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The diffraction of X-rays as they pass through a substance, usually forming an interference pattern that can be captured on film and used to analyze the internal structure of the substance.
The scattering of x-rays by crystal atoms, producing a diffraction pattern that yields information about the structure of the crystal. X-ray diffraction is used in x-ray crystallography .
X-ray diffraction - the scattering of X rays by the atoms of a crystal; the diffraction pattern shows structure of the crystal .
X-rays are electromagnetic radiation with typical photon energies in the range of 100 eV - 100 keV. For diffraction applications, only short wavelength x-rays (hard x-rays) in the range of a few angstroms to 0.1 angstrom (1 keV - 120 keV) are used. Because the wavelength of x-rays is comparable to the size of atoms, they are ideally suited for probing the structural arrangement of atoms and molecules in a wide range of materials. The energetic x-rays can penetrate deep into the materials and provide information about the bulk structure.
X-rays are produced generally by either x-ray tubes or synchrotron radiation. In a x-ray tube, which is the primary x-ray source used in laboratory x-ray instruments, x-rays are generated when a focused electron beam accelerated across a high voltage field bombards a stationary or rotating solid target. As electrons collide with atoms in the target and slow down, a continuous spectrum of x-rays are emitted, which are termed Bremsstrahlung radiation. The high energy electrons also eject inner shell electrons in atoms through the ionization process. When a free electron fills the shell, a x-ray photon with energy characteristic of the target material is emitted. Common targets used in x-ray tubes include Cu and Mo, which emit 8 keV and 14 keV x-rays with corresponding wavelengths of 1.54 Å and 0.8 Å, respectively. (The energy E of a x-ray photon and its wavelength is related by the equation E = hc/, where h is Planck's constant and c the speed of light) (check out this neat animated lecture on x-ray production)
In recent years synchrotron facilities have become widely used as preferred sources for x-ray diffraction measurements. Synchrotron radiation is emitted by electrons or positrons travelling at near light speed in a circular storage ring. These powerful sources, which are thousands to millions of times more intense than laboratory x-ray tubes, have become indispensable tools for a wide range of structural investigations and brought advances in numerous fields of science and technology.
Powder XRD (X-ray Diffraction) is perhaps the most widely used x-ray diffraction technique for characterizing materials. As the name suggests, the sample is usually in a powdery form, consisting of fine grains of single crystalline material to be studied. The technique is used also widely for studying particles in liquid suspensions or polycrystalline solids (bulk or thin film materials).
The term 'powder' really means that the crystalline domains are randomly oriented in the sample. Therefore when the 2-D diffraction pattern is recorded, it shows concentric rings of scattering peaks corresponding to the various d spacings in the crystal lattice. The positions and the intensities of the peaks are used for identifying the underlying structure (or phase) of the material. For example, the diffraction lines of graphite would be different from diamond even though they both are made of carbon atoms. This phase identification is important because the material properties are highly dependent on structure (just think of graphite and diamond).
Powder diffraction data can be collected using either transmission or reflection geometry, as shown below. Because the particles in the powder sample are randomly oriented, these two methods will yield the same data. In the MRL x-ray facility, powder diffraction data are measured using the Philips XPERT MPD diffractometer, which measures data in reflection mode and is used mostly with solid samples, or the custom built 4-circle diffractometer, which operates in transmission mode and is more suitable for liquid phase samples.
A powder XRD scan from a K2Ta2O6 sample is shown below as a plot of scattering intensity vs. the scattering angle 2or the corresponding d-spacing. The peak positions, intensities, widths and shapes all provide important information about the structure of the material.
Thin Film Diffraction
Generally speaking thin film diffraction refers not to a specific technique but rather a collection of XRD techniques used to characterize thin film samples grown on substrates. These materials have important technological applications in microelectronic and optoelectronic devices, where high quality epitaxial films are critical for device performance. Thin film diffraction methods are used as important process development and control tools, as hard x-rays can penetrate through the epitaxial layers and measure the properties of both the film and the substrate.
There are several special considerations for using XRD to characterize thin film samples. First, reflection geometry is used for these measurements as the substrates are generally too thick for transmission. Second, high angular resolution is required because the peaks from semiconductor materials are sharp due to very low defect densities in the material. Consequently, multiple bounce crystal monochromators are used to provide a highly collimated x-ray beam for these measurements. For example, in the Philips MRD used in the x-ray facility, a 4-crystal monochromator made from Ge is used to produce an incident beam with less than 5 arc seconds of angular divergence.
Basic XRD measurements made on thin film samples include:
The following graph shows the high resolution XRD data of the superlattice peaks on the GaN (002) reflections. Red line denotes results of computer simulation of the structure.
Texture Measurement (Pole Figure)
Texture measurements are used to determine the orientation distribution of crystalline grains in a polycrystalline sample. A material is termed textured if the grains are aligned in a preferred orientation along certain lattice planes. One can view the textured state of a material (typically in the form of thin films) as an intermediate state in between a completely randomly oriented polycrystalline powder and a completely oriented single crystal. The texture is usually introduced in the fabrication process (e.g. rolling of thin sheet metal, deposition, etc.) and affect the material properties by introducing structural anisotropy.
A texture measurement is also referred to as a pole figure as it is often plotted in polar coordinates consisting of the tilt and rotation angles with respect to a given crystallographic orientation. A pole figure is measured at a fixed scattering angle (constant d spacing) and consists of a series of -scans (in- plane rotation around the center of the sample) at different tilt or -(azimuth) angles, as illustrated below.
The pole figure data are displayed as contour plots or elevation graphs with zero angle in the center. Below we show two pole figure plots using the same data set. An orientation distribution function (ODF) can be calculated using the pole figure data.
Residual Stress Measurement
Structural and residual stress in materials can be determined from precision lattice constants measurements. For polycrystalline samples high resolution powder diffraction measurements generally will provide adequate accuracy for stress evaluation. For textured (oriented) and single crystalline materials, 4-circle diffractometry is needed in which the sample is rotated so that measurements on multiple diffraction peaks can be carried out. The interpretation of stress measurement data is complicated and model dependent. Consult the reference literature for more details.
Small Angle X-ray Scattering (SAXS)
SAXS measurements typically are concerned with scattering angles < 1o. As dictated by Bragg's Law, the diffraction information about structures with large d-spacings lies in the region. Therefore the SAXS technique is commonly used for probing large length scale structures such as high molecular weight polymers, biological macromolecules (proteins, nucleic acids, etc.), and self-assembled superstructures (e.g. surfactant templated mesoporous materials).
SAXS measurements are technically challenging because of the small angular separation of the direct beam (which is very intense) and the scattered beam. Large specimen-to-detector distances (0.5 m - 10 m) and high quality collimating optics are used to achieve good signal-to-noise ratio in the SAXS measurement.
The MRL x-ray facility has cutting edge capabilities for SAXS measurements with three custom-built SAXS instruments including one 3.5-meter long ultra-small angle SAXS instrument with state-of-the-art optics and area detector for low scattering density samples.
X-ray crystallography is a standard technique for solving crystal structures. Its basic theory was developed soon after x-rays were first discovered more than a century ago. However, over the years it has gone through continual development in data collection instrumentation and data reduction methods. In recent years, the advent of synchrotron radiation sources, area detector based data collection instruments, and high speed computers has dramatically enhanced the efficiency of crystallographic structural determination. Today x-ray crystallography is widely used in materials and biological research. Structures of very large biological machinery (e.g. protein and DNA complexes, virus particles) have been solved using this method.
In x-ray crystallography, integrated intensities of the diffraction peaks are used to reconstruct the electron density map within the unit cell in the crystal. To achieve high accuracy in the reconstruction, which is done by Fourier transforming the diffraction intensities with appropriate phase assignment, a high degree of completeness as well as redundancy in diffraction data is necessary, meaning that all possible reflections are measured multiple times to reduce systematic and statistical error. The most efficient way to do this is by using an area detector which can collect diffraction data in a large solid angle. The use of high intensity x-ray sources, such as synchrotron radiation, is an effective way to reduce data collection time.
One of the central difficulties in structural determination using x-ray crystallography is referred to as the "phase problem", which arises from the fact that the diffraction data contains information only on the amplitude but not the phase of the structure factor. Over the years many methods have been developed to deduce the phases for reflections, including computationally based direct methods, isomorphous replacement, and multi-wavelength anormalous diffraction (MAD) methods.
X-Ray Diffraction Method
At Proto we use the x-ray diffraction method to measure residual stress. X-ray diffraction is presently the only portable nondestructive method that can quantitatively measure residual stress in crystalline and semi-crystalline materials. Our high speed x-ray detector technology enables measurements to be performed easily on metals and ceramics; including traditionally difficult materials such as shot peened titanium. XRD uses the coherent domains of the material (the grain structure) like a strain gage which reacts to the stress state existing in the material. Residual stress and / or applied stress expands or contracts the atomic lattice spacing (d).
How do we Measure Stress?
Actually, we measure strain and convert to stress. The d-spacings are calculated using Bragg's Law: λ = 2 d sin . If a monochromatic () x-ray beam impinges upon a sample with an ordered lattice spacing (d), constructive interference will occur at an angle . Changes in strain and thus the d-spacing translate into changes in the diffraction angle measured by the x-ray detectors. The diffraction pattern is in the shape of a cone for polycrystalline materials. The shape of the diffraction peaks can also be related to the dislocation density and coherent domain size.
Why Use Multiple Detectors?
Unlike other single detector systems. Proto uses two (2) detectors for stress measurements thus capturing both sides of the diffraction cone. This means twice as much data is collected in the same amount of time simply by virtue of the design.
Proto offers a four (4) detector system that can be used for both the four peak % retained austenite method and in multiphase stress measurements.
Proto also offers 3 and 5 detector configurations for use in Simultaneous Stress and % Retained Austenite determination. Proto adheres to SAE SP-453 Retained Austenite and Its Measurement by X-ray Diffraction and ASTM E975-84 Standard Practice for X-ray Determination of Retained Austenite in Steel with Near Random Crystallographic Orientation..
Patented Fiber Optic Based Solid State Detectors
Longevity and Maintenance
Proto uses fiber optic based solid state detectors. The fiber optics allow the detector electronics to be remote from the sensing head making them suitable for measurements in harsh environments. Proto detectors are maintenance free and do not degrade with exposure to x-rays, thus less down time, better productivity and no hidden maintenance costs. Direct expose solid state detectors and position sensitive proportional counters degrade with exposure to x-rays and eventually require replacement which can be extremely costly. Because of x-ray damage, these detectors and counters must constantly be re-calibrated. In addition, some position sensitive proportional counters require periodic (bi-annual) maintenance to refill the sealed gas filled detector housing.
Proto detectors are the fastest detectors on the market today. A stress measurement can be performed in less than 0.3 seconds, an order of magnitude faster than any other detector technology commercially available. Position sensitive proportional counters can only detect one x-ray event at a time. In addition, there is dead time associated with their signal processing which slows data collection. Proto detectors have no dead time associated with them. They are multi-channel solid state detectors that collect many x-ray events simultaneously resulting in unmatched data collection speed. This is particularly important for laboratories with high throughput demands and for industrial on-line and audit station applications.
Position sensitive proportional counters can drift if there is any fluctuation in the DC bias voltage thus causing errors in peak position determination. Ambient temperature fluctuations, gas pressure and oxides on connections, to name a few, can contribute to detector instability and drift. Proto detectors are solid state, thus there is no positional drift associated with them. This means they are much more stable in harsh environments and at elevated or cold temperatures.
Proto's wide 2 detector range, 18.7 degrees 2for the 40 mm goniometer geometry offers increased accuracy on materials with broad diffraction peaks found in hardened tool and bearing steels.
Flexibility in Residual Stress Measurement Techniques
Most systems, particularly one detector systems, offer only double exposure and multiple exposure sin ² techniques. Proto systems offer the double exposure and multiple exposure sin ² techniques as well as the single exposure technique and the multiple exposure sin ² techniques. This translates into more flexibility for characterizing samples with complicated geometries.
Flexibility in Residual Stress Analysis
With Proto equipment, unlike other diffraction systems, diffraction peaks can be fit using a number of mathematical functions including, Parabola, Gaussian, Cauchy, Pearson VII, centroid, and mid-chords. Proto also offers both the difference, and cross-correlation methods for peak position determination. This translates into both improved accuracy and flexibility.
Proto systems operate on a true center of rotation and are delivered pre-calibrated to meet exceed ASTM E915-90 "Standard Test Method for Verifying the Alignment of X-ray Diffraction Instrumentation for Residual Stress" and adhere to SAE J784a "Residual Stress Measurement by X-ray Diffraction" alignment specifications. All Proto systems operate using parafocusing optics thus eliminating the need for Sollier slits and allowing very fine positional accuracy in stress measurements inside 90 mm and 120 mm i.d. confinements (e.g. the i.d. of pipes and holes, or between parallel surfaces). The competition cannot offer access to such small holes.
Simplicity in Use, Sophistication in Results
Proto systems are easy to use and setup:
Quick change apertures allow for easy adjustment of the irradiated area and sample setup (apertures can be changed in about 2 seconds) with beam dimensions (irradiated area) available from 0.3 mm to 5.0 mm.
Sample positioning and focusing can be performed easily using the standoff pointer provided with all systems and through the collimator laser pointer which allows the user to quickly locate measurement locations. This is particularly helpful when using the Automated Stress Mapping option.
The 4-Point bending fixture and Proto strain bridge are used for quick and easy determination of the effective x-ray elastic constant for new materials as per ASTM 1426-91, "Standard Test Method for Determining the Effective Elastic Parameter for X-ray Diffraction Measurements of Residual Stress".
The Proto Portable Electro Polisher is custom manufactured specifically for x-ray diffraction work, making material removal quick and efficient.
Truly portable systems are available weighing less than 18 kg (40 lbs).
Custom systems are available for customers with special requirements.
Comprehensive turnkey systems are offered by Proto to their customers to simplify and expedite their stress measurement needs.
Continuous Research and Development and a commitment to give you the best systems in the world.
· Other Sections▼
4.X-ray diffraction data collection and analysis
Human phosphate-binding protein (HPBP) was serendipitously discovered by crystallization and X-ray crystallography. HPBP belongs to a eukaryotic protein family named DING that is systematically absent from the genomic database. This apoprotein of 38 kDa copurifies with the HDL-associated apoprotein paraoxonase (PON1) and binds inorganic phosphate. HPBP is the first identified transporter capable of binding phosphate ions in human plasma. Thus, it may be regarded as a predictor of phosphate-related diseases such as atherosclerosis. In addition, HPBP may be a potential therapeutic protein for the treatment of such diseases. Here, the purification, detergent-exchange protocol and crystallization conditions that led to the discovery of HPBP are reported.
Keywords: ABC transporters, missing gene, apoproteins, atherosclerosis, paraoxonase
· Other Sections▼HPBP was serendipitously discovered from supposedly pure PON1. The structure of HPBP (Morales et al., 2006 ) relates it to prokaryote phosphate solute-binding protein (SBP; Tam & Saier, 1993; Luecke & Quiocho, 1990 ; Vyas et al., 2003), which is associated with the ATP-binding cassette transmembrane transporters (ABC transporters; Higgins, 1992). Despite the existence of the ABC transporter in eukaryotes, SBPs have never been described or predicted by genomic databases in eukaryotes.
The complete amino-acid sequence of HPBP (376 amino acids with a predicted molecular weight of 38.4 kDa) was assigned from the electron-density map at the 10% error level (Morales et al., 2006). Surprisingly, the deduced HPBP sequence cannot be retrieved from the human genome or other genomic databases. HPBP is related to a family of eukaryotic proteins that are named DING owing to their four conserved N-terminal residues (Berna et al., 2002). Similarly to HPBP, DING genes are also absent from DNA or RNA databases, although they are likely to be ubiquitous in eukaryotes. This raises numerous questions about the peculiarity of DING genes. The HPBP sequence deduced by crystallography is the first complete sequence of a DING protein and provides a precious basis for understanding the genetic mystery associated with DING proteins.
We have provided evidence that HPBP is a new apoprotein mainly located on HDL (good cholesterol) capable of binding inorganic phosphate ions. Furthermore, HPBP presents 59% amino-acid identity with a protein named crystal-adhesion inhibitor (CAI) that may prevent the development of kidney stones by inhibiting the adhesion of calcium oxalate crystals to renal cells (Kumar et al., 2004). Thus, HPBP could be tentatively regarded as a potential predictor and as a possible therapeutic protein for treatment of phosphate-related disorders, including atherosclerosis.
In this article, we report the purification, detergent-exchange protocol and crystallization conditions that led to the discovery of HPBP.
HPBP was discovered by copurification from an apparently pure PON1 preparation. The HPBP/PON1-containing fractions were obtained according to a protocol based on the method of Gan et al. (1991) (Renault et al., in preparation) that was assumed to provide PON1 pure at ≥95%. Briefly, out of date plasma bags from blood donors (Etablissement Français du Sang Rhône-Alpes) were supplemented with CaCl2 to a final concentration of 10 mM before the resulting fibrin clot was separated by filtration. The filtrate was then submitted to a pseudo-affinity chromatography on Cibacron Blue 3GA-agarose (type 3000-CL; Sigma) using 50 mM Tris-HCl buffer pH 8.0 supplemented with 1 mM CaCl2 and 3 M NaCl to avoid the adsorption of albumin. Elution of hydrophobic plasma proteins, mainly lipoproteins, was performed using 0.1% sodium deoxycholate and 0.1% Triton X-100 in Tris-HCl buffer. The PON1-containing fractions were pooled and separated from the other HDL-bound proteins, mainly apolipoprotein A-I, by anion-exchange chromatography on DEAE-Sepharose Fast Flow (Pharmacia Biotech) using 25 mM Tris buffer containing 0.1% Triton X-100 as starting buffer with a gradient of NaCl (0-0.35 M).
Pooled HPBP/PON1-containing fractions were dialyzed and concentrated in the presence of C-12 maltoside (0.64 mM) using a centrifugation device (Centriprep Amicon, 10 kDa cutoff, Millipore, St Quentin-en-Yvelines, France) to a final absorbance of 2.3 at 280 nm. Light-scattering analysis revealed a homogeneous sample with an apparent molecular weight of about 80 kDa (Josse et al., 2002 ). This molecular weight was attributed to dimeric PON1 because the existence of HPBP was unknown at this point.
Some dialyzed fractions spontaneously crystallized overnight. Crystal plates were very numerous and very thin (about 1 µm width). Once useless crystals had formed in the absence of precipitant agent, it was impossible to dissolve them again. Thus, crystallization trials were performed quickly after detergent exchange.
Inspection of the resulting electron-density map clearly indicated that the crystallized protein was not PON1. The sequence deduced from the structure was totally unknown and not predicted by the genomic database. The complete amino-acid sequence was determined from X-ray data. This protein is the first inorganic phosphate transporter characterized in human plasma (Morales et al., 2006). The discovery of this protein by crystallography opens new insight into the physiopathology and medical treatment of phosphate-related diseases
RECENTDEVELOPMENTS IN POLYMER CHARACTERIZATION
In the absence of an orientational force, thelamellae organize into spherulites (1-10 mm indiameter). X-ray scattering can be used to ob-tain structural information at three lengthscales—1, 10 and 100nm—using scattering atwide-, small- and ultra small-angles, respec-tively.A continuum of structures between the ex-tremesof what are generally regarded as amor-phous and crystalline phases are present in areal polymer, and these entities have complexorganization. But, a model that describes thesemicrystalline polymers in terms of two phases, an average amorphous and an averagecrystalline phase, has been found to be ade-quate for many practical purposes. The fractionof the material that is crystalline, the crys-tallinity or crystalline index, is an important pa-rameter in the two-phase model. Crystallinitycan be determined from a wide-angle X-ray dif-
fraction (WAXD) scan by comparing the areaunder the crystalline peaks to the total scatteredintensity . The accuracy and the precision ofthese measurements can be improved by draw-ing a proper base-line, using an appropriateamorphous template, and by carefully choosingthe crystalline peaks [13, 14]. The disorder inthecrystalline domains can be evaluated by measuring the crystallite sizes which are relatedto the radial widths D(2q) of the reflections at ascattering angle 2q by the Scherrer equation. Inreality, there are two contributions to the width:one is the size and the other is the para crystallinity or microstrain [15, 16]. A more detailed
analysis based on the Warren-Averbach methodis widely used in metals and ceramics, but lessso in polymers . The disorder in the crys-talline domains is also reflected in the unit celldimensions. But, calculation of the unit cell pa-rameters requires an accurate measurement ofthe positions of many crystalline peaks, which
can be difficult. Therefore, in practice, relativepositions of selected crystalline peaks are used as accurate measures of the changes unit cellparameters [18, 19].Structures at length scales larger than a unit
cell (10nm instead of 1nm) can be investi-gated using small-angle X-ray scattering(SAXS). The methodology for these analysis isnow highly developed and can be found in anystandard literature [9, 20-24]. While WAXD isused to study the orientation of the crystals,and the packing of the chains within these crys-tals, SAXS is used to study the electron densityfluctuations that occur over larger distances asa result of structural inhomogeneities. SAXS iswidely used to study the lamellar structure bymeasuring parameters such as lamellar spac-ing, height and thickness of the transition layer betweenthe crystalline and amorphous domains. In theanalysis of fibers, SAXS can provide informa-tion about the details of fibrillar morphologysuch as fibril diameter and orientation, and large scale inhomogeneity such as microporesand cracks. This information is somewhat simi-lar to that obtained from a transmission elec-tron micrograph, with one important difference:SAXS requires no sample preparation, and thedata is averaged over the area (typically 0.1mm2) of illumination. SAXS is also used for
studying conformation, size and dynamics ofpolymers in solutions and in gels.
3. New Methods to Study Polymer
The two-phase model for the polymer hasbeen quite useful in providing a qualitative un-derstanding of the polymer properties in termof its structure, but is not adequate for quantita-tive prediction of the polymer properties. For this purpose, a detailed knowledge of the char-acteristics and distribution of soft (amorphous)
and hard (crystalline) domains, and the interac-tions between these domains is necessary. New techniques that have been introduced duringthe past decade provide precisely this informa- tion. Some of these techniques will be discussed here. 3.1. Microbeam Diffraction
Microbeam diffraction, or microdiffraction,has been used in semiconductor industry for over 25 years . It is now being used to ex-amine polymeric materials. In most routine characterization of polymers, it is assumed thatthe structure is homogeneous. But, this is not always the case. Temperature gradients are pre-sent during injection molding, and both temper- ature and stress gradients are present duringextrusion and drawing. These gradients intro- duce structural inhomogeneities that influencepolymer performance. Even filaments that are only 10 mm in diameter show variations in ori-entation and density across the cross section [5, 26]. These structural gradients, and the changesin these gradients during deformation can now be studied at spatial resolutions as small as1 mm using microbeam diffraction . An ex- ample of the typical structural gradients presentin a shown in Figure 2 . This diffractogram was obtained from KevlarTM fiber with a 3 mm
Synchrotron Radiation Facility) synchrotronsource. The data show that the Herman's orien- tation function of the crystalline domains in this12 mm diameter fiber increases from 0.955 at the center to 0.980 at the surface of the fiber.The higher orientation of the skin layer is obvi- ously due to large shear stresses at the spin-neret, extensional forces in the air-gap and the solidification in the coagulation bath. Such astructural gradient implies that the modulus de- creases from the skin to core. It is interesting tonote that these inhomogeneities gradually de- crease and disappear under uniaxial stress.Microbeam techniques have reached a level of sophistication that it is now possible to focus .X-rays on a micron size crystal and follow the changes in the structure from one crystal to thenext within a spherulite . Figure 3 shows a series of hundred patterns registered from a
spherulite of Poly(hydroxyl butarate). The pho-tographs show the changes in texture as the beam was stepped in increments of 3 mm along the vertical line drawn in the polarized optical micrograph of the spherulite shown on the left.The three photographs in the foreground show the differences in the texture of three crystals60 mm apart.In other experiments, liquid crystal molecular alignment of the memory state in polymer dis-persed liquid crystal (PDLC) used for light valves and displays has been investigated .Microbeam diffraction, both SAXS and WAXD, has been used to measure the misalignment ofthe crystalline cellulose microfibrils with respect to the fiber axis from the azimuthal broadeningsboth of the equatorial small-angle scattering streak and of Bragg reflections, and the diffusescattering on the layer lines and the equator of the fiber diffraction diagram is used to identifythe presence of disordered cellulose between the cellulose microfibrils and of defects insidethe crystallites . Microbeam diffraction is also useful in understanding the interfaces, forinstance the morphology of transcrystalline re- gions .Although the experiments described above,and other to be described later, were carried out at synchrotron sources, it should be noted thatit is possible to carry out somewhat less de- manding, but equally important measurementsusing in-house facilities. Microfocus X-ray
beams from glass capillaries are now used toexamine areas as small as 50 mm using sealed or rotating anode generators
3.2. Grazing Incidence Diffraction
Inhomogeneities in materials can be exploredfrom an entirely different perspective usinggrazing incidence diffraction (GID), also knownas glancing-angle diffraction or surface-en-hanced scattering [31-33]. X-rays have a refrac-tive index of slightly less than 1 in a solid andhence undergo total external reflection for an- gles of incidence (a) less than a critical angle acwhich is typically 0.2°. This totally-reflectedbeam penetrates only the top 50Å at the sur-face. A small fraction of this beam will be dif-fracted giving a weak diffraction pattern fromthe surface region alone. For aac, we get dif-fraction from layers below 50Å from the sur- face of the film. Comparison of the two scansshows how the effect of the surface on the poly- mer structure. By keeping the angle a (see insetto Figure 4) that the X-ray beam makes a with the sample surface small (1°), it is possiblelimit the penetration depth of the X-rays intothe sample, thus reducing background scatter-ing from the substrate or the bulk of the poly-mer. By varying a, one can change the penetra-tion depth of the X-rays from several nm up totypically several 100 nm (determined by the ab- sorption length). Depending on the length scaleof the structure of interest, the exit angle can be either small (10nm structures, GISAXS) orlarge (0.1 nm structures, GIXRD). This technique is useful for studying skin-core structural gradi-ents at the surfaces of flat samples at depths from a fraction of a mm to more than a millime-ter, as well structures near the surface at depths as small as a few nm [34-36]. The glancingangle technique is especially well suited if the polymers are heavy absorbers, e.g., fluoropoly-mers, in which the penetration depth of X-rays is as little as 5 mm at even large incidence an-gles of 1°. In industrial laboratories, these mea- surements are useful in analyzing multilayerfilms and in measuring the changes from skin to core in injection molded plastics, for instancein assessing the performance and dimensional stability of engineering plastics.The utility of this technique is illustrated inFigure 4 which shows GID scans obtained atseveral incidence angles (a) from a multilayerpackaging film . The peak at 2q23.4° in the first scan (a0.25°) is due to the crystals ofpolyethylene (PE) at the surface of the top PE layer. The peak at 2q=22.8° in the second scan(a=0.5°) is due to the PE crystals beneath the surface in the top PE layer. As a is increasedfurther, we begin to see the 25° peak from thebiaxially oriented nylon layer. These measure-technique for examining the surfaces, interfaces meric materials.GID technique is useful in many areas thatdeal with surfaces and interfaces including paints and coatings, adhesives, polymer-basedelectronic devices, and biocompatible materials.GID is currently used extensively to studynanostructured surfaces and the structure at air-polymer and polymer-substrate interfaces inpolymer films deposited onto a substrate. Ex-amples include the use of GID to assess the structure the structure formation in multicom- ponent ultrathin polymer blend films at and below the surface , and the study of orienta- tion, conformation and packing modes of the chains near a substrate .