Sublimation Coefficient Research Articles

Euclid preparation

Material outgassing in a vacuum leads to molecular contamination, a well-known problem in spaceflight. Water is the most common contaminant in cryogenic spacecraft, altering numerous properties of optical systems. Too much ice means that Euclid’s calibration requirements cannot be met anymore. Euclid must then be thermally decontaminated, which is a month-long risky operation. We need to understand how ice affects our data to build adequate calibration and survey plans. A comprehensive analysis in the context of an astrophysical space survey has not been done before. In this paper we look at other spacecraft with well-documented outgassing records. We then review the formation of thin ice films, and find that for Euclid a mix of amorphous and crystalline ices is expected. Their surface topography – and thus optical properties – depend on the competing energetic needs of the substrate-water and the water-water interfaces, and they are hard to predict with current theories. We illustrate that with scanning-tunnelling and atomic-force microscope images of thin ice films. Sophisticated tools exist to compute contamination rates, and we must understand their underlying physical principles and uncertainties. We find considerable knowledge errors on the diffusion and sublimation coefficients, limiting the accuracy of outgassing estimates. We developed a water transport model to compute contamination rates in Euclid, and find agreement with industry estimates within the uncertainties. Tests of the Euclid flight hardware in space simulators did not pick up significant contamination signals, but they were also not geared towards this purpose; our in-flight calibration observations will be much more sensitive. To derive a calibration and decontamination strategy, we need to understand the link between the amount of ice in the optics and its effect on the data. There is little research about this, possibly because other spacecraft can decontaminate more easily, quenching the need for a deeper understanding. In our second paper, we quantify the impact of iced optics on Euclid’s data.

Sublimation behavior of AlN in nitrogen and argon at conditions used for high-temperature annealing

High-temperature annealing (HTA) is one of the most promising techniques to produce high-quality, cost-efficient AlN templates for further epitaxial growth of AlGaN devices. Unfortunately, the yield of this process seems to be limited due to the restricting face-to-face configuration that is typically used, in which contaminations of the template surface can occur easily. A high yield is crucial for process transfer into industry. Indeed, templates that are annealed in open-face configuration suffer from surface degradation due to excessive AlN evaporation during the course of the annealing process. To highlight the physics that are restricting the open-face approach of the process, sublimation behavior of AlN at temperatures and atmospheres typically used in HTA processes has to be examined. In this study, we use the Knudsen effusion mass spectrometry technique to confirm the previously published results on equilibrium partial pressures of species above AlN. Based on the experimentally determined data and further AlN sublimation experiments, the apparent sublimation coefficient of AlN in N2 and Ar atmospheres at HTA process conditions can be derived. Despite N2 having a stabilizing effect on AlN during HTA, the still high decomposition rates of several hundred nanometers per hour can explain the excessive damage that is typically observed if AlN/sapphire templates are annealed in an open-face configuration. Finally, based on theoretical considerations, a strategy to reduce the sublimation of AlN during HTA in open-face configuration is suggested.

Evaluation of Sublimation Kinetics for Phenolic Impregnated Carbon Ablator

Recession analyses of stagnation tests conducted in NASA Ames Research Center arcjet facilities with surface heat fluxes high enough for carbon char to sublimate are performed and compared with data. The axisymmetric recession computations are based on both the finite-rate gas–surface interaction model and the standard chemical equilibrium surface ablation model. The finite-rate gas–surface interaction model is studied using three different sets of sublimation coefficients, which are obtained through direct measurements. The standard chemical equilibrium ablation model is established through the tables. The ablating material used in these arcjet tests is phenolic impregnated carbon ablator. The prediction of axisymmetric surface recession is achieved by implicitly coupling a material thermal response code and a flow code. The material thermal response code used in this study is the Two-Dimensional Implicit Thermal-Response and Ablation program, which predicts charring material thermal response and shape change. The flow code solves the reacting Navier–Stokes equations using the data parallel line relaxation method. The recession predictions for three selected arcjet conditions with various base radii are presented. The effect of sticking coefficient for carbon sublimation on recession prediction is investigated, and the prediction discrepancy between finite-rate and chemical equilibrium models is examined and discussed in detail.

Investigation on in-situ water ice recovery considering energy efficiency at the lunar south pole

It is of great significance to realize the in-situ utilization of lunar water ice for the establishment and sustainable operation of the future lunar base. Considering the location of water ice in the lunar polar regions, based on the in-situ thermal mining method, an integrated approach for the water ice recovery was established. The evolution characteristics of average temperature of the icy soil and water vapor collection rate with the mining time were analyzed. The optimal mining temperature for the recovery of water ice was studied. The energy efficiency under various arrangement densities of heating elements was assessed with the optimal number of heating elements determined. The results show that as the mining time increases, for different target mining temperatures, the average temperature of the icy soil rapidly rise at first, and then tend to stabilize. The water vapor collection rates at different target mining temperatures vary greatly due to the difference in saturated vapor pressure of water ice. At high mining temperatures, the sublimation coefficient also significantly affects the process of water vapor collection. The water vapor collection rate with sublimation coefficient being unity is up to 36% larger than that with non-constant sublimation coefficient for the lunar soil under investigation within four earth weeks at the target mining temperature of 240 K. In addition, the increase of the mining temperature increases the water vapor collection rate, and at the same time, the water vapor pressure in the capture tent also increases, which may lead to the instability of the water ice production system. Combining with water vapor collection rate and change rate of water vapor pressure in the capture tent, the temperature of 220 K is obtained as the optimal target mining temperature. Furthermore, for the lunar soil in this work, the energy efficiencies for water ice production with seven and nine heating elements are same, and greater than that with five heating elements. Considering the energy efficiency, the minimum number of heating elements could be determined.

Effect of air parameters on ice sublimation in ice rink

This study aims at the sublimation rate of ice and analyzes the influence of supply air and ice parameters on ice surface smoothness. The sublimation rate can be expressed as the product of the sublimation coefficient and humidity ratio difference. COMSOL Multiphysics is adopted as a simulation tool to calculate the associated ice sublimation rate. In ice rinks, the sublimation coefficient is 0.1–0.2 mm/(h·kPa), and the sublimation rate is 0–0.07 mm/h. The results show that the main factor affecting the sublimation coefficient is air velocity over the ice surface. Therefore, the ice sublimation can be decreased by reducing air velocity and decreasing humidity ratio difference between the air and ice surface. The aforementioned findings were applied in an actual curling venue to reduce the sublimation of the ice surface, and the accumulated sublimation within 10 h was reduced from 0.24 mm to 0.016 mm, which effectively solved the problem of ice surface unevenness. This study working on the ice sublimation rate provides inspiration for maintaining the ice stability in ice rinks and improving the quality of venues.

Sublimation of buried cometary ice

The sublimation of ice covered by dust is a common way of outgassing of comets. The rate of this process depends on the thermal conductivity and permeability of dust, as well as the properties of the ice itself. It can be calculated using the Hertz-Knudsen equation, corrected for temperature dependent sublimation coefficient αs(T) (Gundlach et al., 2011; Kossacki et al., 1999; Kossacki & Leliwa-Kopystynski, 2014; Kossacki et al., 2017) and the Knudsen equation for the permeability of dust. In this work we present direct experimental verification of this set of equations using sand with different granulation: coarse (grain radii rg = 0.5 − 1 mm), medium (rg = 0.25 − 0.5 mm), fine (rg = 0.125 = 0.25 mm) and unsorted (rg = 0 − 1 mm, rg, av = 0.5 mm). We have found that at T < 220 K the measured rate of recession of the surface is correctly reproduced if αs(T) is the same as determined for the uncovered ice (Kossacki & Leliwa-Kopystynski, 2014). The characteristic radius of pores in the Knudsen equation is approximately equal to, or greater than the arithmetic average of the largest and the smallest radii of grains.

Sublimation of cometary ices in the presence of organic volatiles II

Evolution of the surfaces of cometary nuclei is determined by the sublimation of ice. The rate of sublimation is commonly calculated using the simple Hertz–Knudsen formula, which should be corrected by a temperature dependent sublimation coefficient αs (Kossacki et al., 1999; Gundlach et al., 2011; Kossacki and Leliwa-Kopystynski, 2014). In Kossacki et al. (2017) the temperature dependence of αs for water ice with acetone and methanol present in comets was analyzed. In this work the influence of propanal at the temperature ~195–~230 K and formamide at the temperature ~200–~235 K were investigated. Experiments were performed with slab ice and porous fine-grained ice. It is found, that the presence of propanal reduces the sublimation coefficient at T < 207 K and enhances at T > 208 K. The presence of formamide reduced the sublimation coefficient in the whole investigated temperature range. Porous fine-grained ice sublimed up to four times slower than non-porous one.

Sublimation of cometary ices in the presence of organic volatiles

Evolution of the surfaces of cometary nuclei is determined by the sublimation of ice. The rate of sublimation is commonly calculated using the simple Hertz–Knudsen formula, which should be corrected by a temperature dependent sublimation coefficient αs (Kossacki et al., 1999; Gundlach et al., 2011; Kossacki and Leliwa–Kopystynski, 2014). In this work influence of C3H6O (acetone), and CH3OH (methanol) present in cometary ice on the sublimation coefficient is investigated. We have found, that the mass fraction of admixtures ≤ 2% in water ice is sufficient for an increase of αs by a factor about 5, depending on the temperature. The sublimation coefficient is sensitive to very small concentrations of admixtures. When the admixture is acetone and the mass fraction f=0.005 is αs(215 K) ∼ 0.46 instead of ∼ 0.18 for pure water ice. When f=0.01 is αs(215 K) ∼ 0.74, and when f=0.02 is αs(215 K) ∼ 0.78. The presence of 0.01 mass fraction of methanol has similar influence on the sublimation coefficient as the presence of 0.01 mass fraction of acetone. At temperatures T > 235 K for all investigated compositions of ice αs ∼ 0.15.

Comet 9P/Tempel 1: Evolution of the surface

Comet 9P/Tempel 1 was imaged during two consecutive perihelion passages. According to Thomas et al. (Thomas, et al. [2013]. Icarus 222, 453–466) one scarp located at 40°S receded up to 50m. I attempted to use this observation to constrain local material properties of the nucleus. For this purpose I simulated recession of a model scarp due to sub-dust sublimation of ice. I have found, that the observed recession of the scarp can be reproduced when the dust mantle has high porosity about 0.8 and low thermal conductivity about 10mWm−1K−1, as found for artificial dust layers (Krause, M., Blum, J., Skorov, Yu.V., Trieloff, M. [2011]. Icarus 214, 286–296). Taking into account the temperature dependence of the sublimation coefficient of ice reduces the calculated recession rate of the scarp by about 40%.

Temperature dependence of the sublimation rate of water ice: Influence of impurities

The sublimation rate of ice is commonly calculated using the simple Hertz–Knudsen formula. This formula is derived from the kinetic theory of gases and ignores microphysical processes determining the actual sublimation rate. The microphysical processes can be accounted for by including the temperature dependent sublimation coefficient (Kossacki, K.J., et al. [1999]. Planet. Space Sci. 47, 1521–1530; Gundlach, B., Skorov, Y.V., Blum, J. [2011]. Icarus 213, 710–719). Kossacki and Markiewicz (Kossacki, K.J., Markiewicz, W.J. [2013]. Icarus 224, 172–177) discussed to what extent inaccuracy of the simple Hertz–Knudsen equation affects the calculated temperature of Comet 67P/Churyumov-Gerasimenko. Numerical simulations presented in Kossacki and Markiewicz (Kossacki, K.J., Markiewicz, W.J. [2013]. Icarus 224, 172–177) indicate, that derivation of the temperature below the dust mantle from the measured water production rate ignoring temperature dependence of the sublimation coefficient can lead to an underestimate of the temperature by more than 10K. Thus, it is important to know the dependence on the sublimation coefficient of the composition of the real cometary ice, which can be far from purity.We intended to check whether a small amount of dissolved minerals can affect the temperature dependence of the sublimation coefficient of ice. According to our experiments the answer is positive.

Comet 67P/CG: Influence of the sublimation coefficient on the temperature and outgassing

The sublimation rate of ice is commonly calculated using simple Hertz–Knudsen formula. This formula is derived from the kinetic theory of gases and ignores microphysical processes determining the actual sublimation rate. The microphysical processes can be accounted for by including in the Herz–Knudsen equation a temperature dependent sublimation coefficient (Kossacki, K.J., Markiewicz, W.J., Skorov, Y., Koemle, N.I. [1999]. Planet. Space Sci. 47, 1521–1530; Gundlach, B., Skorov, Y.V., Blum, J. [2011]. Icarus, 213, 710–719). Here we address the question to what extent inaccuracy of the simple Hertz–Knudsen equation affects the calculated temperature of a cometary nucleus and the emission rate of water vapor to space. We performed numerical simulations dealing with evolution of a model comet of the orbit the same as Comet 67P/Churyumov-Gerasimenko, target comet of the Rosetta mission (Glassmeier, K.H., Boehnardt, H., Koshny, D., Kuhrt, E., Richter, I. [2007]. Space Sci. Rev. 128, 1–21). We have found, that the temperature below dust mantle is most sensitive to the value of the sublimation coefficient when the mantle is coarse grained, while the sublimation rate is most affected when the mantle is fine grained. We also conclude that derivation of the temperature below the mantle from the measured water production rate ignoring temperature dependence of the sublimation coefficient leads to an underestimate of the temperature by more than 10K when the nucleus is fine grained.

Outgassing of icy bodies in the Solar System – I. The sublimation of hexagonal water ice through dust layers

Our knowledge about the physical processes determining the activity of comets were mainly influenced by several extremely successful space missions (Giotto, Deep Space I, Stardust, Deep Impact and EPOXI), the predictions of theoretical models and the results of laboratory experiments. However, novel computer models should not be treated in isolation but should be based on experimental results and should be verified and calibrated by experimental work. Therefore, a new experimental setup was constructed to investigate the temperature dependent sublimation properties of hexagonal water ice and the gas diffusion through a dry dust layer covering the ice surface. We show that this experimental setup is capable to reproduce known gas production rates of pure hexagonal water ice. The reduction of the gas production rate due to an additional dust layer on top of the ice surface was measured and compared to the results of another experimental setup in which the gas diffusion through dust layers at room temperature was investigated. We found that the relative permeability of the dust layer is inversely proportional to its thickness, which is also predicted by theoretical models. However, the measured absolute weakening of the gas flow was smaller than predicted by models. This lack of correspondence between model and experiment may be caused by an ill-determination of the boundary condition in the theoretical models, which further demonstrates the necessity of laboratory investigations. Furthermore, the impedance of the dust layer to the ice evaporation was found to be similar to the impedance at room temperature, which means that the temperature profile of the dust layer is not influencing the reduction of the gas production. Finally, we present the results of an extended investigation of the sublimation coefficient, which is an important factor for the description of the sublimation rate of water ice and, thus, an important value for thermophysical modeling of icy bodies in the Solar System. The achieved results of this laboratory investigations demonstrate that experimental works are essential for the understanding of the origin of cometary activity.

The molecular and ionic sublimation of holmium tribromide

The molecular and ionic composition of vapor over holmium tribromide was studied by high-temperature mass spectrometry under the conditions of sublimation from a Knudsen effusion cell and from the open single crystal surface. The partial pressures of HoBr3 and Ho2Br6 in saturated vapor and the ratio between their sublimation coefficients under free vaporization conditions were determined. The intensities of lines in the electron impact mass spectra and their temperature dependences were different under Knudsen and Langmuir conditions, which was evidence of superthermal vibrational-rotational excitation of molecules sublimed from the open surface. The enthalpies and activation energies of sublimation of HoBr3 crystals as monomers and dimers were calculated. The emission of HoBr4− and Ho2Br7− negative ions was observed under both sublimation conditions. Ion-molecular equilibria in the LaBr3-HoBr3 system were studied. The enthalpies of formation of the HoBr3 and Ho2Br6 molecules and HoBr4− and Ho2Br7− negative ions in the gas phase were calculated.

Molecular and ionic sublimation of erbium tribromide

The molecular and ionic composition of vapor over erbium tribromide sublimed from the Knudsen effusion cell and the open surface of a single crystal was studied by high-temperature mass spectrometry. The partial pressures of ErBr3 and Er2Br6 molecules in saturated vapor and the ratio between their sublimation coefficients under free vaporization conditions were determined. The enthalpies and activation energies of sublimation of ErBr3 crystals in the form of monomers and dimers were calculated. The emission of and Er2 was recorded in studies of ionic sublimation in both modes. The enthalpies of formation of gas molecules and ions were determined.

A jump change in the sublimation coefficient of the PrBr3 single crystal at the polymophic transition point

The sublimation of praseodymium tribromide under Knudsen and Langmuir conditions was studied by high-temperature mass spectrometry over the temperature range 804–957 K. During sublimation from the open surface of a single crystal, the sublimation coefficient of PrBr3 changed abruptly at the polymorphic transition point (UCl3-type low-temperature polymorph-PuBr3-type high-temperature polymorph, T= 934 ± 3 K). The change was reproducible in the heating-cooling cycles.

A Mass Spectrometric Study of the Sublimation of Lutetium Tribromide under Knudsen and Langmuir Conditions

The molecular and ionic sublimation of lutetium tribromide under thermodynamic equilibrium (Knudsen effusion) conditions and from the open surface of a LuBr3 single crystal (Langmuir conditions) was studied by high-temperature mass spectrometry. Vapor contained the LuBr3, Lu2Br6, Lu3Br9, and Lu4Br12 molecules and the Br−, LuBr4 −, Lu2Br 7 − , and Lu3Br 10 − negative ions. The partial pressures of the molecules in saturated vapor and the ratio between the sublimation coefficients of monomers and dimers under free vaporization conditions were determined. The degree of the electron impact-induced fragmentation of LuBr3 molecules under Knudsen and Langmuir sublimation conditions was analyzed. The second and third laws of thermodynamics were used to calculate the enthalpies of sublimation in the form of monomers and oligomers (Knudsen vaporization) and the corresponding activation energies of sublimation (Langmuir vaporization). Ion—molecular equilibria with the participation of negative ions were studied. The enthalpies of formation of molecules and ions in the gas phase were obtained.

A Mass Spectrometric Study of the Molecular and Ionic Sublimation of Lanthanum Tribromide

The molecular and ionic composition of vapor over lanthanum tribromide was studied by high-temperature mass spectrometry under the conditions of sublimation from a Knudsen effusion cell and from an open single crystal surface. The partial pressures of LaBr3 and La2Br6 in saturated vapor and the ratio between their sublimation coefficients under free vaporization conditions were determined. The second and third laws of thermodynamics were used to calculate the enthalpies of sublimation of LaBr3 in the form of monomers and dimers.In ionic sublimation studies, the emission of the Br−, LaBr −4 , and La2Br t-7 negative ions was recorded in both regimes. Studies of the ionic sublimation of LnX3 single crystals were shown to give reliable data on the thermochemical properties of negative ions.

Effect of the Sublimation Coefficient on the Photophoresis of Aerosol Particles with Inhomogeneous Thermal Conductivity

An analytical expression for the velocity of photophoresis of a large spherical solid aerosol particle is obtained, which takes into account evaporation (sublimation) of the particle material and its inhomogeneity with respect to thermal conductivity.

Sublimation coefficient of water ice under simulated cometary-like conditions

In papers dealing with evolution of cometary nuclei it is commonly assumed that the coefficients of sublimation α s and condensation α c of vapour are both equal to one. The experimental investigation of ice samples under simulated cometary-like conditions (Kossacki, K.J., Kömle, N.I., Leliwa-Kopystyński, J., Kargl, G., 1997. Thermal and structural evolution of cometary subsurface layer: selfconsistent model and experimental verification. Icarus 128, 127–144) suggests, however, that the sublimation flux calculated with the Hertz–Knudsen formula and the above assumption is nearly an order of magnitude too high. This may imply that actual values of α s for the ice/dust sample used in these experiments are of the order of 0.1. A similar conclusion can be drawn for α c from the results of various experiments concerning growth of ice crystals from the vapour phase and their sublimation (Lamb, D., Scott, W.D., 1972. Linear growth rates of ice crystals grown from the vapor phase. Journal of Crystal Growth 12, 21–31; Beckmann, W., Lacmann, R., 1982. Interface kinetics of growth and evaporation of ice II. Journal of Crystal Growth 58, 433–442; Sei, T., Gonda, T., 1989. The growth mechanism and the habit change of ice crystals growing from the vapour phase. Journal of Crystal Growth 94, 697–707). The exact values of both of these coefficients depend on various parameters such as temperature, concentration of surface impurities and deviation of the vapour pressure from that of the phase equilibrium. In this work the temperature dependence of the sublimation and condensation coefficients is discussed and an appropriate formula is proposed to fit the experimental results. This new formulation is then used to analyse the implications for the thermal conductivity of a porous cometary-like ice and the rate of vapour flux from a cometary nucleus.

Phosphorus cracking efficiency and flux transients from a valved effusion cell

The transient behavior of the flux from a valved effusion cell containing red phosphorus is shown to result from a low elemental sublimation coefficient (α=1.3×10−7) and not from the presence of white phosphorus in the sublimator region. The criteria for generating white phosphorus in the sublimator are given. The conversion from tetramers to dimers is modeled as a function of temperature and pressure. At higher pressures, higher temperatures are needed to convert P4 to P2. Experimental results are shown to be in qualitative agreement with results from thermodynamic equilibrium arguments.