Metallic Materials
Ionic Materials
Molecular or van der Waals Materials
Network Covalent Materials
The Laing Tetrahedron of Bonding and Material Type
Transition Species
Structural Theory and The Laing Tetrahedron
Molecular – Network: Molecular Covalent Dimensionality
Ionic–Network: Polar Ceramics and Oxides
Metallic–Molecular: Cluster Compounds
Metallic–Ionic: Alloys
Ionic–Molecular: Polar Bonding
Metallic–Network: Semiconductors
Summary & The Future
Comment from William Jensen

Four Types of Crystal

At an eary stage in the study of chemistry we learn that there are four types of crystalline solid and associated material type:

Metallic Materials
Metals like sodium, Na, iron, Fe, and gold, Au, can be modelled as a lattice of metal cations immersed in a sea of mobile valence electrons delocalised over the entire crystal. Electrons are the agents responsible for the conduction of electricity and heat. At a given temperature, 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. Metals have a characteristic lustre, are often ductile and exhibit a huge range of melting points, from mercury, -39°C, to tungsten at 3200°C.

Ionic Materials
Ionic materials, such as sodium chloride, NaCl, have crystal lattice with anions electrostatically attracted to adjacent cations and cations electrostatically attracted to adjacent 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. Ionic materials have moderately high melting points, usually 300-1000°C.

Molecular 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. It is as if the surface of 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 low 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, SiO2, have atoms arranged in an extended lattice of strong, "shared electron pair" covalent bonds. Materials are hard, refractory solids. They are poor electrical conductors, and they are not soluble in any solvent. Very high melting point, >1500°C, chemically intractable materials.

The Laing Tetrahedron of Structure, Bonding & Material Type

In 1993 Michael Laing expanded the 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:

Like the triangles of bonding discussed on the previous page, the Laing tetrahedron can be richly adorned with real, representative chemical species. Michael Laing suggested the best representative extreeme species were: sodium fluoride (ionic), iodine (van der Waals), copper (metal) and diamond (network covalent):

In the pater, Laing discusses the chemistry with respect to:

• Metals: 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, Ne, etc., nitrogen, N2, benzene, C6H6, sulfur hexafluoride,SF6, carbon tetrachloride, CCl4, hydrogen bonded solids, etc.
• Covalent Network: diamond, silicon dioxide, SiO2, silicon carbide, CSi

Transition Species

Laing is very interested in finding representative compounds with intermediate properties. Now, a triangle has three corners and three edges, but a tetrahedron has four corners, six edges and four sides. Laing discusses:

Van der Waals-Metallic:gallium, Ga2, arsenic and mercury.
Van der Waals-Ionic (polar): aluminium chloride, aluminium bromide and tin tetraiodide.
Ionic-Covalent: zinc sulfide and zinc selenide.
Metallic-Covalent (semiconductors): tin and germanium.
Ionic-Metallic (alloys): Copper-zinc brass and cesium gold alloy.
Covalent-Van der Waals: sulfur, selenium, phosphorus and arsenic.

The Laing Tetrahedron of Bonding & Material Type (rotated)	Ionic Materials Ionic salt: sodium chloride Lattice of electrostatically attracted anions & cations Usually soluble in water to some extent Insulators when solids Conduct electricity when molten Conduct electricity when in aqueous solution Intermediate melting points ~300 – 1000°C
Metallic Materials Metal like aluminium or alloy 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 Diamond Very high melting point, >1500°C Insoluble, insulators Refractory materials
	Molecular van der Waals Materials Molecular material like methane, CH4 Small molecules Strong intramolecular – within molecule – covalent bonds Weak intermolecular – between molecule – bonds: van der Waals forces Low melting and boiling points: liquids & gases at 25°C Insulators Soluble in polar or non-polar solvents

Structural Theory and The Laing Tetrahedron

Models of chemical structure can be mapped onto the Laing tetrahedron. There are three distinct regions:

Band Theory: 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.

Lattice Theory: Ionic materials
It is convenient to think of ionic solids as consisting of spheres of definite size and charge. The structure of many ionic materials can be accounted for in terms of the relative sizes of the positive and negative ions, their relative numbers (radius ratios) and their preference for tetrahedral or octahedral coordination. Structure can be predicted using Pauling's Five rules:

1. 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.
2. 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.
3. The sharing of edges, and particularly faces by two anion polyhedra decreases the stability of a crystal.
4. 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.
5. 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.

VSEPR & MO Theories: Molecular and extended lattice structures
Most of the Laing tetrahedron can be modelled in terms of hybridized atomic centres 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. Structures can be modelled is 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, here.

The Six Edges To The Laing Tetrahedron

There are six edges to the Laing Tetrahedron, and each will be discussed in turn:

Molecular – Network: Molecular Covalent Dimensionality Ionic–Network: Polar Ceramics and Oxides Metallic–Molecular: Cluster Compounds Metallic–Ionic: Alloys Ionic–Molecular: Polar Bonding Metallic–Network: Semiconductors

Molecular – Network: Molecular Covalent Dimensionality

If an extended network covalent structure is three dimensional, 3d, then plates are two dimensional, 2d, chains are one dimensional, 1d, and discrete molecules are zero dimensional, 0d.

Carbon allotropes beautifully illustrate covalent molecular dimensionality:

Diamond has a 3d network covalent structure
Graphite consists of 2d extended covalent plates
Single wall carbon nanotubes are 1d covalent structures
C60 buckyballs are 0d molecules and C2 is known in the gas phase at high temperature

Read a series of reviews about carbon chemistry in Materials Today.

Sulfur forms allotropes which range from 0d to 1d.

Above 600°C sulfur exists as S2, a species isoelectronic with O2.

At 20°C sulfur exists as the crystalline, yellow "flowers of sulfur" 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.

Polymer chemistry involves converting zero dimensional monomers, such as ethylene, into one dimensional thermoplastics like low density polyethylene (LDPE) or three dimensional crosslinked materials like urea-formaldehyde resins.

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.

Ionic–Molecular: Polar Bonding

Like other 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 halogen compounds across a single period:

Reading from right-to-left:

• Molecular materials, non-polar covalent bonding
• Molecular materials, increasingly polar covalent bonding
• Ionic materials, ionic bonding

There is a material type discontinuity a molecular van der Waals material to an ionic material.

For example, from AlCl3 to MgCl2. On heating:

• Aluminium chloride sublimes to give a gas of Al2Cl6 then AlCl3 molecular entities.
• Magnesium chloride melts to give an ionic liquid that conducts electricity.

Ionic–Network: Polar Ceramics and Oxides

Laing identifies zinc sulfide and zinc selenide, ZnS and ZnSe, as intermediate between ionic and network covalent. While there in nothing wrong with this analysis, I find it limited because a whole range of commercially important materials are to be found here.

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:

Two factors determine Ionic-Network-Molecular character amongst main group binaries: valency and electronegativity, although there are some very common exceptions. Consider the various valency combinations and example species:

To summarise:

• If one or both of the elements has a valency of one (H, F, Cl, Br, I) the material will be molecular or ionic, depending upon the difference in electronegativity (delta EN).
• If both of the elements have a valency >=3 the material will be network covalent, and if there is a difference in electronegativity the covalent bonding will be polarised.
• Oxides (and sulfides) of metals and metalloids (electropositive elements) form hard, brittle, (generally) insoluble and insulating materials,
• Oxides of carbon, nitrogen, Group 16, 17 & 18 elements are molecular.
• With respect to the Ionic - Molecular - Network triangle:

Halides range: Ionic <-> Polar Molecular <-> Non-polar Molecular

Oxides range: 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 liners.

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.

Today, high performance engines are all aluminium, but the cylinder bore evenly coated with a few microns of a ceramic material such as silicon carbide. (Different companies have proprietary recipes.)

Planets, including the earth, are made from minerals and rocks.

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, here, 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, [SiO3]2-.

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 minerals.

Metallic–Network: Semiconductors

Laing suggests that tin, Sn, is the ideal intermediate between metallic and network, because Sn has two allotropes, metallic b-tin and network covalent a-tin.

Laing 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 elemental properties when crossing a period, from Li to C or from Na to Si.

• Lithium and beryllium are clearly metals and boron is clearly not. Likewise, sodium, magnesium and aluminium are metals but silicon is a network covalent material.
• This discontinuity occurs due to the phase change from metallic to network covalent (as illustrated by the alpha and beta allotropes of tin, above). This phase change is independent of the onset of conductivity as described by band theory.
• In Periodicity and the s- and p-Block Elements (OCP 51, 1977, pp58), N.C. Norman reminds us that the metalloid elements have a narrow range of electronegativity values, 1.8-2.2:
• B (2.04), Si (1.9), Ge (1.81), As (2.18), Sb (2.05) & Te (2.1)
• Norman points out that binary materials with average electronegativity values in this range can also be metalloid. Examples include:

These materials, like silicon, are of considerable technological importance. For example, the high gain, low noise amplifiers used in cell phones and satellite dishes employ gallium arsenide components.

Ultrapure silicon is 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. A great deal of research is being carried out on the doping of diamond to give it semiconductor properties.

Metallic–Molecular: 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: "How 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.

Small argon clusters (20-50 atoms) exhibit icosahedral (five fold) symmetry. Larger clusters (>100) and solid argon have a face centred cubic crystalline structure and octahedral symmetry.

Copper clusters only adopt the interatomic distance of bulk copper when the cluster size is >10 atoms.

The melting point of gold clusters increases with cluster size:

~20 atoms	mp ~ 500°C
~50 atoms	mp ~ 800°C
~100 atoms	mp ~ 920°C
~200 atoms	mp ~ 980°C
bulk gold	mp = 1064°C

More than 1000 atoms are required before the mp of the mp of the cluster approaches the mp of bulk gold.

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.

Metallic–Ionic: Alloys

Laing discusses the Metallic-Ionic edge with respect to alloys, particularly the various copper-zinc (brass) alloys have properties very different to the pure metals, and the cesium gold intermetallic, 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.

Like 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 are immiscible.
• 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., here.
• The interesting science occurs when molten mixtures are cooled. (There is an excellent introduction here.)
• Solid solution alloys form when two metals are totally soluble in both the liquid and solid states.
• Eutectic alloys 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.
• Partial solubility alloys are intermediate between solid solution and eutectic.
• Intermetallic 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 Cl⁺/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.
• Zintl phases, here, 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, Iron-Carbon Alloy: Steel Alloys and alloy science - metallurgy - can be highly involved. Prof. 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 text): 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). Metals like iron consist of grains, usually microscopic, where each grain is a single crystal. Carbon 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. Increasing 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. Now consider the skilled blacksmith, who from experience knows: Hammering on cold metal hardens it locally (because defects are introduced). Hammering 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 edge. 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. More information on carbon steels, including the phase diagram, can be found here.

Summary & The Future

The Laing tetrahedron is a schema which collects together a wide range of material types and structural concepts:

• Metals
• Ionic salts
• Molecules
• Network solids
• Molecular dimensionality
• Polar-covalent bonding
• Semiconductors
• Cluster compounds
• Alloys
• Ceramics

However, scientists from different disciplines will have very different perspectives on the relative importance of the various types of material.

Chemists [very, very generally] are interested in: ionic salts, molecules & molecular dimensionality and polar covalent bonding. (The majority of the world's chemists are analysts, work in a pharma related industry, or are educators.)

Metallurgists are interested in metals and alloys.

Chemists are only really interested in metals as: metal cations, as sources or electrons (reducing agents) or as catalysts. They are not very interested in "metals as metals".

The study of metal clusters is currently a very specialist, academic sub-discipline.

Solid state physicists are particularly interested in semiconductor science.

Chemists may help to design and make new ceramics, but materials scientists and mechanical engineers develop these materials into commercial products.

Further Work

Further work is needed in quantifying the tetrahedron so that materials can be more accurately (and plausibly) assigned to their correct position. Currently:

Valency and electronegativity data can be used to quantify the van Arkel-Ketelaar triangle of [metallic, ionic, covalent] bonding, here, rather successfully.

Often, valency data can be used to predict whether covalent species are molecular or network, here.

But, it it is not possible to unambiguously assign species to the tetrahedron using valency and electronegativity data alone. For example:

Carbon dioxide is a water soluble molecular gas, but the "similar" silicon dioxide is a high melting point, insoluble, network covalent solid.

Unfortunately, the Laing tetrahedron does not [currently] accommodate these rather well known empirical facts.

The current analysis only assigns species to the corners and edges of the Laing tetrahedron, but as we found we found with metal halides and oxides, it is sometimes necessary to look at the triangular face. The Laing tetrahedron has four triangular faces and one interior:

• There are about 650 binary compounds derived from the main group elements, here.
• Which one is closest to the centre to the Laing tetrahedron of bonding?
• Send me your suggestions - with reasoning - and I will add them.

Binary Material Software Widget

On the next page of this web book there is a Binary Material Software Widget that predicts bonding and material type from pairs of main-group elements. 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 type:

I contacted William Jensen for his comments about this, and the previous van Arkel-Ketelaar triangle page, here, and he kindly sent me the following email, which I reproduce verbatim:

A number of changes have been made to the text on this page as a result of Bill Jensen's communication, but it seems to this author that it is useful to keep the name Laing.

© Mark R. Leach 1999-2008

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