Tetrahedra of Structure, Bonding & Material Type
Arkel-Ketelaar triangle, as discussed on the
previous page of this web book, recognises that the chemical elements & binary compounds exhibit three
extreme types of bonding: Metallic, Ionic & Covalent.
But this can not the whole story because covalently bonded materials are seen to
take two extreme forms. They either have an extended three-dimensional
covalent network-lattice structure, as exemplified by diamond (carbon) and silicon dioxide (sand), SiO2, and silicon, Si. Or they present as discrete molecules like fluorine, F2,
methane, CH4, or glucose, C6H12O6 that interact with each other via weak (van der Waals/dipole-dipole/hydrogen bonding) forces.
This extra dimension leads to a Tetrahedron of Structure, Bonding & Material Type:
The Four General Types of Crystalline Solid
At an early stage in the study of chemistry we learn that there are four general types of crystalline solid and four associated material types: metals, ionic materials like sodium chloride (salts), molecular materials like methane, CH4, and network covalent materials like diamond.
Metals have a characteristic lustre and are excellent conductors of electricity. There are two models of bonding in metals. The classical Drude model of conductivity has a lattice of cations immersed in a sea of mobile valence electrons delocalised over the entire crystal. The positive cations attract the delocalised electrons, and vice versa. The mobile electrons are the agents responsible for the conduction of electricity and heat:
Metals can also be modelled using band theory.
A metal's thermal and electrical conductivities are proportional, but increasing the temperature increases the thermal conductivity and decreases the electrical conductivity, a behaviour quantified by the Wiedemann-Franz Law, here.
From Wikipedia: "The simple classical Drude model provides a very good explanation of DC and AC conductivity in metals, the Hall effect, and thermal conductivity (due to electrons) in metals. The model also explains the Wiedemann-Franz law of 1853.
"However, the Drude model greatly overestimates the electronic heat capacities of metals. In reality, metals and insulators have roughly the same heat capacity at room temperature. Although the model can be applied to positive (hole) charge carriers, as demonstrated by the Hall effect, it does not predict their existence."
Metals are often ductile and exhibit a huge range of melting points, from mercury, -39°C, to tungsten at 3200°C. Read more in Wikipedia.
Ionic materials, such as sodium chloride, NaCl, have an extended crystal lattice with non-metal anions electrostatically attracted to adjacent metal cations and metal cations electrostatically attracted to adjacent non-metal anions:
Ionic materials are insulators as solids, but are electrical conductors when molten and when dissolved in aqueous solution. Ionic materials may dissolve in water (and sometimes in dipolar aprotic solvents such as DMSO), but they are insoluble in non-polar solvents like hexane or chloroform. Ionic binary materials have moderately high melting points, usually in the 300-1000°C range. Read more about ionic bonding in Wikipedia.
Molecular van der Waals Materials
Discrete molecules, such as methane, CH4, are held together internally by strong intramolecular (within molecule) shared electron pair covalent bonds, but when forming condensed solid or liquid phases, the molecules interact via weak intermolecular (between molecule) van der Waals forces:
- There are several types of van der Waals attraction: dipole/dipole, dipole/induced-dipole and spontaneous-dipole/induced-dipole. It is tempting to consider these forces to be of different strengths, but it is the distance range that is more important. The spontaneous-dipole/induced-dipole attractions also known as London dispersion forces (LDF) are surprisingly strong but only act at very short range. These are contact attractions: the surface of even neutral, non-polar molecules like methane are 'sticky'. All molecules have London dispersion forces and the strength increases with the size/surface area of the molecule. This logic is used to explains the increasing boiling and sublimation temperatures of the halogens: F2 < Cl2 < Br2 < I2.
- In addition, some molecules have dipole-dipole, hydrogen bonding, etc., which increase the total amount of interaction between the molecules. Consider iodine chloride, ICl and bromine, Br2. Both are 70-electron systems, but ICl is polar and Br2 is non-polar, yet they have rather similar boiling points of 97° and 59° respectively, showing that the dipole/dipole attraction makes only a minor contribution. (Many thanks to members of the ChemEd list for the above points.)
- Molecular materials may also be hydrogen bonded, where a hydrogen bond involves a proton being shared between two Lewis bases, usually with oxygen, nitrogen or fluorine atomic centres, as discussed here.
Molecular materials exhibit a vast array of properties, but they are generally mechanically weak, have zero electrical conductivity, have low melting and boiling points, and/or a susceptibility to sublime. Molecular materials usually soluble in (or miscible with) non-polar solvents. Hydrogen bonded molecular solids are often soluble in water.
Network Covalent Materials
Network covalent materials, such as diamond, C, silicon, Si, and silicon dioxide (quartz and sand), SiO2, have atoms arranged in an extended 3-dimensional lattice of strong, shared electron pair covalent bonds:
Network covalent materials are hard, refractory, brittle, usually electrical insulators, and they are not soluble in any solvent. Materials have very high melting points, >1500°C, and are chemically intractable materials.
Semiconductors are a sub-set of network covalent materials that conduct electricity, albeit with high resistance when pure. The electrical conductivity, modelled using band theory, can be modified by doping, and this is the basis of the transistor and silicon chip – integrated circuit – technology. Semiconductor elements and binary materials include: silicon, gallium arsinide & indium phosphide.
Several elements have pairs of allotropes, one of which is molecular and insulating, and the other which is metalloid: hard, brittle, with a network covalent structure, a metallic lustre and electrical conductivity. These include: carbon (C60 & graphite), tin (gray & white) & arsenic (yellow & grey).
The Grimm Tetrahedron (1928, but rather forgotten)
William Jensen reports, below, that Grimm and Dehlinger developed an early form of tetrahedron in the nineteen thirties. However, this knowledge appears to have been forgotten. The Grimm Tetrahedron symbolically reflects with the four vertices of a tetrahedron the four main types of bonding in solid chemical compounds: metallic (metallisch), ionic (heteropolar), van der Waals (molecular) & network (homopolar).
From William B. Jensen's paper: Logic, History, and the Chemistry Textbook, J.Chem.Educ. 817-828, 75, 1998:
Dehlinger's 1934 drawing of Grimm's tetrahedron:
Grimm’s two-dimensional projection of his 1934 bond- type tetrahedron redrawn by Jensen using corrected and updated examples:
i = Ionenbindung
a = Atombindung
m = metallische Bindung
z = zwischenmolekulare Kräfte
The six edges between these vertices correspond to the intermediate types of bonds. It is clear that the idea of isolated molecules can be most naturally applied only to one vertex of this diagram (the central one, where the intermolecular interactions are the weak van der Waals forces).
From the Concept of Chemical Periodicity:
from Mendeleev Table to Molecular Hyper-Periodicity Patterns
E. V. Babaev & Ray Hefferlin, here.
Laing's 1993 Tetrahedron
In 1993 Michael Laing published an expansion of the two dimensional van Arkel-Ketelaar triangle of bonding into a tetrahedron by dividing
covalent materials into two types, Covalent Network and
van der Waals Molecular: M. Laing, A Tetrahedron of Bonding, Education
in Chemistry, November, pp160-163 (1993), here:
Copper, Cu, magnesium, Mg, sodium, Na, and chromium, Cr
- Ionic Salts:
Sodium fluoride, NaF, magnesium fluoride, MgF2, sodium chloride, NaCl, and calcium oxide, CaO
- Van der Waals
Molecules: Iodine, I2, carbon dioxide, CO2, naphthalene, C10H8, Group 18 (inert)
gases, nitrogen, N2, benzene, C6H6, sulfur hexafluoride, SF6, carbon tetrachloride, CCl4,
and hydrogen bonded solids
- Network Covalent materials :
Diamond, C, silicon dioxide, SiO2, silicon carbide, SiC
Laing is interested in
finding compounds with intermediate properties. A
triangle has three corners and three edges, but a tetrahedron has four
corners, four sides and six edges. With respect to the six edges, Laing discusses:
- Van der
Waals–to–Metallic: Gallium, Ga2,
arsenic and mercury
- Van der Waals–to–Ionic (polar): Aluminium chloride, AlCl3, aluminium bromide, AlBr3, and tin tetraiodide, SnI4
- Ionic–to–Covalent: Zinc sulfide, ZnS, and zinc selenide, ZnSe
- Metallic–to–Covalent (semiconductors): Tin and germanium
- Ionic–to–Metallic (alloys): Copper-zinc brass and cesium-gold alloy
- Covalent–to–Van der Waals: Sulfur, selenium, phosphorus and arsenic
Mike Laing has sent (personal communication, 2010) an updated version of his triangle/tetrahedron of bonding:
Tetrahedron of Structure, Bonding & Material Type
- Ionic Materials
- Ionic salts like: sodium chloride, NaCl
- Lattice of electrostatically attracted anions & cations. Usually soluble in water to some extent. Insulators when solid. Conduct electricity when molten and when in aqueous solution: Electrolytes
- Intermediate melting points ~300 1000°C
- Metallic Materials
- Metals like aluminium and alloys like brass
- Lattice of metal cations in sea of electrons
- Conduct electricity & heat as solid and liquid
- Metallic lustre & ductility
- Huge range of melting points: mercury 39°C tungsten 3407°C
- Metals may, or may not, alloy with each other
- Network Covalent Materials
- Network of strong covalent bonds
- Very high melting point, >1500°C
- Insoluble, insulators
- Refractory materials
- Molecular van der Waals Materials
- Molecular materials like methane, CH4
- Small molecules
- Strong intramolecular within molecule covalent bonds
- Weak intermolecular between molecule bonds: van der Waals forces
- Generally low melting and boiling points: liquids & gases at 25°C
- Soluble in polar or non-polar solvents
Some Points for Consideration:
Models: Lattice Size
Discrete molecules, ie molecular materials, are rather easy to model using plastic models and/or computer software because molecular materials are, by definition, of limited size and only consist of a few atoms.
Lattice materials – metals, ionic salts & network covalent compounds – are considered to be of infinite size and without surfaces, this is computationally a more difficult task. Indeed, experiment shows that small clusters consisting of hundreds of atoms are required before bulk properties are approached, below.
If one wishes to calculate/model a bulk property of a molecular material, such as boiling point, it is necessary to consider a lattice of molecular entities.
Network covalent materials must, of course, have a surface. The surface does not consist of 'dangling bonds', but can either be oxidised or the surface layer(s) of atoms can rearrange to give a very subtle surface structure.
Click this link to see a movie showing the bulk structure of silicon and how the Si(III) surface comes about... the clip tells us that it took 25 years of research to elucidate the correct structure! This is important information due to the importance of silicon to the semiconductor industry:
This web page is concerned with bonding and material type, not with crystal type.
The science of how atoms, ions and molecules fit together to produce various types of crystallographic unit cell can be explored using resources provided by Oxford University, the University of Hull and Wikipedia.
Bob Hanson of St. Olaf College has developed the Jmol Crystal Symmetry Explorer, a web based tool that allows the visualisation of crystal structures. (Note: Your computer must be allowed to run downloaded java applications use this page. Your network administrator may not allow this.)
Read more in Stephen Lower's Chem1 Virtual Textbook: States of Matter & Solids.
The van Arkel-Ketelaar triangle and the Tetrahedron of structure, bonding & material type are – like the periodic table – visual schemas that map chemical properties to theories of chemical structure.
Like all schemas, anyone is free to have a go at choosing representative species and extending/expanding the property sets.
There is still a great deal to discover about the tetrahedron of structure, bonding and material type, and some of this author's ideas – found by standing on the shoulders of Jensen & Laing – follow.
A Truncated Tetrahedron of Structure, Bonding & Material Type
In 1995 Jensen showed that it is possible to quantify the van Arkel-Ketelaar Triangle of Bonding by looking at average electronegativity and electronegativity difference: A Quantitative can Arkel Diagram, J.Chem.Educ., 395-398, 72 (1995) and here.
The question is: Can the Tetrahedron of Structure, Bonding and Material Type be quantified?
A simple valency rule can be used to predict with good – but admittedly not perfect – accuracy whether a binary compound with covalent bonding will be a molecular or network covalent material.
- If both of the elements have a common (lower) valency of two or greater and the bonding be covalent the binary compound will likely be a network covalent material: mechanically hard, brittle solid with a high melting temperature that will be insoluble in any solvent.
- Otherwise, if one or both of the atoms has a common (lower) valency of one: H, Li, Na, K, F, Cl, Br or I, and the bonding be covalent, the binary compound will be molecular material that will be mechanically soft, have a low melting temp (and may even be a liquid or gas) and will be likely to be soluble in either polar or non-polar solvents, but probably not both.
- CAUTION! This over simple rule does throw up some important errors: CO2, O2 and N2 are predicted to be network covalent materials and therefore solids... where as they are actually molecular gases.
1 + 1
| H2, HCl, Cl2, LiH(gas)
1 + 2
| H2O, OF2, SCl2
1 + 3
| NH3, PCl3, BF3
1 + 4
| CH4, SiCl4
1 + 5
| PCl5, IF5
2 + 2
| O2, S8
2 + 3
aluminium oxide, Al2O3
2 + 4
Special case molecular:
| silicon dioxide, SiO2
carbon dioxide, CO2, however, at high pressure carbon dioxide is now known to form an extended network structure
3 + 3 & 3 + 5
Special case molecular:
| aluminium phosphide, AlP, boron nitride, BN, gallium arsinide, GaAs
nitrogen, N2, white phosphorous, P4
3 + 4
| silicon nitride, Si3N4
4 + 4
Special case clusters:
| silicon carbide, SiC
carbon, C60, etc.
Observation: Three of the corners of the quantitative tetrahedron are clear: Cs, F2 and CsF.
- Metallic: Cesium, Cs, is a metal and the most electropositive element, 0.79.
- Molecular: Fluorine is the most electronegative element, 3.98, it is molecular, F2, and the covalent bond is non-polar.
- Ionic: Cesium fluoride, CsF, is the most ionic binary compound, 3.98 – 0.79 = 3.19.
But what about the fourth corner, Network Covalent?
- The most electronegative element that forms a network covalent material is carbon, 2.55.
It follows that diamond should not be placed at the corner of a tetrahedron at electronegativity 3.98, but at some distance from it, at 2.55.
Indeed, the corner of the tetrahedron should be cut off at 2.55, giving a truncated tetrahedron.
The meta-synthesis Truncated Tetrahedron of Structure, Bonding & Material Type: The Four Faces
The molecular to network edge, with the text "Non-Polar Covalent Bonding" (above) should have the species:
- F2 molecular fluorine
- [-OO-]n polymer chains of oxygen atoms
- [N]n 2D polymeric nitrogen (flat plates like graphite)
- [C]n 3D polymeric carbon, diamond
Unfortunately, the polymeric oxygen and nitrogen allotropes are unknown!
A Physical Truncated Tetrahedron
Click to download truncated_tetrahedron.pdf, print, cut out, score & glue together:
and the Truncated Tetrahedron
Models & theories of chemical structure
& bonding can be mapped onto the Truncated Tetrahedron of Structure, Bonding & Material Type.
The theoretical models for metals and semiconductors use band theory, ionic materials use lattice models, molecular and network materials are modelled either by molecular orbital (MO) theory or by valence shell electron pair repulsion (VSEPR):
Band Theory: Metals, Alloys & Metalloids (Semi-metals)
When metal atoms collect together to form metal, the
atomic orbitals overlap form molecular orbitals which range from completely
bonding to completely antibonding. These MOs can be separated into conducting
and non-conducting bands with as many energy levels as there are electrons.
If a material has electrons in the conduction band it will conduct electricity
and heat, if there are no electrons in the conducting band it will be
an insulator. Semiconductors have a few electrons in the conduction
band. Read more in the Wikipedia.
Coulombic (Electrostatic) Attraction: Ionic Materials
It is convenient to think of ionic solids as consisting
of a lattice of idealised spheres of definite size and charge, subject only to Coulombic (electrostatic) attraction. Positive cations are attracted to adjacent negative anions, and vice versa. In the simplest models electrons are not shared.
The structure of many ionic
materials can be accounted for in terms of the relative sizes of the ions, their relative numbers, the radius ratios, and
their preference for tetrahedral or octahedral coordination. Crystal structure
can usually be explained in terms of Pauling's
- Around every
cation, a coordination polyhedron of anions forms, in which the cation-anion
distance is determined by the radius sums and the coordination number
is determined by the radius ratio.
- The Electrostatic
Valence Rule: An ionic structure will be stable to the extent that
the sum of the strengths of the electrostatic bonds that reach an
anion equals the charge on that anion.
- The sharing
of edges, and particularly faces by two anion polyhedra decreases
the stability of a crystal.
- An extension
of the third rule: In a crystal which contains different cations,
those with high charge and low coordination numbers tend not to share
elements of their coordination polyhedra.
- The Rule of Parsimony
The number of essentially different kinds of constituents in a crystal
tends to be small.
Crystal structures are usually named after a definitive crystal structure, such as: zinc sulfide (structure), sodium chloride, cesium chloride, calcium fluoride (fluorite), rutile, diamond, etc.
MO Theory & VSEPR:
Molecular and Extended Lattice Structures
Molecular and network covalent materials can be modelled in
terms of hybridized atomic centres and/or valence shell electron pair repulsion
(VSEPR) entities. For example, sp3, tetrahedral carbon is found in molecular
methane, CH4, and in the extended network covalent
of diamond. Molecular structures can be modelled in more detail with (paramertised)
molecular mechanics software or with molecular orbital theory.
A more detailed discussion
of structural theory is available elsewhere in the Chemogenesis web book,
Six Edges To
There are six edges to the
Tetrahedron of Structure, Bonding & Material Type and the trends associated with each edge will be discussed in turn:
- Molecular Network: Molecular Covalent Dimensionality
- IonicNetwork: Ceramics & Oxides
- MetallicMolecular (not shown on diagram): Cluster Compounds
- MetallicIonic: Alloys
- IonicMolecular: Polar Bonding
- MetallicNetwork: Semiconductors
Molecular Network: Molecular Covalent Dimensionality
If an extended network covalent
structure is three dimensional, 3d, and plates are two dimensional,
2d, then chains are one dimensional, 1d, and discrete molecules
are zero dimensional, 0d, with respect to extended structure, ie at the millimetre scale.
The molecular to network edge should have the species:
- F2 molecular fluorine
- [-OO-]n polymer chains of oxygen atoms
- [N]n 2D polymeric nitrogen (flat plates like graphite)
- [C]n 3D polymeric carbon, diamond
Unfortunately, the polymeric oxygen and nitrogen allotropes are not known.
Carbon allotropes beautifully
illustrate covalent molecular dimensionality:
- Diamond has a three dimensional,
3d, network covalent structure
- Graphite consists of two dimensional, 2d, covalent plates
- Single wall carbon nanotubes are one dimensional, 1d, tubes
- C60 buckyballs are zero dimensional, 0d, molecules.
C2 is known in the gas phase at high temperature. On the millimetre scale these are point entities.
- Read a series
of reviews about carbon chemistry in Materials
Composite image of three dimensional diamond, two dimensional graphite, one dimensional carbon nanotubes and zero dimensional – with respect to extended structure– C60. From Wikipedia: here, here & here
Sulfur has zero dimensional and one dimensional allotropes.
- Above 600°C
sulfur exists as S2, a species isoelectronic
- At 20°C sulfur
exists as the yellow crystalline allotrope Flowers of Sulfur (Brimstone) which
consist of S8 rings.
- Clever chemistry
can be used to make ring sizes of 6, 7, 9, 10, 11, 12, 18 & 20.
- Heating to 160°C
causes the S8 rings to open and polymerise.
Rapid cooling traps this 1d polymeric state... which slowly turns
back into the flowers of sulfur allotrope at room temperature over several days.
Polymer chemistry involves
converting small monomers, such as ethylene (zero dimensional entities) into one dimensional
thermoplastic chains such as low density polyethylene (LDPE), or three dimensionally
crosslinked (network covalent) materials like urea-formaldehyde resins.
Two further points:
- Between the integer 0d, 1d,
2d and 3d dimensions, there are fractional and fractal dimensions. Take a look at the
fractal dimension calculator here,
and some fractal
chemical systems here.
- Network materials can be ground to fine powders, or synthesized as nano-sized particles. This important because size will strongly influence physical and chemical properties.
IonicMolecular: Polar Bonding
Like many authors, Laing identifies
aluminium chloride, AlCl3, as intermediate between
ionic and molecular because aluminium chloride sublimes (as Al2Cl6)
so is molecular, but the intramolecular Al-Cl bonds are highly polarised. The difference in electronegativity can be used to calculate the % ionic and % covalent character using the Pauling equation, here.
The Ionic-to-Molecular transition
is well illustrated by looking at the fluoride, chloride & bromide (halogen) compounds across their
Molecular, polar covalent
Reading from left to right:
- Ionic materials, ionic bonding, extended crystal lattice
- Molecular materials with polar covalent bonding
- Molecular materials with non-polar covalent bonding
There is a material type discontinuity
going from a molecular van der Waals material to an ionic material. For example, on heating MgCl2 and AlCl3:
- Magnesium chloride, MgCl2, melts to give an ionic liquid that conducts electricity.
- Aluminium chloride, AlCl3, sublimes
to give a gas of dimeric Al2Cl6 then AlCl3 molecular entities.
Ionic and polar materials can be ground to fine powders, or synthesized as nano-sized particles that approach molecular sizes.
IonicNetwork: Polar Ceramics and Oxides
Laing identifies zinc sulfide
and zinc selenide, ZnS & ZnSe, as intermediate between ionic and network
covalent. While there in nothing wrong with this analysis, it limited
because a whole range of commercially important materials are to be found.
To consider polar ceramics
and oxides it is necessary to identify which part of the tetrahedron we
are discussing. For this topic we are not just to looking at Ionic-Network
"edge", but the entire Ionic-Network-Molecular face.
Ionic <-> Polar Network <-> (Non-polar Network)
Ceramics are forming an ever
more important part of our lives, but often in unexpected places. In the 1970s there was much
talk in the engineering research community about building ceramic
internal combustion engines, but the ceramics proved too difficult
to work with and the topic is hardly discussed today. However, ceramics
are now widely used in modern high performance engines, but they are
employed as thin films and coatings rather than as parts.
- Engines used to
be made of low quality cast iron with the pistons running in iron
- In the 1970s aluminium
engines were developed, but they retained their hard wearing iron
liners. However, there were problems with the differential thermal
expansion of the aluminium engine block and the iron liners that limited performance.
- Today, high performance
engines are all aluminium alloy, with the cylinder bore (and possibly the piston rings) evenly coated with
a few microns of a ceramic material such as silicon carbide or titanium nitride. (Different
companies have their own proprietary recipes, for example CKS, a patent coating from Goetze.)
Planets, including the Earth,
are made from rocks & minerals.
- Minerals are characterised
by having a distinct crystal structure, and there can be exchange between
cations, and exchange between anions so that a particular mineral can
have a range of compositions. For example, the mineral rhodonite: manganese
iron magnesium calcium silicate (Mn, Fe, Mg, Ca)5(SiO3)5,
can vary in the exact ratio of Mn, Fe, Mg & Ca cations, as long
as the net charge adds to 10, so as to counter the 5 silicate ions,
- Most of the minerals
that make up the earth's crust are oxides of silicon, aluminium & iron which give rise to polar network covalent materials which are:
high melting point, insulating, insoluble materials.
- Most rocks
when examined closely are found be assemblage of two or more
Laing suggests that tin, Sn,
is the ideal intermediate between metallic and network, because Sn has
two allotropes, metallic β-tin and network
covalent α-tin, and supports this suggestion
with the story of how Napoleon's army had uniform buttons made from metallic
tin, but during the attempted to invasion of Russia in 1812, the intense
cold of winter transformed the metallic tin buttons into the mechanically
weak network covalent allotrope of tin... and to powder...
There is a discontinuity in bonding – from metallic to covalent – when crossing a period:
occurs due to the phase change from metallic to network covalent, as
illustrated by the alpha and beta allotropes of tin. This phase
change is independent of the onset of conductivity as described by band
theory. Silicon has an extended network covalent structure: it is hard, brittle, has a high melting point, 1420°C, and is insoluble. However, Si also conducts electricity (albeit slightly) and has a metallic lustre.
In Periodicity and the
s- and p-Block Elements (OCP 51, 1977, pp58), N.C. Norman reminds
us that the metalloid, or semi-metallic, elements have a narrow range of electronegativity
- B (2.04)
- Si (1.9)
- Ge (1.81)
- As (2.18)
- Sb (2.05)
- Te (2.1)
materials with average electronegativity values in this range can also
be metalloid. Examples include:
Ultrapure silicon is actually a poor conductor
but its electronic properties can be dramatically modified by doping with
small quantities of "impurity" atoms.
- Substitution of
a silicon atom with a phosphorus, arsenic or antimony atom (at the parts
per million level) will increase the number of electrons in the conduction
band and make the material more conducting. This type of material is
classed as an n-doped semiconductor, here.
- Substitution with
boron, aluminium or gallium will reduce the number of electrons so that
there are "electron holes". Such materials are classed as p-doped semiconductors, here.
- When p-doped semiconductors
are joined to n-doped semiconductor so that there is a pn-junction,
a device is formed which will only allow electricity to flow in one
direction. Such a device is called a diode, here.
- Materials like gallium arsenide,
GaAs, and indium antimide, InAs, are isoelectronic with silicon and germanium
and are known as III/V semiconductors.
- Research is being
carried out on the doping of diamond to give it semiconductor properties.
MetallicMolecular: Cluster Compounds
Laing identifies the digallium
molecule, Ga2, as the intermediate between
metallic and van der Waals molecular. I argue, as above, that there many
intermediates and it is possible to identify and describe the gradual
change from metallic to molecular behaviour.
In a News and Views article – Nature, 331, 14th Jan, pp116, 1988 – Tony Stace asks the question:
large does a collection of atoms have to be before it begins to adopt
the properties and features of a solid?"
The question is answered
with reference to metallic clusters.
- It transpires that
when the ionisation energy of mercury clusters is measured there
is a gradual transition from essentially atomic behaviour for small
clusters (5-10 atoms) to metallic behaviour (60-70 atoms). Thus,
it seems that for mercury when a couple of dozen or so atoms bond together,
there is sufficient atomic orbital overlap for a conduction band to
form and for the material to adopt bulk metallic properties.
- Copper clusters
only adopt the interatomic distance of bulk copper when the cluster
size is greater than 10 atoms.
- The melting point
of gold clusters increases with cluster size and more than 1000 atoms
are required before the mp of the cluster approaches the mp
of bulk gold:
Number of Atoms
Melting Point °C
- Non-metals: Small argon clusters (20-50 atoms) exhibit icosahedral (five fold) symmetry. Larger clusters (>100 atoms) and solid argon have a face centred cubic crystalline structure and octahedral symmetry.
A graph of cluster
size vs physical parameter (ionisation energy, interatomic distance,
melting point) typically takes the following form with a distinct inflection
point between molecular and bulk behaviour. The inflection point varies
with element and experimental parameter.
Laing discusses the Metallic-Ionic
edge with respect to alloys, particularly the various copper-zinc (brass)
alloys that have properties very different to the pure metals, and the cesium-gold intermetallic compound, CsAu or Cs+/Au, which
is intermediate between metallic and ionic.
Alloying involves mixing of
two or more metals to create an entirely new material, e.g. the fusion
of copper and tin to make bronze. The mixing is usually carried out by
melting a mixture of the solid metals in the desired proportions.
However, like water and organic solvents not all molten
metals are fully miscible with each other.
- Copper and nickel
are completely soluble in each other. On cooling, the copper and nickel
atoms are randomly distributed in the metallic lattice. These are substitutional
alloys, examples include: Cu/Ni Cu/Au & Na, K, Rb & Cs in all proportions
- When a small amount
of zinc is added to liquid copper it will dissolve and form a substitutional
alloy. However, at >30% zinc, a stoichiometric CuZn phase forms.
- Lithium is only
miscible with sodium above 380°C. It is immiscible with potassium,
rubidium and cesium and it does not form substitutional alloys.
- Lead and copper
- The earth's core
is composed of liquid iron. Elements soluble in liquid iron, called
siderophiles, are depleted in the earth's crust compared with the meteorites
from which the earth was constructed. It is suggested that the siderophile
metals partitioned into the iron core very early in the earth's history.
Siderophile metals include: iron, nickel, cobalt, platinum, gold, etc.,
The interesting science
occurs when molten mixtures are cooled. There is an excellent introduction by Michael Walshe, University of Limerick.
solution alloys form when two metals are totally
soluble in both the liquid and solid states.
form when two metals are soluble in the liquid state but are insoluble
in the solid state. The result, when viewed under a microscope, are
grain boundaries in the solid alloy which consists of two distinguishable
metals. A typical eutectic alloy is formed with cadmium and bismuth.
alloys are intermediate between solid solution and eutectic.
compounds have a fixed stoichiometric composition. For example,
two atoms of magnesium combine with one atom of tin to give Mg2Sn.
Likewise, cesium and gold form an intermetallic, CsAu which has properties
of Cs+/Au. The intermetallic iron carbide
(Fe3C) or cementite is important in the phase
diagram of steel, here.
Intermetallic compounds are usually hard, brittle have low conductivity.
and Wikipedia, are valence compounds formed between electropositive metals and main
group and post-transition elements. Syntheses are performed in liquid
ammonia. Compounds are stoichiometric with salt like structures. In
liquid ammonia polyatomic clusters form. Typically, Zintl phases are
brittle, coloured and are semiconducting.
Metallurgy: Steel as Iron-Carbon Alloy
alloy science - metallurgy - can be highly involved.
Joe Bellina an academic physicist at Saint Mary's College,
Notre Dame, Indiana, USA recently made an interesting contribution
to the ChemEd list on the subject of iron and steel alloys which illustrates
this point. (Many thanks to Joe for permission to use the following
- Steel is
an iron-carbon alloy, where the carbon is present at up to 7%.
- Iron can
adopt different crystallographic structures, the two most important
are austenite (which is FCC and stable at low temperature) and
martensite (which is BCC and stable at high temperature).
like iron consist of grains, usually microscopic, where each
grain is a single crystal.
atoms can either dissolve in the grain or they can collect at
the grain boundaries. On heating the carbon atoms migrate or
dissolve in the grains of iron. Both the rate of dissolution
and the final concentrate increase with temperature.
- Iron changes
its shape when it is bent or hammered. When this happens defects
are created in the crystalline grains which result in the metal
becoming less ductile. Crucially, the presence of defects obstructs
the formation of more defects, so the material becomes more
difficult to deform and becomes less ductile. The defects formed
by deformation are called dislocations.
the temperature causes the defects to "anneal out" or "heal"
because the atoms can migrate. Materials have specific annealing
temperatures. Annealing is a kinetically limited process since
the atoms most migrate to less energetic binding sites. The
higher the temperature the higher the annealing rate. So there
are competing processes: deformation produces dislocations and
annealing removes them.
- The activation
energy for migration is different in different metals: iron
is higher than aluminum or copper. As a result at room temperature,
when iron is bent the creation of dislocations is more rapid
than the elimination by annealing, so the iron "work-hardens".
In copper and aluminum the rate of elimination is greater so
the metal does not work harden and break. Of course the situation
is complicated by the fact that bending the metal also raises
its temperature and hence its annealing rate.
the skilled blacksmith, who from experience knows:
on cold metal hardens it locally (because defects are introduced).
on white-hot iron only changes the shape because the material
is above its annealing temperature.
- Heating the metal serves to dissolve the carbon atoms in the grains.
If these carbon atoms remain in the grains when the metal is
cooled, they act like defects and harden the metal. If they
have time to diffuse back to the grain boundary the metal will
remain relatively soft. The key factor here is the rate of temperature
change. When a smith plunges white-hot metal into cold water
she creates a harder material that will take a hold a sharp
- Only been
in the second half of the 20th century has data been obtained
to support models that explain what is happening to carbon at
grains and grain boundaries.
information on carbon steels, including the phase diagram, can
be found here.
Binary Material Software Widget: A Semi-Quantitative Tetrahedron
On the next page of this web
book there is a Binary Material Software Synthlet
that predicts bonding and material type from pairs of main-group elements in a semi-quantitative manner.
It works by determining whether a material is likely to be molecular or
network from valency data, and then it projects the van Arkel-Ketelaar
on to the appropriate face of the tetrahedron of bonding and material
A Comment from William
I contacted William
Jensen in 2004 for his comments about the earlier version of this page and the Arkel-Ketelaar
triangle page, here. Bill very kindly
sent me the following email, which I reproduce verbatim:
Mark, a few historical corrections:
the 1995 article I have discovered that the first bond-type triangle
was actually given by Fernelius and Robey in 1935 rather than by
van Arkel and was, in turn, partially anticipated by an even earlier
triangle given by Grimm in 1928. Details are found in references
1 and 4 below.
Laing is not
the originator of the tetrahedral diagram and it should not be named
after him. All that he said had been said 60 years before by Grimm
and Dehlinger, who in fact had developed a more sophisticated form
of the tetrahedron. This tetrahedron was used in several materials
science textbooks in the 1950s and 1960s. Details may be found in
references 3 and 4 below.
is a bond type diagram, but the tetrahedron is a structure type
diagram. It is important to recognized that these two concepts are
not identical. Bond type is only one of several parameters which
determine overall structure type. The differences between the two
types of diagram are discussed in references 3 and 4 below.
- W. B. Jensen,
"The Historical Development of the van Arkel Bond-Type Triangle,"
Bull. Hist, Chem, 1992-1993, 13-14, 47-59.
- W.B. Jensen,
"Quantity or Quality?", Educ. Chem., 1994, 31, 10,
- W. B. Jensen,
"Bond Type versus Structure Type," Educ. Chem, 1994, 31, 94.
- W. B. Jensen,
"Logic, History and the Chemistry Textbook II: Can We Unmuddle
the Chemistry Textbook?," J. Chem. Educ., 1998, 75, 817-828.
A number of changes have
been made to the text on this page as a result of Bill Jensen's communication, particularly the point about triangles of bonding but tetrahedra of structure bonding & material type.
|van Arkel-Ketelaar Triangle
Binary Material Synthlet
© Mark R. Leach 1999-
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