Four things are drawn in the viewport. Nothing else in the scene is physical.
Spheres mark atomic positions, not size. Each occupies Wyckoff site 8a; every atom is identical and equivalent by symmetry. Radii here are scaled to 0.28 × the nearest-neighbour distance so bonds stay visible.
Switch on stacking colours and the spheres are tinted by which layer they belong to — A, B, C — instead of by element. That is the only thing separating diamond from lonsdaleite, or 2H graphite from 3R.
Si: [Ne]3s²3p² · C: [He]2s²2p²
Each rod is a two-electron covalent σ bond between sp³ hybrids on adjacent atoms. Four per atom, at 109.47°, pointing to the corners of a tetrahedron. In binary compounds the rod is drawn two-tone because charge sits closer to the more electronegative partner.
Graphite is the exception on this page: its rods are sp² σ bonds inside a sheet, and the 3.35 Å van der Waals contact between sheets is deliberately left undrawn, because it is not a bond.
drawn where r < 1.15 × dnn
The conventional cubic cell: edge a, 8 atoms. The primitive cell is smaller — an FCC rhombohedron holding just 2 atoms, the basis pair at (0,0,0) and (¼,¼,¼).
FCC lattice + 2-atom basis
A single lattice plane of the selected Miller index, placed through the atom nearest the centre. Atoms lying in it are highlighted gold. Look down the normal and you see the surface net that a wafer of that orientation exposes.
dhkl = a / √(h²+k²+l²) for cubic
Blue rows are the properties that are identical — they are what "same lattice" actually means. Everything below them is a consequence of bond length and bond strength.
| Property | Silicon | Diamond | C : Si |
|---|---|---|---|
| Structure type | diamond cubic | diamond cubic | identical |
| Bravais lattice + basis | FCC + 2 atoms | FCC + 2 atoms | identical |
| Space group | Fd3̄m (227) | Fd3̄m (227) | identical |
| Coordination / bond angle | 4 · 109.47° | 4 · 109.47° | identical |
| Packing fraction | 0.34 | 0.34 | identical |
| Lattice constant a | 5.4310 Å | 3.5670 Å | 0.657 |
| Bond length dnn = √3·a/4 | 2.352 Å | 1.545 Å | 0.657 |
| Covalent radius | 1.11 Å | 0.77 Å | 0.69 |
| Cohesive energy | 4.63 eV/atom | 7.37 eV/atom | 1.59 |
| Band gap (both indirect) | 1.12 eV | 5.47 eV | 4.9 |
| Density | 2.329 g/cm³ | 3.515 g/cm³ | 1.51 |
| Atom density | 5.00×10²² cm⁻³ | 1.76×10²³ cm⁻³ | 3.5 |
| Bulk modulus | 98 GPa | 442 GPa | 4.5 |
| Knoop hardness | ~1150 kg/mm² | ~10000 kg/mm² | 8.7 |
| Debye temperature | 645 K | 2230 K | 3.5 |
| Thermal conductivity | 149 W/m·K | 2000–2200 W/m·K | ~14 |
| Breakdown field | ~0.3 MV/cm | ~10 MV/cm | 33 |
| Electron / hole mobility | 1400 / 450 | 2200 / 1800 cm²V⁻¹s⁻¹ | 1.6 / 4.0 |
| Static dielectric constant | 11.7 | 5.7 | 0.49 |
| Intrinsic carriers ni (300 K) | ~1.0×10¹⁰ cm⁻³ | ~10⁻²⁷ cm⁻³ | — |
Room-temperature values, single crystal. Diamond mobilities are for high-purity CVD material and vary strongly with defect density. Elastic moduli in both are anisotropic; bulk modulus quoted for comparison.
Carbon's valence shell is 2s²2p². There is no 1p core state underneath, so the 2p orbital has no radial node and no orthogonality constraint pushing it outward — it stays compact and overlaps hard. Silicon's 3p must stay orthogonal to the filled 2p core, so it is pushed out and its overlap is weaker and longer-ranged. That single difference in core structure sets dnn at 1.545 Å versus 2.352 Å.
Shorter bond → larger σ–σ* splitting → wider gap, stiffer lattice, higher phonon frequencies. Three of the table's rows are the same fact.
Follow it through. Stronger overlap widens the bonding–antibonding split, which is the band gap: 5.47 eV versus 1.12 eV. At 300 K that turns diamond into an insulator with essentially zero intrinsic carriers, while silicon sits in the useful middle where doping controls conduction. The same stiff, light bonds give diamond a Debye temperature of 2230 K — phonons carry heat ballistically enough to reach ~2000 W/m·K, roughly 14× silicon and the best of any bulk material at room temperature.
The wide gap also raises the breakdown field by ~30×, which is the whole argument for diamond power electronics: for the same blocking voltage the drift region can be far thinner and more heavily doped. What blocks it is not physics but crystal growth — large, low-defect, reliably doped single-crystal diamond. Silicon wins on 300 mm boules, native oxide, and a 60-year process base, not on band structure.
One caution on the picture: the diamond structure is not a Bravais lattice on its own. The two basis atoms at (0,0,0) and (¼,¼,¼) are chemically identical but not related by a pure translation — their tetrahedra point in opposite directions. Rotate to [111] in the viewer and the two sublattices separate visibly into the puckered bilayers that make {111} the cleavage plane.
A wafer is a plane cut through this lattice. Which plane you choose fixes surface atom density, dangling-bond count, cleavage behaviour, and carrier mobility along the channel.
The CMOS wafer. Square 2D net, 4-fold symmetry, two dangling bonds per surface atom — which drives the 2×1 dimer reconstruction and, historically, the lowest interface trap density with thermal SiO₂.
Si: 6.78×10¹⁴ atoms/cm² · d = a
Densest plane in the diamond structure and the cleavage plane of silicon — a (100) wafer breaks along orthogonal {110}. Hole mobility along ⟨110⟩ is the highest of the low-index faces, which is why (110) and sidewall FinFET channels were pursued for PMOS.
Si: 9.59×10¹⁴ atoms/cm² · d = a/√2
One dangling bond per surface atom, 3-fold symmetry, stacked as puckered bilayers 0.78 Å apart. Diamond's natural cleavage and octahedral growth habit. Si(111) gives the famous 7×7 reconstruction; also the anisotropic-KOH-etch stop plane in MEMS.
Si: 7.83×10¹⁴ atoms/cm² · d = a/√3
Densities count the full surface bilayer on (111). Interplanar spacings dhkl are geometric; note that for diamond cubic, reflections with mixed-parity hkl and h+k+l = 4n+2 are extinct in diffraction even though the planes exist.
Round brackets name one plane. Curly braces name every plane the crystal's symmetry makes indistinguishable from it. Square brackets name a direction, and angle brackets the family of equivalent directions — four notations that are routinely conflated and mean four different things.
| Notation | Means | Cubic example | Members |
|---|---|---|---|
| (hkl) | One specific plane | (100) — the top face of the cube, and nothing else | 1 |
| {hkl} | All symmetry-equivalent planes | {100} — all six cube faces | 6 |
| [uvw] | One specific direction | [100] — the a axis | 1 |
| <uvw> | All equivalent directions | <100> — the three axes, both senses | 6 |
The three cube faces, related by the four-fold axes. Counting both senses of each normal gives six members. On silicon this is the wafer face.
3 distinct orientations · 6 members counting both senses
The six planes through pairs of opposite cube edges, each cutting a rectangle through the cell. Twelve members. The cleavage planes of the diamond-cubic semiconductors.
6 distinct orientations · 12 members counting both senses
The four planes normal to the body diagonals. Through the cell centre each cuts a regular hexagon, as drawn; nearer a corner the same plane cuts the equilateral triangle usually pictured. Eight members. The close-packed plane, and the KOH etch stop.
4 distinct orientations · 8 members counting both senses
Each cube shows every distinct orientation in the family, drawn where the plane cuts the cell through its centre. A plane and its opposite face have the same orientation but opposite normals, so the member count is twice the number of orientations shown.
The three low-index families carry almost all the practical weight. {100} has six members: the cube faces, related by the three four-fold axes. {110} has twelve: the face diagonals. {111} has eight: the octahedral faces, one per cube corner. The viewer prints the count for whatever plane is selected, including any (hkl) you type in yourself.
Two traps are worth stating plainly. The first: in a cubic crystal the direction [hkl] happens to be the normal to the plane (hkl), which is so convenient that it is easy to forget it is a coincidence of cubic symmetry. In the tetragonal and hexagonal structures in the selector — rutile, quartz, sapphire, the SiC polytypes, every wurtzite — it is false, because the axes are no longer all the same length. The second: equivalent does not mean identical in every respect. GaAs (111)A and (1̅1̅1̅)B are related by symmetry in the lattice but terminate in gallium and arsenic respectively, and they etch and grow completely differently. Zincblende has no inversion centre, so the sign of the normal matters.
Hexagonal faces take a fourth index, written (hkil) with i = −(h+k). It carries no new information — it is fully determined by h and k — but it exists so that symmetry-equivalent faces look alike: the three prism planes of a hexagonal crystal are (10̄10), (1̄100) and (011̄0), which are visibly one family, where the three-index forms (100), (̄110) and (010) are not. The viewer takes h, k and l and displays the four-index form.
Silicon has essentially one ambient-pressure structure. Carbon has a family of them, and they are not variations in bond length — they are different lattices built from the same atom. Three of them are in the selector.
sp³, four-coordinate, 1.545 Å. Tetrahedral bilayers stacked ABC along [111]. The stable dense form, and the one every gem and every CVD wafer is.
a = 3.5670 Å · 3.515 g/cm³ · Eg 5.47 eV
The same sp³ bilayers, the same 1.54 Å bond, the same 109.5° — stacked AB instead. Hexagonal diamond. Found at meteorite impact sites (Canyon Diablo) where graphite was shock-compressed; also made by static HPHT.
a = 2.522, c = 4.119 Å · 3.51 g/cm³
sp², three-coordinate, 1.421 Å inside a flat sheet; 3.354 Å of van der Waals nothing between sheets, stacked AB. A semimetal, soft, and — this is the part people forget — the thermodynamically stable form of carbon at room conditions.
a = 2.4612, c = 6.7079 Å · 2.266 g/cm³
Identical sheets stacked ABC. The graphite analogue of the diamond/lonsdaleite pair. 5–15% of natural graphite, produced by shear, annealing back to 2H above ~1300 °C.
a = 2.456, c = 10.044 Å · 2.28 g/cm³
One graphite sheet with nothing above or below. Not a 3D lattice, so it is not in the viewer — set graphite to 1×1×1 and look at a single layer instead. Zero-gap Dirac semimetal.
a = 2.46 Å · sp²
An FCC lattice whose lattice points are whole C₆₀ molecules, held together by van der Waals forces. The atoms are curved sp², intermediate between sp² and sp³.
a = 14.17 Å · 1.65 g/cm³ · Eg ≈ 1.6 eV
Completes the set: sp³ networks, sp² sheets, sp¹ chains. Linear —C≡C— or =C=C=, predicted to be the stiffest material known. Only short, end-capped chains have been made and confirmed; bulk carbyne remains unverified.
1.28 / 1.34 Å alternating · sp¹
No lattice at all: a random network up to ~88% sp³. Gets most of diamond's hardness with none of its crystallography, which is why it coats tools and hard drives.
3.0–3.3 g/cm³ · Eg 1–3 eV
Diamond is the metastable one. Graphite sits ~0.02 eV/atom lower in energy at ambient conditions.
The reason your ring survives is kinetics, not thermodynamics: converting sp³ to sp² requires breaking every bond in the network, so the barrier is enormous and diamond persists indefinitely below about 1500 K in the absence of oxygen. Above that, in vacuum, it graphitises from the surface inward.
Which is also why there are two ways to make it. HPHT pushes carbon into the stable field — roughly 5–6 GPa and 1600 K — and grows diamond as the equilibrium phase. CVD does the opposite: it grows diamond metastably at a few kPa from a CH₄/H₂ plasma, where atomic hydrogen etches sp² carbon far faster than sp³, so the diamond fraction survives while graphite is removed as it forms.
Lonsdaleite is the ambiguous case. Bulk single crystals have never been produced; what is recovered from impact sites and shock experiments is nanotwinned and faulted diamond containing 2H sequences, and several reported "lonsdaleite" diffraction patterns have been reinterpreted as heavily stacking-faulted 3C. The often-quoted claim that it is 58% harder than diamond comes from a single simulation of a perfect crystal, not a measurement.
The classification a gemmologist or a device engineer actually uses is not about the lattice at all — every one of these is ordinary cubic diamond. What varies is what sits on, or instead of, a carbon site.
Nitrogen present as aggregates — A centres (N pairs) and B centres (4 N around a vacancy), up to ~3000 ppm. The aggregation takes geological time, which is why it marks a stone as natural. Absorbs in the UV; often faintly yellow.
Nitrogen as isolated substitutional atoms (C centres), 10–500 ppm. Strong yellow. Rare in nature (<0.1%), standard in HPHT growth because there is no time for aggregation.
Under ~5 ppm nitrogen. The purest, most thermally conductive, most transparent material; what CVD aims for, and what heat spreaders, X-ray windows and anvils are cut from.
Boron substituting for carbon: a shallow acceptor at 0.37 eV, making the crystal a p-type semiconductor and turning it blue. Heavily boron-doped diamond superconducts below ~4 K.
A substitutional nitrogen next to a vacancy. Optically addressable electron spin with millisecond coherence at room temperature — the basis of diamond magnetometry and one of the leading solid-state qubits. Engineered a few nanometres beneath a (100) surface.
Each step down this list changes one more thing about the diamond structure — the stacking, then the atoms on the sites, then the bonding itself.
FCC lattice, two identical atoms per basis. Centrosymmetric, so no piezoelectricity and no second-harmonic generation in the bulk. Every member is an indirect-gap semiconductor.
The same tetrahedral bilayers as cubic diamond, stacked AB rather than ABC. No bond length, angle or coordination number changes — only the sequence. Wurtzite is to zincblende exactly what this is to diamond cubic.
Leaves the tetrahedral family entirely: sp² sheets, three-coordinate, held together between layers by van der Waals forces alone. Two stackings again — AB and ABC — which is why graphite and diamond each come in a cubic-style and a hexagonal-style variant.
Same geometry, but the two basis sites hold different elements. Inversion symmetry is lost — space group drops to F4̄3m — which buys piezoelectricity, a strong χ⁽²⁾, and, in III-V compounds, a direct gap.
Same tetrahedra, hexagonal ABAB stacking instead of cubic ABCABC. A polar c axis appears, producing the spontaneous and piezoelectric fields that generate the 2DEG in AlGaN/GaN HEMTs.
The same underlying Bravais lattice as diamond cubic, with a one-atom basis. 12-fold coordination, 74% packing, and no directional bonding — hence ductility and metallic conduction.
8-fold coordination, 68% packing. Higher melting points among refractories; the {110}⟨111⟩ slip systems give the ductile-to-brittle transition that FCC metals lack.
12-fold coordination and the same 74% packing as FCC — only the stacking sequence differs (ABAB vs ABCABC). Fewer easy slip systems, so markedly more anisotropic mechanically.
One atom per cell, 6-fold coordination, 52% packing. Essentially unique to polonium among elements — included as the reference case every other structure is measured against.