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Clusters can form and grow from a supersaturated vapor by successive reactions in which molecules (or “monomers”) of the vapor collide with the cluster and stick. In general, these reactions are reversible. The net forward rate of each of these reactions is termed the “nucleation current” of clusters of the size formed by the reaction. If a steady-state cluster size distribution exists, then the nucleation currents for clusters of all sizes are identical and can be equated to the steady-state (or “stationary”) nucleation rate. In that case, one can derive a closed-form expression for the nucleation rate in terms of a summation over clusters of all sizes up to some arbitrarily large size. The key terms in this summation are the forward rate constants and the Gibbs free energies of cluster formation from the monomer vapor. Evaluating the summation requires size-dependent values of these terms. For saturation ratios that lie within the condensation–evaporation regime, the free energy of cluster formation has a maximum at the critical cluster size. The nucleation theorem relates this size to the dependence of the nucleation rate on saturation ratio.
Gas-phase nucleation of condensed-phase particles is important in many contexts, including interstellar dust formation, air pollution, global climate change, combustion and fires, semiconductor processing, and synthesis of nanoparticles for practical applications. Nucleation occurs via the growth of atomic or molecular clusters to “critical size” – the size where further growth is irreversible. These critical-size clusters are the nuclei for particle formation, and the growth of clusters to the size of nuclei is the concern of nucleation theory. Various scenarios occur, including single-component homogeneous nucleation from a supersaturated vapor, multicomponent nucleation, ion-induced nucleation, chemical nucleation, and nucleation in plasmas. Classical nucleation theory, which treats small clusters as having the same properties as the bulk condensed phase, is still widely used to estimate nucleation rates for many kinds of systems. However, it is anticipated that atomistic approaches based on computational chemistry will increasingly be used to facilitate more accurate predictions of gas-phase nucleation rates for substances and chemical systems of interest.
Classical nucleation theory (CNT) models clusters of all sizes as structureless, spherical liquid droplets, having the same surface tension as a flat surface of the bulk liquid in equilibrium with its vapor at the same temperature – the “capillarity approximation.” The cluster free energy is divided into volume and surface contributions, and the rate of monomer addition to a cluster per unit area is equated to the flux of molecules to a plane in an ideal gas. Under these assumptions, together with several mathematical approximations, the summation expression for the steady-state nucleation rate is converted to a closed-form analytical expression for the nucleation rate as a function of temperature, saturation ratio, and substance properties. Comparing the nucleation rate predicted by CNT to experimental results for many substances, one finds considerable disagreement in terms of the magnitude of the nucleation rate as well as the qualitative dependence of nucleation rate on both temperature and saturation ratio. Analyzing the possible sources of this discrepancy, by far the major source of error is the liquid droplet model for the Gibbs free energy of cluster formation.
X-ray diffraction (XRD) characterization of Si powder was carried out using synchrotron and laboratory sources. Microstructural (size-strain) analyses of XRD patterns were carried out using the Rietveld refinement method. Experimentally observed super-Lorentzian shapes of the XRD peaks of Si powder were examined using multimodal profile fitting and bimodal model was found to be adequate. The two components obtained using a bimodal approach are referred as narrow and broad profiles based on their estimated relative peak widths. Peak shapes of crystallite size-dependent parts of narrow and broad profiles were found to be almost Gaussian and Lorentzian in nature, respectively. The simultaneous presence of such peak shapes corresponding to a bimodal microstructure is uncommon in literature. Therefore, in order to explore the role of different natures of XRD peak shapes (size dependent) of the bimodal profiles of Si, detailed microstructural analysis was carried out using the complementary method of whole powder pattern modeling (WPPM) and found to be related to the variance of crystallites' size distribution. Additionally, the effect of instrument resolution (laboratory and synchrotron sources) on the microstructural parameters was also studied. Scanning and transmission electron microscopy were used to characterize the morphology of Si powder and correlate with the microstructural findings of XRD methods.
Crystal structures, microtopography, morphologies, elemental compositions, and ionic conductivity have been investigated for Li5-xLa3(Nb,Ta)O12-y using X-ray diffraction (XRD), field-emission analytical scanning and transmission electron microscopies (S/TEM), and electrochemical impedance spectroscopy. Using Rietveld refinements with powder XRD patterns, we determined that the number of Li atoms in the formula is less than 5 and that Li5-xLa3(NbTa)O12-y crystallizes in the cubic garnet structure with a space group Ia-3d. Sintering at varying temperatures (750–1000 °C) for 5 h in an ambient atmosphere produced distinct outcomes. Rietveld refinements disclosed that the sample sintered at 1000 °C (Li3.43(2)La3Nb1.07(2)Ta0.93(2)O12-y, a = 12.8361(7) Å, V = 2114.96(3) Å3) exhibited the highest ionic conductivity, while the 850 °C sample had the lowest conductivity, characterized by lower Li concentration and impurity phases (Li(Nb,Ta)3O88, Li2CO3). Analyses, including XRD and electron microscopy, confirmed the 1000 °C sample as a relatively phase pure with enhanced Li content (Li/La = 1.2), larger grains (15 μm), and uniform crystallinity. The 1000 °C sample introduced additional partially filled Li3 (96h) sites, promoting Li migration, and enhancing ionic conductivity. The resulting XRD pattern at 1000 °C has been submitted to the Powder Diffraction File as a reference.
Formation of small solid and liquid particles is vital for a variety of natural and technological phenomena, from the evolution of the universe, through atmospheric air pollution and global climate change. Despite its importance, nucleation is still not well understood, and this unique book addresses that need. It develops the theory of nucleation from first principles in a comprehensive and clear way, and uniquely brings together classical theory with contemporary atomistic approaches. Important real-world situations are considered, and insight is given into cases typically not considered such as particle formation in flames and plasmas. Written by an author with more than 35 years of experience in the field, this will be an invaluable reference for senior undergraduates and graduate students in a number of disciplines, as well as for researchers in fields ranging from climate science and astrophysics to design of systems for semiconductor processing and materials synthesis.
The crystal structure of acalabrutinib dihydrate Form III has been refined using synchrotron X-ray powder diffraction data, and optimized using density functional techniques. Acalabrutinib dihydrate Form III crystallizes in space group P21 (#4) with a = 8.38117(5), b = 21.16085(14), c = 14.12494(16) Å, β = 94.5343(6)°, V = 2497.256(20) Å3, and Z = 4 (Z′ = 2) at 295 K. The crystal structure consists of herringbone layers parallel to the ac-plane. Hydrogen bonds between the acalabrutinib and water molecules generate a three-dimensional framework. Each water molecule acts as a donor in two hydrogen bonds and as an acceptor in at least one hydrogen bond. Amino groups and pyridine N atoms link the acalabrutinib molecules into dimers. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®).
The crystal structure of ribociclib hydrogen succinate (commonly referred to as ribociclib succinate) has been solved and refined using synchrotron X-ray powder diffraction data, and optimized using density functional theory techniques. Ribociclib hydrogen succinate crystallizes in space group P-1 (#2) with a = 6.52215(4), b = 12.67120(16), c = 18.16978(33) Å, α = 74.0855(8), β = 82.0814(4), γ = 88.6943(1)°, V = 1430.112(6) Å3, and Z = 2 at 295 K. The crystal structure consists of alternating layers of cations and anions parallel to the ab-plane. The protonated N in each ribociclib cation acts as a donor in two strong N–H⋯O hydrogen bonds to two different succinate anions. Strong O–H⋯O hydrogen bonds link the hydrogen succinate anions into chains parallel to the a-axis. N–H⋯N hydrogen bonds link the cations into dimers, with a graph set R2,2(8). The result is a three-dimensional hydrogen bond network. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®)
Linkage fabrics are gaining in popularity and finding applications in architecture, aerospace, healthcare, and fashion because they can deliver materials with bespoke flexibility and strength through the geometric design of linkage nodes. In this article, we provide a perspective on linkage fabrics as a new class of programmable materials. We describe the theory and design principles of these linkage fabrics and show how they can be designed and simulated using digital tools, and fabricated using 3D printing. This digital approach overcomes a major obstacle to the adoption of these materials, namely their complexity. We show how simulation methods can be verified and calibrated through experimental testing. This perspective article also discusses design-led research challenges for linkage fabrics such as the development of wearable assistive devices for those with physical disabilities.
The values of the signal-to-noise ratio are determined, at which the method of processing X-ray diffraction data reveals reflections with intensity less than the noise component of the background. The possibilities of the method are demonstrated on weak reflections of α-quartz. The method of processing X-ray diffraction data makes it possible to increase the possibilities of X-ray phase analysis in determining the qualitative phase composition of multiphase materials with a small (down to 0.1 wt.%) content of several (up to eight) phases.
Meta-structures, including metamaterials and metasurfaces, possess remarkable physical properties beyond those observed in natural materials and thus have exhibited unique wave manipulation abilities ranging from quantum to classical transports. The past decades have witnessed the explosive development and numerous implications of meta-structures in elastic-wave control under the Hermitian condition. However, more notably, a lot of recent research has been made to show that non-Hermitian meta-structures offer novel means for wave manipulation. Non-Hermiticity has enhanced both the accuracy and efficiency of wave steering capabilities. To this end, starting from electromagnetics and acoustics, we mainly review the up-to-date progress of non-Hermitian elastic meta-structures with a focus on their extraordinary elastic-wave control. A variety of promising scenarios realized by non-Hermitian elastic metamaterials and metasurfaces, such as the parity-time-symmetric system and the skin effect, are summarized. Furthermore, the perspectives and challenges of non-Hermitian elastic meta-structures for future key opportunities are outlined.
The crystal structure of alectinib hydrochloride has been solved and refined using synchrotron X-ray powder diffraction data and optimized using density functional theory techniques. Alectinib hydrochloride crystallizes in space group P21/n (#14) with the following parameters: a = 12.67477(7), b = 10.44076(5), c = 20.38501(12) Å, β = 93.1438(7)°, V = 2693.574(18) Å3, and Z = 4 at 295 K. The crystal structure consists of stacks of molecules along the b-axis, and the stacks contain chains of strong N–H⋯Cl hydrogen bonds. One density functional theory calculation moved a proton from an N atom to the Cl, but another calculation yielded a more chemically reasonable result. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®)
A monoclinic C form of rilpivirine hydrochloride, (N6H19C22)Cl, has been obtained and characterized using solid-state 15N, 13C, and 35Cl NMR spectroscopy and multitemperature synchrotron X-ray powder diffraction. The title compound crystallizes in the monoclinic system (space group C2/c, #15) at both room (295.0(2) K) and low (100.0(2) K) temperatures. At room temperature, the following parameters are a = 19.43051(3), b = 13.09431(14), c = 17.10254(18) Å, β = 109.3937(7), V = 4104.48(9) Å3, and Z = 8. The folded molecular conformation of the cation is similar with that of free base rilpivirine with the exception of cyanovinyl group disposition. The anion links cations to infinite chains parallel to the crystallographic c axis using N–H⋯Cl bonds where both amino groups and the protonated pyrimidine ring take part in the H-bonding. The powder patterns have been submitted to the ICDD for inclusion in the Powder Diffraction File™ (PDF®).
Leucites are tetrahedrally coordinated silicate framework structures with some of the silicon framework cations that are partially replaced by divalent or trivalent cations. These structures have general formulae A2BSi5O12 and ACSi2O6, where A is a monovalent alkali metal cation, B is a divalent cation, and C is a trivalent cation. There are also leucite analogs with analogous tetrahedrally coordinated germanate framework structures. These have general formulae A2BGe5O12 and ACGe2O6. In this paper, the Rietveld refinements of three synthetic Ge-leucite analogs with stoichiometries of AAlGe2O6 (A = K, Rb, Cs) are discussed. KAlGe2O6 is I41/a tetragonal and is isostructural with KAlSi2O6. RbAlGe2O6 and CsAlGe2O6 are $I\bar{4}3d$ cubic and are isostructural with KBSi2O6.
The NIST Workshop: Integrating Crystallographic and Computational Approaches to Carbon-Capture Materials for the Mitigation of Climate Change took place from October 31–November 1, 2023 at the National Cybersecurity Center of Excellence (NCCoE) Compound in Rockville, MD, which is an off-campus NIST facility. This workshop provided a forum for experimentalists and theorists working on the structural aspects of CO2 capture and sequestration materials to review the current state of the art in this field and discuss opportunities for collaborative research required to develop tools for rapid determination of the structure and its effect on the direct air capture performance in porous solid sorbents. We had a total of 33 international participants (18 invited speakers) from 17 institutions who were experimentalists and theorists from academia, government, and industry. The workshop was a great success.
The crystal structure of valbenazine has been solved and refined using synchrotron X-ray powder diffraction data and optimized using density functional theory techniques. Valbenazine crystallizes in space group P212121 (#19) with a = 5.260267(17), b = 17.77028(7), c = 26.16427(9) Å, V = 2445.742(11) Å3, and Z = 4 at 295 K. The crystal structure consists of discrete molecules and the mean plane of the molecules is approximately (8,−2,15). There are no obvious strong intermolecular interactions. There is only one weak classical hydrogen bond in the structure, from the amino group to the ether oxygen atom. Two intramolecular and one intermolecular C–H⋯O hydrogen bonds also contribute to the lattice energy. The powder pattern has been submitted to ICDD for inclusion in the Powder Diffraction File™ (PDF®)