Name: x-ray diffraction in crystal structure
Uploaded: 2020-09-24T15:06:49.000Z
Duration: 2 min 18 s
Channel: JoVE

K12 Standards

ohios-learning-standards-and-model-curriculum

Ohio’s Learning Standards and Model Curriculum

9-12

Physical Geology

Minerals

Crystallinity (crystal structure)

X-ray Crystallography

In 1913, the father and son scientists William Henry Bragg and William Lawrence Bragg noticed that when X-rays strike a crystalline solid at a certain angle, the X-rays diffract and produce a pattern of regularly spaced spots.
This led to the development of X-ray crystallography, which uses this phenomenon to determine the structures of crystalline solids ranging from simple ionic compounds to complex macromolecules like nucleic acids and proteins.
Recall that diffracted electromagnetic waves undergo constructive and destructive interference. This produces interference patterns, or diffraction patterns, showing the varying intensity of the diffracted waves at different points in space.
X-rays are diffracted by the electrons of atoms if the atoms are regularly spaced and the X-ray wavelength is similar to the interatomic distance.
When X-rays diffract from atoms in different planes, the diffracted waves may or may not be in phase. This depends on the interplanar spacing, d, and the angle at which the X-rays struck the atoms, or the incidence angle, theta.
This is because the paths that the X-rays take from the source to the detector have different lengths. If the path difference is

x-ray crystallography

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, termed X-ray crystallography.
Diffraction
Diffraction is the change in the direction of travel experienced by an electromagnetic wave when it encounters a physical barrier whose dimensions are comparable to those of the wavelength of the light. X-rays are electromagnetic radiation with wavelengths about as long as the distance between neighboring atoms in crystals (on the order of a few angstroms). When a beam of monochromatic X-rays strikes a crystal, its rays are scattered in all directions by the atoms within the crystal. When scattered waves traveling in the same direction encounter one another, they undergo interference, a process by which the waves combine to yield either an increase or a decrease in amplitude (intensity) depending upon the extent to which the combining waves&#8217; maxima are separated.
Bragg&#8217;s Law and Bragg&#8217;s Equation
When X-rays of a certain wavelength, &#955;, are scattered by atoms in adjacent crystal planes separated by a distance, d, they may undergo constructive interference when the difference between the distances traveled by the two waves prior to their combination is an integer factor, n, of the wavelength. This is Bragg&#39;s law. This condition is satisfied when the angle of the diffracted beam, &#952;, is related to the wavelength and interatomic distance by the equation: n&#955; = 2d sin &#952;. This relation is known as the Bragg equation in honor of W. H. Bragg and W. L. Bragg, the English physicists who explained this phenomenon. They were awarded the Nobel Prize in Physics in 1915 for their contributions.
This text has been adapted from <a href="https://openstax.org/books/chemistry-2e/pages/10-6-lattice-structures-in-crystalline-solids">Openstax, Chemistry 2e, Section 10.6: Lattice Structures in Crystalline Solids.</a>

The size of the unit cell and the arrangement of atoms in a crystal may be determined from measurements of the diffraction of X-rays by the crystal, ...

Education

JoVE Core

Chemistry

Liquids, Solids, and Intermolecular Forces

KEY TERMS AND CONCEPTS

x-ray diffraction in crystal structure

X-ray diffraction can reveal the unit cell size and atom arrangement in a crystal. This method is called X-ray crystallography. It uses diffraction, which is the bending of an electromagnetic wave when it meets a barrier about the same size as its wavelength.

X-rays work well for this method because their wavelengths are about the same as the spacing between neighboring atoms in crystals. They are measured on the scale of a few angstroms. When monochromatic X-rays, or X-rays with one wavelength, strike a crystal, the atoms scatter the rays in many directions.

The scattered waves can overlap and interfere with one another. Interference means waves combine to make a stronger or weaker signal, depending on how their peaks line up. When X-rays of a certain wavelength scatter from adjacent crystal planes separated by distance d, they may produce constructive interference if the path difference is an integer multiple of the wavelength.

This condition is described by Bragg’s law. The Bragg equation is nλ = 2d sin θ, where θ is the angle of the diffracted beam. The equation links wavelength and interatomic distance in the crystal. It is named for W. H. Bragg and W. L. Bragg, the English physicists who explained the effect and received the 1915 Nobel Prize in Physics.

X-ray Diffraction in Crystal Structure

molecular comparison of gases, liquids, and solids

molecular-comparison-of-gases-liquids-and-solids

How Intermolecular Forces Shape States

Intermolecular forces and particle motion shape the states of matter: solids, liquids, and gases. In a solid, particles are tightly packed and often arranged in a regular pattern. A solid has a fixed shape, and its particles vibrate in place rather than flowing past one another. In a liquid, particles stay close together but do not have a regular arrangement. Liquids have no fixed shape, yet their particles move past each other while remaining in contact. That is why liquids can flow and take...

intermolecular vs intramolecular forces

How Forces Shape Liquids and Solids

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intermolecular forces

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comparing intermolecular forces: melting point, boiling point, and miscibility

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How Molecule Shape Affects Intermolecular Forces

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surface tension, capillary action, and viscosity

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phase transitions

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phase transitions: vaporization and condensation

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Heat and Mass Transfer in Phase Changes

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vapor pressure

Vapor Pressure and Boiling Point

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clausius-clapeyron equation

Predicting Vapor Pressure with Temperature

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phase transitions: melting and freezing

Melting Point and Freezing Equilibrium

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phase transitions: sublimation and deposition

phase-transitions-sublimation-and-deposition

Sublimation, Frost, and Enthalpy Changes

Sublimation is a phase change in which a solid turns directly into a gas. It skips the liquid state. Dry ice is a clear example at room temperature and standard pressure, where solid carbon dioxide seems to disappear as it sublimes without forming a liquid first. Some other solids also sublime under the right conditions. Snow and ice can sublimate below water’s melting point, and wind or the lower air pressure at high altitudes can speed up that slow process. Solid iodine does the same when...

heating and cooling curves

Phase Changes on Heating and Cooling Curves

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phase diagrams

Water and CO2 Phase Behavior

Water and carbon dioxide phase behavior is shown with phase diagrams that map pressure against temperature. These plots show where a substance exists as a solid, liquid, or gas. They also show how melting points, sublimation points, and boiling points change with pressure. In a phase diagram, the labeled regions for solid, liquid, and gas represent single phases. The lines or curves between them show two phases in equilibrium. The triple point is the one condition of pressure and temperature...

structures of solids

Crystalline and Amorphous Solid Patterns

Crystalline and amorphous solids differ in how their particles are arranged. In crystalline solids, atoms, ions, or molecules follow a definite repeating pattern. Metals and ionic compounds typically form these ordered solids. Because the same particles are held in place by the same forces or energy, crystalline solids have a precise melting temperature. Amorphous solids, also called non-crystalline solids or glasses, do not have an ordered internal structure. Their particles are arranged...

molecular and ionic 
solids

Molecular and Ionic Crystal Properties

Crystalline solids are grouped into four types: molecular, ionic, metallic, and covalent network solids. This page focuses on molecular and ionic crystals and how their particle type and attractions shape their properties. Molecular crystalline solids are made of neutral molecules. Common examples include ice, sucrose, and iodine. The molecules are held together by weak intermolecular forces, including London dispersion forces, dipole-dipole interactions, and hydrogen bonds. These forces...

ionic crystal structures

Ionic Crystal Packing and Ion Holes

Ionic crystal packing depends on ion size, charge, and the ratio of cations to anions. In these solids, the ions usually behave like charged spheres. Stable structures form when each ion is surrounded by as many oppositely charged ions as possible and the ions remain in contact. In simple ionic crystals, the larger anions usually form a close-packed array. The smaller cations fit into the spaces between them. Two common spaces are tetrahedral holes, which are surrounded by four anions, and...

metallic solids

Metallic Bonding and Crystal Packing

Metallic solids are made of metal atoms arranged in crystals. Copper, aluminum, and iron are common examples. These solids are often described as metal nuclei spread through a sea of delocalized electrons. The atoms are held together by metallic bonding, and that bonding gives metals many of their useful bulk properties. Metallic solids are shiny, conduct heat and electricity well, and can be shaped without breaking. This shaping ability is called malleability, which means a metal can deform...

band theory

Band Gaps in Conductors and Insulators

Band gaps in solids help explain why some materials conduct electricity and others do not. When many atoms come together, their atomic orbitals combine into molecular orbitals with distinct energies. In a solid, so many orbitals are involved that these energies merge into continuous regions called bands. The energy difference between bands is called the band gap. Electrons in a solid must move across orbitals of different energies to travel through the material. In conductors, the valence...

network covalent solids

Why Network Covalent Solids Are So Hard

Network covalent solids are made of atoms joined in a three-dimensional network of covalent bonds. They appear in the crystal structures of nonmetals such as diamond, graphite, and silicon. Some covalent compounds also form this kind of structure, including silicon dioxide, which is found in sand, and silicon carbide, the abrasive used on sandpaper. Many minerals also contain networks of covalent bonds. These solids are hard to melt or break because their covalent bonds must be broken first.

X-ray diffraction can reveal the unit cell size and atom arrangement in a crystal. This method is called X-ray crystallography. It uses diffraction, which is the bending of an electromagnetic wave when it meets a barrier about the same size as its wavelength. X-rays work well for this method because their wavelengths are about the same as the spacing between neighboring atoms in crystals. They are measured on the scale of a few angstroms. When monochromatic X-rays, or X-rays with one...

lattice centering and coordination number

lattice-centering-and-coordination-number

Crystal Packing in Cubic Unit Cells

Crystal packing in cubic unit cells shows how atoms are arranged in a repeating solid structure. A crystal is best described by its unit cell, which is the smallest repeating part of the lattice. Lattice points mark where atoms or ions are located. The full crystal is built when this unit cell repeats in three dimensions. The cubic lattice has three common unit cells. A simple cubic structure, also called a primitive cubic structure, can be pictured as identical spheres stacked in layers with...

key terms and concepts

Learn how X-ray diffraction reveals crystal unit cell size and atom arrangement, and how Bragg’s law connects wavelength, angle, and spacing.

X-ray Diffraction in Crystal Structure | JoVE K12

chemistry

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Properties of minerals (hardness, luster, cleavage, streak, crystal shape, fluorescence, flammability, density/specific gravity, malleability)

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Properties of minerals (hardness, luster, cleavage, streak, crystal shape, fluorescence, flammability, density/specific gravity, malleability)

X-ray Diffraction in Crystal Structure

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