chemical paper topic of your choice, something in the Lectures in each module that you found interesting.

CHE 102: LECTURE 4 From Frog Legs to Crystals to Snowflakes

The mineral Amethyst is a  violet  variety of  quartz , silicon dioxide (SiO2). The name comes from the Greek word  ἀμέθυστος  (amethystos) from ἀ- a-, "not" and μεθύσκω (methysko) / μεθύω (methyo), "intoxicate", a reference to the belief that the stone protected its owner from  drunkenness . The  ancient Greeks  wore amethyst and carved  drinking  vessels from it in the belief that it would prevent intoxication.

In 1791, Luigi Galvani, an Italian physicist, discovered something he named, "animal electricity" which resulted when two different metals were connected in series with a frog's leg and to one another. His contemporary, Alessandro Volta, realized that the frog's leg served both as a conductor of electricity and as a detector of electricity, but believed that the frog's legs were irrelevant to the electric current. He hypothesized that the electric current was caused by the two differing metals. Volta replaced the frog's leg with brine-soaked paper, and detected the flow of electricity. In 1800, Volta invented the voltaic pile, an early electric battery, which produced a steady electric current. Volta determined after investigating pairs of dissimilar metals that the most effective pair was zinc (Zn) and copper (Cu). Initially he experimented with individual cells in series, each cell being a wine goblet filled with brine (salt water) into which the two dissimilar metals were dipped. The voltaic pile replaced the goblets with cardboard soaked in brine. In chemistry and manufacturing, electrolysis is a technique that uses a direct current from a battery to drive an otherwise non-spontaneous chemical reaction. The English chemist, Humphrey Davy, was the first to realize that electrolysis could be used to separate elements from naturally occurring sources such as minerals and ores. In 1807, he isolated for the first time sodium from table salt (NaCl), and later discovered the elements potassium (K), calcium (Ca), strontium (Sr), barium (Ba), magnesium (Mg), and boron (B) as well as discovering the elemental nature of the nonmetals, chlorine (Cl) and iodine (I). Davy also studied the forces involved in these separations, launching the new field of electrochemistry.

At this point in the saga Michael Faraday enters the stage. Although Faraday received little formal education, he became one of the most influential scientists in history. At the age of 14 he became an apprentice to a local bookbinder and bookseller in London.  During his seven-year apprenticeship Faraday read books, many books, and developed an interest in science, especially electricity. In 1812, at the age of 20 and at the end of his apprenticeship, Faraday attended lectures by the eminent English chemist Humphrey Davy.  Faraday subsequently sent Davy a 300-page book based on notes that he had taken during these lectures. Davy's reply was immediate, kind, and favorable. In 1813, when Davy damaged his eyesight in an accident with nitrogen trichloride (NCl3)

he decided to take on Faraday as his assistant. Faraday subsequently began his own program of research and it was his discovery of the magnetic field around a conductor (a wire) carrying a direct electric current that established the basis for the concept of the electromagnetic field in physics. Faraday also established that magnetism could affect rays of light, that there here was an underlying relationship between the two phenomena. He subsequently discovered the principles of electromagnetic induction and diamagnetism, and the laws of electrolysis. His invention of electromagnetic rotary devices laid the experimental foundation for the electric motor, and it was largely due to his efforts that electricity became practical for use in technology.

As a chemist, Faraday discovered benzene (C6H6),

Geometry Ball and stick model
Space-filling model

invented an early form of the Bunsen burner, and introduced terminology such as electrode (an electrical conductor used to make contact with a nonmetallic part of a circuit), anode (the positively charged electrode), cathode (the negatively charged electrode) and ion (an atom or molecule with a net electric charge due to the loss or gain of one or more electrons).

Faraday believed ions were produced in electrolysis (else how could a battery “work” ?). In 1884, the Swedish chemist, Svante Arrhenius, proposed that, even in the absence of an electric current, solutions of salts contained ions. That is, he proposed that solid crystalline solids, when dissolved in water, dissociated into pairs of charged particles (ions), and that chemical reactions in solution involved reactions between ions. Electrolyte solutions are formed when a salt is placed into a solvent such as water and the individual components dissociate due to the interactions between solvent and solute molecules in a process called solvation. For example, when table salt (sodium chloride) is placed in water, the salt (a solid) dissolves into its component ions, according to the dissociation reaction

NaCl(s) → Na+(aq) + Cl−(aq)

Importantly, prior to being dissolved in water, Arrhenius’ thesis was that the crystal NaCl (a solid) is composed of sodium ions (Na+ not neutral sodium atoms) and chlorine ions (Cl- not neutral chlorine atoms). Recall the graphic from Lecture 1 displaying sodium chloride at the atomic level: Here, the purple balls are sodium ions (Na+) and the green balls are chlorine ions (Cl-). At the macroscopic level, sodium chloride (table salt) forms transparent crystals. Depending on the presence of a small number of other atoms (impurities) the mineral halite can also occur in several other colors.

In Chemistry, the bonding in the NaCl crystal, called ionic bonding, is the complete transfer of a charge (the electron) from sodium to chlorine. Hence, neutral Na becomes Na+ and neutral Cl becomes Cl-. Hence, it is a type of chemical bond that involves two oppositely charged ions. The metal loses electrons to become a positively charged cation, whereas the nonmetal accepts those electrons to become a negatively charged anion. [NOTE: The negatively charged electrode is called the cathode; a positively charged ion is called a cation. Perhaps confusing, but the logic here is that a positive ion (anion) migrates to the negative electrode (cathode) in solution.] The bonding in a crystal like diamond is different and is called covalent bonding. A covalent bond, also called a molecular bond, is a chemical bond that involves the sharing of two electrons between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they share electrons, is known as covalent bonding. In a later module of the course we will review the discovery of the electron, the proton and the neutron, the basic components of an atom. To understand atomic and molecular structure we will find that the classical ideas of Physics, reviewed in the previous Lecture, need to be replaced by a non-classical theory, called quantum mechanics. And to understand nuclear chemistry, the basis for modern medicinal chemistry, we will need to review the properties of light, and the basic ideas of special relativity. By the end of the course, my hope is that you will have a holistic understanding of modern science.

But now, to the problem at hand ….. A crystal structure is an ordered arrangement of atoms, molecules or ions. Ordered structures are a consequence of the intrinsic nature of the constituent particles which form symmetric patterns that repeat along the principal axes (directions) of three-dimensional space.

The smallest group of particles in a material that constitutes this repeating pattern is called the unit cell of the structure. The unit cell captures the symmetry and structure of the entire crystal, which is built up by repetitive translation of the unit cell along its principal axes. Mathematically, translation vectors define the nodes of a lattice, called the Bravais lattice. 

The lengths of the principal axes, or edges, of the unit cell and the angles between them are lattice constants,  also called lattice parameters or cell parameters. The symmetry properties of the crystal are described by the concept of space groups. All possible symmetric arrangements of atoms or molecules in three-dimensional space may be described by 230 space groups.  Every crystal found in Nature belongs to one of these space groups. Crystal structure and symmetry play a critical role in determining many physical properties, such as cleavage and optical transparency. In a crystal, atoms are arranged in straight rows in a three-dimensional periodic pattern. As noted above, the small part of the crystal that can be repeated to form the entire crystal is called a unit cell.

Asymmetric unit	Primitive unit cell	Conventional unit cell	Crystal   Some common crystal structures are shown below.
Simple Cubic	Face Centered Cubic	Body Centered Cubic	Hexagonal Close Packed	Diamond
NaCl	CsCl	Zincblende	Wurzite	Perovskite

Here, Zincblende is one form of zinc sulfide (β-ZnS), Wurzite is another version of ZnS, and Perovskite is a calcium titanium oxide mineral composed of calcium titanate (CaTiO3). Closely related to Zincblende is Sphalerite [ (Zn,Fe)S ], a mineral that is the chief ore of zinc (Zn).  Following are crystals of Sphalerite and Perovskite:

Crystals can be grown under moderate conditions from all 92 naturally occurring elements except helium, and helium can be crystallized at low temperatures by using 25 atmospheres of pressure.  Binary crystals are composed of two elements. There are thousands of binary crystals; some examples are sodium chloride (NaCl), alumina (Al2O3) and ice  (H2O) which, at the macroscopic level, is a crystal familiar to us in Winter in Chicago: Crystals can also be formed with three or more elements.

By repeating the pattern of the unit cell over and over in all directions, an entire crystal lattice can be constructed. A cube is the simplest example of a unit cell. Two other examples are shown in the figure below. The first is the unit cell for a face-centered cubic lattice, and the second is for a body-centered cubic lattice. There are only a few different unit-cell shapes, so many different crystals share a single unit-cell type. An important characteristic of a unit cell is the number of atoms it contains. The total number of atoms in the entire crystal is the number in each cell multiplied by the number of unit cells. Copper (Cu) and aluminum (Al) each have one atom per unit cell, while zinc (Zn) and sodium chloride have two. Most crystals have only a few atoms per unit cell, but there are some exceptions. Crystals of polymers and, especially, proteins, have thousands of atoms in each unit cell. I am presently completing a study of the structural stability of the coronavirus 6LU7, a protein with 2367 atoms in the unit cell, not counting the hydrogens.

Structures of metals

The elements are found in a variety of crystal packing arrangements. The most common lattice structures for metals are those obtained by stacking the atomic spheres into the most compact arrangement. There are two such possible periodic arrangements. In each, the first layer has the atoms packed into a plane-triangular lattice in which every atom has six immediate neighbors. The figure below shows this arrangement for the atoms labeled A. The second layer is shaded in the figure. It has the same plane-triangular structure; the atoms sit in the holes formed by the first layer. The first layer has two equivalent sets of holes, but the atoms of the second layer can occupy only one set. The third layer, labeled C, has the same structure, but there are two choices for selecting the holes that the atoms will occupy. The third layer can be placed over the atoms of the first layer, generating an alternate layer sequence ABABAB . . ., which is called the hexagonal close-packed structure. Cadmium (Cd) and Zinc (Zn) crystallize with this structure. The second possibility is to place the atoms of the third layer over those of neither of the first two but instead over the set of holes in the first layer that remains unoccupied. The fourth layer is placed over the first, and so there is a three-layer repetition ABCABCABC . . ., which is called the face-centered cubic (fcc), or cubic-closest-packed, lattice. Copper, (Cu), Silver (Ag), and Gold (Au) crystallize in fcc lattices. In the hcp and the fcc structures the spheres fill 74 percent of the volume, which represents the closest possible packing of spheres. Each atom has 12 neighbors. The number of atoms in a unit cell is two for hcp structures and one for fcc. There are 32 metals that have the hcp lattice and 26 with the fcc. Another possible arrangement is the body-centered cubic (bcc) lattice, in which each atom has eight neighbors arranged at the corners of a cube.  The cesium chloride (CsCl) structure is a cubic arrangement. If all atoms in this structure are of the same species, it is a bcc lattice. The spheres occupy 68 percent of the volume. There are 23 metals with the bcc arrangement. The sum of these three numbers (32 + 26 + 23) exceeds the number of elements that form metals (63), since some elements are found in two or three of these structures.

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The fcc structure is also found for crystals of the rare gas solids: neon (Ne), argon (Ar), krypton (Kr), and xenon (Xe).

Structures of nonmetallic elements

The elements in the fourth row of the periodic table—Carbon (C), Silicon (Si), Germanium (Ge), and α-tin (α-Sn)—prefer covalent bonding. Carbon has several possible crystal structures. Each atom in the covalent bond has four first-neighbors, which are at the corners of a tetrahedron. This arrangement is called the diamond lattice. See Lecture 2. There are two atoms in a unit cell, which is fcc. Crystals of diamond are valuable (and expensive) gemstones, as every engaged couple knows. The diamond crystal has other interesting properties; it has the highest sound velocity of any solid and is the best conductor of heat. Besides diamond, the other common form of carbon is graphite, which is a layered material. Each carbon atom has three coplanar near neighbors, forming an arrangement called the honeycomb lattice. Three-dimensional graphite crystals are obtained by stacking similar layers. See Lecture 2. Another form of crystalline carbon is based on a molecule with 60 carbon atoms called buckminsterfullerene (C60). The molecular shape is spherical. Each carbon is bonded to three neighbors, as in graphite, and the spherical shape is achieved by a mixture of 12 rings with five sides and 20 rings with six sides. Similar structures were first visualized by the American architect R. Buckminster Fuller for geodesic domes. The C60 molecules, also called buckyballs, are quite strong and almost incompressible. Crystals are formed such that the balls are arranged in an fcc lattice with a one-nanometer (10 -9 meters) spacing between the centers of adjacent balls. The similar C70 molecule has the shape of a soccer ball; C70 molecules also form an fcc crystal when stacked together. The solid fullerenes form molecular crystals, with weak binding between the molecules. The most recent form of Carbon to be discovered is called graphene. It is “just” one sheet

of graphite or, in the analogy I suggested in a previous Lecture, one sheet of “chicken wire.”

The diatomic gases hydrogen (H), oxygen (O), nitrogen (N), fluorine (F), chlorine (Cl), bromine (Br), and iodine (I) , when cooled to low temperature, form solids of diatomic molecules. Nitrogen has the hcp structure, while oxygen has a more complex structure.

The most interesting crystal structures are those of elements that are neither metallic, covalent, nor diatomic. Although boron (B) and sulfur (S) have several different crystal structures, each has one arrangement in which it is usually found. Twelve boron atoms form a molecule in the shape of an icosahedron. Crystals are formed by stacking the molecules. The β-rhombohedral structure of boron has seven of these icosahedral molecules in each unit cell, giving a total of 84 atoms. Molecules of sulfur are usually arranged in rings; the most common ring has eight atoms. The typical structure is α-sulfur, which has 16 molecules per unit cell, or 128 atoms. In the common crystals of Selenium (Se) and Tellurium (Te), the atoms are arranged in helical chains, which stack like cordwood. However, selenium also makes eight-atom rings, similar to sulfur, and forms crystals from them. Sulfur also makes helical chains, similar to selenium, and stacks them together into crystals.

Finally, just for fun, shown below are crystals of Ruby and Emerald.

Natural ruby crystals from Winza, Tanzania
General
Category	Oxide mineral variety
Formula (repeating unit)	aluminium oxide with chromium, Al2O3:Cr
Crystal system	Trigonal
Crystal class	Hexagonal scalenohedral (3m) H-M symbol: (3 2/m)
Space group	R3c[1]

Emerald crystal from Muzo, Colombia
General
Category	Beryl variety
Formula (repeating unit)	Be3Al2(SiO3)6
Crystal system	Hexagonal (6/m 2/m 2/m) Space group: P6/mсc
Space group	(6/m 2/m 2/m) – dihexagonal dipyramidal
Unit cell	a = 9.21 Å, c = 9.19 Å; Z =

Even better, after extraction from the supporting ore,