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Crystal structures

23 unit cells of metals, covalent networks and ionic solids. Every number — formula units per cell Z, coordination numbers, packing fraction and density — is computed on the spot from the lattice parameters and atomic coordinates, then set beside the measured density.

Lattice + basis · counting · coordination

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Cells
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Copper Face-centred cubic (ccp) · Cubic a = 361.49 pm

How many atoms does one cell own?

PositionCentresShareOwned
Cu\ce{Cu} Corner8× 1/8= 1
Cu\ce{Cu} Face6× 1/2= 3
Total per cell4
Formula units Z4
Coordination number
12 cuboctahedron
Nearest-neighbour distance
255.6 pm then 6 more at 361.5 pm
Packing fraction
74.0% touching hard spheres
Density (computed / measured)
8.935 / 8.933 g/cm³
Every position is computed from the lattice parameters and fractional coordinates: an atom’s share depends on whether it sits on a corner, edge, face or inside; coordination numbers are counted from distances (neighbours within 5 % of the nearest form one shell); density is ρ = Z·M/(N_A·V), compared with the measured value. Sphere sizes are schematic: in touching mode metals use half the nearest-neighbour distance and ions use Shannon radii — a hard-sphere model; real atoms have no hard edge.

Metallic

  • Po\ce{Po}

    α-Polonium

    Simple cubic

    Z
    1
    CN
    6
    Packing
    52.4%
    ρ
    9.21

  • Fe\ce{Fe}

    α-Iron

    Body-centred cubic

    Z
    2
    CN
    8
    Packing
    68.0%
    ρ
    7.87 / 7.87

  • Na\ce{Na}

    Sodium

    Body-centred cubic

    Z
    2
    CN
    8
    Packing
    68.0%
    ρ
    0.97 / 0.97

  • Nb\ce{Nb}

    Niobium

    Body-centred cubic

    Z
    2
    CN
    8
    Packing
    68.0%
    ρ
    8.58 / 8.57

  • W\ce{W}

    Tungsten

    Body-centred cubic

    Z
    2
    CN
    8
    Packing
    68.0%
    ρ
    19.25 / 19.30

  • Cu\ce{Cu}

    Copper

    Face-centred cubic (ccp)

    Z
    4
    CN
    12
    Packing
    74.0%
    ρ
    8.94 / 8.93

  • Al\ce{Al}

    Aluminium

    Face-centred cubic (ccp)

    Z
    4
    CN
    12
    Packing
    74.0%
    ρ
    2.70 / 2.70

  • Ni\ce{Ni}

    Nickel

    Face-centred cubic (ccp)

    Z
    4
    CN
    12
    Packing
    74.0%
    ρ
    8.91 / 8.91

  • Au\ce{Au}

    Gold

    Face-centred cubic (ccp)

    Z
    4
    CN
    12
    Packing
    74.0%
    ρ
    19.29 / 19.28

  • Pb\ce{Pb}

    Lead

    Face-centred cubic (ccp)

    Z
    4
    CN
    12
    Packing
    74.0%
    ρ
    11.34 / 11.34

  • Mg\ce{Mg}

    Magnesium

    Hexagonal close-packed

    Z
    2
    CN
    12
    Packing
    73.6%
    ρ
    1.74 / 1.74

  • Zn\ce{Zn}

    Zinc

    Hexagonal close-packed

    Z
    2
    CN
    6
    Packing
    65.1%
    ρ
    7.14 / 7.13

Covalent network

  • C\ce{C}

    Diamond

    Diamond

    Z
    8
    CN
    4
    Packing
    34.0%
    ρ
    3.52 / 3.51

  • Si\ce{Si}

    Silicon

    Diamond

    Z
    8
    CN
    4
    Packing
    34.0%
    ρ
    2.33 / 2.33

  • Ge\ce{Ge}

    Germanium

    Diamond

    Z
    8
    CN
    4
    Packing
    34.0%
    ρ
    5.33 / 5.32

Ionic

  • NaCl\ce{NaCl}

    Sodium chloride (rock salt)

    Rock salt (NaCl type)

    Z
    4
    CN
    Cl⁻ 6 · Na⁺ 6
    Packing
    65.3%
    ρ
    2.16 / 2.17

  • KCl\ce{KCl}

    Potassium chloride

    Rock salt (NaCl type)

    Z
    4
    CN
    Cl⁻ 6 · K⁺ 6
    Packing
    57.5%
    ρ
    1.99 / 1.99

  • CsCl\ce{CsCl}

    Caesium chloride

    Caesium chloride type

    Z
    1
    CN
    Cl⁻ 8 · Cs⁺ 8
    Packing
    66.9%
    ρ
    3.99 / 3.99

  • ZnS\ce{ZnS}

    Zinc sulfide (zinc blende)

    Zinc blende

    Z
    4
    CN
    S²⁻ 4 · Zn²⁺ 4
    Packing
    68.2%
    ρ
    4.09 / 4.04

  • ZnO\ce{ZnO}

    Zinc oxide (wurtzite)

    Wurtzite

    Z
    2
    CN
    Zn²⁺ 4 · O²⁻ 4
    Packing
    50.0%
    ρ
    5.68 / 5.60

  • CaFX2\ce{CaF2}

    Calcium fluoride (fluorite)

    Fluorite

    Z
    4
    CN
    Ca²⁺ 8 · F⁻ 4
    Packing
    60.7%
    ρ
    3.18 / 3.18

  • TiOX2\ce{TiO2}

    Titanium dioxide (rutile)

    Rutile

    Z
    2
    CN
    Ti⁴⁺ 6 · O²⁻ 3
    Packing
    70.5%
    ρ
    4.25 / 4.23

  • SrTiOX3\ce{SrTiO3}

    Strontium titanate (perovskite)

    Perovskite

    Z
    1
    CN
    Sr²⁺ 12 · Ti⁴⁺ 6 · O²⁻ 2
    Packing
    74.5%
    ρ
    5.12 / 5.11

Data table

CrystalStructure typeSystemCell / pmZCNPackingρ computedρ measured
Po\ce{Po} α-PoloniumSimple cubicCubica = 335.2016 octahedron52.4%9.215—
Fe\ce{Fe} α-IronBody-centred cubicCubica = 286.6528 cube68.0%7.8747.874
Na\ce{Na} SodiumBody-centred cubicCubica = 429.0628 cube68.0%0.9670.970
Nb\ce{Nb} NiobiumBody-centred cubicCubica = 330.0428 cube68.0%8.5838.570
W\ce{W} TungstenBody-centred cubicCubica = 316.5228 cube68.0%19.25419.300
Cu\ce{Cu} CopperFace-centred cubic (ccp)Cubica = 361.49412 cuboctahedron74.0%8.9358.933
Al\ce{Al} AluminiumFace-centred cubic (ccp)Cubica = 404.95412 cuboctahedron74.0%2.6992.700
Ni\ce{Ni} NickelFace-centred cubic (ccp)Cubica = 352.40412 cuboctahedron74.0%8.9088.912
Au\ce{Au} GoldFace-centred cubic (ccp)Cubica = 407.82412 cuboctahedron74.0%19.28919.282
Pb\ce{Pb} LeadFace-centred cubic (ccp)Cubica = 495.08412 cuboctahedron74.0%11.34211.342
Mg\ce{Mg} MagnesiumHexagonal close-packedHexagonala = 320.94, c = 521.08212 anticuboctahedron73.6%1.7371.740
Zn\ce{Zn} ZincHexagonal close-packedHexagonala = 266.49, c = 494.6826 planar hexagon65.1%7.1377.134
C\ce{C} DiamondDiamondCubica = 356.7184 tetrahedron34.0%3.5153.510
Si\ce{Si} SiliconDiamondCubica = 543.1084 tetrahedron34.0%2.3292.330
Ge\ce{Ge} GermaniumDiamondCubica = 565.7584 tetrahedron34.0%5.3285.323
NaCl\ce{NaCl} Sodium chloride (rock salt)Rock salt (NaCl type)Cubica = 564.024Cl⁻ 6 · Na⁺ 6 octahedron65.3%2.1632.170
KCl\ce{KCl} Potassium chlorideRock salt (NaCl type)Cubica = 629.314Cl⁻ 6 · K⁺ 6 octahedron57.5%1.9871.988
CsCl\ce{CsCl} Caesium chlorideCaesium chloride typeCubica = 412.301Cl⁻ 8 · Cs⁺ 8 cube66.9%3.9893.988
ZnS\ce{ZnS} Zinc sulfide (zinc blende)Zinc blendeCubica = 540.934S²⁻ 4 · Zn²⁺ 4 tetrahedron68.2%4.0894.040
ZnO\ce{ZnO} Zinc oxide (wurtzite)WurtziteHexagonala = 324.99, c = 520.662Zn²⁺ 4 · O²⁻ 4 tetrahedron50.0%5.6755.600
CaFX2\ce{CaF2} Calcium fluoride (fluorite)FluoriteCubica = 546.264Ca²⁺ 8 · F⁻ 4 cube60.7%3.1813.180
TiOX2\ce{TiO2} Titanium dioxide (rutile)RutileTetragonala = 459.37, c = 295.872Ti⁴⁺ 6 · O²⁻ 3 octahedron70.5%4.2484.230
SrTiOX3\ce{SrTiO3} Strontium titanate (perovskite)PerovskiteCubica = 390.501Sr²⁺ 12 · Ti⁴⁺ 6 · O²⁻ 2 cuboctahedron74.5%5.1175.110

Packing fractions use touching hard spheres for metals and covalent solids and Shannon ionic radii for ionic solids; the two are not directly comparable. ρ: g/cm³.

Related lessons

Sources

  • W. M. Haynes (ed.), CRC Handbook of Chemistry and Physics, 97th ed. (CRC Press, 2016): lattice parameters of the elements; physical constants of inorganic compounds.
  • R. W. G. Wyckoff, Crystal Structures, 2nd ed., vol. 1 (Interscience, 1963).
  • J. W. Anthony, R. A. Bideaux, K. W. Bladh, M. C. Nichols, Handbook of Mineralogy (Mineralogical Society of America): halite, sylvite, fluorite, rutile, zincite.
  • R. J. Desando, R. C. Lange, J. Inorg. Nucl. Chem. 28, 1837 (1966) — α-polonium.
  • B. J. Skinner, Am. Mineral. 46, 1399 (1961) — sphalerite; E. H. Kisi, M. M. Elcombe, Acta Cryst. C45, 1867 (1989) — wurtzite u.
  • S. C. Abrahams, J. L. Bernstein, J. Chem. Phys. 55, 3206 (1971) — rutile; Yu. A. Abramov et al., Acta Cryst. B51, 942 (1995) — SrTiO₃.
  • R. D. Shannon, Acta Cryst. A32, 751 (1976) — effective ionic radii.