Miriam Rossi, a professor of chemistry at Vassar College, provides the following explanation:

Both diamond and graphite are made entirely out of carbon, as is the more recently discovered buckminsterfullerene (a discrete soccer-ball-shaped molecule containing carbon 60 atoms). The way the carbon atoms are arranged in space, however, is different for the three materials, making them allotropes of carbon. The differing properties of carbon and diamond arise from their distinct crystal structures.

In a diamond, the carbon atoms are arranged tetrahedrally. Each carbon atom is attached to four other carbon atoms 1.544 x 10-10 meter away with a C-C-C bond angle of 109.5 degrees. It is a strong, rigid three-dimensional structure that results in an infinite network of atoms. This accounts for diamond's hardness, extraordinary strength and durability and gives diamond a higher density than graphite (3.514 grams per cubic centimeter). Because of its tetrahedral structure, diamond also shows a great resistance to compression. The hardness of a crystal is measured on a scale, devised by Friederich Mohs, which ranks compounds according to their ability to scratch one another. Diamond will scratch all other materials and is the hardest material known (designated as 10 on the Mohs scale). It is the best conductor of heat that we know, conducting up to five times the amount that copper does. Diamond also conducts sound, but not electricity; it is an insulator, and its electrical resistance, optical transmissivity and chemical inertness are correspondingly remarkable.

Moreover, diamonds disperse light. This means that the refractive indices for red and violet light are different (2.409 and 2.465, respectively). As a result, the gemstone acts like a prism to separate white light into rainbow colors, and its dispersion is 0.056 (the difference). The greater the dispersion, the better the spectrum of colors that is obtained. This property gives rise to the "fire" of diamonds. The "brilliance" of diamonds stems from a combination of refraction, internal reflection and dispersion of light. For yellow light, for example, diamond has a high refractive index, 2.4, and a low critical angle of 24.5 degrees. This means that when yellow light passes into a diamond and hits a second face internally at an angle greater than 24.5 degrees, it cannot pass from the crystal into the outside air but instead gets reflected back to the inside of the gemstone.

The carbon atoms in graphite are also arranged in an infinite array, but they are layered. These atoms have two types of interactions with one another. In the first, each carbon atom is bonded to three other carbon atoms and arranged at the corners of a network of regular hexagons with a 120-degree C-C-C bond angle. These planar arrangements extend in two dimensions to form a horizontal, hexagonal "chicken-wire" array. In addition, these planar arrays are held together by weaker forces known as stacking interactions. The distance between two layers is longer (3.347 x 10-10 meter) than the distance between carbon atoms within each layer (1.418 x 10-10 meter). This three-dimensional structure accounts for the physical properties of graphite. Unlike diamond, graphite can be used as a lubricant or in pencils because the layers cleave readily. It is soft and slippery, and its hardness is less than one on the Mohs scale. Graphite also has a lower density (2.266 grams per cubic centimeter) than diamond. The planar structure of graphite allows electrons to move easily within the planes. This permits graphite to conduct electricity and heat as well as absorb light and, unlike diamond, appear black in color.

Answer originally posted May 20, 2002.