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Chapter 4. Chemical Weathering of Minerals in Soils
M L JACKSON AND 0 DONALD SHERMAN
I V Frequency Distribution of Minerals in Soils in Relation t o Chemical Weathering.
1 Soils in the Early Stages of Chemical Weathering
a Early Weathering Stages Occur in Soils of Both Cool and Warm
b Saline Stage of Weathering (Stage 1 )
c Calcareous Stage of Weathering (Stage 2 )
d Ferromagnesian and Feldspar Stages of Weathering (Stages
3. 4. and 5 )
2 Soils of Intermediate Stages of Chemical Weathering
a Intermediate Weathering Stages Occur in Soils of Both Cool
and Warm Regions
b Quartz Stage of Weathering (Stage 6 )
c Mica-Illite Stage of Weathering (Stage 7 ) . . . . . . . . 262
d Interstratified 2 : l Layer Silicate and Vermiculite Stage of
Weathering (Stage 8 )
e Montmorillonite Stage of Weathering (Stage 9 ) . . . . . . 270
3 Soils of Advanced Stages of Chemical Weathering
a The Laterite as the End Product of Weathering
b Kaolin Stage of Weathering (Stage 10)
c. Qibbsite-Allophane Stage of Weathering (Stage 11)
d Hematite-Goethite Stage of Weathering (Stage 12)
e Anatase-Leucoxene Stage of Weathering (Stage 1 3 ) . . . . . 289
V Weathering Release of Nutrient Elements from Soil Minerals . . . . . 291
1 General Level of Soil Fertility I s Related to Weathering Stage
a Influence of Mineral Content in the Temperate Zone . . . . 292
b Influence of Mineral Content in the Tropical Zone . . . . . 292
2 Weathering Release of Nutrient Ions from Soil Minerals
a Weathering Release of Potassium
b Weathering Release of Calcium. Magnesium. Chromium. and
c Weathering Release of Phosphorus
d Weathering Release of Nitrogen and Sulfur
e Weathering Release of Minor Elements
3 Syatema of Utilization of Soil Mineral Weathering Sources of Nutriente
a Patch Agriculture
b Paddy Culture
c Intensive Culture
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CHEMICAL WEATHERING OF MINERALS I N SOILS
Weathering of minerals in relation to soils has two distinct phases:
( a ) Past weathering has broken down hard rocks both physically and
chemically to form the unconsolidated sands, loams, and clays from
which soils may be formed; and ( b ) present weathering of soil minerals
remains the major source of nutrients used by crops, for which the vast
chemical fertilizer industry is but a supplement. The first phase concerns the kinds of minerals found in various kinds of soil and soil parent
material. The second phase concerns the rate at which ions are released
in available form from minerals under specific conditions. As agriculture is intensified in particular areas, the proportion of the nutrients
supplied by weathering becomes relatively smaller compared to that
added as fertilizers. But even in areas of well-developed agriculture,
both in temperate and tropical regions, the weathering release of nutrient
elements is of major importance in soil fertility and crop production.
It is the purpose of this paper to examine the processes and products
of chemical weathering of minerals in soils from the standpoint of each
of these phases.
1. Definition of Weathering
The term “weathering of rocks” refers to the changes in degree of
consolidation and in composition which take place in the earth’s crust
within the sphere of influence of atmospheric and hydrospheric agencies.
Weathering has two distinct aspects, physical and chemical, each of
which can be defined separately. Physical weathering is the change of
consolidated rock to the unconsolidated state. Chemical weathering is
the change in chemical composition of consolidated o r unconsolidated
rock. For clarity, the agencies and processes of weathering (the means
by which the changes are brought about) will be carefully distinguished
from weathering itself (the changes). The term “weathered” means
changed physically or chemically, under atmospheric or hydrospheric
Changes in rock composition which are caused by deuteric and
hydrothermal agencies are termed “alteration” rather than weathering,
although some changes in mineral content of rocks arising through alteration are virtually identical to those arising through weathering. According to Merrill (1906), some scientists have not been precise in making
the distinction between weathering and alteration. He defined weathering as the superficial changes in a rock mass brought about by atmospheric agencies and resulting in a more or less complete destruction of
M. L. JACKSON AND
the rock as a geological body. Physical weathering he termed disintegration ; chemical weathering he termed decomposition.
a. The Province of Physical Weathering. Although the scope of this
paper is limited to the province of chemical weathering, a brief statement
is given on the province of physical weathering for purposes of clarification of the interrelationships between the two. Physical weathering
is the change from solid massive rock to the unconsolidated or elastic
state, under the influence of atmospheric or hydrospheric agencies, as
already explained. Polynov (1937) defines weathering as the complex
process, cyclic in nature, which causes the breaking down of the monolith
of rock or in general, solid body, and produces a n increase in surface or
interface between it and the surrounding media. It is known that every
interface, whether it be the boundary between the solid and liquid or
solid and gaseous states, possesses specific physicodynamic properties
which become more important quantitatively and qualitatively as the
ratio of the interface to the surrounding mass, specific surface, increases.
Weathering is thus, according to Polynov (1937), any process which
breaks down the large units to smaller “more active’’ units; and he defines the “crust of weathering” as “that upper part of the lithosphere
which consists of the loose products of the disintegration of igneous and
metamorphic rocks.” Elsewhere he includes disruption of sedimentary
rocks and makes clear that he includes processes involving transporation.
Physical weathering or disintegration breaks up the rock into smaller
units by mechanical means. The smaller units retain their original identity and composition. A basalt which has been broken down by mechanical means into smaller units can still be recognized as a basalt or, if the
particles are sufficiently fine, as its component mineral grains. Physical
weathering takes place either through agencies which act on the rock in
place or which move the rock about and abrade it. The latter include:
(a) glacial ice, ( b ) moving water, (c) gravity displacement on steep
slopes, and ( d) wind, for example, sand-blasting. These agencies which
move the material about are sometimes excluded as weathering agencies
but should surely be included. Physical weathering in place is brought
about through five principal processes (Reiche, 1950) : (a) unloading,
which permits the expansion of rock masses: when confining pressures
are lessened by uplift and erosion, cracks and joints form in bedrock; (b)
thermal expansion and contraction from insolation, which was once considered a major factor (Polynov, 1937) but has now been shown to be
relatively unimportant by Blaclrwelder (1933) and Origgs (1936) ; (c)
crystal growth, which produces a prying action on rock or mineral-this
includes the action of frost and to some extent of crystals formed by
chemical weathering, as, for example, the physical weathering of quartz
CHEMICAL WEATHERING OF MINERALS IN SOILS
crystals by iron-oxide films (Humbert and Marshall, 1943) and the crumbling of building stones in Switzerland attributed to the growth of ice
crystals and, in the cities, of sulfate crystals in cracks (Quervain, 1945) ;
( d ) colloid plucking, the physical rupture caused by shrinkage of colloidal matter with resultant flaking off of the surface of rocks; and (e )
pressure and abrasion by plants and animals, for example, disruption of
rocks by the enlargement of roots wedged in cracks (Kellogg, 1943, p.
The chief contribution of the physical weathering of rocks to chemical weathering is the increase of specific surface of the material, with
attendant increase in reaction rate. Birot (1947) found that rock Samples of granite and syenite and large crystals of biotite, muscovite, and
orthoclase lost from 1 to 6 per cent of the sample by disintegration into
sand particles after being alternately wetted a t room temperature and
dried a t 70" C. Caillere et al. (1952) obtained the breakdown of 6 per
cent of a slightly weathered gabbro into sand and some montmorin clay
by alternate wetting and drying. Simply keeping some material under
water can cause subdivision of the particles. Dekeyser et al. (1950)
boiled mica in water for a long period of time and obtained a clay-size
product. Henin and Betremieux (unpublished) obtained this same effect
at room temperature. Demolon and Bastisse (1946) found reduction of
the particle size of sieved granite after five and fifteen years of weathering in a lysimeter. Wetting and drying can also bring about the formation of new minerals and thus cannot be considered purely a physical
weathering factor. For example, Caillere et al. (1952) found that when
the gabbro suspension was evaporated and then wetted again, the gabbro
became coated with a ferruginous crust.
I n soils, particles of sand size are almost entirely products of physical
weathering (concretions excepted). Practically all particles of silt size
are products of physical weathering in cool and temperate climates but
are largely products of chemical weathering in tropical climates. Particles of clay size have such high specific surface that every stage of
chemical weathering is represented in this fraction, from early stages in
glacial rock flour (hornblende, biotite, albite) and intermediate stages
(montmorin, kaolin) to highly resistant products and residues (allophane,
anatase, ilmenite) .
b . The Province of Chemical Weathering. Chemical weathering is
the change in chemical composition of rocks under the influence of atmospheric or hydrospheric agencies. Sometimes termed the " decomposition" of rocks and minerals, chemical weathering is better viewed
in more conservative terms : The products of chemical weathering must
either ( a ) be formed as a new mineral (synthesis mechanism) or (b)
Y. L. JACKSON AND
remain as a residue when other constituents are removed (residue mechanism). Polynov (1937) termed these “products of accumulation” and
“ ortho-eluvium, ” respectively, although both are accumulations by different mechanisms. Solutes which pass into the ground water are also
“products” of weathering but are of less concern to soil mineral content
except as they may re-enter the cycle through synthesis (case 1). Likewise, ions which are released from minerals and temporarily held in
adsorbed forms which are available to plants are products of chemical
weathering and are of first importance to crop production; however,
they are not emphasized i n the usual consideration of chemical weathering because their quantities are so small compared to that of the weathered mass.
Decomposition is indeed involved in chemical weathering in the release of reactants for the synthesis mechanism ; likewise, decomposition
of a more readily weatherable substance and its complete removal in
solution are necessary for the operation of the residue mechanism. However, the products of chemical weathering (aside from solutes in ground
water) are in either case something other than a “decomposed” substance. The use of such terms as “decomposition” (Merrill, 1906) and
“katamorphism” (Van Hise, 1904) grew out of the fact that the
products of chemical weathering were formed or left behind from decomposition of something else and were frequently colloidal. Mineralochemical analysis had not developed to the point that the products formed
could be determined as new minerals, and this aspect was not emphasized in early literature as it came to be later.
The province of chemical weathering is, therefore, the formation or
residual accumulation of minerals as a function of their relative stability
to the chemical weathering processes (Sections I1 and 111) ; it includes
the frequency distribution of minerals in soils (Section IV) and the rate
of weathering release of nutrient elements from soil minerals (Section
c. Weathering Akin. t o Deuteric m d Hydrothermal Alt,eration of
Minerals. The layer silicates and other minerals frequently encountered
in weathering studies are also formed by deuteric and hydrothermal
alteration. Consequently, these layer silicates occur in the geologic column at much greater depths than the depths of initiation of weathering.
Although these layer silicates enter soils when the rock formation is exposed at the surface by erosion, these mineral species in such soils do not
re0ect chemical weathering, except by their relative resistance to weathering subsequent to exposure.
Deuteric alterations occur late in the crystallization of rocks (Bowen,
1922). In gabbro, for example, the alkali- and silica-rich interstitial
CHEMICAL WEATHERING OF MIhTERALS IN SOILS
solutions react with the olivine, pyroxene, and amphibole, which typically crystallize out earlier, to form Mg-rich layer silicates such as chlorites and serpentines. They also react with feldspars to form sericite.
The complex mixture can be seen in the rock by means of a microscope.
Similarly, in the metamorphosis of rocks, chlorite may form from garnetbiotite shist and sericite from feldspars (Harker, 1932).
The term “hydrothermal alterations, ” following the usage of Shand
(1944), refers to the changes in rocks resulting from the movement of
hot solutions along well-defined channels or fractures within the earth.
A few examples of hydrothermal alteration are given to show the close
relation of this type of change to weathering. A quartz monzonite was
hydrothermally altered (Sales and Meyer, 1950) to sericite for 20 feet
from the fracture through which the hydrothermal solution circulated.
The potassium was furnished from orthoclase. An isothermal front in
the 300400” C. range is suggested as defining the limit of sericitization.
The next 20 feet were altered to kaolinite, with the orthoclase being unaffected. The next 30-60 feet were altered to montmorillonite. Gradation followed through chloritized rock biotite to the unaltered rock. The
degree of alteration thus varied with the distance from the hot solutions
in the fracture. The rock alteration described above was clearly caused
by solutions moving deep within the earth; yet, there are examples of
similar alterations caused by hot solutions near the surface (Schmitt,
1950). At Yellowstone Park, hot spring waters have converted volcanic
rocks to rocks containing beidellite and kaolinite, quartz and orthoclase,
and zeolites and calcite. The alterations there differ from the deeper
types in that most of the water involved is of meteoric origin warmed
by superheated steam from depth. It is thus a type of surface alteration
activated by a deep-seated heat source.
The layer silicates formed by alteration enter soils when the rocks
are exposed a t the surface, but these layer silicate species in no way reflect the climate in which the soil was formed. These examples are cited
as illustrative of the numerous occurrences in relatively young soils of
minerals of hydrothermal origin, which cannot be related to chemical
No11 (1936a, 1936b, 1 9 3 6 ~ )demonstrated hydrothermal synthesis of
several layer silicates in the laboratory in the system A1208.Si02.Hz0.
Kaolinite formed below 400” C., and pyrophyllite was formed above this
temperature. With the addition of alkali and alkaline earth metallic ions
to the system, kaolinite formed when the metallic ion concentration relative to alumina and silica was low, but montmorillonite was favored by
increasing ratios of these metallic cations, particularly that of MgO. As
the relative potassium content was raised, sericite was formed and then
M. L. JACKSON A N D
feldspar at still higher potassium ratios and higher temperatures. These
experiments in the laboratory are of principal interest in the elucidation
of alteration mechanisms but may be indicative of chemical weathering
2. Pedochemical versus Geochemical Weathering
Viewpoints differ greatly as to the extent to which chemical weathering is identified with soil formation as distinct from parent material formation. The term “pedochemical weathering” is here defined to apply
to the chemical weathering which has taken place in the soil during its
formation and to that which is taking place in the soil currently. The
term “geochemical weathering” is defined to apply to the chemical
weathering which is considered to have taken place in the parent material
before the start of soil formation (granted that geochemical weathering
in a broader sense includes pedochemical weathering also). The general
term “chemical weathering” is employed to include both subdivisions
without distinction. Although i t is not always possible to distinguish
which of these two subdivisions of chemical weathering is primarily responsible for the origin of minerals in a given soil, and although the
distinction is sometimes a matter of definition of “soil formation,’’ different authors often wish to state a preference of viewpoint, and the use
of the two terms as defined is therefore extremely useful for clarity.
That physical weathering is largely completed during soil parent
material formation seems to be generally agreed upon. However, some
writers regard all chemical weathering as soil formation (pedochemical
weathering identical to geochemical weathering), whereas others restrict
the definition of soil to the upper portion of the geologic column which
is greatly influenced by the biological forces. Holding the latter view,
Marbut (1951) stated that “the soil is that layer of the earth’s crust
lying within the reach of those forces which influence, control, and develop organic life.” The geologic material beneath was termed the “soil
material’’ or “soil parent material. ’’ It is ordinarily unconsolidatedthat is, it is physically weathered. Beneath the soil material is consolidated geologic material. These views presented many years ago are adhered to by most of the soil scientists who followed. Kellogg (1943)
discusses weathering under the heading “building materials for soils” ;
this concurs with Marbut’s view of weathering as parent material formation. Physical, chemical, and biological “processes meet and mingle
in the surface film of the earth’s crust to form the soil which is neither
strictly physical nor strictly biological but a combination of both. ” Likewise, according to Robinson (1949, p. 60), “. . it is desirable to bear
strictly in mind the distinction between weathering, which produces the
CHEMICAL WEATHERINQ OF MINERALS I N SOILS
material from which the soil is developed, and pedogenesis, which results
in the development of a soil profile.” As will be brought out subsequently, chemical weathering has had the major part in producing the
colloidal minerals present in soils and thus the properties of soils, regardless of whether it is considered to be largely pedochemical or geochemical.
a. Situations of 21zindrnal Pedochemical Weatherilzg. When the definition of soil is restricted to that portion of the geologic column upon
which biological forces are acting, many soils have developed with little
pedochemical weathering of minerals. The test of little pedochemical
weathering under this restriction is that the mineral content of the solum
be similar to that of the C horizon.
In general, chemical weathering of minerals is slow relative to the time
required for a n unconsolidated material to be called soil. As soon as
biological forces have taken hold on a fresh alluvium, a n azonal soil is
recognized; but the mineral weathering stage (Jackson et al., 1948) is
that of the soil or rock column from which the alluvium was derived.
The same applies to young soils (Regosols) on till, loess, or other unconsolidated deposits. In these cases, pedochemical weathering is minimal.
The accumulation of organic matter and other effects of biological activity, quite apart from weathering, are recognized as initiating soil formation.
Highly weathered geologic columns present a similar situation of minimal pedochemical weathering, if the term “soil” is restricted to that
portion of the geologic column upon which biologic forces have acted.
The main chemical weathering has, under this restriction, occurred in
the soil parent material formation, as forcefully advocated by Nikiforoff
(1949). The test of pedochemical weathering under this restriction is
that mineral content in the solum differ from that in the immediately
underlying parent material. In the Low Humic Latosols of Hawaii
(unpublished data of the authors and associates) there appears to be
little mineral weathering change within the range of biological forces or
immediately beneath. Pedochemical weathering is minimal, even though
the weathering stage is advanced. Deep in the column, the geochemical
weathering profile shows a transition from kaolin to basaltic rock, a t
about 25 feet.
Mineral analyses of the A and B horizons of several soils of intermediate weathering (Coleman and Jackson, 1946) showed similarity to
those of C horizons, and thus illustrate minimal pedochemical weathering
in soils of intermediate weathering stages. The occurrence of sodiumrich feldspars, quartz, muscovite, and even some biotite in weathered rock
of Switzerland led Niggli (1926) to the conclusion that the chemistry of
the soil was similar to that of the parent rock.
M. L. JACKSON AND Q. DONALD SHERMAN
b. Siturctiolzs in Which Pedochemical Weathering I s Clearly Evident.
Situations in which pedochemical weathering is clearly evident include
the following :
1. Release of cations and anions from minerals in the soil, including
those taken up by plants and those lost by leaching.
2. Pedochemical deposition of sesquioxides and layer silicates (“clay
formation”) in the B horizons.
3. Pedochemical accumulation of sesquioxide and titaniferous surface
horizons and crusts.
4. Coincidence of the depth of chemical weathering with the depth of
biological activity and soil development.
The importance of pedochemical weathering in situation (1) both in soil
formation and in practical agriculture is clearly evident and is discussed
further in Section V. Ionic release is the first step in weathering reactions which lead to new weathering products.
To the extent that new minerals colloids are formed and accumulate
in the B horizon, situation (2) arises. The occurrences of the orterde
and ortstein of the Podzol and the clay accumulation in the B horizon
in the Cray-Brown Podzolic, Brown, and Planosol groups seem clearly
to represent mineral colloid formation by pedochemical weathering, in
addition to varying amounts of illuviation and residual accumulations.
Smith (1942) concludes that the development of soils from loess i n
Illinois “is toward the condition of a claypan soil, or Planosol.” Whiteside and Marshall (1944) concluded that clay formation and its distribution within the profile have been the chief result of soil formation in
the Putnam and Cowden soils (Planosols) of Missouri and Illinois. Allen
(1930) and Bray (1935) have described firm evidence of illuviation of
a colloidal montmorin series mineral (beidellite-nontronite) which “fills
cracks and cavities and has the cleavage plates oriented parallel to sides
of the deposit” (Allen, 1930). “The downward movement through
cracks and channels, as a result of water action, of discrete particles’’
was observed by Bray (1935). Bray in unpublished work (personal
communication) states that the same deposition of clay was observed in
worm holes. These observations support the concept of claypan formation by illuviation, as distinguished from clay formation by weathering
in place. Yet the formation of some montmorin series minerals by
weathering is suggested by the quantitative relationships, since there
is an increase with time in total.quantity of montmorin in the profile
(Bray, 1934). Bray (1937a, 1937b) concludes that weathering of
micas produces the expanding layer silicates and finally minerals of
more advanced (‘ ‘lateritic’ ’) stages, as indicated by the silica-sesquioxide ratios.
CHEMICAL WEATHERING OF MINERALS IN SOILS
Accumulations of surface horizons and crusts in the form of ferruginous and titaniferous materials, situation (3), seem clearly to be the
result of pedochemical weathering in the Humic Ferruginous Latosols
(Sherman et al., 1949a). Numerous similar examples undoubtedly occur.
I n situation (4), geochemical weathering has not kept ahead of soil
formation and/or erosion. To the normal processes of geochemical weathing have been added the biological and other processes peculiar to soils.
When the weathering is shallower than biological forces normally extend,
the soil is termed a Lithosol. When soils form on bare rocks, the inception of soil formation is recognized when lichens or other low forms
of life begin to grow. As weathering loosens up some debris on the surfaces of rocks and weathering of some mineral constituents sets in, the
weathering is coincident with soil formation.
The coincidence of the depth of rock weathering with soil formation
arouses the interest of soil scientists in chemical weathering, because the
soil can form only because of the vast changes in rocks wrought by chemical weathering. Thus Jenny (1941) includes weathering as part of soil
formation, while recognizing that many soil scientists sharply distinguish
weathering from soil formation. Haseman and Marshall (1945) state
that a deeper soil layer than that just below the B horizon must be used
to obtain the basal Zr content for calculation of the soil volume changes
resulting from weathering. This further illustrates that the geochemical
weathering profile may be deeper than the solum and the soil profile as
It should be pointed out that chemical weathering in situation (4 )
is no more fundamental than, and often is little different from, that occurring in deeper columns beyond the solum. It is therefore not surprising to find a number of soil scientists who prefer to extend their
definition of soil to include a11 weathered zones, a viewpoint set forth
by Bnshnell (1944, 1950, 1951) and employed in deep profiles studied
by Weaver et al. (1949).
c. Chemical Weathering I m p o r t a n t in Determining Soil Colloids.
From the examples given, both those in which pedochemical weathering
is minimal and those in which it is clearly evident, it is uniformly apparent that chemical weathering is largely the avenue by which the colloidal minerals of soils are supplied. As already mentioned, deuteric
and hydrothermal alteration supplies some of the colloidal minerals
to soils. It is also evident that the minerals of coarser sizes persist in
soils after more easily weathered ones are removed by chemical weathering. It is not critical for our present review whether the definition of
soil includes the entire weathering profile (geochemical plus pedochemical) or not. The degree of chemical weathering and the processes of
Y. L. JACKSON AND 0. DONALD SHERMAN
it remain the same, whether classified ( a ) as being geochemical, i.e., occurring in the parent material (Kellogg, 1943 ; Nikiforoff, 1949 ;Marbut,
1951), or (b) as being pedochemical, i.e., occurring in the soil profile,
however deep (Jenny, 1941; Bushnell, 1944, 1951; Haseman and Marshall, 1945 ; Weaver e t al., 1949). I n either case, chemical weathering of
minerals somewhere, not necessarily in their present site, for the most
part determines the nature of the minerals present in soil colloids. If it
is held that most of the chemical weathering occurs in the parent material
formation, case (a), rather than in soil formation, then the attendant
conclusion must be accepted that the mineralogy of soil colloids (and
many important soil properties, both chemical and physical) is determined to like extent by the parent material.
3. Terminology for Weathering Products
The term “clay fraction” will include the particles less than 2 p in
equivalent diameter, whereas the term “mineral colloid” will refer to
the finer clay fractions, including particles less than 0.2, 0.1, 0.08, etc.,
p in diameter, according to the individual report. The term “clay
mineral” refers to minerals in the clay fraction, including both layer
and other silicates and feralitic clay minerals. I n the interest of preciseness and clarity, the term “layer silicate” is employed for that structural
group of silicates.
Because colloidal layer silicates are universally involved in a consideration of the results of chemical weathering, passing reference will be
made to the extensive reviews available on their structure and nomenclature. Modern concepts of the layer silicates minerals (those silicates
with closely knit layer units of crystal structure) have been reviewed in
detail by Grim (1942), Ross and Kerr (1931), Ross and Hendricks (1945),
and Gieseking (1949). The nomenclatural and broad structural relationships of layer silicates to other silicates are reviewed by Jackson et al.
(1949), and details of layer silicate structures and properties are reviewed in detail by Marshall (1949) and Brindley (1951). These topics
will therefore be excluded from present consideration.
In agreement with Ross and Kerr (1931), the term “kaolin” will be
employed as a general name for the 1:1 family of layer silicates, including kaolinite, halloysite, and their hydrates and polymorphic relatives.
Following the reasoning of Correns (1950,1951), the term “montmorin”
is employed to include the isomorphous series of 2 :1layer silicates, including montmorillonite, beidellite, sa.ponite, nontronite, and other
isomorphous relatives, all having the property of expansion to approximately 18 A. in the presence of glycerol. The terms “montmorin,”
‘‘montmorin series, ” and ‘‘montmorin isomorphous series” have iden-