Crystallography INTRODUCTION
•Download as PPTX, PDF•
1 like•456 views
This document discusses the classification and structure of crystalline solids. It begins by introducing the differences between solids, liquids, and gases, and how the properties of solids depend on their structure at the atomic level. Solids are then classified as either crystalline or amorphous based on whether the atoms are arranged in a systematic pattern or irregularly. Crystalline solids can be single crystals or polycrystals. Crystallography studies the structures, properties, and symmetries of crystals. Crystals have a repeating lattice structure defined by lattice points, lines, and planes. This lattice structure combined with a basis of atoms forms the overall crystal structure. Crystals are further classified into seven crystal systems and fourteen Bravais latt
Report
Share
Report
Share
Recommended
Symmetry
Crystals are composed of repeating unit cells that generate the entire crystal structure when translated through space. A crystal's symmetry is defined by symmetry elements like rotations, translations, and reflections that leave the crystal unchanged. There are 32 possible point groups and 14 Bravais lattices that combine to form 230 unique space groups describing all possible crystal symmetries. The asymmetric unit is the smallest portion of the unit cell that generates the full crystal structure through symmetry operations.
An Introduction to Crystallography
This document provides an introduction to crystallography. It defines crystallography as the study of crystals, which are solid substances with regular internal structures bounded by flat planar faces. The document outlines the key elements of crystals, including crystallographic axes, axial angles, crystal systems, symmetry elements, Miller indices, and habits. It also briefly discusses atomic structure, chemical bonding, and polymorphism as relevant concepts in crystallography.
Introduction to Crystallography
Crystallography is the branch of science that studies crystals, their growth and structure. It deals with crystals' external form, internal arrangement of atoms, and physical properties. Crystals have a regularly repeating internal structure. Miller indices are a notation system used to describe crystal planes and directions within a crystal lattice by three integers h, k, l. The law of rational indices states that the intercepts made by a crystal plane with the unit cell axes are inversely proportional to integers that become the Miller indices. Determining Miller indices involves finding intercepts with axes, converting to fractional coordinates, and taking reciprocals.
Introduction to Crystallography
Crystallography is the study of crystals, their growth, structure, and properties. A crystal is a solid with a regular, repeating internal structure at the atomic scale. Crystals have long-range order and are bounded by smooth, flat faces. Crystals can be classified based on their degree of crystallinity as euhedral, subhedral, or anhedral. Crystals exhibit symmetry properties like planes, axes, and centers of symmetry. They can also take on specific crystallographic forms like prisms, bipyramids, and rhombohedra. A crystal's habit describes its external shape and is influenced by its structure and growth conditions like temperature, pressure, and impurities.
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
- Crystallography is the study of crystalline solids using techniques like X-rays, electron beams, and neutron beams.
- In 1912, Max von Laue proved X-rays were diffracted by crystals, demonstrating diffraction patterns. He received the 1914 Nobel Prize in Physics for this discovery.
- In 1913, father and son team William and Lawrence Bragg developed Bragg's Law to explain X-ray diffraction by crystals and their invention of the X-ray spectroscope earned them the 1914 Nobel Prize in Physics.
Crystal Systems
Crystals are solids with atoms arranged in regular repeating patterns in all directions. There are several key concepts in crystallography:
1) Crystals have a crystal lattice structure defined by lattice vectors and a unit cell that repeats to form the crystal.
2) Unit cells have lattice constants and contain one or more atoms. Primitive, body-centered, and face-centered unit cells have different atomic packing factors.
3) Crystal structures demonstrate symmetry operations like translation and rotation that leave the structure unchanged. Miller indices represent crystallographic planes and directions.
Crystallography 32 classes
All 32 Crystal classes including triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic or isometric system.
Recommended
Symmetry
Crystals are composed of repeating unit cells that generate the entire crystal structure when translated through space. A crystal's symmetry is defined by symmetry elements like rotations, translations, and reflections that leave the crystal unchanged. There are 32 possible point groups and 14 Bravais lattices that combine to form 230 unique space groups describing all possible crystal symmetries. The asymmetric unit is the smallest portion of the unit cell that generates the full crystal structure through symmetry operations.
An Introduction to Crystallography
This document provides an introduction to crystallography. It defines crystallography as the study of crystals, which are solid substances with regular internal structures bounded by flat planar faces. The document outlines the key elements of crystals, including crystallographic axes, axial angles, crystal systems, symmetry elements, Miller indices, and habits. It also briefly discusses atomic structure, chemical bonding, and polymorphism as relevant concepts in crystallography.
Introduction to Crystallography
Crystallography is the branch of science that studies crystals, their growth and structure. It deals with crystals' external form, internal arrangement of atoms, and physical properties. Crystals have a regularly repeating internal structure. Miller indices are a notation system used to describe crystal planes and directions within a crystal lattice by three integers h, k, l. The law of rational indices states that the intercepts made by a crystal plane with the unit cell axes are inversely proportional to integers that become the Miller indices. Determining Miller indices involves finding intercepts with axes, converting to fractional coordinates, and taking reciprocals.
Introduction to Crystallography
Crystallography is the study of crystals, their growth, structure, and properties. A crystal is a solid with a regular, repeating internal structure at the atomic scale. Crystals have long-range order and are bounded by smooth, flat faces. Crystals can be classified based on their degree of crystallinity as euhedral, subhedral, or anhedral. Crystals exhibit symmetry properties like planes, axes, and centers of symmetry. They can also take on specific crystallographic forms like prisms, bipyramids, and rhombohedra. A crystal's habit describes its external shape and is influenced by its structure and growth conditions like temperature, pressure, and impurities.
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
- Crystallography is the study of crystalline solids using techniques like X-rays, electron beams, and neutron beams.
- In 1912, Max von Laue proved X-rays were diffracted by crystals, demonstrating diffraction patterns. He received the 1914 Nobel Prize in Physics for this discovery.
- In 1913, father and son team William and Lawrence Bragg developed Bragg's Law to explain X-ray diffraction by crystals and their invention of the X-ray spectroscope earned them the 1914 Nobel Prize in Physics.
Crystal Systems
Crystals are solids with atoms arranged in regular repeating patterns in all directions. There are several key concepts in crystallography:
1) Crystals have a crystal lattice structure defined by lattice vectors and a unit cell that repeats to form the crystal.
2) Unit cells have lattice constants and contain one or more atoms. Primitive, body-centered, and face-centered unit cells have different atomic packing factors.
3) Crystal structures demonstrate symmetry operations like translation and rotation that leave the structure unchanged. Miller indices represent crystallographic planes and directions.
Crystallography 32 classes
All 32 Crystal classes including triclinic, monoclinic, orthorhombic, tetragonal, trigonal, hexagonal, and cubic or isometric system.
Unit i-crystal structure
The document discusses different types of crystal structures including simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC). It defines key terms like unit cell, lattice points, coordination number, and atomic packing factor. SC has a coordination number of 6 and atomic packing factor of 52%. BCC has a coordination number of 8 and packing factor of 68%. FCC has a coordination number of 12 and packing factor of 74%.
Crystal structures
The document discusses various crystal structures. It defines crystalline and amorphous solids, and explains that a crystal structure consists of a crystal lattice and a basis. The main crystal systems are described including cubic, tetragonal, orthorhombic, monoclinic, triclinic, trigonal, and hexagonal. Important crystal structures like sodium chloride, cesium chloride, hexagonal close-packed, diamond, and zinc blende are summarized. Coordination number, atomic packing factor, and properties of unit cells are also covered.
Bravais lattices
This document discusses Bravais lattices, which are the 14 possible arrangements of points in a crystal lattice. It defines a unit cell as the smallest repeating pattern that generates the entire crystal lattice when translated in three dimensions. Unit cells can be primitive, containing particles only at the corners, or centered, containing additional particles in the body, face, or end centers. There are 7 common crystal systems classified by the angles and ratios of the unit cell vectors a, b, c. The 14 Bravais lattices represent all possible geometric arrangements of points in 3D space that generate the entire lattice through translation. Examples are provided of common crystal structures corresponding to each Bravais lattice.
Crystal systems
There are four basic atomic arrangements that determine the properties of metals: simple cubic, body-centered cubic, face-centered cubic, and hexagonal close-packed. The atomic packing factor, which represents the fraction of unit cell volume occupied by atoms, increases in the order of simple cubic, body-centered cubic, and face-centered cubic structures. Face-centered cubic has the highest atomic packing factor of 0.74 and is therefore the most dense arrangement. Different metallic crystal structures can explain variations in density and other material properties between metals.
Crystal Structure, BCC ,FCC,HCP
The document discusses different types of solids and their crystal structures. It defines crystalline and amorphous solids. Crystalline solids have an orderly arrangement of atoms and distinct crystal structures, while amorphous solids lack any orderly pattern. Common crystalline structures include face-centered cubic, body-centered cubic, and hexagonal close-packed. These structures differ in how atoms are arranged within the unit cell. The document also discusses properties like atomic radius, packing efficiency, and symmetry elements of different crystal structures.
Crystallography
This document discusses crystallography and crystal structure. It defines key terms like crystalline solids, amorphous solids, unit cell, crystal lattice, crystallographic planes, and Miller indices. It describes the seven crystal systems (cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, trigonal) based on their symmetry characteristics. It also discusses crystal forms, symmetry operations like rotation axes and planes of symmetry, and the notation used to describe crystal planes and orientations.
Crystal structure
The document discusses various topics related to crystals, including:
- Crystals have a periodic arrangement of atoms and can have regular shapes categorized by symmetry. Pharmaceutical crystals often have irregular dendritic shapes.
- 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.
Twinning in crystals(crystallography)
This document discusses twinning in crystals. It begins by defining twinning as the symmetrical intergrowth of two or more crystals that have different orientations but are of the same substance. The key elements of twinning are then introduced, including the twin plane, twin axis, and composition plane. Several types of twinning are described, such as contact, penetration, simple, and multiple twins. Common twinning systems are also outlined for different crystal classes, highlighting examples like calcite and quartz. The document concludes by noting the importance of studying twinning, such as for mineral identification and understanding its effects on crystal properties.
Elements of crystal
This document summarizes the key elements of crystals. It discusses that crystals are natural solids bounded by flat surfaces called faces, and the intersections of faces are called edges. It then describes the main parts of crystals as faces, edges, angles, and axes. The document outlines several properties of crystals including symmetry, distortion, unit cells, and axial ratios. It provides examples of different types of symmetry that can be seen in crystals like planes of symmetry and centers of symmetry.
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHD
The document provides information about crystal structures, including:
1) It discusses space lattices, which are arrangements of points that repeat periodically in 3D space, with every point having an identical surrounding. The smallest repeating unit of a lattice is called the primitive cell.
2) There are 14 possible crystal structures defined by unique combinations of lattice parameters (a, b, c values and α, β, γ angles). The structures differ in packing efficiency and symmetry.
3) Miller indices are used to specify crystallographic directions and planes, helping to understand properties that vary by orientation like strength and conductivity. Understanding planes and directions is important for predicting deformation and failure modes in materials.
Crystallography
This document provides information on crystallography and the structure of crystalline solids. It defines key terms like crystalline solids, amorphous solids, space lattice, unit cell, and Bravais lattices. It describes the primary crystalline structures of metals including simple cubic, body centered cubic, face centered cubic, and hexagonal close packed. It provides details on the characteristics of each structure like atoms per unit cell, coordination number, and packing factor. Crystalline solids are described as having a regular orderly arrangement of atoms compared to the random arrangement in amorphous solids.
6 - Lattice defects.pdf
There are four main types of lattice defects: point, line, surface, and volume. Point defects include vacancies, interstitial atoms, and impurities. Line defects called dislocations are regions of localized lattice distortion that allow for plastic deformation. Dislocations include edge and screw types defined by their Burgers vector. Surface defects occur at grain boundaries, which separate crystalline grains and impede dislocation movement, increasing strength. Volume defects like pores and cracks form during processing.
Twinning
Twinning occurs when two or more crystals share lattice points, adding apparent symmetry. There are three types of twinning: growth twins from accidents during crystal formation, transformation twins from changes in pressure/temperature, and deformation twins from stress. Common twinning includes albite twins in plagioclase feldspar and Carlsbad twins in orthoclase. Twinning can be identified by planes or axes of added symmetry like reflection or rotation.
Crystal imperfections dislocations
Dislocations are line defects in crystals that represent disrupted planes of atoms. They allow plastic deformation via slip along crystallographic planes and directions.
A dislocation is characterized by its Burgers vector, which represents the lattice displacement caused by the dislocation and determines the direction of slip. The Burgers vector connects one lattice position to another.
Dislocations lower the theoretical shear strength of crystals by several orders of magnitude, enabling plasticity. Their motion through glide and climb allows crystals to deform plastically under stress.
Dislocations
This document discusses different types of dislocations that occur in crystalline materials including edge dislocations, screw dislocations, and mixed dislocations. It describes how dislocations move through the crystal lattice during plastic deformation from the application of stress. It also covers characteristics of dislocations like lattice strain, slip systems, and deformation mechanisms in both single crystals and polycrystalline materials including twinning.
Isometric tetragonal system
The document provides information on crystal systems, including the isometric and tetragonal systems. It discusses the isometric system, which includes crystals with three equal perpendicular axes. It notes there are five classes in the isometric system with different forms and symmetry properties. The tetragonal system is then introduced, which includes crystals with two equal horizontal axes and a vertical axis that may be shorter or longer. There are seven classes in the tetragonal system with different forms and symmetry features. Examples of minerals that crystallize in each system are provided.
ISOMORPHISM & POLYMORPHISM.ppt
Isomorphism refers to substances with analogous formulas that have closely related crystal structures. Mitscherlich first introduced the term in 1819 when he found that crystals of KH2PO4, KH2AsO4, (NH4)H2PO4 and (NH4)H2AsO4 showed the same forms and interfacial angles between corresponding faces were very similar, despite their different chemical compositions. Isomorphism is common among minerals and is the basis for how some minerals are classified into groups based on their crystal structure. Substances can be isomorphous even if their formulas do not appear analogous, as long as the ions are similar in size and coordination.
Structure of solids
Solids are characterized by their definite shape and also their considerable mechanical strength and rigidity. The particles that compose a solid material(with few exceptions), whether ionic, molecular, covalent or metallic, are held in place by strong attractive forces between them.
Solid state physics lec 1
This document discusses solid state physics and crystal structures. It begins by defining solid state physics as explaining the properties of solid materials by analyzing the interactions between atomic nuclei and electrons. It then discusses different types of solids including single crystals, polycrystalline materials, and amorphous solids. Single crystals have long-range periodic atomic order, while polycrystalline materials are made of many small crystals joined together and amorphous solids lack long-range order. The document goes on to describe crystal structures including crystal lattices, unit cells, and common crystal systems such as cubic, hexagonal, and orthorhombic. It provides examples of crystal structures including sodium chloride and its cubic lattice structure.
Chapter 4 Crystal Structures
This document discusses crystal structures and their properties. It describes how atoms are arranged in crystalline solids through ordered unit cells that form a repeating lattice. The main crystal structures for metals are body-centered cubic, face-centered cubic, and hexagonal close-packed. It explains how to calculate properties like density from the unit cell parameters and atomic positions. Direction vectors are used to describe crystallographic directions.
crystal structure1.pptx
This document discusses the different types of solids and their structures. It defines crystalline and amorphous solids, with crystalline solids having a specific organized arrangement of particles and amorphous solids having a random arrangement. Crystalline solids are further divided into ionic, covalent network, molecular, and metallic crystals based on the type of bonding between particles. The document also discusses crystal lattices, unit cells, lattice parameters, crystal systems, and Bravais lattices which describe the geometric arrangements of particles in crystalline solids.
Crystal structure
This document discusses crystal structures and their importance in determining material properties. It defines key terms like crystal lattice, basis, unit cell and crystal systems. There are two main types of solids - crystalline and amorphous - based on atomic arrangement. Common metallic crystal structures are face-centered cubic, body-centered cubic and hexagonal close-packed. Face-centered cubic structure is described in detail, where atoms are located at unit cell corners and centers, giving a coordination number of 12. Crystal structures are crucial for understanding the properties and behaviors of different materials.
More Related Content
What's hot
Unit i-crystal structure
The document discusses different types of crystal structures including simple cubic (SC), body centered cubic (BCC), and face centered cubic (FCC). It defines key terms like unit cell, lattice points, coordination number, and atomic packing factor. SC has a coordination number of 6 and atomic packing factor of 52%. BCC has a coordination number of 8 and packing factor of 68%. FCC has a coordination number of 12 and packing factor of 74%.
Crystal structures
The document discusses various crystal structures. It defines crystalline and amorphous solids, and explains that a crystal structure consists of a crystal lattice and a basis. The main crystal systems are described including cubic, tetragonal, orthorhombic, monoclinic, triclinic, trigonal, and hexagonal. Important crystal structures like sodium chloride, cesium chloride, hexagonal close-packed, diamond, and zinc blende are summarized. Coordination number, atomic packing factor, and properties of unit cells are also covered.
Bravais lattices
This document discusses Bravais lattices, which are the 14 possible arrangements of points in a crystal lattice. It defines a unit cell as the smallest repeating pattern that generates the entire crystal lattice when translated in three dimensions. Unit cells can be primitive, containing particles only at the corners, or centered, containing additional particles in the body, face, or end centers. There are 7 common crystal systems classified by the angles and ratios of the unit cell vectors a, b, c. The 14 Bravais lattices represent all possible geometric arrangements of points in 3D space that generate the entire lattice through translation. Examples are provided of common crystal structures corresponding to each Bravais lattice.
Crystal systems
There are four basic atomic arrangements that determine the properties of metals: simple cubic, body-centered cubic, face-centered cubic, and hexagonal close-packed. The atomic packing factor, which represents the fraction of unit cell volume occupied by atoms, increases in the order of simple cubic, body-centered cubic, and face-centered cubic structures. Face-centered cubic has the highest atomic packing factor of 0.74 and is therefore the most dense arrangement. Different metallic crystal structures can explain variations in density and other material properties between metals.
Crystal Structure, BCC ,FCC,HCP
The document discusses different types of solids and their crystal structures. It defines crystalline and amorphous solids. Crystalline solids have an orderly arrangement of atoms and distinct crystal structures, while amorphous solids lack any orderly pattern. Common crystalline structures include face-centered cubic, body-centered cubic, and hexagonal close-packed. These structures differ in how atoms are arranged within the unit cell. The document also discusses properties like atomic radius, packing efficiency, and symmetry elements of different crystal structures.
Crystallography
This document discusses crystallography and crystal structure. It defines key terms like crystalline solids, amorphous solids, unit cell, crystal lattice, crystallographic planes, and Miller indices. It describes the seven crystal systems (cubic, tetragonal, orthorhombic, monoclinic, triclinic, hexagonal, trigonal) based on their symmetry characteristics. It also discusses crystal forms, symmetry operations like rotation axes and planes of symmetry, and the notation used to describe crystal planes and orientations.
Crystal structure
The document discusses various topics related to crystals, including:
- Crystals have a periodic arrangement of atoms and can have regular shapes categorized by symmetry. Pharmaceutical crystals often have irregular dendritic shapes.
- 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.
Twinning in crystals(crystallography)
This document discusses twinning in crystals. It begins by defining twinning as the symmetrical intergrowth of two or more crystals that have different orientations but are of the same substance. The key elements of twinning are then introduced, including the twin plane, twin axis, and composition plane. Several types of twinning are described, such as contact, penetration, simple, and multiple twins. Common twinning systems are also outlined for different crystal classes, highlighting examples like calcite and quartz. The document concludes by noting the importance of studying twinning, such as for mineral identification and understanding its effects on crystal properties.
Elements of crystal
This document summarizes the key elements of crystals. It discusses that crystals are natural solids bounded by flat surfaces called faces, and the intersections of faces are called edges. It then describes the main parts of crystals as faces, edges, angles, and axes. The document outlines several properties of crystals including symmetry, distortion, unit cells, and axial ratios. It provides examples of different types of symmetry that can be seen in crystals like planes of symmetry and centers of symmetry.
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHD
The document provides information about crystal structures, including:
1) It discusses space lattices, which are arrangements of points that repeat periodically in 3D space, with every point having an identical surrounding. The smallest repeating unit of a lattice is called the primitive cell.
2) There are 14 possible crystal structures defined by unique combinations of lattice parameters (a, b, c values and α, β, γ angles). The structures differ in packing efficiency and symmetry.
3) Miller indices are used to specify crystallographic directions and planes, helping to understand properties that vary by orientation like strength and conductivity. Understanding planes and directions is important for predicting deformation and failure modes in materials.
Crystallography
This document provides information on crystallography and the structure of crystalline solids. It defines key terms like crystalline solids, amorphous solids, space lattice, unit cell, and Bravais lattices. It describes the primary crystalline structures of metals including simple cubic, body centered cubic, face centered cubic, and hexagonal close packed. It provides details on the characteristics of each structure like atoms per unit cell, coordination number, and packing factor. Crystalline solids are described as having a regular orderly arrangement of atoms compared to the random arrangement in amorphous solids.
6 - Lattice defects.pdf
There are four main types of lattice defects: point, line, surface, and volume. Point defects include vacancies, interstitial atoms, and impurities. Line defects called dislocations are regions of localized lattice distortion that allow for plastic deformation. Dislocations include edge and screw types defined by their Burgers vector. Surface defects occur at grain boundaries, which separate crystalline grains and impede dislocation movement, increasing strength. Volume defects like pores and cracks form during processing.
Twinning
Twinning occurs when two or more crystals share lattice points, adding apparent symmetry. There are three types of twinning: growth twins from accidents during crystal formation, transformation twins from changes in pressure/temperature, and deformation twins from stress. Common twinning includes albite twins in plagioclase feldspar and Carlsbad twins in orthoclase. Twinning can be identified by planes or axes of added symmetry like reflection or rotation.
Crystal imperfections dislocations
Dislocations are line defects in crystals that represent disrupted planes of atoms. They allow plastic deformation via slip along crystallographic planes and directions.
A dislocation is characterized by its Burgers vector, which represents the lattice displacement caused by the dislocation and determines the direction of slip. The Burgers vector connects one lattice position to another.
Dislocations lower the theoretical shear strength of crystals by several orders of magnitude, enabling plasticity. Their motion through glide and climb allows crystals to deform plastically under stress.
Dislocations
This document discusses different types of dislocations that occur in crystalline materials including edge dislocations, screw dislocations, and mixed dislocations. It describes how dislocations move through the crystal lattice during plastic deformation from the application of stress. It also covers characteristics of dislocations like lattice strain, slip systems, and deformation mechanisms in both single crystals and polycrystalline materials including twinning.
Isometric tetragonal system
The document provides information on crystal systems, including the isometric and tetragonal systems. It discusses the isometric system, which includes crystals with three equal perpendicular axes. It notes there are five classes in the isometric system with different forms and symmetry properties. The tetragonal system is then introduced, which includes crystals with two equal horizontal axes and a vertical axis that may be shorter or longer. There are seven classes in the tetragonal system with different forms and symmetry features. Examples of minerals that crystallize in each system are provided.
ISOMORPHISM & POLYMORPHISM.ppt
Isomorphism refers to substances with analogous formulas that have closely related crystal structures. Mitscherlich first introduced the term in 1819 when he found that crystals of KH2PO4, KH2AsO4, (NH4)H2PO4 and (NH4)H2AsO4 showed the same forms and interfacial angles between corresponding faces were very similar, despite their different chemical compositions. Isomorphism is common among minerals and is the basis for how some minerals are classified into groups based on their crystal structure. Substances can be isomorphous even if their formulas do not appear analogous, as long as the ions are similar in size and coordination.
Structure of solids
Solids are characterized by their definite shape and also their considerable mechanical strength and rigidity. The particles that compose a solid material(with few exceptions), whether ionic, molecular, covalent or metallic, are held in place by strong attractive forces between them.
Solid state physics lec 1
This document discusses solid state physics and crystal structures. It begins by defining solid state physics as explaining the properties of solid materials by analyzing the interactions between atomic nuclei and electrons. It then discusses different types of solids including single crystals, polycrystalline materials, and amorphous solids. Single crystals have long-range periodic atomic order, while polycrystalline materials are made of many small crystals joined together and amorphous solids lack long-range order. The document goes on to describe crystal structures including crystal lattices, unit cells, and common crystal systems such as cubic, hexagonal, and orthorhombic. It provides examples of crystal structures including sodium chloride and its cubic lattice structure.
Chapter 4 Crystal Structures
This document discusses crystal structures and their properties. It describes how atoms are arranged in crystalline solids through ordered unit cells that form a repeating lattice. The main crystal structures for metals are body-centered cubic, face-centered cubic, and hexagonal close-packed. It explains how to calculate properties like density from the unit cell parameters and atomic positions. Direction vectors are used to describe crystallographic directions.
What's hot (20)
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHD
Space lattice and crystal structure,miller indices PEC UNIVERSITY CHD
Similar to Crystallography INTRODUCTION
crystal structure1.pptx
This document discusses the different types of solids and their structures. It defines crystalline and amorphous solids, with crystalline solids having a specific organized arrangement of particles and amorphous solids having a random arrangement. Crystalline solids are further divided into ionic, covalent network, molecular, and metallic crystals based on the type of bonding between particles. The document also discusses crystal lattices, unit cells, lattice parameters, crystal systems, and Bravais lattices which describe the geometric arrangements of particles in crystalline solids.
Crystal structure
This document discusses crystal structures and their importance in determining material properties. It defines key terms like crystal lattice, basis, unit cell and crystal systems. There are two main types of solids - crystalline and amorphous - based on atomic arrangement. Common metallic crystal structures are face-centered cubic, body-centered cubic and hexagonal close-packed. Face-centered cubic structure is described in detail, where atoms are located at unit cell corners and centers, giving a coordination number of 12. Crystal structures are crucial for understanding the properties and behaviors of different materials.
BME 303 - Lesson 2 - Structure of Solids.pptx
This document provides an overview of the structure of solids. It discusses the characteristics of solids, including their definite shape, rigidity, and resistance to changes in shape or volume. Solids exist in either crystalline or amorphous forms. Crystalline solids have a regular repeating structure, while amorphous solids like glass lack long-range order. There are seven crystal systems that solids can belong to, which are determined by the lengths of the unit cell axes and angles between them. Key concepts covered include unit cells, crystal lattices, bonding in ionic, covalent and metallic solids, and the different arrangements of atoms in simple cubic, body-centered cubic and face-centered cubic unit cells
What is a Crystal Structure.ppt
We offer discreet and reliable packaging and delivery. - fast and reliable shipping within 48 hours, using courier, DHL, EMS, TNT, FEDEX, UPS, these are in stock and we only sell items above 99%, if you are interested Quote the best for you.We do supply others products upon request if you need and we offer the most reliable transaction.
solid state
The document discusses solid state physics and the properties of solid materials. It explains that solid state physics formulates laws governing the behavior of solids and explores why materials like carbon can exist in different states with varying electrical properties. The document also classifies solids as crystalline, polycrystalline, or amorphous and discusses crystal structure, lattice, and unit cells - the basic repeating units that make up crystalline solids. Understanding these atomic arrangements is important for explaining the behavior and properties of different materials.
Solid state
This document provides information about solid state properties and the structure of crystalline solids. It defines that solids have a definite shape and volume, and are made up of atoms, ions, or molecules as constituent particles. Crystalline solids have these particles arranged in a regular, periodic structure, whereas amorphous solids have a random arrangement. There are four main types of crystalline unit cell structures - primitive, body-centered, face-centered, and base-centered. Overall, there are 14 possible Bravais lattices that describe the seven crystal systems into which all solid structures can be categorized.
Characteristics of crystalline solid
This document provides an overview of solid state chemistry and properties of solid surfaces. It discusses the following key points:
- Solids have definite shapes and volumes due to strong forces holding their atoms, molecules, or ions in fixed positions. This gives solids their rigidity and mechanical strength.
- There are two main types of solids - crystalline solids which have a regular repeating structure and amorphous solids which lack long-range order.
- Techniques for characterizing solid surfaces include low-energy electron diffraction (LEED) and X-ray photoelectron spectroscopy (XPS) which can provide information about surface structure and composition.
- LEED specifically works by bombarding a crystalline surface
meera
Crystals are solid structures where molecules or atoms are arranged in a repeating pattern. They form through phase changes in fluids, usually liquids, through processes like freezing or crystallization from solution. Different substances form different types of crystal structures, which can be studied through crystallography. Crystals play important roles in applications like electronics and lasers due to their optical and electronic properties. Their structure is defined by a repeating unit cell, with particles arranged in specific positions and orientations within the cell. There are 14 possible arrangements of these unit cells in 3D crystal lattices.
Solid state physics lec 1
This document discusses solid state physics and crystal structures. It begins by defining solid state physics as explaining the properties of solid materials by analyzing the interactions between atomic nuclei and electrons. It then discusses different types of solids including single crystals, polycrystalline materials, and amorphous solids. Single crystals have long-range periodic atomic order, while polycrystalline materials are made of many small crystals joined together and amorphous solids lack long-range order. The document goes on to describe crystal structures including crystal lattices, unit cells, and common crystal systems such as cubic, hexagonal, and orthorhombic. It provides examples of crystal structures including sodium chloride and its cubic lattice structure.
SOLID STATE.pdf
This document provides an overview of solid state chemistry. It defines solids as matter with a definite shape and volume, where the constituent particles possess fixed positions and can only oscillate. Solids are classified as crystalline or amorphous based on the ordering of particles. Crystalline solids have long-range order while amorphous solids only have short-range order. Important properties of solids discussed include density, rigidity, melting points, and electrical conductivity. The document also describes different types of crystalline solids based on bonding - ionic, molecular, metallic, and covalent network solids. Unit cell structure, crystal systems, and packing efficiency of particles in cubic unit cells are also summarized.
Chapter 1: Material Structure and Binary Alloy System
This is an introduction to material structure and periodic table system. This topic also describes microstructure of the metals and alloys solidification.
Chapter1 150109004625-conversion-gate01
1) Elements are pure substances made of one type of atom, while compounds are made of two or more elements chemically bonded together. Mixtures are combinations of substances mixed but not chemically bonded.
2) Atoms are made up of protons, neutrons, and electrons. The atomic structure of an element determines its properties.
3) Materials can have crystalline or non-crystalline structures. Crystalline structures are regular arrangements of atoms, while non-crystalline structures are irregular. The type of bonding between atoms also influences properties.
Solid state
This document provides an overview of solid state structures. It discusses the two main types of solids - crystalline and amorphous - and explains their distinguishing characteristics. Crystalline solids have a definite, orderly arrangement of atoms while amorphous solids do not. The document then covers various topics related to crystalline solids, including crystal structures, unit cells, Bravais lattices, and the structures of materials like NaCl, diamond, and graphite. It also discusses crystal imperfections and different types of defects that can occur in ionic crystals.
CHEMICAL ENGG. MATERIALS- CRYSTALLINE & NON-CRYSTALLINE SOLIDS
Difference between CRYSTALLINE & NON-CRYSTALLINE SOLIDS , useful for studying subject like CHEMICAL ENGG. MATERIALS
Chap-1_IMF-Part3.pptx for high school Chemistry
This document discusses the nature of solids. It describes the difference between crystalline and amorphous solids. Crystalline solids have a highly ordered structure and are classified as ionic, covalent, metallic or molecular based on the interactions between particles in the crystal lattice. Amorphous solids lack long-range order. The document also describes phase changes between solid, liquid and gas states in terms of energy and molecular order. An activity on sublimation is presented along with questions.
Solid state class 12 CBSE
The document discusses the characteristics of solids and different types of crystalline structures. It describes that solids can be crystalline or amorphous based on the ordering of particles. Crystalline solids have long-range order and a repeating pattern, while amorphous solids only have short-range order. Crystalline solids are further classified as ionic, molecular, metallic or covalent networks based on bonding. Crystals consist of lattice structures with primitive or centered unit cells containing particles in specific arrangements. Close packing of spheres in one, two or three dimensions results in different crystal structures like simple cubic, body centered cubic or hexagonal close packed.
SOLID STATE -XII BY SULEKHA RANI R , PGT CHEMISTRY
Here are the definitions and differences you asked for:
Short range order - Atoms are arranged in a disordered manner within a small region but this arrangement does not extend over long distances.
Anisotropic - A material whose physical properties vary with the direction of measurement.
Unit cell - The smallest repeating unit that constructs the entire crystal by translation.
Voids - Empty spaces between closely packed spheres in crystal structures. There are two types - octahedral and tetrahedral voids.
Impurity defect - Occurs when an atom of one element replaces an atom of the host element in its normal lattice position.
Monoclinic - Unit cell with two axes at 90 degrees and one axis not at 90 degrees
Solids
A solid is a state of matter characterized by particles arranged in a stable, close-packed structure that gives solids a definite shape and volume. Solids can be crystalline or amorphous. Crystalline solids have particles arranged in a regular, repeating pattern throughout the crystal lattice. Amorphous solids lack long-range order and have particles arranged irregularly over short distances. The crystal lattice is made up of repeating units called unit cells, which define the symmetry and geometry of the crystal structure. Unit cells come in seven main types depending on their parameters. Crystalline solids are further classified based on the type of bonds between particles as ionic, covalent, metallic, or molecular solids.
The solid state
1) Solids have a definite shape and volume and their particles vibrate about fixed positions. In contrast, liquids and gases allow particle movement and flow.
2) Solids can be classified as crystalline or amorphous based on particle arrangement. Crystalline solids have orderly arrangements while amorphous solids do not.
3) The smallest repeating unit of a crystal lattice is the unit cell, which is defined by its edges and angles. There are seven possible primitive unit cell types and 14 total unit cell types when including centered unit cells.
Similar to Crystallography INTRODUCTION (20)
Chapter 1: Material Structure and Binary Alloy System
Chapter 1: Material Structure and Binary Alloy System
Chapter 3 -Materials Science - Crystal structures.pdf
Chapter 3 -Materials Science - Crystal structures.pdf
CHEMICAL ENGG. MATERIALS- CRYSTALLINE & NON-CRYSTALLINE SOLIDS
CHEMICAL ENGG. MATERIALS- CRYSTALLINE & NON-CRYSTALLINE SOLIDS
SOLID STATE -XII BY SULEKHA RANI R , PGT CHEMISTRY
SOLID STATE -XII BY SULEKHA RANI R , PGT CHEMISTRY
Recently uploaded
3D Hybrid PIC simulation of the plasma expansion (ISSS-14)
3D Particle-In-Cell (PIC) algorithm,
Plasma expansion in the dipole magnetic field.
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
Although Artemia has been known to man for centuries, its use as a food for the culture of larval organisms apparently began only in the 1930s, when several investigators found that it made an excellent food for newly hatched fish larvae (Litvinenko et al., 2023). As aquaculture developed in the 1960s and ‘70s, the use of Artemia also became more widespread, due both to its convenience and to its nutritional value for larval organisms (Arenas-Pardo et al., 2024). The fact that Artemia dormant cysts can be stored for long periods in cans, and then used as an off-the-shelf food requiring only 24 h of incubation makes them the most convenient, least labor-intensive, live food available for aquaculture (Sorgeloos & Roubach, 2021). The nutritional value of Artemia, especially for marine organisms, is not constant, but varies both geographically and temporally. During the last decade, however, both the causes of Artemia nutritional variability and methods to improve poorquality Artemia have been identified (Loufi et al., 2024).
Brine shrimp (Artemia spp.) are used in marine aquaculture worldwide. Annually, more than 2,000 metric tons of dry cysts are used for cultivation of fish, crustacean, and shellfish larva. Brine shrimp are important to aquaculture because newly hatched brine shrimp nauplii (larvae) provide a food source for many fish fry (Mozanzadeh et al., 2021). Culture and harvesting of brine shrimp eggs represents another aspect of the aquaculture industry. Nauplii and metanauplii of Artemia, commonly known as brine shrimp, play a crucial role in aquaculture due to their nutritional value and suitability as live feed for many aquatic species, particularly in larval stages (Sorgeloos & Roubach, 2021).
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
Nucleophilic Addition of carbonyl compounds.pptx
Nucleophilic addition is the most important reaction of carbonyls. Not just aldehydes and ketones, but also carboxylic acid derivatives in general.
Carbonyls undergo addition reactions with a large range of nucleophiles.
Comparing the relative basicity of the nucleophile and the product is extremely helpful in determining how reversible the addition reaction is. Reactions with Grignards and hydrides are irreversible. Reactions with weak bases like halides and carboxylates generally don’t happen.
Electronic effects (inductive effects, electron donation) have a large impact on reactivity.
Large groups adjacent to the carbonyl will slow the rate of reaction.
Neutral nucleophiles can also add to carbonyls, although their additions are generally slower and more reversible. Acid catalysis is sometimes employed to increase the rate of addition.
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Sharlene Leurig - Enabling Onsite Water Use with Net Zero WaterTexas Alliance of Groundwater Districts
Presented at June 6-7 Texas Alliance of Groundwater Districts Business MeetingRandomised Optimisation Algorithms in DAPHNE
Slides from talk:
Aleš Zamuda: Randomised Optimisation Algorithms in DAPHNE .
Austrian-Slovenian HPC Meeting 2024 – ASHPC24, Seeblickhotel Grundlsee in Austria, 10–13 June 2024
https://ashpc.eu/
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...University of Maribor
Slides from talk:
Aleš Zamuda: Remote Sensing and Computational, Evolutionary, Supercomputing, and Intelligent Systems.
11th International Conference on Electrical, Electronics and Computer Engineering (IcETRAN), Niš, 3-6 June 2024
Inter-Society Networking Panel GRSS/MTT-S/CIS Panel Session: Promoting Connection and Cooperation
https://www.etran.rs/2024/en/home-english/8.Isolation of pure cultures and preservation of cultures.pdf
Isolation of pure culture, its various method.
Thornton ESPP slides UK WW Network 4_6_24.pdf
ESPP presentation to EU Waste Water Network, 4th June 2024 “EU policies driving nutrient removal and recycling
and the revised UWWTD (Urban Waste Water Treatment Directive)”
Cytokines and their role in immune regulation.pptx
This presentation covers the content and information on "Cytokines " and their role in immune regulation .
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills of Minnesota developed a method to convert waste into high-value dry fertilizer, significantly enriching soil quality. By providing farmers with a valuable resource derived from waste, Travis Hills helps enhance farm profitability while promoting environmental stewardship. Travis Hills' sustainable practices lead to cost savings and increased revenue for farmers by improving resource efficiency and reducing waste.
bordetella pertussis.................................ppt
Bordettela is a gram negative cocobacilli spread by air born drop let
THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...
THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...Abdul Wali Khan University Mardan,kP,Pakistan
hematic appreciation test is a psychological assessment tool used to measure an individual's appreciation and understanding of specific themes or topics. This test helps to evaluate an individual's ability to connect different ideas and concepts within a given theme, as well as their overall comprehension and interpretation skills. The results of the test can provide valuable insights into an individual's cognitive abilities, creativity, and critical thinking skillsDeep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
What is greenhouse gasses and how many gasses are there to affect the Earth.
What are greenhouse gasses how they affect the earth and its environment what is the future of the environment and earth how the weather and the climate effects.
SAR of Medicinal Chemistry 1st by dk.pdf
In this presentation include the prototype drug SAR on thus or with their examples .
Syllabus of Second Year B. Pharmacy
2019 PATTERN.
Recently uploaded (20)
3D Hybrid PIC simulation of the plasma expansion (ISSS-14)
3D Hybrid PIC simulation of the plasma expansion (ISSS-14)
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Sharlene Leurig - Enabling Onsite Water Use with Net Zero Water
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
Remote Sensing and Computational, Evolutionary, Supercomputing, and Intellige...
8.Isolation of pure cultures and preservation of cultures.pdf
8.Isolation of pure cultures and preservation of cultures.pdf
Cytokines and their role in immune regulation.pptx
Cytokines and their role in immune regulation.pptx
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
Travis Hills' Endeavors in Minnesota: Fostering Environmental and Economic Pr...
bordetella pertussis.................................ppt
bordetella pertussis.................................ppt
THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...
THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...
aziz sancar nobel prize winner: from mardin to nobel
aziz sancar nobel prize winner: from mardin to nobel
What is greenhouse gasses and how many gasses are there to affect the Earth.
What is greenhouse gasses and how many gasses are there to affect the Earth.
Crystallography INTRODUCTION
- 2. INTRODUCTION ● The matters in this world are classified as solids, liquids and gases. ● These materials are made up ofatoms and molecules. ● Materials differ from one another on their properties. ● These differences in properties of the solids are due to their structures. ● The behaviour of a solid material is closely related to its structure.
- 3. CLASSIFICATION OF SOLIDS On the basis of crystal structure materials are broadly classified as (i) Crystalline solids (ii) Non-Crystalline or Amorphous solids
- 4. (i) Crystalline solids Materials in which the atoms are arranged in systematic pattern are known as crystalline solids. They have well defined geometrical form. Eg: Diamond, copper, platinum, silver, polonium, etc. The crystals are of two forms: 1. Single crystal 2. Poly crystal --- Single crystal contains only one crystal. --- Poly crystal is an aggregate of many small crystals separated by well defined grain boundaries.
- 5. (ii) Non-Crystalline or Amorphous solids Materials in which the atoms are arranged in an irregular fashion are known as non-crystalline solids. Eg: Plastics, Rubber and Glass
- 6. Crystallography The branch of physics that deals with the structure, properties and external or internal symmetries in crystals are known as crystal physics or crystallography.
- 7. Fundamentals of crystallographic terms Lattice : ● It is defined as an array of points which represents the position of atoms in the crystals in three dimensions. ● It is an imaginary concept.
- 8. Space lattice: The geometrical representation of the crystal structure in terms of lattice points is called space lattice , provided the environment about every point is identical to that of every other point.
- 9. Lattice points: The points in the space lattice are called lattice points. Lattice line: The lines joining the lattice points are called as lattice line. Lattice plane: The place containing the lattice points are called as lattice plane. Basis: The crystal structure is formed by associating unit assembly of atoms or molecules with every lattice point. This unit assembly of atoms or molecules is called basis or motif. Crystal structure: Crystal structure is formed by combining space lattice with a basis. Space lattice + Basis Crystal Structure
- 10. Unit cell: A unit cell is defined as the smallest geometric figure which on repetition gives the actual crystal structure. It is also defined as fundamental elementary pattern with minimum number of atoms or molecules which represents the total characteristics of the crystal.
- 11. Lattice parameters: The intercepts a, b and c are nothing but the edges of the unit cell. These are known as primitives or characteristic intercepts. The distance between two lattice points are known as axial length. The angles between a, b and b, c and c, a are called interfacial angles. Both intercepts and interfacial angles form the lattice parameters of unit cell.
- 12. Primitive cell: The primitive cell is the simplest type of unit cell which contains only one lattice point (only one atom) per unit cell. Eg: Simple cubic Non – Primitive cells: If more than one lattice point (more than one atom) in an unit cell, it is called a non- primitive cell. Eg: BCC and FCC
- 13. CRYSTAL SYSTEMS AND BRAVAIS LATTICES Crystals are classified into 7 crystal systems on the basis of lattice parameters. Bravais Lattices: -> According to Bravais, there are only 14 possible ways of arranging points in space lattice from the seven crystal systems such that all the lattice points have exactly the same surroundings. -> These 14 space lattices are called the Bravais lattices.
- 14. CRYSTAL SYSTEMS
- 15. CRYSTAL SYSTEMS