Crystal Structure PDF

# Crystal Structure A crystal is comprised of matter arranged in a structured three-dimensional pattern of atoms, molecules, or ions. A crystal structure is a distinctive arrangement of atoms, molecules, or ions in a crystal. It is highly ordered and repetitive, creating a characteristic pattern t...

# Crystal Structure A crystal is comprised of matter arranged in a structured three-dimensional pattern of atoms, molecules, or ions. A crystal structure is a distinctive arrangement of atoms, molecules, or ions in a crystal. It is highly ordered and repetitive, creating a characteristic pattern that defines the crystal's shape and properties. ## Bravais Lattice The Bravais lattice is the basic building block from which all crystals can be constructed. The concept originated as a topological problem of finding the number of different ways to arrange points in space where each point would have an identical "atmosphere". That is, each point would be surrounded by an identical set of points as any other point, so that all points would be indistinguishable from each other. Mathematician Auguste Bravais discovered that there were 14 different collections of the groups of points, which are known as Bravais lattices. These lattices fall into seven different "crystal systems", as differentiated by the relationship between the angles between sides of the "unit cell" and the distance between points in the unit cell. The unit cell is the smallest group of atoms, ions or molecules that, when repeated at regular intervals in three dimensions, will produce the lattice of a crystal system. The "lattice parameter" is the length between two points on the corners of a unit cell. Each of the various lattice parameters are designated by the letters a, b, and c If two sides are equal, such as in a tetragonal lattice, then the lengths of the two lattice parameters are designated a and c, with b omitted. The angles are designated by the Greek letters α, β, and γ such that an angle with a specific Greek letter is not subtended by the axis with its Roman equivalent. For example, α is the included angle between the b and c axis. ## The Role of Unit Cell in Crystal Structure A fundamental idea in crystal structures is the unit cell. It is the smallest unit of volume that allows identical cells to be arranged together to occupy all available space. Unit cells are made of a lattice and basis. - Lattices tell you how the crystal is repeated. - The basis tells you what is repeated The geometrical basis of all crystals is the lattice. A lattice can be viewed as a regular and infinite arrangement of points or atoms, where each point or atom has an identical surrounding environment. ## Crystal System A crystal system refers to the classification of crystals based on the geometric arrangement and symmetry of their lattice structures. There are seven main crystal systems: 1. **Cubic (isometric)** - Characterized by three equal-length axes that intersect at right angles. 2. **Orthorhombic** – Characterized by three mutually perpendicular axes, all of different lengths. 3. **Trigonal (rhombohedral)** – Characterized by three equal axes that intersect at equal angles, not necessarily right angles. 4. **Monoclinic** - Characterized by three unequal axes, two of which intersect at an oblique angle, while the third is perpendicular to the plane of the other two. 5. **Triclinic** - Characterized by three unequal axes that intersect at oblique angles. 6. **Hexagonal** – Characterized by four axes, three of which are equal in length and intersect at 120 degrees, with a fourth axis perpendicular to the other three. 7. **Tetragonal** - Characterized by three mutually perpendicular axes, two of which are equal in length, while the third is longer or shorter and perpendicular to the other two. ## Atom Positions and Crystal Axes The structure of a crystal is defined with respect to a unit cell. As the entire crystal consists of repeating unit cells, this definition is sufficient to represent the entire crystal. Within the unit cell, the atomic arrangement is expressed using coordinates. There are two systems of coordinates commonly in use, which can cause some confusion. Both use a corner of the unit cell as their origin. - The first, less-commonly seen system is that of Cartesian or orthogonal coordinates (X, Y, Z). These usually have the units of Angstroms and relate to the distance in each direction between the origin of the cell and the atom. These coordinates may be manipulated in the same fashion as are used with two- or three-dimensional graphs. It is very simple, therefore, to calculate inter-atomic distances and angles given the Cartesian coordinates of the atoms. Unfortunately, the repeating nature of a crystal cannot be expressed easily using such coordinates. - The second system uses fractional coordinates, (x, y, z). This coordinate system is coincident with the cell axes (a, b, c) and relates to the position of the atom in terms of the fraction along each axis. ## Crystal Directions The designation of the individual vectors within any given crystal lattice is accomplished by the use of whole number multipliers of the lattice parameter of the point at which the vector exits the unit cell. The vector is indicated by the notation [hkl], where h, k, and l are reciprocals of the point at which the vector exits the unit cell. The origination of all vectors is assumed defined as [000]. For example, the direction along the a-axis according to this scheme would be [100] because this has a component only in the a-direction and no component along either the b or c axial direction. A vector diagonally along the face defined by the a and b axis would be [110], while going from one corner of the unit cell to the opposite corner would be in the [111] direction. Crystal directions may be grouped in families. To avoid confusion, there exists a convention in the choice of brackets surrounding the three numbers to differentiate a crystal direction from a family of direction. - Square brackets [hkl] are used to indicate an individual direction. - Angle brackets <hkl> indicate a family of directions. A family of directions includes any directions that are equivalent in length and types of atoms encountered. For example, in a cubic lattice, the [100], [010], and [001] directions all belong to the <100> family of planes because they are equivalent. ## Description of Crystal Structures Crystal structures may be described in a number of ways. The most common manner is to refer to the size and shape of the unit cell and the positions of the atoms (or ions) within the cell. However, this information is sometimes insufficient to allow for an understanding of the true structure in three dimensions. Consideration of several unit cells, the arrangement of the atoms with respect to each other, the number of other atoms they in contact with, and the distances to neighboring atoms, often will provide a better understanding. A number of methods are available to describe extended solid-state structures. The most applicable with regard to elemental and compound semiconductor, metals, and the majority of insulators is the close packing approach. ## Close Packed Structures: Hexagonal Close Packing and Cubic Close Packing Many crystal structures can be described using the concept of close packing. This concept requires that the atoms (ions) are arranged so as to have the maximum density. - **The most efficient way for equal sized spheres to be packed in two dimensions** is shown in Figure, in which it can be seen that each sphere (the dark gray shaded sphere) is surrounded by, and is in contact with, six other spheres (the light gray spheres in Figure). It should be noted that contact with six other spheres is the maximum possible if the spheres are the same size, although lower density packing is possible. - **The most efficient way for equal sized spheres to be packed in three dimensions is to stack close packed layers on top of each other to give a close packed structure.** There are two simple ways in which this can be done, resulting in either a hexagonal or cubic close packed structures. - **Hexagonal Close Packed:** If two close packed layers A and B are placed in contact with each other so as to maximize the density, then the spheres of layer B will rest in the hollow (vacancy) between three of the spheres in layer A. - **Cubic Close Packed: Face-centered Cubic:** In a similar manner to the generation of the hexagonal close packed structure, two close packed layers are stacked (Figure however, the third layer (C) is placed such that it does not exactly cover layer A, while sitting in a set of troughs in layer B, then upon repetition the packing sequence will be ...ABCABCABC.... ## Coordination Number The coordination number of an atom or ion within an extended structure is defined as the number of nearest neighbor atoms (ions of opposite charge) that are in contact with it. ## Octahedral and Tetrahedral Vacancies As was mentioned above, the packing fraction in both fcc and hcp cells is 74.05%, leaving 25.95% of the volume unfilled. ## Interstitial Impurity An interstitial impurity occurs when an extra atom is positioned in a lattice site that should be vacant in an ideal structure (Figure). Since all the adjacent lattice sites are filled the additional atom will have to squeeze itself into the interstitial site, resulting in distortion of the lattice and alteration in the local electronic behavior of the structure. ## Vacancies The converse of an interstitial impurity is when there are not enough atoms in a particular area of the lattice. These are called vacancies. Vacancies exist in any material above absolute zero and increase in concentration with temperature. ## Substitution Substitution of various atoms into the normal lattice structure is common, and used to change the electronic properties of both compound and elemental semiconductors. Any impurity element that is incorporated during crystal growth can occupy a lattice site. Depending on the impurity, substitution defects can greatly distort the lattice and/or alter the electronic structure. ## Antisite Defects Antisite defects are a particular form of substitution defect, and are unique to compound semiconductors. An antisite defect occurs when a cation is misplaced on an anion lattice site or vice versa (Figure). ## Extended Defects: Dislocations in a Crystal Lattice Extended defects may be created either during crystal growth or as a consequence of stress in the crystal lattice. The plastic deformation of crystalline solids does not occur such that all bonds along a plane are broken and reformed simultaneously. Instead, the deformation occurs through a dislocation in the crystal lattice. ## Epitaxy Epitaxy, is a transliteration of two Greek words epi, meaning "upon", and taxis, meaning "ordered". With respect to crystal growth it applies to the process of growing thin crystalline layers on a crystal substrate. ## Types of Crystalline Solids- Molecular, Ionic, and Atomic Crystalline substances can be described by the types of particles in them and the types of chemical bonding that take place between the particles. - **Ionic Crystals** - The ionic crystal structure consists of alternating positively-charged cations and negatively-charged anions (see Figure below). - **Metallic Crystal** - Metallic crystals consist of metal cations surrounded by a "sea" of mobile valence electrons (see figure below). These electrons, also referred to as delocalized electrons, do not belong to any one atom, but are capable of moving through the entire crystal. - **Covalent Network Crystals** - A covalent network crystal consists of atoms at the lattice points of the crystal, with each atom being covalently bonded to its nearest neighbor atoms (see figure below). - **Molecular Crystals** - Molecular crystals typically consist of molecules at the lattice points of the crystal, held together by relatively weak intermolecular forces (see figure below). ## Summary - Ionic crystals are composed of alternating positive and negative ions. - Metallic crystals consist of metal cations surrounded by a "sea" of mobile valence electrons. - Covalent crystals are composed of atoms which are covalently bonded to one another. - Molecular crystals are held together by weak intermolecular forces. # Metals Metal, any of a class of substances characterized by high electrical and thermal conductivity as well as by malleability, ductility, and high reflectivity of light. ## Physical Properties of Metals - All the metals are good conductors of heat and electricity. - Ductility is the ability of the material to be stretched into a wire. - Malleability is the property of substances which allows them to be beaten into flat sheets. - Metals are sonorous because they produces a deep or ringing sound when struck with another hard object. - Usually, all the metals have a shiny appearance but these metals can also be polished to have a shiny appearance. ## Chemical Properties of Metals - **Reaction with water:** Only highly reactive metals react with water and not all the metals. For example, Sodium reacts vigorously with water and oxygen and gives a large amount of heat in the process. - **Reaction with acids:** Hydrogen gas is produced when metals react with acids. For example, when zinc reacts with hydrochloric acid it produces zinc chloride and hydrogen gas. - **Reaction with bases:** Not all the metals react with bases and when they do react, they produce metal salts and hydrogen gas. - **Reaction with oxygen:** Metal oxides are produced when metals burn in the presence of oxygen. These metal oxides are basic in nature. For example: When a magnesium strip is burned in the presence of oxygen it forms magnesium oxide and when magnesium oxide dissolves in water it forms magnesium hydroxide. ## Metallic Bonding Most metals have very compact crystal structures involving either the body-centered cubic, face-centered cubic, or hexagonal closest-packed lattices. Thus every atom in a metal is usually surrounded by 8 or 12 equivalent nearest neighbors. ## Metallurgy Metallurgy, art and science of extracting metals from their ores and modifying the metals for use. ## Types of Metals - **Steel** is a type of alloy of several chemical elements that are made of iron with carbon to improve its strength and fracture resistance. - **Carbon steel** is defined as steel that has its properties mainly due to its carbon content and does not contain more than 0.5% of silicon and 1.5% manganese. - **Alloy Steel** is the steel that has elements other than carbon added in sufficient quantity, in order to obtain special properties for the metal, which is known as alloy steel. - **Stainless Steel** is defined as that steel when directly heat-treated and finished resists oxidation and corroding from corrosive media. ## Polymers Prior to the early 1920's, chemists doubted the existence of molecules having molecular weights greater than a few thousand. This limiting view was challenged by Hermann Staudinger, a German chemist with experience in studying natural compounds such as rubber and cellulose. ## Addition Polymers - Polymers are long chain giant organic molecules are assembled from many smaller molecules called monomers. Polymers consist of many repeating monomer units in long chains. - Polymers are analogous to a necklace made from many small beads (monomers). Many monomers are alkenes or other molecules with double bonds which react by addition to their unsaturated double bonds. ## Condensation Polymers A large number of important and useful polymeric materials are not formed by chain-growth processes involving reactive species such as radicals, but proceed instead by conventional functional group transformations of polyfunctional reactants. These polymerizations often (but not always) occur with loss of a small byproduct, such as water, and generally (but not always) combine two different components in an alternating structure. ## Nanomaterials Nanomaterials describe, in principle, chemical substances or materials of which a single unit is sized (in at least one dimension) between 1 and 100 nm. ## Synthesis The goal of any synthetic method for nanomaterials is to yield a material that exhibits properties that are a result of their characteristic length scale being in the nanometer range (1 - 100 nm). ## Characterization Novel effects can occur in materials when structures are formed with sizes comparable to any one of many possible length scales, such as the de Broglie wavelength of electrons, or the optical wavelengths of high energy photons. ## Metal-based nanoparticles Inorganic nanomaterials, (e.g. quantum dots, nanowires, and nanorods) because of their interesting optical and electrical properties, could be used in optoelectronics. ## Nanoporous materials The term nanoporous materials contain subsets of microporous and mesoporous materials. ## Nanoparticles Nanoparticles have all three dimensions on the nanoscale. Nanoparticles can also be embedded in a bulk solid to form a nanocomposite. ## Fullerenes The fullerenes are a class of allotropes of carbon which conceptually are graphene sheets rolled into tubes or spheres. ## Mechanical Properties The ongoing research has shown that mechanical properties can vary significantly in nanomaterials compared to bulk material. Nanomaterials have substantial mechanical properties due to the volume, surface, and quantum effects of nanoparticles. This is observed when the nanoparticles are added to common bulk material, the nanomaterial refines the grain and forms intergranular and intragranular structures which improve the grain boundaries and therefore the mechanical properties of the materials. ## Applications specific to Mechanical Properties: - Lubrication - Nano-manufacturing - Coatings ## Applications Nano-materials have found applications across a wide range of industries due to their unique properties. Some notable applications include: - **Electronics** - Nano-materials are revolutionizing the electronics industry by enabling the development of smaller, faster, and more efficient devices. - **Medicine** - In the medical field, nano-materials are being used for diagnostics, drug delivery, and tissue engineering. - **Energy** - Nano-materials are playing a crucial role in the development of sustainable energy solutions. ## Environmental Science Nano-materials are being used to address environmental challenges through applications such as: - **Water Purification** - Nano-filters and photocatalysts can remove contaminants and pathogens from water more effectively than traditional methods. - **Air Quality** - Nano-materials are being used in air filters and catalytic converters to reduce pollution and improve air quality.