Solid nitrogen

Solid nitrogen is the solid form of the element nitrogen. It is an important component of the surfaces of Pluto^[1] and outer moons of the Solar System such as Neptune's Triton.^[2] Under low or moderate pressure solid nitrogen contains dinitrogen molecules held together by London dispersion forces.^[3] Non-molecular forms of solid nitrogen produced by extreme pressures, have a higher energy density than any other non-nuclear material.^[4]

Solid nitrogen was first made in 1884, by first liquefying hydrogen with evaporating liquid nitrogen, and then allowing the liquid hydrogen to freeze the nitrogen.^[5] Karol Olszewski achieved a world record lowest temperature by evaporating vapour from solid nitrogen getting down to 48 K.^[6] Solid nitrogen is normally made in a laboratory by evaporating liquid nitrogen in a vacuum. The solid produced is porous.^[7]

Bulk properties

Solid nitrogen has several properties relevant to its formation of rocks in the outer Solar System. Even at the low temperatures of solid nitrogen it is fairly volatile and can sublime to form an atmosphere, or condense back into nitrogen frost. At 58 K the ultimate compressive strength is 0.24 MPa. Strength increases as temperature lowers becoming 0.54 MPa at 40.6 K. Elastic modulus varies from 161 to 225 MPa over the same range.^[8] Compared to other materials, solid nitrogen loses cohesion at low pressures and flows in the form of glaciers when amassed. Yet its density is higher than that of water ice, so the forces of buoyancy will naturally transport blocks of water ice towards the surface. This effect has been most clearly observed on Pluto (by the New Horizons space probe in 2015), where water ice makes up a major part of the surface layers as icebergs on top of nitrogen ice.^[9]

Solid nitrogen mixes with solid carbon monoxide and solid methane on the surface of Pluto.^[9]

The thermal conductivity of solid nitrogen is 0.7 W m⁻¹ K⁻¹.^[10] Thermal conductivity varies with temperature and the relation is given by k=180.2×T^0.1041 watts per kelvin.^[11] Specific heat is given by 926.91×e^0.0093T.[11] Its appearance at 50 K (Kelvins) is transparent, while at 20 K it is white.

Nitrogen frost has a density of 0.25 g cm⁻³.^[12] As a bulk material the crystals are pressed together and density is near that of water. It is temperature dependent and given by ρ = 0.0134T² − 0.6981T + 1038.1 kgm⁻³.^[11] The volume coefficient of expansion is given by 2×10⁻⁶T² − 0.0002T + 0.006 K⁻¹.^[11]

The index of refraction at 6328 Å is 1.25 and hardly varies with temperature.^[12]

The speed of sound in solid nitrogen is 1452 m s⁻¹ at 20 K and 1222 m s⁻¹ at 44 K. The longitudinal velocity ranges from 1850 m s⁻¹ at 5 K to 1700 m s⁻¹ at 35 K. With temperature rise the nitrogen changes phase and the longitudinal velocity drops rapidly over a small temperature range to below 1600 m s⁻¹ and then it slowly drops to 1400 m s⁻¹ near the melting point. The transverse velocity is much lower ranging from 900 m s⁻¹ to 800 m s⁻¹ over the same temperature range.^[3]

The bulk modulus of s-N₂ is 2.16 GPa at 20 K, and 1.47 GPa at 44 K.^[3] At temperatures below 30 K solid nitrogen will undergo brittle failure, particularly if strain is applied quickly. Above this temperature the failure mode is ductile failure. Dropping 10 K makes the solid nitrogen 10 times as stiff.^[3]

Melting

Solid nitrogen melts at a higher temperature with increasing ambient pressure.^[13] The slope of the melting point line of the phase diagram is 190 K GPa⁻¹.^[13] At 2.8 GPa nitrogen melts at 308 K, at 4 GPa it melts at 368 K, and at 7 GPa it melts at 484 K.^[13] The melting point increases all the way to 1920 K at a pressure of 50 GPa. Above this pressure the melting point decreases. This is due to a change in the liquid, which becomes denser than the solid at that pressure. The liquid is predicted to become a polymer. The melting point drops to 1400 K at 71 GPa.^[14]

Solid nitrogen is slightly soluble in liquid hydrogen. At 15K there are somewhere between 10¹⁰ and 10¹¹ molecules of nitrogen per cm³ of liquid hydrogen.^[15] At the boiling point of hydrogen the amount in solution is 10⁻⁸ molar fraction.^[16] At 32.5 K the molar concentration of dissolved N₂ in close to critical H₂ is 7.0×10⁻⁶.^[16]

Sublimation

When the pressure is below the triple point, solid nitrogen directly sublimes to gas. The triple point is at 63.14±0.06 K and 0.1255±0.0005 bar.^[17] The vapour pressure has been measured from 20 K up to the triple point. For α-nitrogen (below 35 K) the logarithm of the pressure is given by 12.40 −807.4 × T⁻¹ −3926 T⁻² +6.297×10^{+ 4}T⁻³ −4.633× 10 ⁺⁵T⁻⁴ 1.325× 10^{+ 6}T⁻⁵. For β-nitrogen it is given by 8.514 −458.4T⁻¹ −19870 T⁻² 4.800 × 10^{+ 5}T⁻³ −4.524 × 10⁺⁶T⁻⁴.^[17] Where the solid is not pure nitrogen, the vapour pressure can be estimated using Raoult's law in which the pressure is reduced by the molar concentration. This calculation is relevant for the atmosphere of outer solar system bodies, where there could be a 1% contamination with carbon monoxide and methane.^[17]

Crystal structure

β

There are several known solid forms of molecular dinitrogen. At ambient pressures there are two solid forms. β-N₂ is a hexagonal close packed structure which exists from 35.6 K up to 63.1 5K at which point it melts.^[13] At 45 K the unit cell has a=4.050 Å and c=6.604 Å.^[13] At 4125 atmospheres pressure, and 49K the unit cell sizes have shrunk to a=3.861 Å c=6.265 Å.^[18] If the pressure is increased the c/a ratio stays the same.^[18]

In the β phase, the molecule centres are hexagonal close packed. This means that the c/a ratio is ≈ 1.633 = √8/3. The nitrogen molecules are randomly tipped at an angle of 55° from the c-axis. There is a strong quadrapole-quadrapole interaction between the molecules.^[18]

α

Another phase termed α-N₂ exists below 35.6 K at low pressure and has a cubic structure. The space group is Pa3. At 21 K the unit cell dimension is 5.667 Å.^[13] Under 3785 bars this reduces to 5.433 Å.^[18] At low temperatures the α-phase can be compressed to 3500 atmospheres before it changes (to γ), and as the temperature rises above 20 K, this pressure rises to about 4500 atmospheres.^[18]

The nitrogen molecules are located on the body diagonals of the unit cell cube.^[18]

γ

The tetragonal γ form exists at low temperatures below 44.5 K between about 0.3 GPa and 3 GPa pressure.^[13] The triple point for α/β/γ₂ is at 0.47 GPa and 44.5 K.^[13] The space group of the γ phase is P4₂/mnm and its unit cell has lattice constants a=3.957 Å, c=5.109 Å at 20 K and 4000 bar.^[13] The ¹⁵N isotope converts at a pressure 400 atmospheres lower to the γ form than natural nitrogen, at 20 K.^[18]

In the γ form, nitrogen molecules appear to have the shape of a prolate spheroid, 4.34 Å in the long dimension, and 3.39 Å in the short diameter. The boundary of the molecule appears at an electron density of 0.0135 eÅ⁻³. The molecules line up in rows end to end diagonally on the ab plane. These rows stack side by side with molecules offset by half their length to form layers in the (001) plane, perpendicular to the c-axis. Layers stack on top of each other each rotated by 90° compared to the plane below. Coordinates of atoms in the unit cell are given by (x,x,0),(-x,-x,0),(1/2+x,1/2-x,1/2),(1/2-x,1/2+x,1/2) with x=r/a√8 and r=interatomic distance in nitrogen molecule, = 1.10 Å. (unit cell dimension as above a=3.957 Å). The molecules can vibrate up to 10° on the ab plane, and up to 15° in the direction of the c axis.^[18]

δ

δ-N₂ has a triple point with β and γ Nitrogen at 2.3 GPa and 150 K. δ-N₂ has a cubic structure with space group pm3m. The lattice constant is 1.164 at 300 K but 4.9 GPa.^[13] At room temperature and high pressure δ-nitrogen is ordered in its molecular orientation^[19]

Above the pressure of 2 GPa there is the lower temperature rhombohedral phase ε-N₂ and above 80 K cubic δ-N₂.^[13] The triple point of δ-N₂, β-N₂ and liquid is somewhere between 8 and 10 GPa and 555 and 578 K.^[13]

ε

ε-N₂ is rhombohedral with space group R3c is a high pressure form of dinitrogen, stable at 13 GPa.^[20] Cell dimensions are a=8.02 Å, b=8.02 Å, c=11.104 Å, α=β=90°, γ=120°, volume 618.5 Å³, Z=24.^[21] ε-nitrogen has disordered orientation.^[19]

In the phase diagram ε-N₂ appears at pressures above 2 GPa at temperatures below 50 K. Below this the γ form is stable. When heated ε-N₂ transforms to δ-N₂^[22] 10.1063/1.450310

ζ

Above 69 GPa ε-N₂ transforms to an orthorhombic phase designated by ζ-N₂ with a 6% reduction in volume. The space group of ζ-N₂ is P222₁. The lattice constants are a=4.159 Å, b=2.765 Å, c=5.039 Å with eight atoms per unit cell.^[4] At 80 GPa the distance between nitrogen atoms in the molecules is 0.982 Å, but the closest distance to other nitrogen atoms is 1.93 Å. As the pressure increases to 138 GPa the bond in the molecules actually lengthens to 1.002 Å while intermolecular distances shorten.^[4]

θ

A ζ-N₂ phase compressed to 95 GPa and then heated to over 600 K produces a new structure called θ nitrogen which has a uniform translucent appearance.^[23]

ι

When ε-N₂ is heated to 750 K at a pressure between 65 and 70 GPa a high temperature phase ι-N₂ forms. This can also be formed from θ nitrogen by decompression and heating.^[23]

μ

When the ζ-N₂ phase is compressed at room temperature over 150 GPa an amorphous form is produced.^[4] This is designated as the μ-phase. It is a narrow gap semiconductor. The μ-phase has been brought to atmospheric pressure by first cooling it to 100 K.^[24]

Cubic gauche

Under pressures higher than 110 GPa and temperatures around 2000 K nitrogen forms a network solid, bound by single covalent bonds in what is called a cubic-gauche structure, abbreviated as cg-N. This substance is very stiff with a bulk modulus around 298 GPa, similar to diamond.^[25] It is very high energy and is metastable when pressure is released.^[26] The cubic-gauche form has space group I2₁3.^[20] The unit cell edge is 3.805 Å.^[20] There are eight nitrogen atoms per unit cell.^[20] The bond angles are very close to tetrahedral. The structure contains rings of nitrogen atoms that are fused together. The position of the lone pairs of electrons is ranged so that their overlap is minimised.^[24] The difference in bond energy varies from 0.83 eV per atom in nitrogen gas to 4.94 eV per atom, so having a difference in energy of over 4 eV per atom. This cubic-gauche nitrogen is the highest energy non-nuclear material and is being investigated for use in explosives and rocket fuel.^[4] Its energy density is 33 kJ g⁻¹ which is over three times the energy density of HMX.^[27] cg-N has all bonds the same length^[4] of 1.346 Å at 115 GPa.^[25] The cubic-gauche structure for nitrogen was predicted by Christian Mailhiot, Lin Yang and A. K. McMahan in 1992.^[28] Their prediction was for a bond lengths of 1.40 Å, bond angles of 114.0° and dihedral angless of −106.8°. The term gauche refers to the odd dihedral angles, if it was 0° it would be called cis, and if 180° it would be called trans. The dihedral angle Φ is related to the bond angle θ by sec(Φ) = sec(θ) − 1. The coordinate of one atom in the unit cell at x,x,x also determines the bond angle by cos(θ) = x(x-1/4)/(x^{2+(x-1/4)2).[28]}

Poly-N

Another network solid nitrogen called poly-N and abbreviated pN was predicted in 2006.^[20] pN has space group C2/c and cell dimensions a = 5.49 Å, β = 87.68°. Other higher pressure polymeric forms are predicted in theory, and a metallic form is expected if the pressure is high enough.^[29]

Layered polymetric

The LP-N phase is an actually produced, layered polymetric phase stable between 120 and 180 GPa. It has a density of 4.85 g cm⁻³ at the low pressure end of its range.^[30] The structure contains layers of fused rings of seven nitrogen atoms.^[24]

Others

Yet other phases of solid dinitrogen are termed ζ'-N₂ and κ-N₂.^[24]

Related substances

Under pressure nitrogen can form crystalline van der Waals compounds with other molecules. It can form an orthorhombic phase with methane above 5 GPa.^[31] With helium He(N₂)₁₁ is formed.^[19] N₂ crystallizes with water in nitrogen clathrate and in a mixture with oxygen O₂ and water in air clathrate.^[32]

Helium

Solid nitrogen can dissolve 2 mole % He under pressure in its disordered phases such as the γ-phase. Under higher pressure 9 mol% He can react with ε-nitrogen to form a hexagonal birefringent crystalline van der Waals compound. The unit cell contains 22 nitrogen atoms and 2 helium atoms. It has a volume of 580 Å³ for a pressure of 11 GPa decreasing to 515 Å³ at 14 GPa.^[19] It resembles the ε-phase.^[33] At 14.5 GPa and 295 K the unit cell has space group P6₃/m and a=7.936 Å c=9.360 Å. At 28 GPa a transition happens in which the orientation of N₂ molecules becomes more ordered. When the pressure on He(N₂)₁₁ exceeds 135 GPa the substance changes from clear to black, and takes on an amorphous form similar to η-N₂.^[34]

Methane

Solid nitrogen can crystallise with some solid methane included. At 55 K the molar percentage can range up to 16.35% CH₄, and at 40 K only 5%. In the complementary situation, solid methane can include some nitrogen in its crystals, up to 17.31% nitrogen. As the temperature drops, less methane can dissolve in solid nitrogen, and in α-N₂ there is a major drop in methane solubility. These mixtures are prevalent in outer Solar System objects such as Pluto that have both nitrogen and methane on their surfaces.^[35] At room temperature there is a clathrate of methane and nitrogen in 1:1 ratio formed at pressures over 5.6 GPa.^[36]

Carbon monoxide

The carbon monoxide molecule (CO) is very similar to dinitrogen in size, and it can mix in all proportions with solid nitrogen without changing crystal structure. Carbon monoxide is also found on the surfaces of Pluto and Triton at levels below 1%. Variations in the infrared linewidth of carbon monoxide absorption can reveal the concentration.^[37]

Noble gases

Neon or xenon atoms can also be included in solid nitrogen in the β and δ phases. Inclusion of neon pushes the β−δ phase boundary to higher pressures.^[38] Argon is also very miscible in solid nitrogen.^[38] For compositions of argon and nitrogen with 60% to 70% nitrogen, the hexagonal form remains stable to 0 K.^[39] A van der Waals compound of xenon and nitrogen exists above 5.3 GPa.^[38] A van der Waals compounds of neon and nitrogen was shown using Raman spectroscopy.^[38] The compound has formula (N₂)₆Ne₇. It has a hexagonal structure, with a=14.400 c=8.0940 at a pressure of 8 GPa. A van der Waals compound with argon is not known.^[40]

Hydrogen

With dideuterium, a clathrate (N₂)₁₂D₂ exits around 70 GPa.^[41]

Oxygen

Solid nitrogen can take up to a one fifth substitution by oxygen O₂ and still keep the same crystal structure.^[42] δ-N₂ can be substituted by up to 95% O₂ and retain the same structure. Solid O₂ can only have a solid solution of 5% or less of N₂.^[42]

Radiation treatment

When solid nitrogen is irradiated by high speed protons or electrons, several reactive radicals are formed, including atomic nitrogen (N), nitrogen cations (N⁺), dinitrogen cation (N₂⁺), trinitrogen radicals (N₃ and N₃⁺), and azide (N₃⁻).^[43]

Use

Solid nitrogen is used in a slush mixture with liquid nitrogen in order to cool faster than with liquid nitrogen alone, useful for applications such as sperm cryopreservation.^[44] The semi-solid mixture can also be called slush nitrogen^[45] or SN2.^[46]

Solid nitrogen is used as a matrix on which to store and study reactive chemical species, such as free radicals or isolated atoms.^[47] One use is to study dinitrogen complexes of metals in isolation from other molecules.^[48]

Natural occurrence

Much of the surface of Triton is covered in the hexagonal form of solid nitrogen (the β crystal phase), which can be seen as a bluish green band around the equator in this photomosaic.

Solid nitrogen forms a large part of the surface of Pluto and the Neptunian moon Triton. On Pluto it was directly observed for the first time in July 2015 by the New Horizons space probe and on Triton it was directly observed by the Voyager 2 space probe in August 1989.

On Triton, solid nitrogen takes the form of frost crystals and a transparent sheet layer of annealed nitrogen ice, often referred to as a "glaze".^[2] Geysers of nitrogen gas were observed by Voyager 2 to spew from the subpolar regions around Triton's southern polar ice cap.^[49] A possible explanation of this observed phenomenon is that the sun shines through the transparent layer of nitrogen ice, heating the layers beneath. Nitrogen sublimes and eventually erupts through holes in the upper layer, carrying dust along with it and creating dark streaks.

References