Allotropes & Polymorphs

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© 1998-2008 by Glenn Elert -- A Work in Progress
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Discussion

introduction

An element that can exist in two or more forms is said to be allotropic, the different forms are called allotropes, and the existence of these other forms as a phenomena called allotropy. Allotropes exist when there is more than one way for the atoms of a particular element to combine with each other to form molecules or a crystalline array.

Likewise, there are often several ways to arrange the particles of a substance in the solid phase. Such substances are said to be polymorphic or polymorphous, the variations are called polymorphs, and the existence of these other forms as a phenomena is called polymorphy or polymorphism. Polymorphs exist when there is more than one way for the particles of a particular substance to arrange themselves into a crystalline array.

Allotropy vs. Polymorphy
  particles involved are … particles combine to form …
allotropy atoms of an element molecules or crystals
polymorphy atoms or molecules crystals

Allotropes of an element and polymorphs of a substance differ in their chemical and physical properties. These differences can be subtle (like the polymorphy of cocoa butter in chocolate bars) or extreme (like the differences between graphite and diamond). The rest of this section will be taken up with a discussion of examples of allotropy and polymorphism.

carbon

This discussion is so common, what can I say that hasn't been already said?

Primary Allotropes of Carbon (The Elementary Version)
diamond graphite
the hardest substance known
(10 on the mohs scale)
used as an abrasive		 among the softest substances
(0.5 on the mohs scale)
used as a lubricant
usually transparent
colorless to red or blue
used in jewelry		 always opaque
black (somewhat metallic)
used in pencils (thus the name)
a good electrical insulator
~TΩ·m resistivity		 a good electrical conductor
650 nΩ·m resistivity
high thermal conductivity
(higher than any metal)
895 W/m·K		 dual thermal conductivity
1950 W/m·K parallel to plane layers
5.7 W/m·K perpendicular to layers

Other Stuff

Junk I've come across

Primary Allotropes of Carbon (The Advanced Version)
property diamond (I) graphite
hardness 1010 kg/m2  
hardness, mohs 10 0.5
hardness, knoop   7000
strength, tensile > 1.2 GPa  
strength, compressive > 110 GPa  
speed of sound 18,000 m/s  
density 3510 kg/m3 2250 kg/m3
young's modulus 1.22 GPa  
poisson's ratio 0.2  
thermal expansion coefficient 1.2 × 10−6 K−1 4.3 × 10−6 K−1
thermal conductivity 895 W/m·K 1950 W/m·K
thermal shock parameter 30 MW/m  
debye temperature 2340 K  
specific heat 472 J/kg·K 715 J/kg·K
optical index of refraction 2.417 opaque
optical transmissivity 225 opaque
loss tangent at 40 Hz 0.0006  
dielectric constant 5.87  
dielectric strength 10 TV/m  
electron mobility 0.22 m2/V·s  
hole mobility 0.16 m2/V·s  
electron saturated velocity 270 km/s  
hole saturated velocity 100 km/s  
photoelectric work function small and negative 4.8 eV
bandgap 5.45 eV  
resistivity 1011 - 1014 Î©·m 650 nΩ·m
Source: Molecule of the Month

cocoa butter

Chocolate is a preparation made from the seeds of the cacao bush (Theobroma cacao). These are often mistakenly called cocoa beans, but they are neither made of cocoa nor are they beans. Cacao is a small evergreen tree, not a legume — the seeds of which are fermented, roasted, husked, pulverized, and pressed. Cocoa is the dry residue that separates from the fat (cocoa butter) during the pressing stage. If pulverized cacao is heated to the point of liquefaction (conched) and then cooled (tempered) instead of pressed the resulting product is called chocolate. Sugar is also almost always added to the mix. Straight chocolate is far too bitter for most people.

During the cooling process the cocoa butter in chocolate can solidify into one of six different polymorphs identified with roman numerals in order of their melting point. Form V is the polymorph found in good quality, well-tempered chocolate confections. The other forms feel too sticky or thick in the mouth or are associated with fat bloom — a condition where the cocoa butter separates out during storage. Chocolate bars suffering from fat bloom look dusty or cloudy, taste bland, and melt too easily. Although form V is the best tasting polymorph of cocoa butter, form VI is the most stable. Well-tempered and well-processed chocolate can transform into the stable but undesirable form VI if it is stored in a warm place or kept on the shelf for too long. This is why chocolate should be stored somewhere cool and dark and eaten soon after it is bought. The first condition is the responsibility of the producers, distributors, and retailers. The second condition is the responsibility of the consumer. Due to chocolate's inherent power over people, it is highly unlikely that it will ever last in the hands of the consumer long enough to undergo fat bloom. Most people buy and eat their candy bars and such within a few days or hours after they are purchased.

Food scientists in the chocolate industry seek to develop techniques that encourage cocoa butter to solidify in the desirable form V polymorph. One of the more interesting techniques involves irradiating molten cocoa butter with low level x-rays. This is done not to produce an x-ray photograph like a doctor would, but to see the resulting interference pattern generated. The technique is called x-ray diffraction and will be discussed in another chapter. An expert technician can interpret the pattern and infer the configuration of the atoms or molecules in the solid lattice. Different heating, cooling, and stirring regimes are tested until an optimum process evolves.

Interestingly, form V cocoa butter has a melting point of 34 to 36 °C; slightly less than the interior of the human body — 37 °C. This is one reason why chocolate melts so well in the mouth. This property is also exploited by pharmaceutical companies in the preparation of suppositories. A suppository is a bullet-shaped drug delivery system consisting of cocoa butter mixed with a medication that is then inserted into an orifice other than the mouth. (Think about what this last phrase is saying for a second.) As the cocoa butter melts away the drug is released gradually. The drugs may remain near the surface (as is the case for hemorrhoidal suppositories) or they may diffuse into the capillaries and spread to the rest of the body via the circulatory system (as is the case with narcotic suppositories). Suppositories are also made from other compounds, but when they are made from cocoa butter, form V is still the desired polymorph.

Polymorphs of Cocoa Butter
polymorph melting point (°C) comments
form I 17.3 Produced by rapid cooling of melt. Successive polymorphs are then obtained sequentially by heating at 0.5 °C/min.
form II 23.3 Produced by cooling melt at 2 °C/min or rapid cooling of melt followed by storing from several minutes up to one hour at 0 °C. This form is stable at 0 °C for up to 5 hours.
form III 25.5 Produced by solidification of melt at 5-10 °C or transformation of form II by storing at 5-10 °C.
form IV 27.3 Produced by solidification of melt at 16-21 °C or transformation of form III by storing at 16-21 °C.
form V 33.8 Produced by tempering (cooling then reheating slightly while mixing). The most desirable form with good gloss, texture, and "snap".
form VI 36.3 The transformation of form V after spending 4 months at room temperature. Leads to the white, dusty appearance of "bloomed" chocolate.
Source: The Materials Science of Chocolate

ice

Nice summary from Physics Today

Water can exist in many different crystalline forms, 13 of which have been identified to date. Of those, nine are stable over some range of temperature and pressure--for example, at atmospheric pressure, ordinary hexagonal ice is stable between 72 and 273 K--and the other forms are metastable.

George Lucas freely admits that Star Wars is really an ancient myth cloaked behind futuristic-looking technology and I've heard Star Trek described (rather accurately in my opinion) as a "space opera" In an age where science fiction is everywhere, it seems that very little of it contains any science. Cat's Cradle is an exception in that it's a real marriage of science and fiction.

"There are several ways," Dr. Breed said to me, "in which certain liquids can crystallize -- can freeze -- several ways in which their atoms can stack and lock in an orderly, rigid way."

That old man with spotted hands invited me to think of the several ways in which cannonballs might be stacked on a courthouse lawn, of the several ways in which oranges might be packed into a crate.

"So it is with atoms in crystals, too; and two different crystals of the same substance can have quite different physical properties."

"Now suppose," chortled Dr. Breed, enjoying himself, "that there were many possible ways in which water could crystallize, could freeze. Suppose that the sort of ice we skate upon and put into highballs -- what we might call ice-one -- is only one of several types of ice. Suppose water always froze as ice-one on Earth because it had never had a seed to teach it how to form ice-two, ice-three, ice-four … ? And suppose," he rapped on his desk with his old hand again, "that there were one form, which we will call ice-nine -- a crystal as hard as this desk -- with a melting point of, let us say, one-hundred degrees Fahrenheit, or, better still, a melting point of one-hundred-and-thirty degrees."

ellipsis

And that old man asked me to think of United States Marines in a Godforsaken swamp.

"Their trucks and tanks and howitzers are wallowing," he complained, "sinking in stinking miasma and ooze."

He raised a finger and winked at me. "But suppose, young man, that one Marine had with him a tiny capsule containing a seed of ice-nine, a new way for the atoms of water to stack and lock, to freeze. If that Marine threw that seed into the nearest puddle … ?"

"The puddle would freeze?" I guessed.

"And all the muck around the puddle?"

"It would freeze?"

"And all the puddles in the frozen muck?"

"They would freeze?"

"And the pools and the streams in the frozen muck?"

"They would freeze?"

"You bet they would!" he cried. "And the United States Marines would rise from the swamp and march on!"

iron and steel

Iron: undergoes three solid state phase transitions as its temperature increases from room temperature to 1535 °C, where it melts. Steel: Above about 1,600 degrees Fahrenheit, the crystal structure of steel shifts to a softer, weaker form. This is why the World Trade Center towers collapsed. It was a phase change.

The first steels were probably created accidentally when iron sword blanks were heated in charcoal forges and some carbon worked its way into the iron matrix. With the increased carbon, steel is harder and has a much higher tensile strength than iron, but is also more brittle. Classic steels are iron-carbon alloys, but modern steels may also contain other metals such as chromium, manganese, nickel, or vanadium. Chromium is the most important of these as the resulting alloy resists oxidation (commonly known as rusting) and corrosion (the eating away of a material due to chemical action). Any metal alloy that is at least half iron by mass and with a chromium content of 12% or more is called stainless steel. There are three basic types of stainless steel identified by crystal structure: ferritic, austenitic, and martensitic.

Basic Types of Steel in Order of Increasing Carbon Content
type composition and comments
ferrite (zero carbon)
  carbon = 0% chromium = 0%  
  • Pure Iron
  • Body-entered cubic lattice
  • Atomic planes slide easily (for a solid) across one another making iron soft
ferritic stainless steel (low carbon)
  carbon < 0.08% chromium ≈ 12–26% (molybdenum, aluminum)
  • Ferrites are iron ceramics
  • Body-entered cubic lattice
  • Named after the Latin word for iron
  • Magnetic with a high permeability
  • Cannot be hardened by heat treatment
  • Found in automotive trim, exhaust pipes, household appliances, and water tanks
austenitic stainless steel (medium carbon)
  carbon < 0.12% chromium ≈ 17–25% nickel ≈ 7–20% (Mo, Ti, Cu)
  • Austenite is a solid solution of iron and carbon that can only exist at temperatures greater than 723 °C. The addition of chromium, nickel, and other metals (typically manganese) allow the austenitic crystal structure to survive at lower temperatures.
  • Named after the English metallurgist W.C. Roberts-Austen
  • Face-centered cubic
  • Carbon is more soluble in austenite than ferrite
  • Nonmagnetic
  • Cannot be hardened by heat treatment, but can be hardened by cold-working
  • The most widely used group of stainless steels. Found in cookware, kitchen sinks, food processing equipment, floppy disk shutters, piercing jewelry, and surgical hardware. The most common type is 18/8, which contains 18% chromium and 8% nickel.
martensitic stainless steel (high carbon)
  carbon < 1.2% chromium ≈ 12–18% (molybdenum, nickel)
  • Martensite is a class of hard minerals composed of plate-shaped crystals.
  • Martensitic steel is formed during the rapid cooling of austenitic steel by quenching in oil.
  • The hardest of all steels
  • Named after the German metallurgist Adolf Martens
  • Tetragonal crystals
  • Magnetic
  • Can be hardened by heat treating
  • Used in cutlery, scalpels, wrenches, turbines and any other application where hardness is important
non stainless steel (very high carbon)
  carbon < 2% chromium < 11% (typically contains no chromium)
  • Also known as carbon steel
  • Any iron-carbon alloy with less than 11% chromium
  • Magnetic

more, so many more

Summary

Problems

practice

  1. Write something.
    • Answer it.
  2. Write something else.
    • Answer it.
  3. Write something different.
    • Answer it.
  4. Write something completely different.
    • Answer it.

investigative

  1. Find an example of polymorphism not discussed in this section. Be prepared to discuss it briefly in class.

Resources

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