Crystal structure
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joThis document discusses crystal structures, including periodic arrays of atoms, fundamental lattice types, crystal planes indexed using Miller indices, and imaging atomic structures. It covers common lattice types like simple cubic, body-centered cubic, and face-centered cubic. Simple crystal structures presented include sodium chloride, cesium chloride, diamond, and zinc sulfide. Non-ideal crystal structures can involve random stacking or polytypism with long repeat units along stacking axes.
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1. Crystals are composed of atoms arranged in regular repeating patterns in three dimensions. The basic repeating unit is called the unit cell, which is defined by its lattice parameters of a, b, c, and the angles between them.
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Crystals are solids with atoms arranged in a repeating pattern. They consist of a lattice, which defines the points of repetition, and a motif or basis, which defines the entity associated with each lattice point. Common crystal structures include simple cubic, body-centered cubic, and face-centered cubic, which differ in their lattice and packing arrangements. Crystals can be one-dimensional, two-dimensional, or three-dimensional depending on the dimensionality of the lattice and motif.
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Crystals have basic building blocks called unit cells that are arranged in a periodic pattern described by a lattice. The unit cells contain motif groups of atoms associated with each lattice point. There are 14 possible types of space lattices belonging to 7 crystal systems characterized by distinct unit cell shapes and symmetries. The crystal structure is defined by the space lattice and the motif or basis group of atoms.
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There are two types of materials - crystalline and non-crystalline. Crystalline materials have atoms arranged in a regular pattern, making them anisotropic, while non-crystalline materials have atoms in a random arrangement, making them isotropic. Crystalline materials can exist as polycrystalline, with many regularly ordered grains, or single crystalline, with a single regularly ordered grain. An important concept in crystalline materials is the unit cell, which is the smallest repeating unit that extends in three dimensions to form the entire crystal structure. There are three main types of unit cells - simple cubic, body centered cubic, and face centered cubic - which differ in their atomic arrangements and packing fractions.
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The document discusses various topics related to crystals, including:
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- There are seven crystal systems categorized by symmetry elements like axes and planes. The main systems discussed are cubic, tetragonal, orthorhombic, monoclinic, triclinic, rhombohedral, and hexagonal.
- Unit cells are the smallest repeating units that make up the overall crystal structure. They can be primitive, containing one lattice point, or non-primitive with multiple points.
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Crystals are solids with atoms arranged in a repeating pattern. They consist of a lattice, which defines the points of repetition, and a motif or basis, which defines the entity associated with each lattice point. Common crystal structures include simple cubic, body-centered cubic, and face-centered cubic, which differ in their lattice and packing arrangements. Crystals can be one-dimensional, two-dimensional, or three-dimensional depending on the dimensionality of the lattice and motif.
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Crystals are solid materials made of repeating microscopic arrangements of atoms or molecules. There are several common crystal structures for metals including simple cubic, body-centered cubic, face-centered cubic, and hexagonal close-packed. Each structure has a distinct unit cell geometry that determines properties like packing efficiency and the coordination number of individual atoms. Body-centered cubic and face-centered cubic are the most prevalent crystal structures for metallic elements.
Space lattices
Crystals have basic building blocks called unit cells that are arranged in a periodic pattern described by a lattice. The unit cells contain motif groups of atoms associated with each lattice point. There are 14 possible types of space lattices belonging to 7 crystal systems characterized by distinct unit cell shapes and symmetries. The crystal structure is defined by the space lattice and the motif or basis group of atoms.
Crystal structure
There are two types of materials - crystalline and non-crystalline. Crystalline materials have atoms arranged in a regular pattern, making them anisotropic, while non-crystalline materials have atoms in a random arrangement, making them isotropic. Crystalline materials can exist as polycrystalline, with many regularly ordered grains, or single crystalline, with a single regularly ordered grain. An important concept in crystalline materials is the unit cell, which is the smallest repeating unit that extends in three dimensions to form the entire crystal structure. There are three main types of unit cells - simple cubic, body centered cubic, and face centered cubic - which differ in their atomic arrangements and packing fractions.
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3) Diffraction patterns provide information about the crystal structure by revealing the symmetry and dimensions of the unit cell. Analyzing diffraction patterns is how crystal structures are solved.
Crystal Structure
The document discusses the atomic arrangements in crystalline solids. It defines key concepts such as crystals, lattice, basis, unit cell, coordination number, Miller indices, and common crystal structures including simple cubic, body centered cubic, and face centered cubic. It provides examples of calculating the number of atoms in a unit cell, lattice parameter, atomic packing factor, atomic concentration, and drawing and identifying crystallographic planes from their Miller indices.
Ch 27.2 crystalline materials & detects in crystalline materials
Crystalline materials have atoms arranged in a specific, repeating pattern called a crystal structure. There are several common crystal structures including face-centered cubic, body-centered cubic, and hexagonal close packed.
A crystal structure is built from a repeating three-dimensional pattern called a unit cell, which contains one or more atoms. The unit cell is characterized by the types and positions of atoms within it, the cell dimensions and angles, and the number of atoms per cell. Common unit cells include simple cubic, body-centered cubic, and face-centered cubic.
Miller indices are used to describe directions and planes in a crystal structure. They are represented by sets of integers that indicate the intercepts of a plane or
Crystallography
This document provides an overview of crystallography. It defines key terms like crystalline solids, unit cell, space lattice, and basis. Crystalline solids have long-range order of atoms while amorphous solids do not. There are 7 crystal systems based on lattice parameters. Miller indices (hkl) are used to describe planes in a crystal lattice. Bragg's law relates the wavelength of X-rays to the diffraction pattern produced by the crystal structure. Common defects in crystal structures are discussed like vacancies, interstitials, and Frenkel and Schottky defects. Methods for determining crystal structures include X-ray crystallography and powder diffraction.
Introduccion a la fisica del estado solido
The document discusses solid state physics and the structure of solid materials. It covers the following key points:
1) Solids can be crystalline or amorphous, with crystalline solids having long-range order defined by a periodic arrangement of points in space.
2) There are 14 types of 3D crystal lattices known as Bravais lattices. Crystals are composed of a lattice plus a basis of atoms.
3) Important concepts in understanding crystal structure include unit cells, lattice vectors, Miller indices for crystal planes, and calculating the number of atoms in unit cells for different crystal structures like simple cubic and body-centered cubic.
4) Solid state physics studies the mechanical, thermal, electrical
Crystal Structure and Lattice types.pptx
The document discusses the structure and properties of crystal lattices. It defines a lattice as a periodic array of identical building blocks, with the positions of atoms in a solid being exactly periodic to form a crystal. It describes how lattice points are related by basis vectors and the translational symmetry of lattices. It also discusses unit cells, Bravais lattices, and the 14 possible lattice types based on their symmetry properties.
Physics
- The document discusses different crystal structures including simple cubic, body-centered cubic, face-centered cubic, and hexagonal closely packed.
- Key properties like number of atoms per unit cell, atomic radius, coordination number, and atomic packing factor are defined and calculated for each structure.
- There are seven basic crystal systems that materials can belong to depending on their lattice parameters and angles between axes. The most common systems are cubic, hexagonal, and tetragonal.
Similar to Crystal structure (20)
Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
Engineering Physics - Crystal structure - Dr. Victor Vedanayakam.S
Ch 27.2 crystalline materials & detects in crystalline materials
Ch 27.2 crystalline materials & detects in crystalline materials
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Amphiboles
The amphiboles are a group of chain silicate minerals with some substitution of F and Cl for OH. They have a general formula of (W,X,Y)7-8(Z4O10)2(OH)2 where W represents large cations like Ca and Na, X represents smaller cations like Mg and Fe2+, Y represents Fe3+, Ti, and Al, and Z represents Si and Al. Amphiboles have elongate prismatic crystals and two prismatic cleavages that meet at 124 degrees, whereas pyroxenes have squat prisms and cleavages that meet at 88 degrees. Common amphiboles include hornblende, tremolite, actinolite
Amphiboles
The amphiboles are a group of chain silicate minerals with some substitution of F and Cl for OH. They have a general formula of (W,X,Y)7-8(Z4O10)2(OH)2 where W represents large cations like Ca and Na, X represents smaller cations like Mg and Fe2+, Y represents Fe3+, Ti, and Al, and Z represents Si and Al. Amphiboles have elongate prismatic crystals and two prismatic cleavages that meet at 124 degrees, whereas pyroxenes have squat prisms and cleavages that meet at 88 degrees. Common amphiboles include hornblende, tremolite, actinolite
Amphiboles
The amphiboles are a group of chain silicate minerals with some substitution of F and Cl for OH. They have a general formula of (W,X,Y)7-8(Z4O10)2(OH)2 where W represents large cations like Ca and Na, X represents smaller cations like Mg and Fe2+, Y represents Fe3+, Ti, and Al, and Z represents Si and Al. Amphiboles have elongate prismatic crystals and two prismatic cleavages that meet at 124 degrees, whereas pyroxenes have squat prisms and cleavages that meet at 88 degrees. Common amphiboles include hornblende, tremolite, actinolite
Amphiboles
The amphiboles are a group of chain silicate minerals with some substitution of F and Cl for OH. They have a general formula of (W,X,Y)7-8(Z4O10)2(OH)2 where W represents large cations like Ca and Na, X represents smaller cations like Mg and Fe2+, Y represents Fe3+, Ti, and Al, and Z represents Si and Al. Amphiboles are distinguished from pyroxenes by having a different Si:O ratio and containing essential OH groups in their structure. Common amphiboles include hornblende, tremolite, actinolite, anthophyllite, cummingtonite, grunerite,
Amphiboles
The amphiboles are a group of chain silicate minerals with some substitution of F and Cl for OH. They have a general formula of (W,X,Y)7-8(Z4O10)2(OH)2 where W represents large cations like Ca and Na, X represents smaller cations like Mg and Fe2+, Y represents Fe3+, Ti, and Al, and Z represents Si and Al. Amphiboles have elongate prismatic crystals and two prismatic cleavages that meet at 124 degrees, whereas pyroxenes have squat prisms and cleavages that meet at 88 degrees. Common amphiboles include hornblende, tremolite, actinolite
Nature and behaviour of light
Light can vibrate in one plane (be polarized) through selective absorption or reflection. When light passes from one medium to another of different density, some of the light will be reflected and some will pass through but be bent and slowed down (refracted). The angle of reflection equals the angle of incidence, while the angle of refraction depends on the change in velocity.
The index of refraction and relief of a mineral are used to identify it. Index of refraction is a measure of how light slows down when passing into a mineral and is related to its crystal structure. Relief refers to the difference in index of refraction between a mineral and its surroundings, and is used to estimate the index of ref
Copy of nature and behaviour of light
Light can vibrate in one plane (be polarized) through selective absorption or reflection. When light passes from one medium to another of different density, some of the light will be reflected and some will pass through but be bent and slowed down (refracted). The angle of reflection equals the angle of incidence, while the angle of refraction depends on the change in velocity.
The index of refraction and relief of minerals can be used to identify them. Index of refraction refers to how much light is refracted when passing from one substance to another. It varies based on crystallographic orientation in anisotropic minerals. Relief and birefringence are properties related to the index of refraction.
Twinning
Twinning occurs when two crystals of the same substance grow together in a crystallographically controlled manner. There are several types of twinning defined by the twinning element, which can be a twin plane, twin axis, or twin center. Twinning is common across different crystal systems, with typical twinning elements being low index crystal planes or directions. Characteristic twinning patterns can be used to identify minerals under the microscope.
Rhombohedron
The document summarizes different crystallographic forms in the trigonal and tetragonal crystal systems. It describes rhombohedrons as solids bounded by six rhomb-shaped faces, and scalenohedrons as solids bounded by 8 or 12 scalene triangle faces. It also discusses sphenoids as four-faced solids resembling tetrahedrons but with isosceles triangle faces, and tetragonal scalenohedrons bounded by eight similar scalene triangles.
Presentation1
Crystals are defined as a 3D periodic arrangement of atoms in space, known as a lattice, with a motif or basis of atoms associated with each lattice point. A lattice is a 3D periodic arrangement of points without the atoms. Together, the lattice and motif define the crystal structure. There are 14 possible lattice arrangements, known as Bravais lattices, which are categorized into 7 crystal systems based on their symmetry properties. The lattice and basis completely specify the crystal structure.
Forms of crystals.
This document describes several crystal classes and forms. It discusses:
1) The pyritahedral class which includes forms like the pyritahedron and diploid bounded by 12 or 24 faces respectively.
2) The tetrahedral class including forms like the tetrahedron, deltoid dodecahedron, trigonal tristetrahedron, and hextetrahedron bounded by 4, 12, 12, and 24 faces.
3) Prism forms in the tetragonal, hexagonal, and orthorhombic crystal systems defined by their faces being parallel to the c-axis including first, second, and third order prisms.
Crystal forms.
The document describes several common crystal forms including the cube, octahedron, and rhomb-dodecahedron. It provides details on the number of faces, their shapes, and how they intersect the crystallographic axes for each crystal form. Some common crystal forms mentioned are the cube, octahedron, rhomb-dodecahedron, tetrahexahedron, trapezohedron, trisoctahedron, hexoctahedron, pyritohedron, diploid, and tetrahedron.
Nature and behaviour of light
Light can vibrate in one plane (be polarized) through selective absorption or reflection. When light passes from one medium to another of different density, some of the light will be reflected and some will pass through but be bent and slowed down (refracted). The angle of reflection equals the angle of incidence, while the angle of refraction depends on the change in velocity. Minerals can be characterized by their index of refraction (n), which is a measure of how much light is bent when passing into the mineral. It determines properties like relief and birefringence. Some minerals like calcite have the property of double refraction, where a single ray of light enters and splits into two rays.
Feldspar
Feldspar is the most abundant mineral group found in igneous and metamorphic rocks. It has a continuous three-dimensional network structure of silicon-oxygen and aluminum-oxygen tetrahedra with positively charged sodium, potassium, calcium, or barium ions situated between. The two most common feldspar types are orthoclase (potassium feldspar) and plagioclase (sodium-calcium feldspar). Plagioclase can form as a solid solution or break down into intergrowths of sodic and potassic lamellae called perthites. Feldspars are found in a wide range of igneous and metamorphic rocks depending on their
Silica
Quartz is one of the most abundant minerals and is composed of silicon dioxide (SiO2). It has a complex crystal structure and exists in several polymorphs including alpha-quartz, beta-quartz, tridymite, cristobalite, coesite, and stishovite. The stability of these polymorphs depends on temperature and pressure conditions. Cryptocrystalline varieties of quartz include chalcedony, agate, jasper, chert, and flint. Macrocrystalline varieties include rock crystal, milky quartz, amethyst, rose quartz, citrine, and smoky quartz.
Pyroxene
The document discusses the pyroxene group of minerals. Pyroxenes have a single chain crystal structure and are ionosilicates containing elements like calcium, sodium, magnesium, iron, and aluminum. They can be orthorhombic or monoclinic in crystal form. The general chemical formula of pyroxenes is (W,X,Y)2Z2O6, where W, X, Y, and Z can be elements like calcium, magnesium, iron, aluminum, sodium, lithium, silicon, and more. Some common pyroxenes mentioned include enstatite, hypersthene, diopside, hedenbergite, augite, and pigeonite.
Mica group
This document summarizes several types of phyllosilicate minerals in the mica group, including their chemical formulas, crystal structures, and common occurrences. Muscovite, biotite, and phlogopite are some of the most common micas. They have layered structures and perfect basal cleavage. Muscovite is widely used in electrical and insulation applications due to its properties. The document also describes lepidolite and its identification by lithium content and lilac color.
Feldspathoids
Feldspathoids are silicate minerals that are chemically similar to feldspars but deficient in silica. They form in place of feldspars when magma lacks sufficient silica. Common feldspathoids include leucite, nepheline, sodalite, cancrinite, and analcime. Some feldspathoids contain unusual anions like chloride, carbonate, sulfate, or sulfide. Leucite is characteristic of potassium-rich volcanic rocks. Nepheline occurs in both plutonic and volcanic alkaline, silica-poor rocks. Sodalite forms blue veinlets and masses and is found in nepheline syenites and phonolites.
Forms of crystals.
This document describes several crystal classes and forms. It discusses:
1) The pyritahedral class which includes forms like the pyritohedron bounded by 12 faces and the diploid bounded by 24 faces.
2) The tetrahedral class including the tetrahedron bounded by 4 faces and the deltoid dodecahedron bounded by 12 quadrilateral faces.
3) Different types of prisms in the tetragonal, hexagonal, and orthorhombic crystal systems defined by their orientation relative to the crystal axes and number of faces.
Pyroxenes pdf
- Pyroxene is a group of minerals that are abundant in mantle rocks and basalts. They commonly form in both igneous and metamorphic environments.
- Pyroxenes have the general formula XY(Si,Al)2O6 and are inosilicate minerals consisting of single chains of silicate tetrahedra. Common cations that occupy the X and Y sites include calcium, sodium, iron, magnesium, and manganese.
- There are two main crystal structure types for pyroxenes: orthorhombic orthopyroxenes and monoclinic clinopyroxenes. Solid solution series exist between endmembers within each group.
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Crystal structure
- 13. The separation between adjacent planes in a cubic crystal is given by: The angle between planes is given by:
- 15. 1.5 Imaging of Atomic Structure The direct imaging of lattices is accomplished with TEM. One can see, for example, the density of atoms along different crystalographic directions.