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Measurement method of compressibility and thermal expansion coefficients for density standard liquid at 2329 kg/m3 based on hydrostatic suspension principle

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Abstract

The accurate measurement on the compressibility and thermal expansion coefficients of density standard liquid at 2329kg/m3 (DSL-2329) plays an important role in the quality control for silicon single crystal manufacturing. A new method is developed based on hydrostatic suspension principle in order to determine the two coefficients with high measurement accuracy. Two silicon single crystal samples with known density are immersed into a sealed vessel full of DSL-2329. The density of liquid is adjusted with varying liquid temperature and static pressure, so that the hydrostatic suspension of two silicon single crystal samples is achieved. The compression and thermal expansion coefficients are then calculated by using the data of temperature and static pressure at the suspension state. One silicon single crystal sample can be suspended at different state, as long as the liquid temperature and static pressure function linearly according to a certain mathematical relationship. A hydrostatic suspension experimental system is devised with the maximal temperature control error ±50 μK; Silicon single crystal samples can be suspended by adapting the pressure following the PID method. By using the method based on hydrostatic suspension principle, the two key coefficients can be measured at the same time, and measurement precision can be improved due to avoiding the influence of liquid surface tension. This method was further validated experimentally, where the mixture of 1, 2, 3-tribromopropane and 1,2-dibromoethane is used as DSL-2329. The compressibility and thermal expansion coefficients were measured, as 8.5×10−4 K−1 and 5.4×1010 Pa−1, respectively.

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References

  1. ELWENSPOEK M, JANSEN H. Silicon micromachinmg [M]. Beijing: Chemical Industry Press, 2006.

    Google Scholar 

  2. LI D S, YANG D R, QUE D L. Progress in study of crystal silicon mechanical properties[J]. Material Science and Engineering, 2000, 18(3): 100–104.

    Google Scholar 

  3. LUO Z Y, YANG L F, GU Y Z, et al. The absolute measurement of density of silicon crystals for determing avogadro constant[J]. Acta Me’irolocica Sinica, 2008, 29(3): 211–215.

    Google Scholar 

  4. FUJII K, TANAKA M, NEZU Y, et al. Determination of the Avogadro constant by accurate measurement of the molar volume of a silicon crystal[J]. Metrologia, 1999, 36: 455–464.

    Article  Google Scholar 

  5. BECKER P. History and progress in the accurate determination of the avogadro constant[J]. Report on Progress in Physics, 2001, 64: 1945–2008.

    Article  Google Scholar 

  6. KENICHI F J, MITSURU T. Density standard at NMIJ and related activities in the CCM WG on deastiy [C]//14th International Conference on The Properties of Water And Steam, Kyoto, Japan, August 29–September 3, 2006: 132–139.

  7. HUI J, GUAN S C, CHEN H L. The progress of Avogadro constant and new definition of kilogram [J]. Physics, 1995, 24(7): 396–401.

    Google Scholar 

  8. TEGETMEIER A, DITTMAR D, FREDENHAGEN A, et al. Density and volume of water and triglyceride mixtures in contact with carbon dioxide[J]. Chemical Engineering and Processing, 2000, 39: 399–405.

    Article  Google Scholar 

  9. WASEDA A, FUJII K, KURAMOTO N Development of a silicon density standard and precision density measurements of solid materials by hydrostatic weighing[J]. Meas. Sci. Technol., 2001, 12: 2039–2045.

    Article  Google Scholar 

  10. KOZDON A F, SPIEWECK F. Determination of differences in the density of silicon single crystals[J]. IEEE Trans. Instrum. Meas., 1992,41:420–426.

    Article  Google Scholar 

  11. XIE X Z, FANG J M, ZHANG X W, et al. The dynamic measurement of liquid volume modulus and its application in the dynamic pressure calibration [J]. Journal of Test and Measurement Technology of NOT, 2000, 14: 537–542.

    Google Scholar 

  12. FENG B, GONG G F, WANG J, et al. Structure design and FEA analysis of a measuring device for hydraulic oil bulk modulus[J]. Machine Tool & Hydraulics, 2007, 35(5): 177–179.

    Google Scholar 

  13. GEORGE H F, BARBER A. What is bulk modulus and when is it important[J]. Hydraulics & Pneumatics, 2007 (7): 34–39.

    Google Scholar 

  14. HAYWARD A T J. How to measure the isothermal compressibility ofliquidsaccurately[J]. J. Phys. D-Appl. Phys., 1971 (7): 938–949.

    Google Scholar 

  15. ZHANG F L, JI X. Measurement of liquid bulk modulus of elasticity [J]. Journal of Yanbian University(Natural Science), 2002, 28(3): 168–170.

    Google Scholar 

  16. WANG J, GONG G F, YANG H Y. Research and online measurement of bulk modulus of hydraulic oil[J]. Journal of Mechanical Engineering, 2009, 45(7): 120–125.

    Article  Google Scholar 

  17. CHRISTOPHER N, JOHN K, KARTHIK B. Piezoelectric-based fluid bulk modulus sensor[J]. Journal of Intelligent Material Systems and Structures, 2004, 15(12): 893–899.

    Article  Google Scholar 

  18. CHRISTOPHER D Lane, DAVID J H, ANDREW J L, et al. Measurement of the bulk modulus of a liquid using a pump-probe laser technique[J]. The Chemical Educator, 2001, 6(4): 235–237.

    Article  Google Scholar 

  19. WANG Y G, SHAO L H. Ultrasonic testing research of HCL bulk modulus[J]. Journal of Tongji University, 1995, 2(23): 170–174.

    Google Scholar 

  20. MUSTAFA V, ALI B K, CANER K. Ultrasonic velocity measurements in ethanol-water and methanol-water mixtures[J]. Eur Food Res Technol, 2007, 225: 525–532.

    Article  Google Scholar 

  21. LIU Y F, LIU Z Q. Based on SV-DH test instrument to calculate and measure of liquid compressibility [J]. Science Technology and Engineering, 2012, 12(16): 3941–3943.

    Google Scholar 

  22. MANRING N D. The effective fluid bulk-modulus within a hydrostatic transmission [J]. Journal of Dynamic Systems, Measurement, and Control, 1997, 119(3): 462–466.

    Article  Google Scholar 

  23. AN J, SUN Y Q, ZHANG H P, et al. Online measuring elastic modulus of hydraulic medium[J]. Navigation of CHINA, 2008, 31(3): 248–251.

    Google Scholar 

  24. KARJALAINEN J P, KARJALAINEN R. Fluid dynamics-comparison and discussion on system-related differences[C]//Proc. 10th SICFP, Tampere, Finland, May 21–23, 2007, 2: 371–381.

  25. YAN X L, GU L C H. Online measurement of effective bulk modulus in hydraulic system by the soft-sensing model[J]. Journal of Mechanical Engineering, 2011, 10(7): 126–132.

    Article  Google Scholar 

  26. YAN H. Measuring liquid expansion coefficient using silicon force sensor[J]. Physics Experimentation, 2010, 30(4): 35–37.

    Google Scholar 

  27. FUJH K, WASEDA A, KURAMOTO N, et al. Present state of the avogadro constant determination from silicon crystals with natural isotopic compositions[J]. IEEE Transactions on Instrumentation and Measurement, 2005, 54(2): 854–859.

    Article  Google Scholar 

  28. MARTIN J, BETTIN H, KUETGENS U, et al. About the existing discrepancy in the determinations of the avogadro constant[J]. IEEE Transactions on Instrumentation and Measurement, 1999, 48(2): 216–220.

    Article  Google Scholar 

  29. FUJII K, TANAKA M, NEZU Y, et al. Determination of the Avogadro constant from accurate measurement of the molar volume of a silicon crystal[J], Metrologia, 1999, 36: 455–464.

    Article  Google Scholar 

  30. KURAMOTO N, FUJII K. Volume determination of silicon sample using an improved interferometer with optical frequency tuning[J]. IEEE Transaction on Instrumentation & Measurement, 2005, 54(2): 868–871.

    Article  Google Scholar 

  31. FUJII K. Present state of the solid and liquid density standards[J]. Metrologia, 2004, 41: 1–15.

    Article  Google Scholar 

  32. NICOLAUS R A, FUJH K. Primary calibration of the volume of silicon samples[J]. Meas Sci Technol, 2006, 17: 2527–2539.

    Article  Google Scholar 

  33. LUO Z Y, YANG L F, GU Y Z, et al. A study on solid density primary standard[J]. Chinese Science Bulletin, 2007, 52(21): 2881–2886.

    Article  Google Scholar 

  34. NICOLAUS R A, BONSCH G. Absolute volume determination of a silicon sample with the spherical interferometer of PTB[J]. Metrologia, 2005, 42: 24–31.

    Article  Google Scholar 

  35. LUO Z Y, GU Y Z, ZHANG J T, et al. Interferometric measurement of the diameter of a silicon sample with a mechanical scanning method[J]. IEEE Transaction on Instrumentation and Measurement, 2010, 59 (11): 2991–2996.

    Article  Google Scholar 

  36. BETTIN H, GLASER M, SPIEWECK F, et al. International intercomparison of silicon density standards[J]. IEEE Transactions on Instrumentation and Measurement, 1997, 46(2): 556–559.

    Article  Google Scholar 

  37. OSAMA I. Hydraulic hydrokineties[M]. Beijing: Science Press, 1980.

    Google Scholar 

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Authors and Affiliations

  1. Division of Mechanics and Acoustics, National Institute of Metrology, Beijing, 100013, China

    Jintao Wang, Ziyong Liu, Changhong Xu & Zhanhong Li

Authors
  1. Jintao Wang
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  2. Ziyong Liu
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  3. Changhong Xu
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  4. Zhanhong Li
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Corresponding author

Correspondence to Jintao Wang.

Additional information

Supported by National Natural Science Foundation of China(Grant No. 51105347), and National Key Technology R&D Program of Ministry of Science and Technology of China(Grant No. 2011BAI02B03)

WANG Jintao, born in 1976, is currently an assistant research fellow at National Institute of Metrology, China. He received his PhD degree from Xi’an Jiaotong University, China, in 2006. His research interests include precise measurement on density and volume for liquid and solid.

LIU Ziyong, born in 1955, is currently a senior engineer at National Institute of Metrology, China. He received his bachelor degree on physics in Shanxi University, China, in 1978.

XU Changhong, born in 1978, is currently an assistant research associate at National Institute of Metrology, China. She received her master degree on physics in National Institute of Metrology, China, in 2006.

LI Zhanhong, born in 1974, is currently an assistant research associate at National Institute of Metrology, China. He received his master degree on instrument in Beijing Institute of Technology, China, in 2000.

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Wang, J., Liu, Z., Xu, C. et al. Measurement method of compressibility and thermal expansion coefficients for density standard liquid at 2329 kg/m3 based on hydrostatic suspension principle. Chin. J. Mech. Eng. 27, 779–784 (2014). https://doi.org/10.3901/CJME.2014.0422.080

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  • DOI: https://doi.org/10.3901/CJME.2014.0422.080

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