Why does a crystal lattice form

Silicon carbide SiC is also known as carborundum. Its structure is very much like that of diamond, with every other carbon replaced by silicon. Silicon carbide exists in about crystalline forms. It is used mostly in its synthetic form because it is extremely rare in nature. It is found in a certain type of meteorite that is thought to originate outside of our solar system. Structurally, silicon carbide is very complex; at least 70 crystalline forms have been identified.

Its extreme hardness and ease of synthesis have led to a diversity of applications — in cutting tools and abrasives, high-temperature semiconductors and other high-temperature applications, the manufacturing of specialty steels and jewelry, and many more. Tungsten carbide WC is probably the most widely encountered covalent solid, owing to its use in carbide cutting tools and as the material used to make the rotating balls in ball-point pens. In many of its applications, it is embedded in a softer matrix of cobalt or coated with titanium compounds.

Silicon Carbide : Silicon carbide is an extremely rare mineral, and in nature is is mostly found in a certain type of meteorite. Recall that a molecule is defined as a discrete aggregate of atoms bound together sufficiently tightly by directed covalent forces to allow it to retain its individuality when the substance is dissolved, melted, or vaporized.

The two words italicized in the preceding sentence are important. Covalent bonding implies that the forces acting between atoms within the molecule intra molecular are much stronger than those acting between molecules inter molecular , The directional property of covalent bonding gives each molecule a distinctive shape which affects a number of its properties. Liquids and solids composed of molecules are held together by van der Waals or intermolecular forces, and many of their properties reflect this weak binding.

Molecular solids tend to be soft or deformable, have low melting points, and are often sufficiently volatile to evaporate directly into the gas phase. This latter property often gives such solids a distinctive odor. Thus, many corresponding substances are either liquid water or gaseous oxygen at room temperature. Molecular solids also have relatively low density and hardness. The elements involved are light, and the intermolecular bonds are relatively long and are therefore weak.

Because of the charge neutrality of the constituent molecules, and because of the long distance between them, molecular solids are electrical insulators.

Because dispersion forces and the other van der Waals forces increase with the number of atoms, large molecules are generally less volatile, and have higher melting points than smaller ones. Also, as one moves down a column in the periodic table, the outer electrons are more loosely bound to the nucleus, increasing the polarisability of the atom, and thus its propensity to van der Waals-type interactions.

This effect is particularly apparent in the increase in boiling points of the successively heavier noble gas elements. Interactive: Charged and Neutral Atoms : There are two kinds of attractive forces shown in this model: Coulomb forces the attraction between ions and Van der Waals forces an additional attractive force between all atoms.

What kinds of patterns tend to form with charged and neutral atoms? How does changing the Van der Waals attraction or charging the atoms affect the melting and boiling point of the substance? When white phosphorus is converted to the covalent red phosphorus, the density increases to 2. Both red and black phosphorus forms are significantly harder than white phosphorus. Although white phosphorus is an insulator, the black allotrope, which consists of layers extending over the whole crystal, does conduct electricity.

Similarly, yellow arsenic is a molecular solid composed of As 4 units; it is metastable and gradually transforms into gray arsenic upon heating or illumination. Certain forms of sulfur and selenium are each composed of S 8 or Se 8 units, and are molecular solids at ambient conditions.

However, they can convert into covalent allotropes having atomic chains extending all through the crystal. The vast majority of molecular solids can be attributed to organic compounds containing carbon and hydrogen, such as hydrocarbons C n H m.

Spherical molecules consisting of different number of carbon atoms, called fullerenes, are another important class. Less numerous, yet distinctive molecular solids are halogens e. Its solid form is an insulator because all valence electrons of carbon atoms are involved into the covalent bonds within the individual carbon molecules.

However, inserting intercalating alkali metal atoms between the fullerene molecules provides extra electrons, which can be easily ionized from the metal atoms and make the material conductive, and even superconductive. Fullerene Crystals : Fullerene solid is an insulator, but it can become a superconductor when intercalating metal ions are inserted between the fullerene molecules C Metallic crystals are held together by metallic bonds, electrostatic interactions between cations and delocalized electrons.

In a metal, atoms readily lose electrons to form positive ions cations. These ions are surrounded by delocalized electrons, which are responsible for conductivity. The solid produced is held together by electrostatic interactions between the ions and the electron cloud. These interactions are called metallic bonds.

Metallic bonding accounts for many physical properties of metals, such as strength, malleability, ductility, thermal and electrical conductivity, opacity, and luster. Metallic Bonding : Loosely bound and mobile electrons surround the positive nuclei of metal atoms.

In a quantum-mechanical view, the conducting electrons spread their density equally over all atoms that function as neutral non-charged entities. Atoms in metals are arranged like closely-packed spheres, and two packing patterns are particularly common: body-centered cubic, wherein each metal is surrounded by eight equivalent metals, and face-centered cubic, in which the metals are surrounded by six neighboring atoms.

Several metals adopt both structures, depending on the temperature. Snowflakes are examples of crystals! They are formed when water precipitation cools to ice, creating crystals. Image source: By Cassie Gates.

Formation Of Crystals When crystals are formed the process is known as crystallization. There are various ways this can occur such as: Precipitation : solid crystals can form by manipulating a solution. Crystal Structures The organized structure of crystals has repeating patterns throughout. The crystal lattice describes the organization of the crystal, while the unit cell describes the simplest repeating pattern in the overall crystal.

Image Source: By Cassie Gates. Related Lessons. View All Related Lessons. You've reached the end. As shown in Figure , a solid with this type of arrangement consists of planes or layers in which each atom contacts only the four nearest neighbors in its layer; one atom directly above it in the layer above; and one atom directly below it in the layer below.

The number of other particles that each particle in a crystalline solid contacts is known as its coordination number. For a polonium atom in a simple cubic array, the coordination number is, therefore, six. In a simple cubic lattice, the unit cell that repeats in all directions is a cube defined by the centers of eight atoms, as shown in Figure.

Atoms at adjacent corners of this unit cell contact each other, so the edge length of this cell is equal to two atomic radii, or one atomic diameter. A cubic unit cell contains only the parts of these atoms that are within it. Since an atom at a corner of a simple cubic unit cell is contained by a total of eight unit cells, only one-eighth of that atom is within a specific unit cell. Calculation of Atomic Radius and Density for Metals, Part 1 The edge length of the unit cell of alpha polonium is pm.

Solution Alpha polonium crystallizes in a simple cubic unit cell:. Therefore, the radius of Po is. Since a Po unit cell contains one-eighth of a Po atom at each of its eight corners, a unit cell contains one Po atom. Note that the edge length was converted from pm to cm to get the usual volume units for density.

Therefore, the density of. Check Your Learning The edge length of the unit cell for nickel is 0. The density of Ni is 8. Does nickel crystallize in a simple cubic structure? If Ni was simple cubic, its density would be given by: Then the density of Ni would be Since the actual density of Ni is not close to this, Ni does not form a simple cubic structure. Most metal crystals are one of the four major types of unit cells.

For now, we will focus on the three cubic unit cells: simple cubic which we have already seen , body-centered cubic unit cell , and face-centered cubic unit cell —all of which are illustrated in Figure.

Note that there are actually seven different lattice systems, some of which have more than one type of lattice, for a total of 14 different types of unit cells. We leave the more complicated geometries for later in this module.

Some metals crystallize in an arrangement that has a cubic unit cell with atoms at all of the corners and an atom in the center, as shown in Figure. This is called a body-centered cubic BCC solid. Atoms in the corners of a BCC unit cell do not contact each other but contact the atom in the center. A BCC unit cell contains two atoms: one-eighth of an atom at each of the eight corners atom from the corners plus one atom from the center. Any atom in this structure touches four atoms in the layer above it and four atoms in the layer below it.

Thus, an atom in a BCC structure has a coordination number of eight. Elements or compounds that crystallize with the same structure are said to be isomorphous. Many other metals, such as aluminum, copper, and lead, crystallize in an arrangement that has a cubic unit cell with atoms at all of the corners and at the centers of each face, as illustrated in Figure.

This arrangement is called a face-centered cubic FCC solid. A FCC unit cell contains four atoms: one-eighth of an atom at each of the eight corners atom from the corners and one-half of an atom on each of the six faces atoms from the faces. The atoms at the corners touch the atoms in the centers of the adjacent faces along the face diagonals of the cube. Because the atoms are on identical lattice points, they have identical environments. This structure is also called cubic closest packing CCP.

In CCP, there are three repeating layers of hexagonally arranged atoms. Each atom contacts six atoms in its own layer, three in the layer above, and three in the layer below. In this arrangement, each atom touches 12 near neighbors, and therefore has a coordination number of The fact that FCC and CCP arrangements are equivalent may not be immediately obvious, but why they are actually the same structure is illustrated in Figure.

Because closer packing maximizes the overall attractions between atoms and minimizes the total intermolecular energy, the atoms in most metals pack in this manner. We find two types of closest packing in simple metallic crystalline structures: CCP, which we have already encountered, and hexagonal closest packing HCP shown in Figure. Both consist of repeating layers of hexagonally arranged atoms.

In both types, a second layer B is placed on the first layer A so that each atom in the second layer is in contact with three atoms in the first layer. The third layer is positioned in one of two ways.

In HCP, atoms in the third layer are directly above atoms in the first layer i. In CCP, atoms in the third layer are not above atoms in either of the first two layers i. About two—thirds of all metals crystallize in closest-packed arrays with coordination numbers of The edge length of its unit cell is Two adjacent edges and the diagonal of the face form a right triangle, with the length of each side equal to Solving this gives. A face-centered Ca unit cell has one-eighth of an atom at each of the eight corners atom and one-half of an atom on each of the six faces atoms , for a total of four atoms in the unit cell.

Then, the density of. The edge length of its unit cell is pm. The axes are defined as being the lengths between points in the space lattice. Consequently, unit cell axes join points with identical environments. There are seven different lattice systems, some of which have more than one type of lattice, for a total of fourteen different unit cells, which have the shapes shown in Figure.

The Structures of Ionic Crystals Ionic crystals consist of two or more different kinds of ions that usually have different sizes. The packing of these ions into a crystal structure is more complex than the packing of metal atoms that are the same size. Most monatomic ions behave as charged spheres, and their attraction for ions of opposite charge is the same in every direction. Consequently, stable structures for ionic compounds result 1 when ions of one charge are surrounded by as many ions as possible of the opposite charge and 2 when the cations and anions are in contact with each other.

Structures are determined by two principal factors: the relative sizes of the ions and the ratio of the numbers of positive and negative ions in the compound.

In simple ionic structures, we usually find the anions, which are normally larger than the cations, arranged in a closest-packed array. As seen previously, additional electrons attracted to the same nucleus make anions larger and fewer electrons attracted to the same nucleus make cations smaller when compared to the atoms from which they are formed. The smaller cations commonly occupy one of two types of holes or interstices remaining between the anions. The smaller of the holes is found between three anions in one plane and one anion in an adjacent plane.

The four anions surrounding this hole are arranged at the corners of a tetrahedron, so the hole is called a tetrahedral hole. The larger type of hole is found at the center of six anions three in one layer and three in an adjacent layer located at the corners of an octahedron; this is called an octahedral hole.

Figure illustrates both of these types of holes. Depending on the relative sizes of the cations and anions, the cations of an ionic compound may occupy tetrahedral or octahedral holes, as illustrated in Figure. Not all ionic compounds are formed from only two elements. Many polyatomic ions exist, in which two or more atoms are bound together by covalent bonds.

They form a stable grouping which carries a charge positive or negative. The group of atoms as a whole acts as a charged species in forming an ionic compound with an oppositely charged ion. Polyatomic ions may be either positive or negative, for example:. The principles of ionic bonding with polyatomic ions are the same as those with monatomic ions. Oppositely charged ions come together to form a crystalline lattice, releasing a lattice energy.

Based on the shapes and charges of the polyatomic ions, these compounds may form crystalline lattices with interesting and complex structures.

Ionic bonds are formed when positively and negatively charged ions are attracted by electrostatic forces. Consider a single pair of ions, one cation and one anion.

How strong will the force of their attraction be? The proportionality constant k is equal to 2. The equation can also be written using the charge of each ion, expressed in coulombs C , incorporated in the constant. In this case, the proportionality constant, k , equals 8.

Energy is always released when a bond is formed and correspondingly, it always requires energy to break a bond. Because ions occupy space and have a structure with the positive nucleus being surrounded by electrons, however, they cannot be infinitely close together.

The total energy of the system is a balance between the attractive and repulsive interactions. This distance is the same as the experimentally measured bond distance. The energy of the system reaches a minimum at a particular distance r 0 when the attractive and repulsive interactions are balanced.

The negative value indicates that energy is released. Our convention is that if a chemical process provides energy to the outside world, the energy change is negative.

If it requires energy, the energy change is positive. This is the energy released when 1 mol of gaseous ion pairs is formed, not when 1 mol of positive and negative ions condenses to form a crystalline lattice. Because of long-range interactions in the lattice structure, this energy does not correspond directly to the lattice energy of the crystalline solid.