Crystals

In the physical sense, a crystal is a set of atoms, molecules, or ions arranged in a definite geometric pattern in three dimensions. The ideal crystal is made up of unit cells which are the smallest parallelepipeds that can be fitted together to form the crystal. Each unit cell of a given crystal is identical to every other unit cell of the crystal in that each one contains the same set of atoms, molecules, or ions, arranged in exactly the same way.

The atoms, molecules, or ions which make up the crystal are arranged in rows, columns, and planes. The natural faces of the cleavage planes of the crystal tend to be parallel to planes of atoms. The distances between the planes of atoms and the dihedral angles between the nonparallel planes are as characteristic of the crystals as its density or its chemical composition.  Crystallographers long ago deduced much about the internal structure of crystals by studying their external forms. (See Crystallography)

The Inner Structure

The external differences between crystals are based on differences in internal structure. The particles of matter within a crystal are arranged in a framework called a crystal lattice. There are four types of structural units in crystal lattices. They are small molecules, giant molecules, ions or electrically charged molecules and atoms.

Crystals Made Up Of Small Molecules

In substances like ice, iodine and solid carbon dioxide or dry ice, the structural units of the crystal lattice are small molecules. Rather weak electrical forces hold these together. There is much space between the molecules and the crystals are light in weight. That is why ice is lighter than liquid water, though both substances are built up of the very same water molecules. It is important to know that ice is unique because if ice would sink, life in the ocean would be at stake. Fish and other aquatic life will freeze. Usually, crystals in which small molecules are the structural units have low melting points; they are good insulators and are relatively soft. In some cases the bonds between the molecules are so weak that the solid will change into a gas without first becoming a liquid. This process is called sublimation. This is what happens in the case of dry ice, which is solid carbon dioxide.

Crystals Made Up Of Giant Molecules

Some crystals consist of giant molecules. These may be built up in one, two, or three dimensions. Asbestos is a good example of a substance that forms one-dimensional giant molecule. The asbestos giant molecule consists of a long chain of atoms; this accounts for the fibrous structure of the mineral. The molecules are set side by side; they are linked together by weak forces of attraction.

The giant molecules of graphite, made up entirely of carbon atoms, are two-dimensional; they are joined together in flat hexagonal plates, which lie parallel to each other. The bonds between layers are weak in comparison with those within the hexagons; hence one layer slips easily over the one beneath it. That is why graphite is one of the best lubricants known.

The diamond is a giant molecule built up in three dimensions. Diamond consists exclusively of carbon atoms. Each atom is bonded to four neighboring atoms, which are grouped about it at equal distances. Since the distances between the atoms in this type of giant molecule are equal, the bonds are of equal strength. The result is a very rigid formation. The diamond is the hardest substance known and it is very difficult to cleave or split it. It has a high melting point; is a good insulator and is transparent.

Crystals Made Up Of Ions

In salts, the unit making up the crystal is an ion, an electrically charged molecule or atom. Each atom has a nucleus or central core made up chiefly of protons, each with a positive electrical charge, and neutrons, which have no charge. Around this central core revolve the electrons, each of which has a negative charge. Normally the charge of an atom is neutral; which means that there will be as many negative charges as there are positive charges. If an atom loses an electron, it has one excess positive charge; it becomes a positive ion. If an atom gains an electron, it has one excess negative charge; it becomes a negative ion. Look at what happens when sodium, normally a metal, and chlorine, normally a gas react to form the solid called sodium chloride, NaCl, which is table salt. Each sodium atom transfers an electron to a chlorine atom. The sodium atom becomes a positive ion since it now has an excess positive charge. Each chlorine atom acquires a single excess negative charge; it is now a negative ion.

Ions with unlike charges attract each other, the chlorine ions will attract the sodium ions; but will hold off the other chlorine ions since ions with like charges repel each other. As a result of the attraction between the oppositely charged particles, each chlorine ion will surround itself with six sodium ions; each sodium ion will surround itself with six chlorine ions.

This pattern will be repeated throughout the crystal. Substances that have the ionic type of lattice have moderate insulating properties and high melting points. They are hard, but they can be split along definite lines.

Crystals Made Up of Electrically Neutral Atoms

In metals, the atom is the structural unit in the formation of a crystal. The atoms may be thought of as spheres having the same diameter and packed together as closely as possible. To illustrate one arrangement, let us imagine that fifteen billiard balls are racked up to form the base, or foundation layer. Six more are set on top of the first layer of balls; then another ball is placed on the second layer. This shows the closest packing possible in a cube. Iron, lead, gold, silver, and aluminum assume this kind of pattern. There are several other arrangements of atoms in metallic crystal lattices. Lattices of this kind are opaque; they have moderate harness; they have high melting points; they are the best conductors of heat and electricity. These qualities make metals very useful.

The Internal Structure Of A Crystal Affects Its Properties

The variations in internal structure shown by different crystals have a direct bearing upon their properties. Different crystals have different lines of cleavage, which are lines along which they split most readily. They conduct heat at different rates. They react differently to magnetic and electrical forces. A few crystals, like those of the mineral Iceland spar, allows only light waves that vibrate in parallel planes to pass through them. This effect is called plane-polarized light. For example, try to pass a knife blade between the pages of a closed book. This will be possible only if the knife blade is held parallel to the pages. The book in this case would correspond to the Iceland spar crystal; the knife would correspond to one of the parallel planes in which the light would vibrate.

If a light is allowed to pass through a selected crystal of quartz, the plane of polarized light is twisted to the plane to the same angle to the left. Crystal of the first type are called right-handed, those of the second type, left handed.

The fact that different crystals will rotate the plane of polarized light in different directions forms a reliable means of identifying certain substances. For example, sugars in solution will rotate the planes of light through different angles; the angle of rotation will identify each sugar in question.

I. Atoms, Elements, and Compounds

The building blocks of all things are the tiny atoms that make up the many elements, which we can see on the periodic table. The minerals we will be studying are made of these elements or combinations of elements called compounds. The basic atom is composed of positively charged protons, negatively charged electrons, and neutrons, which have no electrical charge at all. Protons and neutrons are located in the nucleus of a cell.  There is always the same number of protons as electrons, and therefore the same number of positive charges and negative charges are found in the neutral atom.

A. The Bohr Model

Although our best understanding of the atom tells us that the electrons are in constant and rapid motion around the nucleus and the exact location of any electron cannot be known, we can by experimental means determine the most probable locations of electrons and establish energy levels or shells which we can use to help us understand the relations of atoms. In 1913 a Danish Scientist, Niels Bohr, developed a model that can be used to understand the way atoms combine into compounds. This model is called the Bohr model and shows a central nucleus with the protons and neutrons either drawn in or simply enumerated. Around this central core are the shells or energy levels. These levels are sometimes referred to as the K, L, M, N, O shells or alternatively, the first, second, third, fourth, fifth, energy levels.  Each of these levels has a specific number of electrons it can maximally hold. The degree to which these shells are filled determines how readily it will combine with other elements and in what proportion.

Since the shells fill using definite laws and patterns involving energy, they are predictable. Beyond the element calcium, however, the laws become quite complex and need extensive explanation and understanding of sub shells.

B. Ionic Bonding

By drawing a Bohr model of sodium we can see that its K and L shells are filled and the one remaining electron is by itself in the outer M shell. It will take very little energy to coax that electron away from its atom, leaving only ten electrons with ten negative charges to balance with the eleven protons with their eleven positive charges. When this happens we will have an ion with a +1 charge. In the same way if we draw a shell that has seven electrons, one short of that “magic number” eight. In this case the chlorine atom would be very happy to grab another electron and fill that shell. In doing so the chlorine atom now would have seventeen protons and eighteen electrons, resulting in a net charge on the atom of -1. This would be a negative ion. When two elements come together in this way we refer to it as an ionic bond. The opposing charges on the two ions cause them to be attracted together.

C. Covalent Bonding

Next we will draw out an oxygen atom. In this case we can see that its outer shell has six electrons, two short of the “magic number” eight. And if we draw a hydrogen atom we can see that it has one electron in its outer shell, half of what it needs to fulfill the “magic” two count. From this we could deduce that by bringing in another hydrogen atom we can combine the three atoms into H₂O, and each atom’s outermost shell would be filled. This is the basis for an understanding of covalent bonds, in which atoms come together and share electrons in their outer shells. The electron clouds overlap and the electrons circle both atoms.

 The bonds of compounds can influence some substances’ physical properties. And bonds exist not just between individual atoms but also throughout a crystal. We can look at two forms of the element carbon for an example. Graphite is a slippery black solid; the bonds form sheets of carbon, which slide loosely over one another. Diamond on the other hand is a hard, clear crystal with tight tetrahedral bonding that holds the carbon atoms of diamonds securely in place.

II. Crystals and Crystal Systems

A. Unit Cells

When atoms or molecules are lined up in an orderly arrangement and connected by bonds, and these atoms or molecules have a repeating pattern, we can then say this material is a crystalline substance. The smallest subdivision of a crystal is a unit cell. It is a regular pattern of atoms held together by electrical forces or bonds. These unit cells are far too minute to be seen individual but can be combined together in incredibly large numbers to form visible shapes. As an example of the staggeringly large numbers of unit cells we are talking about we can take as an example sodium chloride, table salt. One typical salt grain has about 5.6x1018 unit cells. (Each salt unit cell is composed of four atoms of sodium and four atoms of chlorine.)¹

B. Crystal Systems

When the unit cells group together they leave no empty spaces between themselves. This results in a limited number of crystal systems that can form. These systems can be grouped as follows:

1.      Isometric or cubic — three edges of equal length and at right angles to one another.

2.      Tetragonal — three edges at right angles but only two edges of equal length.

3.      Orthorhombic — three edges at right angles but all edges of different lengths.

4.      Monoclinic — two edges at right angle, the other angle not; and all edges of different lengths.

5.      Triclinic — all three edges of different lengths and all angles not at right angles.

6.      Hexagonal — two edges are equal and make angles of 60 to 120 degrees with each other. The third edge is at right angles to them and of different length.

C. Anisotrophy

Crystals differ from noncrystalline solids in that many of the physical properties of the crystal are dependent upon the direction they are measured in the crystal.  In noncrystalline or amorphous material the physical properties are generally independent of direction.  (There are exceptions in organic and designer materials.) Since crystals are orderly arrangements of atoms in space it is somewhat intuitive that physical properties will have a relationship to the alignment of the material structure. 

A striking example of anisotropy is the electrical conductivity of quartz, which is about 1000 time greater in one direction than another in the crystal. Except for a few properties such as density, specific heat, melting point, etc. , most properties of crystalline materials are direction dependent. 

D. Growing Crystals

The solute is the substance being dissolved and the solvent is the substance doing the dissolving. A solvent can hold in solution just so much of the solute. At this point we say the solution is saturated. If there is less solute in the solution than it would ideally hold we would then say it is an unsaturated solution. And in some cases such as when we heat the solvent we can continue to add solute and it will dissolve. When the heat source is removed and the solution’s temperature falls the extra solute may remain in solution. This fragile situation is called supersaturation and is the basis for crystal growth.

Solubility, or the amount of solute which can be dissolved in the solvent, is affected by a number of factors, one of which it the temperature of the solvent. Generally speaking we increase solubility of solid solute when we increase the temperature of the solvent. (This is not true of the solubility of gases in a solvent as is witnessed by anyone who has sipped a glass of warm, flat soda

Crystal growth is a very orderly and regulated process. A crystal grows with the atoms of the compound being added according to a very specific pattern. If there is not enough space for the crystal to grow unhindered it will increase only until it meets something, which gets in its way and then stop. Often many small crystals begin forming at the same time, and they grow until their edges meet at varying angles. They do not join to form a single large crystal but rather remain a jumble of small individual crystals forming a polycrystalline mass. The adjoining faces of the crystals are called the grain boundaries. These boundaries are particularly evident in metals, which have formed by fairly rapid cooling of the molten form. During the cooling process innumerable small crystals form and grow until they bump into a neighboring crystal.

Crystals can form from the cooling or evaporation of solutions, or form the cooling of molten solid, or the cooling of vaporized substances.

III. Minerals

A. Definitions

Minerals are natural substances that are inorganic and not the result of any living process, therefore ruling out coal, oil, or pearls. It must also have a specific chemical formula, made up of atoms in a definite ratio. In addition the atoms must have a definite and specific arrangement in space. It is because of these characteristics that minerals have unique properties that can be used to differentiate them form one another.

B. Terms of Identification

Some of a mineral’s properties are easily determined by simple visual examination: crystal shape, color, and luster. But for most minerals the surface color can vary tremendously depending on impurities included in the crystal structure.

Color is usually a definitive way to identify a mineral. Many minerals are made up primarily of elements that impart no strong color of their own and only minute amounts of a coloring agent can have striking results. Some color guidelines are: red may indicate the presence of chromium or hematite, green can indicate chlorite or chromium, and blue can indicate the presence of titanium or titanium and iron. The presence of copper ions can result in shades of green or blue and manganese can result in shades of red.

Hardness of a mineral is shown by its resistance to being scratched. This is related to the crystal structure in that the more tightly bonded the atoms the harder the surface resistance to being etched will be. Diamond is the hardest. In 1812 Friedrich Mohs devised a rough scale of hardness that is invaluable in mineral identification. Diamond at number 10 is the hardest, and talc at number 1 is the softest. The intervals between the numbers are not equal, however, and the difference between corundum at 9 and diamond at 10 is greater than the entire range of 1 to 9!

Mohs Scale of Mineral Hardness

1. Talc

2. Gypsum

3. Calcite

4. Fluorite

5. Apatite

6. Feldspar

7. Quartz

8. Topaz

9. Corundum

10. Diamond

Cleavage is a reflection of the electrical forces acting between the atoms, which result in the crystal breaking along atomic planes that are parallel to crystal faces.

Specific gravity is another means to help identify a mineral.  This measurement can be the most helpful identifying characteristic of all as it is apt to be the most reliable.  The story of Archimedes and his quest for a way to determine the value of the king’s is a good illustration of how specific gravity may be used.

 According to the legend, in about 250 B.C. Archimedes was given the task of determining if a crown belonging to King Hiero was pure gold or only an alloy of gold and silver. It is said that upon easing into his tub the bath water spilled over the edge and it came to him that the volume of water lost was the same as the volume of his body, and he could use the same technique to determine the volume of the crown. Since it was known that gold and silver have different densities, the only thing that would remain would be to take an accurate measure of the weight of the crown and divide this by the volume of the crown. The resulting density figure could be compared with the density of gold, and the truth would be known. It is said that with this revelation, Archimedes leaped from his bath and ran, forgetting the state of his undress, through the streets of Syracuse in Sicily exclaiming, “Eureka! — I have found it!” on his way to the palace! A sad footnote to the story is that the crown was indeed not the pure gold it had been portrayed as, and the unfortunate merchant met an uncomfortable end.

Carried one step further, the concept of specific gravity is based on the physical law that an object immersed in water loses as much weight as an equivalent volume of water would weigh.

Copyright ©  2001 thru 2013  by Theodore Lind