing insights into the formation of superlattices. And last and definitely not least, my collaborations with George Malliara' group at Cornell as well as Aram Amassian and his crew at KAUST sparked an amazing program in organic electronics, encompassing OLEDs, OFETs, and OPV with the hottest materials at the time. Special thanks to Ruipeng Li, who worked with me for many years, as a student, as a collaborator, and finally as a colleague at CHESS and who contributed much to the development of sample environments, microbeam capability, and the use of fast detectors at D-line. Ruipeng has continued this line of work as scientist at the NSLS-II Complex Materials Scattering beamline at Brookhaven. Thank you all who inspired me and kept my interest peaked - it has been a wild journey all over the nanoworld!

Mirror site

A final comment

Starting around 2007 GISAXS and GIWAXS experiments, particularly for the characterization of soft materials thin films, started to experience tremendous popularity and it has become hard to keep this tutorial up to date. Many new user groups and beamlines have gotten involved and are building up their own expertise and publication lists. Please do not hesitate to point out papers describing new applications or technical break-throughs that I may have missed. And please take a moment to fill out the feedback below. DS

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