COMPILATION OF THE ENGINEERING PROPERTIES OF SOLID HYDROGEN
Prepared by
40 Nutmeg Lane
Glastonbury, CT 06033
Last Update March, 2002
Table of Contents
1. Introduction
2. Reference Data on Solid Hydrogen
3. Material/Thermal Data
4. Mechanical
5. Thermodynamic
Solid Hydrogen
Introduction. Hydrogen is probably the most extensively studied form of matter that exists (e.g. [1], [2] because many of its important properties can be predicted theoretically from first principles, and because these results can be compared with experimental data. The theory of hydrogen has often functioned as a testbed of general theories of atomic and molecular behavior. Not withstanding all of this work, most of the common mechanical properties of solid molecular hydrogen are beyond calculation, in part as a result of the non-ideality of the macroscopic crystal.
Figure 1. Conversion of Ortho- to Para Hydrogen for Uncatalyzed Liquid Hydrogen.
The description of molecular hydrogen is complicated by the existence of macroscopic crystals characterized by different nuclear spin states; parahydrogen has its nucleon spins antialigned, and orthohydrogen has nucleon spins aligned. The stable relative concentration of these states is temperature dependent; 75% of hydrogen is orthohydrogen at room temperature (defined as "normal" hydrogen) whereas equilibrium solid hydrogen is almost pure parahydrogen. The spin states are metastable, however, and any concentration of either spin state can be created at any temperature through the action of catalysts. Since the natural equilibrium concentration often changes with time as the hydrogen is cooled or heated, many properties of solid hydrogen are given as a function of spin state concentration. Most of the physical properties of hydrogen are mildly dependent on the relative spin state mixture, but there is a significant difference between the specific heats and thermal conductivities of normal and parahydrogen in some temperature ranges [3]. As shown in Fig. 1 the conversion from normal to parahydrogen is slow. Rotational diffusion is a significant phenomenon also. The conversion rate of ortho to parahydrogen has implications for any experiment forming solid hydrogen because cooling a room temperature hydrogen gas must either catalyze the spin transformation or absorb the large heat of conversion as the solid is formed.
M/Mo is the Fraction of the Original Amount of Liquid Remaining [3].
Hydrogen has a triple point temperature of 14 K and a triple point pressure of 0.070 atm (54 torr) [3]. Condensation from the vapor to the solid is naturally relatively slow because of these low pressures.
Hydrogen is highly reactive. Bulk solid hydrogen, when grown from a melt in equilibrium with its vapor pressure forms as a hcp lattice for both ortho and para species [2]. The description of the crystal structure is complicated, however, because an fcc lattice is stable at temperatures below 3 K, and can occur at higher temperatures for a solid grown from a gas [1], [2]. Parahydrogen is always most stable as an hcp lattice, whereas orthohydrogen undergoes a phase transition at low temperatures. It can be expected that these two crystals have very different properties. The fcc crystal will convert to hcp at higher temperatures.
Solid hydrogen has many peculiar properties as a result of its single proton and electron atoms. The solid is a translational quantum solid, where the atoms are not localized at T = 0 K [2]. It is also relatively highly compressible - by 100% at 10 kbar. The density of solid hydrogen and its isotopes are low (0.088, 0.20 and 0.31 g/cm3 for H2, D2 and T2, respectively). The yield strength of the solid is also small (~ 5 bar).
Past work has centered on microstructural and thermodynamic properties. The microscopic properties are both calculated and derived from macroscopic experiments. As a Van der Waals solid, the attraction between hydrogen molecules is weak and solid condensations will tend not to form a stable surface layer or hard particles. Because hydrogen tends to be very pure when used it usually exhibits significant supercooling when approaching phase changes. Questions of lattice packing and how to achieve even mixing of solids are important. The important engineering properties of solid hydrogen fall into the following categories: Mechanical, Thermal, Thermodynamic, Chemical, Optical, and Others.
Reference Data on Solid Hydrogen. The following is a summary of the known engineering properties of solid cryogenic molecular hydrogen that have been found through ongoing literature searches by Dr. Bates. This work compilation has been reported in a less complete form previously [4]. Other major compilations that are more extensive include work at NBS (now NIST) [5]. A summary of more modern research is planned by the Institute of Low Temperature.
Solid hydrogen is a crystal that forms when liquid hydrogen is cooled much below 14 K (supercooling usually occurs). The properties of solid hydrogen will be grouped by generic type. The values given are engineering values; extreme precision is avoided as being irrelevant to engineering design, and slight variations of a property as a function of some other varying parameter are not listed. All parameters are listed for completeness; a lack of entry does not necessarily imply that a value does not exist in the literature, only that it has not yet been found. The properties of the equilibrium spin mixture are given in general, unless there is a significant variation for normal hydrogen.
Material/Thermal
Crystal Structure ---------------- High Temperature (>4 K) - hexagonal close packed (hcp)* (low pressure)
Low Temperature (< 4 K) - fcc*
The issue of phase change is complicated by the quantum nature of the solid and the marginal stability of the fcc phase. Parahydrogen will remain in the hcp phase if formed from a melt and cooled to 0 K. However, it will form the fcc structure if condensed to a solid from the vapor. Orthohydrogen will behave similarly except that it will change slowly to the fcc phase, although this is not usually relevant since orthohydrogen itself is not stable at these temperatures. If formed, the fcc phase can remain stable at higher temperatures. Other phases are thought to exist at higher pressures.
Small crystallites tend to be formed rather than larger crystals as a result of strain caused by large thermal expansion. [2]
Density ------------------------------ 22.7 cm 3/mole, 0.088 g/cm3 [6] (does not vary significantly with ortho/para concentration [2])
An increase of 1% in density results from the application of approximately 19 atm of pressure: [2] the density increase decreases with pressure; see compressibility. The density increase with phase change temperature was an early motivation of cryogenic engineers for the interest in solid hydrogen, and remains an advantage.
Boiling point ----------------------- 20.4 K [3] (0.21% ortho, 99.79% para - equilibrium)
Freezing point ---------------------- 14 K [6]
Critical temperature --------------- 33 K [6]
Critical pressure ------------------- 13 atm [6]
Critical density --------------------- 66 cm 3/mole [6]
Triple point temperature ---------- 13.8 K [6]
Triple point pressure -------------- 0.070 atm [7]
Vapor pressure --------------------- Vapor pressure of the solid (20.4 K equilibrium hydrogen) follows the equation
log P (mm Hg) = A + B/T + CT,
where A = 4.62, B = -47.02, C = 0.02023, although the vapor pressures for a mixtures closer to normal hydrogen are somewhat lower [3].
Solid Vapor Pressure: 10 K 1.93 mm Hg
11 K---5.62
12 K---13.9
13 K---30.2
Recrystallization rate -------------- No Information
Solid structure of mixtures -------- No Information
Frost structure ---------------------- No Information
Absorption of liquids into the solid --------No Information
Mass diffusivity ---------------- Thermally activated: 6.3 x 10-12 cm2/sec. - at 10 K - t = 3.8 x 10 -5 mean interchange time [2]
D = Doe-E/kT, E/k = 200 ± 10 K, Do = 3 x 10-3 cm2/sec. [2]
Enhanced quantum rotational diffusion occurs at low (1 K) temperatures [2]
Mechanical
Mechanical - Solid hydrogen is known to behave as almost a hydraulic fluid at temperatures near its melting point, with a measured shear strength of approximately 5 atm at about 10 K. The strength varies with temperature, such that at liquid helium temperatures and below the solid is at least a factor of 2 stronger and harder; its degree of brittleness is not known. The term for behavior near the melting point in metallurgy is "hot strength". Strength, hardness and other cohesion-related properties will decrease near the melting point. Usually the decrease is not linear, but much greater as the melting point is reached. If there are significant changes in properties, temperature control may be a means of controlling material properties to achieve a variety of different goals. Extensive work on the mechanical properties of solid hydrogen has been done at Karkov in the former Soviet Union.
Shear Strength --------------------- 0.75 MPa at 10 K [8]
Compressive Strength -------------- No Information
Figure 2. Temperature Dependences of the Mechanical Properties of Normal and Parahydrogen [8] (1 g/mm2 = 1.422 psi) 1 - Young's Modulus, 2 - Shear Modulus, 3 - Tensile Strength, 4. Nominal Yield Stress, ε - Relative Elongation.
Compressibility ----------- density increase of ~100 % at ~20 kbar (most solids compress a few %) The following equation applies [2]:
P(V) = Y5 ∑ Bn (Y2 - 1)n n = 1,2 Y = (Vo/V) 1/3
B1 = 2786.8 bar B2 = 6336.4 bar V o = 23.14 cm3/mole
This equation implies a 1% increase in density under a 19 atm pressure increase from vacuum.
Poissons ratio ------------- 0.25 (isothermal) [9]
Hardness ----------------------------- No Information
Impact Strength --------------------- No Information
Creep and relaxation behavior --- No Information
Brittle fracture characteristics ---- No Information
Abrasiveness/Friction coefficient No Information
Sound velocity (4K) --------------- Vlong = 2100, Vtransv = 1140 m/s [9]
Thermodynamic
Specific heat ----------------------- Shown in Fig. 3. approximately 1 cal/mole-K at 14 K for normal
hydrogen; the specific heats of different mixtures diverge below 10 K, and there is an anomaly associated with an orientation transition temperature near 1 K, shown in Fig. 4. Figure 5 places the specific heat of the solid in the context of the behavior of the liquid.
Figure 3. The Specific Heat of Solid Hydrogen Plotted as a Function of Ortho Percentage [10], (0% [10a] .
Figure 4. λ -Anomalies in Solid Hydrogen, (a) 74% Orthohydrogen, (b) 66% Orthohydrogen [10]
>
Figure 5. The Heat Capacity of Saturated Liquid and Solid Parahydrogen. (Below 20 K [11], Above 20 K [12]).
Debye Temperature ----------------------- 120 K [2]
Thermal conductivity ---------------- Liquid parahydrogen: 0.153 +- 0.058 Btu/dr-ft-F
Solid parahydrogen: 0.153 +- 0.058 Btu/dr-ft-F
The thermal conductivity depends dramatically on ortho concentration, changing from a peak of 1.5 watts/cm-K for 0.34% ortho at 4 K (decreasing rapidly at higher temperatures), to a broad peak at 0.07 watts/cm-K for n-hydrogen at 10 K. It has never been measured for the fcc low temperature phase [2].
Thermal Diffusivity ----------------- Calculating the thermal diffusivity of gamma solid hydrogen:
For normal hydrogen:
thermal diffusivity = (0.07 watts/cm-K)/(1/23 mole/cm 3)(4.18 J/mole-K)
= 0.385 cm2/sec
For pure parahydrogen:
thermal diffusivity = 8.25 cm2/sec
Thermal expansion coefficient ------- H2 shrinks as much as 3% when cooled from 4 K to 1 K [2].
Heat of Fusion ---------------- 28.0 cal/mol at 14 K and 53 mm Hg. [6]
Heat of Sublimation ---------------- 89 K/molecule [2] (for parahydrogen)
Heat of Conversion --------------- 338 cal/mol, [6] (intrinsic rate in the zero pressure solid: 1.90%/hr [2])
Heat of Vaporization -------------- The heat of vaporization of liquid hydrogen is given by:
Lv = 217.0 - 0.27(T-16.6)2 + 1.4x + 2.9x2 cal/mole
where x is the orthohydrogen male fraction, and T the kelvin temperature.
Temperature
Figure 6. Thermal Conductivity of Hydrogen at Constant Orthohydrogen Concentration vs. Temperature [5].
Chemical
Reactivity --------------------------- No Information
Solubility ---------------------------- not soluble in helium
Optical
Index of refraction (liquid) --------- 1.1358 @19 K and 546 nm [14]
Index of refraction (solid) --------- Figure 7
Figure 7. Index of Refraction of Solid para-H2
Absorption -------------------------- The absorption spectrum of hydrogen is well known.
Optical activity ---------------------- No Information
Color ------------------------------- Solid hydrogen is a clear crystal.
Gamma Ray Attenuation --------- No Information
Figure 8. Thermal Conductivity of Hydrogen at Constant Orthohydrogen Concentration vs. Temperature for Low Ortho Concentrations. [13]
Electrical/Magnetic
Conductivity ------------------------ Insulator
Dielectric strength ------------------ 1.294 [15]
Dielectric constant ----------------- No Information
Power/Dissipation factor ---------- No Information
Volume resistivity ------------------ 1019 (not constant) [16]
Susceptibility ------------------------ No Information
Notes on Solid H2:
3.1.2. Properties of Cryogenic Liquid Hydrogen. It is important to put into the context of the engineering behavior of materials that we are familiar with the material property data for the various cryogens that will be encountered in this program. The difference in surface tension between common liquids and liquid cryogens has been discussed above. The numerical data is as follows:
Surface Tension(dynes/cm): Room temp. Liquids: - 10-70 N2 (70 K): 10.5
Hydrogen (18 K): - 2.3 Helium (4 K): - 0.12
Viscosity (micropoise): Room Temp. Gases: - 100-300 Hydrogen Gas - 90 (300 K), 10 (20 K) Helium Gas - 200 (300 K), 21 (10 K) Room Temp. Liquids: 500-1500 (not oils) Hydrogen Liquid - 234 - 131 (15 - 21 K) Helium Liquid - 20 - 30 (2 - 4 K)
Temp.(K).............Density(g/cm3 ).................Sound velocity(m/sec)
......20........................0.0712......................1200
......18........................0.0732......................1250
......16........................0.0752......................1302
Dielectric constant ---------- 1.25 [3] for triple point hydrogen liquid
REFERENCES
1. J. van Kranendonk, Solid Hydrogen, Plenum Press, New York, NY, (1983).
2. I. F. Silvera, "The solid molecular hydrogens in the condensed phase:Fundamentals and static properties.," Rev. of Mod. Phys., 522, 2, Part 1, 393 (1980).
3. R. B. Scott, Cryogenic Engineering, Met-Chem Research, Boulder, CO, (1959).
4. S. C. Bates, "Prototype Cryogenic Solid Hydrogen Storage and Pellet Injection System," SBIR Phase I Final Report, USAF Phillips Lab Contract F04611-93-C-0086, Report #PL-TR-94-3015, (1994).
5. H. M. Roder, G. E. Childs, R.D. McCarty and P.E. Angerhofer, "Survey of the Properties of the Hydrogen Isotypes Below Their Critical Temperature," NBS Technical Note 641, (1973).
6. H.W. Wooley, R.B. Scott, and F.G. Brickwedde, "J," J. Research NBS, 41, RP 1932, 379 (1948).
7. H. G. Hoge and J. W. Lassiter, "J Research NBS, 47, 75, RP 2229, (1951).
8. Y. E. Stetsenko, D.N. Bol'shutkin, and L.A. Indan, "Influence of Orientational Ordering of Molecules on the Mechanical Properties of Hydrogen," Sov. Phys. Solid State, 12, 12, 2958 (1971).
9. P. A. Bezuglyi, R. O. Plakhotin, and L.M. Tarasenko, "Velocities of Ultrasonic Waves in Polycrystalline Para-Hydrogen," Sov. Phys. Solid State, 13, 1, 309 (1971).
10. R.W. Hill and B.W.A. Ricketson, "A λ -Anomaly in the Specific Heat of Solid Hydrogen," Phil. Mag., 45, 277 (1954).
11. A. L. Smith, N. C. Hallet, and H. L. Johnston, "J. Amer. Chem. Soc., 76, 1486 (1954).
12. H.L. Johnston, J.T. Clark, E.B. Rifkin, and E.C. Kerr, "e," J. Amer. Chem. Soc., 72, 3933 (1950).
13. R.G. Bohn and C.F. Mate, "Thermal Conductivity of Solid Hydrogen," Phys. Rev. B, 2, 2121 (1970).
14. G. E. Childs, "Cryogenic Engineering Conference 15th, Los Angeles, CA, Paper D-2, (1961).
15. B.G. Udovidchenko and V.G. Manzhelii, "Isothermal Compressibility of Solid Parahydrogen," J. Low Temp. Phys., 3, 4, 429 (1970).
16. W. L. Willis, "Electrical Conductivity of Some Cryogenic Fluids," Cryogenics, 6, 5, (1966).