TIIE EFFECTS OF SOIL PHYSICAL PARAMETERS

ON THE DIFFUSION OF PHOSPHORUS IN HAWAIIAN SOILS

A THESIS SUBMITTED TO THE GRADUATE DIVISION OF THE

UNIVERSITY OF HAWAII IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

MASTER OF SCIENCE

IN AGRONOMY & SOIL SCIENCE

DECEMBER 1971

By

Jonathan Oka Braide

Thesis Committee:

Dr. Gora Uehara, Chairman Dr. Samir El-Swaify

Dr. Yoshinori Kanehiro Dr. Tung Ming Lai

We certify that we have read this thesis and that in our opinion it

it satisfactory in scope and quality as a thesis for the degree of Master

of Science in Agronomy & Soil Science.

THESIS COMMITTEE

Chairman

ACKNOWLEDGEMENT

The author wishes to express his sincere appreciation to the

Agronomy Department of the Experiment Station of the Hawaiian Sugar

Planters' Association, for the use of their facilities during the course

of this study.

ABSTRACT

A soil belonging to the Haiku series collected from field H43 of

Lihue Sugar Company on the Island of Kauai, was used to study the effect

of phosphorus concentration, moisture content, and bulk density on the

diffusion of phosphorus. Similarly, a soil in the Honokaa series

collected from phosphate test plots on the Island of Hawaii was used to

show the relationship between the apparent diffusion coefficient and the

phosphorus concentration in the soil solution.

The experimental approach involved the use of wax blocks for soil

core preparation, and a radiotracer technique for diffusion measurement.

The results show that phosphorus diffusion in the Haiku soil is

strongly dependent on phosphorus concentration, particularly after

a critical concentration of 2 micro-moles of P applied per cm2 of cross­

sectional area of soil, is reached. Moisture effect becomes apparent

only at high water contents. The apparent diffusion coefficient, Dp,

decreases as the bulk density is increased from 0.8 to 1.2 gm/cm3, but

then increases as the bulk density is increased to 1.4 gm/cm3. The

decrease in Dp is attributed to the overriding influence of chemical

adsorption, while the increase is attributed to the greater continuity

of water filled pores at high volumetric moisture content.

A significant regression was shown to exist between the phosphorus

concentration in the soil solution and the apparent diffusion coefficient

of phosphorus in Honokaa soil.

ACKNOWLEDGEMENT

ABSTRACT

LIST OF TABLES

LIST OF FIGURES

INTRODUCTION

REVIEW OF LITERATURE

Theory ••••.•

TABLE OF CONTENTS

Soil Parameters Affecting the Diffusion of Phosphorus

The Effect of Soil Moisture •.•

The Effect of Soil Bulk Density ••

The Effect of P Concentration

The Effect of P Adsorption . The Effect of Soil Aggregation . The Effect of Temperature . .

The Effect of Soluble Salts . . The Effects of Biological Activity

MATERIALS AND METHODS

Soil Description.

Haiku Series

Honokaa Series

Reeve Angel SB-2 Resin Paper .

Preparation of P Solution

Soil Preparation

Dry Sieving

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TABLE OF CONTENTS (Contd.)

Wetting and Moisture Equlibration

Preparation of Soil Cores

Soil Compact ion . • . • • •

Labelling of Resin Paper Discs with p32

Setting Up the Diffusion Experiment

Diffusion Measurement Ill • • • • •

Diffusion Measurement in the Haiku Soil

Diffusion Measurement in the Honokaa Soil

Determination of the Diffusion Coefficient.

RESULTS AND DISCUSSION

Test of Method .•.

The Effect of Concentration

The Effect of Moisture Content ••

The Effect of Bulk Density •••

DP Measurements of Phosphorus Plots ..••

SUMMARY AND CONCLUSION •••••••.••••••

APPENDIX

LITERATURE CITED

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LIST OF TABLES

Table Page

1 Chemical and Mineralogical Properties of Soils ..•.•••••••.• 16

2 Diffusion Measurement in the Haiku Soil 23

Figure

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LIST OF FIGURES

Method of Preparing Wax Block: (a) Plexiglass Mould, (b) Plexiglass Mould with Glass Vial, (c) Mould Assembly with Wax •••••••...

Forms of Soil Core: (a) Cross-Section; (b) Longitudinal Section of Wax Block Soil Core; and (c) Cross-Section of Brass-Ring Soil Core

Geiger-Muller Counter and Microtome Assembly

Microtome, Geiger-Muller Tube and Soil Core Arrangement . • • . • • • • • . • . .

Close-up View of Microtome and Soil Core before Slicing (a), and During Slicing (b) • . • • ••.

The Relationship Between y (from equation 22) and x (distance from the origin) .••.•

The Effect of Phosphorus Concentration and Moisture Content on the Apparent Diffusion Coefficient of Pin the Haiku Soil at 0.8 gm/cm3 Bulk Density .•....••..

The Effect of Phosphorus Concentration and Moisture Content on the Apparent Diffusion Coefficient of P in the Haiku Soil at 1.2 gm/cm3 Bulk Density •...

The Effect of Phosphorus Concentration and Moisture Content on the Apparent Diffusion Coefficient of P in the Haiku Soil at 1.4 gm/cm3 Bulk Density ••..

The Effect of Moisture Content and Phosphorus Concentration on the Apparent Diffusion Coefficient of Pin Haiku Soil at 0.8 gm/cm3 Bulk Density •.••••••••••••..

The Effect of Moisture Content and Phosphorus Concentration on the Apparent Diffusion Coefficient of Pin Haiku Soil at 1.2 gm/cm3 Bulk Density • • • • • . • • . . • • • • , .

12 The Effect of Moisture Content and Phosphorus Concentration on the Apparent Diffusion Coefficient of Pin Haiku Soil at 1.4 gm/cm3 Bulk Density

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Figure

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LIST OF FIGURES (Contd.)

P Adsorption Isotherm for Honokaa Soil. (Fox et al., 1971)

The Effect of Bulk Density on the Apparent Diffusion Coefficient of Phosphorus Applied at 0.02 micro-moles of P per cm2 of the Cross­Sectional Area of the Haiku Soil •...•

The Effect of Bulk Density on the Apparent Diffusion Coefficient of Phosphorus Applied at 0.2 micro-moles of P per cm2 of the Cross­Sectional Area of the Haiku Soil .•.•••

The Effect of Bulk Density on the Apparent Diffusion Coefficient of Phosphorus Applied at 2.0 micro-moles of P per cm2 of the Cross­Sectional Area of the Haiku Soil •.•••.

The Effect of Bulk Density on the Apparent Diffusion Coefficient of Phosphorus Applied at 20.0 micro-moles of P per cm2 of the Cross­Sectional Area of the Haiku Soil •...•

The Dependence of the Apparent Diffusion Coefficient on the Phosphorus Concentration (C) in the Soil Solution of the Honokaa Soil ..••..

Yield Response Curve for Corn Grown on Honokaa Soil Fertilized to Various Levels of Phosphate Concentration (C) in the Soil Solution

The Relationship Between Corn Yield and the Apparent Diffusion Coefficient of Phosphorus in Honokaa Soil •..••••

The Relationship Between Corn Yield and the Product of P Concentration and the Apparent Diffusion Coefficient of Pin Honokaa Soil

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INTRODUCTION

When phosphorus fertilizer is applied to a soil, a number of things

can happen to the phosphorus. In soils high in oxides of iron and

aluminum, most of the phosphorus is inunediately adsorbed on the colloid

surface. A very small fraction of the total phosphorus added to the soil

remains in solution. This is the phosphorus utilized by plants. When a

plant root intercepts a soil solution containing dissolved P, it soon

depletes the solution of its P. Phosphorus must diffuse from zones of

high concentration to a zone near the root where phosphorus has been

depleted. Replenishment of phosphorus near the root surface is now

generally believed to occur through diffusion. Without diffusion the

plant root would soon be bathed in soil solution with little or no

phosphorus. In theory then even a soil containing large quantities of

phosphorus may not supply adequate amounts of phosphorus to the plant

if the mobility of phosphorus is too low. The problem at hand is to

ascertain the nature and magnitude of soil factors which control the

movement of phosphorus in soils.

More precisely then the objectives of this study are: (1) to

determine the effect of phosphorus concentration, soil moisture content

and bulk density on the diffusion of phosphorus in high oxide tropical

soils, and (2) to learn how the diffusion of phosphorus is related to

soil phosphorus concentration and crop yield under field conditions.

REVIEW OF LITERATURE

The diffusion of phosphorus in soil is very slow indeed. A report

(Taylor, 1967) shows that during a three year period there was no

detectable movement below one inch in a sandy loam soil when 80 pounds

of P2o5 as superphosphate was applied as top dressing. Similarly,

laboratory studies on P diffusion (Graham-Bryce, 1963; Olsen et al.,

1962, 1965; Lewis and Quirk, 1965; and Vaidyanathan and Nye, 1966)

further confirm that the movement of this element in the soil is

exceedingly slow.

The diffusion coefficient of phosphorus in soils cannot exceed the

value for diffusion in pure water. This is because of the tortuous

nature of the diffusion path in soils. In this review of literature the

geometric, physical, chemical and mineralogical properties affecting the

diffusion of phosphorus in soil will be examined.

Theory

The laws of diffusion relate the flux of a difusing substance to

the concentration gradient and the diffusion coefficient, Hence, the

Fickian theory of diffusion (Crank, 1956) is based on the hypothesis

that the flux "F" of a substance through a plane of unit area,

perpendicular to the direction of flow is directly proportional to the

concentration gradient. Therefore, Fick's first law may be written as:

F = -D _lg_ ax (1)

where F represents the flux or quantity of substance diffusing through

a unit area of section per unit time:

Dis the diffusion coefficient,

C is the concentration, and

xis the distance in the direction of net movement of the

substance. In the transient case the first law and the

equation of continuity can be combined to give Fick's

second law,

_a£_= Dp at (2)

where tis time, and DP is the diffusion coefficient of the porous

system. The assumption here is that the diffusion coefficient is

independent of concentration although this does not hold at high levels

of concentration.

SOIL PARAMETERS AFFECTING THE DIFFUSION OF PHOSPHORUS

The Effect of Soil Moisture

The relationship between the apparent diffusion coefficient of P

and the moisture content of the soil is influenced by geometric and

electrical factors such as tortuosity, changes in the cross-sectional

area of the pore spaces and ionic interaction in the diffuse double

layer.

Olsen (1965) has indicated that the diffusion coefficient in a

porous medium is highly dependent upon the volumetric moisture content.

Similarly, Klute and Letey (1958) have stated that as the volumetric

moisture content of the soil decreases, the effective path length for

diffusion increases. Thus, at low soil moisture content, as the large

3

4

pores are drained, the effective cross-sectional area available for

diffusion diminishes in size; and most of the soil solution exists as

thin films in narrow pores. According to Kemper (1960) such thin

moisture films can be described as wedge-shaped volumes which are

isolated by air pockets. Diffusion through solution rather than surface

migration is the important mechanism for phosphorus transport (Lewis and

Quirk, 1965). Therefore, since liquid phase diffusion can occur only in

that fraction of the pore space which is filled with solution (Gardner,

1965), the absence of a continuous water film in the pore space would

become a limiting factor in the diffusion of phosphorus in soil.

Furthermore, water in close proximity to clay mineral surfaces has

been observed to differ in properties and configuration from that in

bulk solution. These differences have been attributed to the increased

viscosity of water at or near clay mineral surfaces (Low, 1958; Kemper

et al., 1964). Hydration water of cations in the diffuse double layer

has a much lower average free energy than bulk water. Consequently, the

average free energy of water molecules in solutions containing large

nwnbers of cations is lower and fewer water molecules have sufficient

energy to break loose from the surrounding water lattice and move.

Hence, cations in the diffuse double layer increase the viscosity and

decrease the diffusivity of water near clay mineral surfaces. This,

therefore, explains why the rate of ionic diffusion decreases in the

proximity of clay mineral surfaces. According to Porter et al. (1960)

this rate of ionic diffusion is inversely proportional to the viscosity

of the water.

5

However, under conditions of high volumetric moisture content

continuity of the moisture stream is re-established with the elimination

of air pockets; and a considerable reduction in tortuosity results as

the large pores become filled with the soil solution. Also, ionic

interaction with the surface charges drops to a minimum as the nutrients

move in the bulk solution, away from the walls of the pore spaces.

The relationship between a porous system diffusion coefficient,

Dp, and its corresponding diffusion coefficient, D, in aqueous media,

has been reported by Olsen (1965), and Olsen and Kemper (1968) as

follows:

(3)

where y accounts for negative adsorption (dimensionless) (Porter et al.,

1960; Van Schaik and Kemper, 1966); « is a factor for the viscosity of

water (dimensionless) (Kemper et al., 1964); Lis the distance between

two points and Le is the effective distance between these same points;

Q is the volumetric water content, and (L/Le) 29 accounts for tortuosity,

(dimensionless) (Porter et al., 1960).

Therefore, in re-writing Fick's second law, the diffusion equation

becomes

(4)

The Effect of Soil Bulk Density

Another important factor, the effect of which is associated with

that of moisture, is the soil bulk density. Although, earlier results

(Heslep and Black, 1954) were inconclusive, Graham-Bryce (1963), Olsen

and Watanabe (1963), Evans and Barber (1964), and Phillips and Brown

(1965, 1966) have all indicated that in general, an increase in the

soil bulk density is accompanied by a similar increase in the apparent

diffusion coefficient. For a given gravimetric water content, the

volumetric water content increases with increasing bulk density. With

an increase in the water content therefore, air pockets are eliminated

and a continuous water stream is established, which would tend to

increase the apparent diffusion coefficient. According to Olsen and

Watanabe (1963) the size of the capacity factor also increases as the

bulk density is increased, and this would obviously have a positive

effect on the value of Dp, the apparent diffusion coefficient. Also,

the charge density per unit volume increases due to an increase in clay

content and this would result in close packing of the exchange sites

and subsequent overlapping of oscillation volumes of ions.

6

The work of Graham-Bryce (1963) and Phillips and Brown (1965)

indicates that there is an initial increase in the diffusion coefficient

as the bulk density is increased, but then at some critical level of

compaction, the magnitude of the diffusion coefficient approaches a

limit beyond which further compaction has a negative effect. In other

words, the apparent diffusion coefficient decreases.

Several theories have been given to explain this decrease in

diffusivity. One such explanation is the obvious fact that the capacity

of the soil to adsorb P increases as the clay content increases (Evans

and Barber, 1964; Olsen and Kemper, 1968), Also, a reduction in the

cross-sectional area of the diffusion path results as the pore spaces

become smaller due to compression by the solid particles. Since the

7

clay content per unit volume of soil is increased, the tortuosity factor

and negative adsorption become greater. In addition, heterogeneity of

pore size reduces anion movement due to negative adsorption. The

explanation here is that as anions (e.g. H2Po4-) diffuse through

a sequence of large to small to large pores in the soil, the negatively

charged surfaces in the smaller pores being in close proximity to the

diffusing anions tend to exclude them (negative adsorption) from

solution. As a re~ult these anions tend to accumulate in the larger

pores where they are not in close proximity to the charged surfaces.

Therefore, this tends to reduce anion movement in a soil where pore

size distribution is heterogeneous. According to Olsen and Kemper

(1968) negative adsorption is greater for divalent anions such as

HP04= ions.

Lai and Mortland (1961) have indicated that as the "hopping

distance" becomes smaller due to close packing of the clay minerals,

there is a reduction in the activation energy of the diffusing ions.

This would tend to increase the value of the apparent diffusion

coefficient, as the energy required for the ion to diffuse from one

exchange site to another is reduced. Similarly, the apparent diffusion

coefficient would increase as a continuous water film is established in

the pores, with such close packing. However, a reduction in diffusivity

would result as the tortuosity factor increases due to increased path

length and reduced cross-sectional area of the diffusion path. Thus,

this explains why the diffusivity of Pin soil increases and then

decreases as the bulk density continues to increase.

The Effect of P Concentration

Several workers including Heslep and Black (1954), Lawton and

Vomocil (1954), Lai and Mortland (1961, 1962), Place and Barber (1964),

Olsen (1965), Lewis and Quirk (1967), Phillips et al. (1968), Ellis

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et al. (1970), and Mahtab et al. (1971) have recognized that the rate

and extent of diffusion of Pin soil are largely governed by the P

concentration in the soil solution and the rate at which solid phase P

is released into solution. Thus, the general trend shows an increasing

apparent diffusion coefficient associated with an increasing concentra­

tion of solution P. The dependence of diffusion on the solution P

concentration is in agreement with the statement of Lewis and Quirk

(1965) and Rowell et al. (1967) that there is no solid contribution to

the diffusion of phosphorus, i.e., the P must be in solution in order to

diffuse.

According to the second law, the apparent diffusion coefficient,

Dp, is independent of concentration. However, the results of Lai and

Mortland (1962) showed that at infinite dilution, DP obeys this theory,

but at high concentration it becomes concentration dependent. Their

explanation for this is that at high P concentration there is what is

called "channel" diffusion. This means that the P ions in the

concentrated soil solution diffuse in the bulk solution in the pores

without interference from the surface charges. The reason for this

"free" diffusion at high level of P concentration is that all the charges

at the adsorptive sites are satisfied, such that there is an excess

amount left in solution. Hence, the apparent diffusion coefficient

increases as the concentration of dissolved P increases.

The Effect of P Adsorption

P adsorption affects the rate of diffusion through its effect on

lowering the solution P concentration. P applied to soil is readily

adsorbed on the surface of clay minerals and by the hydrous oxides of

Al and Fe. This is especially true of the highly weathered tropical

soils of Hawaii. With such high adsorptive capacity the soils tend to

extract P from solution, thereby lowering the concentration in the thin

capillary films. P adsorption increases as the solution P concentration

increases (Heslep and Black, 1954; Olsen et al., 1965). Heslep and

Black (1954) also found that P applied to soil does not follow the

simple theory of free diffusion but rather, the diffusion coefficient

decreases with time. This they concluded is due to the removal of P

from the soil solution by adsorption.

Phosphorus has a strong time dependent adsorption as indicated by

the work of Tamimi et al. (1968) which shows that the reaction of

phosphorus in soil is very rapid initially, but then the reaction rate

decreases with increasing time. The initial rapid reaction is due to

the interaction of phosphate ions with hydrous oxides of Al and Fe,

while the slow reaction occurs between the phosphate ions and clay

minerals.

Muljadi et al. (1967) have found that at high concentration, P ions

penetrate the clay mineral lattice.

9

When P' interacts with soil it causes peptization of the clays, which

could result in clay materials clogging pore spaces and thereby

significantly reducing the diffusion rate.

Under field conditions most of the P potentially available for

diffusion exists in the solid phase and this P contributes to the total

amount of P diffusing by renewing the solution concentration. Hence,

the capacity factor which relates the solid phase P with the solution

P becomes an important soil parameter affecting the apparent diffusion

coefficient. By definition, the capacity factor is the amount (grams)

of diffusible P per cubic centimeter of soil required to raise the

solution concentrat~on by one unit (grams/ml of soil solution). This

capacity factor enters the diffusion equation for transient state

systems, as represented by Olsen (1965), thus

_.a.9_ = DP c)t (b + 8)

(5)

where bis the ratio of adsorbed P to solution P, and the quantity

(b + 8) is the capacity factor. This factor is a constant for any

particular soil and it is independent of C, t, and x.

10

To mathematically illustrate the effect of adsorption on diffusion,

Crank (1956, pp. 121-134) developed an equation for a reversible

reaction, which he called a linear adsorption isotherm. Based on the

symbols used by Olsen and Kemper (1962, 1968) this equation may be

expressed as

acs a2c aca

= D s (6) d t c) x2 a t

where Ca is concentration of adsorbed P, and

cs is the concentration of P in solution.

11

Assuming DP is constant throughout the medium, the above equation takes

the following form (Olsen, 1965):

where (b + Q)

__a,£_ = at (b + Q)

becomes the diffusion coefficient; Q is the C

moisture content and b = c: is the ratio of adsorbed P to

(7)

volumetric

solution P.

This review clearly shows that the effect of P adsorption is to slow

down the diffusion process.

The Effect of Soil Aggregation

An important property of an aggregated medium is the existence of

pores between aggregates. It is through these pores that the bulk of

the diffusion process takes place. Thus, diffusion in a porous medium

is limited by two factors: (1) physical barrier due to the solid

particles and (2) non-uniform pore size distribtuion. However, the

diffusion rate is relatively independent of the pore size but rather

depends more upon the amount of volumetric water in the pore (Olsen,

1965).

Furthermore, the total pore space may be partly filled by the soil

solution and partly by air. Thus, the coexistence of these two components

within the pore space gives rise to the formation of air pockets. Since

diffusion of phosphorus can occur only in that fraction of the pore space

which is filled with water, the thickness and continuity of the moisture

stream become limiting (Graham-Bryce, 1963).

It has been observed that soils contain three sizes of pores through

which ions move towards plant roots (Vaidyanathan and Talibuden, 1968).

These consist of: (1) inter-aggregate pores which transport the bulk

of the solution by mass flow (Larsen and Gunnary, 1965; Vaidyanathan

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and Talibuden, 1968; and (2) intra-aggregate pores which may be further

subdivided into larger and smaller pores. While the larger pores are

involved in film diffusion, the smaller pores account for particle

diffusion. By definition, film diffusion is the interdiffusions of

ions in the adherent films on the aggregate; and particle diffusion is

the interdiffusion of ions in the aggregate. Differences in pore-size

distribution among soil types have been observed to play an important

part in diffusion (Brown, 1953). Studies in this area indicate that

pore size distribution is determined by the texture and structure of the

soil system, and it is one of the major factors which control the water

holding properties of the soil (Sharma and Uehara, 1968), Similarly,

according to Kanehiro (1947) and Olsen and Kemper (1962) soil texture

greatly affects the mobility of soluble nutrients in the soil.

The Effect of Temperature

The diffusion coefficient, DP, is highly dependent on temperature

(Heslep and Black, 1954; Lai and Mortland, 1962; and Gardner, 1965).

Temperature effect shows itself in accordance with the Arrhenius

equation, thus,

= Ae-E/RT (8)

where E is the activation energy;

A is the activation constant;

T is the absolute temperature (OK);

and R, the gas constant.

13

For an ion to move from one equilibrium position to another, it

must acquire an energy level equal in magnitude to the activation

energy. Rate of movement of an ion decreases as the activation energy

increases, and vice versa. Thus, Lai and Mortland (1962) observed that

low rates of diffusion were in general accompanied by high activation

energies.

The Effect of Soluble Salts

The presence of soluble salts in soil tends to depress the

diffusion rate of phosphorus. This was observed by Peaslee and Phillips

(1970). They found that P diffusion was inhibited significantly in the

presence of calcium salts. The reason is that calcium fixes P by

forming compounds which are either insoluble or only sparingly soluble.

Therefore, the concentration of Pin the soil solution is reduced. This

depresses the diffusion rate since phosphorus diffusion is largely

controlled by the P concentration in the soil solution.

The implication of this is that the addition of relatively moderate

quantities of salts that are connnonly present in fertilizers may slow

down the rate of diffusion of phosphorus from the site of application.

Very often, after phosphorus fertilization, there is a zone of soil

surrounding the fertilizer granules in which pH and concentration of

salts may hinder phosphorus diffusion.

The Effects of Biological Activity

Biological activity in the soil includes microbial population and

plant roots.

Soil microorganisms play a significant role in the diffusion of P.

Since phosphorus is a vital constituent of their energy cycle, these

soil microorganisms can retard the rate of diffusion by absorbing the

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P from solution. Furthermore, through their respiratory activity, they

can increase the CO2 content of the soil air and thereby decrease the

pH of the soil solution. This can affect the rate of diffusion of P,

depending upon the level of acidity.

Plant root activity creates a concentration gradient at the

vicinity of the soil-root interface. It is this concentration gradient

that is responsible for the diffusion of P to the root surface.

MATERIALS AND METHODS

Soil Description

The soils used in this study belong to the Haiku and the Honokaa

soil series.

Haiku Series

This soil was collected from field H43 of Lihue Sugar Company on

the Island of Kauai, in a region receiving an average annual rainfall

of 65 inches. The Haiku soil series belongs to the clayey, ferritic,

isohyperthermic family of the subgroup Orthoxic Tropohumult. It is a

dark yellowish brown soil (lOYR 3/4). In the natural state this soil

has an average bulk density ranging from 1.1 to 1.2 gm/cm3, with a clay

loam texture. Table 1 shows its chemical and mineralogical properties.

Honokaa Series

This soil series belongs to the Thixotropic isothermic family of the

subgroup Typic Hydrandept. It is a highly weathered soil developed in

a high rainfall region from volcanic ash and possesses a high capacity

to adsorb phosphate. It is a dark reddish brown (SYR 3/2), very friable

soil with granular structure and a very low bulk density (<1.0 gm/cm3).

Soil samples for this study were collected from phosphate test plots on

the Hamakua Coast of the Island of Hawaii. These plots were limed prior

to the phosphate treatments. The chemical and mineralogical properties

are shown in Table 1.

Reeve Angel SB-2 Resin Paper

This is an anion exchange resin paper prepared by loading micro-

16

Table 1. Chemical and Mineralogical Properties of Soils

p* %

Soil Depth pH C.E.C. Ca Al Fe Organic Clay (m.e. /100 gm soil) (ppm) Matter Mineral

Haiku 0-12" 5.0 21.02 1.95 0.30 0.15 28.1 5.0 goethite gibbsite

Honokaa 0-12" 5.9 58.55 10.50 1.69 0.16 22.0 20.9 Amorphous Fe and Al hydrous oxides

*NaHC03 (Olsen, S. R. and L.A. Dean, 1965) extractable.

pulverized ion exchange resins into high quality alpha-cellulose pulp.

The specific ion exchange resin contained in this paper is amberlite

IRA-400 which is a strong base resin type with a high molecular weight

copolymer containing quartenary ammonium groups which give this resin

anion exchange properties. The paper contains 45-50 percent resin by

weight and is usually supplied in the chloride form.

The IRA-400 resin paper is 14 mils thick, possesses good wet

strength and has an approximate exchange capacity of 3.3 m.e./gm dry

resin. The resin functions in the pH range 0-12.

Preparation of P Solution

62.89 ml of 85% orthophosphoric acid was diluted with distilled

water to one liter in a standard volumetric flask, to make 1.0 molar P

stock solution. Using 100 ml, 10 ml and 1 ml of this solution

respectively and diluting with water to one liter, the following stock

solutions of P were also prepared: 0.1, 0.01 and 0.001 molar.

Soil Preparation

(a) Dry sieving: The soil was air dried, crushed and sieved.

Soil aggregates (0.15-0.42 nun) passing through a 40 mesh

sieve but retained on a 100 mesh sieve were collected.

(b) Wetting and moisture equilibration: A quantity of the

aggregates was weighed and placed on a polyethylene sheet.

Then a measured amount of distilled water to give a desired

moisture content, was sprayed on the soil. After mixing,

the wet soil was put into a polyethylene bag, tied with a

rubber band and placed in a constant temperature incubator

to allow the moisture to equilibrate. After one week of

equilibration, the soil was again mixed thoroughly and

samples were taken for moisture determination.

Preparation of Soil Cores

17

A technique described by Khasawneh and Soileau (1969), was used in

the preparation of soil cores. A wax-petrolatum jelly mixture was

melted over a water bath. The mixture was three parts paraffin wax and

one part petrolatum jelly. Heating over the water bath was necessary

to prevent the mixture from becoming brittle from overheating.

A cylindrical glass vial 8 cm long with an external diameter of

2.5 cm, and half filled with cold water was placed in the center of a

4x4x5 cm plexiglass mould. The molten wax mixture was poured around

the vial. Figure 1 illustrates the mould assembly.

After the mixture had solidified at room temperature, it was

placed in a refrigerator for further hardening. The result was a wax

block with a circular hollow running through the length of it. The

(a) (b) (c)

Figure 1. Method of Preparing Wax Block: (a) Plexiglass Mould, (b) Plexiglass Mould with Glass Vial, (c) Mould Assembly with Wax

19

block was then trinnned to a height of 2.5 cm and the edges at the basal

portion were bevelled to give the shape of a trapezoid. This was done

to facilitate the gluing of a 4x4 cm piece of cheese cloth to one and

of the wax form. Finally, the cheese cloth was waxed so that there

would be no moisture loss from the soil through this end during the

period of incubation for diffusion to occur. A soil core is shown

in Figure 2.

Soil Compaction

Different amounts of the moist soil were compacted to give three

3 different bulk densities: 0.8, 1.2, and 1.4 gram/cm.

(a) 0.8 gm/cm3 bulk density: For this bulk density, a weighed

amount of moist soil was placed in the wax block. The

placement of soil in the block was on incremental basis,

and the height to which it was compacted was 2.5 cm.

Tapping the wall of the wax container was sufficient to

compact the soil to this bulk density.

(b) 1.2 gm/cm3 bulk density: To obtain this bulk density a

weighed amount of soil was again placed in the column in

small increments. Also, the amount weighed was such that

after compaction it would give the desired bulk density.

Compaction was by means of a cylindrical steel rod, 2.4 cm

in diameter, designed specially for this purpose.

(c) 1.4 gm/cm3 bulk density: Owing to the possibility of the

wax block crumbling under pressure during soil compaction

at high bulk density, a different technique was used to

achieve this. This time a cylindrical brass ring, 1.0 cm

(a) (b) (c)

Figure 2. Forms of Soil Core: (a) Cross-Section of Wax Block Soil Core; (b) Longitudinal Section of Wax Block Soil Core; (c) Cross-Section of Brass­Ring Soil Core

N 0

high and 2.0 cm in diameter, was placed in a hollow

cylindrical steel jacket 2.0 cm in diameter. A weighed

amount of soil was placed in the hollow such that on

applying pressure it was compacted in the brass cylinder.

The idea was to have about 0.5 cm of soil protruding

above the height of the brass ring, in order to facilitate

slicing during diffusion measurement. The walls of that

portion of the soil core protruding above the ring was

coated with wax to prevent moisture loss.

One difficulty encountered in this approach was the problem

of maintaining the same moisture content in the soil during

compression. As a result of this difficulty the highest

bulk density that could be attained was 1.4 gm/cm3,

Labelling of Resin Paper Discs with p32

21

Anion exchange resin paper discs measuring 2.5 cm in diameter were

cut out and placed in planchets. Then 0.1 ml of each of the p31 stock

solutions was pipetted into separate reaction vials, and one micro-curiel

of p32 solution was added to each. After thorough shaking of each vial,

the mixtures were transferred onto the resin paper discs.

Setting Up the Diffusion Experiment

The soil core was mounted on a sliding microtome and the upper

surface cut to obtain an even surface. A p32 labelled anion exchange

resin paper disc was placed on the soil surface and the initial time for

1curie is the basic unit used to describe the intensity of radio­activity in a sample. 1 curie= 3.7xlol0 disintegrating atoms per second (d/s). 1 micro-curie= 3.7xl04 d/s.

diffusion was recorded. To hold the resin paper disc in place and to

maintain good contact at the boundary surface, about three or four

rubber discs of similar size were placed on it. This was then covered

with a polyethylene sheet to prevent evaporation.

Finally, it was placed in a constant temperature incubator set

at 20°c, and left for about 72 hours for diffusion of p32 to occur.

Diffusion Measurement

22

At the end of about 72 hours, the soil core was mounted in a

vertical position on a sliding microtome directly under an end-window

Geiger-Muller tube assembly for diffusion measurement. Cutting thin

slices of 50 µ thickness each time, P32 activity was measured by direct

counting. Figure 4 shows the microtome, Geiger-Muller tube and soil

core arrangement.

First, the activity at x = 0 was measured and this value was

recorded as Ao, Then an unknown soil thickness of x microns was cut

off to expose a new surface Ax as a baseline for determining x; and the

activity at this surface was measured. Following this, a number of

cuts each 50 µ thick, were successively sliced to expose new surfaces.

Background activity was also measured and recorded,

Diffusion Measurement in the Haiku Soil

Phosphorus diffusion in the Haiku soil was measured at four

different phosphorus concentrations, 0.02, 0.2, 2.0 and 20 micro-moles

of P per cm2 of the soil cross-sectional area2 (Figure 2); three

2cross-sectional area of soil= 4.95 cm2

23

Table 2. Diffusion Measurement in the Haiku Soil

Time: Sample A:Initial: 4:38 p.m., 11/16/70 Final: 3:11 p.m., 11/19/70 Total: 70 hrs. 33 min.

Sample B:Initial: 4:40 p.m., 11/16/70 Final: 3:33 p.m., 11/19/70 Total: 70 hrs. 53 min.

T t 2ooc empera ure: Source: 0.2 MP/cm2

Moisture Content: 64% (volume) Background: 330/2 min. = 165 cpm.

X Total Counts

Ao 16851/2 min.

Ax 12966/2

100 JJ 11023/2

200 µ 9474/ 2

300 µ 7729/2

400µ 5658/2

500µ 4252/2

600µ 2766/2

700µ 1951/2

Bo 10431/2 min.

Bx 8970/2

100µ 7493/2

200µ 5560/2

300µ 4331/2

400µ 3241/2

550µ 1974/2

650µ 1384/2

Slope(S) s2

CpM Ax(-BKG)

8425.5 8260.5

6483.0 6318.0

5511.5 5346.5

4737.0 4572.0

3864.5 3699.5

2829.0 2664.0

2126.0 1961.0

1383.0 1218.0

975.0 810.0

5215.5 5050.5

4485.0 4320.0

3746. 5 3581. 5

2780.0 2615.0

2165.5 2000.5

1620.5 1455.5

987.0 822.0

692.0 527.0

A 15.4 237.16 948.64 2.41 X 108

B 16.3 265.69 1062.76 2.71 X 108

Ax/ Ao 1 - Ax/Ao Y

1.00000 0.00000 0.000

0.76484 0.23516 0.212

0.64723 0.35277 0.323

0.55347 0.44653 0.419

0.44785 0.55215 0.537

0.32249 0.67751 0. 700

0.23739 0.76261 0.835

0.14744 0.85256 1.024

0.09811 0.90189 1.169

1.00000 0.00000 0.000

0.85536 0.14464 0.129

0.70913 0.29087 0.263

o. 51777 0.48223 0.458

0.39609 0.60391 0.600

0.28818 0.71182 0.751

0.16275 0.83725 0.987

0.10434 0.89566 1.148

1 / 4s2t ( 2 -1) D ,cm. sec.

4.15 X 10-9

3.69 X 10- 9

3.92 X 10-9 (Average)

24

Figure 3. Geiger-Muller Counter and Microtome Assembly

Figure 4. Microtome, Geiger-Muller Tube and Soil Core Arrangement

25

26

(a) Before Slicing

(b) During Slicing

Figure 5. Close-up View of Microtome and Soil Core

different bulk densities, 0.8, 1.2 and 1.4 gm/cm3 ; and at various

volumetric moisture contents.

Diffusion Measurement in the Honokaa Soil

Phosphorus diffusion was measured in soil samples provided by Dr.

R. L. Fox of the Department of Agronomy and Soil Science, at the

University of Hawaii. DP values were obtained for the following

conditions:

(1) Phosphorus applied= 0.02 micro-moles/cm2•

(2) Volumetric moisture content= 55 percent.

(3) Bulk density= 0.8 gm/cm3 .

The field experiment involved establishing ten levels of phosphate

in the soil solution by adding fertilizer phosphate to field plots as

prescribed by adsorption isotherms for each plot. The concentrations

chosen, covered the range from severe deficiency to phosphate excess.

These concentrations were: unfertilized, 0.003, 0.006, 0.012, 0.025,

0.05, 0.1, 0.2, 0.4 and 1.6 ppm. Prior to the establishment of every

crop in the cropping sequence the soil was sampled to the depth of

cultivation and a new adsorption curve was determined for each plot.

The new crop was then fertilized in accordance with the new phosphate

adsorption curve. After cropping, the amounts of P remaining in the

soil solution were determined for each treatment by equilibrating the

soil with 0.01 molar Cac1 2 solution for six days. The results3 are

presented in Table 4 of the Appendix.

3nata furnished by Dr. R. L. Fox

27

28

Determination of the Diffusion Coefficient

Solutions to test Fick's law of diffusion can be applied to various

systems under a variety of boundary conditions. According to Lai and

Mortland (1961), when a quantity, Q, of a substance is deposited as a

uniform and infinitely thin layer on a plane surface and allowed to

diffuse into a semi-infinitely thick medium, the boundary condition can

be treated as Fick's law for instantaneous sources. Thus the following

solution (Barrer, 1941, pp.45)

Cx = __ ....,.Q __

l,rDt

2 e-X /4Dt (9)

to the diffusion equation applies for these initial and boundary

conditions:

C = 0 at x > 0 and t = O;

C = Q when x = 0 and t = O;

C = Cx at x > 0 and t > O.

The quantity Cx is the concentration of the diffusing substance at time

t and distance x from the boundary, and Dis the diffusion coefficient.

However, since the total activity of the diffusing ion is measured

at the surface, that portion of the total activity which is underneath

is absorbed by the soil. According to Lai and Mortland (1961) this

absorption follows the exponential absorption law

(10)

where I0

is the measured activity without absorption, and I is the

activity observed through an absorber of thickness x with absorption

29

coefficient k. Hence, any radiotracer at a distance x below the surface

will contribute an amount of radioactivity at the surface proportional

to

(11)

By integrating between x = 0 and x = + oo the total radioactivity

measured at the original boundary surface becomes

Ao =

Similarly, when the soil core is sliced to a depth x, the

radioactivity measured at the new surface will be

Now, by letting .

y = __ x_ + k(rITT)

and integrating between

y = y0

= k /I5t and y = oo

gives the following equation

(12)

(13)

(14)

(15)

(16)

where erf (y) is called the error function or probability integral.

Similarly, equation (13) can be written

Ax 2

Qek Dt(l - erf yx)

Dividing equation (17) by equation (16) gives

~ ---= Ao

1 - erf Yx 1 - erf y0

(17)

(18)

The condition~~ 1 is attained when the measurement of P32 activity Ao

is made at any depth below the original boundary surface of the soil

core. Since erf y << 1, equation (18) becomes

~ = 1 - erf Yx Ao

(19)

Therefore,

erf Yx = 1 - ~ Ao

(20)

30

The values of Ao and Ax are computed from the P32 counts, and the value

of y is obtained from erf Yx in a standard probability table.

In plotting the experimental values of y against x a straight line

curve is predicted, which if obtained will show that there is agreement

between the theoretical equations and the results. Using the slope of

this curve the diffusion coefficient can be determined by the following

relationship as illustrated in Figure 6.

s = 1 (21) 2/Dt

where s is the slope,

t is time,

and D is the diffusion coefficient.

RESULTS AND DISCUSSION

This study was designed to show: (1) the effect of phosphorus

concentration, soil moisture content and bulk density on the apparent

diffusion coefficient of phosphorus in soil; and (2) how the apparent

diffusion coefficient, Dp, is related to soil phosphorus concentration

and crop yield under field conditions.

Test of Method

Several techniques have been used in the study of ionic diffusion;

but the method adopted in this study involves a combination of the

techniques of Khasawneh and Soileau (1969) for preparing soil cores,

and Lai and Mortland (1961, 1962) for diffusion measurement. This

combined method has been used because it is simple and provides a

method for measuring phosphorus concentration accurately through use

of labelled phosphorus.

The results as presented in Figure 6 show a plot of y versus x for

two replications, according to the following relationship

y = X

2 /i5F + Yo (22)

The value of y is obtained from an error function table. xis the depth

of slicing, and

Yo = k( v'Dt) (23)

This method of analysis is based on the approximate graphical method of

Anderson and Richards (1964) and Lai and Mortland (1961, 1962). Figure

6 shows a straight line relationship, and this indicates that the results

32

l· 3 e

1•2 5)u~~ = 2..Y:nt

I· { ~ )(

1- :/ 0 - 2.1/J)t l•O I

'j O·~

1aJ ~ 1s-,4 -i: I

0•8 ,- _J - -

0•7 I

~~Jh~ I O•C:i J" I I 0•5

O·f

0 ·.3

0·2

<J. I

0 A)( too zoo 3~0 4-00 !iOo Goo 700

X (Mic. rons)

Figure 6. The Relationship Between y (from Equation 22) and x (distance from the origin)

33

are in agreement with the mathematical development.

A preliminary study on the effect of time on Dp showed that the

longer the diffusion time t, the smaller the slope of they versus x

relationship, and the smaller the percentage error in measuring the

distance x. This tends to give more accurate results as an equilibrium

condition is approached. Since the soil core was treated as a semi­

infinitely thick medium, a time limit was set such that the P32 would

not diffuse to the other end of the core. However, in all cases the

time was sufficiently long so that Dp did not change with time.

The Effect of Concentration

The results obtained in this study clearly illustrate the marked

dependence of the apparent diffusion coefficient Dp on concentration.

Figures 7, 8, and 9 illustrate the relationship between Dp and the

amount of phosphorus applied. This is in accord with the findings of

other workers (Heslep and Black, 1954; Lai and Mortland, 1961, 1962;

Place and Barber, 1964; Lewis and Quirk, 1967; Phillips et al., 1968;

Ellis et al., 1970; and Mahtab et al., 1971) which show that the

apparent diffusion coefficient increases as the concentration of

applied Pis increased. Examination of the results presented in

Figures 7, 8, and 9 shows that there is a critical concentration level

at which the effect on Dp becomes quite apparent. This critical

concentration lies between the 2 and 20 micro-moles/cm2 P concentration.

At this concentration there is a marked increase in Dp for all moisture

levels and bulk densities. However, it is observed that for phosphorus

concentration below 2 micro-moles/cm2 only a very slight increase in

Dp occurs.

0 w CJ) ......

N :E 0

0) 0 .... )(

Cl. C

34

60

' 50 I I

I 40 % MOISTURE

I

I I

• 58

0 34 30

6 24

I I

• 18

20

I 10

---() ------·----------~- -------------------0,02 0.2 2.0 20.0

P APPLIED(MICROMOLES/CM2)

Figure 7. The Effect of Phosphorus Concentration and Moisture Content on the Apparent Diffusion Coefficient of P in the Haiku Soil at 0.8 gm/cm3 Bulk Density.

cJ w u,

N' :E 0

a, 0 -)(

Q. 0

60

• I 50

I I

40 I % MOISTURE I

• 64

I 0 54 30

I! 42 I 27

I 9 • I

I I 20 I I

/. // 10

I I ,~

/ / ,,' ,

,, ,,'

,,' --- , . --------- ,,,,,,' ,

- :.::.: -:.:,a.--~ - -==: - ,, 0 ----0.02 0,2 2.0 20.0

P APPLIED(MICROMOLES/CM2)

Figure 8. The Effect of Phosphorus Concentration and Moisture Content on the Apparent Diffusion Coefficient of Pin the Haiku Soil at 1.2 gm/cm3 Bulk Density.

35

90

80

70

60

. (J w en

N' 50

:I (J

0) 0 .... 40 )(

CL 0

30

20

10

36

' I

I I

I I

% MOISTURE

I

Figure 9.

• 63

• 49

o 42

1:;. 39

• 32

I

I I

I I

I

0.2 2.0 20.0 P APPLIED(MICROMOLES/CM2)

Tiie Effect of Phosphorus Concentration and Moisture Content on the Apparent Diffusion Coefficient of P in the Haiku Soil at 1.4 gm/cm3 Bulk Density.

37

Lai and Mortland (1962) have indicated that at high ionic concentra­

tion, some of the ions move through the middle of the "channel" (the

external pore space between aggregates); and that when this occurs the

diffusion rate is faster than that at lower concentration. This

therefore is an explanation for the marked increase at the 20 micro­

moles/cm2 phosphorus concentration. However, the reason for this

"channel" diffusion is that at high phosphorus concentration the

adsorption sites are presumably satisfied. And so the phosphorus

remaining in solution is capable of diffusing through the pores

uninterrupted by surface adsorption. On the other hand, at low

phosphorus concentration there is an insufficient amount of phosphorus

in solution to satisfy these adsorption sites. Hence, much of the

phosphorus is removed from solution, and this accounts for the low Dp

values.

It is important to note also that much of the variation in the

magnitude of the Dp values at each phosphorus concentration is due to

the differences in the moisture content of the samples.

The Effect of Moisture Content

Figures 10, 11, and 12 show that the apparent diffusion coefficient,

Dp, increases with increasing soil moisture content. However, it is

evident that the rate of increase of Dp is greater at the higher moisture

content than at the lower moisture content. This relationship can be

explained on the basis of the geometric and electrical factors which

operate in_.t;he soil.

It has been observed by other workers (Klute and Letey, 1958;

Porter et al., 1960; Graham-Bryce, 1963; Patil et al., 1963; Romkens and

(J UJ (/) .......

N :E (J

(7) 0

)(

a.

60

50

40

30

o 20

10

0

P-APPLIED(,UM/CM2)

.t. 20.0

o 2.0.

A 0.2

e. 0.02

I

I

,,.

/ /

/ /

/

I

/

__ o

------- -- ----------..... ---------------10 20 30 40 50

PERCENT MOISTURE (VOLUME)

60

Figure 10. The Effect of Moisture Content and Phosphorus Concentration on the Apparent Diffusion Coefficient of Pin Haiku Soil at 0.8 gm/cm3 Bulk Density.

38

0 w ,.,, .......

N :E 0

0) 0 ... ><

Q. Q

60

50

40

30

20

10

0

p-APPLIED ( µM/CM 2)

• 20.0

o 2.0

1:1,. 0.2

• 0.02

10 20

~ - -- -- ----· ~sz wa.a.u •••• ::;i::::: .. :a:c -0~---····

30 40 50 60 PERCENT MOISTURE (VOLUME)

Figure 11. The Effect of Moisture Content and Phosphorus Concentration on the Apparent Diffusion Coefficient of Pin Haiku Soil at 1.2 gm/cm3 Bulk Density.

39

70

. 0 w fl)

90

80

70

60

N' 50 :E 0

0) 0

>< 40 Q.

0

30

20

10

I I

I I

p -APPLIED(,UM/CM2) I I

.... 20.0

I 0 2.0

A 0.2 I

• 0.02 I I

) / /.- ;P

/ /

/ /

/ .............

_____ _. _____ ...

0 10 20 30 40 50 60 PERCENT MOISTURE (VOLUME)

Figure 12. The Effect of Moisture Content and Phosphorus Concentration on the Apparent Diffusion Coefficient of Pin Haiku Soil at 1.4 gm/crn3 Bulk Density.

40

70

41

Bruce, 1964; Olsen et al., 1965; and Rowell et al., 1967) that at low

soil moisture content the rate of ionic diffusion is impeded by the

increased path length for diffusion, and the decreased cross sectional

area of the water filled pores. The low Dp values obtained for the

Haiku soil at the low moisture contents therefore are due to these

geometric factors operating in the soil.

However, before geometric factors become important to phosphate

movement in soils, other limiting factors (if they exist) must first be

overcome. In the Haiku soils, as in many other Hawaii soils, phosphate

adsorption is the most important single factor which restricts movement

of soil phosphorus. The mechanism of phosphorus adsorption in Hawaii

soils has been described by Mekaru (1969). He favors the ligand

exchange model proposed by Hingston et al. (1967) to explain phosphorus

adsorption by soil colloids. Mekaru has shown that phosphorus adsorption

is strongly concentration and pH dependent.

When a given quantity of phosphorus is applied to a soil, a portion

of this Pis adsorbed by the soil and the remainder stays in solution.

The fraction of the applied P which remains.in solution increases as the

' quantity of P applied increases. This can be verified in almost all

phosphate sorption curves. In the soils of Hawaii, particularly those

with high content of iron and aluminum, one would have to apply as much

as a ton of phosphorus per acre of land in order to maintain a soil

solution concentration of 0.1 ppm P (Fox et al., 1971). Also, phosphorus

concentration in the soil solution increases logarithmically with applied

phosphorus. Therefore to increase solution phosphorus by a unit amount,

more phosphorus is required at the lower concentration than at the higher

•.

42

concentration. This is illustrated in Figure 13.

Th~ overriding influence of chemical factors in oxide soil does not

permit geometry factors to be expressed, until the limitation imposed by

chemical adsorption is removed. This occurs in the Haiku soil when the

applied Pis greater than 2 micro-moles per cm2 of the cross-sectional

area.

At lower applied P concentration a small increase in Dp is noted at

moisture contents greater than 50 percent and at a soil bulk density of

1.4 gm/cm3 . This point is of academic interest only since water contents

and bulk density of these magnitudes do not occur in the field for this

soil.

The Effect of Bulk Density

The relationship between the apparent diffusion coefficient and

soil bulk density is shown in Figures 14, 15, 16, and 17. The Dp values

are interpolated values from Figures 10, 11, and 12. Since it was

difficult to maintain the described moisture content at all bulk

densities, the effect of bulk density on DP was obtained in this manner.

According to these results bulk density has little effect on Dp in

the range 0.8 to 1.4 gm/cm3, at low phosphorus concentration. Also, as

the bulk density increases from 0.8 to 1.2 gm/cm3 , DP tends to decrease

even at high phosphorus concentration. Here again the lowering of DP

values can be explained by chemical interaction between phosphorus and

soil. As the bulk density of a sample is increased the colloid content

and therefore the adsorbent concentration is increased (Evans and Barber,

1964), thus increasing phosphate adsorption. This effect is clearly

illustrated in Figure 17 where Dp is plotted as a function of bulk density.

4000

-..J 03000

"' :E <, ...... <, ~.

- 2000 C LIJ co a: 0

"' C

ct 1000 a.

0.01 0.1

P IN SOLUTION (PPM)

1.0

Figure 13. P Adsorption Isotherm for Honokaa Soil. (Fox et al., 1971)

0 w "' N' ::e 0

a, 0 -)(

a. C

30.

% MOISTURE

D 58

20 • 55

0 45

• 35

10

II: --&-:- :__;~ 0 L--...._-~-~~~-..i...-----~-_.;;.;;;.;.;;,;;;;~.

0.5 0.8 1.2 1,4

0..------ ·-------------::...-

BULK DENSITY (GM/CM 3 )

Figure 14. Tiie Effect of Bulk Density on the Apparent Diffusion Coefficient of Phosphorus Applied at 0.02 micro-moles of P per cm2 of the Cross-sectional Area of the Haik~ Soil.

(.) w en

N'-:I (.)

O> 0 ... )(

00.

45

30

% MOISTURE

0 58

20 A 55

0 45

• 35

10

--:.:__ __ --0 ..__....__ ........... _ ..... _____ _,___....,. _____ ..... _......,.

0.5 0.8- 1.2 1.4

BULK DENSITY (GM/CM3)

Figure 15. The Effect of Bulk Density on the Apparent Diffusim Coefficient of Phosphorus Applied at 0.2 micro­moles of P per cm2 of the Cross-sectional Area of the Haiku Soil.

0 w u,

N'-:I 0

0) 0 ... )(

ao.

30

% MOISTURE

a 58

20 • 55

0 45

• 35

10

<> e- - - - - - - - _------_,-~ o ______ ..._ _____ ...__....,. __ ..._ _ __. _____ _

0.5 0.8 1.2 1.4

BULK DENSITY (GM/CM3 )

Figure 16. Tii.e Effect of Bulk Density on the Apparent Diffusion Coefficient of Phosphorus Applied at 2.0 micro-moles of P per cm2 of the Cross­sectional Area of the Haiku Soil.

46

0 w "' ~ 2 0

O> 0 ... )(

Q. Q

60

!

°"' I

I 50

I

' I 40 ""' Q., ' ~/ .... ' .. .. ", ', ',,

' ,, ',

' ' 30 ' ', .... ' ' ..... ..

', ' ' ',

' ' ' '

' ' ' .....

' ' ', % MOISTURE ' ' 20 ' 'u ..

' ....

58 ....

a ' .... ....

' ............

55 ' ............ 0

~ ........ 45 ' 0 ' ' 10 _35 ' • 'e

O~------i.-~~-....__......, _ _...__~---~ 0.5 0.8 1.2 1.4

BULK DENSITY (GM/CM3)

Figure 17. 'Ibe Effect of Bulk Density on the Apparent Diffusion Coefficient of Phosphorus Applied at 20.0 micro-moles of P per cm2 of the Cross­sectional Area of the Haiku Soil.

47

48

However, as the bulk density increases from 1.2 to 1.4 gm/cm3 the

moisture content becomes important, and Dp values tend to increase at

higher moisture content (>45 percent). The decrease in Dp at the lower

moisture content for this bulk density range, is probably due to the

greater percentage of air filled pores in which discontinuity of moisture

films can limit diffusion. Similarly, the increase in Dp at the higher

moisture content can be accounted for by the greater continuity of water

filled pores in this bulk density range.

In sunnnary therefore, Dp decreases as the bulk density increases from

0.8 to 1.2 gm/cm3 because of the overriding influence of chemical

adsorption; and it increases as the 1.2 gm/cm3 bulk density is exceeded

because of the greater continuity of water filled pores.

Dp Measurements of Phosphorus Plots

Based on the preceding data, one would expect the apparent diffusion

coefficient for phosphorus to be measurably different among field plots

treated with varying amounts of phosphorus fertilizer. In a field

experiment conducted by Dr. R. L. Fox of the Department of Agronomy and

Soil Science, varying amounts of phosphorus fertilizer were applied to a

Honokaa soil and planted to corn. Table 4 of the Appendix shows the

amount of phosphorus applied and the predicted and actual phosphorus

concentration in the soil solution. Figure 18 shows the relation between

Dp and phosphorus concentration of samples collected from the plots.

This relation shows that one consequence of phosphorus fertilization is

to increase the mobility of phosphorus in soils.

Figures 19, 20, and 21 show the relationship between yield and

P-soil concentration, yield and~' and yield and the product of

0

"' C/J N'

::E 0

0 0 ... ><

Q. C

5.0

4.0

3.0

2.0

1.0

•

DP= 4.62 + 0.80 X 10-10109 C

R2 = 0.64••

49

o __________________ .................... __ ...__...._...r.. .................

0.001 0.01 0.1 1.0

P IN SOLUTION (PPM)

Figure 18. The Dependence of the Apparent Diffusion Coefficient on the Phosphorus Concentration (C) in the Soil Solution of the Honokaa Soil.

100

';:° 80 z UJ 0 ,:x: UJ a.. - 60 C ..J UJ

>

UJ 40 > ~ c( ..J w 20 ,:x:

•

Y = 85.37- 28.31 log C-14.82(1og C)2

R2: 0.94 **

50

0 ________ ..._. ..... ...._ ____________ ....., ____ .._......i.__ ....................

0.001 0.01 0.1 1.0

P IN SOLUTION PPM

Figure 19. Yield Response Curve for Corn Grown on Honokaa Soil Fertilized to Various Levels of Phosphate Concentration (C) in the Soil Solution.

100

80

--~ z w 0 a: w 60 0.

C ..J w > w 40 > ~ c:( ..J w a:

20

• ., •

•

• •

• ,..

1010

0 Y = 13.97 + 20.59 X

R2: 0.53* p

0 1.0 2.0 3.0 4.0 5.0 10 2

Dp X 10 C M / SEC.

Figure 20. The Relationship Between Corn Yield and the Apparent Diffusion Coefficient of Phosphorus in Honokaa Soil.

51

100

- 80 .... z w u a: w a. 60 -C ..J w ->

40 w > .... < ..J w 20 a:

··-------"-1.__

• " Y = 98.99 - 2.65 log(C X Dp) - 9.27(1og C x Dp)2

.R2= o.91 ••

Q01 Q1 1.0 2.0

C X Dp ( PPM CM2/SEC.)

Figure 21. The Relationship Between Corn Yield and the Product of P Concentration and the'Apparent Diffusion Coefficient of P In Honokaa Soil.

V, N

53

P concentration and Dp respectively. Since there is a significant

regression between P concentration and Dp, it is not surprising that

yield is significantly related to P concentration, Dp or P concentration

x Dp. Such an analysis would be more useful if data from many soils were

available. In such cases the dependence of Dp on P concentration may not

be as good, and the yield may not be as clearly related to Dp or P

concentration. The reasoning here is that in such cases the relation

between yield and P concentration x Dp would be better than the relation

between yield and either Dp or P concentration alone. In Honokaa soil,

so much of the yield variations could be attributed to P concentration

2 that inclusion of the Dp variable while increasing the R could not do

so to any great extent.

The results however suggest that variations in crop yield can be

explained quite adequately by Dp, and that when many soils are analyzed

for yields, a soil parameter which includes both an intensity factor

(P concentration) and a rate factor (Dp) could be used to better account

for yield variations.

SUMMARY AND CONCLUSION

The effect of phosphorus concentration, moisture content and bulk

density on the apparent diffusion coefficient of phosphorus in two

Hawaiian soils was studied. From the results the following conclusions

were made:

1. Soil phosphorus concentration is the most important variable

which controls the diffusion of phosphorus in oxidic soils.

2. Soil moisture content also controls phosphorus diffusion

but this effect is not expressed until sufficient phosphorus

is applied to satisfy P-adsorption sites.

3. Increasing soil bulk density tends to reduce the apparent

diffusion coefficient of phosphorus in oxidic soils, but this

trend is reversed as a greater continuity of water filled

pores is attained at high volumetric moisture content and

high bulk density.

APPENDIX

Bulk

Table 1. The Effect of Phosphorus Concentration and Moisture Content on the Apparent Diffusion Coefficient of

Phosphorus in the Haiku Soil at 0.8 gm/cm3 Bulk Density

% Apparent Diff~sion Coefficient

{D x 10 cm2/sec.2 Density Volumetric P Applied (gm/cm3) Moisture (micro-moles/cm2)

0.02 0.2 2.0

2.79 3.07 7.60

0.8 58 3.47 3.08 4.94

Ave. 3.13 3.08 6.27

0.61 1.30 1. 79

0.8 34 0.64 1.52 2.62

Ave. 0.63 1.41 2.20

0.37 0.84 1.83

0.8 24 0.57 0.95 1.00

Ave. 0.47 0.90 1.43

0.24 0.36 o. 77

0.8 18 0.22 0.69 0.38

Ave. 0.23 0.53 0.58

56

20

56.88

52.27

54.58

24.50

28.60

26.60

4.81

9.41

7 .11

12.55

7.82

10.19

Bulk

Table 2. The Effect of Phosphorus Concentration and Moisture Content on the Apparent Diffusion Coefficient of

Phosphorus in the Haiku Soil at 1.2 gm/cm3 Bulk Density

Apparent Diffusion Coefficient

% ~D 9 2 x 10 cm /sec.}

Density Volumetric P Applied (gm/cm3) Moisture (micro-moles/cm2)

0.02 0.2 2.0

3.06 4.15 6.13

1. 2 64 2.04 3.69 4.05

Ave. 2.55 3.92 5.09

0.87 1.49 1.80

1.2 54 0.42 0.23 1.91

Ave. 0.65 0.86 1.86

1.40 1.53 2.13

1.2 42 1.50 1.93 3.75

Ave. 1.45 1. 73 2.94

0.66 1.48 1.15

1.2 27 2.24 0.94

Ave. 1.45 1.48 1.05

57

20

55.30

52.40

53.85

31. 63

21.07

26.35

22.83

14.19

18.51

10.66

10.66

Bulk

Table 3. The Effect of Phosphorus Concentration and Moisture Content on the Apparent Diffusion Coefficient of

Phosphorus in the Haiku Soil at 1.4 gm/cm3 Bulk Density

Apparent Diffusion Coefficient % {D x 109 cm2/sec.}

Density Volumetric P Applied (gm/cm3) Moisture (micro-moles/cm2)

0.02 0.2 2.0

2.18 6.22 5.40

1.4 63 2.80 2.16 19.43

Ave. 2.49 4.19 12.42

0.55 4.64 1.83

1.4 49 0.53 1.16 3.00

Ave. 0.54 2.90 2.42

0.15 0.60 0.83

1.4 42 0.21 0.07 0.93

Ave. 0.18 0.34 0.88

0.47 0.23 1. 72

1.4 39 0.59 0.24 0.96

Ave. 0.53 0.24 1. 34

0.22 0.17 0.34

1.4 32 0.53 0.35 0.98

Ave. 0.38 0.26 0.66

58

20

81. 90

81. 90

22.60

16.60

19.60

14.50

12.30

13.40

11. 70

12.46

12.08

6.91

6.34

6.63

Plot No.

1

2

3

4

5

6

7

8

9

10

59

Table 4. The Relationship Between the Amounts of Phosphorus Applied, and the Predicted and Actual Amounts of

Phosphorus in the Soil Solution of the Honokaa Soill

P applied Predicted P Actual P ~g/gm soil) in solution in solution

(ppm) (ppm)

0.0 0.000 0.0010

200.0 0.003 0.0016

350.0 0.006 0.0030

670.0 0.012 0.0060

1220.0 0.025 0.0150

1820.0 0.050 0.0230

3030.0 0.100 0.0620

3800.0 0.200 0.0600

5800.0 0.400 0.0950

9200.0 1.600 0.2900

1These data were obtained from Fox et al. (1971). The 11 Predicted P in solution" refers to the adjusted P concentration of the soil solution before cropping, and the "Actual Pin solution" is the P concentration of the soil solution after cropping.

60

Table 5. The Relationship Between Phosphorus in the Soil Solution, the Apparent Diffusion Coefficient, the

Product of P Concentration and the Diffusion Coefficient, and Yield of Corn in the Honokaa Soil

Plot Pin DP x lOlO p X DP Yield No. solution

(ppm) (cm2/sec.) (ppm cm2 /sec.) (bu/acre) %

A B Ave.

1 0.0010 1. 94 2.06 2.00 0.0020 39.0 29.1

2 0.0016 1.50 2.10 1.80 0.0028 80.0 59.7

3 0.0030 2.57 4.01 3.29 0.0098 83.0 61. 9

4 0.0060 2.81 3.29 3.05 0.0183 99.0 73.9

5 0.0150 3.83 3.61 3. 72 0.0558 109.7 81.9

6 0.0230 3.27 3.15 3.21 0.0738 131.0 97.8

7 0.0620 3.59 2.61 3.10 0.1922 127.7 95.3

8 0.0600 3.96 3.74 3.85 0.2310 134.0 100.0

9 0.0950 2.81 3.50 3.15 0.2992 129.0 96.3

10 0.2900 4.16 5.04 4.60 1.3340 131.0 97.8

LITERATURE CITED

Avnimelech, Y. and J. Hagin. 1965. Phosphorus Fixation as a Transfer Controlled Process. Soil Sci. Soc. Amer. Proc. 29:394-396.

Barber, S. A. 1962. A Diffusion and Mass Flow Concept of Soil Nutrient Availability. Soil Sci. 93:39-49.

Barber, S. A., E. H. Halstead and R. F. Follet. 1966. Significant Mechanisms Controlling the Movement of Manganese and Molybdeum to Plant Roots Growing in Soil. Int. Soc. Soil Sci. (Aberdeen) Trans. II and IV:299-304.

Barber, S. A., J.M. Walker and E. H. Vasey. 1962. Principles of Ion Movement Through the Soil to the Plant Root. Int. Soc. Soil Sci. (New Zealand) Trans. IV and V:121-124.

Barber, S. A., J, M. Walker and E. H. Vasey. 1963. Mechanisms for the Movement of Plant Nutrients from the Soil and Fertilizer to the Plant Root. Jour. Agric. and Food Chem. 11:204-207.

Barrer, R. M, 1941. Diffusion in and Through Solids. Cambridge University Press, London. 464 pp.

Blake, G. R. 1965. Bulk Density. pp. 374-390. In C. A. Black (ed.). Methods of Soil Analysis, Part I. American Society of Agronomy, Inc. Madison, Wisconsin.

Brewster, J. L. and P. B. Tinker. 1970. Nutrient Cation Flows in Soil Around Plant Roots. Soil Sci. Soc. Amer. Proc. 34:421-426.

Brown, D. A. 1953. Cation Exchange in Soils Through the Moisture Range, Saturation to the Wilting Percentage. Soil Sci. Soc. Amer. Proc. 17:92-95.

Burns, G. R. and L.A. Dean. 1964. The Movement of Water and Nitrate Around Bands of Sodium Nitrate in Soils and Glass Beads. Soil Sci. Soc. Amer. Proc. 28:470-474.

Cagauan, B. G. 1969. Solute Dispersion in Selected Tropical Soils. Ph.D. Thesis. University of Hawaii, Honolulu.

Clarke, A. L. and K. P. Barley. 1968. in Relation to Solute Diffusion.

Uptake of Nitrogen from Soils Austr. Jour. Soil Sci. 6:75-92.

Clarke, A. L. and E. R. Graham. 1968. Zinc Diffusion and Distribution Coefficients in Soil as Affected by Soil Texture, Zinc Concentration and pH. Soil Sci. 105:409-418.

Crank, J. 1956. Mathematics of Diffusion. Clarendon Press, Oxford. 347 pp.

Dakshinamurti, C. 1955. Ionic Diffusion in Soil. Proc. Nat. Acad. (India) Sci. 24A:25-27.

Deb, D. L. and N. P. Datta. 1967. Effect of Association Anions on Phosphorus Retention in Soil: I. Under Variable Phosphorus Concentration. Plant and Soil. 26:303-316.

Dutt, G. R. and P. F. Low. 1962. Diffusion of Alkali Chlorides in Clay-Water Systems. Soil Sci. 93:233-240.

62

Ellis, J. H., R. I. Barnhisel and R. E. Phillips. 1970. The Diffusion of Copper, Manganese and Zinc as Affected by Concentration, Clay Mineralogy and Associated Anions. Soil Sci. Soc. Amer. Proc. 34:866-870.

Ellis, J. H., R. E. Phillips and R. I. Barnhisel. 1970. The Diffusion of Iron in Montmorillonite as Determined by X-ray Emission. Soil Sci. Soc. Amer. Proc. 34:591-595.

Evans, S. D. and S. A. Barber. 1964. The Eff8gt of Cation Exchange Capacity, Clay Content and Fixation on Rb Diffusion in Soil and Kaolinite Systems. Soil Sci. Soc. Amer. Proc. 28:53-56.

Evans, S. D. and S. A. Barber. 1964. The Effect of Rb86 Diffusion on the Uptake of Rb86 by Corn. Soil Sci. Soc. Amer. Proc. 28:56-57.

Farr, E., L. V. Vaidyanathan and P. H. Nye. 1970. The Measurement and Mechanism of Ion Diffusion in Soils: V. Diffusion of H-Ion in Soils. Journ. Soil Sci. 21:1-14.

Fox, R. L., J. R. Thompson, R. S. de la Pena and H. Y. Young. 1971. Yield of Corn and Residual Effects of Phosphate Fertilization in Relation to Adjusted Levels of Phosphorus in Soil Solutions. Presented Before the 21st Conference, Western Phosphate Work Group, Reno, Nevada.

Fried, M. and H. Broeshart. 1967. Movement of Ions to the Root. pp. 54-68. In The Soil-Plant System. Academic Press, New York.

Fried, M. and H. Broeshart. 1967. The Soil-Plant System in Relations to Inorganic Nutrition. Academic Press, New York. pp. 54-68.

Gardner, W.R. 1965. Movement of Nitrogen in Soil. pp. 550-606. In W. V. Bartholomew (ed.). Soil Nitrogen. American Society of Agronomy, Inc. Madison, Wisconsin.

Gardner, W.R. 1965. Movement of Nitrogen in Soil. Agron. Monograph 10:550.

Gardner, W.R. 1968. Nutrient Transport to Plant Roots. Trans. 9th Int. Congr. Soil Sci. I:135-141.

63

Graham-Bryce, I. J. 1963. Effect of Moisture Content and Soil Type on Self-Diffusion of Rb86 in Soils. Jour. Agr. Sci. 60:239-244.

Graham-Bryce, I. J. 1963. Self-Diffusion of Ions in Soils. I. Cations. Jour. Soil Sci. 14:188-194.

Graham-Bryce, I. J. 1963. Self-Diffusion of Ions in Soils. II. Anions. Jour. Soil Sci. 14:195-200.

Heslep, J.M. and C. A. Black. 1954. Diffusion of Fertilizer Phosphorus in Soils. Soil Sci. 78:389-401.

Hingston, F. J., R. J. Atkinson, A. M. Posner, and J. P. Quirk. 1967. Specific adsorption of Anions. Nature 215:1459-1461.

Hsu, P.H. 1964. Adsorption of Phosphate by Aluminum and Iron in Soils. Soil Sci. Soc. Amer. Proc. 28:474-478.

Husted, R. F. and P. F. Low. 1954. Ion Diffusion in Bentonite. Soil Sci. 77:343-353.

Kanehiro, Y. 1947. Movement and Availability of Nitrogen in Soils. M.S. Thesis. University of Hawaii, Honolulu.

Khasawneh, F. E. and J.M. Soileau. 1969. Techniques for Studying Ion Movement. 33:476-477.

Soil Preparation and Sampling Soil Sci. Soc. Amer. Proc.

Kemper, W. D. 1960. Water and Ion Movement in Thin Films as Influenced by the Electrostatic Charge and Diffuse Layer of Cations Associated with Clay Mineral Surfaces. Soil Sci. Soc. Amer. Proc. 24:10-16.

Kemper, W. D. 1961. Movement of Water as Effected by Free Energy and Pressure Gradients: I. Application of Classic Equations for Viscous and Diffusive Movements to the Liquid Phase in Finely Porous Media. Soil Sci. Soc. Amer. Proc. 25:255-260.

Kemper, W. D. 1961. Movement of Water as Effected by Free Energy and Pressure Gradients: II. Experimental Analysis of Porous Systems in Which Free Energy and Pressure Gradients Act in Opposite Directions. Soil Sci. Soc. Amer. Proc. 25:260-265.

Kemper, W. D., D. E. Maasland and L, K. Porter. 1964. Mobility of Water Adjacent to Mineral Surfaces. Soil Sci. Soc. Amer. Proc. 28:164-167.

Klute, A. and J. Letey. 1958. The Dependence of Ionic Diffusion on the Moisture Content of Non-Adsorbing Porous Media. Soil Sci. Soc. Amer. Proc. 22:213-215.

Lai, T. M. and M. M. Mortland. 1961. Diffusion of Ions in Bentonite and Vermiculite. Soil Sci. Soc. Amer. Proc. 25:353-357.

Lai, T. M. and M. M. Mortland. 1962. Self-Diffusion of Exchangeable Cations in Bentonite. Clays and Clay Minerals. 9:229-247.

Lai, T. M. and M. M. Mortland. 1968. Cationic Diffusion in Clay Minerals. Soil Sci. Soc. Amer. Proc. 32:56-61.

64

Larsen, S. and D. Gunary. 1965. Diffusion in Soil Crumbs. pp. 78-84. In Plant Nutrient Supply and Movement. Intern. Atomic Energy Agency, Technical Report No. 48.

Lawton, K. and J. A. Vomocil. 1954. The Dissolution and Migration of Phosphorus from Granular Superphosphate in Some Michigan Soils. Soil Sci. Soc. Amer. Proc. 18:26-32.

Letey, J. and A. Klute. 1960. Apparent Mobility of Potassium and Chloride Ions in Soil and Clay Pastes. Soil Sci. 90:259-265.

Lewis, D. G. and J. P. Quirk. 1962. Diffusion of Phosphate in Soil. Intern. Soc. Soil Sci. Trans. IV and V:132-138 . .

Lewis, D. G. and J. P. Quirk. 1965. Diffusion of Phosphate to Plant Roots. Intern. Atomic Energy Agency Tech. Report No. 48, p. 71.

Lewis, D. G. and J. P. Quirk. 1967. Phosphate Diffusion in Soil and Uptake by Plants. I. Self-Diffusion of Phosphate in Soils. Plant and Soil. 26:99-118.

Low, P. F. 1958. Apparent Mobilities of Exchangeable Alkali Metal Cations in Bentonite-Water Systems. Soil Sci. Soc. Amer. Proc. 22:395-398.

Low, P. F. 1959. The Viscosity of Water in Clay-Water Systems. Clays and Clay Minerals. 8:170-182.

Low, P. F. 1960. Influence of Adsorbed Water on Electrochemistry of Clays. 7th Intern. Congr. Soil Sci. 2:328-336.

Low, P. F. 1960. Influence of Adsorbed Water on Exchangeable Ion Movement. Clays and Clay Minerals. 9:219-228.

Mahtab, S. K., C. L. Godfrey, A. R. Swoboda, and G. W. Thomas. 1971. Phosphorus Diffusion in Soils: I. The Effect of Applied P, Clay Content and Water Content. Soil Sci. Soc. Amer. Proc. 35:393-397.

Marriot, F. H. and P. H. Nye. 1968. The importance of mass flow in the Uptake of Ions by Roots from the Soil. Trans. 9th Intern. Congr. Soil Sci. 1:127-134.

Mekaru, T. 1969. Anion Adsorption in Hawaiian Soils. M.S. Thesis. University of Hawaii, Honolulu.

Mokady, R. S. and D. Zaslavasky. 1966. Movement and Fixation of Phosphates Applied to Soils. Soil Chemistry and Fertility. Intern. Soil Sci. Soc. Trans. (Aberdeen) II and IV:329-334.

Mokady, R. S. and D. Zaslavsky. 1967. On the Use of Radioactive Tracers in Diffusion Experiments. Soil Sci. Soc. Amer. Proc. 31:604-608.

Mortvedt, J. J. and P. M. Giordano. 1967. Zinc Movement from Fertilizer Granules. Soil Sci. Soc. Amer. Proc. 31:608-613.

Muljadi, D., A. M. Posner, and J. P. Quirk. 1966. The Mechanism of Phosphate Adsorption by Kaolinite, Gibbsite and Pseudoboehmite. II. The Location of the Adsorption Sites. Jour. Soil Sci. 17:231-237.

Nye, P.H. 1966. The Measurement and Mechanism of Ion Diffusion in Soil. I. The Relation Between Self-Diffusion and Bulk Diffusion. Jour. Soil Sci. 17:16-23.

Nye, P.H. 1968. Processes in the Root Environment. Jour. Soil Sci. 19:205-215.

Nye, P. H. and J. A. Spiers. 1964. Simultaneous Diffusion and Mass Flow to Plant Roots. Trans. 8th Intern. Congr. Soil Sci. III:535-541.

O'Connor, G. A., W. L. Lindsay ands. R. Olsen. 1971. Diffusion of Iron and Iron Chelates in Soil. Soil Sci. Soc. Amer. Proc. 35:407-410.

65

Oliver, S. and S. A. Barber. 1966. Mechanisms for the Movement of Mn, B, Fe, Zn, Al and Sr from One Soil to the Surface of Soybean Roots. Soil Sci. Soc. Amer. Proc. 30:468-470.

Olsen, S. R. 1965. Phosphorus Diffusion to Plant Roots. pp. 130-139. In Plant Nutrient Supply and Movement. Intern. Atomic Energy Agency, Tech. Report No. 48.

Olsen, S. R. and L.A. Dean. 1965. Phosphorus. pp. 1035-1049. In C. A. Black (ed.). Methods of Soil Analysis, Part 2. American Society of Agronomy, Inc. Madison, Wisconsin.

Olsen, S. R. and W. D. Kemper. 1968. Movement of Nutrients to Plant Roots. pp. 91-151. In A. G. Norman (ed.). Advances in Agronomy, Vol. 20. Academic Press, New York.

Olsen, S. R., W. D. Kemper and R. D. Jackson. 1962. Phosphate Diffusion to Plant Roots. Soil Sci. Soc. Amer. Proc. 26:222-227.

Olsen, S. R., W. D. Kemper and J. C. Van Schaik. 1965. Self-Diffusion Coefficients of Phosphorus in Soil Measured by Transient and Steady State Methods. Soil Sci. Soc. Amer. Proc. 29:154-158.

Olsen, S. R. and F. S. Watanabe. 1962. Diffusion of Phosphorus as Related to Soil Texture and Plant Uptake. Soil Sci. Soc. Amer. Proc. 27:648-652.

Patil, A. S., K. M. King and M. H. Millar. 1963. Self-Diffusion of Rubidium as Influenced by Soil Moisture Tension. Canad. Jour. Soil Sci. 43:44-51.

Peaslee, D. E. and R. E. Phillips. 1970. Self-Diffusion of Pin Kaolinite Treated With Ca or NH4-Salts and With an Organic Dye. Soil Sci. Soc. Amer. Proc. 34:198-201.

66

Phillip, J. R. 1967. Dead-End Pore Volume and Diffusion Measurements. Soil Sci. Soc. Amer. Proc. 31:711-712.

Phillips, R. E. and D. A. Brown. 1964. Ion Diffusion: II. Comparison of Apparent Self-Diffusion and Counter Diffusion Coefficients. Soil Sci. Soc. Amer. Proc. 28:758-763.

Phillips, R. E. and D. A. Brown. 1965. Ion Diffusion: III. The Effect of Soil Compaction on Self-Diffusion of Rb86 and sr89, Soil Sci. Soc. Amer. Proc. 29:647-661.

Phillips9

R. E. and D, A. Brown. 1966. Counter Diffusion of Rb56 and sr8 in Compacted Soil. Jour. Soil Sci. 17:200-211.

Phillips, R. E., G. A. Place and D. A. Brown. 1968. Self-Diffusion of Phosphorus in Clays and Soils. I. The Effect of Phosphorus Rate. Soil Sci. Soc. Amer. Proc. 32:41-44.

Place, G. A. and S. A. Barber. 1964. The Effect Soil Moisture and Rubidium Concentration on Diffusion and Uptake of Rb86. Soil Sci. Soc. Amer. Proc. 28:239-243.

Place, G. A., R. E. Phillips and D. A. Brown. 1968. Self-Diffusion of Phosphorus in Clays and Soils. II. The Effect of pH. Soil Sci. Soc. Amer. Proc. 32:657-660.

Porter, L. K., W. D. Kemper, R. D. Jackson and B. A. Stewart. 1960. Chloride Diffusion in Soils as Influenced by Moisture Content. Soil Sci. Soc, Amer. Proc. 24:460-463.

Reeve Angel Ion Exchange Resin Loaded Papers. Tech Bull.

Romkens, M. J.M. and R.R. Bruce. 1964. Nitrate Diffusivity in Relation to Moisture Content of Non-Adsorbing Porous Media. Soil Sci. 98:332-337.

Rowell, D. L., M. W. Martin and P.H. Nye. 1967. The Measurement and Mechanism of Ion Diffusion in Soil. II. The Effect of Moisture Content and Soil Solution Concentration on the Self-Diffusion of Ions in Soils. Jour. Soil Sci. 18:204-221.

Sharma, M. L. and G. Uehara. 1968. Influence of Soil Structure on Water Relation in Low Humic Latosols. I. Water Retention. Soil Sci. Soc. Amer. Proc. 32:765-770.

Snedecor, G. W. and W. G. Cochran. 1967. Statistical Methods. 6th edition. The Iowa State University Press, Ames, Iowa. 593 pp.

Soileau, J.M., W. A. Jackson and R. J. McCracken. 1964. Cutans (Clay Films) and Potassium Availability to Plants. Jour. Soil Sci. 15:117-123.

Stewart, B. A. and H. V. Eck. 1958. The Movement of Surface Applied Nitrate into Soils at Five Moisture Levels. Soil Sci. Soc. Amer. Proc. 22:260-262.

Tamimi, Y. N., Y. Kanehiro and D. Sherman. 1968. Effect of Time and Concentration on the Reactions of Ammonium Phosphate With Humic Latosol. Soil Sci. 105:434-439.

Taylor, A. W. 1967. Phosphorus and Water Pollution. Jour. Soil and Water Conserv. 22:228-230.

67

Tinker, P. B. 1969. The Transport of Ions in the Soil Around Plant Roots. pp. 135-147. In I. H. Rorison (ed.). Ecological Aspects of the Mineral Nutrition of Plants. Blackwell Scientific Publica­tions Ltd. Oxford, England.

Van Schaik, J. C. and W. D. Kemper. 1966. Chloride Diffusion in Clay Water Systems. Soil Sci. Soc. Amer. Proc. 30:22-25.

Van Schaik, J. c., W. D. Kemper and S. R. Olsen. 1966. Contribution of Adsorbed Cation to Diffusion in Clay Water Systems. Soil Sci. Soc. Amer. Proc. 30:17-22.

Vaidyanathan, L. V., M. C. Drew and P.H. Nye. 1968. The Measurement and Mechanism of Ion Diffusion in Soils. IV. The Concentration Dependence of Diffusion Coefficients of Potassium in Soils at a Range of Moisture Levels and a Method for Estimation of the Differential Diffusion Coefficient at any Concentration. Jour. Soil Sci. 19:94-107.

Vaidyanathan, L. V. and P. H. Nye. 1966. The Measurement and Mechanism of Ion Diffusion in Soils. II. An Exchange Resin Paper Method for Measurement of the Diffusive Flux and Diffusion Coefficient of Nutrient Ions in Soils. Jour. Soil Sci. 17:175-183.

Vaidyanathan, L. V. and P. H. Nye. 1970. The Measurement and Mechanism of Ion Diffusion in Soils. IV. The Effect of Concentration and Moisture Content on the Counter-Diffusion of Soil Phosphate Against Chloride Ion. Jour. Soil Sci. 21:15-26.

Vaidyanathan, L. V. and O. Talibudeen. 1968. Rate Controlling Processes in the Release of Soil Phosphate. Jour. Soil Sci. 19:342-353.

68

Wilkinson, H.F., J. F. Loneragan and J.P. Quirk. 1968. The Movement of Zinc to Plant Roots. Soil Sci. Soc. Amer. Proc. 32:831-833.