PbS(s) + O2(g) → PbO(s) + SO2(g)
Most metals in the solid state behave as if the atoms were small spheres. When placed together in a solid, they adopt an arrangement in which the amount of empty space between the spheres is minimized. This is known as close-packing. If you place a number of marbles of the same size in a box and shake them around, they will ultimately adopt this arrangement, except perhaps around the edges. A second close-packed layer will fit nicely on the first, with the spheres fitting into the depressions between the spheres - every where ther is a triangle of three atoms, there will be a slight depression in the layer as seen in the figure. When a third layer is added, however, there is now a choice in how the next layer can be added. One possibility is that the third layer lines up exactly with the first layer. This type of packing, which has the layers A and B alternating, is known as hexagonal close-packing because the unit cell of that arrangement adopts a hexagonal unit cell. On the other hand, the third layer could be offset from the first layer in which case the arrangment is an A-B-C stacking. This gives rise to cubic close-packing because the unit cell for this lattice is face-centered cubic. These stacking arrangements are the most efficient with 74% of the space in the unit cell taken up by the spherical atoms. A good exercise is to calculate this yourself using standard geometry.
The existence of the metallic elements in nature relies on how easily oxidized the metal is. Most metals are so readily oxidized that they are always found in oxidized form as a mineral. This can be readily understood by looking at the electrochemical potentials. Normally these are given as reduction numbers and the more positive the number, the more easily the substance is to be reduced. Conversely, the more positive the reduction potential, the harder it is to oxidize the element.
The ability to resist oxidation means that some metals can be found in nature as the elements, while others had to await discovery until the chemistry was developed sufficiently to allow their isolation. Aluminum is one of the most easily oxidized of the metals and it was not isolated as the pure element until 1825 and cost-effective commercial production did not happen for several decades after that. It is hard to image now, but aluminum was more expensive than gold until late in the second half of the 19th century. On the other hand, gold, silver, copper, mercury and the platinum metals (platinum, ruthenium, rhodium, palladium, osmium and iridium) can be found in nature as the metals. The platinum metals were first used by the pre-Columbian Americans and were first introduced to the Spanish in 1555. Because of their inertness to corrosion, ruthenium, rhodium, palladium, osmium, iridium, platinum, silver and gold are also known as the noble metals. Gold, silver and copper are also collectively termed the coinage metals for obvious reasons. As these metals have become more expensive, their use as coins has decreased and coins of gold and silver are almost exclusively considered collectors' items. Even the use of copper in coinage has come under scrutiny. Since 1982, copper pennies have had a zinc core to make them more cost effective, but even with the inclusion of copper the worth of a U.S. penny is less than the cost of making it.
Metals are a class of the chemical elements that exhibit the properties of ductility, malleability, luster and electrical conductivity. In the periodic table, the metals lie to the left, and most elements are metals. Metals have a range of physical and chemical properties. Some are much better electrical conductors than others, some melt at low temperatures while others have very high melting points ( Selected Metal Melting Points ), and some are much more easily oxidized than others. The oxidation of copper by nitric acid has become a classical chemical demonstration with interesting color changes that fun to watch. A video version is available on Youtube thanks to the Royal Society of Chemistry.
While hexagonal and cubic close packing are the most efficient ways of stacking small spheres, they are not the only tupes of lattices found for metals. Some metals will adopt a body-centered lattice, while others will assume a simple cubic lattice. The packing efficiency of a body centered lattice is 68%, while that of a simple cubic unit cell is only about 52%.
Alloys are a combination of two or more elements in a random fashion. Alloys differ from compounds in that they do not have a fixed ratio of elements, rather they exist over a range of compositions. Like metals, the hardness, ductility, maleability and melting points of alloys have a wide range and vary with the amounts of the component elements present. Many of the early alloys were discovered by accident in the process of smelting metals that employed ores contaminated with other elements, but even in the early stages pf the development of metallurgy, the observations of different properties of the alloys based on these impurities were exploited. There are two fundamental types of alloys - substitutional and interstitial.
Substitutional Alloys
Substitutional alloys contain different metals randomly distributed throughout the structure, and substitutional alloys are found in nature. Electrum, a naturally-occurring alloy of gold and silver has been known since antiquity. The crystal structure of the alloy if only a small amount of a metal is substituted is usually based on the crystal lattice of the major metal present, although the dimensions of the lattice may vary slightly because of the different sizes of the substituted elements.
Jewelers use the karat (K) scale to describe the purity of gold, with 24K being the value of the pure element. White gold is the name given today for alloys of gold with a "white" metal such as silver, nickel or palladium. Yellow gold often contains copper as well as silver, while rose, pink or red gold is a gold-copper alloy with the darker pinks and red gold having a higher percentage of copper. Some samples of electrum are yellow-green in color, and a green color can also be created by addition of cadmium, but this element is toxic and creates health concerns for wearing Cd-containing gold as jewelry. Purple gold and blue gold are encountered far less often and are gold-aluminum (purple) or gold-gallium or -indium (blue) alloys. The ternary phase diagram for Cu-Ag-Au illustrates the variations in color with relative amounts of each element. For an explanation of how to read a ternary phase diagram, check out Ternary Phase Diagram Basics on Youtube. Similarly, the platinum group elements are largely found deposited together in their mineral forms as alloys.
Meteorites, which are one of the few sources of elemental iron found in nature, are most often composed primarily of iron but contain alloy phases with other metals such as nickel or p-block elements such as phosphorus.
Bronze: One of the oldest known substitutional alloys is bronze, which is an alloy of copper and tin. It is likely that the first bronze made was obtained from the smelting of copper that was contaminated with tin-containing minerals. Bronze is signicantly harder than copper, and was therefore useful for making tools and weapons. Tin in the metallic state is rare, but it was first smelted around 1750 BC from the the ore cassiterite, SnO2. It is not clear where the first tin was mined, but deposits from what is now Germany and the Czech Republic are among the oldest sources known. Later deposits were found in Brittany (France) and Devon and Cornwall in UK. Bronze contains around ~12% tin in addition to small amounts of other metals such as Al, Mn, Ni or Zn and sometimes non-metals such as As, P, Si. The Bronze Age lasted roughly from the mid-4th millenium BC through ~1300 BC, when the iron become the dominant metal for tools and weapons.
Brass: Brass is a substitutional alloy based on copper, but instead of tin, zinc is incorporated into the lattice. Brass has also been known since ancient times, but its use was increased in Roman times with the intential production of brass using copper and cadmia, an ore of zinc oxide. As with bronze, other elements may also be present including As, Pb, P, Al, Mn and/or Si. Brass is more malleable than bronze and has a lower melting point.
Interstitial Alloys
The other major classification of alloys are interstitial alloys. These are alloys that are made by placing small amounts of smaller atoms in the empty spaces between the atoms of the host metal. The most well-known interstitial alloy is steel, which is iron with small amounts of carbon located between the iron atoms. Iron at ambient temperatures adopts the body-centered cubic structure known as ferrite. The lattice rearranges to a face-centered cubic lattice (austenite), which can accommodate more carbon. In these structures, the carbon sits in an octahedral site between the iron atoms. Ultimately cementite, Fe3C, is obtained. Modern steels are more complex, and the structure may contain a mixture of ferrite, austenite and cemntite at the microscopic level. Steel is often both an interstitial and substitution alloy. Other metals may replace iron, including, manganese, chromium, etc. These complex compositions are tuned to produce alloys with the desired hardness, corrosion-resistance, etc. In the structures of these materials, the substitutional and interstitial atoms often adopt random locations. This means that only a few of their lattice sites in the crystal lattice may be occupied. For example, in the structure of Fe4C0.63 shown below, the average occupancy of C atoms at any of those locations is either 0.06 for some sites and 0.19 for the others.
The Iron Pillar of Dehli in the Qutb complex near Delhi, India. Photo by Mark A. Wilson, Department of Geology, College of Wooster, Public Domain via Wikipedia.
An interesting column made of iron is the Iron Pillar of Dehli, which was produced during the reign of King Chandragupta II at the end of the fourth or beginning of the fifth century CE. The pillar is notable because of its high corrosion resistance in spite of its age. The iron was found to have a high content of phosphorus which forms a protective iron phosphate coating to the statue that prevents further deterioration.
Controlling the Composition of Metals and Alloys
Alloys, both substitutional and interstitial, can have substantially different properties from the metals of which they are made. This is illustrated in the melting points tabulated below. Identifying pure metals and alloys has been of prime commercial importance for thousands of years. The iconic example is the legend of Archimedes determining that the crown of King Hiero of Syracuse was not pure gold by a water displacement test. Silver has a lower density than gold, so a crown of pure gold would displace less water than a silver-gold alloy. Density measurements are an easy way to get a rough idea of identity of a metal. One simply needs to measure the mass and the volume of the metal object, usually by water displacement as in the case of Archimedes, and calculate the density. A table of selected densities is found below.
Whether this tale is true in all of its details is not so important as the fact that it illustrates why the study of the properties of alloys compared to pure metals has been studied for thousands of years. In fact, metallurgy starting with the smelting and refining of metals and the production of alloys has been a strong driver of the study of chemistry since ancient times. Not only are the properties of these materials crucial to their use but the costs associated with making them are also important.
Densities, Selected Metals Metal/Alloy density, g·cm-3 Copper 8.96 Chromium 7.15 Gold 19.3 Iron 7.87 Nickel 8.90 Platinum 21.5 Silver 10.5 Tin 7.26 Tungsten 19.3 Zinc 7.14
Melting Points, Selected Metals Metal Melting Point, °C Aluminum 660 Copper 1084 Gold 1063 Iron 1536 Lead 327.5 Manganese 1244 Nickel 1453 Silver 961 Tin 232 Zinc 419.5
Densities, Selected Alloys Alloy Density, g·cm-3 Admiralty Brass 8.5 Cupronickel 8.9 Monel 8.37-8.82 Cast Iron 6.85-7.75 Carbon Steel 7.85 Stainless Steel 7.48-7.95 Yellow Brass 8.47 Red Brass 8.75 Manganese Bronze 8.37 Aluminum Bronze 7.8-8.6
Melting Points, Selected Alloys Alloy Melting Point, °C Admiralty Brass 900-940 Cupronickel 1179-1240 Monel 1300-1350 Cast Iron 1175-1290 Carbon Steel 1425-1540 Stainless Steel 1510 Yellow Brass 905-932 Red Brass 990-1025 Manganese Bronze 865-890 Aluminum Bronze 600-655