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Ind. Eng. Chem. Res. 2004, 43, 3194-3199
GENERAL RESEARCH Physicochemical Properties of Acidic Ammonium Phosphate Slurries Tang Shengwei, Guo Hui, Ying Jiankang, and Liang Bin* Multiphase Transfer and Reaction Engineering Laboratory, Department of Chemical Engineering, Sichuan University, Chengdu 610065, P. R. China
Acidic ammonium phosphate slurries with different degrees of neutralization were obtained by neutralizing dilute phosphoric acid with ammonia. They were then concentrated to different water contents. The effects of the degree of neutralization and water content on the density, boiling point, fluorine volatility, thermal conductivity, and viscosity were studied. The results indicate that the density of the slurry increases with decreasing water content and/or neutralization degree. The density of acidic ammonium phosphate slurries can be calculated by the formula F ) k[FSxv + FL(1 - xv)]. The experiments show that the boiling point of an acidic ammonium phosphate slurry increases with decreasing water content and/or neutralization degree. When the water content is below 40%, the boiling point strongly depends on the water content. The fluorine in the slurry, brought in with wet-process phosphoric acid, volatilizes when the slurry is heated. The volatility increases with increasing concentration of the slurry. The volatilization is significant in low range of neutralization degrees. It increases sharply with decreasing neutralization degree. Increasing the degree of neutralization above 0.6 causes the volatility to drop to a rather low level. The thermal conductivity of acidic ammonium phosphate slurries varies from 0.471 to 0.608 W‚m-1‚K-1. For an acidic ammonium phosphate solution, the thermal conductivity increases with increasing water content or neutralization degree. However, for such a slurry, the presence of a crystalline phase makes the thermal conductivity increase with decreasing water content. The viscosity is the lowest for a slurry with a neutralization degree of 0.52. The viscosity increases with decreasing water content. The slurry behaves as a Newtonian fluid when its water content is above 40%. However, it switches to act as a pseudoplastic fluid when its water content decreases below 40%. Increasing the temperature can reduce the viscosity. 1. Introduction As an important compound in fertilizers, ammonium phosphate is commercially manufactured by neutralizing wet-process phosphoric acid with ammonia. The wet-process phosphoric acid is usually a dilute solution containing about 50-60% water obtained by leaching phosphate ore with sulfuric acid. In a traditional plant, the wet-process phosphoric acid is first concentrated by an evaporator and then neutralized with ammonia to produce ammonium phosphate. The quality of the phosphate ore is strictly limited, because impurities such as aluminum, iron, and magnesium are likely to form a scale that adheres on the heating surface of the evaporator.1,2 Problems of scaling can be solved by using a new process, APPSC (ammonium phosphate production by slurry concentration).1-3 In this process, the concentration of the wet-process phosphoric acid is substituted by a concentration of ammonium phosphate slurry. APPSC is an effective process for devices that use middle-quality ore as the material for producing am* To whom correspondence should be addressed. Tel.: +8628-85460556. Fax: +86-28-85461108. E-mail: binliang@ mail.sc.cninfo.net.
monium phosphate. However, the evaporation of the slurry hardly occurs at water contents below 22% because of low fluidity. A higher operating temperature is required in the subsequent drying unit to remove the residual moisture. As a result, the energy consumption increases. A conceptual combination of the two processes seems to be quite attractive. The wet-process phosphoric acid is partially neutralized. Most of the harmful impurities are precipitated in the period of initial neutralization. The acidic slurry obtained is then concentrated in the evaporator. The acidic slurry contains lower levels of impurities than the dilute wet-process acid and also has a lower solid content than the completely neutralized slurry. It makes the evaporation easy to reach lower water content. The concentrated acidic slurry is further neutralized and dried to produce ammonium phosphate. Furthermore, the reaction heat of supplementary neutralization is effectively used to evaporate the residual moisture. The energy consumption in the drying process can be greatly reduced. However, the available physicochemical data on the acidic slurry are insufficient to evaluate this new process. Zhong et al.1,2 measured the boiling points of slurries with neutralization degrees slightly above 1.0.
10.1021/ie030839y CCC: $27.50 © 2004 American Chemical Society Published on Web 05/06/2004
Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 3195
The boiling points of the slurries increase with decreasing water content. When the water content drops below 20%, the boiling point sharply increases with any further reduction of the water content in the slurry. Broxki et al.4 found that the viscosity of the slurry is the lowest when the neutralization degree is 0.7. Some fragmental data on boiling points, viscosities, and densities of acidic slurries have been reported.4,5 However, such information is far from a systemic description about the behavior of the acidic slurry. In addition to the physicochemical data, many factors, such as viscosity, fluorine evaporation, impurities, corrosion, heat transfer, etc., will affect the behavior of a slurry during evaporation. This work focuses on the measurement of fundamental data and briefly discusses the probability of realization of this new process. 2. Experimental Section 2.1. Materials. The wet-process phosphoric acid used in this work was obtained from a commercial source, Yinshan Chemical Co., Sichuan, China. The composition of this phosphoric acid is listed in Table 1. Pure phosphoric acid (analytical reagent) was used to prepare samples for comparison, which provided a baseline to show the influence of impurities. 2.2. Apparatus and Procedure. Phosphoric acid was neutralized with gaseous ammonium in a 1500-mL Mo2Ti tank. A series of acidic ammonium phosphate slurries with different degrees of neutralization were obtained by controlling the flow rate of ammonium. Then, the acidic slurries were concentrated. Neutralization degree is defined as the mole ratio of ammonium to phosphoric acid. The neutralization degrees were measured by acid-base titration.1,6 A pH meter (pHS-2C, Shanghai Leici, China) was employed to measure the pH values of slurries at room temperature. Under atmospheric pressure, each slurry was heated with an electric heater and stirred with a magnetic agitator. The boiling point of the slurry was determined with a precision thermometer ((0.05 K). Density was measured at atmospheric pressure and room temperature with a plug-type pycnometer. A fluorine ion electrode (pF-1, Shanghai Leici, China) was used to measure the fluorine content in the acidic ammonium phosphate slurries.7 Fluorine brought in with the wet-process phosphoric acid volatilizes when the slurry is heated during the concentration process. The amount of fluorine released into the vapor is an important parameter in the design of evaporation units because fluorine-containing vapor is corrosive to cooling devices. The volatilization ratio is expressed as the percentage of the initial fluorine content.
xFi )
F0 - Fi × 100% F0
(1)
A coaxial cylinder technique was developed to measure the thermal conductivity of the acidic slurries.8 The viscosities of the slurries at different shearing velocities and/or different water contents was measured with an NXS-11 rotation viscometer. 3. Results and Discussion 3.1. Densities. The densities of acidic ammonium phosphate slurries are listed in Tables 2 and 3. The
Table 1. Composition (wt %) of Phosphoric Acids1,6 phosphoric acid component
wet-process
dilute pure
P2O5 SO3 CaO MgO SiO2 Fe2O3 Al2O3 F
19.41 1.98 3.34 1.47 0.35 0.65 0.67 0.16
23.68 0.03 0.30 0.02 0.10 0.04 0.44 0.01
density increases with decreasing water content and/ or neutralization degree. Under the same conditions, a slurry from wet-process phosphoric acid shows a slightly higher density than that from reagent acid. As a three-component system of H3PO4-NH4H2PO4H2O, the acidic slurry was considered as a system of solid ammonium phosphate + phosphoric acid + ammonium phosphate solution. For an ideal mixture, the density of the slurry is the weighted average of the densities of both the solid phase and the liquid phase. In eq 2, a calibration coefficient, k, is introduced as a correction for the real properties of the acidic ammonium phosphate slurry. The density can be evaluated by the following equations:
xac )
F ) k[FSxv + FL(1 - xv)]
(2)
xac 1 - xac 1 ) + FL Fac FamL
(3)
(1 - xw)(1 - x)Mac (1 - xS)[Mac(1 - x) + Mamx] x(1 - xw)Mam
xam )
Mam x + Mac(1 - x)
(4)
- xS
(1 - xS)(1 - xac)
(5)
Data fitting shows that the coefficient k is unity for slurries from dilute pure phosphoric acid and 1.03 for slurries from wet-process acid. For slurries from wetprocess acid, the prediction errors with the above model are under 5%, and the average relative error in our experiments is 1.68%. For acidic slurries from pure phosphoric acid, the average relative error is 0.95%, and the largest error is less than 4%. 3.2. Boiling Points. The boiling points of the acidic slurries are also listed in Tables 2 and 3. For a dilute solution, the boiling point is insensitive to both the neutralization degree and the water content. However, when the water content of the slurry decreases to near 40%, the boiling point increased rapidly, and the neutralization degree showed a significant influence on the boiling point. This is consistent with the results of Zhong.1 According to Raoult’s law, both H3PO4 and NH4H2PO4, as involatile solutes, can cause an increase in the boiling point of the slurry. The increase of the boiling point can be estimated with the following formula:
1000(1 - xw) ∆Tb ) Kb xw[Mam x + Mac(1 - x)]
(6)
The constant Kb is 0.52, obtained from experimental data fitting. A higher boiling point corresponds to a
3196 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 Table 2. Densities, Boiling Points, and Thermal Conductivities of the Slurries from Wet-Process Phosphoric Acid density (103 kg‚m-3)
boiling point (°C)
neutralization degree
water content (wt %)
experiment
calculation
error (%)
experiment
calculation
error (%)
thermal conductivity at 90 °C (W‚m-1‚K-1)
0.312 0.312 0.312 0.312 0.312 0.385 0.385 0.385 0.385 0.385 0.385 0.385 0.575 0.575 0.575 0.575 0.575 0.575 0.786 0.786 0.786 0.786 0.971 0.971 0.971 0.971 0.971
66.3 59.8 44.7 34.8 27.7 66.1 59.7 54.0 45.5 35.0 27.1 10.3 65.5 58.3 43.5 36.6 26.8 18.8 64.0 54.4 40.4 33.0 60.5 56.9 46.6 39.4 17.0
1.23 1.3 1.43 1.51 1.57 1.23 1.26 1.32 1.39 1.5 1.57 _ 1.23 1.27 1.42 1.48 1.22 1.29 1.41 1.49 1.21 1.25 1.32 1.41 1.58
1.23 1.27 1.39 1.47 1.54 1.23 1.27 1.31 1.38 1.47 1.54 1.24 1.28 1.4 1.46 1.24 1.31 1.42 1.48 1.26 1.29 1.36 1.43 1.64
0 -2.31 -2.8 -2.65 -1.91 0 0.79 -0.76 -0.72 -2 -1.91 0.81 0.79 -1.41 -1.35 1.64 1.55 0.71 -0.67 4.13 3.2 3.03 1.42 3.8
101.98 102.78 105.85 108.35 110.25 100.92 101.39 102.50 103.63 105.25 109.85 130.55 100.65 101.35 104.41 107.59 110.71 116.80 101.20 102.20 104.85 105.49 100.62 101.42 103.22 104.20 109.89
100.88 101.70 104.56 107.77 111.48 100.87 101.67 102.55 104.27 107.54 111.72 141.43 100.86 101.77 104.58 106.69 111.50 119.23 100.95 102.23 105.22 107.78 101.29 101.76 103.52 105.31 120.45
-1.08 -1.05 -1.22 -0.54 1.12 -0.05 0.28 0.05 0.62 2.18 1.70 8.33 0.21 0.41 0.16 -0.84 0.71 2.08 -0.25 0.03 0.35 2.17 0.67 0.34 0.29 1.07 9.61
0.518 0.498 0.473 0.476 0.471 0.538 0.546 0.538 0.549 0.518 0.509 0.602 0.542 0.539 0.520 0.524 0.569 0.600 0.543 0.526 0.515 0.559 0.535 0.522 0.504 0.497 0.578
Table 3. Densities, Boiling Points, and Thermal Conductivities of the Slurries from Dilute Pure Phosphoric Acid density (103 kg‚m-3)
boiling point (°C)
neutralization degree
water content (wt %)
experiment
calculation
error (%)
experiment
calculation
error (%)
thermal conductivity at 90 °C (W‚m-1‚K-1)
0.184 0.184 0.184 0.184 0.184 0.407 0.407 0.407 0.407 0.407 0.595 0.595 0.595 0.595 0.595 0.830 0.830 0.830 0.830 0.830 0.946 0.946 0.946 0.946 0.946
65.4 51.0 43.9 33.6 24.5 65.9 55.6 46.3 38.3 21.6 70.2 58.9 47.2 35.8 20.3 61.4 50.1 36.3 29.4 21.9 59.6 48.4 38.8 29.4 21.4
1.19 1.3 1.35 1.45 1.54 1.2 1.25 1.33 1.4 1.55 1.18 1.23 1.33 1.43 1.57 1.22 1.27 1.39 1.48 1.55 1.22 1.29 1.36 1.44 1.56
1.19 1.3 1.35 1.44 1.52 1.19 1.27 1.33 1.38 1.49 1.17 1.24 1.32 1.4 1.56 1.22 1.3 1.41 1.47 1.55 1.23 1.3 1.38 1.45 1.55
0 0 0 -0.69 -1.3 -0.83 1.6 0 -1.43 -3.87 -0.85 0.81 -0.75 -2.1 -0.64 0 2.36 1.44 -0.68 0 0.82 0.78 1.47 0.69 -0.64
100.80 103.80 106.20 112.90 121.60 100.60 102.00 103.80 107.50 117.40 100.50 101.70 103.50 107.90 119.20 101.30 102.10 104.60 108.60 111.50 100.80 101.90 104.10 107.60 109.60
101.04 103.27 104.89 108.47 114.15 100.89 102.27 104.06 106.31 116.29 100.36 101.67 103.70 106.95 117.16 101.24 102.95 106.48 109.47 114.87 101.41 103.18 105.52 109.25 115.06
0.24 -0.51 -1.23 -3.92 -6.13 0.29 0.26 0.25 -1.11 -0.95 -0.14 -0.03 0.19 -0.88 -1.71 -0.06 0.83 1.80 0.80 3.02 0.61 1.26 1.36 1.53 4.98
0.583 0.534 0.515 0.488 0.476 0.593 0.538 0.526 0.506 0.505 0.606 0.551 0.502 0.500 0.551 0.608 0.558 0.501 0.534 0.553 0.600 0.554 0.541 0.541 0.608
lower water content. At water contents above 25%, predictions from eq 6 are rather consistent with the measured values. The prediction errors are less than 10% over a wide range. Neutralizing the solution of phosphoric acid resulted in a decrease of boiling point. At high neutralization degree and low water content, phosphate salt precipitated from the solution. No significant difference was observed between wet-process acid and pure acid. Most of the metallic ion impurities in the wet-process acid are likely to precipitate at the beginning of neutraliza-
tion; thus, they do not affect the boiling point in the following concentration operation. 3.3. Thermal Conductivities. The thermal conductivities of acidic ammonium phosphate slurries were measured under 90 °C. To avoid the error caused by suspended solid particles, the thermal conductivities were calculated by the method proposed by Verma.9 The results are listed in Tables 2 and 3. The thermal conductivities range from 0.471 to 0.608 W‚m-1‚K-1. Both neutralization degree and water content exhibit significant influences on the thermal con-
Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 3197
Figure 2. Effect of neutralization degree on viscosity. (The shear velocity is 991.6 s-1, and the water content is 45 ( 3%.)
Figure 1. Volatility of fluorine.
ductivity. Because water has a higher thermal conductivity than both phosphoric acid and ammonium phosphate solution, the conductivity of a slurry is often expected to decrease with decreasing water content. However, the conductivity showed an increase at the end of the concentration range. This was due to the precipitation of ammonium phosphate. The thermal conductivity of solid ammonium phosphate is rather high (>0.71 W‚m-1‚K-1).10 The thermal conductivity of the acidic slurry from wet-process phosphoric acid is slightly lower than that from dilute phosphoric acid. The impurities contained in wet-process phosphoric acid form insoluble salts that give rise to a poor conductivity. 3.4. Volatilization Ratio of Fluorine. The fluorine contained in wet-process phosphoric acid is volatile at elevated temperatures. The percentages of fluorine evaporating during the concentration operation are illustrated in Figure 1. The amount of evaporating fluorine decreases with increasing neutralization degree. For neutralization degrees of 0.312 and 0.385, the fluorine in the slurry is mainly in the form of SiF4 and HF, which are volatile. For neutralization degrees of 0.585, 0.786, and 0.971, reactions occur to form (NH4)2SiF6 or other fluorine-containing compounds. Fluorine is fixed in the liquid or solid phase. From Figure 1, the curves for neutralization degrees of 0.786 and 0.971 lie at a low level, and the neutralization degree exerts little influence on the volatility. With decreasing water content during the concentration operation, more fluorine is released from the slurry because of the increase of the boiling point and the reduction of the solvent content. 3.5. Viscosities. Figure 2 illustrates the viscosity of the acidic slurries as a function of neutralization degree. The viscosity is between 6 and 8 mPa‚s when the neutralization degree is below 0.52, but it increases sharply at neutralization degrees above 0.52 and shows a peak at the neutralization degree of 0.85. When the neutralization degree is above 1.05, the viscosity slightly increases with the increasing neutralization degree. These results do not agree with those reported by Broxki et al.4
Figure 3. Effects of shear velocity and water content on viscosity.
To ensure the fluidity of a slurry during the evaporation operation, a slurry with a neutralization degree around 0.5 is most attractive. The sample for ND (neutralization degree) ) 0.52 was tested for evaporation to measure its dynamic properties. The effects of the water content and shear velocity on the viscosity are illustrated in Figure 3. Decreasing water content resulted in precipitation of the solid phase from the solution. The slurry exhibited non-Newton fluid behavior. The viscosity greatly depended on the shear velocity. According to Figure 3, the viscosity of the slurry decreases at high shear velocity. At low water content, the solid content in the slurry is very high (more than 30%). The presence of solid particles makes the viscosity more sensitive to the shear stress. When the water content is as low as 25.15%, the change in the viscosity is significant. The relationship between shear stress and shear velocity is plotted in Figure 4. Linear fits are obtained for water contents above 40%, indicating that the shear stress is proportional to the shear velocity. The slurry shows Newtonian fluid behavior: the viscosity is low. When the water content drops below 40%, the shear stress is an exponential function of the shear velocity.
3198 Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 Table 4. β and λ Values in the Eq 10 water content (wt %)
ln β
λ
31.2 35.1 40.7 42.6 45.2 47.5
-2.188 -3.127 -4.165 -4.600 -5.291 -5.659
1.751 1.934 2.138 2.173 2.330 2.381
on the viscosity can be described by the following formula:
ln η ) ln β + λ/T
(10)
The values of β and λ in eq 10 are listed in Table 4. This expression fits the data well. 4. Conclusions
Figure 4. Effects of shear velocity and water content on shear stress.
Figure 5. Effect of temperature on viscosity. (The neutralization degree is 0.52, and the shear velocity is 719.1 s-1.)
The slurry becomes a pseudoplastic fluid: its apparent viscosity is large. Experimental data, obtained in a shear velocity from 15.5 to 996.1 s-1, were used to determine the relationship between shear stress and shear velocity. The shear stress model can be described by the following equations:
(1) The density of acidic ammonium phosphate slurry increases with decreasing water content and/or neutralization degree. It can be calculated with the equation F ) k[FSxv + FL(1 - xv)]. (2) The boiling point of such an acidic slurry increases upon concentration. At water contents below 40%, the boiling point strongly depends on the water content. Raoult’s law can be applied to estimate the increase of the boiling point. (3) The neutralization degree greatly influences the fluorine evaporation. The evaporation rate is higher at a lower degrees of neutralization. Using a neutralization degree higher than 0.6 can control the volatility of fluorine at a low level. (4) The thermal conductivities of acidic ammonium phosphate slurries are in the range of 0.471-0.608 W‚m-1‚K-1, increasing with increasing water content or neutralization degree. With decreasing water content, the presence of a solid precipitate greatly enhances the thermal conduction and the thermal conductivity. The thermal conductivity of a slurry from wet-process phosphoric acid is slightly lower than that of a slurry from dilute pure phosphoric acid. (5) The viscosity is lowest for slurries with a neutralization degree of 0.52. The viscosity increases with decreasing water content. A slurry behaves as a Newtonian fluid when its water content is above 40%. However, it switches to act as a pseudoplastic fluid when its water content decreases below 40%. Increasing the temperature can also reduce the viscosity. Acknowledgment We are thankful to the Ministry of Education of China for financial support. Nomenclature
τ ) Kγn
(7)
n ) 1.3638 - 0.1787/xw
(8)
ln K ) -8.947 + 1.9356/xw
(9)
The effect of temperature on the slurry viscosity is illustrated in Figure 5. The apparent viscosity of the slurry decreases with increasing temperature. At elevated temperatures, the solubility of ammonium phosphate increases, and the amount of solid particles present in the slurry decrease. The effect of temperature
Fi ) fluorine content after the slurry has been concentrated i times, g F0 ) initial fluorine content, g k ) calibration coefficient K ) consistency coefficient Kb ) ebullioscopic constant, K‚kg‚mol-1 Mac ) molecular weight of phosphoric acid, g‚mol-1 Mam ) molecular weight of ammonium phosphate, g‚mol-1 n ) characteristic parameter of fluidity x ) neutralization degree xFi ) volatilization ratio of fluorine after the slurry has been concentrated i times, %
Ind. Eng. Chem. Res., Vol. 43, No. 12, 2004 3199 xac ) mass fraction of H3PO4 in the liquid phase xam ) mass fraction of NH4H2PO4 in its aqueous solution xS ) mass fraction of solid in the slurry xv ) volume fraction of solid in the slurry. xw ) mass fraction of water in the slurry T ) temperature, K ∆Tb ) elevation of the boiling point, °C β ) constant γ ) shear velocity, s-1 η ) viscosity of the slurry, mPa‚s λ ) constant in eq 10 F ) density of the slurry, kg‚m-3 FL ) density of the liquid phase. kg‚m-3 FS ) density of solid ammonium phosphate, kg‚m-3 Fac ) density of pure phosphoric acid, kg‚m-3 FamL ) density of ammonium phosphate aqueous solution when the concentration of MAP (monoammonium phosphate) is xam, kg‚m-3 τ ) shear stress, mPa
Literature Cited (1) Zhong, B. H.; Wei, W. Y.; Lin, L.; Zhang, Y. X. Gu Ti Lin An de Sheng Chan yu Ying Yong (Production and Application of Solid Ammonium Phosphate); Sichuan Science and Technology Press: Chengdu, China, 1986 (in Chinese). (2) Luo, C. Y.; Lin, L.; Zhong, B. H.; Zhang, Y. X. Shi Fa Lin Suan An Hua Liao Jiang de Zheng Fa Nong Suo (Evaporation and Concentration of Ammoniated Slurry from Wet-Process Phosphoric Acid). Lin Fei Yu Fu Fei (Phosphate & Compound Fertilizer). 1999, 6, 70-75 (in Chinese). (3) Zhong, B.; Li, J.; Zhang, Y.; Liang, B. Principle and technology of ammonium phosphate production from middle-
quality phosphate ore by a slurry concentration process. Ind. Eng. Chem. Res. 1999, 38, 4504-4506. (4) Broxki, A. A.; Novikov, M. M. Rheological Behavior of Ammoniated Phosphate Slurry in Ammonium Phosphate Production. Chem. Ind. (Russ.) 1987, 5, 280-283. (5) Wu, Z. W. Lin Suan An de Sheng Chan Ji Qi Shi Yong (Production and Application of Ammonium Phosphate); Chemical Fertilizer Industry Graduate School, Chemical Industry Department of China: Beijing, China, 1988. (6) Zhang, Y. X.; Feng, Y. Q.; Ying, J. K.; Zeng, X. S. Liao Jiang Fa Zhi Lin An de Sheng Chan yu Cao Zuo (Production and Operation of Ammonium Phosphate by a Slurry Process); Chengdu University of Science and Technology Press: Chengdu, China. 1987. (7) National Standard of the People’s Republic of China. Phosphate rock and concentratesDetermination of fluorine contentsSpecific ion electrode method. GB/T 1872-1995. (8) Tang, S. W.; Wu, P.; Ying, J. K.; Liu, D. J.; Qiu, L. Y.; Liang, B. Measurement of the Thermal Conductivity of Acidic Ammonium Phosphate Slurry by a Coaxial Cylinder Technique. Gao Xiao Hua Xue Gong Cheng Xue Bao (J. Chem. Eng. Chin.ese Univ.) 2001, 6, 583-586. (9) Verma, L. S.; Singh, Ramvir; Chaudhary, D. R. Geometry dependent resistor model for predicting effective thermal conductivity of two phase systems. Int. J. Heat Mass Transfer 1994, 4, 704-714. (10) Dwight, E. G. American Institute of Physics Handbook; McGraw-Hill Book Company, Inc.: New York, 1975.
Received for review November 21, 2003 Revised manuscript received March 8, 2004 Accepted March 23, 2004 IE030839Y
