Skip to main content
SpringerLink
Log in

Effects of liming on phosphate availability in acid soils

A critical review

  • Published:
Plant and Soil Aims and scope Submit manuscript

Summary

The critical factors involved in the plant-soil-phosphorus-lime interaction are outlined and discussed. Conflicting reports suggest that the prior liming of highly weathered acid soils can result in an increase, a decrease, or no change in the availability of applied phosphate. Adsorption of phosphate by amphoteric soil surfaces generally decreases slowly as the pH is raised from 4.0 to 7.0. However, in soils initially high in exchangeable Al3+, liming results in the formation of new, highly active, phosphate adsorbing surfaces as the Al3+ ions precipitate as insoluble polymeric hydroxy-Al cation species. Thus, if an acid soil is reacted with lime and then phosphate, without intervening air drying, liming can increase phosphate adsorption. If the same limed soil is air dried before reaction with phosphate (e.g. adsorption isotherm studies), liming decreases phosphate adsorption. Apparently, air drying alters the surface characteristics of recently limed soils, probably by promoting the crystallization of the hydroxy-Al cation polymers as gibbsite.

An important phenomenon, which is often overlooked, is that liming can increase phosphate availability by stimulating mineralization of soil organic phosphorus. However, at high soil pH values, the precipitation of insoluble calcium phosphates can decrease phosphate availability. Since Al toxicity is characterised by the inhibition of the uptake, translocation and utilization of phosphate by plants, liming often increases the utilization of soil phosphate by plants through amelioration of Al toxicity.

When making lime recommendations or interpreting the data collected from lime-phosphate experiments, it is important to consider all the complex interacting soil and plant factors involved.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Aleksandrova A M, Krupskiy N K, Daragan Yu V and Prikhadko Ye D 1980 Movement of aluminium into salt extracts from soils depending on the pH of the medium. Sov. Soil Sci. 12, 546–551.

    Google Scholar 

  2. Amarasiri S L and Olsen S R 1973 Liming as related to solubility of P and plant growth in an acid tropical soil. Soil Sci. Soc. Am. Proc. 37, 716–721.

    Google Scholar 

  3. Anderson G 1980 Assessing organic phosphorus in soils.In The Role of Phosphorus in Agriculture. Eds. F E Khasawneh, E C Sample and E J Kamprath, pp 411–431. American Society of Agronomy, Madison, Wisconsin.

    Google Scholar 

  4. Andrew C S and Vandenburg P J 1973 The influence of aluminium on phosphate sorption by whole plants and excised roots of some pasture legumes. Aust. J. Agric. Res. 24, 341–351.

    Google Scholar 

  5. Appelt H, Coleman N T and Pratt P F 1975 Interactions between organic compounds, minerals and ions in volcanic-ash-derived soils. II. Effects of organic compounds on the adsorption of phosphate. Soil Sci. Soc. Am. Proc. 39, 628–630.

    Google Scholar 

  6. Arai S and Kumada K 1981 Factors controlling stability of Al-humate. Geoderma 26, 1–12.

    Google Scholar 

  7. Atwell B J, Veerkamp M T, Stuiver B, Kuiper P J C 1980 The uptake of phosphate of Carex species from oligotrophic to wutrophic swamp habits. Physiol. Plant. 49, 487–494.

    Google Scholar 

  8. Awan A B 1964 Effect of lime on availability of phosphate in Zamorano soils. Soil Sci. Soc. Am. Proc. 28, 672–673.

    Google Scholar 

  9. Barrow N J 1965 Further investigations of the use of lime on established pastures. Aust. J. Exp. Agric. Anim. Husb. 5, 442–448.

    Google Scholar 

  10. Barrow N J, Bowden J W, Posner A M and Quirk J P 1980 Describing the effects of electrolyte on adsorption of phosphate by a variable charge surface. Aust. J. Soil Res. 18, 395–404.

    Google Scholar 

  11. Barrow N J and Shaw T C 1979 Effects of ionic strength and nature of the cation on desorption of phosphate from soil. J. Soil Sci. 30, 53–65.

    Google Scholar 

  12. Bloom P R 1981 Phosphorus adsorption by an aluminium-peat complex. Soil Sci. Soc. Am. J. 45, 267–272.

    Google Scholar 

  13. Bowden J W, Nagarajah S, Barrow N J, Posner A M and Quirk J P 1980 Describing the adsorption of phosphate, citrate and selenite on a variable-charge mineral surface. Aust. J. Soil Res. 18, 49–60.

    Google Scholar 

  14. Bowden J W, Posner A M and Quirk J P 1980 Adsorption and charging phenomena in variable charge soils.In Soils with Variable Charge. Ed. B.K.G. Theng, pp. 147.166. New Zealand Society of Soil Science, Lower Hutt, New Zealand.

    Google Scholar 

  15. Chan K Y, Davey B G and Geering H R 1979 Adsorption of magnesium and calcium by a soil with variable charge. Soil Sci. Soc. Am. J. 43, 301–303.

    Google Scholar 

  16. Clarkson D T 1967 Interactions between aluminium and phosphorus on root surfaces and cell wall material. Plant Soil 27, 347–356.

    Google Scholar 

  17. Colemena N T, Thorup J T and Jackson W A 1960 Phosphate sorption reactions that involve exchangeable aluminium. Soil Sci. 90, 1–7.

    Google Scholar 

  18. Dalal R C 1977 Soil organic phosphorus. Adv. Agron. 29, 85–117.

    Google Scholar 

  19. Enwezor W O 1976 The mineralization of nitrogen and phosphorus in organic materials of varying C∶N and C∶P ratios. Plant and Soil 44, 237–240.

    Google Scholar 

  20. Farina M P W, Sumner M E, Plank C O and Letzsch W S 1980 Exchangeable aluminium and pH as indicators of lime requirement for corn. Soil Sci. Soc. Am. J. 44, 1036–1041.

    Google Scholar 

  21. Fox R L, De Datta S K and Wang J M 1964 Phosphorus and aluminium uptake by plants from latosols in relation to liming. Trans. 8th Int. Congr. Soil Sci., IV, 595–603.

    Google Scholar 

  22. Foy C D and Fleming A L 1978 The physiology of plant tolerance to excess available aluminium and manganese in acid soils.In Crop Tolerance to Suboptimal Land Conditions. Ed. G A Jung. pp 301–328. American Society of Agronomy, Madison, Wisconsin.

    Google Scholar 

  23. Fried M and Dean L A 1955 Phosphate retention by iron and aluminium in cation exchange systems. Soil Sci. Soc. Am. Proc. 19, 143–147.

    Google Scholar 

  24. Friesen D K, Juo A S R and Miller M H 1980 Liming and lime-phosphorus-zinc interactions in two Nigerian Ultisols: I. Interactions in the soil. Soil Sci. Soc. Am. J. 44, 1221–1226.

    Google Scholar 

  25. Griffin G F 1971 Effect of liming on soil test level of phosphorus as determined by three methods. Soil Sci. Soc. Am. Proc. 35, 540–542.

    Google Scholar 

  26. Hall J K and Baker D E 1971 Phosphorus fixation by montmorillonite and vermiculite clays as influenced by pH and soluble aluminium. Soil Sci. Soc. Am. Proc. 25, 876–881.

    Google Scholar 

  27. Halstead R L, Lapensee J M and Invarson K C 1963 Mineralization of soil organic phosphorus with particular reference to the effect of lime. Can. J. Soil Sci. 43, 97–106.

    Google Scholar 

  28. Haynes R J 1980 Ion exchange properties of roots and ionic interactions within the root apoplasm: their role in ion accumulation by plants. Bot. Rev. 46, 75–90.

    Google Scholar 

  29. Haynes R J and Ludecke T E 1981 Effect of lime and phosphorus applications on concentrations of available nutrients and on P, Al and Mn uptake by two pasture legumes in an acid soil. Plant and Soil 62, 117–128.

    Google Scholar 

  30. Haynes R J and Ludecke T E 1981 Yield, root morphology and chemical composition of two pasture legumes as affected by lime and phosphorus applications to an acid soil. Plant and Soil 62, 241–254.

    Google Scholar 

  31. Helyar K R and Anderson A J 1971 Effects of lime on the growth of five species, on aluminium toxicity, and on phosphorus availability. Aust. J. Agric. Res. 22, 707–721.

    Google Scholar 

  32. Helyar K R, Munns D N and Bureau R G 1976 Adsorption of phosphate by gibbsite. I. Effects of neutral chloride salts of calcium, magnesium, sodium and potassium. J. Soil. Sci. 27, 307–314.

    Google Scholar 

  33. Hingston F J, Atkinson R J, Posner A M and Quirk J P 1967 Specific adsorption of anions. Nature London 215, 1459–1461.

    Google Scholar 

  34. Hsu Pa Ho 1979 Effect of phosphate and silicate on the crystallization of gibbsite from OH−Al solutions. Soil Sci. 127, 219–226.

    Google Scholar 

  35. Huett D O and Menary R C 1979 Aluminium uptake by excised roots of cabbage, lettuce and kikuyu grass. Aust. J. Plant Physiol. 6, 643–653.

    Google Scholar 

  36. Huffman E O 1962 Reactions of phosphate in soils: recent research by TVA. Proc. Fert. Soc. No. 71.

  37. Hutchinson F E, Newbauer B F, Verill D B and Kesar M 1971 The influence of aluminium and manganese ions on the growth of sugar beets grown in solution and soil culture. Project Completion Rep. for Maine Agric. Exp. Stn. and Crops Res. Div., ARS, USDA, Beltsville, Maryland.

    Google Scholar 

  38. Hutton E M, Williams W T and Andrew C S 1978 Differential tolerance to manganese in introduced and bred lines ofMacroptilium atropurpureum. Aust. J. Agric. Res. 29, 67–79.

    Google Scholar 

  39. Islam A and Ahmed B 1973 Distribution of inositol phosphates, phosphorus, and nucleic acids and mineralization of inositol phosphates in some Bangladesh soils. J. Soil Sci. 24, 193–198.

    Google Scholar 

  40. Janghorbani M, Roberts S and Jackson T L 1975 Relationship of exchangeable acidity to yield and chemical composition of alfalfa. Agron. J. 67, 350–354.

    Google Scholar 

  41. Jones J P and Fox R L 1978 Phosphorus nutrition of plants influenced by manganese and aluminium uptake from an Oxisol. Soil Sci. 126, 230–236.

    Google Scholar 

  42. Juo A S R and Fox R L 1977 Phosphate sorption characteristics of some benchmark of West Africa. Soil Sci. 124, 370–376.

    Google Scholar 

  43. Kamprath E J 1971 Potential detrimental effects from liming highly weathered soils to neutrality. Soil Crop Sci. Soc. Fla. Proc. 31, 200–203.

    Google Scholar 

  44. Kinniburgh D G, Jackson M L and Syers J K 1976 Adsorption of alkaline earth, transition, and heavy metal cations by hydrous oxide gels of iron and aluminium. Soil Sci. Soc. Am. J. 40, 796–799.

    Google Scholar 

  45. Kinniburgh D G, Syers J K and Jackson M L 1975 Specific adsorptions of trace amounts of calcium and strontium by hydrous oxides of iron and aluminium. Soil Sci. Soc. Am. Proc. 39, 464–470.

    Google Scholar 

  46. Kodama H and Schnitzer M 1980 Effect of fulvic acid on the crystallization of aluminium hydroxides. Geoderma 24, 195–205.

    Google Scholar 

  47. Kwong K F, Ng Kee and Huang P M 1978 Sorption of phosphate by hydrolytic reaction products of aluminium. Nature London 271, 336–338.

    Google Scholar 

  48. Kwong K F, Ng Kee and Huang P M 1979 Surface reactivity of aluminium hydroxides precipitated in the presence of low molecular weight organic acids. Soil Sci. Soc. Am. J. 43, 1107–1113.

    Google Scholar 

  49. Lanyon L E, Naghshineh-Pour B and McLean E O 1977 Effects of the pH levels on yields and compositions of pearl millet and alfalfa in soils with differing degrees of weathering. Soil Sci. Soc. Am. J. 41, 389–394.

    Google Scholar 

  50. Le Mare P H 1977 Experiments on effects of phosphorus on the manganese nutrition of plants. III. The effect of calcium: phosphorus ratio on manganese in cotton grown in Buganda soil. Plant and Soil 47, 621–630.

    Google Scholar 

  51. Lindsay W L 1979 Chemical Equilibria in Soils. John Wiley, New York.

    Google Scholar 

  52. Loganathan P and Fernando W T 1980 Phosphorus sorption by some coconut-growing acid soils of Sri Lanka and its relationship to selected soil properties. J. Sci. Food Agric. 31, 709–717.

    Google Scholar 

  53. Lonanathan P, Bureau R G and Fuerstenau D W 1977 Influence of pH on the sorption of Co2+, Zn2+ and Ca2+ by a hydrous manganese oxide. Soil Sci. Soc. Am. J. 41, 57–62.

    Google Scholar 

  54. Lopez-Hernandez I D and Burnham C P 1974 The covariance of phosphate sorption with other soil properties in some British and tropical soils. J. Soil Sci. 25, 196–206.

    Google Scholar 

  55. Lopez-Hernandez I D and Burnham C P 1974 The effect of pH on phosphate adsorption in soils. J. Soil Sci. 25, 207–217.

    Google Scholar 

  56. Lucas L N and Blue W G 1972 Effects of lime and phosphorus on selected alluvial entisols from eastern Costa Rica. I. Phosphorus retention and soil phosphorus fractions. Trop. Agric. 49, 287–295.

    Google Scholar 

  57. Martini J A, Kochman R A, Siqueira O J and Borkert C M 1974 Response of soybeans to liming as related to soil acidity, Al and Mn toxicities and P in some oxisols of Brazil. Soil Sci. Soc. Am. Proc. 38, 616–620.

    Google Scholar 

  58. Matsumoto H F, Hirasawa H, Torikai H and Takahashi E 1976 Localization of absorbed aluminium in pea root and its binding to nucleic acid. Plant Cell Physiol. 17, 127–137.

    Google Scholar 

  59. Matsumoto H, Morimura S and Takahashi E 1977 Less involvement of pectin in the precipitation of aluminium in pea roots. Plant Cell Physiol. 18, 325–335.

    Google Scholar 

  60. Matsumoto H and Morimura S 1980 Repressed template activity of chromatin of pea roots treated by aluminium. Plant Cell Physiol. 21, 951–959.

    Google Scholar 

  61. McLean E O 1976 Chemistry of soil aluminium. Commun. Soil Sci. Plant Anal. 7, 637–652.

    Google Scholar 

  62. Mokwunye U 1975 The influence of pH on the adsorption of phosphate by soils from the Guinea and Sudan savannah zones of Nigeria. Soil Sci. Soc. Am. Proc. 39, 1100–1102.

    Google Scholar 

  63. Morimura S and Matsumoto H 1978 Effect of aluminium on some properties and template activity of purified pea DNA. Plant Cell Physiol. 19, 429–436.

    Google Scholar 

  64. Mugwira L M 1979 Aluminium effects on the growth and mineral levels of triticale, wheat and rye. J. Plant Nutr. 1, 219–240.

    Google Scholar 

  65. Mugwira L M 1980 Growth and Ca, Mg, K, and P uptake by triticale, wheat and rye at four Al levels. J. Plant Nutr. 2, 591–606.

    Google Scholar 

  66. Munns D N and Fox R L 1976 The slow reactions which continues after phosphate adsorption: kinetics and equilibrium in some tropical soils. Soil Sci. Soc. Am. J. 40, 46–51.

    Google Scholar 

  67. Murrmann R P and Peech M 1969 Effect of pH on labile and soluble phosphates in soils. Soil Sci. Soc. Am. Proc. 33, 205–210.

    Google Scholar 

  68. Murrmann R P and Peech M 1969 Relative significance of labile and crystalline phosphates in soil. Soil Sci. 107, 247–255.

    Google Scholar 

  69. Naidoo G, Stewart J McD and Lewis R J 1978 Accumulation sites of Al in snapbean and cotton roots. Agron. J. 70, 489–492.

    Google Scholar 

  70. Norris D O 1967 The intelligent use of inoculants and lime pelleting for tropical legumes. Trop. Grassl. 1, 107–121.

    Google Scholar 

  71. Oades J M 1979 Interaction of metal ion species with clays.In Colloids in Soils — Principles and Practice. Ed. D E Yates. pp 6.1–6.34. Royal Australian Chemical Institute, Victoria, Australia.

    Google Scholar 

  72. Obihara C H and Russell E W 1972 Specific adsorption of silicate and phosphate by soils. J. Soil Sci. 23, 105–117.

    Google Scholar 

  73. Ohki K 1975 Mn and B effects on micronutrients and P in cotton. Agron. J. 67, 204–207.

    Google Scholar 

  74. Parfitt R L 1978 Anion adsorption by soils and soil materials. Adv. Agron. 30, 1–50.

    Google Scholar 

  75. Pearson R W 1975 Soil acidity and liming in the humid tropics. Cornell Int. Agric. Bull. 30, Cornell University, Ithaca, New York.

    Google Scholar 

  76. Perrott K W, Langdon A G and Wilson A T 1974 Sorption of phosphate by aluminium and iron (III)-hydroxy species on mica surfaces. Geoderma 12, 223–231.

    Google Scholar 

  77. Quin B F, and Rickard D 1981 Pasture production and changes in soil fertility on a long-term irrigated superphosphate trial at Winchmore, New Zealand. Proc. Int. Grassl. Congr. XIVth (in press).

  78. Rengasmy P and Oades J M 1978 Interaction of monomeric and polymeric species of metal ions with clay surfaces. III. Aluminium (III) and chromium (III). Aust. J. Soil Res. 16, 53–66.

    Google Scholar 

  79. Rengasmy P and Cades J M 1979 Interaction of monomeric and polymeric species of metal ions with clay surfaces. IV. Mixed systems of aluminium (III) and iron III. Aust. J. Soil Res. 17, 141–153.

    Google Scholar 

  80. Rhue R D 1976 The time-concentration interaction of Al toxicity in wheat root meristems. PhD Thesis, Oregon State University.

  81. Robarge W P and Corey R B 1979 Adsorption of phosphate by hydroxy-aluminium species on a cation exchange resin. Soil Sci. Soc. Am. J. 43, 481–487.

    Google Scholar 

  82. Robson A D and Loneragan J F 1970 Growth of annualMedicago species on an acid soil. Proc. 11th Int. Grassl. Congr., pp. 434–438.

  83. Ryan J and Smillie G W 1975 Liming in relation to soil acidity and P fertilizer efficiency. Commun. Soil Sci. Soc. Plant Anal. 6, 409–420.

    Google Scholar 

  84. Ryden J C and Syers J K 1975 Rationalization of ionic strength and cation effects on phosphate sorption by soils. J. Soil Sci. 26, 395–406.

    Google Scholar 

  85. Sample E C, Soper R L and Rancz G J 1980 Reactions of phosphate fertilizers in soils.In The Role of Phosphorus in Agriculture. Eds. F E Khasawneh, E C Sample and E J Kamprath. pp 263–310. American Society of Agronomy, Madison, Wisconsin.

    Google Scholar 

  86. Sanchez P A and Uehara G 1980 Management considerations for acid soils with high phosphorus fixation capacity.In The Role of Phosphorus in Agriculture. Eds. F E Khasawneh, E C Sample and E J Kamprath. pp 471–514. American Society of Agronomy, Madison, Wisconsin.

    Google Scholar 

  87. Serna C J, White J L and Hem S L 1977 Anionaluminium hydroxide gel interactions. Soil Sci. Soc. Am. J. 41, 1009–1013.

    Google Scholar 

  88. Shoop G J, Brooks C R, Blaser R E and Thomas G W 1961 Differential responses of grasses and legumes to liming and phosphorus fertilization. Agron. J. 53, 111–115.

    Google Scholar 

  89. Singh B B and Tabatabai M A 1976 Effects of equilibrating salt solutions on phosphate sorption by soils. Commun. Soil Sci. Plant Anal. 7, 677–688.

    Google Scholar 

  90. Sinha M K 1971 Organo-metallic phosphates. II. Physical-chemical characteristics of humic and fulvic metal phosphates. Plant and Soil 35, 485–493.

    Google Scholar 

  91. Smyth J T and Sanchez P A 1980 Effects of lime, silicate and phosphorus applications to an oxisol on phosphorus sorption and ion retention. Soil Sci. Soc. Am. J. 44, 500–505.

    Google Scholar 

  92. Soltanpour P N, Adams F and Bennett A C 1974 Soil phosphorus availability as measured by displaced soil solutions, calcium chloride extracts, dilute-acid extracts, and labile phosphorus. Soil Sci. Soc. Am. Proc. 38, 225–227.

    Google Scholar 

  93. Stol R L, Van Helden A K and de Bruyn P L 1976 Hydrolysis-precipitation studies of Al(III) solutions. 2. A kinetic study and model. J. Colloid Interface Sci. 57, 115–131.

    Google Scholar 

  94. Sumner M E 1979 Response of alfalfa and sorghum to lime and P on highly weathered soils. Agron. J. 71, 763–766.

    Google Scholar 

  95. Sumner M E, Farina P M W and Hurst V J 1978 Magnesium fixation — a possible cause of negative yield responses to lime applications. Commun. Soil Sci. Plant Anal. 9, 995–1007.

    Google Scholar 

  96. Syers J K, Sumner M E and Sharpley A N 1981 Chemistry of lime-phosphorus interactions in four acid soils.In Soils with Variable Charge — Programme and Abstracts 98–99. New Zealand Society of Soil Science, Lower Hutt, New Zealand.

    Google Scholar 

  97. Taylor R W and Ellis B G 1978 A mechanism of phosphate adsorption on soil and anion exchange resin surfaces. Soil Sci. Soc. Am. J. 42, 432–436.

    Google Scholar 

  98. Thompson L M, Black C A and Zoellner J A 1954 Occurrence and mineralization of organic phosphorus in soils with particular reference to associations with nitrogen, carbon, and pH. Soil Sci. 77, 185–196.

    Google Scholar 

  99. Veith J A 1978 Formation of X-ray amorphous aluminium phosphates from precipitation and secondary precipitation. Z. Pflanzenernaehr. Bodenkd. 141, 29–42.

    Google Scholar 

  100. Veith J A and Sposito G 1977 Reactions of alumino-silicates, aluminium hydrous oxides and aluminium oxide with-phosphate: the formation of X-ray amorphous analogs of variscite and montebrasite. Soil Sci. Soc. Am. J. 41, 870–876.

    Google Scholar 

  101. Vickers J C and Zak J M 1978 Effects of pH, P and Al on the growth and chemical composition of crownvetch. Agron. J. 70, 748–751.

    Google Scholar 

  102. Violante A and Violant P 1980 Influence of pH, concentration, and chelating power of organic anions on the synthesis of aluminium hydroxides and oxyhydroxides. Clays Clay Minerals, 26, 153–159.

    Google Scholar 

  103. Volkweiss S J 1973 Factors affecting phosphate sorption by soils and minerals. PhD. Thesis, University of Wisconsin, Madison.

    Google Scholar 

  104. Webber M D 1978 Effects of temperature and time on hydroxy aluminium phosphatemontmorillonite complex. Soil Sci. 125, 107–114.

    Google Scholar 

  105. White R E 1976 Studies on mineral ion absorption by plants. III. The interaction of aluminium, phosphate and pH on the growth ofMedicago sativa. Plant and Soil 46, 195–208.

    Google Scholar 

  106. White R E and Taylor A W 1977 Effect of pH on phosphate adsorption and isotopic exchange in acid soils at low and high additions of soluble phosphate. J. Soil Sci. 28, 48–61.

    Google Scholar 

  107. White R E and Thomas G W 1981 Hydrolysis of aluminium on weakly acidic organic exchangers: implicators for phosphate adsorption. Fert. Res. 2, 159–167.

    Google Scholar 

  108. White R E, Tiffin L O and Taylor A W 1976 The existence of polymeric complexes in dilute solutions of aluminium and orthophosphate. Plant and Soil 45, 521–529.

    Google Scholar 

Download references

Author information

Author notes

  1. R. J. Haynes

    Present address: Research Division, Ministry of Agriculture and Fisheries, P.O. Box 24, Lincoln, Canterbury, New Zealand

Authors and Affiliations

  1. Department of Soil Science, Lincoln College, Canterbury, New Zealand

    R. J. Haynes

Authors
  1. R. J. Haynes
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Haynes, R.J. Effects of liming on phosphate availability in acid soils. Plant Soil 68, 289–308 (1982). https://doi.org/10.1007/BF02197935

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02197935

Key words

Search

Navigation