31: Solids and Surface Chemistry
- Page ID
- 11827
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- 31.1: The Unit Cell is the Fundamental Building Block of a Crystal
- This page discusses cubic crystal systems, specifically face-centered cubic (fcc) and body-centered cubic (bcc) structures. The fcc arrangement features a close-packed structure with 12 nearest neighbors and 4 atoms per unit cell, while bcc has 8 nearest neighbors and 2 atoms per unit cell.
- 31.2: The Orientation of a Lattice Plane is Described by its Miller Indices
- This page explains the orientation of crystal planes using Miller Indices (hkl), detailing how to identify intercepts, convert them to fractional coordinates, and derive indices for cubic crystals. It includes examples of low index planes like (100), (110), and (111), as well as symmetry-equivalent surfaces denoted by {100}. Additionally, it provides equations for calculating the perpendicular distance between planes in different crystal systems, with a primary focus on the cubic system.
- 31.3: The Spacing Between Lattice Planes Can Be Determined from X-Ray Diffraction Measurements
- This page provides an overview of X-ray crystallography, highlighting its historical development and significance in determining atomic arrangements in crystals through X-ray diffraction. It explains Bragg's law, which describes the interaction of X-rays with crystal planes and the conditions for constructive interference. The text includes calculations for diffraction angles in cesium metal and offers resources for further exploration in crystallography.
- 31.4: The Total Scattering Intensity is Related to the Periodic Structure of the Electron Density in the Crystal
- This page discusses the systematic absences observed in diffraction patterns from face-centered cubic crystals, resulting from destructive interference of X-rays. These absences reveal underlying crystal symmetry, which is crucial for structure determination. The structure factor \(F(hkl)\) determines reflection intensities and is influenced by atomic scattering factors.
- 31.5: The Structure Factor and the Electron Density Are Related by a Fourier Transform
- This page explains the Fourier transform as a mathematical tool that transitions functions from the time to the frequency domain, similar to translating music notes to sound. In x-ray diffraction, it aids in determining electron density around atoms by expanding functions, resulting in complex structure factors that link diffracted beam intensity to atomic positions. It also discusses iterative refinements for enhancing models using experimental data.
- 31.6: Atoms and Molecules can Physisorb or Chemisorb to a Surface
- This page explores the energetics and kinetics of adsorption, focusing on the potential energy curve of adsorbates near surfaces. It contrasts physisorption, which involves weak van der Waals forces, with chemisorption, characterized by stronger chemical bonds. The text outlines the adsorption process of hydrogen molecules (H2), discussing two pathways: direct chemisorption and precursor-mediated chemisorption, which includes initial physisorption.
- 31.7: Isotherms are Plots of Surface Coverage as a Function of Gas Pressure at Constant Temperature
- This page examines the equilibrium between gas molecules and adsorbed species on solid surfaces, introducing the Langmuir isotherm, which connects surface coverage to gas pressure at constant temperature. The isotherm predicts increased surface coverage with rising pressure until a monolayer is achieved. The derivation involves temperature-dependent constants and assumptions about surface site energies, emphasizing the importance of constant enthalpy of adsorption for the model's validity.
- 31.8: Using Langmuir Isotherms to Derive Rate Laws for Surface-Catalyzed Gas-Phase Reactions
- This page discusses the kinetics of heterogeneously-catalyzed reactions, emphasizing unimolecular decomposition and bimolecular processes using Langmuir isotherm expressions. It covers how pressure affects reaction rates, with distinct behaviors observed in first-order kinetics at low pressures and zero-order at high pressures.
- 31.9: The Structure of a Surface is Different from that of a Bulk Solid
- This page discusses the influence of solid surface structure, including defects, on chemisorption and physisorption kinetics and thermodynamics. It highlights the importance of techniques such as Secondary Electron Microscopy (SEM) for topography and Scanning Auger Microscopy (SAM) for compositional analysis.
- 31.10: The Haber-Bosch Reaction Can Be Surface Catalyzed
- This page discusses the Haber-Bosch process, an industrial method for synthesizing ammonia from nitrogen and hydrogen gases. It highlights the contributions of Karl Bosch and Fritz Haber, along with operational parameters like high pressure and intermediate temperatures. The process utilizes a catalyst and focuses on maximizing ammonia yield through recycling unreacted gases. Ongoing research aims to enhance catalysts and further comprehend the reaction's energetics.