Past and present crystallographic work at the NBS/NIST reactor.Neutron diffraction Neutron diffraction The phenomenon associated with the interference processes which occur when neutrons are scattered by the atoms within solids, liquids, and gases. at NBS/NIST started soon after the NBS (National Bureau of Standards) See NIST. NBS - National Bureau of Standards: part of the US Department of Commerce, now NIST. reactor became operational in the summer of 1969. Since that time, literally hundreds of crystal structures have been determined and refined using single crystal and powder neutron diffraction data, collected with a variety of instruments. This work has been usually done in collaboration with other NBS/NIST divisions and/or universities and industrial laboratories. In parallel with the technical developments and the experimental work, also theoretical aspects of crystal geometry have been clarified, and significant improvements in the techniques of profile refinements have been made. It is therefore understandable that a comprehensive description of all the crystallographic crys·tal·log·ra·phy n. The science of crystal structure and phenomena. crys  tal·log studies carried
out up to the present is impossible under the constraints of space and
time imposed by a review of this type, and, in the following sections,
we will limit ourselves to give, only a brief account of the topics
which, in our opinion, represent the highlights of the w ork carried out
at the reactor.Key words: collaborative research; historical research highlights; NBS Reactor; profile refinement; single-crystal and powder neutron diffraction; theoretical crystal geometry. 1. Introduction Neutron diffraction at NBS/NIST started soon after the NBS reactor became operational in the summer of 1969. Since that time, literally hundreds of crystal structures have been determined and refined using single crystal and powder neutron diffraction data, collected with a variety of instruments. This work has been usually done in collaboration with other NBS/NIST divisions and/or universities and industrial laboratories. In parallel with the technical developments and the experimental work, also theoretical aspects of crystal geometry have been clarified, and significant improvements in the techniques of profile refinements have been made. It is therefore understandable that a comprehensive description of all the crystallographic studies carried out up to the present is impossible under the constraints of space and time imposed by a review of this type, and, in the following sections, we will limit ourselves to give, only a brief account of the topics which, in our opinion, represent the highlights of the w ork carried out at the reactor. It is well known that crystal structure analysis provides information, which is fundamental for the understanding of the physical and technological properties of materials. To mention a few examples, drug design would be impossible without the detailed structural knowledge of the complex molecules involved in biological processes, and the assessment of safety margins in metallic parts and components does require measurements of the residual stress Residual stresses are stresses that remain after the original cause of the stresses (external forces, heat gradient) has been removed. They remain along a cross section of the component, even without the external cause. done with neutron neutron, uncharged elementary particle of slightly greater mass than the proton. It was discovered by James Chadwick in 1932. The stable isotopes of all elements except hydrogen and helium contain a number of neutrons equal to or greater than the number of protons. and x-ray diffraction methods. As described in other chapters of this volume, diffraction measurements are also essential in the study of the magnetic behavior of many materials, and in clarifying how systems such as ice change under the effect of high pressure. The instrumentation available to the crystallographer crys·tal·log·ra·phy n. The science of crystal structure and phenomena. crys tal·log today at the
NIST (National Institute of Standards & Technology, Washington, DC, www.nist.gov) The standards-defining agency of the U.S. government, formerly the National Bureau of Standards. It is one of three agencies that fall under the Technology Administration (www.technology. reactor must be considered as the best in the United States United States, officially United States of America, republic (2005 est. pop. 295,734,000), 3,539,227 sq mi (9,166,598 sq km), North America. The United States is the world's third largest country in population and the fourth largest country in area. , and,
in particular, the new high-resolution neutron powder diffractometer A Diffractometer (Main Entry: dif·frac·tom·e·ter Pronunciation: di-"frak-'tä-m&-t&r Function: noun) is a measuring instrument for analyzing the structure of a usually crystalline substance from the scattering pattern produced when a beam of radiation or particles (as X rays or is
a world-class instrument whose usefulness will last for many years to
come. The crystallographic equipment, coupled with other techniques also
available at the reactor, give to the intelligent experimenter the
possibility to determine the crystal structure of many materials, even
when they can be prepared only in small quantities, and to relate the
structural results to those obtained with other techniques.2. Instrumentation 2.1 Introduction By inserting a collimator collimator (kol´imātur), n a diaphragm or system of diaphragms made of an absorbent material and designed to define the dimensions and direction of a beam of radiation. into the face of a reactor, we can extract a beam essentially consisting of neutrons which have been slowed down by a large number of collisions with the moderator and which are in thermal equilibrium thermal equilibrium The condition under which two substances in physical contact with each other exchange no heat energy. Two substances in thermal equilibrium are said to be at the same temperature. See also thermodynamics. Noun 1. at the reactor's temperature. The distribution of wavelengths in the collimated beam See collimated. may be obtained by plotting the function [phi]([lambda]) = (const. /[[lambda].sup.5])exp exp abbr. 1. exponent 2. exponential [-[h.sup.2]/2mkT[[lambda].sup.2])] (1) as function of [lambda] (1). In this expression, h is Plank's constant (6.625 X [10.sup.-27] erg s), k is Boltzmann's constant Noun 1. Boltzmann's constant - constant used in the calculation of the ideal gas constant constant - a number representing a quantity assumed to have a fixed value in a specified mathematical context; "the velocity of light is a constant" (1.381 X [10.sup.-16] erg/K), m the neutron mass (1.675 X [10.sup.-24] g) and K the absolute temperature. The function [phi]([lambda]) can be defined by saying that [phi]([lambda])d[lambda] is the number of neutrons with wavelengths between [lambda] and [lambda] + d[lambda] emerging from the collimator in one second, and its maximum value occurs for the wavelength [lambda] = h/[(5mkT[[lambda].sup.2]).sup.1/2]. (2) A plot of [phi]([lambda]) versus [lambda] is shown in Fig. 1 for T = 350 K, the equilibrium temperature of our reactor. For crystallographic experiments, we must select a narrow band of wavelengths from the beam emerging from the in-pile collimator, and this task is usually accomplished by using as monochromator A monochromator is an optical device that transmits a mechanically selectable narrow band of wavelengths of light or other radiation chosen from a wider range of wavelengths available at the input. a single crystal of high reflectivity re·flec·tiv·i·ty n. pl. re·flec·tiv·i·ties 1. The quality of being reflective. 2. The ability to reflect. 3. , cut and oriented so that it will diffract dif·fract intr. & tr.v. dif·fract·ed, dif·fract·ing, dif·fracts To undergo or cause to undergo diffraction. [Back-formation from diffraction. , in the best possible geometric conditions, a beam of wavelengths comprised in a small interval of [lambda] centered at [lambda] = 2 [d.sub.m] sin [[theta Theta A measure of the rate of decline in the value of an option due to the passage of time. Theta can also be referred to as the time decay on the value of an option. If everything is held constant, then the option will lose value as time moves closer to the maturity of the option. ].sub.m] (3) where [d.sub.m] is the interplanar spacing of the set of planes involved in the diffraction process, and 2[[theta].sub.m] is the take-off angle of the monochromator (Fig. 2). The monochromatic monochromatic /mono·chro·mat·ic/ (-kro-mat´ik) 1. existing in or having only one color. 2. pertaining to or affected by monochromatic vision. 3. staining with only one dye at a time. beam, after passing through a second collimator, impinges on the sample, is diffracted in a direction which depends on the geometry of the crystal and the technique employed in the experiment, and after passing through a third collimator, is measured by an appropriate detector. The diffracted intensities depend, both for the single crystal and the powder methods Noun 1. powder method - a process for identifying minerals or crystals; a small rod is coated with a powdered form of the substance and subjected to suitably modified X-rays; the pattern of diffracted rings is used for identification , on the structure and the physical state of the sample and on the luminosity luminosity, in astronomy, the rate at which energy of all types is radiated by an object in all directions. A star's luminosity depends on its size and its temperature, varying as the square of the radius and the fourth power of the absolute surface temperature. (i.e., transmission) of the diffractometer used in the experiment. On the other hand, the shapes of the observed peaks are given by the convolution convolution /con·vo·lu·tion/ (-loo´shun) a tortuous irregularity or elevation caused by the infolding of a structure upon itself. of the instrumental profile, due exclusively to the geometrical characteristics of the diffractometer, and the pure profile, i.e., the profile that we would observe if the effects of the instrument were negligible. In order to understand the evolution in the design of the diffractometers used at different times at the NBS/NIST reactor, we will briefly discuss the above concepts and their influence on the quality of the collected data. 2.2 Instrumental Resolution and Luminosity Let us assume that the three collimators of a single crystal or powder diffractometer have horizontal angular divergences [[alpha].sub.1], [[alpha].sub.2] and [[alpha].sub.3] (these are defined by the spacing and the length of the Soller slits), and that their transmission function in the horizontal plane horizontal plane n. A plane crossing the body at right angles to the coronal and sagittal planes. Also called transverse plane. horizontal plane of the instrument (which is coincident co·in·ci·dent adj. 1. Occupying the same area in space or happening at the same time: a series of coincident events. See Synonyms at contemporary. 2. with the plane of Fig. 2) is Gaussian. Let us also assume that the monochromator is a mosaic crystal with blocks having a Gaussian spread with width at half maximum [[beta].sub.m], and oriented with a take-off angle 2[[theta].sub.m]. It has been shown (2-4) that, under these assumptions, any diffraction peak centered at the angle 2[theta] (where [theta] is the Bragg angle Bragg angle n. The angle between an incident x-ray beam and a set of crystal planes for which the secondary radiation displays maximum intensity as a result of constructive interference. of the peak) has a Gaussian instrumental shape with full width at half maximum A full width at half maximum (FWHM) is an expression of the extent of a function, given by the difference between the two extreme values of the independent variable at which the dependent variable is equal to half of its maximum value. [H.sub.1/2] given by the equation. [H.sup.2.sub.1/2] = [U.sub.0]([tan.sup.2][theta])/[tan.sup.2][[theta].sub.m])[+ or -][v.sub.0](tan[theta]/tan[[theta].sub.m])+W (4) where [U.sub.0], [V.sub.0] and W are function of the angular divergences [[alpha].sub.1], [[alpha].sub.2] and of [[beta].sub.m] (in the case of single crystal instruments, also the mosaic spread [[beta].sub.c] of the sample must be taken into consideration). Equation (4) is usually written [H.sup.2.sub.1/2] = U [tan.sup.2][theta] [+ or -] V tan[theta] + W (5) where U = [U.sub.0]/[tan.sup.2][[theta].sub.m] and V = [V.sub.0]/tan[[theta].sub.m]. (6) In Eqs. (4) and (5) the plus and minus signs This article is about mathematical symbols. For the banking network, see PLUS. For the student loan, see PLUS loan. For the record label, see Minus (record label). For the comic, see Minus (comic). apply to the anti-parallel and parallel positions, respectively, (see Fig. 2) and, since V and [V.sub.0] are always positive, the value of [H.sub.1/2] for the anti-parallel geometry is always greater than that obtained when the peaks are scanned with the parallel configuration. The differences of the full widths at half maximum for the two geometries are significant at all values of [theta] (and have been fully discussed in Refs. [2-4]), and for this reason all two-and three-axes spectrometers are designed to work in the parallel position. Equation (4) has a minimum at a value of [theta] given by tan[[theta].sub.min] = ([V.sub.0]/2 [U.sub.0])tan[[theta].sub.m] (7) with a width [([H.sub.1/2]).sup.2] = W - ([V.sub.0.sup.2]/2 [U.sub.0]). (8) These expressions show that the resolution function of a diffractometer can be controlled, within limits, by choosing appropriately the horizontal divergences of the collimators and the take-off angle of the monochromator. This may not be too important in many cases of single crystal work, where reflections are rarely close enough to one another to cause overlapping, but is essential in the case of the powder method, where serious overcrowding overcrowding overcrowding of animal accommodation. Many countries now publish codes of practice which define what the appropriate volumetric allowances should be for each species of animal when they are housed indoors. Breaches of these codes is overcrowding. of reflections occurs even for moderately large unit cells. 2.3 Powder Diffractometers The equations discussed before help to explain the evolution in the design of the powder diffractometers at the BT-1 beam port at our reactor. In the initial machine, the monochromatic beam was produced by the 220 reflection of a flat copper monochromator with mosaic spread [[beta].sub.m] of about 15', oriented with a take-off angle 2[[theta].sub.m] of about 70[degrees]. With this configuration the wavelength of the monochromatic beam is about 1.5 A, i.e., comparable to the wavelength [CuK.sub.[alpha]], extensively used in x-ray diffraction experiments. The horizontal divergences of the three Soller collimators were of the order of 20' and the diffracted intensities were measured using a single detector in the interval 5[degrees] [less than or equal to] 2[theta] [less than or equal to] 100[degrees], in steps of 0.05[degrees]. The advent of the Rietveld method (5,6) in the analysis of crystal structures had the effect of increasing the complexity of the materials that could be studied with the powder method, thus requiring resolutions higher than those obtainable with our original instrument. This was accomplished in the mid seventies by reducing the horizontal divergences of the first and third collimator to about 10', without changing the basic design of the diffractometer and the take-off angle of the monochromator. The loss of luminosity caused by a collimating system tighter than the one in place before, was more than compensated by replacing the single counter with a bank of five detectors with an angular separation of 20[degrees] (Fig. 2). Examples of the resolution obtainable with this instrument are illustrated in Fig. 3 and show that the minima of the resolution functions (i.e., the values of 2[theta] corresponding to the greatest resolution) are all comprised in a region of 2[theta] around 45[degrees] to 55[degrees]. Thi s is a significant disadvantage because, depending on the unit cell volume and the chemical and physical nature of the sample, severe overcrowding, and consequent overlapping, of the diffraction lines may occur below or above this region of 2[theta]. In these cases it is clearly desirable to have the best instrumental resolution in the angular intervals most affected by overlapping, and Eq. (7) shows that this can be best accomplished by varying the take-off angle of the monochromator. Such change, however, must occur without a significant variation of the wavelength of the monochromatic beam, and with the lowest possible loss of luminosity. The instrument best satisfying these often conflicting requirements was built following a design proposed by E. Prince, of the Reactor Radiation Division, and is schematically illustrated in Fig. 4. Its features have been described in detail (7) and will only be summarized here. With this instrument, the experimenter can measure a powder pattern with any one of three monochromators having take-off angles 2[[theta].sub.m] equal to 75[degrees], 90[degrees] or 120[degrees]. The horizontal divergences of the in-pile collimator can be set at 15 'or 7 ', While the divergences [[alpha].sub.2] are fixed at the values indicated in Fig. 4 and those of the collimators in front of each of the 32 detectors located on the recording arm of the instrument are all equal to 7'. With these conditions, and assuming the mosaic spreads of the monochromators indicated in the figure, one obtains the resolution functions illustrated in Fig. 5. As expected, the minima of these functions occur in different 2[theta] regions. Thus, for the beam generated by the 311 reflection of Ge the minimum is located at 2[theta] [approximately equal to] 75[degrees] and is mostly used for studying materials with large unit cells and for magnetic materials Magnetic materials Materials exhibiting ferromagnetism. The magnetic properties of all materials make them respond in some way to a magnetic field, but most materials are diamagnetic or paramagnetic and show almost no response. , since in these cases the intense peaks needed to determine and/or refine the structure are concentrated in the low 2[theta] region of the pattern. On the other extreme, the 531 reflection of the Si monochromator, with its minimum at about 120[degrees], offers high resolution in the region 90[degrees] [less than or equal to] 2[theta] 130[degrees], and is most effectively used in those cases in which it is important to detect splits of the diffraction lines (as in the case of phase transitions), or when it is essential to measure with high precision the thermal factors of the atoms in the structure. Finally, the 311 reflection of copper is a compromise between the two configurations described before, and is routinely used to refine structures of average unit cell volumes (between 1000 [A.sup.3] and 4000 [A.sup.3]), such as those of most ceramic materials, su perconductors, etc. The luminosity of the diffractometer is significantly enhanced by the use of curved, focusing monochromators and, thanks to the presence of 32 detectors, the time required to record an entire diffraction pattern diffraction pattern The interference pattern that results when a wave or a series of waves undergoes diffraction, as when passed through a diffraction grating or the lattices of a crystal. , with samples as large as a few grams of material, is reduced to a few hours. As we have mentioned previously, the observed peak shapes are the convolution of the instrumental profile and the profile generated by the sample. If both these functions are Gaussian with full width at half maximum [H.sub.1/2] and [h.sub.1/2] respectively, then their convolution is also Gaussian, with width [B.sub.1/2] given by [B.sup.2.sub.1/2] = [H.sup.2.sub.1/2]+[h.sup.2.sub.1/2]. (9) If [h.sub.1/2] is small compared to [H.sub.1/2] (i.e., the size of the crystallites in the sample is in the range of 1500 A to 3000 [Angstrom angstrom (ăng`strəm), abbr. Å, unit of length equal to 10−10 meter (0.0000000001 meter); it is used to measure the wavelengths of visible light and of other forms of electromagnetic radiation, such as ultraviolet ] with no significant structural distortions and/or strains), then [B.sub.1/2] [approximately equal to] [H.sub.1/2] and Eq. (5) is a valid description of [B.sub.1/2] as function of [theta]. If, on the other hand, the pure profile is broadened by crystallite crys·tal·lite n. Any of numerous minute rudimentary, crystalline bodies of unknown composition found in glassy igneous rocks. crys size effects, then we may express [h.sub.1/2] by means of Scherrer's Eq. (8) and introduce it in Eq. (5) obtaining the expression [B.sup.2.sub.1/2] = [U+([K.sup.2][[lambda].sup.2]/[D.sup.2])[tan.sup.2][theta]]-V tan[theta]+[W+([K.sup.2][[lambda].sup.2]/[D.sup.2])] (10) where K is a constant ([approximately equal to]0.9) and D is defined as the thickness of the crystallites in the direction perpendicular to the reflecting planes (it should be noted that, sensu stricto, Eq. (10) is valid only when the instrumental and pure profiles are both Gaussian). When the crystallites have odd shapes (such as plate-like or needle-like), D changes from reflection to reflection and an expression like Eq. (5) cannot be used to describe the dependence of [B.sub.1/2] on [theta]. If, on the other hand, the crystallites are approximately spherical spher·i·cal adj. Having the shape of or approximating a sphere; globular. and of uniform size, D is constant and Eq. (10) has the same form as Eq. (5). It is remarkable that in the majority of cases encountered in practice, this condition is satisfied and the observed peaks are very nearly Gaussian with widths having a dependence on [theta] well described by Eq. (5). Examples of single peaks obtained with the high-resolution diffractometer now in use at the BT-1 beam port are shown in Fig. 6. The excellent quality of the data that can be collected with the instrument is clearly illustrated in Fig. 7, which shows the agreement between observed and calculated intensities after the refinement of the structure of [MgCNi.sub.3] [9]. It is proper here to point out that this unusual and important perovskite Perovskite (calcium titanium oxide, CaTiO3) is a relatively rare mineral on the Earth's crust. Perovskite crystallizes in the orthorhombic (pseudocubic) crystal system. compound is a superconductor A material that has little resistance to the flow of electricity. Traditional superconductors operate at absolute zero (-459.67 degrees Fahrenheit or -273.15 degrees Celsius). Experiments in the 1980s raised the temperature to -321 degrees Fahrenheit. with [T.sub.c] [approximately equal to] 9 K, and that its structure was determined and refined by Q. Huang, a guest scientist of the NIST Center for Neutron Research, using a sample prepared in the Department of Chemistry of Princeton University Princeton University, at Princeton, N.J.; coeducational; chartered 1746, opened 1747, rechartered 1748, called the College of New Jersey until 1896. Schools and Research Facilities . 2.4 Single Crystal Diffractometers Since overlapping of reflections is rarely a problem in single crystal diffraction work, the neutron diffractometers used in this type of analysis are usually designed to maximize luminosity and without paying too much attention to resolution. Consistently with this concept, the single crystal instruments installed at the BT-7 and BT-8 beam ports used graphite or copper monochromators with large mosaic spreads and essentially no collimators. The crystal mounting is in general a three-circle goniometer goniometer /go·ni·om·e·ter/ (go?ne-om´e-ter) 1. an instrument for measuring angles. 2. a plank that can be tilted at one end to any height, used in testing for labyrinthine disease. of the type schematically represented in Fig. 8. The rotations [theta], [chi] and [omega] allow the experimenter to bring any reflection h k l into diffracting position on the equatorial plane e·qua·to·ri·al plane n. The plane that contains all of the centromeres and their spindle attachments during metaphase of mitosis. , defined by the incident and diffracted beams, and to rotate the crystal of any angle [psi] about the scattering vector. This last option is important in those cases in which multiple diffraction must be avoided (10). Our original diffractometer was equipped with a single detector rotating about the axis of the the diameter of the sphere which is perpendicular to the plane of the circle. See also: Axis 2[theta] ci rcle, and the diffracted intensities were measured following the automatic procedure described in Ref. (11). During the seventies, the BT-7 beam port was used to develop a new type of single crystal instrument suitable for protein crystallography. Since the unit cells of protein materials are very large, it is essential to design the instrument so that as many reflections as possible are measured simultaneously. Consistently with this requirement, our diffractometer was equipped with a linear position-sensitive detector, and the crystal, mounted on a three-circle goniometer of the type illustrated in Fig. 8, was rotated according to according to prep. 1. As stated or indicated by; on the authority of: according to historians. 2. In keeping with: according to instructions. 3. the flat-cone Weissenberg geometry (12). With this technique, all reflections of any given layer of the reciprocal lattice In crystallography, the reciprocal lattice of a Bravais lattice is the set of all vectors K such that for all lattice point position vectors R. develop on a single plane, which is made to coincide with the plane formed by the linear detector and the incident beam, as shown schematically in Fig. 9 (13). This machine became obsolete with the advent of two-dimensional detectors, but in its lifetime valuable data were collected with it, which were used to solve the structure of the bovine bovine /bo·vine/ (bo´vin) pertaining to, characteristic of, or derived from cattle. bovine pertaining to, characteristic of, or derived from the ox or cattle, members of the family Bovidae. See also cattle. pancreatic pancreatic /pan·cre·at·ic/ (pan?kre-at´ik) pertaining to the pancreas. pancreatic pertaining to the pancreas. See also pancreatitis, diabetes mellitus, cystic pancreatic duct. trypsin trypsin, enzyme that acts to degrade protein; it is often referred to as a proteolytic enzyme, or proteinase. Trypsin is one of the three principal digestive proteinases, the other two being pepsin and chymotrypsin. inhi bitor (14). 3. Structural Studies 3.1 Neutrons and X-Rays In order to understand the type of structural problems studied by neutron diffraction at the NBS/NIST reactor is it necessary to briefly summarize the main properties of the neutron radiation Noun 1. neutron radiation - radiation of neutrons (as by a neutron bomb) ionizing radiation - high-energy radiation capable of producing ionization in substances through which it passes and to underline underline an animal's ventral profile; the shape of the belly when viewed from the side, e.g. pendulous, pot-belly, tucked up, gaunt. the differences between the neutron techniques and the older and more conventional x-ray methods. The wavelength of monochromatic beams of thermal neutrons thermal neutron n. See slow neutron. thermal neutron See slow neutron. used in structural investigations is of the order of 1 [Angstrom], i.e., similar to that of x rays used for the same purpose. The two types of radiation, however, are scattered by atoms in quite different ways. In the case of x rays, the fundamental scattering is generated by the extra nuclear electrons, which, by virtue of their charge, interact with the incident beam. In the case of neutrons, the fundamental scattering is generated by the atomic nuclei nuclei /nu·clei/ (noo´kle-i) [L.] plural of nucleus. nu·cle·i n. Plural of nucleus. nuclei plural of nucleus. , except for magnetic materials where also electronic scattering can be significant (see article entitled "Magnetic Structure Determinations at NBS/NIST" in this Special Issue). The two scattering processes result in qualitative and quantitative differences in the way in which structural experiments are carried out and in the type of results obtained in the two cases, as we will soon describe. Since the dimension of the electron clouds
Electron cloud is a term used, if not originally coined, by the Nobel Prize laureate and acclaimed educator Richard Feynman in The surrounding the atomic nuclei are comparable with the wavelengths of the x-rays used in crystallography (0.7 [Angstrom] to 2.0 [Angstrom]), the amplitude of the scattered radiation will fall off rapidly when the angle between incident and scattered directions increases. On the other hand, neutron scattering The term "Neutron Scattering" encompasses all scientific techniques whereby the deflection of neutron radiation is used as a scientific probe. It falls into two basic categories - elastic and inelastic scattering. is essentially isotropic Refers to properties that do not differ no matter which direction is measured. For example, an isotropic antenna radiates almost the same power in all directions. In practice, antennas cannot be 100% isotropic. because the size of the atomic nuclei is small compared with the wavelength of thermal neutrons. In other words Adv. 1. in other words - otherwise stated; "in other words, we are broke" put differently , the scattering amplitude The scattering amplitude describes the amplitude of an outgoing, elementary, spherical wave relative to a plane, incoming wave scattered on a point size particle. Since the spherical wave amplitude varies with  yttrium yttrium (ĭt`rēəm) [for Ytterby, a town in Sweden], metallic chemical element; symbol Y; at. no. 39; at. wt. 88.9059; m.p. about 1,522°C;; b.p. 3,338°C;; sp. gr. about 4.45; valence +3. Yttrium is a highly crystalline iron-gray metal. atom are shown as
function of (sin [theta]/[gamma]). The consequence of this effect is
that the intensities of x-ray diffraction patterns are significantly
weakened at high values of [theta], while those of neutrons are not. In
practical terms this means that in a neutron experiment we can collect
data also at high values of [theta], where the intensities are very
sensitive to both the positional and thermal parameters of the atoms in
a structure. It is worthwhile to note that a precise knowledge of the
atomic temperature factors is important not only to evaluate appropriate
corrections to the bond lengths, but also to understand the role of
molecular motions in phase transitions. An example of this application
of neutron diffraction is the study by Choi and Prince of several metal
azides (specifically, [beta]-[NaN.sub.3], [KN.sub.3], [RbN.sub.3], and
[TlN.sub.3]) done at the NBS reactor (15,16). In this series of
experiments it was shown that the azide azideinhibitor of cytochrome c oxidase (or complex IV) of the respiratory electron-transfer chain. ions are linear and centrosymmetric and that their thermal vibrations could be treated as rigid body Rigid body An idealized extended solid whose size and shape are definitely fixed and remain unaltered when forces are applied. Treatment of the motion of a rigid body in terms of Newton's laws of motion leads to an understanding of certain important motions. As mentioned previously, since the x rays interact with the extra nuclear electrons, the amplitude scattered by an atom is generated by the contribution of all the electrons surrounding the nucleus. It follows that the intensities diffracted by crystals containing heavy and light atoms at the same time will be dominated by the heavy atoms. While this property has been used in the past as a way to solve a large number of crystal structures (especially, but not exclusively, of organic compounds) (17-19), in many cases its presence makes it difficult to locate with precision the light atoms and to determine their thermal and occupancy parameters. In the case of neutrons the scattering amplitude of all atoms is in general of the same order (within a factor of 2 or 3) and does not show a regular dependence on the atomic number atomic number, often represented by the symbol Z, the number of protons in the nucleus of an atom, as well as the number of electrons in the neutral atom. Atoms with the same atomic number make up a chemical element. . As a consequence, positional and thermal parameters of light atoms can be determined in a neutron experiment even when the number of heavy atoms in a compound is large. Examples illustratin g this property of neutrons are numerous in the literature. In the case of the azides mentioned previously, the position of the N atoms could be easily determined in the neutron experiment since the coherent scattering length b of N is of the same order as those of the metal atoms (e.g., 0.926 x [10.sup.-12] and 0.878 X [10.sup.-12] cm for N and Tl, respectively; note that the atomic numbers of the two elements are 7 and 81). Another example is the 123 superconductor [YBa.sub.2][Cu.sub.3][O.sub.6+x] (with 0 [less than or equal to]x<7), for which the scattering lengths of oxygen, copper, yttrium and barium barium (bâr`ēəm) [Gr.,=heavy], metallic chemical element; symbol Ba; at. no. 56; at. wt. 137.33; m.p. 725°C;; b.p. 1,640°C;; sp. gr. 3.5 at 20°C;; valence +2. are 0.581 X [10.sup.-12], 0.772 X [10.sup.-12], 0775 X [10.sup.-12], and 0.507 X [10.sup.-12] cm, respectively, and the corresponding atomic numbers 8, 29, 39, and 56. This situation has allowed crystallographers to solve the structure with great precision and to determine the number and the location of the oxygen vacancies over the entire range of x (20-22). An additional, important difference between x rays and thermal neutrons is the extent to which they are absorbed in materials. In a significant number of cases, which include the majority of heavy atom elements, the absorption of thermal neutron is negligible, while that of x rays is very large and requires special experimental procedures to reduce its effects and/or the evaluation of complicated corrections to the observed intensities, even when small samples are used. This point is illustrated in Table 1 for the 123 compound [YBa.sub.2][Cu.sub.3][O.sub.7]. The absorption of this material for x rays and neutrons of wavelengths 1.54 [Angstrom] and 1.08 [Angstrom], respectively, is expressed in terms of the mass absorption coefficient absorption coefficient n. 1. The milliliters of a gas at standard temperature and pressure that will saturate 100 milliters of liquid. 2. The amount of light absorbed in 1 atom or in 1 unit of thickness or mass of a given substance. ([micro]/[rho]) (where [micro] is the linear absorption coefficient in [cm.sup.-1] and [rho] density of the sample in [gcm.sup.-3]) because this quantity is approximately independent of the physical state of the compound and its value can be obtained, to a good approximation approximation /ap·prox·i·ma·tion/ (ah-prok?si-ma´shun) 1. the act or process of bringing into proximity or apposition. 2. a numerical value of limited accuracy. , by adding the mass absorption coefficients of the elements according to the equation [micro]/[rho] = [summation summation n. the final argument of an attorney at the close of a trial in which he/she attempts to convince the judge and/or jury of the virtues of the client's case. (See: closing argument) over (i)][[gamma].sub.i][([micro]/[rho]).sub.i] (11) where [[gamma].sub.i] is the mass fraction contributed by element i of mass absorption coefficient [([micro]/[rho]).sub.i], and the summation is taken over all the constituent elements i. The low value of [micro]/[rho] evaluated for neutrons means that the attenuation Loss of signal power in a transmission. Attenuation The reduction in level of a transmitted quantity as a function of a parameter, usually distance. It is applied mainly to acoustic or electromagnetic waves and is expressed as the ratio of power densities. of the primary beam in a neutron experiment is essentially due to the diffraction taking place in the sample (secondary extinction), rather than to true absorption. An important consequence of this property is that it makes it possible to use large or bulky samples, thus reducing the data collection time, and to minimize, or eliminate, preferred orientation effects in experiments done with the powder technique Noun 1. powder technique - a process for identifying minerals or crystals; a small rod is coated with a powdered form of the substance and subjected to suitably modified X-rays; the pattern of diffracted rings is used for identification . As we will show later, the low absorption of thermal neutron has been used to great advantage in texture studies of bulky samples of metals and alloys. 3.2 Crystal Structure Analyses 3.2.1 Solid State Ionics In general, the structures of ionic i·on·ic adj. Of, containing, or involving an ion or ions. ionic pertaining to an ion or ions. ionic medication iontophoresis. conductors are made of two parts, one formed by atoms or ions in fixed positions and the other by ions of high mobility, which account for the ionic conductivity conductivity /con·duc·tiv·i·ty/ (kon?duk-tiv´i-te) the capacity of a body to transmit a flow of electricity or heat; the conductance per unit area of the body. con·duc·tiv·i·ty n. 1. . The atoms in fixed positions form the so-called framework structure (24), which may have a wide range of complexity. For example, in [alpha]-AgI it is a simple body centered arrangement of I ions with cubic symmetry (25); in Na[beta]- and [beta]"- alumina alumina (əl  `mĭnə) or aluminum oxide, Al2O3, chemical compound with m.p. about 2,000°C; and sp. gr. about 4.0. it is a block of two or
three units of a spinel-like structure (26), and in some zeolites it may
be a still more complex assemblage assemblage: see collage. assemblage Three-dimensional construction made from household materials such as rope and newspapers or from any found materials. of cage-like units (27). An accurate knowledge of the geometry of the framework structure is essential for understanding the conduction conduction, transfer of heat or electricity through a substance, resulting from a difference in temperature between different parts of the substance, in the case of heat, or from a difference in electric potential, in the case of electricity. mechanisms in these compounds. In fact, the mobility of the disordered ions between sites depends, among other things, on the size of the opening through which the ions move. An example of the analysis of the geometrical factors involved in this process is given in Ref. (28) for the compound [Na.sub.4][Zr.sub.2][Si.sub.3][O.sub.12]. In this structure there are theoretically four possible pathways for diffusion, but only one of them is sufficiently large In mathematics, the phrase sufficiently large is used in contexts such as:
The mobile ions are somehow distributed among sites of multiplicity greater than the actual number of ions in the unit cell, and their diffusion within the framework structure may occur with different mechanisms. In [alpha]-AgI, for example, the two [Ag.sup.+] cations in the unit cell are distributed over twelve energetically equivalent sites and may move in a three-dimensional system of pathways (25). In sodium [beta]"-alumina, the [Na.sup.+] cations are free to move in two-dimensional layers between the rigid spinel-like blocks (26). Finally, in materials such as [ZrO.sub.2] stabilized with CaO, the [O.sup.2-] ions are located in well defined crystallographic sites which are only partially occupied, and the conduction takes place through this defective structure, with the oxygen ions diffusing from the occupied to the vacant sites (29). The above discussion shows that, in order to prepare compounds which are potential ionic conductors it is necessary to start with appropriate framework structures into which the mobile ions are inserted. The insertion reaction An insertion reaction is a chemical reaction where one chemical entity interposes itself into an existing bond of typically a second chemical entity e.g.: A + B-C → B- changes the chemical and structural nature of the host in ways that are largely unpredictable. A knowledge of the insertion mechanism and of the changes that the inserted ions cause is therefore needed to prepare solid state ionics and/or to predict which framework structures are most favorable for the formation of these useful materials. In particular, compounds which undergo topotactic insertion of lithium lithium (lĭth`ēəm) [Gr.,=stone], metallic chemical element; symbol Li; at. no. 3; at. wt. 6.941; m.p. about 180.54°C;; b.p. about 1,342°C;; sp. gr. .534 at 20°C;; valence +1. Lithium is a soft, silver-white metal. are interesting because of their potential use as electrodes Electrodes Tiny wires in adhesive pads that are applied to the body for ECG measurement. Mentioned in: Electrocardiography in secondary batteries. Lithium is ionic in these materials and the charge introduced by [Li.sup.+] in the host structure is compensated by a corresponding reduction in the oxidation state oxidation state See valence. Noun 1. oxidation state - the degree of oxidation of an atom or ion or molecule; for simple atoms or ions the oxidation number is equal to the ionic charge; "the oxidation number of hydrogen is +1 and of the host cations. Since the insertion of extra ions usually causes significant changes which may pulverize pul·ver·ize v. pul·ver·ized, pul·ver·iz·ing, pul·ver·iz·es v.tr. 1. To pound, crush, or grind to a powder or dust. 2. To demolish. v.intr. the starting materials, i t is in general difficult or impossible to grow single crystals of the inserted compounds, and consequently the powder technique, coupled with profile refinement analysis, is the only method for studying this type of structures. As we have discussed previously, neutrons must be used, since they are more sensitive than x-rays in locating the light [Li.sup.+] ions in the structure. Lithium inserted materials were being studied in the early 1980s at the Ceramics Division of NBS and at Bell Laboratories (#) in Murray Hill Murray Hill may refer to one of the following places:
Compounds such as [ReO.sub.3] (and [WO.sub.3]) are suitable framework structure for [Li.sup.+] and, in fact the system [Li.sub.x][ReO.sub.3] exists in three distinct phases with composition 0 [less than or equal to] x [less than or equal to] 0.35, x = 1.0 and 1.8 [less than or equal to] x [less than or equal to] 2.0. The structure of [ReO.sub.3] has the perovskite arrangement of the [ReO.sub.6] octahedra (Fig. 11) and the cuboctahedral cavity, normally occupied by the large A cations in the A B [O.sub.3] perovskites, is in this case empty. For concentrations less than 0.35 Li atoms per formula unit, the [Li.sup.+] ions occupy this cavity (30). The symmetry for the composition [Li.sub.0.2][ReO.sub.3] is that of the cubic space group [Im.sub.3], and is produced by a distortion of the original [ReO.sub.3] structure caused by a cooperative rotation of the [ReO.sub.6] octahedra, as illustrated in Fig. 12. The nature of the distortion can be understood if we remember that in the perovskite configuration (see Fig. 11) the octahedra share corners, so that if any one of them is tilted, all the others will also rotate. This situation is illustrated in Fig. 13 for the simple case in which the tilt axis is Axis I Psychiatry A classification dimension used with DSM-IV, which includes clinical disorders and syndromes and/or other areas of concern. See DSM-IV, Multiaxial system. parallel to the vertical axis of the structure. In [Li.sub.0.2][ReO.sub.3], the geometry of the final configuration is more complex because a tilt of the same angle occurs about all three crystallographic axes simultaneously. It can be shown (31) that the tilt angle Noun 1. tilt angle - the angle a rocket makes with the vertical as it curves along its trajectory angle - the space between two lines or planes that intersect; the inclination of one line to another; measured in degrees or radians [phi] is related to the a-parameter of the Im3 structure (a = 7.3979 [Angstrom]) and to the Re-O bond distance (d = 1.887 [Angstrom]) by the equation cos [phi] = (3a-4 d)/8d (12) so that, for our structure the tilt angle is [phi] [approximately equal to] 14[degrees]. It is worthwhile noting that in general, in this type of distortions the octahedra remain essentially the same. For example, the Re-O distances in [ReO.sub.3] and in [Li.sub.0.2][ReO.sub.3] are practically unchanged, the difference being of the order of one hundredth of an [Angstrom], and the O-Re-O angles are quite close to 90[degrees]. The tilt system that accompanies the Li insertion when [LiReO.sub.3] and [Li2ReO.sub.3] are formed is more complex and more extensive than the one discussed previously (32). In this configuration, the angle [phi] is of the order of 30[degrees] and in the resulting structure the cub-octahedral cavity of [ReO.sub.3] is changed into two face-sharing octahedra with six tetrahedra on the re-entrant (programming) re-entrant - Used to describe code which can have multiple simultaneous, interleaved, or nested invocations which will not interfere with each other. This is important for parallel processing, recursive functions or subroutines, and interrupt handling. faces (see Fig. 14). The symmetry of this structure is R3c and the two octahedra are fully occupied by Li in [Li.sub.2][ReO.sub.3] and only half occupied in [LiReO.sub.3]. This result shows that the tilt system of the [ReO.sub.3] host structure produces a coordination favorable to the insertion of one and two atoms of Li per formula unit, and it is made possible by the fact that the [ReO.sub.6] octahedra share corners. 3.2.2 Crystallography of Superconductors: the System Ba ([Pb.sub.1-x][Bi.sub.x])[O.sub.3] It is important to point out that high-temperature superconductivity Unsolved problems in physics: What is the responsible mechanism that causes certain materials to exhibit superconductivity at temperatures much higher than around 50 kelvin? High-temperature superconductors (abbreviated high in ceramic materials was first observed in the system Ba ([Pb.sub.1-x][Bi.sub.x])[O.sub.3] (33). Soon after this discovery, structural studies were carried out over the entire range of compositions 0 [less than or equal to]x< 1 (34-39). Although the general structural features of Ba ([Pb.sub.1-x][Bi.sub.x])[O.sub.3] do not change dramatically with composition, the type of distortions present in the basic atomic arrangement does vary with x. At room temperature, the symmetry changes according to the sequence 0[less than or equal to]x[less than or equal to]0.05 orthorhombic 0.05[less than or equal to]x[less than or equal to]0.35 tetragonal 0.35[less than or equal to]x[less than or equal to]0.90 orthorhombic 0.90[less than or equal to]x[less than or equal to]1.00 monoclinic Superconductivity superconductivity, abnormally high electrical conductivity of certain substances. The phenomenon was discovered in 1911 by Kamerlingh Onnes, who found that the resistance of mercury dropped suddenly to zero at a temperature of about 4.2°K;. exists only in the tetragonal tet·ra·gon n. A four-sided polygon; a quadrilateral. [Late Latin tetrag phase. The value of the critical temperature [T.sub.c] increases with x, reaches a maximum of [T.sub.c] [approximately equal to] 13 K for x [approximately equal to] 0.25, and then decreased between 0.25 and 0.35. The arrangement of the atoms in this system is closely related to that of Perovskite and the structure of the superconducting su·per·con·duct·ing adj. Having, exhibiting, or capable of superconductivity: "a revolutionary superconducting magnetic propulsion system" Colin Nickerson. tetragonal phase, schematically shown in Fig. 15, can be generated by tilting consecutive ([Pb.sub.1-x][Bi.sub.x])[O.sub.6] octahedra of the same angle (about 8[degrees] for x = 0.25), but in opposite directions, about the c-axis of the unit cell. For a complete characterization of this system we have to know the oxidation state of the Bi atoms, since two formulations are possible as indicated below Ba ([Pb.sup.4+.sub.1-x] [Bi.sub.x.sup.4+])[O.sub.3] and Ba[[Pb.sup.4+.sub.1-x] ([Bi.sup.3+.sub.1-x] [Bi.sup.5+.sub.0.5])x][O.sub.3]. Most of the structural studies carried out to determine the valence Valence, city, France Valence (väläNs`), city (1990 pop. 65,026), capital of Drôme dept., SE France, in Dauphiné, on the Rhône River. of Bi have been done with samples of [BaBiO.sub.3] (37,39), in which Bi is located in two crystallographically crys·tal·log·ra·phy n. The science of crystal structure and phenomena. crys tal·log independent positions of the
monoclinic mon·o·clin·ic adj. Of or relating to three unequal crystal axes, two of which intersect obliquely and are perpendicular to the third. monoclinic Adjective Crystallog space group 12/m. Powder neutron diffraction results have shown that the distances Bi(1)-O and Bi(2)-O are significantly different (2.283 [Angstrom] and 2.126 [Angstrom], respectively) and, from these values, it was concluded that the site Bi(l) is occupied by [Bi.sup.3+] cations, and site Bi(2) by [Bi.sup.5+]. X-ray photoemission spectroscopy Photoemission Spectroscopy (PES) also known as photoelectron spectroscopy, refers to energy measurement of electrons emitted from solids, gases or liquids by the photoelectric effect, in order to determine the binding energies of electrons in a substance. on single crystal of BaBiO3 confirmed that there are two independent positions for Bi (40). However, the difference in electrons density was found to be too small to justify a complete disproportionation Disproportionation or dismutation is used to describe two particular types of chemical reaction:[1]
tr.v. cor·rob·o·rat·ed, cor·rob·o·rat·ing, cor·rob·o·rates To strengthen or support with other evidence; make more certain. See Synonyms at confirm. in subsequent neutron diffraction experiments at the reactor (42) which showed that there are in fact two polymorphs of BaBi[O.sub.3], one in which the site Bi(1) has a valence of about 3.5+ and site Bi(2) a valence of 4.5+, and the other in which the two sites have both valence 4.0+, i.e., contain an almost equal proportion of [Bi.sup.3+] and [Bi.sup.5+]. The charge ordering between the two sites, i.e., the existence of one polymorph polymorph /poly·morph/ (pol´i-morf) colloquial term for polymorphonuclear leukocyte. polymorph a colloquial term for a polymorphonuclear leukocyte. or the other, depends on the method of preparation of the samples and on their thermal history, and in fact, the two phases can be transformed into one another by heat treatment. It is interesting to note that the same assumption of a disordered distribution of the Bi ions has been made to explain the behavior of the system [Ba.sub.1-x][K.sub.x][BiO.sub.3] (43,44). 3.2.3 The System [La.sub.2-x][M.sub.x][CuO.sub.4-y] (M = Ba, Sr) The discovery of superconductivity in this system was made on a sample consisting of a mixture of phases (45), and only in subsequent experiments was the superconducting material identified as [La.sub.2-x][Ba.sub.x][CuO.sub.4-y] (46,47). This compound has the [K.sub.2][NiF.sub.4]-type structure at room temperature, consisting of alternate layers with the perovskite and rocksalt structure, as illustrated in Fig. 16. The value of the critical temperature [T.sub.c] is also, in this case, a function of x and reaches its maximum of about 35 K for x[approximately equal to]0.15. The detailed structure for this composition was determined by neutron powder diffraction Powder diffraction is a scientific technique using X-Ray or neutron diffraction on powder or microcrystalline samples for structural characterization of materials. Ideally, every possible crystalline orientation is represented equally in a powdered sample. (48,49) which showed that the symmetry at room temperature is tetragonal I4/mmm and that a transition to an orthorhombic or·tho·rhom·bic adj. Of or relating to a crystalline structure of three mutually perpendicular axes of different length. orthorhombic phase with space group Cmca occurs at about 180 K (49). The lattice parameters of the two phases are related so that [a.sub.0] [approximately equal to] [c.sub.0] [approximately equal to] [a.sub.t][square root of (2)] and [b.sub.0] [approximately equal to] [c.sub.t], where [a.sub.0], [b.sub.0], and [c.sub.0] are the parameters of the orthorhombic cell and [a.sub.t] and [c.sub.t] these of the tetragonal cell. At this stage attempts were being made to prepare compounds with values of [T.sub.c] higher than 35 K, and the system [La.sub.2-x] [Ba.sub.x] [CuO.sub.4-y] was considered as a candidate at Bell Laboratories. The composition x[approximately equal to]0.15 was found to have [T.sub.c] [approximately equal to] 40 K and its structure was refined at the NBS reactor using neutron powder diffraction data (5). This analysis showed that the Ba and Sr compounds are isomorphic (mathematics) isomorphic - Two mathematical objects are isomorphic if they have the same structure, i.e. if there is an isomorphism between them. For every component of one there is a corresponding component of the other. at room temperature and that also the Sr compound undergoes a phase transition from tetragonal to orthorhombic at about 200 K. At all temperatures, the lanthanum lanthanum (lăn`thənəm) [Gr.,=to lie hidden], metallic chemical element; symbol La; at. no. 57; at. wt. 138.9055; m.p. about 920°C;; b.p. about 3,460°C;; sp. gr. 6.19 at 25°C;; valence +3. and strontium strontium (strŏn`shēəm) [from Strontian, a Scottish town], a metallic chemical element; symbol Sr; at. no. 38; at. wt. 87.62; m.p. 769°C;; b.p. 1,384°C;; sp. gr. 2.6 at 20°C;; valence +2. atoms were found to be distributed at random over the same equivalent positions. A schematic picture of the tetragonal structure is shown in Fig. 17, where the perovskite-like planes are emphasized to illustrate the two-dimensional nature of the copper-oxygen layers perpendicular to the c-axis. These layers are separated by the La/Sr-oxygen planes, so that the copper atoms in on e plane do not share oxygen atoms with copper atoms located on other planes. The Cu-O distances within the perovskite-like planes are short (about 1.89 [Angstrom]) while those in the perpendicular direction are long (about 2.41 [Angstrom]), and consequently the coordination polyhedron polyhedron (pŏl'ēhē`drən), closed solid bounded by plane faces; each face of a polyhedron is a polygon. A cube is a polyhedron bounded by six polygons (in this case squares) meeting at right angles. around copper is a bi-pyramid, rather than an octohedron. The shape of the bi-pyramid changes in a subtle way when the symmetry is lowered from tetragonal to orthorhombic. More specifically, the base becomes rectangular and the copper-oxygen planes are buckled as a consequence of small but significant rotations of the bi-pyramids about axes parallel to the a- and b- directions, as shown in Fig. 18. The neutron diffraction studies of the Ba and Sr compounds showed no oxygen deficiency. This means that the charge compensation for the substitution of [La.sup.3+] with [Ba.sup.2+] or [Sr.sup.2+] must be accomplished entirely by oxidation of copper from 2+ to 3+. By assuming a simple ionic model, the oxidation state of copper in [La.sub.1.85][M.sub.0.15][CuO.sub.4] is 2.15+, i.e., the Cu sites are occupied by [Cu.sup.2+] and [Cu.sup.3+] in the ratio 17/3. 3.2.4 The System [YBa.sub.2][Cu.sub.3][O.sub.x] Superconductivity with [T.sub.c] [approximately equal to] 94 K was discovered in a sample which was a mixture of phases (51) and, again, the superconducting compound was identified later in several laboratories as [YBa.sub.2][Cu.sub.3][O.sub.x], with x [approximately equal to] 7.0 (52-54). Profile analysis based on neutron powder data quickly gave an accurate description of the structure which is shown in Fig. 19, next to the structure of perovskite to underline the similarities and the differences between the two atomic arrangements. The refined structural parameters obtained in some of the most accurate neutron diffraction studies of the composition x [approximately equal to] 7.0 are given in Table 2, which has been taken from Ref. (55), and the bonding scheme and the atomic coordinations are illustrated in Fig. 20. Figure 19 shows that the structure of [YBa.sub.2][Cu.sub.3][O.sub.7] is obtained from that of perovskite by tripling the c-axis, by eliminating in an orderly fashion some of the oxygen atoms, and by ordering the Y and Ba atoms along the c-axis of the unit cell. The copper atoms are located on two crystallographically independent sites of the orthorhombic space group Pmmm. The first, labeled Cu(1), has four-fold planar A technique developed by Fairchild Instruments that creates transistor sublayers by forcing chemicals under pressure into exposed areas. Planar superseded the mesa process and was a major step toward creating the chip. coordination in which the near square [CuO.sub.2] units share corners and form chains along the b-axis, and the second, Cu(2) has a pyramidal coordination with two Cu(2)-O(2) and two Cu(2)-O(3) short bonds (1.930 [Angstrom] and 1.961 [Angstrom], respectively) and one Cu(2)-O(1) long bond (2.295 [Angstrom]). Because of this peculiar structural feature, there are in the structure two dimensional layers of composition [CuO.sub.2] perpendicular to the c-axis. The oxygen atoms in the layers are slightly shifted from their ideal perovskite positions, producing a buckling buckling Mode of failure under compression of a structural component that is thin (see shell structure) or much longer than wide (e.g., post, column, leg bone). Leonhard Euler first worked out in 1757 the theory of why such members buckle. of the Cu(2)-O(23) bonds, as in dicated in Fig. 19. It was soon observed that the oxygen stoichiometry stoichiometry Determination of the proportions (by weight or number of molecules) in which elements or compounds react with one another. The rules for determining stoichiometric relationships are based on the laws of conservation (see in [YBa.sub.2][Cu.sub.3][O.sub.x] may be lower than seven atoms per formula unit, depending on the preparation and the thermal history of the sample, and that the oxygen vacancies associated with the decrease of the oxygen content involve only the O(4) sites of the [CuO.sub.2] chains (20). When the number of vacancies becomes sufficiently large, the sites O(5), which are empty for x = 7.0, become gradually filled and, at some point, the structure from or thorhombic Pmmm becomes tetragonal P4/mmm. The transition is a function of temperature and oxygen content, and, using appropriate procedures, the orthorhombic modification can be retained at compositions as low as x = 6.3. The value of the critical temperature [T.sub.c] decreases as x decreases, and it becomes equal to zero when the orthorhombic to tetragonal transition takes place. When x = 6.0, all O(4) and O(5) sites are empty, and the coordinations of Cu(l) and Ba became two and eight-fold, respectively (58). The structural changes occurring in [YBa.sub.2][Cu.sub.3][O.sub.x] over the entire range of compositions 6.0[less than or equal to]x<7.0 have been studied in two accurate and extensive sets of neutron diffraction experiments (21,22), and the interpretation of these observations has been provided by Brown, using the bond valence method The bond valence method (or bond valence sum) (not to be mistaken for the valence bond theory in quantum chemistry) is a popular method in coordination chemistry to estimate the oxidation states of atoms. of analysis (59,60). By comparing the a-axis parameter measured experimentally with that calculated from the theoretical Ba-O(l), Cu(l)-O(4) and Cu(2)-O(23) distances consistent with different valences of the chain and pyramidal copper atom, Brown was able to prove that the oxidation states of Cu(1) and Cu(2) in [YBa.sub.2][Cu.sub.3][O.sub.6] are 1+ and 2+, respectively, while they are approximately the same (2.33 +) for x = 7.0. This means that adding oxygen to the O(4) sites on the plane of the Cu(1) atoms increases not only the oxidation state of Cu(l), but also that of Cu(2), i.e., a charge transfer between the two copper atoms takes place during the oxidation, or reduction , of the compound. The Ba-O (1) and Cu(2)-O(23) bonds at x = 6.0 are strained because they are incommensurate in·com·men·su·rate adj. 1. a. Not commensurate; disproportionate: a reward incommensurate with their efforts. b. Inadequate. 2. Incommensurable. when the oxidation states of Cu(1) and Cu(2) are 1+ and 2+. As the oxidation progresses, however, the incommensurability in·com·men·su·ra·ble adj. 1. a. Impossible to measure or compare. b. Lacking a common quality on which to make a comparison. 2. Mathematics a. of these bonds decreases, and the strains are almost completely relieved at x = 7.0. This behavior, therefore, suggests that the observed charge distribution (and all the properties related to it) at different oxygen stoichiometries is a consequence of the commensurability com·men·su·ra·ble adj. 1. Measurable by a common standard. 2. Commensurate; proportionate. 3. Mathematics Exactly divisible by the same unit an integral number of times. Used of two quantities. of the Cu-O and Ba-O bonds. 3.2.5 The System [RBa.sub.2][Fe.sub.3][O.sub.8+x] The substitution of copper by other metal species in the structure of [YBa.sub.2][Cu.sub.3][O.sub.x] has been used extensively to investigate the correlation between the changes induced into the structure by the substituting cations and the variation of the superconducting properties. The first studies in this direction involved the partial replacement of either the chain copper atoms Cu(l), e.g., (61), or the plane copper atoms Cu(2), e.g., (62). From these experiments it was found that the introduction of dopants decreases the value of Tc and that the change is very drastic when the atoms Cu(2) are replaced even by small amounts of other elements such as Zn and Ni. These results were taken as evidence that the two-dimensional Cu(2)O[(23).sub.2] layers play a fundamental role in the super-conducting process. Full replacement of copper by other elements, therefore, is important for understanding why copper, of all transition metals, seems to be necessary for superconductivity to occur in this structural type. For this reason collaboration between the NBS reactor and the University of Oslo The University of Oslo (Norwegian: Universitetet i Oslo, Latin: Universitas Osloensis) was founded in 1811 as Universitas Regia Fredericiana (the Royal Frederick University was established in the early nineties to study the system in which copper is entirely replaced by iron. The first compound investigated in this series of experiments was stoichiometric stoi·chi·om·e·try n. 1. Calculation of the quantities of reactants and products in a chemical reaction. 2. The quantitative relationship between reactants and products in a chemical reaction. [YBa.sub.2][Fe.sub.3][O.sub.8] (63). The nuclear structure of this material has the symmetry of space group P 4/nmm and is illustrated in Fig. 21. The configuration of the atoms in the unit cell is very similar to that of the superconductor [YBa.sub.2][Fe.sub.3][O.sub.7], with the exception that the iron atoms Fe(1), corresponding to Cu(l), have octahedral oc·ta·he·dral adj. Having eight plane surfaces. oc ta·he dral·ly adv. coordination, rather than
fourfold fourfoldAdjective 1. having four times as many or as much 2. composed of four parts Adverb by four times as many or as much Adj. 1. planar, and the Fe(1)[O.sub.6] octahedra are arranged in layers. This significant difference is a consequence of the fact that all possible oxygen sites on the Fe(1) plane are fully occupied, giving an oxygen content of eight atoms per formula unit. A second consequence is that the Ba atoms have twelve-fold cuboctahedral coordination. This configuration results in a rather strained structure in which the polyhedron around Ba is considerably compressed. During the structural refinements based on neutron diffraction data, it was realized that the nuclear structure of the iron compound did not account for all the observed intensities, and especially for those of some strong reflections at low values of the 2 [theta] angle. Polarized A one-way direction of a signal or the molecules within a material pointing in one direction. neutron diffraction experiments revealed that these intensities have magnetic origin, and a subsequent analysis showed that they are consistent with a magnetic structure in which the iron moments lie on the a, b plane and are coupled antiferromagnetically within each [FeO.sub.2] layer, as well as along the c-axis, as indicated by the arrows associated with the Fe atoms in Fig. 21. The magnetic moments of the two iron atoms were found to be equal to each other (3.49 [[micro].sub.B] in both cases) thus showing that the oxidation states of Fe(l) and Fe(2) are also the same (3+). The results of our study were confirmed later by x-ray powder diffraction, magnetic susceptibility Magnetic susceptibility The magnetization of a material per unit applied field. It describes the magnetic response of a substance to an applied magnetic field. and Mossbauer spectroscopy spectroscopy Branch of analysis devoted to identifying elements and compounds and elucidating atomic and molecular structure by measuring the radiant energy absorbed or emitted by a substance at characteristic wavelengths of the electromagnetic spectrum (including gamma ray, (64, 65). In another experiment, however, the differences between the magnetic hyperfine fields at Fe(1) and Fe(2) were interpreted as evidence that the valence states and the magnetic moments of the two iron sites are not the same (66). In order to resolve this uncertainty we have carried out a complete bond-valence analysis of the structure and found that the atomic configuration of the iron compound is consistent with an equal distribution of charge on the Fe(1) and Fe(2) sites, thus confirming our original conclusion based on the determination of the magnetic structure (67). Soon after the original study described in Ref. (63), it was realized that [YBa.sub.2][Fe.sub.3][O.sub.8+x] can exit in a narrow range of compositions, with -0.2 <x< 0.1. The location of the oxygen in excess of the [O.sub.8] stoichiometry was determined in the analysis of the Ca-doped compound ([Y.sub.1-y] [Ca.sub.y]) [YBa.sub.2][Fe.sub.3][O.sub.8+x] (68). As indicated in Fig. 21 these atoms occupy the O(int.) sites, on the plane of the Y atoms. Their presence in the structure introduces significant disordering of the atoms in the O(23) sites and increases the average coordination of Y and Fe(2). On the other hand, the presence of oxygen vacancies involves the O(45) sites and cause a decrease of the average coordination of Ba and Fe(2). 3.2.6 Hg-Based Superconductors In the early nineties, superconductivity with [T.sub.c] [approximately equal to] 94 K was discovered in the mercury based compound [HgBa.sub.2][CuO.sub.4+x] (69). The structure of this material was first determined by x-ray powder diffraction and is schematically illustrated in Fig. 22. The atomic configuration of this compound can be conveniently described by means of the layer sequence ...[[(BaO).sub.c][(Hg[O.sub.x]).sub.0][(BaO).sub.c][(Cu[O.sub.2]).sub .0][(BaO).sub.c]... where the square brackets square bracket n. One of a pair of marks, [ ], used to enclose written or printed material or to indicate a mathematical expression considered in some sense a single quantity. include the content of one unit cell and the subscripts c and o indicate if the cation cation (kăt'ī`ən), atom or group of atoms carrying a positive charge. The charge results because there are more protons than electrons in the cation. is at the center or at the origin, respectively, of the mesh of each layer. The formulae in parentheses See parenthesis. parentheses - See left parenthesis, right parenthesis. indicate the chemical composition of the layers. Since the extra oxygen atoms O(3) located on the plane of the Hg atoms are necessary to increase the oxidation state of copper, it is important to know how many of them can be incorporated in the structure and where exactly they are located on the layer. As we have mentioned earlier, x rays are not sufficiently sensitive to small amounts of oxygen in the presence of heavy atoms such as Ba and Hg, and for this reason the compound was studied at the NIST reactor in a collaborative project with the French and Russian authors who discovered this important material (70). The copper atoms in this structure (see Fig. 22) have a bi-pyramidal coordination similar to that found for [La.sub.1.85][Sr.sub.0.15][CuO.sub.4], with an apical apical /ap·i·cal/ (ap´i-k'l) pertaining to an apex. a·pi·cal adj. 1. Relating to the apex of a pyramidal or pointed structure. 2. Cu-O(2) distance of 2.78 [Angstrom], compared with the in-plane distance Cu-O(l) of 1.94 [Angstrom]. Most of the Ba atoms have eight-fold coordination. However, those located below and above the atoms O(3) are nine-coordinated and the coordination polyhedron may be considered a mono-capped square antiprism In geometry, the square antiprism is the second in an infinite set of antiprisms formed by an even-numbered sequence of triangle sides closed by two polygon caps. If all its faces are regular, it is a semiregular polyhedron. . Similarly, the Hg atoms are generally two-coordinated, except in those unit cells in which the sites O(3) are occupied by oxygen atoms. The compound [HgBa.sub.2][CuO.sub.4+x] is the first member of a homologous series homologous series (h  ·m of formula
[HgBa.sub.2][R.sub.n-1][Cu.sub.n][O.sub.2n+2+x] and having a structure
represented by the layer sequence...[[(BaO).sub.c][(Hg[O.sub.x]).sub.0][(BaO).sub.c][(Cu[O.sub.2]).sub .0] {(n-1)[(R).sub.c][(Cu[O.sub.2]).sub.0]}][(BaO).sub.c]... where R is an element situated on a layer that does not contain oxygen atoms and is therefore similar to the yttrium layer in [YBa.sub.2]R[Cu.sub.3][O.sub.x]. Thus, the layer sequence of the compound [HgBa.sub.2][Cu.sub.2][O.sub.6-x], corresponding to n = 2 is ...[[(BaO).sub.c][(Hg[O.sub.x]).sub.0][(BaO).sub.c][(Cu[O.sub.2]).sub .0][(R).sub.c][(Cu[O.sub.2]).sub.0]][(BaO).sub.c]... and so on. The sequences show that the structures of these compounds are made by blocks ... [(Cu[O.sub.2]).sub.0][(R).sub.c][(Cu[O.sub.2]).sub.0] ... having the configuration of perovskite, and by blocks ... [(BaO).sub.c][(Hg[O.sub.x]).sub.0][(BaO).sub.c] ... with the rock-salt structure. To avoid writing complex formulae, these materials are usually identified by indicating the number of the Hg, Ba, R, and Cu cations, respectively. Thus, the first member of the series is 1201, the second 1212, etc.. All members have the tetragonal symmetry of space group P 4/mmm and approximate lattice parameters a [approximately equal to] 3.85 [Angstrom] and c [approximately equal to] 9.5 + 3.2 (n-1) [Angstrom]. The oxygen content x depends on the preparation method and the annealing annealing (ənēl`ĭng), process in which glass, metals, and other materials are treated to render them less brittle and more workable. conditions of the sample. The maximum value of x in each member of the series, however, seems also to be function of n, i.e., of the number of layers that constitute the perovskite block (71, 72). The critical temperature [T.sub.c] is strongly dependent on x. An example of the behavior of [T.sub.c] is provided by the 1201 compound and is illustrated by the graph of Fig. 23, taken from Ref. (73). For x < 0.06, [T.sub.c] is equal to zero, then it increases with increasing x, reaches a maximum of [T.sub.c] [approximately equal to] 94 K for x [approximately equal to] 0.17, and then decreases. Similar behavior has been observed also for other members of the series. For each of these compounds, in which R = Ca, the maximum value of [T.sub.c] is a function of n, and, more specifically, it increases for increasing n up to n = 3, and then decreases as shown Table 3. 4. Zeolitic Ze`o`lit´ic a. 1. Of or pertaining to a zeolite; consisting of, or resembling, a zeolite. Materials (This section was written by B. H. Toby, Leader, Crystallography Team) 4.1 Introduction Zeolites and related microporous materials A microporous material is a material containing pores with diameters less than 2 nm. Porous materials are classified into several kinds by their size. According to IUPAC notation (see J. Rouquerol et al., Pure & Appl. (herein referred to as zeolitic materials) are crystalline materials consisting of alternating regions of framework atoms and voids. The framework is typically composed of tetrahedral tet·ra·he·dral adj. 1. Of or relating to a tetrahedron. 2. Having four faces. tet aluminum and silicon atoms linked by oxygen atoms and the voids or pores can range to just accommodating a water molecule, to pores large enough to fit a [C.sub.60] molecule or DNA DNA: see nucleic acid. DNA or deoxyribonucleic acid One of two types of nucleic acid (the other is RNA); a complex organic compound found in all living cells and many viruses. It is the chemical substance of genes. fragment. Zeolitic materials frequently form highly symmetric and complex structures that are elegant to behold be·hold v. be·held , be·hold·ing, be·holds v.tr. 1. a. To perceive by the visual faculty; see: beheld a tiny figure in the distance. b. . Further, these materials are industrially important for a number of diverse applications. At least one zeolite-based catalyst, and likely more than one, is employed to produce all domestic gasoline. Zeolitic catalysts are in creasingly used for the preparation of pharmaceuticals and other fine chemicals. Zeolitic materials have novel capabilities, which can often be enhanced to perform a particular chemical separation. They are frequently used commercially to separate gases, for example producing [N.sub.2] or [O.sub.2] from air. Another application is to absorb water, for example to keep double-pane windows from fogging. Most zeolitic materials have negatively charged Adj. 1. negatively charged - having a negative charge; "electrons are negative" electronegative, negative charged - of a particle or body or system; having a net amount of positive or negative electric charge; "charged particles"; "a charged battery" frameworks that require cations for charge balance. This allows these materials to be used for ion exchange ion exchange n. A reversible chemical reaction occurring between an insoluble solid and a solution during which ions may be interchanged, used in the separation of radioactive isotopes. . In our homes, zeolites are formulated in detergents to remove the calcium ions Noun 1. calcium ion - ion of calcium; a factor in the clotting of blood factor IV atomic number 20, Ca, calcium - a white metallic element that burns with a brilliant light; the fifth most abundant element in the earth's crust; an important component of most that make water hard. Different materials are used to sequester sequester v. to keep separate or apart. In so-called "high-profile" criminal prosecutions (involving major crimes, events, or persons given wide publicity) the jury is sometimes "sequestered" in a hotel without access to news media, the general public or their radioactive ions for environmental remediation Generally, remediation means providing a remedy, so environmental remediation deals with the removal of pollution or contaminants from environmental media such as soil, groundwater, sediment, or surface water for the general protection of human health and the environment or from a . Zeolitic materials rarely crystallize crys·tal·lize also crys·tal·ize v. crys·tal·lized also crys·tal·ized, crys·tal·liz·ing also crys·tal·iz·ing, crys·tal·liz·es also crys·tal·iz·es v.tr. 1. as single crystals. This means that most structural studies must utilize powder diffraction. Further, these materials frequently contain both light and heavy atoms and thus neutron scattering information is essential to determine sitting of light atoms. The use of both neutron and synchrotron synchrotron: see particle accelerator. synchrotron Cyclic particle accelerator in which the particle is confined to its orbit by a magnetic field. The strength of the magnetic field increases as the particle's momentum increases. x-ray diffraction data in many cases has been a prerequisite for accurate structural determinations (for example, see (74)). The following paragraphs summarize results from many recent studies performed at NIST where neutron diffraction played a pivotal role. The 32 detector BT-l neutron powder diffractometer in the NIST Center for Neutron Research allows the instrumental resolution to be tailored to suit the needs of the sample (75). This has been very effective for the study of zeolitic materials, since optimum resolution is needed at relatively low Q values
Q values are the difference of energies of the parent nuclides to the daughter nuclides. , as opposed to dense-phase materials. The instrument was further improved for zeolitic materials in the mid-1990s, when the 1.54 [Angstrom] Cu(220) 75[degrees] takeoff angle monochromator was replaced with a Ge(311) monochromator with a wavelength of 2.078 [Angstrom]. Data can be collected approximately twice as fast with Ge(311) compared with the Cu(220) monochromator and resolution is even better tailored to the needs of zeolitic diffraction experiments. 4.2 Zeolite zeolite Any member of a family of hydrated aluminosilicate minerals that have a framework structure enclosing interconnected cavities occupied by large metal cations (positively charged ions)—generally sodium, potassium, magnesium, calcium, and barium—and water RHO The zeolite RHO framework is shown in schematically in Fig. 24. This material has been of interest in part due to the extreme flexibility of the framework, as shown in Fig. 25. Cesium-exchanged zeolite RHO was one of the first materials to be studied in the early 1970s on the then new five-detector BT-1 instrument (76). The framework topology topology, branch of mathematics, formerly known as analysis situs, that studies patterns of geometric figures involving position and relative position without regard to size. has continued to be of interest. In one recent study, an aluminosilicate Aluminosilicate minerals are minerals composed of aluminum, silicon, and oxygen. Andalusite, kyanite, and sillimanite are naturally occuring aluminosilicate minerals that have the composition Al2SiO5. RHO material, [Li.sub.7.6][Cs.sub.1.3][Na.sub.2.0][Al.sub.11.4][Si.sub.36.6][O.sub. 96], was compared to a novel aluminogermanate RHO material, [Li.sub.13.9][Cs.sub.5.24][Na.sub.0.24][Al.sub.24][Ge.sub.24][O.sub.9 6] (77). This study demonstrated that despite having the same framework, the different compositions resulted in different cation sites. In these systems, Li sites could not be determined without use of neutron diffraction. The high degree of flexibility in the RHO framework leads to what is known as the trap door See trapdoor. trap door - Or "trapdoor" 1. back door. 2. trap-door function effect with some cations, such as Cd. At room temperature, the cation binds in the single-eight ring window (S8R, see in (24)) but at elevated temperatures, the cations migrate to higher coordination sites. Initial reports indicated that when the material was cooled, the cations returned to the S8R sites (78, 79). When the cations are located in the S8R site, they block access to the zeolite pores. Thus it is possible to trap species in this material, by sorbing the guest at elevated temperatures. When the temperature is lowered, the guest is trapped when the cations return to the S8R sites. Subsequent study indicated that cations are stable in the S8R site only when hydrated hy·drat·ed adj. Chemically combined with water, especially existing in the form of a hydrate. Adj. 1. hydrated - containing combined water (especially water of crystallization as in a hydrate) hydrous and that [H.sub.2]O (or possibly [OH.sup.-]) remains bound to the cations at much higher temperatures that previously understood (80). With heating, the water desorbs and the cation migrates to a higher coordination site. The cation remains in this higher coord ination site when the temperature is reduced, except in the presence of water vapor. Thus, the trap door effect is actually a hydration/dehydration phenomenon rather than simply a temperature-mediated effect. These results also call into question the observation of negative thermal expansion Negative Thermal Expansion (NTE) is a physicochemical process in which some materials contract upon heating rather than expanding as most materials do. Materials which undergo this unusual process have a range of potential engineering, photonic, electronic, and structural in Sr exchanged RHO (81, 82). It is now believed the contraction of the unit cell upon heating is due to a reversible reversible, adj capable of going through a series of changes in either direction, forward or backward (e.g., reversible chemical reaction). reversible hydrocolloid, n See hydrocolloid, reversible. loss of water. 4.3 Structure-Directing Agents in Synthesis of CON Framework Materials Many zeolitic materials are prepared from gels containing a sacrificial sac·ri·fi·cial adj. Of, relating to, or concerned with a sacrifice: a sacrificial offering. sac organic amine amine (əmēn`, ăm`ēn): see under amino group. amine Any of a class of nitrogen-containing organic compounds derived, either in principle or in practice, from ammonia (NH3). , called a structure-directing agent (SDA SDA abbr. specific dynamic action Serotonin dopamine antagonist (SDA) The newer second-generation antipsychotic drugs, also called atypical antipsychotics. ), that is trapped in the pores during synthesis. To free the pore pore (por) a small opening or empty space. alveolar pores openings between adjacent pulmonary alveoli that permit passage of air from one to another. spaces, the SDA is oxidized oxidized having been modified by the process of oxidation. oxidized cellulose see absorbable cellulose. away by calcinations in air. The influence of the SDA species during crystallization Crystallization The formation of a solid from a solution, melt, vapor, or a different solid phase. Crystallization from solution is an important industrial operation because of the large number of materials marketed as crystalline particles. is poorly understood. Indeed a single SDA can be used to produce different materials from the same gel composition, by variation of processing conditions (83). A study combining neutron and synchrotron diffraction with molecular mechanics The term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. The potential energy of all systems in molecular mechanics is calculated using force fields. was recently undertaken to investigate how SDA cations interact with a set of zeolitic materials (84). The borosilicate bo·ro·sil·i·cate n. A salt that is derived from both boric acid and silicic acid and occurs naturally in dumortierite. Noun 1. zeolitic materials, SSZ-33 and CIT-1 have related structures and have been designated the structure code CON by the Structure Commission of the International Zeolite Association. Unlike CIT-1, which is nearly free of defects, SSZ-33 has a very high density of stacking faults ([greater than or equal to]30 %) (85). Several organiccations, such as species SDA 1 shown in Fig. 26, can be used to synthesize To create a whole or complete unit from parts or components. See synthesis. SSZ-33. However, only SDA 2 has been found to synthesize CIT-1. Interestingly, cation SDA 3, while quite similar to SDA 2, cannot be used to prepare any material in the CON family. The location of the SDA cation in CIT-l prior to calcinations was determined using a simultaneous Rietveld fit to both neutron powder diffraction data and synchrotron x-ray powder diffraction data. Determination of the cation orientation was made possible by selective deuteration of the methyl groups Noun 1. methyl group - the univalent radical CH3- derived from methane methyl, methyl radical alkyl, alkyl group, alkyl radical - any of a series of univalent groups of the general formula CnH2n+1 derived from aliphatic hydrocarbons of the quaternary quaternary /qua·ter·nary/ (kwah´ter-nar?e) 1. fourth in order. 2. containing four elements or groups. qua·ter·nar·y adj. 1. Consisting of four; in fours. nitrogen. Since crystallographic methods do not prove uniqueness of the resulting model, molecular modeling was used to tabulate (1) To arrange data into a columnar format. (2) To sum and print totals. all possible sites where the SDA cation could be accommodated in the CIT-1 pores. Based on these computations, it was concluded that the crystallographic model is the only plausible result. This model, shown in Fig. 27, demonstrates the very tight fit between the SDA ions and with the CIT-i framework. Subsequent molecular modeling work was performed using the crystallographic model as a starting point Noun 1. starting point - earliest limiting point terminus a quo commencement, get-go, offset, outset, showtime, starting time, beginning, start, kickoff, first - the time at which something is supposed to begin; "they got an early start"; "she knew from the . These results confirmed that four molecules of either SDA 1 or SDA 3 can pack in the CIT-1 pores without any unfavorable energetic interactions and with similar energetic. However, packing SDA 3 in the same voids required significantly more energy, due to Van der Waals repulsions. This suggests why SDA 3 does not synthesize the CON framework, since it cannot pack effectively to form the same voids. Molecular modeling of SDA packing in the presence of stacking faults showed no significant energetic differences between SDA 1 and SDA 2, indicating that these stacking faults likely arise as a kinetic effect rather than due to thermodynamics thermodynamics, branch of science concerned with the nature of heat and its conversion to mechanical, electric, and chemical energy. Historically, it grew out of efforts to construct more efficient heat engines—devices for extracting useful work from expanding . 4.4 Novel Lithosilicate Molecular Sieves A molecular sieve is a material containing tiny pores of a precise and uniform size that is used as an adsorbent for gases and liquids. Molecules small enough to pass through the pores are adsorbed while larger molecules are not. There is great interest in finding new zeolitic frameworks, e.g., materials with new pore structures, since these materials have the potential to offer unique properties. For this reason there was considerable excitement accompanying the discovery that novel microporous materials can be prepared with frameworks composed of [SiO.sub.4] and [LiO.sub.4] tetrahedral (86, 87). The [LiO.sub.4] tetrahedral appear to be more flexible than [SiO.sub.4] or [AlO.sub.4] tetrahedral and thus these lithosilicate materials contain building units that would be highly strained in an aluminosilicate. The framework of one such material, RUB-29 is shown in Fig. 28. The approximate framework structure was determined using single-crystal synchrotron diffraction from an extremely small ([approximately equal to]200 [micro][m.sup.3]) crystal. Neutron diffraction was then used to determine the Li sitting. NMR NMR: see magnetic resonance. measurements indicate that RUB-29 is also novel in that all Li atoms in this material appear to be mobile below 250[degrees]C. This suggests that lithosilicates could be useful as ion conductors, perhaps in batteries or fuel cells. 5. Crystallography in Engineering Research (This section was written by Thomas Gnaupel-Herold, NIST Center for Neutron Research) 5.1 Introduction An important role of mechanical engineering is the calculation of safety margins and the lifetime prediction of parts and components. A key factor for these considerations is the knowledge of stresses a component would experience in service. While the fraction of external stresses is usually well-known, residual stresses can be problematic because they superimpose su·per·im·pose tr.v. su·per·im·posed, su·per·im·pos·ing, su·per·im·pos·es 1. To lay or place (something) on or over something else. 2. on the external stresses resulting in a total stress level that can exceed the strength of the material, thus causing unexpected failures. In addition to manufacturing induced residual stresses, there are also service-induced stresses originating from fatigue, corrosion and other processes that often determine the lifetime of an engineering component. Due to the high penetration of neutrons in many materials, neutron diffraction residual stress analysis (NDRSA) is one of the few methods able to provide information about the three-dimensional strain and stress distribution at depths of several centimeters in engineering components nondestructively. In comparison, x rays from laboratory sources in the energy range 5 keV to 20 keV are limited to about 20 [micro]m penetration. Thus, NDRSA can act as a tool for providing basic data for the design of a component, model validation of finite element See FEA. calculations or even for quality control at certain stages of the life of a part. Recognizing these uses and the need for such a tool for American industry and academia, a collaborative program of research in this area was begun in the early 1980s. The NIST Center for Neutron Research began construction of a new, dedicated double axis system In music the axis system, proposed by Ernő Lendvai (1971, p.1-16) in his analysis of the use of tonality in the music of Béla Bartók, is an assignment of harmonic function to all twelve pitch classes in relation to an assigned tonic, determined by that pitch classes interval for residual stress, texture and single crystal analysis (DARTS) in1991. The instrument has been in operation successfully since fall 1995. 5.2 Principle of the Method As diffraction is basically a length measurement, lattice spacing act as a strain gauge strain gauge Device for measuring the changes in distances between points in solid bodies that occur when the body is deformed. Strain gauges are used either to obtain information from which stresses in bodies can be calculated or to act as indicating elements on devices for for a stress in a certain direction of the part or component. The relationship between the wavelength of the neutrons [lambda], the lattice spacing [d.sub.hkl] of the atomic planes described by the Miller indices hkl, and the diffraction angle is given by Bragg's law Bragg's law n. The fundamental law of x-ray crystallography, n  = 2dsin .[lambda] = 2[d.sub.hkl] sin [[theta].sub.hkl]. (13) The d-spacing information does not come from a point, it describes the volume average over a region called the sampling volume. The shape and dimensions of the sampling volume are prescribed by two slit systems. The first set of slits defines the incident beam which is diffracted throughout its entire path through the sample. The secondary slits in front of a neutron detector single out a narrow part of that diffracted beam. The intersection of both beams defines the sampling volume (see Fig. 29). Usually the wavelength is chosen so that 2[[theta].sub.hkl] is approximately 90[degrees] because then the cross-section of the sampling volume becomes rectangular. Then, its dimensions are the width of primary beam times the height times the horizontal opening of the receiving slit. The position of the sampling volume is constant. Three-dimensional mapping of strain in a component is accomplished by using an x-y-z-positioning table which can move any point in the component into the sampling volume. If a reference value for the d-spacing can be found, e.g., by measuring d-spacings in a small coupon in which all long-range stresses are relieved, so that the calculation of strain from the measured d-spacings becomes straightforward [epsilon](hkl, [phi], [psi]) = [d.sub.hkl] - [d.sup.0.sub.hkl]/[d.sup.0.sub.hkl]. (14) The angles [phi] and [psi] describe the orientation of the component (specimen) with respect to the reference frame. Using strain measurements in at least six independent directions, the complete strain tensor The strain tensor, ε, is a symmetric tensor used to quantify the strain of an object undergoing a small 3-dimensional deformation:
[epsilon](hkl, [phi], [psi]) = [summation over (ij)] [[epsilon].sub.ij][n.sub.i][n.sub.j] (15) in which n = (cos [phi] sin [psi], sin [phi] sin [psi], cos [psi]). In order to obtain stress from strain, the elastic moduli in Hooke's law Hooke's law: see elasticity. have to replaced by the plane specific values [E.sub.hkl], and [v.sub.hkl] for translating lattice strain into macroscopic macroscopic /mac·ro·scop·ic/ (mak?ro-skop´ik) gross (2). mac·ro·scop·ic or mac·ro·scop·i·cal adj. 1. Large enough to be perceived or examined by the unaided eye. 2. stress. 5.3 Instrumentation A residual stress neutron diffractometer is nothing more than a specialized powder diffractometer. The differences are in the sophisticated slit assembly, the available wavelength range, the resolution and, most of all, an x-y-z-table for moving and positioning heavy specimens. A residual stress measurement requires slit systems that define the sampling volume because this is the best way to assign the measured d-spacing to a point or, because it is not possible to measure a point, to a small region within the sample. Without these slits, the d-spacing would represent the spatial average over the entire illuminated region. Also, because of the large penetration of neutrons, this region would extend over several [cm.sup.3] instead of a few [mm.sup.3] as required by most problems. The available neutron flux Noun 1. neutron flux - the rate of flow of neutrons; the number of neutrons passing through a unit area in unit time flux - the rate of flow of energy or particles across a given surface usually makes sampling volumes <0.5 [mm.sup.3] unfeasible. Because of the requirement of having 2[[theta].sub.hkl] around 90[degrees] for good spatial resolution (Data West Research Agency definition: see GIS glossary.) A measure of the accuracy or detail of a graphic display, expressed as dots per inch, pixels per line, lines per millimeter, etc. It is a measure of how fine an image is, usually expressed in dots per inch (dpi). , there is no need for a large angular opening in the scattering plane. At NIST, the detector is a linear position sensitive detector of 100 mm length which under normal conditions
In order to bring almost any desired peak to 90[degrees] the instrument has a total of three different monochromators with six available reflections. Together with a variable monochromator diffraction angle [[theta].sub.M], the wavelength range is from 0.95 [Angstrom] to 3.13 [Angstrom]. There is also enough overlap between the wavelength range of each monochromator so that the optimal setting can be chosen that is given by the figure of merit Noun 1. figure of merit - a numerical expression representing the efficiency of a given system, material, or procedure efficiency - the ratio of the output to the input of any system (FM). The FM is, roughly speaking, the neutron flux at the sample position divided by the square of the standard deviation In statistics, the average amount a number varies from the average number in a series of numbers. (statistics) standard deviation - (SD) A measure of the range of values in a set of numbers. of the recorded diffraction peak. It is a measure of the counting time necessary to reach a certain for the chosen d-spacing. In fact, a residual stress machine is optimized for the best possible FM which makes it more of a medium resolution diffractometer. Unlike powder diffractometers which may be more tuned towards better resolution and make up for the loss of intensity by bigger samples, bigger beams, and multiple detectors, the design of a resi dual stress diffractometer is driven by the size of the sampling volume. The goal is to measure a strain with a given accuracy for a volume [approximately equal to]30 [mm.sup.3] or smaller in the shortest possible time. Big improvements in the figure of merit were made possible by the recent development of perfect silicon double focusing monochromators. The concept is to utilize the large in-pile acceptance (area about 18 [cm.sup.2] x 13 [cm.sup.2]) and to focus otherwise unused neutrons into a narrower spot at the sample position. The last generation of these devices utilizes packets of thin silicon wafer blades that are stacked vertically and tilted slightly with respect to one another so that the whole assembly has a fixed vertical curvature curvature Measure of the rate of change of direction of a curved line or surface at any point. In general, it is the reciprocal of the radius of the circle or sphere of best fit to the curve or surface at that point. . Horizontally, i.e. within the scattering plane, the curvature is produced by elastic bending of the packets in a fourpoint bending device. Figure 30 shows a schematic diagram of the device used at NIST. The optimal horizontal curvature, i.e., the curvature that produces the highest FM, depends on a variety of factors but the most important one is the monochromator diffraction angle [[theta].sub.M]. Because the versatility of a variable [[theta].sub.M] is needed for changing the neutron wavelength it is also necessary to change the horizontal curvature to the respective optimal setting. Such a device is used at the DARTS diffractometer at the NCNR NCNR NIST Center for Neutron Research NCNR Non-Cancelable, Non-Returnable NCNR National Center for Nursing Research (NIH) NCNR Nearest Common Node Rerouting (ATM) NCNR National Center for Neutron Research . Aside from the instrumentation for delivery and detection of neutrons, there is also peripheral equipment. This includes a four-circle goniometer for single crystal and preferred orientation measurement, a load frame for the investigation of elastic and plastic deformation plastic deformation, n any irreversible deformation of tissues. characteristics and heating devices for the measurement of stress at elevated temperatures. 5.4 Examples of Neutron Diffraction Residual Stress Measurements Most of the residual stress measurements are related in one way or another to industrial applications. Therefore the most frequently investigated samples are the technologically important materials such as steel, aluminum, nickel-alloys and ceramics. The diagram of Fig. 31 shows an overview of the materials that were investigated 1999 at the residual stress diffractometers at NIST, HIFR HIFR Helicopter In-Flight Refueling HIFR Hover Inflight Refueling (Oak Ridge Oak Ridge, city (1990 pop. 27,310), Anderson and Roane counties, E Tenn., on Black Oak Ridge and the Clinch River; founded by the U.S. government 1942, inc. as an independent city 1959. ), ILL (France) and ISIS (UK). NDRSA provides depth profiling capabilities at spatial resolutions that match both the requirements imposed by finite element meshing and by the characteristic length scale within which steep strain gradients are present in a sample. This way even detailed maps of three dimensional strain and stress distributions can be obtained. Examples for the work that has been done at the NIST Center for Neutron Research include welds in aluminum, steel and stainless steel stainless steel: see steel. stainless steel Any of a family of alloy steels usually containing 10–30% chromium. The presence of chromium, together with low carbon content, gives remarkable resistance to corrosion and heat. ; automotive springs; ceramics and metal-matrix composites; induction-hardened fatigue specimens; structural parts of aircrafts. A good example for the strain mapping capabilities of NDRSA is a project done in collaboration with the U.S. Department of Transportation and residual stresses in rails. The purpose of this investigation was to determine the effect of grinding strategies on the distribution and magnitude of service-induced residual stresses. Their importance relies on the fact that they are critical parameters in the estimation of the growth rate of fatigue defects. This information is used to assess rail inspection frequencies to assure defect detection prior to catastrophic rail failure. Figure 32 shows the two dimensional residual stress distribution a unworn un·worn adj. 1. Not worn out or worn away. 2. Not worn before; new. 3. Not stale or overused; fresh. unworn Adjective 1. and a worn rail obtained from a mesh of sampling volumes of 3 [mm.sup.3] X 3 [mm.sup.3] X 3 [mm.sup.3] (right side). The above example illustrates current capabilities of NDRSA. Stresses can be obtained from depths of about 3 cm in steel, 6 cm in aluminum and 2 cm in nickel using sampling volumes of 30 [mm.sup.3] to 50 [mm.sup.3]. Further instrumental improvements will not increase that depth significantly because of the exponential attenuation of the neutron beam. The gains in the figure of merit will rather go into improved stress accuracy and smaller sampling volumes. For example, an improvement in the figure of merit by a factor of two enables a sampling volume half the previous size at the same counting time and stress accuracy. 6. Search for Novel Superconducting Materials (This section was written by Q. Huang, NIST Center for Neutron Research) As mentioned above, a lot of work has been done on the structural determinations of the high [T.sub.c] superconducting materials using neutron powder diffraction. In particular, materials with the oxide perovskite type structure have attracted interest in recent years because this structure type seems to be an excellent structural framework for promoting superconductivity, eclipsing the intermetallic compounds Intermetallic compounds Materials composed of two or more types of metal atoms, which exist as homogeneous, composite substances and differ discontinuously in structure from that of the constituent metals. They are also called, preferably, intermetallic phases. which have been the source of many superconducting materials in the past. However, the recent discovery of superconductivity in [MgB.sub.2] (88) suggests that intermetallic compounds with simple structure types are worth serious reconsideration as sources of new superconducting materials. This suggestion is corroborated by the discovery of superconductivity at 8 K in the intermetallic compound [MgCNi.sub.3], which has the perovskite structure (9). The high proportion of Ni in the compound suggests that magnetic interactions may be important to the existence of the superconductivity. [MgCNi.sub.3], in fa ct is best considered as the three-dimensional analog of the layered nickel borocarbides, typified by [LuNi.sub.2][B.sub.2]C, which has a [T.sub.c] near 16 K (89). The discovery also indicates that [MgB.sub.2] and [MgCNi.sub.3] will not be the only superconductors of this kind, and that a significant new class of superconducting materials may be found down this path in the future. Figure 33 shows the structure of the non-oxide perovskite intermetallic compound [MgC.sub.x][Ni.sub.3] which has a Pm 3m symmetry with atomic positions of Mg: (0, 0, 0), C: (1/2, 1/2, 1/2), and Ni: (0, 1/2, 1/2). The C atom is surrounded by Ni atoms forming [CNi.sub.6] octahedra which, in the oxide perovskites, are formed by a metallic atoms with six surrounding oxygen atoms. The magnetization data (89) show that the magnetic onset for the superconducting transition ranges between 7.1 K for a nominal carbon content of 1.1 per [MgCXNi.sub.3], to 7.4 K for nominal carbon content x = 1.5. For nominal C contents between x = 1.1 and x = 1.0 the superconducting transition turns off abruptly. The C content x in the structure must play a major role for the superconductivity to exist. [MgC.sub.0.96][Ni.sub.3] shows no magnetic or structural transitions between 2 K and 295 K (90). Fitting with a Gausian function all the peaks above 70[degrees] 2-theta at different temperatures indicates that the peak width and shape are close to the instrumental resolution, i.e., no observable particle and/or strain broadening are present in the measured temperature range, and that no evidence of other str uctural distortions was found with decreasing temperature. The refined lattice parameter a and Debye-Waller factors The Debye-Waller factor (DWF), named after Peter Debye and Ivar Waller, is used in condensed matter physics to describe the attenuation of x-ray scattering or neutron scattering caused by thermal motion or quenched disorder. decrease smoothly as the temperature decreases. Careful measurements near [T.sub.c] (7.3 K) show, as shown in Fig. 34, that the changes of those parameters are within the experimental uncertainties, which are relatively small. Therefore if there is any structural anomaly at [T.sub.c], it would be undetectable with the degree of precision of these measurements, which is of the order of 0.01 %. The structure refinement, using the neutron powder diffraction data collected at BT1, reveals that the composition of the superconducting phase for nominal x = 1 .25 ([T.sub.c] = 7.3 K) is [MgC.sub.0.96][Ni.sub.3]. This result is in agreement with the small amount of unreacted graphite (2% by weight) found in the sample. Therefore the data suggest that the highest [T.sub.c] in the perovskite is obtained for the stoichiometric composition [MgC.sub.1.0][Ni.sub.3]. Further the data suggest that the superconductivity disappears abruptly for carbon contents between 0.96 and approximately 0.90 per formula unit. [FIGURE 1 OMITTED] [FIGURE 3 OMITTED] [FIGURE 5 OMITTED] [FIGURE 6 OMITTED] [FIGURE 7 OMITTED] [FIGURE 9 OMITTED] [FIGURE 10 OMITTED] [FIGURE 23 OMITTED] Fig. 31 Materials investigated with residual strees diffractometers world wide (selected). FerroElectrics 2% Solid-Oxide-Fuel-Cell 1% Organic Composites 3% Aluminum 4% Functionally Graded Material 4% Ceramic Composites 7% Metal-Matrix-Composites 10% Thermal Sprayed Coatings 10% Ni-based Superalloys 12% Other Metals, Metal/Metal-Composite 16% Steel 32% Note: Table made from pie chart [FIGURE 32 OMITTED] [FIGURE 33 OMITTED] [FIGURE 34 OMITTED]
Table 1
Absorption in [YBa.sub.2][Cu.sub.3] [O.sub.7] (molecular weight: 666.5)
Elements Atomic wt. X-Ray
([lambda] =1.546) [Angstrom]
[micro]/[rho] (a) [micro]/[rho][gamma] (b)
Y 88.9 X 1 134 17.9
2[B.sub.2] 137.4 x 2 330 136.1
3Cu 63.6 X 3 52.9 15.2
70 16.0 X 7 11.5 1.9
[SIGMA] 666.5 171.0
Elements Neutron
([lambda] = 1.08) [Angstrom]
[micro]/[rho] [micro]/[rho][gamma]
Y 0.006 0.001
2[B.sub.2] 0.003 0.001
3Cu 0.002 0.001
70 0.000 0.000
[SIGMA] 0.003
(a)[cm.sup.2] [g.sup.-1] [23]
(b)[gamma] is the mass fraction of the corresponding chemical element.
Table 2
Comparison of Rietveld refinements for [gamma][Ba.sub.2][Cu.sub.3]
[O.sub.7] obtained in four laboratories
Atom Parameter Ref. (55) Ref. (56) Ref. (57) Ref. (20)
Ba z 0.1839(3) 0.1841(3) 0.1843(3) 0.1839(2)
B 0.4(1) 0.6(1) 0.54(5) 0.65(5)
Y B 0.2(1) 0.6(1) 0.46(4) 0.56(4)
Cu(1) B 0.2(1) 0.4(1) 0.50(5) 0.55(4)
Cu(2) z 0.3546(2) 0.3549(3) 0.3556(1) 0.3547(1)
B 0.3(1) 0.5(1) 0.29(4) 0.49(4)
O(1) z 0.1589(3) 0.1581(4) 0.1584(2) 0.1581(2)
B 0.5(2) 0.9(1) 0.67(5) 0.78(5)
n 2.01(3) 2.0 2.0 2.0
O(2) z 0.3783(3) 0.3779(4) 0.3773(2) 0.3779(2)
B 0.5(2) 0.1(1) 0.56(5) 0.57(5)
n 2.01(3) 2.0 1.89(2) 2.0
O(3) z 0.3780(3) 0.3777(5) 0.3789(3) 0.3776(2)
B 0.4(2) 0.3(1) 0.37(5) 0.55(5)
n 2.02(3) 2.0 2.0 2.0
O(4) B 1.6(3) 2.4(3) (a) 1.35(5) 1.73(9)
n 0.96(2) 1.0 0.92(2) 1.0
O(5) B 1.6
n 0.04(1)
a 3.8172(1) 3.8206(1) 3.8231(1) 3.8198(1)
b 3.8822(1) 3.8851(1) 3.8863(1) 3.8849(1)
c 11.6707(4) 11.6757(4) 11.6809(2) 11.6762(3)
(a)Equivalent isotropic B from anisotropic results.
Table 3
Composition and [T.sub.c] values in the homologous series
[HgBa.sub.2][Ca.sub.n-1] [O.sub.n+2+x]
Compound x [T.sub.c]
[HgBa.sub.2][Ca.sub.5][Cu.sub.6] 1256 0.065 126-128 K
[O.sub.14+x]
[HgBa.sub.2][CuO.sub.4+x] 1201 0.065 94-95 K
[HgBa.sub.2][CaCu.sub.2][O.sub.6+x] 1212 0.22 126-128 K
[HgBa.sub.2][Ca.sub.2][Cu.sub.3] 1223 0.41 133 K
[O.sub.8+x]
[HgBa.sub.2][Ca.sub.5][Cu.sub.6] 1256 0.40 114 K
[O.sub.14+x]
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Michor, in Studies on High Temperature Superconductors, A.V. Narlikar, ed., Nova Science Publishers, Vol. 28, New York (1999) p. 241. (90.) Q. Huang, T. He, K. A. Regan, N. Rogado, M. Hayward, M. K. Haas, K. Inumaru, and R. J. Cava , Temperature Dependence of the Structural Parameters of the Non-Oxide Perovskite Superconductor [MgCNi.sub.3], to be submitted to Physica C (2001). About the author: Antonio Santoro has been a research scientist in the NIST Center for Neutron Research, Materials Science and Engineering Materials science and engineering A multidisciplinary field concerned with the generation and application of knowledge relating to the composition, structure, and processing of materials to their properties and uses. Laboratory for over 30 years. He has carried out both theoretical and experiential ex·pe·ri·en·tial adj. Relating to or derived from experience. ex·pe ri·en research in many areas of crystallography including neutron
profile refinement, structure determination of superconductors,
geometrical crystallography, and the bond-valence method of analysis.
The National Institute of Standards and Technology is an agency of the
Technology Administration, U.S. Department of Commerce.
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