Vapor Pressure of Dichlorosilane, Trichlorosilane ... - ACS Publications

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Vapor Pressure of Dichlorosilane, Trichlorosilane, and Tetrachlorosilane from 300 K to 420 K Kenneth N. Marsh,*,#,∥ Tony K. Morris,‡ G. P. Peterson,§ Thomas J. Hughes,† Quentin Ran,⊥ and James C. Holste¶ #

Centre for Energy and †Fluid Science & Resources Division, School of Mechanical & Chemical Engineering, University of Western Australia, Crawley, Western Australia, Australia 6009 ‡ 5216 Sun Meadow Drive, Flower Mound, Texas 75022, United States § Office of President, Georgia Institute of Technology, Atlanta, Georgia 30332, United States ⊥ LINN Energy Llc, 600 Travis Street, Suite 5100, Houston, Texas 77002, United States ¶ Chemical Engineering Department, Texas A&M University, College Station, Texas 77843, United States ∥ Department of Chemical and Process Engineering, University of Canterbury, Christchurch, New Zealand S Supporting Information *

ABSTRACT: The method for the preparation of elemental silicon of sufficient purity for the fabrication of electronic devices is by first converting silicon oxide to silicon−hydrogenchloride compounds, purifying the material as a fluid mixture, and then converting the product to solid silicon. During the purification process a mixture of dichlorosilane (SiH2Cl2), trichlorosilane (SiHCl3), and tetrachlorosilane or silicon tetrachloride (SiCl4) are formed with each of the components in significant quantities. Models that describe the vapor−liquid equilibrium behavior for the mixtures are required to design appropriate separation and purification processes. Pure fluid properties form the starting point for most mixture models, hence the importance of vapor pressures for the pure materials. In this work we report measurements of the vapor pressures for three of the most important fluids in the silicon production process, dichlorosilane, trichlorosilane, and tetrachlorosilane. Our results are compared with measurements reported previously. The instability of chlorosilanes complicates the experimental procedures because of the corrosive nature of the products formed, and in particular the potential for self-ignition upon exposure to moist air. The experimental procedures used to minimize the hazards and to avoid contamination of the fluids are described.

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INTRODUCTION Silanes are a group of silicon compounds containing silicon along with hydrogen or chlorine, or both. Silanes most commonly are associated with applications requiring precise control of the placement and thickness of layers of pure silicon. A group of silanes that contain chlorine are usually referred to as chlorosilanes. Some of the more common chlorosilanes are dichlorosilane, trichlorosilane, and tetrachlorosilane (silicon tetrachloride). Although commonly associated with the semiconductor industry, silanes are used in other applications including the production of fiber optics. Pure silicon for semiconductor applications can be manufactured by redox reactions or thermal decomposition of silanes or chlorosilanes. The stringent purity requirements of the semiconductor industry require extremely high purity levels in both the manufactured silicon and the intermediate silanes. Design of the silane purification processes requires information about the vapor pressures of the pure materials as well as mixture properties. Information about the vapor pressure of some silanes is sparse or is very uncertain, and most published work on pure chlorosilanes is either dated, at low pressure, or insufficient. Vapor pressure data are especially scarce for © XXXX American Chemical Society

dichlorosilane. An extensive search of the literature located only five sources of experimental vapor pressure data for dichlorosilane,1−5 with two published in the last 50 years.4,5 One additional source of vapor pressure data found was an online industry datasheet from the gas supplier Matheson.6 The vapor pressure of trichlorosilane has been studied in more detail,5,7−13 but most measurements were at lower temperatures than those reported here. The vapor pressure of tetrachlorosilane has also been extensively studied10,13−26 with all but the study by Toczylkin and Young26 (whose measurements were close to the critical temperature) and the industry measurements of Dow Corning 13 (a private communication in the DIPPR database27) being at lower temperatures. In the majority of the studies reported above the purity of the samples and the uncertainties in the measurements were not reported. In this paper we present the results of Special Issue: In Honor of Kenneth R. Hall Received: February 17, 2016 Accepted: May 26, 2016

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DOI: 10.1021/acs.jced.6b00142 J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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water content in the air that initiates the reaction, which is why the sample cylinder had to be purged with a dry gas. Leak testing was performed by pressurizing with argon then probing all connections with a Matheson Gas Products leak detector. To ensure the purity of the sample, the chlorosilanes were subjected to an extensive degassing procedure before being transferred to the sample cell in the isochoric apparatus. First, the sample cylinder was submerged in a liquid nitrogen bath. Next, the valve at the top of the cylinder was opened to a vacuum to remove any gaseous impurities. Finally, the sample was allowed to thaw completely. This cycle was repeated a total of four times, which was how long it took to achieve a pressure of less than 1 Pa above the frozen sample. After this process, the sample was allowed to thaw partially before it was exposed to a vacuum for approximately 2 s. This second procedure was repeated three times. Both methods involve freezing and thawing, but each has unique significance. The first method should eliminate impurities with freezing points which are lower than the boiling point of nitrogen, but some gases may be trapped in the liquid during the freezing process. The second method was intended to remove trapped gases from within the partially thawed liquid. None of these steps were likely to remove the other chlorosilanes impurities. All intermediate tubing lines between the degassing cylinder and the sample volume in the apparatus were rinsed with a small amount of the chlorosilanes under study. A valve was then opened to the cold trap to allow the chlorosilane to be condensed, then it was closed. The degassing cylinder then was heated with a bath of warm water, while the isochoric cell was cooled by a chilled water loop. A valve connected to a dipstick in the liquid was opened, and the distillation transfer process was allowed to proceed for approximately 2 h for the measurements on sample 1 and a considerably shorter time for sample 2 and the other chlorosilanes, as only sufficient sample to approximated half fill the cell was required. After disassembling the transfer setup, great care was taken to purge all external lines of tubing with argon. Exposed surfaces also were cleaned with a highly absorbent lab towel designed especially for chemical cleanup. Acetone also was used to help polish the surface. Over a period of approximately 3 days, a corrosion layer was evident on all exposed surfaces; however, internal surfaces remained visibly clean. The conclusion was that the chlorosilanes tended to be highly adsorbed on stainless steel in the presence of moist air. Copper or brass fittings are not an option because copper reacts with the chlorosilanes in the presence of moisture.7 Stainless steel valves and tubing that have contact with the chlorosilanes in the presence of moist air can also be corroded, although to a lesser extent. Extraordinary caution was taken to shield them from such exposure.

vapor pressure measurements made using an isochoric method on high-purity samples of the three chlorosilanes.

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EXPERIMENTAL SECTION The isochoric measurements were made in an apparatus which has been described in detail previously.28−30 Only a brief description will be given here. The sample cell was made of 316 stainless steel, and the inner surfaces of the cell were polished to minimize adsorption. A built-in differential pressure transducer (DPT) was located at the top of the cell. The temperature variation of the cell was measured with a platinum resistance thermometer (Leeds and Northrup) (with resistance measured using a Hewlett-Packard 6 digit digital voltmeter and standard resistance) to ± 0.001 K and an uncertainty (relative to the ITS-90) of ± 0.010 K. Temperature variations across the cell were less than ± 0.003 K. The cell temperature was controlled to ± 0.002 K using a proportional−integral control algorithm implemented with a microcomputer. The equilibrium vapor pressure resulted in a force on the bottom of the DPT that was counterbalanced by an inert gas (argon) on the top side. A linear variable differential transformer (LVDT), described in detail in ref 28, detected deflections of the 0.05 mm thick stainless steel diaphragm, which was the functional component of the DPT. A calibration for the null position was performed immediately prior to each series of experiments. Previously the null position shift was shown by repeated tests to be stable to better than ± 0.1 kPa.29 The pressure of the counterbalancing inert gas was measured with a DH (Desgranges et Hout) force-balance piston pressure gauge model 26410, certified by the manufacturer to have a relative uncertainty of 0.005 %.

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MATERIALS Two samples of dichlorosilane (SiH2Cl2) were used. Research grade SiH2Cl2 (sample 1) was purchased from Sigma-Aldrich Chemicals. The second (sample 2) dichlorosilane, trichlorosilane, and tetrachlorosilane were from Matheson. The manufacturers specifications of the purities and impurities are given in Table 1. The samples were not analyzed further. Each Table 1. Manufacturers Specified Purity of the Three Chlorosilanes. Samples Were Used as Received and Degassed Prior to Measurement As Discussed in the Text compound dichlorosilane (sample 1) dichlorosilane (sample 2) trichlorosilane tetrachlorosilane

source

mass faction purity

major impurities

Aldrich

0.9999+

not specified

Matheson

0.999

Matheson Matheson

0.9995 0.9994

HCl, SiH3Cl, SiHCl3, and SiCl4 SiH2Cl2 and SiCl4 other chlorosilanes, not specified

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RESULTS Measurements were made on the two SiH2Cl2 samples. The experimental results for sample 1 are given in Table 2. The results for sample 2 are given in Table 3 along with the results for SiHCl3 and SiCl4. For sample 1, eight isochores were measured at temperatures ranging from 300 K to 420 K. The volume of the sample added was such that the overall average density was greater than the critical density but there was initially a vapor space. The cell became entirely filled with liquid as the temperature increased. Thus, the final value for each isochore was representative of the final point before the DPI experienced a hydraulic pressure. After the first isochore a small portion of the sample was discharged from the cell to reduce

chlorosilane was transferred from the original container to a 1 liter stainless steel sample cylinder for degassing. Prior to transfer, the degassing cylinder was purged with argon and then evacuated. The transfer was completed with a combination of pressure and temperature differentials used as the driving forces. The pressure differential was generated by evacuation, and the temperature differential was achieved by submerging the degassing cylinder into liquid nitrogen. All connections were tested regularly for leaks because the three chlorosilanes exhibit a rapid reaction with water in the atmosphere. It is the B



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Table 2. Vapor Pressure of DichlorosilaneSample 1a isochore 1 T/K

p/kPa

300.001 319.998 330.017

216.5 380.4 492.2

isochore 4

isochore 2 T/K

p/kPa

299.994 319.983 339.992 349.989 isochore

214.5 377.6 625.6 789.0 5

T/K

p/kPa

T/K

p/kPa

329.994 349.990 359.988 369.984

485.8 784.7 978.0 1205

349.996 369.992 379.985

785 1205 1469

isochore 7

isochore 8

95 % confidence interval in the vapor pressure measurements was estimated at 1 %, determined from the uncertainties in T and p and the differences between the vapor pressure values for duplicate measurements along an isochore and from the differences seen when the vapor pressure values from different isochores were fit to an equation.

isochore 3 T/K

p/kPa

299.999 319.996 339.991 359.983 isochore T/K

214.2 377.3 625.3 981.9 6

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DISCUSSION The data, including all the literature data, were initially plotted as log p against 1/T, where p is the vapor pressure at temperature T, and on the basis of the plot discordant data were eliminated from further analysis (see Tables S5, S6, and S7 in Supporting Information). The remaining data were fit to the Wagner vapor pressure equation,31 eq 1:

p/kPa

299.999 212.1 309.992 284.3 349.992 786.4 359.992 982.2 369.992 1209 379.989 1479 389.994 1779 isochore 9

T/K

p/kPa

T/K

p/kPa

T/K

p/kPa

299.993 319.993 339.998 359.991 379.99 389.991

214.4 377.9 628.6 985.9 1477 1784

299.988 339.991 379.99 389.99 399.989 410.004

213.33 626.4 1475.9 1780.5 2099 2534

299.993 319.995 339.991 359.991 379.992 399.992 409.984 419.991

216.53 381.43 631.6 990.3 1484 2138 2559 3016

ln(p /pc ) = (T c/T )(A1τ + A 2 τ1.5 + A3τ 2.5 + A4 τ 5)

pc/kPa Tc/K A1 A2 A3 A4 u(A1)c u(A2)c u(A3)c u(A4)c all fitted data RSD (pWag) our data RSD (pWag) Tmin/Kd Tmax/Kd

Uncertainty in T, u(T) = 0.01 K, uncertainty in p, u(p)/p = 0.006, combined standard uncertainty at the 95 % confidence in p including possible effects due to impurities, uc(p)/p = 0.01.

Table 3. Vapor Pressure of Dichlorosilane (Sample 2), Trichlorosilane, and Tetrachlorosilanea dichlorosilane

trichlorosilane

tetrachlorosilane

p/kPa

T/K

p/kPa

T/K

p/kPa

323.006 343.007 362.990

407.8 672.6 1052.1

310.000 320.000 329.996 340.000 350.000 359.995 369.996 379.995 380.499 384.998 390.000 394.995

121.89 167.53 225.35 297.4 385.6 492.1 619.6 770.2 778.2 854.6 946.0 1044.2

332.991 339.996 340.001 350.015 359.999 370.001 379.998 389.995 399.996

113.02 139.15 138.98 185.05 241.64 311.49 395.69 495.9 614.0

c

Table 4. Fitted Wagner Vapor Pressure Equation Coefficients for Dichlorosilane, Trichlorosilane, and Tetrachlorosilane

a

T/K

(1)

where T is the critical temperature, p is the critical pressure, τ = 1 − T/Tc and A1 to A4 are the fitted coefficients given in Table 4. In the analysis the accepted literature results and the c

dichlorosilane

trichlorsilane

tetrachlorosilane

4950a 451.527 −7.3787 2.6330 −1.5588 −6.9091 0.1819 0.5854 0.9169 1.4135 9.2 % 0.87 % 163 420

417036,b 47935,36,b −7.3803 2.7614 −3.6628 0.14046 0.2738 0.8352 1.1748 1.54823 3.1 % 0.71 % 188 438

359326 508.0626 −6.7361 1.0337 −2.3808 −0.41128 0.3042 0.8767 1.1430 1.46687 4.5 % 1.4 % 203 505

a

Extrapolated from a log p vs 1/T plot from our data to the predicted Tc, see Supporting Information. bCritical temperature was measured in Nisel’son et al. 35 without a value for p c . In Sladkov and Pobedonostseva37 a value for pc is referenced to Lapidus and Nisel’son.36 cStandard uncertainties (k = 1). dThe temperatures Tmin and Tmax are the minimum and maximum temperature of the data to which the Wagner vapor pressure equation was fitted.

present data were fit with weighting for uncertainties using the Levenberg−Marquardt32,33 nonlinear least-squares optimization algorithm (“FuncFit”) in WaveMetrics IGOR Pro 6.37.34 The relative standard deviation (RSD) of the fitted Wagner equation pressure from the vapor pressure data was quantified through eq 2:

a Uncertainty in T, u(T) = 0.01 K, uncertainty in p, u(p)/p = 0.006, combined standard uncertainty at the 95 % confidence in p including possible effects due to impurities, uc(p)/p = 0.01

the average density, and a new isochore was measured. This method allowed for multiple replications of several points along each isochore to verify the internal consistency of the results. The experiment was terminated after the series of expansions from the cell gave a density that was below the estimated critical density. For sample 2 and the two other chlorosilanes the liquid volume was sufficient to approximately half fill the cell. Only three temperatures were measured for SiH2Cl2, while measurements were made at 12 temperatures for SiHCl3 and 9 temperatures for SiCl4. The combined relative uncertainty at a

N

∑ RSD =

i

{(p − p i

Wag, i

N−m

2

)/pi

}

(2)

where pi is a measured vapor pressure, pWag,i is a calculated vapor pressure from the Wagner equation, i is a counter which represents a single measurement point, N is the total number of measurement points, and m is the number of adjustable parameters (in this case m = 4 for the Wagner equation). For C



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the low temperature data of Vorotyntsev et al.4 were eliminated. The remaining data were fit to the Wagner eq (eq 1) with the resulting coefficients given in Table 4. Also included in Table 4 is the RSD of 9.2 % when all the data were fit to the parameters of eq 1 and 0.87 % for our data fit to the same parameters. The deviations of the data from the equation along with the estimated uncertainties are given in Figure 2. Except for the low temperature data of Stock and Somieski3 the data fit within their estimated uncertainties.

literature data in NIST/TRC ThermoData Engine (TDE) that accesses the NIST/TRC Source database, their estimated uncertainties were initially used but were adjusted if the selfconsistency of the data appeared worse than the estimated uncertainty. For data not in TDE, estimates of the uncertainties were based on either the authors’ assessment or estimated from the experimental technique used. Some measurements, particularly the earlier measurements, most likely have larger uncertainties, in part due to the unknown purity of the samples. All the literature data along with their estimated uncertainties are given in the Supporting Information. The uncertainties of the measurements reported here are given in Tables 2 and 3. The fit to the Wagner equation requires the critical temperature Tc and critical pressure pc. The values used are given in Table 4. For SiH2Cl2 the Tc and pc have not been measured. For SiH2Cl2 the value of pc was based on the extrapolation of our data to the estimated critical temperature (as shown in Figure S1 of the Supporting Information) from the DIPRR database.27 For SiHCl3 the critical temperature was measured by Nisel’son et al.35 A value of pc, assumed to be measured, is referenced to Lapidus and Nisel’son36 in Sladkov and Pobedonostseva.37 We note that these values of pc and Tc are the recommended values used in the DIPPR database.27 For SiCl4 the measured values of Tc and pc by Toczylkin and Young26 were used. Other estimates of the critical properties of both SiH2Cl2 are given in the Supporting Information. The vapor pressure of dichlorosilane was measured between (300 and 420) K. There were no differences within the experimental uncertainties between measurement on sample 1 and sample 2. The measurements of Stock and Somieski1 in 1919 were between (163 and 281) K, those of Wintgen2 in 1919 were between (162 and 224) K, those of Vorotyntsev et al.4 in 1986 were between (183 and 349) K and those by Olson5 in 1989 between (344 and 396) K. There are a number of measurements at a single temperature that were not included in the analysis. The literature values and their estimated uncertainties are given in the Supporting Information. Only the measurements reported by Olson lie within the range covered by this work. The Matheson Gas Data Book6 also provides values for dichlorosilane, but does not present information about the source or the uncertainties of the values presented. On the basis of the plot of log p as a function of 1/T (Figure 1)

Figure 2. Relative deviations of measured vapor pressure of dichlorosilane, p, from those calculated with Wagner vapor pressure equation, pWag, as a function of temperature fitted to the data of this work and the literature data sets excluding that of Vorotyntsev et al.:4 blue ◊, Stock and Somieski;1 black □, Wintgen;2 red ○, Glemser and Lohmann;3 green △, Vorotyntsev et al.;4 purple ×, Olson;5 blue +, Matheson datasheet;6 black ○, this work (sample 1), red ∗, this work (sample 2). The inset shows an expanded scale for data at T > 280 K.

For trichlorosilane a plot of log p as a function of 1/T (Figure 3) indicated that the data of Lapidus and Nisel’son12 were inconsistent with other literature data and hence that data was discarded in the Wagner fit. The coefficients of eq 1 are given in Table 4. In this case the RSD is much smaller at 3.1 % with the RSD for our data alone is 0.71 %. The deviations are shown in Figure 4 again with all the deviations close to the estimated uncertainties. The inset shows the deviations within

Figure 3. Vapor pressure of trichlorosilane (note: the temperature axis has been scaled inversely): blue ◊, Stock and Zeidler;7 black □, Booth and Stillwell;8 red ∗, Pirenne;9 green △, Jenkins and Chambers;10 purple ×, Shakhparonov et al.;11 black +, Nisel’son and Lapidus;19 black ○, Lapidus and Nisel’son;12 green ∗, Dow Corning Private Communication;13,27 blue +, Olson;5 red □, this work. The inset shows an expanded scale for 380 < T/K < 400.

Figure 1. Vapor pressure of dichlorosilane (note: the temperature axis has been scaled inversely): blue ◊, Stock and Somieski;1 black □, Wintgen;2 red ○, Glemser and Lohmann;3 green △, Vorotyntsev et al.;4 purple ×, Olson;5 blue +, Matheson datasheet;6 black ○, this work (sample 1), red ∗, this work (sample 2). D



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Figure 4. Relative deviations of measured vapor pressure of trichlorosilane, p, from those calculated with Wagner vapor pressure equation, pWag, as a function of temperature fitted to the data of this work and the literature data sets excluding that of Lapidus and Nisel’son:12 blue ◊, Stock and Zeidler;7 black □, Booth and Stillwell;8 red ∗, Pirenne;9 green △, Jenkins and Chambers;10 purple ×, Shakhparonov et al.;11 black +, Nisel’son and Lapidus;19 black ○, Lapidus and Nisel’son;12 black ∗, Dow Corning Private Communication;13,27 blue +, Olson;5 red □, this work. The inset shows an expanded scale for 280 < T/K < 400.

Figure 6. Relative deviations of measured vapor pressure of tetrachlorosilane, p, from those calculated with Wagner vapor pressure equation, pWag, as a function of temperature fitted to the data of this work and the literature data sets excluding that of Becker and Meyer:15 blue ◊, Regnault;14 black □, Becker and Meyer;15 red ∗, Stock et al.;16 blue □, Wintgen;2 green △, Kearby;17 purple ×, Jenkins and Chambers;10 black ○, Korchemskaya et al.;18 blue +, Nisel’son and Seryakov;20 red ◊, Nisel’son and Lapidus;19 black ◊, King and Canjar;21 red △, Crookston and Canjar;22 blue ○, Capkova and Fried;23 black ∗, Jain and Yadav;24 green ○, Weiwad et al.;25 green +, Toczylkin and Young;26 black △, Dow Corning Private Communication;13,27 red □, this work. The inset shows an expanded scale for 280 < T/K < 440.

the temperature range studied. The higher temperature data of Dow Corning agree with our data to just within the combined estimated experimental uncertainties. For tetrachlorosilane the plot of log p as a function of 1/T shown in Figure 5 indicated that the data of Becker and

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CONCLUSIONS Vapor pressure measurements on dichlorosilane, trichlorosilane, and tetrachlorosilane were made in a higher temperature range for which there were not extensive measurements. An analysis of both the measured and literature data resulted in some literature data being eliminated. The accepted data and the data measured in this work were then fit to a four parameter Wagner equation, and the majority of the literature data showed deviations that were within their estimated uncertainties.

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ASSOCIATED CONTENT

S Supporting Information *

. The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jced.6b00142. Log p vs 1/T plot showing calculation of extrapolated critical pressure for dichlorosilane, table of estimated critical pressures, and temperatures of dichlorosilane; tables of literature references to vapor pressure data for dichlorosilane, trichlorosilane, and tetrachlorosilane, and tables of literature vapor pressure data including estimated uncertainties (PDF)

Figure 5. Vapor pressure of tetrachlorosilane (note: the temperature axis has been scaled inversely): blue ◊, Regnault;14 black □, Becker and Meyer;15 red ∗, Stock et al.;16 blue □, Wintgen;2 green △, Kearby;17 purple ×, Jenkins and Chambers;10 black ○, Korchemskaya et al.;18 blue +, Nisel’son and Seryakov;20 red ◊, Nisel’son and Lapidus;19 black ◊, King and Canjar;21 red △, Crookston and Canjar;22 blue ○, Capkova and Fried;23 black ∗, Jain and Yadav;24 green ○, Weiwad et al.;25 green + , Toczylkin and Young;26 black △, Dow Corning Private Communication;13,27 red □, this work. The inset shows an expanded scale for 280 < T/K < 320.

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AUTHOR INFORMATION

Corresponding Author

Meyer15 are inconsistent with both the present data and other literature data and hence were excluded from further analysis. The coefficients for eq 1 are given in Table 4, and in this case the RSD was 4.5 % for all the accepted data and 1.4 % for the present data. The deviations of all the data from the Wagner equation are shown in Figure 6 with an inset showing the deviations within the temperature range studied. Except for the low temperature values of Stock et al.16 the deviations are within the estimated uncertainties. There is excellent agreement with the Dow Corning data.13

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Agnes Haber for her help translating papers written in German. We thank Vladimir M. Vorotyntsev for suppling the experimental data that were not included in his paper.4 We thank Eric May for assistance with the IGOR Pro software. The E



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Silicon Tetrachloride/n-Hexane System. Indian J. Chem. 1973, 11, 28− 30. (25) Weiwad, F.; Kehlen, H.; Kuschel, F.; Sackmann, H. Behavior of Binary Liquid Mixed Phases. 7. Free Excess Enthalpies in Tetrachloride Systems. Z. Phys. Chem. (Leipzig) 1973, 253, 114−124. (26) Toczylkin, L. S.; Young, C. L. Vapor Pressures of some Liquids of Quasi-Spherical Molecules Near their Critical Points and the Applicability of the Principle of Corresponding States. Aust. J. Chem. 1977, 30, 1591−1593. (27) Design Institute for Physical Properties (DIPPR) 801 Database. https://app.knovel.com/web/toc.v/cid:kpDIPPRPF7/ (accessed 09Feb-2016); AICHE. (28) Yurttas, L. New Isochoric Apparatus with Application to p−V− T and Phase Equilibria Studies. Ph.D. Thesis, Texas A&M University, College Station, TX, 1986. (29) Yurttas, L.; Holste, J. C.; Hall, K. R.; Gammon, B. E.; Marsh, K. N. Semiautomated Isochoric Apparatus for p-V-T and Phase Equilibrium Studies. J. Chem. Eng. Data 1994, 39, 418−423. (30) Morris, T. K. Vapor Pressure Measurements for Dichlorosilane. Master’s Thesis, Texas A&M University, College Station, TX, 1997. (31) Wagner, W. New Vapor Pressure Measurements for Argon and Nitrogen and a New Method for Establishing Rational Vapor Pressure Equations. Cryogenics 1973, 13, 470−482. (32) Levenberg, K. A Method for the Solution of Certain Non-Linear Problems in Least Squares. Q. Appl. Math. 1944, 2, 164−168. (33) Marquardt, D. W. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. Soc. Ind. Appl. Math. 1963, 11, 431−441. (34) IGOR Pro 6.3.7.2, WaveMetrics Inc., 2014. (35) Nisel’son, L. A.; Sokolova, T. D.; Lapidus, I. I. Orthobaric Densities and Critical Parameters of SiCl4, SiHCl3, SiBr4, and SiHBr3. Rus. J. Inorg. Chem. 1967, 12, 752−754. (36) Lapidus, I. I.; Nisel’son, L. A. Tetrakhlorsilan i Trikhlorsilan; Khimiya: Moscow, 1978. (37) Sladkov, I. B.; Pobedonostseva, E. V. Calculation of the Critical Parameters of Inorganic Compounds by the Additive Method. Russ. J. Appl. Chem. 2005, 78, 1245−1248.

measurements were made in the Department of Chemical Engineering, Texas A&M University.

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REFERENCES

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