Materials Science · Ceramics, glasses and inorganic networks

Bonding and structures in ceramics

Compare an ionic oxide arrangement with a covalently connected carbide, then distinguish neighbour counts, elastic response, slip and charge transport. Use an original load-path example to explain why strong bonding does not eliminate flaw-sensitive failure.

Useful background: Atoms, bonding, structure and defects; Energy, stability and environmental context. Each worked case explains the quantities it uses.

Back to the chapter

After reading, you can

Explain how ceramic bonding and structure permit varied properties.
Describe sixfold coordination in rock-salt MgO and fourfold connectivity in a representative SiC crystal.
Distinguish a local coordination environment from a molecule or whole-crystal formula.
Explain why bond stiffness, accessible plastic rearrangement and charge transport are different questions.
Use a supplied ceramic specimen geometry and measured endpoints without mistaking net-section stress or hardness for fracture toughness.

Ceramics form a broad family

A ceramic used as an abrasive can resist local indentation yet chip at an edge. Another ceramic can carry an electronic current in a semiconductor device. Neither observation contradicts strong bonding. The missing questions concern how the atoms connect, what can move, and where a load is carried.

Oxides, carbides, nitrides and other inorganic materials can have substantial ionic or covalent bonding character. Their structures include crystals and combinations of phases. Strong interactions can support stiffness and high-temperature usefulness, but the family includes many electrical and mechanical behaviours.

An oxide contains oxygen combined with other elements; carbides contain carbon and nitrides contain nitrogen. These chemical family names do not identify a complete structure or property set. A ceramic body can contain many crystalline grains, several phases, glassy regions and pores. Here we begin with two ideal crystalline arrangements, then add a specimen-scale geometric interruption.

Ionic and covalent character are useful descriptions of electronic interactions, not mutually exclusive boxes. Ionic character emphasises attractions between differently charged species along with repulsions and the rest of the crystal environment. Covalent character emphasises shared electronic states associated with particular neighbours and preferred directions. Real ceramic bonds can combine these characters. The earlier bonding lesson explains why a bond-energy depth is different from the restoring response near equilibrium.

An ionic oxide is a crystal of shared neighbours

Magnesium oxide, MgO, provides an ionic example. In its ordinary rock-salt crystal structure, a magnesium site has six nearest oxygen neighbours along three perpendicular directions, in positive and negative pairs. Their positions form the vertices of an octahedron around the magnesium site. Each oxygen site also has six nearest magnesium neighbours. Coordination number counts this chosen shell of neighbours; it does not count all interactions in the crystal.

The usual ionic labels Mg²⁺ and O²⁻ balance equal numbers of magnesium and oxygen sites. They are a useful formal charge description, not a claim that an electron-density measurement must assign exactly an integer charge to each atom. Attraction is not confined to one Mg–O pair: electrostatic interactions extend through the lattice, with like-charge repulsion and short-range repulsion contributing to the stable arrangement.

One magnesium site drawn with six oxygen neighbours is therefore not an isolated MgO₆ molecule. Those oxygen sites are also neighbours of other magnesium sites in the extended crystal. A local coordination sketch and the chemical formula answer different questions. MgO gives the bulk one-to-one ratio in the ideal stoichiometric crystal; it does not say each Mg has only one oxygen neighbour.

For comparison, silicon carbide, SiC, has a predominantly covalent, three-dimensional connected structure with polar character as well. In the representative common SiC structures considered here, each Si has four nearest C neighbours arranged tetrahedrally, and each C has four Si neighbours. A tetrahedron has four vertices enclosing its centre; it is not four neighbours in one flat square. Different SiC layer stackings can retain this local coordination, so a four-neighbour sketch alone does not specify every crystal property.

The first figure shows local environments in three-dimensional projection. Its lines identify nearest-neighbour relationships; they do not mean every interaction is an isolated spring. In the SiC panel, dashed connections identify the negative-depth directions of the schematic, not weaker or broken bonds. Sphere sizes and projected lengths are illustrative, not measured ionic radii or bond lengths.

Two original idealised local coordination environments shown in three-dimensional projection. The magnesium oxide panel has one magnesium site labelled Mg2+ at the centre with six oxygen sites labelled O2− in the positive and negative x, y and z directions, an octahedral environment. Every oxygen in the ideal bulk also has six magnesium neighbours. The silicon carbide panel has one silicon site labelled Si at the centre and four carbon sites labelled C at tetrahedral vertices. Each carbon in the ideal bulk also has four silicon neighbours. Two dashed Si–C connections mark the negative-depth directions in this schematic; they are not weaker or broken connections. Lines identify nearest-neighbour relationships, not isolated molecules or independent equal springs. Sphere sizes and projected lengths are illustrative, not measured radii or bond lengths. The shared environments are consistent with bulk MgO and SiC, rather than MgO6 and SiC4 molecular collections.

Count connections without inventing a molecular formula

Use an ideal periodic counting model, ignoring surfaces, vacancies and other defects. Suppose it contains 100 Mg sites and 100 O sites, each with the sixfold coordination just described. Counting Mg–O nearest-neighbour contacts from the Mg ends gives 100 × 6 = 600 distinct contacts. Counting from the O ends gives the same 600, not a second independent set. Adding both endpoint counts gives 1200 and counts every contact twice.

Likewise, a model with 100 Si and 100 C sites, each fourfold coordinated to the other species, has 400 distinct Si–C nearest-neighbour connections. The 100 Si-centred tetrahedra do not require 400 different C atoms: each C site participates in the neighbour environments of four Si sites. That sharing is consistent with SiC, not a collection of isolated SiC₄ units.

More generally, if all counted connections join an M site to an X site, consistency requires N_M z_M = N_X z_X. Here N is the number of sites of the stated species and z its number of neighbours of the other species. This is a count of connection endpoints, not a bond-energy equation. Sixfold coordination on both species is consistent with equal numbers; fourfold coordination on both is also consistent with equal numbers.

Neither the 600 versus 400 contact count nor the formula predicts which real material has the larger Young’s modulus, fracture resistance or conductivity. These counts omit bond force response, direction, actual lengths and the collective crystal response. A consistent neighbour count is necessary for the proposed ideal network; it does not by itself prove that the structure is stable or can be made.

Resisting a small strain differs from rearranging permanently

Under a small elastic strain, neighbouring positions and bond angles change slightly, and restoring interactions oppose that change. A stiff crystal develops a large stress for a given small elastic strain in the stated direction. The measured modulus depends on the arrangement and electronic interactions throughout the structure, not only on the number of neighbours. This response can be largely reversible without bonds being permanently broken and replaced.

Permanent slip requires another route. A moving dislocation lets neighbouring regions shift by local rearrangements rather than moving a whole perfect plane at once. In an ionic arrangement, a proposed path changes the pattern of attractive and repulsive interactions; some relative shifts bring like-charged neighbours into unfavourable registry. In a directional covalent network, changing neighbour relationships and bond angles can also face a large barrier. Which dislocation can form and move depends on the actual structure and slip direction.

Cracking can compete with that motion. If plastic rearrangement cannot relax the stressed region sufficiently before a crack advances, the specimen can fracture with little macroscopic permanent strain. Differently oriented grains must also accommodate one another; an available slip route in one single crystal does not guarantee enough compatible deformation throughout a polycrystal.

This is a mechanism comparison, not a rule that ionic crystals have no dislocations or that every ceramic is brittle at every temperature. MgO single crystals can exhibit dislocation-mediated plastic deformation in room-temperature compression under suitable specimen and defect conditions. Changing dimensions, pre-existing dislocations, temperature, orientation or loading mode can change the competition with cracking. A small compressed crystal is not proof that an arbitrary large tensile tile can be bent safely.

Bonding does not remove flaws

A ceramic component can contain pores, inclusions or cracks introduced during manufacture or use. Limited plastic relaxation often makes flaw sensitivity important. Neither high hardness nor a high melting temperature alone establishes resistance to fracture or thermal shock.

Use an original, invented mechanical comparison at 25 °C under centred, slowly increased axial tension. D and P are made from the same nominal ceramic composition, phase and grain state and have the same outer width W = 10 mm and thickness t = 2 mm. D is intact at the section examined. P has a circular through-hole of diameter d = 6 mm, used as a simple model pore. The hole passes through the thickness. Dimensions are treated as unchanged during the small-deformation readings.

The gross section area is Wt = 20 mm² for both. At the section through the hole’s centre, only two solid ligaments remain in P: their combined width is W − d = 4 mm, so the net area is (W − d)t = 8 mm². A ligament here is a remaining strip of solid connecting material above and below the opening. The two specimen ends carry equal and opposite forces of magnitude F; this transmits internal axial force F, not 2F.

At F = 160 N, gross nominal stress is F/(Wt) = 8 N/mm² = 8 MPa in both. D has the same net-section mean under this simple geometry. In P, equilibrium requires that the remaining net section transmit 160 N, giving a net-section mean of 160/8 = 20 MPa. The mean rises by a factor of 2.5 without changing the assumed chemistry of the solid.

The drawing shows why force cannot be transmitted through the empty hole and must pass through the surrounding solid. Its curves are schematic load routes, not calculated stress trajectories or a measured field. The stress around the opening is nonuniform; the largest tensile component can exceed the section mean. Net area alone does not determine that maximum, a crack-tip field or a fracture load. A sharper defect can be more consequential even with similar missing volume.

Original model comparison of two ceramic gauge regions at 25 degrees Celsius under centred axial tension. Each has outer width 10 millimetres and thickness 2 millimetres out of the page. The left specimen D is intact; the right P has a circular through-hole of diameter 6 millimetres. Equal and opposite forces of magnitude 160 newtons are shown at each specimen’s ends. Straight and curved blue lines illustrate load routes through solid material; they are not calculated stress trajectories. An orange dashed section through the hole centre crosses two remaining ligaments in P, whose combined width is 4 millimetres. Both gross areas are 20 square millimetres and both gross nominal stresses are 8 megapascals. P has a net section area of 8 square millimetres and net-section mean stress of 20 megapascals; D’s corresponding net mean is 8 megapascals. Neither this mean nor the schematic gives the maximum local stress or a fracture load. The drawn regions are cropped; no total pore-volume fraction or full specimen length is specified.

Read the separate failure observations

To distinguish calculation from observation, a separate original invented pair of destructive tests gives failure forces 1200 N for an intact D coupon and 320 N for a P coupon with this geometry. Their gross engineering failure stresses are 60 and 16 MPa. P’s net-section mean at its failure endpoint is 40 MPa; that is still not its maximum local stress or a fracture-toughness value. These are illustrative single-specimen endpoints, not a strength distribution or a universal porosity law.

A lower nominal failure stress does not by itself demonstrate that every remaining bond became weaker. Geometry, critical flaws and the limited ability to redistribute a local stress provide another explanation. Actual attribution requires the surface and defect state, residual stresses, comparable tests and suitable structural evidence. Porosity, defects and brittle failure develops populations and sampling more fully; Cracks and stress concentration develops local fields and their validity.

Original invented comparison, not a named ceramic datasheet. Same outer dimensions, 25 °C, centred axial tension and negligible geometric change. Means use the stated original gross or net section; the separate failure forces are supplied observations.
Specimen	Gross area (mm²)	Net area at chosen section (mm²)	Gross stress at 160 N (MPa)	Net mean at 160 N (MPa)	Separate observed failure force (N)
D: intact	20	20	8	8	1200
P: 6 mm through-hole	20	8	8	20	320

Ask which carrier and which operating condition

An ionic crystal contains charged species, but charge being present is different from charge being transported over a distance. Small vibrations about lattice sites do not by themselves establish a sustained current. Under suitable conditions, ions can migrate through available vacancies or other paths; temperature, defect populations, interfaces and chemical surroundings affect that motion. Ionic conduction does not require the whole solid to melt.

An extended covalent network also does not guarantee electrical insulation. SiC can serve as a semiconductor: available electronic states and charge-carrier populations permit a controlled electronic response. Doping, which introduces selected impurities, and temperature can change that population and response without turning the whole material into a metal or moving its nuclei together as an electric current. The simple neighbour sketch supplies no electrical conductivity value.

For an abrasive edge, compare the specified contact response, crack resistance, geometry and loading. For an electrically insulating support, require measured leakage or conductivity at the intended temperature and environment; hardness or sixfold coordination is not that evidence. For a semiconductor function, relevant carrier control and interfaces matter. Heat transfer introduces another mechanism because lattice vibrations can carry energy even when electronic charge transport is weak.

The useful progression is bonding character → actual connections and structure → available mechanism → measured response under stated conditions. It is not a table assigning one guaranteed behaviour to every oxide, carbide or nitride. Keep the local crystal, microstructure and component geometry distinct while connecting them.

Worked examples

A coordination sketch is not a molecule

The ideal periodic MgO model has 100 Mg and 100 O sites with six opposite-species neighbours each. The SiC model has 100 Si and 100 C sites with four each. How many distinct nearest-neighbour connections does each contain, and does their ratio determine a stiffness ratio?

Count each connection from one species only: MgO gives 100 × 6 = 600 Mg–O contacts; SiC gives 100 × 4 = 400 Si–C connections.
Summing endpoints on both species gives 1200 and 800 respectively. Divide by two to avoid double counting. Shared neighbours make these whole-crystal one-to-one compositions consistent with local coordination greater than one.
The contact-count ratio is 600/400 = 1.5. It has no stress or strain information and is not a modulus ratio. Force response, geometry and collective interactions have not been supplied.

600 and 400 distinct nearest-neighbour connections in the stated periodic models. No material stiffness or toughness ratio follows from their count.

The same nominal load reaches a smaller solid section

Use D and P at 160 N. Calculate their gross and net-section means, then interpret the separate measured failure endpoints without claiming a material fracture-toughness value.

Both gross areas are 10 × 2 = 20 mm². Their gross nominal stress at 160 N is 160/20 = 8 MPa.
P’s net area is (10 − 6) × 2 = 8 mm²; its net mean is 160/8 = 20 MPa. D’s intact net mean remains 8 MPa. The ratio is 20/8 = 2.5.
For the separate destructive observations, D’s gross engineering failure stress is 1200/20 = 60 MPa; P’s is 320/20 = 16 MPa. Using P’s net area instead gives 320/8 = 40 MPa, a different reference quantity.
The net mean is not the local maximum and neither stress is fracture toughness. Defect shape, spatial stress and crack resistance have not been reduced to a fracture law here. A pair of single endpoints also gives no population scatter or guaranteed service strength.

At 160 N the gross mean is 8 MPa for both; the net means are 8 MPa for D and 20 MPa for P. Supplied failure forces correspond to gross 60/16 MPa; none of these values is a fracture-toughness measurement.

Work through the case

A hard ceramic tile chips when struck at its edge. Are hardness and fracture resistance contradictory?

Hardness concerns a defined local indentation or scratch response.
An edge impact can initiate and extend a crack.
The governing tests and mechanisms differ.
Strong restoring interactions can resist a local indentation while a stressed edge flaw extends before enough plastic rearrangement relieves it. Contact geometry and crack growth probe different responses; one is not a contradiction of the other.

No. A material can be hard and still be susceptible to crack-driven failure.

Try the reasoning

Are all ceramics electrical insulators?
Show the answer and reasoning
No.
Electronic and ionic transport depend on composition and structure. SiC is an actual semiconductor counterexample to a universal insulating-network rule. Ionic charge can also migrate through suitable defect paths under appropriate conditions; the existence of ions alone does not establish a useful current.
Does a dense-looking surface rule out internal pores?
Show the answer and reasoning
No.
Internal structure needs suitable evidence. A surface image does not measure every internal ligament, pore or crack. Keep the sampled region and method with the claim.
A local Si-centred drawing shows four C neighbours. A learner writes the bulk formula SiC₄. Repair the inference using the fact that each C also has four Si neighbours.
Show the answer and reasoning
The local drawing is a shared neighbour environment. Equal fourfold counts on both species are consistent with SiC, not isolated SiC₄ units.
N_Si × 4 = N_C × 4 requires equal site numbers in this ideal complete network. A C vertex belongs to the neighbour environments of four Si sites. Do not count every drawn local cluster as a separate molecule.
A hypothetical periodic M–X network has six X neighbours around every M and three M neighbours around every X. If it has 80 M sites, how many X sites and distinct M–X connections are required? Is the count enough to prove a stable crystal?
Show the answer and reasoning
160 X sites and 480 distinct connections are required; no stable structure is proved.
80 × 6 = N_X × 3, hence N_X = 160. Counting from the M ends gives 480 connections; counting both ends would give 960 incidences. Geometry, energetics and actual structure evidence are still needed. This is a necessary counting relation for an invented network, not a named ceramic prediction.
Keep the 6 mm through-hole, 2 mm thickness and 160 N tension, but increase the outer width from 10 to 14 mm. Find the new gross and net-section means. Does the result certify that the maximum local stress is below 12 MPa?
Show the answer and reasoning
The gross mean is about 5.71 MPa and the net mean is 10 MPa. A maximum-local-stress limit of 12 MPa is not certified.
Gross area is 14 × 2 = 28 mm², so 160/28 ≈ 5.71 MPa. Net area is (14 − 6) × 2 = 16 mm², so the mean is 160/16 = 10 MPa, half the previous net mean. Local stress concentration is not supplied by that average, and changing width also changes the geometric field.
The ideal MgO counting region has 600 nearest-neighbour contacts and the SiC region 400. A report says MgO must have 1.5 times SiC’s Young’s modulus and fracture resistance. What information is missing?
Show the answer and reasoning
Contact force response, directions, lengths, collective structure and the mechanisms relevant to each measured property are missing.
A dimensionless neighbour count is not a stress-to-strain relation or crack-resistance measurement. More coordination does not define a universal property ranking, and the comparison has not specified equivalent volume, direction or specimen condition.
A small MgO single crystal shows permanent deformation in room-temperature compression. Does that establish that a large polycrystalline MgO tile will bend plastically before cracking in tension?
Show the answer and reasoning
No. The specimen, defect state, grain compatibility and loading conditions changed.
The result establishes a possible dislocation-mediated route under its actual conditions. It rejects an absolute no-plasticity rule, but supplies no universal tensile ductility or large-component fracture guarantee.
The model hole occupies 6 mm of a 10 mm width at its widest section. May that be reported as 60% porosity by volume, or as proof that every point has 2.5 times the intact stress?
Show the answer and reasoning
Neither follows. It is a width fraction at one section, and the 2.5 ratio concerns the net-section mean only.
Total void volume would also require the complete three-dimensional specimen volume and geometry. The local field is nonuniform. A section-area calculation does not assign one identical stress to all points or reconstruct a sharp crack.

What to carry forward

Ceramic is a family, not one property set.
Evaluate flaws and the relevant failure mechanism.
Coordination counts shared neighbours; it is not a molecular formula or a universal property ranking.
Small elastic restoring response, permanent slip and charge transport depend on different accessible mechanisms.
A missing region redirects force through the remaining solid; net-section mean, local stress and fracture toughness are different quantities.
Use the actual phase, defects, geometry and conditions to compare ceramic responses.

References

Teaching resources and research supporting this lesson’s explanations and examples.