Matter is commonly encountered in one of three states—solid, liquid, or gas. Air is an example of a gas and water an example of a liquid. Objects such as rocks, concrete buildings, or pages in a book can be classified as solids. But what exactly is a solid?
Defining the solid state is difficult because while many things are described as solids, they may be heterogeneous (i.e., they may contain molecules of liquids or gases). Consider, for example, the pages of a book, which are made from paper and are primarily cellulose. Even though there is no question that they are solid, they do contain a quantity of water within the cellulose structure—typically about 5 percent. Paper is not described as a liquid, however, because it would not be a useful way to describe its properties.
The defining characteristics of a solid are a question of molecular motion. Atoms and molecules in a gaseous state move rapidly and independently, with little interaction. A gas therefore occupies the shape of the container that holds it as the gas molecules bounce off the walls. Particles in the liquid state do not move as rapidly or as independently as molecules in a gas, but they do move past one another, forming only loose and temporary associations. Liquids also lack definable shape, adopting the shape of the container that holds them. Conversely, particles in a solid do not change position and can interact strongly with their neighbors. They may vibrate in place and oscillate about their average position, but they do not shift from one location to another. It is incorrect to say that particles in a solid do not move, as they do "jiggle" in place, but they do not move from their fixed position. In the case of paper, the molecules of cellulose and water are, in the absence of an external force, fixed in place. An external force is required to allow the atoms of a solid to shift, such as when a piece of paper is ripped or a strip of metal is bent.
An analogy for the three states of matter is students in a classroom. Sitting at their desks, they represent a solid. Moving around the classroom, they are like a liquid. Once the bell rings, they are like a gas that is spread throughout the neighborhood. The arrangement of the components of a solid—in this analogy, how the students' desks would be arranged—allows for solids to be classified in one of two broad categories: amorphous or crystalline.
Glass is a classic example of an amorphous material and diamond of a crystal material. Both are transparent solids with molecules and atoms that are held together with strong covalent bonds. Yet it would be hard to mistake one for the other, as diamonds are the hardest known natural substance while glass breaks fairly easily. To use the classroom analogy, the difference between glass and diamonds is that in glass, the desks are arranged completely at random, whereas in diamonds, the desks are lined up in neat and orderly rows.
Glass is a heterogeneous material formed from silicon, oxygen, sodium, and a variety of other elements, depending upon the type of glass. It lacks long-range structure: Short units of silicon dioxide are bound together, but there is no overall order. At an atomic level, glass looks like a frozen liquid. Individual clusters exist, but they are not connected to each other and are held together only by van der Waals interactions. This is why when glass breaks it forms curved or jagged edges and why it shatters if struck with a hard blow.
Glass is only one example of an amorphous material. Another is paper, composed of randomly oriented cellulose molecules. Many familiar objects are made up of amorphous solid materials, all lacking long-range structure or order. They are aperiodic substances—substances that do not display periodicity. Consequently, it is hard to analyze the structure of amorphous materials as each sample is unique.
Crystalline solids make up a much smaller percentage of everyday objects, but they are easier to understand. A subdiscipline of chemistry called crystallography is devoted to analyzing crystalline material. The defining characteristic of a crystalline material is that it is periodic with an underlying structure that is regular and repeating. A crystal displays long-range structure made up of the same building block used over and over.
Consider a crystal of gold, composed of endless planes of gold atoms. Within each plane, gold atoms adopt a regular pattern, with each atom occupying the center of a hexagon and surrounded by its closest neighbors. Each gold atom looks just like the one next to it—the pattern is repeated countless times. Also consider the diamond, which is like glass in appearance but is a covalent network solid with a three-dimensional lattice of tetrahedrally bound carbon atoms. Each carbon is attached to four neighbors in endless repetition. The three-dimensional structure and covalent bonds ensure that diamonds are incredibly hard.
The critical feature of crystalline material is that it is periodic. Although it may not be intuitively obvious, there are only seven shapes in nature that can be packed in a long-range periodic three-dimensional pattern. Packing a collection of spheres leaves a hollow shape between one sphere and the next, so a sphere is not one of the basic shapes for packing crystals. A cube, on the other hand, gives a three-dimensional, repeating structure with no voids. Considering the difference between a stack of boxes and a stack of bowling balls, it is easy to see that the boxes make a much more solid structure.
This is not to say that atoms and molecules are little boxes but rather that particles are arranged in a solid as if they were contained in molecular-size boxes. Each of these boxes is called a unit cell, and the overall arrangement of the unit cells is called a lattice. There are seven unit cell types possible for crystal growth, and all crystals belong to one of these seven crystal systems (see Table 1).
The spatial arrangement of atoms and molecules in any crystalline solid can be assigned to one of these seven geometric systems, even though the atoms themselves are spherical in shape. For example, the lattice of tetrahedrally bonded carbon atoms in a diamond can be described using a repeating cube. Another example is the cube that is described by sodium chloride (NaCl), or common table salt. In this instance, a sodium atom can be found at the center of the cube, surrounded by six chloride ions, each
|hexagonal||a=b≠c||α=β=90 ° ;γ=120 °|
|monoclinic||a=b≠c||α=γ=90 ° ;β=90 °|
occupying one of the faces. Twelve more sodium atoms occupy the edges and eight more chlorides occupy the corners. Considering that each chloride at each corner resides in eight different cubes, that each sodium along an edge resides in four different cubes, and that each chloride on a face resides in two different cubes, only one ion—the central sodium—is contained entirely within the unit cell. However, one-eighth of the eight chlorides at the corners and two of the six chlorides on the faces result in a total of four chlorides in the unit cell. Similarly, one-fourth of the twelve sodium atoms along the edges and the one in the middle results in a total of four sodium ions. The net result is that each repeating unit—each cube of sodium and chloride—has four of each atom and, overall, the formula for table salt can be written as NaCl.
This idea of repetition—of using unit cells to build up a crystalline solid—allows crystallographers to use x-ray diffraction and neutron diffraction to map out electron density within a unit cell. Using mathematics and a knowledge of where the electrons are located, it is possible to determine the exact position of each and every atom within the cell. From this, it is possible to determine which atoms are in close contact. Physically, two atoms are said to be bonded together by a covalent interaction when the distance between them is less than the sum of their respective van der Waals radii. Chemists and physicists have been able to use the concept of bonding and the techniques of crystallography to determine the structure of a great many substances. Indeed, approximately 100,000 crystal structures have been determined and registered in the Cambridge Crystallographic Database.
Diamonds represent a class of compounds called network crystals because they extend the full length of the crystal. Every carbon in a diamond is connected, via covalent bonding, with every other carbon atom. Sodium chloride, or table salt, represents a class of compounds called ionic crystals because it is composed of oppositely charged ions held in place by electrostatic attraction. These interactions can be incredibly strong and give rise to minerals and gemstones, such as magnetite and rubies. Ionic interactions are the binding force in all salts, regardless of whether they are crystalline. In the crystalline state, however, they give rise to almost all minerals and gems.
Two other classes of crystalline solids are molecular crystals and metallic crystals. Molecular crystals are assembled through the interaction of molecules to form a regular and repeating lattice. The most familiar example would be solid water (ice). Each water molecule in a crystal of ice is independent and internally bonded through covalent interactions. In the gaseous state, water molecules move independently and do not interact. In the solid state, the amount of energy present is insufficient to overcome hydrogen bonding interactions, and the molecules link one to the other to form an extended hexagonal lattice. Each molecule is held tightly in place by its neighbors. The interactions between molecules tend to be weaker than in either a network or ionic crystal, with the result that these crystals are easily broken—think of trying to crush an ice cube versus a diamond.
In a metallic crystal, the latticework of the atoms is bound together by a sea of electrons. Each atom—or, more accurately, each nucleus—occupies a position within a crystalline lattice. The electrons, on the other hand, move among all of the available atoms in a series of conduction bands. The net result is that even in an amorphous state metals readily conduct electricity and heat, they are ductile and malleable, and they exhibit the luster seen on metallic surfaces. In the crystalline form, metals can do all of the above and exhibit other properties such as magnetism (which requires ordered crystalline domains).
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