Hydrometallurgical process for recovery of metal values from spent lithium-ion secondary batteries

hydrometallurgy ELSEVIER

Hydrometallurgy 47 (1998) 259-271

Hydrometallurgical process for recovery of metal values from spent lithium-ion secondary batteries Pingwei Zhang a,b,*, Toshiro Yokoyama b, Osamu Itabashi Toshishige M. Suzuki b, Katsutoshi Inoue c

b,

~'Japan Science and Technology Corporation, 4-2-1 Nigatake Mi7agino-ku, Sendai 983, Japan b Tohoku National Industrial Research Institute, 4-2-1 Nigatake, Miyagino-ku, Sendai 983, Japan c Department of Applied Chemistry, Saga Universi~, Honjo-machi 1, Saga 840, Japan

Received 22 May 1997; accepted 23 July 1997

Abstract

We report studies on the separation and recovery of metal values such as cobalt and lithium from spent lithium-ion secondary batteries. Effects of leachant concentration, temperature, reaction time and solid-to-liquid ratio on leaching of cobalt and lithium contained in the anode material of the batteries were examined using several reagents such as sulfurous acid, hydroxylamine hydrochloride and hydrochloric acid as leachants. Hydrochloric acid was found to be the most suitable leachant among the three reagents. A leaching efficiency of more than 99% of cobalt and lithium could be achieved when 4 M HCI solution was used at a temperature of 80°C and a reaction time of 1 h. The pH of the final pregnant liquor obtained was around 0.6 and the concentrations of cobalt and lithium were approximately 17 and 1.7 (g l - I ) , respectively. The cobalt in the leach liquor was extracted selectively and nearly completely with 0.90 M PC-88A in kerosene at equilibrium pH = 6.7 in a single stage at an O:A ratio of 0.85:1. Then the cobalt in the loaded organic phase was recovered as cobalt sulfate with high purity ( L i / C o < 5 X 10 -5) after lithium scrubbing with a dilute hydrochloric acid solution containing 30 g 1 ~ of cobalt at an O:A phase ratio of 10:1. This was followed by stripping with a 2 M H2SO 4 solution at an O:A ratio of 5:1. The raffinate was concentrated and the lithium remaining in the aqueous solution was readily recovered as lithium carbonate precipitate by the addition of a saturated sodium carbonate solution at close to 100°C. The content of cobalt in the lithium precipitate was found to be less than 0.07%. Lithium recovery approached 80%. A flowsheet of the hydrometallurgical process for the recovery of cobalt and lithium from the spent lithium-ion secondary batteries has been established based on the experimental results. © 1998 Elsevier Science B.V.

* Corresponding author. Fax: + 81-22-2375215; E-mail: [email protected]. 0304-386X/98/$19.00 © 1998 Elsevier Science B.V. All rights reserved. PII S0304-3 86X(97)00050-9

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1. Introduction

Today there is an increasing motivation to recover and recycle as much waste material as is possible because of rapidly deleting primary metal resources (e.g. ores) and ever increasing demand for energy. In the authors' earlier publications [1-5], solvent-extraction processes were described for the recovery of molybdenum, vanadium, cobalt and nickel from secondary raw materials such as spent hydrodesulfurization catalysts which are generated from the petroleum industry. The present paper deals with the separation and recovery of cobalt and lithium from another secondary raw material, namely spent lithium-ion batteries. The lithium-ion battery is a rechargeable cell with high energy density. It is generally composed of a positive electrode in which LiCoO 2 (as the active material) is used and a negative electrode in which carbon, electrolyte and organic solvent are used. The two electrodes are separated by an inert insulating layer. The chemical reactions in the two electrodes can be simply expressed as follows: The cathodic reaction: 6C + Li++ e ~ C6Li

(1)

The anodic reaction: LiCoO 2 ~ CoO 2 + Li++ e

(2)

where the forward direction is the charge reaction and the reverse is the discharge reaction. The lithium-ion batteries possess the following advantages [6] over other batteries such as the nickel-cadmium (Ni-Cd) rechargeable battery. (i) High performance of electrochemical properties. (a) High energy density ( ~ 120 W h / k g [7]). (b) High battery voltage (the average voltage of the lithium-ion batteries is 3.6 V, which is 3 times as large as that of the Ni-Cd battery or the nickel-metal hydride (Ni-MH) battery). (c) Long charging-discharging cycle (500-1000 cycles). (d) Large temperature range ( - 20 to + 60°C). (ii) Safe and acceptable towards the environment. No pollution occurs as no hazardous materials are used, such as lead and cadmium which are used in the Pb and Ni-Cd batteries. Due to such advantages, lithium-ion batteries have been widely used in portable electronic applications including the personal computer, video-camera and telephone since they were commercialized in 1991. The output of lithium-ion batteries approached 7 million units in Japan in 1993, and the estimated consumption in the year 2000 will cover approximately 30% of the market. (The N i - M H batteries will probably share 50% and Ni-Cd batteries 20%.) Research has been concerned with the development of large lithium-ion batteries necessary for use in electric vehicles, the area with the largest growth potential. Therefore, it can be predicted that an appreciable amount of spent lithium-ion batteries will be generated in the near future. The expected tonnages of both primary and secondary scrap are potentially very large. Recycling of these batteries after use has thus become an urgent matter. The objective of the present work was to develop an effective hydrometallurgical process for the separation and recovery of metal values

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261

like cobalt and lithium from spent lithium-ion secondary batteries. The overall experimental approach used was to leach the anode material with several reagents like sulfurous acid, hydroxylamine hydrochloride and hydrochloric acid followed by metal recovery techniques of different types including solvent extraction and precipitation. To date, there is no technology and information available for the recycling of spent lithium-ion batteries in the open literature, although numerous investigations have been reported or patented with respect to the separation and recovery of metal values from other spent batteries such as lead [8,9], nickel-cadmium [10-13], nickel-metal hydride [14-17] and lithium batteries [18-20].

2. Experimental 2.1. Materials The lithium-ion batteries used in this work were cylinder-shaped batteries (SONY NP-F530 type). The commercial extractants employed were bis(2-ethylhexyl) phosphoric acid (D2EHPA) and 2-ethylhexylphosphonic acid mono-2-ethylhexyl ester (PC-88A). Both reagents were kindly provided by Daihachi Chemical Industry. Kerosene was used as a diluent. All reagents were utilized as received without any further purification. Other chemicals were reagent grade.

2.2. Experimental procedure The lithium-ion batteries used were packed in a plastic case, so the battery package was first demolished to remove the batteries. Then the batteries were cut in half crosswise to separate the metallic cases from the internal battery rolls which consisted of the cathode and anode plus an insulator. The anode materials consisting mostly of LiCoO~ and a small amount of polymeric substance and carbon powder, pasted on aluminum foil were collected completely by scraping. The weight was approximately 13.8 g in one battery. Various factors which may affect the leaching efficiency (leachant concentration, temperature (T), time (t), solid-to-liquid ratio (S:L)) were examined in a series of 50 ml beakers under electromagnetic stirring. After leaching, the leach solution and insoluble residue were separated by filtration. The concentrations of cobalt and lithium in the leach solutions were determined. Solvent extraction tests were carried out batchwise by shaking mechanically both the organic and aqueous phases in a 50 mt centrifuge tube or a 500 ml separatory funnel at ambient temperature ( ~ 25°C). A contact time of 30 min was found to be sufficient for attaining equilibrium. The pH was adjusted to the desired level by the addition of concentrated sodium hydroxide solution. After centrifugation, the two phases were disengaged and the aqueous phase was taken to determine the pH and the concentrations of cobalt and lithium. Precipitation tests were carried out at 96-100°C by the addition of a saturated sodium carbonate solution to the concentrated raffinate obtained from the extraction step. The

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100

75

--j

50

25

I

I

I

2

4

6

[H2SO~], % Fig. 1. Effect o f H 2 S O 3 concentration on leaching o f cobalt a n d lithium (T = 60°C, t = 30 min, S:L = 1:100).

1oo

5O

25

0 0

2

i

I

4

6

[NH.~OH HC1], M Fig. 2. Effect o f N H 2 O H . H C I S:L = 1:100).

concentration on leaching o f cobalt and lithium ( T = 8 0 ° C ,

t = 30 rain,

100

75 ©

o 50

,.J

25

0 0

I

I

I

2

4

6

[HCI], M Fig. 3. Effect o f HC1 concentration on leaching o f cobalt and lithium ( T = 80°C, t = 30 min, S:L = 1:100).

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P. Zhang et al. / Hydrometallurgy 47 (1998) 259-271 100

75

50

25

0 0

I

i

30

60

90

Temperature,°C Fig. 4. Effect of temperature on leaching of cobalt and lithium with 6% sulfurous acid solution (t = 30 min, S:L = 1:100).

Figs. 4 - 6 illustrate that the metal leaching is significantly affected by temperature. The increase of temperature enhances remarkably the leaching of the metals. However, in the case of sulfurous acid, when the temperature is raised from 60°C to 80°C, the percentages of cobalt and lithium leached decrease. This likely resulted from the evaporation of SO 2 in the sulfurous acid at high temperature. Figs. 7 - 9 give the time dependency of the leaching of cobalt and lithium with H2SO 3, NH2OH. HC1 and HC1. It is apparent that increasing the reaction time is beneficial to metal leaching. About 92% of cobalt and lithium can be leached within 30 min in the case of NH2OH • HC1 and HC1. It is noteworthy that, although the leaching of cobalt and lithium by H2SO 3 and NH2OH • HC1 increases with the decrease of the solid-to-liquid ratio (i.e. the increase of

100

75

50 ,.d

25

i

i

30

60

90

Temperature,°C Fig. 5. Effect of temperature on leaching of cobalt and lithium with 1 M hydroxylamine hydrochloride solution (t = 30 min, S:L = 1:100).

P. Zhang et al. / Hydrometallurgy 47 (1998) 259-271

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100

75

K

50

25

i

i

30

60

90

Temperature, °C Fig. 6. Effect of temperature on leaching of cobalt and lithium with 4 M hydrochloric acid solution (t = 30 min, S:L = 1:100). 100

75

K

50

-~

25

Y 0

i

i

i

I0

20

30

40

Time, rain Fig. 7. Effect of reaction time on leaching of cobalt and lithium with 6% sulfurous acid solution ( T = 60°C, S:L = 1:100). 100

75 E

K

50

25

0

0

i

i

i

10

20

30

40

Time, min Fig. 8. Effect of reaction time on leaching of cobalt and lithium with 1 M hydroxylamine hydrochloride solution (T = 80°C, S:L = 1 : 100).

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P. Zhang et a l . / Hydrometallurgy 47 (1998) 259-271 100

~- 50

0

0

I

I

I

20

40

60

Time, rain Fig. 9. Effect of reaction time on leaching of cobalt and lithium with 4 M hydrochloric acid solution (T = 80°C, S:L = 1:100).

the volume of leachant solution), no obvious change in leach percentage of metals was observed for the HC1 system within the experimental range as indicated in Table 1. From the above observations, it is clear that NH2OH • HC1 and HC1 can leach cobalt and lithium more effectively than HzSO 3. However, from the standpoint of price of the leaching agent and investment cost, hydrochloric acid would be a better leachant than hydroxylamine hydrochloride. Thus, the final optimum operating conditions were determined as follows: 4 M HC1, 80°C, a 1 h reaction time, solid-to-liquid ratio of 1:10. Under these experimental conditions, almost all of the cobalt and lithium could be leached. The average composition of the resulting leach liquor was found to be approximately 17 g 1-1 cobalt and 1.7 g 1-1 lithium. The pH was around 0.6.

Table 1 Effect of solid-to-liquid ratio (S:L) on leaching of cobalt and lithium with various leachants Leachant

S:L (g:ml)

6% H2SO 3 6% H2SO 3 6% H2SO 3 6% HzSO 3 1 M NH2OH. HC1 1 M NH2OH. HC1 I M NH2OH. HC1 1 M NH2OH. HC1 4 M HCI 4 M HC| 4 M HCI 4 M HCI

1:200 1:150 1:100 1:50 1:100 1:50 1:25 1:12.5 1:100 1:60 1:40 1:20

Leach efficiency (%) Co

Li

84.5 69.3 65.2 33.3 95.6 89.3 76.4 46.4 89.9 89.8 88.2 90.6

81.1 61.9 62.6 29.7 92.7 92.2 74.8 38.8 92.8 92.7 92.7 93.1

Leaching temperature: 80°C for the HC1 and NH2OH-HCI systems and 60°C for the H2SO 3 system. Reaction time: 30 min.

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1oo 80

~

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60

~

4o 20

1

0

1

~ 3

4

3 5

6

7

8

Equilibrium pH Fig. 10. pH dependence of extraction of cobalt and lithium with 0.29 M D2EHPA and 0.30 M PC-88A in kerosene (feed solution: [Co] = 17.25, [Li] = 1.73 (g 1-1 ); pH = 0.6).

4.3. Recovery of cobalt Separation of cobalt from lithium from the hydrochloric acid leach liquor was performed employing solvent extraction. Fig. 10 gives the pH dependence of the extraction of cobalt and lithium from the leach solution containing 17.25 g 1- J Co and 1.73 g 1 1 Li with 0.29 M D2EHPA and 0.30 M PC-88A in kerosene. It was found that the extraction of cobalt increases rapidly with the increase of pH in the region of pH < 5 and essentially complete extraction occurs when the pH is higher than 6.5. On the other hand, lithium is not extracted at all at pH < 5.5 in all cases. Above pH 5.5, lithium begins to extract slightly into the organic phase. It appears that the extraction ability of D2EHPA for lithium is greater than that of PC-88A. Additionally, it can be seen from Table 2 that the C o / L i separation factors (defined as /3 = Dco/DLi, where D is distribution coefficient for each corresponding metal) for PC-88A system are 2 - 3 orders of magnitude greater than those for D2EHPA system at similar pH values. In fact, the amount of cobalt remaining in the aqueous solution after extraction with PC-88A was extremely small, i.e., its concentration was only in the range of 10-4-10 -3 g 1-j. On the other hand, for the D2EHPA system, the concentration of cobalt was approximately 10-2_10 1 g 1-~ even at pH values as high as 7.2. Such results indicate that PC-88A is

Table 2 Comparison for separation of cobalt from lithium using D2EHPA and PC 88A Extractant

O:A

Equilibrium pH

Separation factor (

0.29 0.29 0.30 0.30

2.2:1 2.2:1 2.5:1 2:1

6.71 7.17 7.03 7.05

7.1 x 102 6.5 × 102 8.8 X 104 1.3 x 105

M M M M

D2EHPA D2EHPA PC-88A PC-88A

Feed solution: [Co]= 17.25, [Li]= 1.73 (g 1-I ); pH = 0.6.

~Co/Li)

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Table 3 Extraction of cobalt and lithium at various concentrations of PC-88A at different phase ratios [PC-88A] (mol 1- i )

O:A

Equilibrium pH

0.30 0.60 0.90 1.20 1.50

2.3:1 1.2:1 0.85:1 0.65:1 0.50:1

7.03 6.93 6.72 6.96 6.87

Extraction (%) Co

Li

99.98 99.99 > 99.99 > 99.99 > 99.99

4.2 7.3 12.6 14.3 a 14.8 ~

Feed solution: [ C o ] = 17.32, [ L i ] = 1.72 (g 1 l), pH = 0.59. aln both cases, slow phase disengagement was observed.

capable of extracting cobalt more completely and has a better selectivity for cobalt over lithium than does D2EHPA. Consequently, PC-88A was chosen as the extractant for the selective recovery of cobalt from the leach liquor specified in the current work. In order to raise the operating capacity, the concentration of PC-88A in the organic phase should be increased. However, the experimental results showed that higher concentrations of PC-88A resulted in slow phase disengagement as seen from Table 3. 0.90 M PC-88A was found to be relatively reasonable at an O:A ratio of 0.85:1. Under these conditions, good phase disengagement was observed and over 99.99% of cobalt could be extracted in one stage, while the extraction of lithium was only about 13%. A small amount of lithium co-extracted into the organic phase was removed by scrubbing with a CoC12 + HC1 solution. The scrubbing process can be represented by the following displacement reaction: 2LiA +

C o 2+ ---)' CoA

2 + 2Li +

where the bars over the symbols denote the species present in the organic phase and A represents the monomeric PC-88A anion. The effect of three variables: pH, the concentration of cobalt in scrub feed and the phase ratio on lithium scrubbing was examined. The results are summarized in Table 4.

Table 4 Scrubbing of lithium from the loaded organic phase using CoC12 + H C I solutions under the different conditions Composition of scrub feed pH

[Co] (g 1- 1)

1.20 1.00 0.90 1.00 1.00 1.00 1.00

20.27 20.15 19.76 24.79 32.17 20.15 20.15

Phase ratio (O:A)

10:1 10:1 10:1 10:1 10:1 8:1 5:1

Equilibrium concentration in scrubbed solvent (g 1 - l ) [Co]

[Li]

21.65 21.61 21.35 21.5l 21.58 21.80 21.86

1.7× 10 -3 1.6X10 3 1.4×10 3 1.2X 10 3 1.0X 10 3 9.0X10 4 6.0×10 4

Solvent: 0.90 M PC-88A in kerosene. Solvent loading: [Co] = 20.29, [Li] = 0.27 (g 1- l ).

L i / C o ratio

7.8× l0 5 7.4X10 5 6.6X10 5 5.6X 10 -5 4.6X 10 - s 4.1x10 5 2.7×10 5

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It is seen that decreasing the O:A ratio or pH, or increasing the concentration of cobalt decreases the content of lithium in the scrubbed solvent. Rather low lithium-cobalt ratios in the scrubbed solvent can be obtained even at a high phase ratio O:A of 10:1 by single contact. Such results demonstrate how effective CoC12 + HC1 solution as a scrub feed is in removing the co-extracted lithium from the loaded solvent. The cobalt in the scrubbed solvent was easily stripped by contact with a 2 M H 2SO4 solution at an O:A ratio of 5:1. A typical strip solution contained 108 g 1-~ of cobalt and its pH was 0.8. If required, the cobalt sulfate hexahydrate may be crystallized readily from such a strip liquor. The cobalt may be also readily recovered as high-purity electrolytic cobalt by electrowinning. 4.4. Recovery o f lithium

After the recovery of cobalt by solvent extraction, the raffinate was concentrated and treated with a saturated sodium carbonate solution to precipitate lithium carbonate. Since the solubility of lithium carbonate in an aqueous solution is inversely proportional to temperature, e.g., SLi2CO3= 1.52 at 0°C and SLi2CO3= 0.71 ( g / 1 0 0 g H20) at 100°C [21], the precipitation process was performed at close to 100°C. The lithium carbonate was recovered after filtration and washing with hot water to remove the residual mother liquor. A trace of cobalt remaining in the raffinate was also precipitated along with lithium. However, the analytical results showed that the content of cobalt in the precipitate was less than 0.07% and about 80% of the lithium was recovered as a precipitate.

5. Conclusions A hydrometallurgical process for the separation and recovery of cobalt and lithium from spent lithium-ion secondary batteries has been developed. This process is relatively simple, consisting basically of: (a) leaching of the anode materials of the lithium-ion batteries with hydrochloric acid; (b) separation of cobalt from lithium with solvent extraction and (c) precipitation of lithium as carbonate. The best conditions for leaching were found to be 4 M hydrochloric acid at a temperature of 80°C and a S:L ratio of 1:10 for 1 h. Under these conditions, over 99% of cobalt and lithium could be leached and a leach liquor containing approximately 17 g 1-J of cobalt and 1.7 g 1-~ of lithium was obtained. The pH of the leach liquor was around 0.6. Solvent extraction with PC-88A was very effective in separating cobalt from lithium in the leach liquor. Quantitative recovery of cobalt was achieved by extraction with 0.90 M PC-88A in kerosene at an O:A ratio of 0.85:1 and pH = 6.7 in a single stage. This was followed by single stage lithium scrubbing from the loaded solvent by a chloride solution containing 30 g 1 i of cobalt at an initial pH of 1.0 and an O:A ratio of 10:1, and then by stripping with a 2 M H2SO 4 solution at an O:A ratio of 5:1. The purity of the cobalt recovered could reach 99.99% or better.

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Spent Li-ion batteries

I Removalof the cases* I 4 M HCI S:L = 1:10/ SO'(7, I h Leaching of l anode material ~

r................

Leach solution ~ 0.90MPC-88A/ O:A = 0.85:1 /

I

Solventextraction

~0 ~L, co,~ chloride,/ pH 10, O:A = 10:1 ~ Scrubbing Scrub solution . of lithium "

Residue (carbon,organic polymers,ere)

I Organic solvent ~

2 M H2SO4~ O:A = 5:1 ~ Stripping of cobalt /

. . . . . . . . . ',

[

" Raffinate

[ Concentration I saturated I Na2CO3 . Precipitation of lithium [

Li2CO3

Crystallization COSO46Hf ) Fig. 11. Flowsheet of the hydrometallurgical process for the recovery of cobalt and lithium from spent lithium-ion secondary batteries (The dotted line indicates that the organic phase is returned to the extraction step for reuse.). *The cases involve an external plastic and an internal mettalic case.

The recovery of lithium was accomplished by a conventional precipitation method as lithium carbonate at a temperature close to 100°C. The content of cobalt in the lithium precipitates was less than 0.07%. The recovery of lithium approached 80%. An overall process flowsheet is suggested based on the experimental investigations Fig. 11.

Acknowledgements The authors thank Dr. T. Goto, Director, Molecular Chemistry Division, and Dr. M. Ono, Director General, Tohoku National Industrial Research Institute, for granting permission to publish this work. They also gratefully acknowledge Daihachi Chemical Industry Co. Ltd., Osaka, Japan, for the free samples of D2EHPA and PC-88A.

References [1] Inoue, K., Zhang, P., Proc. Int. Nickel Conference, Nickel 93, Jingchan, China, 1993, pp. 274-279. [2] P. Zhang, K. Inoue, H. Tsuyama, Nihon Kagaku Kaishi 5 (1995) 407-412, (in Japanese). [3] P. Zhang, K. Inoue, H. Tsuyama, Energy Fuels 9 (2) (1995) 231-239.

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[4] P. Zhang, K. Inoue, K. Yoshizuka, H. Tsuyama, Hydrometallurgy 41 (1996) 45-53. [5] P. Zhang, K. Inoue, K. Yoshizuka, H. Tsuyama, Kagaku Kogaku Ronbunshu 23 (1) (1997) 1-10, (in Japanese). [6] Yoshio, M., Kozawa, A. (Eds.), Lithium-ion Secondary Battery - Materials and Application, Nikkan Kougyo Shinbunsya, 1996, p. 194 (in Japanese). [7] Yoshio, M., Kozawa, A. (Eds.), Lithium-ion Secondary Battery --Materials and Application, Nikkan Kougyo Shinbunsya, 1996, p. 106. [8] P.R. David, JOM 47 (1) (1995) 31-33. [9] N. Mani, S. Ambalavanan, Bull. Electrochem. 9 (5-7) (1993) 383. [10] Liotta, J.J., Onuska, J.C., Hanewald, R.H., in: H.A. Frank, O. Henrry (Eds.), Proc. Annu. Battery Conf. Appl. Adv. 10th, 1995, p. 83. [11] M. Bartolozzi, G. Braccini, S. Bonvini, P.F. Marconi, J. Power Sources 55 (2) (1995) 247-250. [12] van Erkel, J., van Deelen, C.L., Kamphuis, B.A., Visser, A.J., 6th Int. Seminar on Battery Waste Management, November 1994, Deerfield Beach, FL, USA. [13] Z. Xue, Z. Hua, N. Yao, S. Chen, Separation Sci. Technol. 27 (2) (1992) 213-22t. [14] Klaus, K., Uwe, K., Alezander, B., Andreas, F., Ger. Often. DE 4,445,496, 1996. [15] Lyman, J.W., Palmer, G.R., US Pat. Appl. US 242,1995,900. [16] Lyman, J.W., Palmer, G.R., in: Warren, G.W. (Ed.), EPD Congr. 1994, Proc. Symp. TMS Annual Mtg., Miner. Met. Mater. Soc., Warrendale, PA, 1994, pp. 1209-1225. [17] Kaneko, A., Kitazume, N., Okada, C., PCT Int. Appl. WO 94 23,073, 1994. [18] Kawakani, S., Eur. Pat. Appl. EP 613,1994,198. [19] E. Kunugita, J. Kim, 1. Komasawa, Kagaku Kogaku Ronbunshu 15 (4) (1989) 857-862, (in Japanese). [20] Shibata, J., Baba, Y., Treatment minimization of heavy metal-containing wastes, in: Hager, J.P. (Ed.), Proc. Int. Syrup. 1995, Miner. Met. Mater. Soc., Warrendale, PA, pp. 257-261. [21] Kirk and Othmer, in: Grayson, M. (Ed.), Encyclopedia of Chemical Technology, 3rd ed., vol. 14, Wiley, New York, 1981, p. 448