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Density and surface tension of molten calcium fluoride
Journal of Crystal Growth 240 (2002) 445–453
Density and surface tension of molten calcium fluoride Xiumei Chena, Suguru Jinguub, Suzuka Nishimurac, Yasunao Oyamad, Kazutaka Terashimab,* b
a Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, People’s Republic of China Department of Material Science and Technology, Shonan Institute of Technology 1-1-25 Tsujido-nishikaigan, Fujisawa, Kanagawa 251-8511, Japan c Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522, Japan d Optron Inc., Toride-shi, Ibaraki 302-0023, Japan
Received 14 November 2001; accepted 24 January 2002 Communicated by K.W. Benz
Abstract The density and the surface tension of molten calcium fluoride have been measured in the temperature range from 1690 to 1790 K by an improved Archimedian method and a ring depressing technique (J. Crystal Growth 187 (1998) 391), respectively. The ring depressing technique was demonstrated as an effective technique to measure the surface tension in comparison with the conventional ring pulling technique. The density varied with the temperature change corresponding to a linear relationship: r ¼ 3:767 6:94 104 T (K). The density of the CaF2 melt at the melting point is 2.594 g/cm3, which is equal to the result obtained by Shiraishi and Watanabe (Bull. Res. Inst. Miner. Dressing Metal, Tohoku Univ. 34 (1978) 1), but the temperature coefficient of the density is different from the results obtained by other investigators. The thermal expansion coefficient of calcium fluoride melt linearly increases with temperature heating. The surface tension of molten calcium fluoride indicates a negative linear relationship as a function of the melt temperature: gðTÞ ¼ 442:4 0:0816 TðKÞ (mN/m). The surface tension measured using the ring depressing technique is larger than those results obtained by other techniques. r 2002 Elsevier Science B.V. All rights reserved. PACS: 81.10.h Keywords: A1. Density; A1. Surface tension; A2. Ring depressing technique; B1. Calcium fluoride melt
1. Introduction Calcium fluoride (CaF2) is a representative alkaline earth fluoride that has been the subject of experimental and theoretical studies for years. It *Corresponding author. Tel./fax: +81-466-300226. E-mail address: [email protected] (K. Terashima).
has for many years been one of the important materials used in the design of optical components and systems. At the present time, there are various methods available for the production of fluoride single crystals. In some earlier investigations, the horizontal-growth technique [3], normal crystal pulling [3,4] and Bridgman–Stockbarger technique [5,6] were used to grow the fluoride single crystal. However, those crystals grown by the
0022-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 2 ) 0 0 8 7 9 - 5
446
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
horizontal-growth technique had two kinds of imperfections, first is that the crystals exhibited extensive internal strain; second, the formation of minute amounts of oxide cannot be completely eliminated. So, the fundamental properties are for designing crystal growth condition to grow a large size crystal with high perfection from the melt. The density is considered to be one of the melt fundamental properties of a liquid material, and also the liquid thermal expansion coefficient of the materials can be obtained from the temperature dependence of the density. The surface tension represents a state of the surface of the melt. The temperature gradient of the surface results in a Marangoni flow near the surface of the melt, which affects the mass and energy transportation significantly during the crystal growth. However, there were not many works on the measurements of the physico-chemical properties of CaF2 melt, and also the accurate data were very poor. There were some reports about the properties of the molten CaF2, but the data were scattered very much, and there were large differences for the data of density [7–11] and surface tension [2–15]
obtained by different investigators. At the same temperature the maximum of the difference was over 10% for density and surface tension. So the accurate and reliable data are still lacking for the fundamental properties of CaF2 melts, because CaF2 melt has higher reactivity to container materials and also to gas phase. In this work, the density and surface tension of CaF2 melt have been measured accurately within about 100 K around the melting point of CaF2 (1690 K).
2. Experimental procedure The apparatus used for measuring the density and surface tension consists of evacuation and argon gas outlet. A schematic of the setup is shown in Fig. 1. The whole furnace heater and an electric balance were sealed in a chamber with cooling water. The CaF2 samples were melted in a vertical furnace heated by two high pure graphite heaters, which were regulated by two separate controllers, respectively. The temperature of the melt was directly measured by an immersed Pt/Pt-10%
Electronic balance Pt thermal couple Ar Inlet
Tungsten wire
Graphite ring probe Graphite crucible
Water cooled chamber
Upper graphite heater Molten calcium fluoride
Carbon fiber insulator Lower graphite heater
Exhaust
Fig. 1. The scheme of the experimental apparatus for measuring the density and surface tension.
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
Rh-type thermocouple covered with alumina tube. In order to reduce the convection in hightemperature melt, the crucible was placed at a proper position in the furnace so that the temperature of the upper region of the melt was slightly higher about 5 K than that of the bottom part of the melt. The fluctuation of the temperature in the melt was controlled within 70.5 K. Single crystalline CaF2 was used as the starting materials, the purity of the sample was guaranteed at over 99.99% (Optron Inc.). High pure graphite crucible (99.9999%) with an inner diameter of 50 mm and a height of 90 mm was used for holding CaF2 melts in which the depth of the melt was about 50 mm. The starting materials were dried at 200oC for 2 h under vacuum for the dehydration, and then melted under dry Ar atmosphere to protect against oxidation at the required temperature until a homogeneous melt was obtained. Dry Ar gas was kept flowing throughout the whole experiment, whose flow rate was 0.5l/min, the pressure in the chambers was maintained at 760 Torr.
Position 2
25mm Position1
V
3.1. Density measurement The probe was made of high pure graphite (99.9999%) which has an extremely low reactivity with CaF2 melt. To eliminate any influence resulted from the surface tension of the melt on density measurement, the density was measured by an improved Archimedian version, a single-bob probe with two equivalent arms [16], as shown in Fig. 2. The effect of the surface tension term could be cancelled by measuring the weight of the probe at various dipped depths in the melt. An accurate density of the melt can be obtained according to the following formula: W1 W 2 r¼ ; ð1Þ Vr where W1 is the weight of the probe when the surface of the melt was in position 1, and W2 is the weight of the probe at position 2. Vr is the volume of the probe in the part between positions 1 and 2.
10mm 12mm
3mm
Fig. 2. Schematic of one-bob probe for measuring the density.
Vr was measured in advance with the same method by using Hg at room temperature T0 : Because of thermal expansion in high temperature, the volume of the probe was modified in high temperature T by the following formula: Vr ðTÞ ¼ Vr ðT0 Þ½1 þ 3bðT T0 Þ;
3. Measuremental principles
447
ð2Þ
where b is the linear thermal expansion coefficient of the pure graphite, which is 3.6 106 K1. An electric balance with an accuracy of 0.1 mg was used to measure the weight of the probe. The relative error of the density measurement was estimated to be within 70.2%.
4. Surface tension measurement The conventional ring technique used to measure the surface tension is based on the measurement of the maximum equilibrium force to detach a circular ring from the surface of the liquid. The surface tension g can be determined by the formula g¼
F f; 4pR
ð3Þ
where R is the radius of the ring, and F is the maximum equilibrium force. The dimensionless correction factor, f ; is the Harkins–Jordan factor [17], which is indicated by the equation of dimensionless parameters R3 =Vg and R=r; where
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
448
Vg is the volume of the liquid pulled up by the ring, represented as Vg ¼
F ; gðr1 r2 Þ
ð4Þ
where r1 is the density of the liquid, r2 is the density of the gas above the surface of the liquid and g is the gravity.
Contact Angle (° )
120
100
80
1713(K) 1733(K) 1753(K)
θ
CaF2 melt Graphite base
60 0
20
40
60
80
100
120
Time (min)
Fig. 3. The result of the contact angle.
5
.2
For the accurate measurement of surface tension, the materials for the probe ring must have good wettability and no reactivity with the measured liquid. For the lower wettability, there will be larger error of the surface tension measured using the conventional ring technique. Pure graphite has no reactivity with CaF2 melt, so the graphite probe ring was used in this work. The side view of droplet or graphite is given in Fig. 3. Contact angle variation of molten CaF2 has been measured by using pure graphite as substrate. No time dependence has been found as shown in Fig. 3. It is thought that this graphite material is suitable for measurement set to an experiment of longer duration. A new ring depression technique [1] was used to measure the surface tension of CaF2 melt. The tensiometer made of pure graphite is shown in Fig. 4. The entire tensiometer assembled included a ring and a graphite case. The ring was attached on the graphite case. In order to push the ring easily into the melt, a 70 g tungsten weight was mounted into the graphite case. During the experiment, down the tensiometer with 0.01 mm/s, because of the lower wettability of
Tungsten weight
R0
0.5mm
Graphite case
f15mm Carbon ring
Fig. 4. Scheme of graphite ring for measuring surface tension.
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
graphite with CaF2 melt, the surface of the CaF2 will push up the tensiometer, the shape of the surface is shown in Fig. 5. Before the surface was broken, the tensiometer will be given a maximum resistant force F : According to formula (4), the surface tension of the melt can be calculated. The surface tension was measured three times at every temperature, and then an average surface tension value was obtained.
Fig. 5. The shape of the surface of the melt with ring depressing.
1650 2.64
1700
1750
5. Results and discussion The temperature dependence of the density of molten CaF2 are shown in Fig. 6, where open circles and triangles show datum points from separated two runs during cooling in the present work, and also with those results obtained by many investigators. When cooling speed was at 2 K/min, no supercooled phenomenon occurred. The melt started to crystallize when the temperature was down to the melting point. It was found that the density versus the temperature for two experiments is the same corresponding to a linear relationship: r ¼ 3:767 6:94 104 TðKÞ: The density of the CaF2 melt at the melting point is 2.594 g/cm3, which is near to the result obtained by Shiraishi and Watanabe [2], but the temperature coefficient of the density attached in this work is larger than the their results. The density measured by other authors is given in Table 1, compared with the present work. Zhmoidin [10] computed the density by the maximum gas bubble pressure method. His data remained at about 1% difference as compared with our results. The error of weight signal is o0.1%. The volume error of probe was o0.1% by canceling the surface tension term. The total error of our method was estimated as o1%.
1800
1850
1900 2.64
First Second 1 V.K.Kulifeev 2 A.Mitchell 3 A.D.Kirshenbaum 4 S.Hara 5 Y.Shiraishi
2.60
Density (g/cm3)
449
2.56
2.60
2.56 5
4
2.52
2.52
2
1
2.48
2.48
3
2.44 1650
2.44 1700
1750
1800
1850
1900
Temperature (K) Fig. 6. Temperature dependence of the density of molten CaF2 in comparison with the available data.
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
450
In the present work, a pure graphite probe was used to measure the density of molten CaF2, which has no wettability with melt, so no CaF2 melt attach to the probe when the probe was pulled out from the melt every time. The volume of the probe can only be modified by formula (2) due to the thermal expansion of the probe. In this case, the error of density measurement will be reduced. From the temperature coefficient of density, the thermal expansion coefficient of the CaF2 melt b can be obtained as follows: b¼
1 dV 1 dr ¼ : V dT rdT
ð5Þ
The temperature dependence of the thermal expansion coefficient of the CaF2 melt is shown
in Fig. 7. The thermal expansion coefficient of CaF2 melt linearly increases with rise in temperature. We used the conventional ring technique and ring depressing technique to measure the maximum equilibrium force. For the conventional ring technique, the ring was dipped into melt about 5 mm in advance, and then the ring was pulled up with a slow velocity of 0.01 cm/s; while for depressing ring technique reported by Nakanishi et al. [1], the ring was placed in contact with the melt surface, and then it was depressed into the melt with the same velocity. Because graphite has no wettability with CaF2 melt, the graphite ring was resisted into CaF2 melt. The resistant from the surface of the melt gradually increased with
Table 1 Densities of CaF2 melt measured by different investigators r ¼ a2b 104 Tr (g/cm3) b=4.021 b ¼ 5:25 b ¼ 2:86 b ¼ 3:60 b ¼ 3:91 b ¼ 5:06 b ¼ 4:45 b ¼ 6:940
Thermal expansion coefficient β 10- 4 (K-1 )
a ¼ 3:257; a ¼ 3:416; a ¼ 3:059; a ¼ 3:203; a ¼ 3:179; a ¼ 3:405; a ¼ 3:299; a ¼ 3:767;
Temperature range (K)
rTm (g/cm)
Impurity
Method
Ref.
1693–2100 1700–2000 1673–1973 1723–1823 1650–2300 1723–1873 1714–1859 1690–1790
2.557 2.528 2.575 2.594 2.519 2.549 2.547 2.594
Pure Pure Pure 99.96 99.96 99.9 98.0 99.99
Archimedian Gas bubble pressure Archimedian Archimedian Archimedian Archimedian Archimedian Improved Archimedian
10 13 14 2 15 15 15 Present work
1680 2.76
1700
1720
1740
1760
1780 2.76
2.74
2.74
2.72
2.72
2.70
2.70
2.68
2.68
2.66 1680
2.66 1700
1720
1740
1760
1780
Temperature (K) Fig. 7. Temperature dependence of the thermal expansion coefficient of CaF2 melt.
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453 Pulling height (mm) -0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
4 1.4
Ring depression technique Conventional ring technique
1.2 1.0 0.8
2
0.6 1
0.4
Pulling force (g)
Resistant force (g)
3
0.2 0
0.0 -0.2
-1 0
50
100
150
200
250
300
Depressing depth (mm)
Fig. 8. The equilibrium force measured by ring depressing technique and the conventional ring technique.
depressing depth, and reached a maximum resistant force, then decreased slightly before the surface of the melt was broken. The result is shown in Fig. 8. It can be seen that there exist big differences to measure the maximum equilibrium force using the conventional ring technique and ring depressing technique for the present work. The maximum equilibrium force for pulling ring 1 technique is only 0.45 g, which is about 60 th of that measured by depressing ring technique. The surface tension value measured by pulling ring technique for CaF2 melt will be much smaller than its true value. So the conventional ring technique cannot be used if the ring probe material has no good wettability with the measured melt. The temperature dependence of the surface tension of CaF2 melt measured by depressing ring technique is shown in Fig. 9, compared with some results obtained by other investigators. It can be found that the measured surface tension using the ring depressing technique is larger than that measured by other techniques. The surface tension of CaF2 indicates a negative linear relationship as a function of the melt temperature: gðTÞ ¼ 442:4 0:0816 TðKÞ (mN/m). The surface tension at the melting point was obtained to be 304.4 N/m, which is 2% larger than the surface tension value at the melting point obtained by Hara and Ogino [11] using maximum bubble pressure method. Surface tensions of CaF2 melts measured by other
451
researchers are given in Table 2. The result of the present work is close to that of Hara and Ogino [15]. The error sources on the determination of surface tension are (1) the horizontality of the ring; (2) accuracy of the ring radius; and (3) temperature fluctuation. The contribution of Nos. (1) and (2) to the error can be estimated to be o0.1%. The error from the dimension of the ring was estimated to be 0.1% due to the construction accuracy of 0.01 mm. The density of Ar in high temperature is very low compared with that of CaF2 melt, about 0.001 g/cm, which is within the error of the density measurement. So r2 in formula (4) was cancelled in the calculation. The total error was estimated at about 70.3 mN/m. Compared with these results obtained by different authors, it can be illustrated that the probe materials has no good wettability with measured melt. The ring depressing technique is an effective way to measure the surface tension. The decrease in the difference of the measured value is thought to be due to the improvement in measurement accuracy and measurement sample. The buoyancy of the tensiometer due to Ar gas during the measurement was small owing to the high temperature. The error caused by these factors was estimated to be o0.2%. The total uncertainty of the measurement is thus estimated to be within 2.0%.
6. Conclusion The density of molten CaF2 was measured in the temperature range of 1690–1790 K by an improved Archimedian method. The density linearly increased with temperature cooling corresponding to a linear relationship: r ¼ 3:767 6:94 104 T (K). The density of the CaF2 melt at the melting point is 2.594 g/cm3, which is equal to the result reported by Shiraishi, but the temperature coefficient of the density is different from their results. The thermal expansion coefficient of CaF2 melt linearly increases with temperature. A new ring depressing technique was used to measure the surface tension of CaF2 melt. An effective technique to measure the surface tension of the
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
452
1680 306
1700
1720
1740
1760
1780 306
Surface tension (mN/m)
Ring Depressing Technique 304
304
302
302
300
300
298
298
1680
1700
1720
1740
1760
1780
Temperature (K) 1700
1750
1800
1850
1900
Surface tension (mN/m)
320
320 present work 1 G.I.Zhmodin 2 G.I.Kipov 3 S.Hara 4 V.K.Kulifeev
300
3
280 2
300
280 1
260
260
4
240
240
1700
1750
1800
1850
1900
Temperature (K) Fig. 9. Temperature dependence of the surface tension of CaF2 melt.
Table 2 Surface tensions of CaF2 melt g ¼ a2b Tg (N/m) a ¼ 464:3; a ¼ 848:0; a ¼ 307:7; a ¼ 440:7; a ¼ 453:6; a ¼ 459:0; a ¼ 442:4;
b ¼ 0:1016 b ¼ 0:33 b ¼ 0:033 b ¼ 0:0844 b ¼ 0:0925 b ¼ 0:0956 b ¼ 0:0816
Temperature range (K)
gTm (mN/m)
Impurity
Method
Ref.
1700–2000 1698–1733 1703–2000 1723–1853 1718–1861 1724–1859 1690–1790
292.5 290.0 251.9 298.0 297.2 297.3 304.4
Pure Pure Pure 99.9 99.0 98.0 99.99
Gas bubble pressure Gas bubble pressure Gas bubble pressure Gas bubble pressure Gas bubble pressure Gas bubble pressure Repression ring
13 16 12 15 15 15 Present work
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
melt which has no good wettability with the ring probe material in comparison with the conventional ring pulling technique was demonstrated. The surface tension of CaF2 melt measured using the ring depressing technique is larger than those results measured by other techniques. The surface tension indicates a negative linear relationship as a function of the melt temperature: gðTÞ ¼ 442:4 0:0816 TðKÞ (mN/m), which is close to the results reported by Hara et al. using maximum bubble pressure method.
Acknowledgements The authors express their appreciation to Optron Inc. for providing the raw calcium fluoride materials. This work was conducted as JSPS Research for the Future Program in the area of Atomic-Scale Surface and Interface Dynamics.
References [1] H. Nakanishi, K. Nakazato, S. Asaba, K. Abe, S. Maeda, K. Terashima, J. Crystal Growth 187 (1998) 391.
453
[2] Y. Shiraishi, S. Watanabe, Bull. Res. Inst. Miner. Dressing Metal Tohoku Univ. 34 (1978) 1. [3] H. Guggenheim, J. Appl. Phys. 32 (1961) 1337. [4] K. Nassau, J. Appl. Phys. 32 (1961) 1820. [5] D.C. Stockbarger, J. Am. Opt. Soc. 39 (1949) 731. [6] H. Guggenheim, J. Phys. Chem. 64 (1960) 938. [7] V.K. Kulifeev, V.I. Panchishnyi, G.P. Stanolevich, Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. 2 (1968) 116. [8] P.P. Evseev, A.F. Filippov, Izv. Vuzov. Cher. Metall. 3 (1965) 30. [9] A.D. Kirshenbaum, J.A. Cahill, C.S. Stokes, J. Inorg. Nucl. Chem. 15 (1960) 297. [10] G.I. Zhmoidin, Russ. J. Phys. Chem. 49 (1975) 874. [11] A. Mitchell, S. Joshi, Metall. Trans. 3 (1972) 2306. [12] V.K. Kulifeev, V.I. Panchishnyi, G.P. Stanolevich, Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. 1 (1969) 80. [13] G.I. Kipov, S.N. Zadumkin, J. Phys. Chem. 46 (1972) 1063. [14] G.I. Kipov, S.N. Zadumkin, Zh. Fiz. Khim. 46 (1972) 1852. [15] S. Hara, K. Ogino, ISIJ Int. 29 (1989) 477. [16] H. Sasaki, E. Tokizaki, K. Terashima, S. Kimura, J. Crystal Growth 139 (1994) 225. [17] W.D. Harkins, H.F. Jordan, J. Am. Chem. Soc. 52 (1930) 1751.
Density and surface tension of molten calcium fluoride Xiumei Chena, Suguru Jinguub, Suzuka Nishimurac, Yasunao Oyamad, Kazutaka Terashimab,* b
a Institute of Physics, Chinese Academy of Sciences, P.O. Box 603, Beijing 100080, People’s Republic of China Department of Material Science and Technology, Shonan Institute of Technology 1-1-25 Tsujido-nishikaigan, Fujisawa, Kanagawa 251-8511, Japan c Keio University, 3-14-1 Hiyoshi, Kohoku-ku, Yokohama-shi, Kanagawa 223-8522, Japan d Optron Inc., Toride-shi, Ibaraki 302-0023, Japan
Received 14 November 2001; accepted 24 January 2002 Communicated by K.W. Benz
Abstract The density and the surface tension of molten calcium fluoride have been measured in the temperature range from 1690 to 1790 K by an improved Archimedian method and a ring depressing technique (J. Crystal Growth 187 (1998) 391), respectively. The ring depressing technique was demonstrated as an effective technique to measure the surface tension in comparison with the conventional ring pulling technique. The density varied with the temperature change corresponding to a linear relationship: r ¼ 3:767 6:94 104 T (K). The density of the CaF2 melt at the melting point is 2.594 g/cm3, which is equal to the result obtained by Shiraishi and Watanabe (Bull. Res. Inst. Miner. Dressing Metal, Tohoku Univ. 34 (1978) 1), but the temperature coefficient of the density is different from the results obtained by other investigators. The thermal expansion coefficient of calcium fluoride melt linearly increases with temperature heating. The surface tension of molten calcium fluoride indicates a negative linear relationship as a function of the melt temperature: gðTÞ ¼ 442:4 0:0816 TðKÞ (mN/m). The surface tension measured using the ring depressing technique is larger than those results obtained by other techniques. r 2002 Elsevier Science B.V. All rights reserved. PACS: 81.10.h Keywords: A1. Density; A1. Surface tension; A2. Ring depressing technique; B1. Calcium fluoride melt
1. Introduction Calcium fluoride (CaF2) is a representative alkaline earth fluoride that has been the subject of experimental and theoretical studies for years. It *Corresponding author. Tel./fax: +81-466-300226. E-mail address: [email protected] (K. Terashima).
has for many years been one of the important materials used in the design of optical components and systems. At the present time, there are various methods available for the production of fluoride single crystals. In some earlier investigations, the horizontal-growth technique [3], normal crystal pulling [3,4] and Bridgman–Stockbarger technique [5,6] were used to grow the fluoride single crystal. However, those crystals grown by the
0022-0248/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 0 2 4 8 ( 0 2 ) 0 0 8 7 9 - 5
446
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
horizontal-growth technique had two kinds of imperfections, first is that the crystals exhibited extensive internal strain; second, the formation of minute amounts of oxide cannot be completely eliminated. So, the fundamental properties are for designing crystal growth condition to grow a large size crystal with high perfection from the melt. The density is considered to be one of the melt fundamental properties of a liquid material, and also the liquid thermal expansion coefficient of the materials can be obtained from the temperature dependence of the density. The surface tension represents a state of the surface of the melt. The temperature gradient of the surface results in a Marangoni flow near the surface of the melt, which affects the mass and energy transportation significantly during the crystal growth. However, there were not many works on the measurements of the physico-chemical properties of CaF2 melt, and also the accurate data were very poor. There were some reports about the properties of the molten CaF2, but the data were scattered very much, and there were large differences for the data of density [7–11] and surface tension [2–15]
obtained by different investigators. At the same temperature the maximum of the difference was over 10% for density and surface tension. So the accurate and reliable data are still lacking for the fundamental properties of CaF2 melts, because CaF2 melt has higher reactivity to container materials and also to gas phase. In this work, the density and surface tension of CaF2 melt have been measured accurately within about 100 K around the melting point of CaF2 (1690 K).
2. Experimental procedure The apparatus used for measuring the density and surface tension consists of evacuation and argon gas outlet. A schematic of the setup is shown in Fig. 1. The whole furnace heater and an electric balance were sealed in a chamber with cooling water. The CaF2 samples were melted in a vertical furnace heated by two high pure graphite heaters, which were regulated by two separate controllers, respectively. The temperature of the melt was directly measured by an immersed Pt/Pt-10%
Electronic balance Pt thermal couple Ar Inlet
Tungsten wire
Graphite ring probe Graphite crucible
Water cooled chamber
Upper graphite heater Molten calcium fluoride
Carbon fiber insulator Lower graphite heater
Exhaust
Fig. 1. The scheme of the experimental apparatus for measuring the density and surface tension.
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
Rh-type thermocouple covered with alumina tube. In order to reduce the convection in hightemperature melt, the crucible was placed at a proper position in the furnace so that the temperature of the upper region of the melt was slightly higher about 5 K than that of the bottom part of the melt. The fluctuation of the temperature in the melt was controlled within 70.5 K. Single crystalline CaF2 was used as the starting materials, the purity of the sample was guaranteed at over 99.99% (Optron Inc.). High pure graphite crucible (99.9999%) with an inner diameter of 50 mm and a height of 90 mm was used for holding CaF2 melts in which the depth of the melt was about 50 mm. The starting materials were dried at 200oC for 2 h under vacuum for the dehydration, and then melted under dry Ar atmosphere to protect against oxidation at the required temperature until a homogeneous melt was obtained. Dry Ar gas was kept flowing throughout the whole experiment, whose flow rate was 0.5l/min, the pressure in the chambers was maintained at 760 Torr.
Position 2
25mm Position1
V
3.1. Density measurement The probe was made of high pure graphite (99.9999%) which has an extremely low reactivity with CaF2 melt. To eliminate any influence resulted from the surface tension of the melt on density measurement, the density was measured by an improved Archimedian version, a single-bob probe with two equivalent arms [16], as shown in Fig. 2. The effect of the surface tension term could be cancelled by measuring the weight of the probe at various dipped depths in the melt. An accurate density of the melt can be obtained according to the following formula: W1 W 2 r¼ ; ð1Þ Vr where W1 is the weight of the probe when the surface of the melt was in position 1, and W2 is the weight of the probe at position 2. Vr is the volume of the probe in the part between positions 1 and 2.
10mm 12mm
3mm
Fig. 2. Schematic of one-bob probe for measuring the density.
Vr was measured in advance with the same method by using Hg at room temperature T0 : Because of thermal expansion in high temperature, the volume of the probe was modified in high temperature T by the following formula: Vr ðTÞ ¼ Vr ðT0 Þ½1 þ 3bðT T0 Þ;
3. Measuremental principles
447
ð2Þ
where b is the linear thermal expansion coefficient of the pure graphite, which is 3.6 106 K1. An electric balance with an accuracy of 0.1 mg was used to measure the weight of the probe. The relative error of the density measurement was estimated to be within 70.2%.
4. Surface tension measurement The conventional ring technique used to measure the surface tension is based on the measurement of the maximum equilibrium force to detach a circular ring from the surface of the liquid. The surface tension g can be determined by the formula g¼
F f; 4pR
ð3Þ
where R is the radius of the ring, and F is the maximum equilibrium force. The dimensionless correction factor, f ; is the Harkins–Jordan factor [17], which is indicated by the equation of dimensionless parameters R3 =Vg and R=r; where
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
448
Vg is the volume of the liquid pulled up by the ring, represented as Vg ¼
F ; gðr1 r2 Þ
ð4Þ
where r1 is the density of the liquid, r2 is the density of the gas above the surface of the liquid and g is the gravity.
Contact Angle (° )
120
100
80
1713(K) 1733(K) 1753(K)
θ
CaF2 melt Graphite base
60 0
20
40
60
80
100
120
Time (min)
Fig. 3. The result of the contact angle.
5
.2
For the accurate measurement of surface tension, the materials for the probe ring must have good wettability and no reactivity with the measured liquid. For the lower wettability, there will be larger error of the surface tension measured using the conventional ring technique. Pure graphite has no reactivity with CaF2 melt, so the graphite probe ring was used in this work. The side view of droplet or graphite is given in Fig. 3. Contact angle variation of molten CaF2 has been measured by using pure graphite as substrate. No time dependence has been found as shown in Fig. 3. It is thought that this graphite material is suitable for measurement set to an experiment of longer duration. A new ring depression technique [1] was used to measure the surface tension of CaF2 melt. The tensiometer made of pure graphite is shown in Fig. 4. The entire tensiometer assembled included a ring and a graphite case. The ring was attached on the graphite case. In order to push the ring easily into the melt, a 70 g tungsten weight was mounted into the graphite case. During the experiment, down the tensiometer with 0.01 mm/s, because of the lower wettability of
Tungsten weight
R0
0.5mm
Graphite case
f15mm Carbon ring
Fig. 4. Scheme of graphite ring for measuring surface tension.
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
graphite with CaF2 melt, the surface of the CaF2 will push up the tensiometer, the shape of the surface is shown in Fig. 5. Before the surface was broken, the tensiometer will be given a maximum resistant force F : According to formula (4), the surface tension of the melt can be calculated. The surface tension was measured three times at every temperature, and then an average surface tension value was obtained.
Fig. 5. The shape of the surface of the melt with ring depressing.
1650 2.64
1700
1750
5. Results and discussion The temperature dependence of the density of molten CaF2 are shown in Fig. 6, where open circles and triangles show datum points from separated two runs during cooling in the present work, and also with those results obtained by many investigators. When cooling speed was at 2 K/min, no supercooled phenomenon occurred. The melt started to crystallize when the temperature was down to the melting point. It was found that the density versus the temperature for two experiments is the same corresponding to a linear relationship: r ¼ 3:767 6:94 104 TðKÞ: The density of the CaF2 melt at the melting point is 2.594 g/cm3, which is near to the result obtained by Shiraishi and Watanabe [2], but the temperature coefficient of the density attached in this work is larger than the their results. The density measured by other authors is given in Table 1, compared with the present work. Zhmoidin [10] computed the density by the maximum gas bubble pressure method. His data remained at about 1% difference as compared with our results. The error of weight signal is o0.1%. The volume error of probe was o0.1% by canceling the surface tension term. The total error of our method was estimated as o1%.
1800
1850
1900 2.64
First Second 1 V.K.Kulifeev 2 A.Mitchell 3 A.D.Kirshenbaum 4 S.Hara 5 Y.Shiraishi
2.60
Density (g/cm3)
449
2.56
2.60
2.56 5
4
2.52
2.52
2
1
2.48
2.48
3
2.44 1650
2.44 1700
1750
1800
1850
1900
Temperature (K) Fig. 6. Temperature dependence of the density of molten CaF2 in comparison with the available data.
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
450
In the present work, a pure graphite probe was used to measure the density of molten CaF2, which has no wettability with melt, so no CaF2 melt attach to the probe when the probe was pulled out from the melt every time. The volume of the probe can only be modified by formula (2) due to the thermal expansion of the probe. In this case, the error of density measurement will be reduced. From the temperature coefficient of density, the thermal expansion coefficient of the CaF2 melt b can be obtained as follows: b¼
1 dV 1 dr ¼ : V dT rdT
ð5Þ
The temperature dependence of the thermal expansion coefficient of the CaF2 melt is shown
in Fig. 7. The thermal expansion coefficient of CaF2 melt linearly increases with rise in temperature. We used the conventional ring technique and ring depressing technique to measure the maximum equilibrium force. For the conventional ring technique, the ring was dipped into melt about 5 mm in advance, and then the ring was pulled up with a slow velocity of 0.01 cm/s; while for depressing ring technique reported by Nakanishi et al. [1], the ring was placed in contact with the melt surface, and then it was depressed into the melt with the same velocity. Because graphite has no wettability with CaF2 melt, the graphite ring was resisted into CaF2 melt. The resistant from the surface of the melt gradually increased with
Table 1 Densities of CaF2 melt measured by different investigators r ¼ a2b 104 Tr (g/cm3) b=4.021 b ¼ 5:25 b ¼ 2:86 b ¼ 3:60 b ¼ 3:91 b ¼ 5:06 b ¼ 4:45 b ¼ 6:940
Thermal expansion coefficient β 10- 4 (K-1 )
a ¼ 3:257; a ¼ 3:416; a ¼ 3:059; a ¼ 3:203; a ¼ 3:179; a ¼ 3:405; a ¼ 3:299; a ¼ 3:767;
Temperature range (K)
rTm (g/cm)
Impurity
Method
Ref.
1693–2100 1700–2000 1673–1973 1723–1823 1650–2300 1723–1873 1714–1859 1690–1790
2.557 2.528 2.575 2.594 2.519 2.549 2.547 2.594
Pure Pure Pure 99.96 99.96 99.9 98.0 99.99
Archimedian Gas bubble pressure Archimedian Archimedian Archimedian Archimedian Archimedian Improved Archimedian
10 13 14 2 15 15 15 Present work
1680 2.76
1700
1720
1740
1760
1780 2.76
2.74
2.74
2.72
2.72
2.70
2.70
2.68
2.68
2.66 1680
2.66 1700
1720
1740
1760
1780
Temperature (K) Fig. 7. Temperature dependence of the thermal expansion coefficient of CaF2 melt.
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453 Pulling height (mm) -0.5
-0.4
-0.3
-0.2
-0.1
0.0
0.1
0.2
0.3
4 1.4
Ring depression technique Conventional ring technique
1.2 1.0 0.8
2
0.6 1
0.4
Pulling force (g)
Resistant force (g)
3
0.2 0
0.0 -0.2
-1 0
50
100
150
200
250
300
Depressing depth (mm)
Fig. 8. The equilibrium force measured by ring depressing technique and the conventional ring technique.
depressing depth, and reached a maximum resistant force, then decreased slightly before the surface of the melt was broken. The result is shown in Fig. 8. It can be seen that there exist big differences to measure the maximum equilibrium force using the conventional ring technique and ring depressing technique for the present work. The maximum equilibrium force for pulling ring 1 technique is only 0.45 g, which is about 60 th of that measured by depressing ring technique. The surface tension value measured by pulling ring technique for CaF2 melt will be much smaller than its true value. So the conventional ring technique cannot be used if the ring probe material has no good wettability with the measured melt. The temperature dependence of the surface tension of CaF2 melt measured by depressing ring technique is shown in Fig. 9, compared with some results obtained by other investigators. It can be found that the measured surface tension using the ring depressing technique is larger than that measured by other techniques. The surface tension of CaF2 indicates a negative linear relationship as a function of the melt temperature: gðTÞ ¼ 442:4 0:0816 TðKÞ (mN/m). The surface tension at the melting point was obtained to be 304.4 N/m, which is 2% larger than the surface tension value at the melting point obtained by Hara and Ogino [11] using maximum bubble pressure method. Surface tensions of CaF2 melts measured by other
451
researchers are given in Table 2. The result of the present work is close to that of Hara and Ogino [15]. The error sources on the determination of surface tension are (1) the horizontality of the ring; (2) accuracy of the ring radius; and (3) temperature fluctuation. The contribution of Nos. (1) and (2) to the error can be estimated to be o0.1%. The error from the dimension of the ring was estimated to be 0.1% due to the construction accuracy of 0.01 mm. The density of Ar in high temperature is very low compared with that of CaF2 melt, about 0.001 g/cm, which is within the error of the density measurement. So r2 in formula (4) was cancelled in the calculation. The total error was estimated at about 70.3 mN/m. Compared with these results obtained by different authors, it can be illustrated that the probe materials has no good wettability with measured melt. The ring depressing technique is an effective way to measure the surface tension. The decrease in the difference of the measured value is thought to be due to the improvement in measurement accuracy and measurement sample. The buoyancy of the tensiometer due to Ar gas during the measurement was small owing to the high temperature. The error caused by these factors was estimated to be o0.2%. The total uncertainty of the measurement is thus estimated to be within 2.0%.
6. Conclusion The density of molten CaF2 was measured in the temperature range of 1690–1790 K by an improved Archimedian method. The density linearly increased with temperature cooling corresponding to a linear relationship: r ¼ 3:767 6:94 104 T (K). The density of the CaF2 melt at the melting point is 2.594 g/cm3, which is equal to the result reported by Shiraishi, but the temperature coefficient of the density is different from their results. The thermal expansion coefficient of CaF2 melt linearly increases with temperature. A new ring depressing technique was used to measure the surface tension of CaF2 melt. An effective technique to measure the surface tension of the
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
452
1680 306
1700
1720
1740
1760
1780 306
Surface tension (mN/m)
Ring Depressing Technique 304
304
302
302
300
300
298
298
1680
1700
1720
1740
1760
1780
Temperature (K) 1700
1750
1800
1850
1900
Surface tension (mN/m)
320
320 present work 1 G.I.Zhmodin 2 G.I.Kipov 3 S.Hara 4 V.K.Kulifeev
300
3
280 2
300
280 1
260
260
4
240
240
1700
1750
1800
1850
1900
Temperature (K) Fig. 9. Temperature dependence of the surface tension of CaF2 melt.
Table 2 Surface tensions of CaF2 melt g ¼ a2b Tg (N/m) a ¼ 464:3; a ¼ 848:0; a ¼ 307:7; a ¼ 440:7; a ¼ 453:6; a ¼ 459:0; a ¼ 442:4;
b ¼ 0:1016 b ¼ 0:33 b ¼ 0:033 b ¼ 0:0844 b ¼ 0:0925 b ¼ 0:0956 b ¼ 0:0816
Temperature range (K)
gTm (mN/m)
Impurity
Method
Ref.
1700–2000 1698–1733 1703–2000 1723–1853 1718–1861 1724–1859 1690–1790
292.5 290.0 251.9 298.0 297.2 297.3 304.4
Pure Pure Pure 99.9 99.0 98.0 99.99
Gas bubble pressure Gas bubble pressure Gas bubble pressure Gas bubble pressure Gas bubble pressure Gas bubble pressure Repression ring
13 16 12 15 15 15 Present work
X. Chen et al. / Journal of Crystal Growth 240 (2002) 445–453
melt which has no good wettability with the ring probe material in comparison with the conventional ring pulling technique was demonstrated. The surface tension of CaF2 melt measured using the ring depressing technique is larger than those results measured by other techniques. The surface tension indicates a negative linear relationship as a function of the melt temperature: gðTÞ ¼ 442:4 0:0816 TðKÞ (mN/m), which is close to the results reported by Hara et al. using maximum bubble pressure method.
Acknowledgements The authors express their appreciation to Optron Inc. for providing the raw calcium fluoride materials. This work was conducted as JSPS Research for the Future Program in the area of Atomic-Scale Surface and Interface Dynamics.
References [1] H. Nakanishi, K. Nakazato, S. Asaba, K. Abe, S. Maeda, K. Terashima, J. Crystal Growth 187 (1998) 391.
453
[2] Y. Shiraishi, S. Watanabe, Bull. Res. Inst. Miner. Dressing Metal Tohoku Univ. 34 (1978) 1. [3] H. Guggenheim, J. Appl. Phys. 32 (1961) 1337. [4] K. Nassau, J. Appl. Phys. 32 (1961) 1820. [5] D.C. Stockbarger, J. Am. Opt. Soc. 39 (1949) 731. [6] H. Guggenheim, J. Phys. Chem. 64 (1960) 938. [7] V.K. Kulifeev, V.I. Panchishnyi, G.P. Stanolevich, Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. 2 (1968) 116. [8] P.P. Evseev, A.F. Filippov, Izv. Vuzov. Cher. Metall. 3 (1965) 30. [9] A.D. Kirshenbaum, J.A. Cahill, C.S. Stokes, J. Inorg. Nucl. Chem. 15 (1960) 297. [10] G.I. Zhmoidin, Russ. J. Phys. Chem. 49 (1975) 874. [11] A. Mitchell, S. Joshi, Metall. Trans. 3 (1972) 2306. [12] V.K. Kulifeev, V.I. Panchishnyi, G.P. Stanolevich, Izv. Vyssh. Uchebn. Zaved. Tsvetn. Metall. 1 (1969) 80. [13] G.I. Kipov, S.N. Zadumkin, J. Phys. Chem. 46 (1972) 1063. [14] G.I. Kipov, S.N. Zadumkin, Zh. Fiz. Khim. 46 (1972) 1852. [15] S. Hara, K. Ogino, ISIJ Int. 29 (1989) 477. [16] H. Sasaki, E. Tokizaki, K. Terashima, S. Kimura, J. Crystal Growth 139 (1994) 225. [17] W.D. Harkins, H.F. Jordan, J. Am. Chem. Soc. 52 (1930) 1751.