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Game of Thrones Physics
Dr. Jay Maron

Valyrian steel
Dawn sword
Wildfire
The Lightbringer Sword
Ballistas and Trebuchets


Dragons

Dragon     Birth  Death  Size  Riders

Balerion    -126    94   1     Aegon I,  Maegor I,  Viserys I      Died of old age
Meraxes      -90    10    .75  Rhaenys                             Killed by an arrow
Vhagar       -50   131    .8   Visenya,  Leana Velaryon,  Aemond   Died in fight with Caraxes
Cannibal     -50   145    .8   Riderless                           Lived past the Dance of Dragons
Quicksilver    6    42    .25  Aenys I,  Aegon                     Killed by Balerion
Dreamfyre     32   131    .7   Rhaena,  Helaena                    Killed in the dragonpit by a mob
Vermithor     32   131    .6   Jaehaerys I, Hugh Hammer            Died in the Dance of Dragons from fighting Seasmoke
Silverwing    32   145    .6   Alysanne, Ulf the White, Riderless  Fought in the Dance of Dragons and was the only survivor
Sheepstealer  32   145    .6   Nettles                             Lived past the Dance of Dragons
Caraxes       71   131    .6   Daemon                              Died in fight with Vhagar
Meleys        75   130    .6   Rhaenys                             Killed by Sunfyre and Vhagar
Seasmoke      95   131    .4   Leanor, Addam                       Killed by Vermithor in the Dance of Dragons
Syrax         97   131    .5   Rhaenyra                            Killed in the dragonpit by a mob
Sunfyre      107   131    .45  Aegon II                            Died of injuries from dragon fights
Tessarion    115   131    .3   Daeron  Aegon II                    Died in the Dance of Dragons from fighting Seasmoke
Vermax       116   131    .35  Jacaerys                            Killed by an arrow
Grey Ghost   121   131    .3   Riderless                           Killed by Sunfyre
Stormcloud   122   131    .3   Aegon III                           Died naturally
Arrax        115   129    .3   Lucerys Velaryon                    Killed by Vhagar
Tyraxes      118   131    .3   Joffrey                             Killed in the dragonpit by a mob
Moondancer   126   131    .15  Baela                               Killed by Sunfyre
Morghul      124   131    .2   Jaehaera                            Killed in the dragonpit by a mob
Shrykos      124   131    .2   Jaehaerys                           Killed in the dragonpit by a mob
Morning      128   145    .15  Rhaena                              Lived past the Dance of Dragons
Drogon       298          .4   Daenerys                            Alive after "Game of Thrones"
Rhaegal      298   303    .3   Jon Snow                            Killed by an arrow
Viserion     298   302    .3   Night King                          Killed by the Night King. Undead version killed by Arya

Kings of Westeros

          #  Years Start  End  Dragon        Nickname

Aegon     I    37    0   37    Balerion      Conquerer
Aenys     I     5   37   42    Quicksilver
Maegor    I     6   42   48    Balerion      Cruel
Jaehaerys I    55   48  103    Vermithor     Conciliator
Viserys   I    26  103  129    Balerion
Aegon     II    2  129  131    Sunfyre
Rhaenyra  I     0  131  131    Syrax
Aegon     II    0  131  131    Sunfyre
Aegon     III  26  131  157    Stormcloud    Dragonbane      The last dragon died during his reign
Daeron    I     4  157  161                  Young Dragon
Baelor    I    10  161  171                  Beloved
Viserys   II    2  171  173      
Aegon     IV   11  172  184                  Unworthy
Daeron    II   25  184  209                  Good
Aerys     I    12  209  221
Maekar    I    12  221  233
Aegon     V    25  233  258                  Unlikely
Jaehaerys II    3  258  261
Aerys     II   18  262  280                  Mad King
Robert    I    18  280  298
Joffrey   I     3  298  301
Tommen    I     2  301  303
Cersi     I     2  303  305
Daenerys  I     0  305  305   Drogon         Breaker of Chains
Bran      I        305                       Broken

War of Dragons

At the start of the war, Aegon II had 6 dragons and Rhaenyra had 12. After the war, Aegon II had 2 and Rhaenyra had none. Rhaenyra was toasted by Aegon II's dragon Sunfyre.

The war was precipitated by the death of King Viserys I. The Westeros lords were split on the successor, with some favoring Aegon II and some favoring Rhaenyra. Rhaenyra had more dragons and decided to fight for the throne. She managed the war poorly and lost all her dragons.

At the end of the war, Sunfyre died and Silverwing went rogue. At this point, there were 4 dragons left in the world and the Targaryens controlled none of them. They were all rogue.

The war started when Aemond and Vhagar killed Lucerys and Arrax. The killing was unwise, because the likely result is war and the death of dragons. The war weakened the Targaryen house.

Sunfyre killed 3 dragons, a mob killed 4 dragons, and 3 dragons died in the Dance of Dragons.

Westeros is a balance of power between Targaryens, Lords, and the Faith of the Seven. The balance of power disintegrated.

A synergistic relationship is possible between Targaryens and lords. Targaryens have the virtue of dragons, which protect the realm from invasion. Lords have the virtue that they can manage the people. An example of a synergistic balance of power is that lords let the Targaryens have the throne, and that the Targaryens respect the autonomy of lords.

The lords need to be unified to keep the Targaryens in check. A Targaryen king should require the support of lords. Once Aegon II and Rhaenyra started fighting, lords should have demanded that neither be monarch, and the lords should have chosen a different Targaryen.

Faction    Dragon       Rider

Aegon II   Vhagar       Aemond                   Died in fight with Caraxes
Aegon II   Sunfyre      Aegon II                 Died of injuries from dragon fights
Aegon II   Silverwing   Alysanne, Ulf, Riderless Survived the Dance of Dragons
Aegon II   Vermithor    Jaehaerys I, Hugh        Died of injuries from fighting Seasmoke in the Dance of Dragons
Aegon II   Tessarion    Daeron                   Died of injuries from fighting Seasmoke in the Dance of Dragons
Aegon II   Dreamfyre    Helaena                  Killed in the dragonpit by a mob

Rhaenyra   Meleys       Rhaenys                  Killed by Sunfyre and Vhagar
Rhaenyra   Moondancer   Baela                    Killed by Sunfyre
Rhaenyra   Grey Ghost                            Killed by Sunfyre
Rhaenyra   Caraxes      Daemon                   Died in fight with Vhagar
Rhaenyra   Arrax        Lucerys                  Killed by Vhagar
Rhaenyra   Vermax       Jacaerys                 Killed by an arrow
Rhaenyra   Seasmoke     Leanor, Addam            Killed by Vermithor in the Dance of Dragons
Rhaenyra   Syrax        Rhaenyra                 Killed in the dragonpit by a mob
Rhaenyra   Tyraxes      Joffrey                  Killed in the dragonpit by a mob
Rhaenyra   Morghul                               Killed in the dragonpit by a mob
Rhaenyra   Shrykos                               Killed in the dragonpit by a mob
Rhaenyra   Sheepstealer Nettles                  Seceded from Rhaenyra's command

Targaryens


Westeros


World


Valyrian steel

"Ice" is the sword with the red handle

Valyrian steel is a fictional substance from "Game of Thrones" that is stronger, lighter, and harder than steel. The only elements that qualify are beryllium, titanium, and vanadium, none of which were known in Earth history until the 18th century. Valyrian steel could be of these elements, an alloy, or a magical substance. According to George Martin, magic is involved.

The fact that it is less dense than steel means that it can't be a fancy form of steel such as Damascus steel or Wootz steel. Also, fancy steel loses its special properties if melted and hence cannot be reforged, whereas Valyrian steel swords can be reforged.

In Earth history, the first metal discovered since iron was cobalt in 1735. This launched a frenzy to smelt all known minerals and most of the smeltable metals were discovered by 1800. Then the battery and electrochemstry were discovered in 1800 and these were used to obtain the unsmeltable metals, which are lithium, beryllium, magnesium, aluminum, titanium, vanadium, niobium, and Uranium. Almost all of the strong alloys use these metals, and so the Valyrians must have used either electrochemistry or magic to make Valyrian steel.


Candidates for Valyrian steel

The following metals and alloys are both stronger and lighter than steel and could hypothetically be Valyrian steel.

                Yield     Density  Strength/Density
                strength  (g/cm3)   (GJoule/kg)
                (GPascal)
Beryllium            .34     1.85     .186
Aluminum + Be        .41     2.27     .181
LiMgAlScTi          1.97     2.67     .738
Titanium             .22     4.51     .050
Titanium + AlVCrMo  1.20     4.6      .261
Vanadium             .53     6.0      .076
AlCrFeCoNiTi        2.26     6.5      .377
AlCrFeCoNiMo        2.76     7.1      .394
Steel                .25     7.9      .032     Iron plus carbon
Copper               .12     9.0      .013
"Yield strength" is the maximum pressure a material can sustain before deforming. "Strength/Density" is the strength-to-weight ratio. Steel is stronger and lighter than copper.
Lore

Petyr Baelish: Nothing holds an edge like Valyrian steel.

Tyrion Lannister: Valyrian steel blades were scarce and costly, yet thousands remained in the world, perhaps two hundred in the Seven Kingdoms alone.

George Martin: Valyrian steel is a fantasy metal. Which means it has magical characteristics, and magic plays a role in its forging.

George Martin: Valyrian steel was always costly, but it became considerably more so when there was no more Valyria, and the secret of its making were lost.

Ned Stark's stord "Ice" is melted down and reforged into two smaller swords, "Oathkeeper" and "Widow's Wail". This rules out Valyrian steel being Wootz steel because Wootz steel loses its special properties when reforged.

Appearances of Valyrian steel in Game of Thrones:

        Name          Owner

Sword   Longclaw      Jon Snow
Sword   Heartsbane    Samwell Tarly
Dagger                Arya
Sword   Ice           Eddard Stark         Reforged into Oathkeeper and Widow's Wail
Sword   Oathkeeper    Brienne of Tarth
Sword   Widow's Wail  The Crown
Sword   Lady Forlorn  Ser Lyn Corbray
Sword   Nightfall     Ser Harras Harlow
Sword   Red Rain      Lord Dunstan Drumm
Arakh                 Caggo
Armor                 Euron Greyjoy
Horn    Dragonbinder  The Citadel of The Maesters
Some Maesters carry links of Valyrian steel, a symbol of mastery of the highest arts.
The Dawn Sword

Metal meteorite
Dawn
Metal meteorite slice

The Dawn sword was forged from meteorite metal, which has the composition:

          Mass    Yield strength  Density
        fraction     MPascal      gram/cm3

 Iron     .91         200          7.9
 Nickel   .067        480          8.9
 Cobalt   .0063       480          8.9

Nickel and cobalt are 2.5 times stronger than iron, and the alloy of iron, nickel, and cobalt is even stronger. Alloys are usually stronger than their constituent metals.

Dawn is described as being more reflective than steel. The reflectivity of various metals is:

Silver      .98
Aluminum    .97
Copper      .96
Nickel      .93
Steel       .93

Steel and nickel have the same reflectivity. A meteorite sword has the same reflectivity as steel.


Wildire

Copper

The burn rate of gasoline is limited by the supply of oxygen.

C8H18 + 12.5 O2  →  8 CO2 + 9 H2O
Gunpowder has oxygen in the mixture in the form of KNO3 which makes it burn faster.
3 C + S + 2 KNO3  →  K2S + N2 + 3 CO2
We know that wildfire contains an oxidizer otherwise it wouldn't be able to explode as it did on the show. Wildfire is made from manure, which contains KNO3.

Copper burns with a green flame. Adding copper powder to the explosive adds energy to the blast.

Three types of incendiaries are:

Gasoline:          Flame spreads slowly. Needs oxygen from the air.
Gunpowder:         Contains oxygen. Buns faster than gasoline. Subsonic pressure wave.
Plastic explosive: Pressure wave spreads supersonically as a shock.

The Lightbringer Sword

The Lightbringer sword is perpetually hot. This can achieved within the laws of physics by adding a radioactive isotope to the metal.

The composition of the sword is unknown. If it's steel then the maximum temperature is 900 Kelvin and if it's another metal the temperature could potentially be much higher. Steel loses strength as it heats and at 900 Kelvin it has half its room-temperature strength.

Typical parameters for a sword are:

Sword mass                =  M  =  DLWH  =   1.2   kg
Sword length              =  L           =   1.0   meters
Sword width               =  W           =    .05  meters
Sword thickness           =  H           =    .003 meters
Sword density             =  D           =7900     kg/meter2

The sword temperature is determined by a balance between radioactive heating and blackbody radiation. If the sword has a temperature of 900 Kelvin then the heating power/mass is:

Sword blackbody emissivity=  f           =  .07          For steel
Stefan-Boltzmann constant =  C           =5.670⋅10-8  Watts/m2/Kelvin4
Blackbody power/area      =  f C T4  =  2604  Watts/meter2
Sword heat power/mass     =  p           =  220  Watts/kg
Sword heat power/area     = ½ p D H  =  f C T4  =  2604 Watts/meter2
Sword total power         =  P  =  pM  =  264  Watts

Many radioactive isotopes have a sufficiently high power/mass to make such a sword. The isotopes with a half life larger than 10 years and with a power/mass larger than 100 Watts/kg are:

            Power/Mass  Energy/Mass  Halflife  Decay   Decay
             Watts/kg   GJoules/kg    years     MeV    mode

Californium-250   5779     2385      13.1      6.02    α or SF
Plutonium-241     4315     1961      14.4      4.90    α
Curium-244        4014     2293      18.1      5.80    α
Curium-243        2666     2449      29.1      6.169   α
Caesium-137       1736     1654      30.2      2.35    β
Hydrogen-3        1538      598      12.32      .0186  β
Europium-152      1194      509      13.5       .802   EC,β-+,γ
Uranium-232       1035     2251      68.9      5.414   α
Plutonium-238      818     2265      87.7      5.59    α
Strontium-90       648      589      28.8       .55    β
Curium-250         241    63170    8300        5.17    SF or α
Americium-241      161     2197     432        5.49    α

The sword was forged 8000 years ago and there is a question of if it would still be hot. The only isotope capable of powering the sword this long is curium-250, which has a half life of 8300 years. It has a superlatively high power/mass because it's the only isotope that decays primarily by spontaneous fission.

The metal emissivity should be as low as possible to minimize heat loss. You also want to polish the sword to minimize emissivity.

The metals with high melting points are:

                   Melt    Density
                  Kelvin    g/cm3

Tungsten            3695   19.2
Rhenium             3459   21.0
Osmium              3306   22.6
Tantalum            3290   16.7
Molybdenum          2896   10.3
Niobium             2750    8.57
Iridium             2719   22.6
Ruthenium           2607   12.4
Hafnium             2506   13.3
Technetium          2430   11
Boron               2349    2.34
Rhodium             2237   12.4
Vanadium            2183    6.0
Chromium            2180    7.15
Zirconium           2128    6.52
Titanium            1941    4.51
Palladium           1828   12.0
Scandium            1814    2.98
Steel               1811    7.86
Cobalt              1768    8.90
Nickel              1728    8.91
Curium              1613   13.5

The metal with the best combination of high melting point and low density is molybdenum.

The hottest the sword could be is if it's made of tungsten, which at 1700 Kelvin has half its room temperature strength. At 1700 Kelvin it has a power/mass of 1600 Watts/kg. The isotopes with a sufficiently large power/mass are californium-250, promethium-146, plutonium-241, curium-244, and curium-243. The one with the longest half life is curium-243, with a half life of 29 years.


Pre-gunpowder weapons

                   Speed   Mass     Energy
                    m/s     kg      Joules

Bow                  74      .021        57
Compound bow        113      .035       223
Crossbow             75      .040       112
Slingshot            75      .0063       18
Ballista             75     5         14000
Trebuchet            40   100         80000
Cannonball 6 lb     438     2.7      261000
Cannonball 36 lb    450    16.3     1653000

Bow

Typical parameters for a bow and arrow are:

Arrow speed           = 74    meters/second
Arrow mass            = 20.6  g
Arrow kinetic energy  = 57    Joules
Bow energy            = 74    Joules
Energy efficiency     =   .77
Maximum bow force     =200    Newtons
Bow mass              =  6.5  kg
Bow mass / Arrow mass =316
Arrow length          =   .70 meters
Arrow radius          =  3.63 mm
Arrow wall thickness  =   .50 mm
Arrow tip mass        =  6.2  g
Arrow shaft mass      = 11.7  g
Arrow fin mass        =  1.4  g
Arrow nock mass       =  1.2  g
Carbon fiber stiffness= 85    GPascals
Data from the paper "Applications of Physics to Archery", Dr. H. O. Meyer.
Air drag
Arrow mass            = M
Air density           = D               =  1.19 kg/meters2
Arrow cross section   = A
Air drag coefficient  = C               =  1.94
Arrow speed           = V
Air drag force        = F = ½ C D A V2
Arrow acceleration    = W = F/M = c V2
Air drag parameter    = c = ½ C D A M-1 =.00231 meters-1
Arrow initial speed                     = 74    meters/second
Arrow speed at .1 km                    = 66    meters/second

Trebuchet

The Warwick Castle trebuchet is the largest trebuchet in the world.

Trebuchet mass     =  22  tons
Projectile mass    =  15  kg
Projectile range   = 168  meters
Counterweight mass =2000  kg
Trebuchet height   =  19  meters

Compound bow


Range

For a projectile fired at 45 degrees,

Horizontal speed  =  v
Vertical speed    =  v
Total speed       =  V  =  2½ v
Gravity           =  g  =  9.8 meters/second2
Flight time       =  T  =  2 v/g
Range             =  R  =  vT  =  V2/g

Ancient metallurgy

Stone
Copper
Bronze
Iron
Carbon

The earliest metals were gold and silver, the only ones that occur naturally in pure form. Iron can occasionally be found as iron meteorites.

Gold nugget
Silver nugget
Iron meteorite

Copper was discovered around 7000 BCE by smelting copper minerals in a wood fire. Around 3200 BCE it was found that copper is strenghened by tin, and this is called bronze. Around 2000 BCE it was found that copper is also strengthed by zinc, and this is called brass.

The earliest metals were smeltable with a wood fire and they consist of copper, lead, silver, tin, zinc, and mercury. They come from the following minerals:

Gold and silver were known since antiquity, but gold mining didn't start until 6000 BC, and silver smelting didn't start until 4000 BC.

The minerals that were used by ancient civilizations to smelt metal are:

Lead. Galena. PbS
Copper. Chalcocite. Cu2S
Silver. Acanthite. Ag2S
Tin. Cassiterite. SnO2
Zinc. Sphalerite. ZnS
Mercury. Cinnabar. HgS

The next metal to be discovered was iron (c. 1200 BC), which requires a bellows-fed coal fire to smelt.

Iron. Hematite. Fe2O3
Iron. Pyrite. FeS2

No new metals were discovered until cobalt in 1735. Once cobalt was discovered, it was realized that new minerals may have new metals, and the race was on to find new minerals. This yielded nickel, chromium, manganese, molybdenum, and tungsten.

Cobalt. Cobaltite. CoAsS
Nickel. Millerite. NiS
Chromium. Chromite. FeCr2O4
Manganese. Pyrolusite. MnO2
Molybdenum. Molybdenite. MoS2
Tungsten. Wolframite. FeWO4

Chromium is lighter and stronger than steel and it was discovered in 1797. It satisfies the properties of "Valyrian steel" from Game of Thrones. There's no reason chromium couldn't have been discovered earlier.

Coal smelting can't produce the metals lighter than chromium. For these you need electrolysis. The battery was invented in 1799, enabling electrolysis, and the lighter metals were discovered shortly after. These include aluminum, magnesium, titanium, and beryllium.

Aluminum. Bauxite. Al(OH)3 and AlO(OH)
Mangesium. Magnesite. MgCO3
Titanium. Rutile. TiO2
Beryllium. Beryl. Be3Al2(SiO3)6

Carbon fiber eclipses metals. The present age could be called the carbon age. The carbon age became mature in 1987 when Jimmy Connors switched from a wood to a carbon racket.

The plot shows the strength of materials.

Alloys can be much stronger than pure metals.

Wood rivals alloys for strength.


Currency

Gold was the densest element known until the discovery of platinun in 1735. It was useful as an uncounterfeitable currency until the discovery of tungsten in 1783, which has the same density as gold. Today, we could use iridium, platinum, or rhenium as an uncounterfeitable currency.


Modern chemistry and the discovery of elements

Prior to 1800, metals were obtained by smelting minerals, and the known metals were gold, silver, copper, iron, tin, zinc, mercury, cobalt, manganese, chromium, molybdenum, and tungsten. Elements to the left of chromium titanium and scandium cant's be obtained by smelting, and neither can aluminum, magnesium, and beryllium. They require electrolysis, which was enabled by Volta's invention of the battery in 1799.

Prior to 1800, few elements were known in pure form. Electrolyis enabled the isolation of most of the rest of the elements. The periodic table then became obvious and was discovered by Mendeleev 1871. The battery launched modern chemistry, and the battery could potentially have been invented much earlier.

Electrolysis enabled the isolation of sodium and potassium in 1807, and these were used to smelt metals that can't be smelted with carbon.

         Discovery   Method of             Source
          (year)     discovery

Carbon     Ancient   Naturally occuring
Gold       Ancient   Naturally occuring
Silver     Ancient   Naturally occuring
Sulfur     Ancient   Naturally occuring
Lead         -6500   Smelt with carbon     Galena       PbS
Copper       -5000   Smelt with carbon     Chalcocite   Cu2S
Bronze (As)  -4200   Copper + Arsenic      Realgar      As4S4
Tin          -3200   Smelt with carbon     Calamine     ZnCO3
Bronze (Sn)  -3200   Copper + Tin
Brass        -2000   Copper + Zinc         Sphalerite   ZnS
Mercury      -2000   Heat the sulfide      Cinnabar     HgS
Iron         -1200   Smelt with carbon     Hematite     Fe2O3
Arsenic       1250   Heat the sulfide      Orpiment     As2S3
Zinc          1300   Smelt with wool       Calamine     ZnCO3 (smithsonite) & Zn4Si2O7(OH)2·H2O (hemimorphite)
Antimony      1540   Smelt with iron       Stibnite     Sb2S3
Phosphorus    1669   Heat NaPO3 Excrement
Cobalt        1735   Smelt with carbon     Cobaltite    CoAsS
Platinum      1735   Naturally occuring
Nickel        1751   Smelt with carbon     Nickeline    NiAs
Bismuth       1753   Isolated from lead
Hydrogen      1766   Hot iron + steam      Water
Oxygen        1771   Heat HgO
Nitrogen      1772   Isolated from air
Manganese     1774   Smelt with carbon     Pyrolusite   MnO2
Molybdenum    1781   Smelt with carbon     Molybdenite  MoS2
Tungsten      1783   Smelt with carbon     Wolframite   (Fe,Mn)WO4
Chromium      1797   Smelt with carbon     Crocoite     PbCrO4
Palladium     1802   Isolated from Pt
Osmium        1803   Isolated from Pt
Iridium       1803   Isolated from Pt
Rhodium       1804   Isolated from Pt
Sodium        1807   Electrolysis
Potassium     1807   Electrolysis
Magnesium     1808   Electrolysis          Magnesia     MgCO3
Cadmium       1817   Isolated from zinc
Lithium       1821   Electrolysis of LiO2  Petalite     LiAlSi4O10
Zirconium     1824   Smelt with potassium  Zircon       ZrSiO4
Aluminum      1827   Smelt with potassium
Silicon       1823   Smelt with potassium
Beryllium     1828   Smelt with potassium  Beryl        Be3Al2Si6O18
Thorium       1929   Smelt with potassium  Gadolinite   (Ce,La,Nd,Y)2FeBe2Si2O10
Vanadium      1831   Smelt VCl2 with H2    Vanadinite   Pb5(VO4)3Cl
Uranium       1841   Smelt with potassium  Uranite      UO2
Ruthenium     1844   Isolated from Pt
Tantalum      1864   Smelt with hydrogen   Tantalite    [(Fe,Mn)Ta2O6]
Niobium       1864   Smelt with hydrogen   Tantalite    [(Fe,Mn)Ta2O6]
Fluorine      1886   Electrolysis
Helium        1895   From uranium ore
Titanium      1910   Smelt with sodium     Ilmenite     FeTiO3
Hafnium       1924   Isolated from zirconium
Rhenium       1928   Isolated from Pt
Scandium      1937   Electrolysis          Gadolinite   FeTiO3

History of mineralogy

 -384  -322   Aristotle. Wrote "Meteorology"
 -370  -285   Theophrastus. Wrote "De Mineralibus"
         77   Pliny the Elder publishes "Natural History"
  973  1050   Al Biruni. Published "Gems"
       1546   Georgius Agricola publishes "On the Nature of Rocks"
       1556   Georgius Agricola publishes "On Metals"
       1609   de Boodt publishes a catalog of minerals
       1669   Brand: Discovery of phosphorus
       1714   John Woodward publishes "Naturalis historia telluris illustrata & aucta", a mineral catalog
       1735   Brandt: Discovery of cobalt
       1777   Lavoisier: Discovery of sulfur
       1778   Lavoisier: Discovery of oxygen and prediction of silicon
       1783   Lavoisier: Discovery of hydrogen
       1784   T. Olof Bergman publishes "Manuel du mineralogiste, ou sciagraphie du regne mineral",
              and founds analytical chemistry
       1778   Lavoisier: Discovery of oxygen
       1801   Rene Just Huay publishes "Traite de Mineralogie", founding crystallography
       1811   Avogadro publishes "Avogadro's law"
       1860   The Karlsruhe Congress publishes a table of atomic weights
       1869   Mendeleev publishes the periodic table

Appendix

Metals known since antiquity

For a metal, the stiffness is characterized by the "shear strength" and the sword worthiness is characterized by the shear strength over the density (the "strength to weight ratio"). For example for iron,

Shear modulus    =  S         =   82 GJoules/meter3
Density          =  D         = 7900 kg/meter3
Sword worthiness =  Q  = S/D  = 10.4 MJoules/kg

Metals

This plot includes all metals with a strength/density at least as large as lead, plus mercury. Beryllium is beyond the top of the plot.


Wootz steel

-600  Wootz steel developed in India and is renowned as the finest steel in the world.
1700  The technique for making Wootz steel is lost.
1790  Wootz steel begins to be studied by the British Royal Society.
1838  Anosov replicates Wootz steel.
Wootz steel is a mix of two phases: martensite (crystalline iron with .5% carbon), and cementite (iron carbide, Fe, 6.7% carbon).

Iron meteorites

In prehistoric times iron meteorites were the only source of metallic iron. They consist of 90% iron and 10% nickel.


Metal smelting

Prehistoric-style smelter

Most metals are in oxidized form. The only metals that can be found in pure form are gold, silver, copper, platinum, palladium, osmium, and iridium.

Smelting is a process for removing the oxygen to produce pure metal. The ore is heated in a coal furnace and the carbon seizes the oxygen from the metal. For copper,

Cu2O + C  →  2 Cu + CO
At low temperature copper stays in the form of Cu2O and at high temperature it gives the oxygen to carbon and becomes pure copper.

For iron, the oxidation state is reduced in 3 stages until the pure iron is left behind.

3 Fe2O3 + C  →  2 Fe3O4 + CO
Fe3O4   + C  →  3 FeO   + CO
FeO     + C  →    Fe   + CO
Oxidation state  =  Number of electrons each iron atom gives to oxygen

       Oxidation state
CuO          2
Cu2O         1
Cu           0
Fe2O3        3
Fe3O4       8/3
FeO          2
Fe           0

Smelting temperature

The following table gives the temperature required to smelt each element with carbon.

        Smelt  Method  Year  Abundance
         (C)                   (ppm)

Gold        <0   *   Ancient      .0031
Silver      <0   *   Ancient      .08
Platinum    <0   *    1735        .0037
Mercury     <0  heat -2000        .067
Palladium   <0  chem  1802        .0063
Copper      80   C   -5000      68
Sulfur     200   *   Ancient   420
Lead       350   C   -6500      10
Nickel     500   C    1751      90
Cadmium    500   C    1817        .15
Cobalt     525   ?    1735      30
Tin        725   C   -3200       2.2
Iron       750   C   -1000   63000
Phosphorus 750  heat  1669   10000
Tungsten   850   C    1783    1100
Potassium  850   e-   1807   15000
Zinc       975   C    1746      79
Sodium    1000   e-   1807   23000
Chromium  1250   C    1797     140
Niobium   1300   H    1864      17
Manganese 1450   C    1774    1120
Vanadium  1550   ?    1831     190
Silicon   1575   K    1823  270000
Titanium  1650   Na   1910   66000
Magnesium 1875   e-   1808   29000
Lithium   1900   e-   1821      17
Aluminum  2000   K    1827   82000
Uranium   2000   K    1841       1.8
Beryllium 2350   K    1828       1.9

Smelt:      Temperature required to smelt with carbon
Method:     Method used to purify the metal when it was first discovered
            *:  The element occurs in its pure form naturally
            C:  Smelt with carbon
            K:  Smelt with potassium
            Na: Smelt with sodium
            H:  Smelt with hydrogen
            e-: Electrolysis
            heat:  Heat causes the oxide to decompose into pure metal. No carbon required.
            chem:  Chemical separation
Discovery:  Year the element was first obtained in pure form
Abundance:  Abundance in the Earth's crust in parts per million
Elements with a low carbon smelting temperature were discovered in ancient times unless the element was rare. Cobalt was discovered in 1735, the first new metal since antiquity, and this inspired scientists to smelt every known mineral in the hope that it would yield a new metal. By 1800 all the rare elements that were carbon smeltable were discovered.

The farther to the right on the periodic table, the lower the smelting temperature, a consequence of "electronegativity".

The battery was invented in 1800, launching the field of electrochemistry and enabling the the isolation of non-carbon-smeltable elements. Davy used electrolysis in 1807 to isolate sodium and potassium and then he used these metals to smelt other metals. To smelt beryllium with potassium, BeO + 2 K ↔ Be + K2O.

Titanium can't be carbon smelted because it forms the carbide Ti3C.

Data

For an expanded discussion of smelting physics, see jaymaron.com/metallurgy.html.


Thermite

Thermite is smelting with aluminum. For example, to smelt iron with aluminum,

Fe2O3 + 2 Al  →  2 Fe + Al2O3

Smelting reactions

The following table shows reactions that change the oxidation state of a metal. "M" stands for an arbitrary metal and the magnitudes are scaled to one mole of O2. The last two columns give the oxidation state of the metal on the left and right side of the reaction. An oxidation state of "0" is the pure metal and "M2O" has an oxidation state of "1".

                            Oxidation state   Oxidation state
                                at left          at right
 2  M2O   ↔  4  M     + O2        1                0
 4  MO    ↔  2  M2O   + O2        2                1
 2  M3O4  ↔  6  MO    + O2       8/3               2
 6  M2O3  ↔  4  M3O4  + O2        3               8/3
 2  M2O3  ↔  4  MO    + O2        3                2
 2  MO    ↔  2  M     + O2        2                0
2/3 M2O3  ↔ 4/3 M     + O2        3                0
 1  MO2   ↔  1  M     + O2        4                0
 2  MO2   ↔  2  MO    + O2        4                2

Minerals

These elements are not necessarily on the Science Olympiad list.

We list minerals by element, with the most abundant mineral for each element listed first.

Lithium

Spodumene: LiAl(SiO3)2
Stilbite: LiAlSi2O6
Tourmaline: (Ca,Na,K,)(Li,Mg,Fe+2,Fe+3,Mn+2,Al,Cr+3,V+3)3(Mg,Al,Fe+3,V+3,Cr+3)6((Si,Al,B)6O18)(BO3)3(OH,O)3(OH,F,O)

Beryllium

Beryl: Be3Al2(SiO3)6
Morganite: Be3Al2(SiO3)6
Emerald

Carbon

Diamond: C

Sodium

Halite: NaCl

Magnesium

Periclase: MgO
Magnesite: MgCO3
Dolomite: CaMg(CO3)2
Peridot: (Mg,Fe)2SiO4
Spinel: MgAl2O4
Spinel: MgAl2O4

Aluminum

Bauxite: Al(OH)3 and AlO(OH)
Alumstone: KAl3(SO4)2(OH)6
Muscovite mica: KAl2(AlSi3O10)(F,OH)2 or KF2(Al2O3)3(SiO2)6(H2O)
Corundum: Al2O3
Topaz: Al2SiO4(F,OH)2

Epidote: Ca2(Al2,Fe)(SiO4)(Si2O7)O(OH)
Jadeite: NaAlSi2O6
Albite: NaAlSi3O8
Amazonite: KAlSi3O8
Labradorite: (Na,Ca)(Al,Si)4O8

Silicon

Amethyst: SiO2
Quartz: SiO2
Citrine: SiO2
Opal: SiO2·nH2O
Agate: SiO2

Sulfur

Volcanic sulfur

Calcium

Fluorite: CaF2
Calcite: CaCO3
Satin Spar: CaSO4 · 2H2O
Selenite: CaSO4 · 2H2O
Aragonite: CaCO3
Pearl: CaCO3
Calcite: CaCO3

Titanium, vanadium, chomium, and manganese

Rutile: TiO2
Vanadinite: Pb5(VO4)3Cl
Chromite: FeCr2O4
Pyrolusite: MnO2
Rhodonite: MnSiO3
Rhodochrosite: MnCO3

Iron

Hematite: Fe2O3
Hematite: Fe2O3
Pyrite: FeS2
Iron meteorite
Goethite: FeO(OH)

Cobalt and nickel

Cobaltite: CoAsS
Millerite: NiS

Copper

Chalcocite: Cu2S
Chalcopyrite: CuFeS2
Malachite: Cu2CO3(OH)l2
Azurite: Cu3(CO3)2(OH)2
Bornite: Cu5FeS4
Turquoise: CuAl6(PO4)4(OH)8•4(H2O)

Zinc and germanium

Sphalerite: ZnS
Germanite: Cu26Fe4Ge4S32

Strontium, zirconium, molybdenum

Celestine: SrSO4
Strontianite: SrCO3
Zircon: ZrSiO4
Molybdenite: MoS2

Silver

Argentite: Ag2S
Acanthite: Ag2S
Silver nugget

Tin

Cassiterite: SnO2

Caesium, barium, rare-earths

Pollucite: (Cs,Na)2Al2Si4O12·2H2O
Barite: BaSO4
Monazite: (Ce,La,Nd,Th)PO4

Tungsten

Wolframite: FeWO4
Scheelite: WCaO4
Hubnerite: WMnO4

Platinum, gold, mercury, lead

Sperrylite: PtAs2
Platinum nugget
Gold nugget
Cinnabar: HgS
Galena: PbS
Anglesite: PbSO4
Thorite: (Th,U)SiO4


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