Properties of Crystals PDF

PROPERTIES OF CRYSTALS LATTICE - a periodic array of points BASIS - entities of atoms, ions or molecules Lesson 1 CRYSTAL STRUCTURE - an...

PROPERTIES OF CRYSTALS LATTICE - a periodic array of points BASIS - entities of atoms, ions or molecules Lesson 1 CRYSTAL STRUCTURE - an arrangement of CRYSTALS - are solids materials having a regularly atoms, ions or molecules around the lattice site repeating arrangement of atoms. UNIT CELL - basic structure unit of crystal - built up by the continuing three-dimensional structure. Atoms located within a parallelepiped translational repetition of some basic structural (or prisms) volume. Building block of structure. pattern. - any solid that has an organized structure. CRYSTALLOGRAPHY - is the science that examines crystals. CRYSTALLOGRAPHERS - use the properties and inner structures of crystals to determine the arrangement of atoms and generate knowledge that is used by chemists, physicist, biologists, and other disciplines. CRYSTAL STRUCTURE - is composed of unit cell. - a set of atoms arranged in a particular way, which is periodically repeated in three dimensions on a LATTICE. SOME OF THE CHARACTIZATION TECHNIQUES THAT ARE USED IN SCIENCE MATERIALS. XRD - X-ray Diffraction TEM - Transmission Electron Microscopy - Crystal Structure may be broken down into a lattice and a bases. AMORPHOUS SOLIDS with irregular arrangement - 2 Dimensions and 3 Dimensions of atoms in patches also breaks unevenly whenever CRYSTALLINE - are solids in which the constitute force is applied or is broken. These solids do not particles of matter are arranged and organized in a break in any regular pattern as is evident in crystals specific manner. but rather break at random as the weakest bond - contain crystals in their structure and each at places is not evenly placed within the crystal has definite geometry amorphous solid structure - have well defined shapes because their particles — atoms, molecules, or ions—occur in an orderly arrangement consist of particles tightly packed into a regular array called a lattice. NON-CRYSTALLINE OR AMORPHOUS - which the constituent particles of matter are arranged in a random manner. - no proper arrangement of atoms in the solid lattice. - have poorly defined shapes because their particles lack an orderly arrangement throughout the sample. Example of amorphous solid are rubbers, glasses, and obsidians (volcanic glasses).  PROPERTIES OF CRYSTALS 3. Tetragonal Systems In tetragonal Bravais lattices, the following Lesson 2 The CRYSTAL STRUCTURE is made of several relations are observed: repeating unit cells. The unit cell has three sides: a, a=b≠c b, and c. 𝛂 = 𝞫 = 𝝲 = 90° The angle between a and b is called the gamma The two types of tetragonal systems are (γ) simple tetragonal cells and body-centered The angle between a and c is named the beta tetragonal cells, as illustrated below. (β) The angle between b and c is the alpha (α) THERE ARE SEVEN (7) CRYSTAL SYSTEMS, 4 TYPES OF UNITS CELLS, AND 14 BRAVAIS 4. Monoclinic Systems LATTICES ACCORDING TO THE ANGLES AND Bravais lattices having monoclinic systems obey LENGTH OF SIDES the following relations: a≠b≠c 1. Cubic Systems 𝞫 = 𝝲 = 90° and 𝛂 ≠ 90° In Bravais lattices with cubic systems, the following The two possible types of monoclinic systems relationships can be observed. are primitive and base centered monoclinic a=b=c cells, as illustrated below. 𝛂 = 𝞫 = 𝝲 = 90° Cubic cells are – Monoclinic Sulfur (simple The 3 possible types of cubic cells have been monoclinic) and sodium sulfate decahydrate illustrated below. (base centered monoclinic). 2. Orthorhombic Systems 5. Triclinic System The Bravais lattices with orthorhombic systems There exists only one type of triclinic Bravais obey the following equations: lattice, which is a primitive cell. It obeys the a≠b≠c following relationship. 𝛂 = 𝞫 = 𝝲 = 90° a≠b≠c The four types of orthorhombic systems 𝛂 ≠ 𝞫 ≠ 𝝲 ≠ 90° (simple, base centered, face-centered, and An illustration of a simple triclinic cell is given body-centered orthorhombic cells) are below. illustrated below. Such unit cells are found in the structure of potassium dichromate (K2Cr2O7). 6. Rhombohedral System Only the primitive unit cell for a rhombohedral PROPERTIES OF CRYSTALS Lesson 3 system exists. Its cell relation is given by: Coordination number - are used to know how a=b=c many atoms is near to the unit cell. 𝛂 = 𝞫 = 𝝲 ≠ 90° - the coordination number of an atom in a An illustration of the primitive rhombohedral molecule is the number of atoms bonded to the cell is provided below atom. THERE ARE THREE TYPES OF CUBIC UNIT CELLS: THE SIMPLE CUBIC CELL (SCC), BODY-CENTERED CUBIC (BCC) CELL, AND FACE-CENTERED CUBIC (FCC) CELL. 1. Simple cubic cell (scc) - is a unit cell in which a particle occupies each corner of a cube the basic, 7. Hexagonal System repeating unit in the array of spheres. The only type of hexagonal Bravais lattice is the - The particles touch along the cube edges simple hexagonal cell. It has the following relations but they do not touch diagonally along the cube between cell sides and angles. faces or through its center. a=b≠c - coordination number of each particle is 6: 𝛂 = 𝞫 = 90° and 𝝲 = 120° four in its own layer, one in the layer above, and An illustration of a simple hexagonal cell is one in the layer below. provided below. - A simple cubic unit cell contains 8 x 1/8 particle = 1 particle. 2. Body-centered cubic cell, the identical particles lie at each corner and in the center of the cube. Those at the corners do not touch each other, but they all touch the one in the center. - Each particle is surrounded by eight nearest neighbors, four above and four below. The coordinate number is 8. - A body-centered cubic unit cell contains 8 x 1/8 particle = 1 particle plus 1 particle in the center Total = 2 particles 3. Face-centered cubic (fcc) cell, the identical Body-centered cubic unit cell particles lie at each corner and in the center of The second layer (colored green for clarity) is each face but not in the center of the cube. placed on the diamond-shaped spaces in the first Particles at the corners touch those in the faces layer. The third layer is packed onto the diamond- but not each other. shaped spaces in the second, which makes the - The coordinates number is 12 first- and third-layers line up vertically. The packing - A face-centered cubic unit cell contains 8 x efficiency is 68%. Several metallic elements, 1/8 particle including chromium and iron, have a crystal = 1 particle plus one-half particle in each of the six structure based on this unit cell. faces = 6 x ½ particle = 3 particles Total =1+3 = 4 particles Hexagonal and face-centered cubic unit cells Spheres are packed most efficiently in these cells. Packing Efficiency - is the percentage of the First, in the bottom layer (labeled a, orange), every volume of the unit cell occupied by the spheres. other row is shifted laterally so that the large - Unit cells result from the ways atoms pack diamond-shaped spaces become smaller triangular together, which are similar to the ways that spaces. Then the second layer (labeled b, green) is macroscopic spheres—marbles, golf balls, fruit— placed over these spaces. are packed. In layer b, some spaces are orange because they - The higher the coordination number is, the lie above spheres in layer a, whereas other spaces greater packing efficiency are white because they lie above spaces in layer a. would be. The third layer can be placed in either of two ways, which gives rise to two different unit cells: Simple Cubic Unit In the first layer, each sphere lies next to another horizontally and vertically; note the large diamond- shaped spaces. If the spheres in the next layer lie directly over those in the first, the packing is based on the simple cubic unit cell (pale orange cube, lower right corner). The spheres occupy only 52% of the unit- cell volume. 48% is empty space between them. This is a very inefficient way to pack spheres, so neither fruit nor atoms are typically packed this way.  There are four ways of packing identical spheres in Metallic Solids cubic system. In this table below, take note that Most metallic elements crystallize in one of the face-centered cubic (fcc) is equivalent to cubic two closest packed structures. closest packed (ccp). Powerful metallic bonding forces hold atoms together. TYPES OF CRYSTALLINE SOLIDS The properties of metals—high electrical and Atomic Solids thermal conductivity, luster, and malleability— Individual atoms held together only by result dispersion forces from their delocalized electrons. Noble gases [Group 8A (18)] are the only substances that form such solids. The very weak forces among the atoms mean melting and boiling points and heats of vaporization and fusion are all very low. Network Covalent Solids Molecular Solids Strong covalent bonds link the atoms; Individual molecules occupy the lattice points. Various combinations of dipole-dipole, separate particles are not present. dispersion, and H-bonding forces account for a These substances adopt a variety of wide range of physical properties. crystal structures depending on the Most molecular solids have much higher melting details of their bonding. points than atomic solids (noble gases) but All network covalent solids have much lower melting points than other types of solids. extremely high melting and boiling Methane crystallizes with a face-centered points, but their conductivity cubic unit cell, and the center of each carbon is and hardness vary. the lattice point. Two examples with the same composition but strikingly different properties are the two common crystalline forms of elemental carbon, graphite and diamond. Ionic Solids The unit cell contains particles with whole, rather than partial, charges The interparticle forces (ionic bonds) are much stronger than the van der Waals forces in atomic or molecular solids. Ionic compounds adopt several different crystal structures, but many use cubic closest packing.