Clay Minerals (1984) 19, 521-539
THE INFLUENCE
OF A L U M I N I U M
ON IRON
O X I D E S : X. P R O P E R T I E S OF A L - S U B S T I T U T E D
GOETHITES
D.
G. SCHULZE*
AND U . S C H W E R T M A N N
lnstitutffir Bodenkunde, Technische Universitdt Mfinchen, 8050 Freising-Weihenstephan, FR G
(Received 23 September 1983; revised 3 May 1984)
A B S T R A C T : Fifty-seven goethites, synthesized by a variety of procedures and with A1
substitutions of 0-33 mole%, were characterized by XRD, IR, DTA, TEM and chemical
techniques. Most of the properties measured showed significant intercorrelations. Mole% A1
substitution (measured chemically) did not explain all the relationships among variables, but the
inclusion of Aa, defined as the observed a dimension minus the a dimension predicted by the
Vegard rule, explained much of the variation not explained by A1 substitution. OH stretching
frequency, in particular, was better correlated with Aa than the AI substitution or other
properties. The properties of the goethites could best be explained by a combination of A1
substitution and structural defects, with Aa being a measure of the defects. In general, the effect
of structural defects was opposite to that of A1 substitution. Increase in AI substitution led to a
decrease in all three unit-cell dimensions and OH stretching frequency and to an increase in the
distance between the two OH bending vibrations (6OH-yOH) and the temperature of dehydroxylation. Increase in structural defects, on the other hand, caused the a dimension, Aa,
and OH stretching frequency to increase and 6OH-yOH and the average temperature of dehydroxylation to decrease. Crystal size tended to decrease with increases in both A1 substitution
and structural defects. Surface area was significantly correlated with the reciprocal of the mean
crystal thickness in the a direction. Comparison of XRD and TEM data showed that many
samples consisted of crystals with several coherently scattering domains. The nature of the
defects, i.e. whether they occur primarily in the interdomain areas or whether they are also
distributed throughout the coherently diffracting domains, could not be determined.
The ionic substitution of A1 for F e in the structure o f goethite has a m a r k e d effect on
goethite crystal properties. The most obvious structural change is-a decrease in unit-cell
size (Thiel, 1963; Jdn~is & S o l y m ~ , 1970) caused b y the slightly smaller A1 cation. This
reduction is, however, not regular. Schulze (1984) has shown that only the c dimension
decreases strictly linearly with increasing AI substitution, whereas the a dimension can be
quite variable for samples with the same degree of A1 substitution and is always greater
than the a dimension predicted b y the Vegard rule. The b dimension also decreased linearly
with AI substitution but it was slightly more variable than the c dimension.
It might be expected that the changes in crystal chemistry (A1 instead o f Fe) and unitcell size would also lead to a variation in the properties of Al-substituted goethites.
Variations in crystal size and surface area, I R spectra, structural O H content, thermal and
magnetic properties, phosphate adsorption, and dissolution behaviour in H C I have been
observed ( F e y & Dixon, 1981; Golden et al., 1979; J6n~ts & Solym~tr, 1970; Mendelovici
et al., 1979; M u r a d & Schwertmann, 1983; Schwertmann, 1984b).
* Present address: Department of Agronomy, Purdue University, West Lafayette, Indiana 47907, USA.
9 1984 The Mineralogical Society
D. G. Schulze and U. Schwertmann
522
The purpose of the present work was to investigate further the structural properties of
Al-substituted goethites and to attempt to correlate structural modifications with other
chemical and physical properties.
MATERIALS
AND
METHODS
Fifty-seven goethites, synthesized by a variety of procedures, were studied. These included
the samples listed by Schulze (1984) and those listed in Table 1. The amount of A1substitution varied between 0 and 33.3 mole% A1.
The unit-cell dimensions were calculated from X-ray powder diffraction data as
described by Schulze (1984). The thickness perpendicular to a given hkl plane was calculated using the Scherrer formula (Klug & Alexander, 1974, p. 687) after correcting the
measured width at half-height (WHH) for instrumental broadening by subtracting the
instrumental W H H from the observed W H H (Schulze, 1984). Instrumental broadening
was determined from 5-20 g m quartz. The product of peak height and observed (uncorrected) W H H was taken as the line intensity.
A1 contents of the samples were determined as described by Schulze (1984).
IR absorption spectra were obtained on a Beckman Model IR 4250 spectrophotometer
using KBr disks (1 mg sample per 300 mg KBr). Spectra were obtained at scan rates of
150 cm-1/min and 50 cm-1/min with a gain setting of 55, period of 2 sec, and speed
suppression set at 3. The standard slit program was used with a slit setting of 0.3 mm at
3000 cm -~. The band positions were measured graphically from expanded strip-chart
recordings of the slow-speed scan. The OH stretching band was broad, making determination of the peak position difficult.
Differential thermal analysis (DTA) was carried out on a Linseis Model L62 analyser
using 50 mg samples, a heating rate of 10~
and hematite as the inert material. The
sample chamber was flushed with dry N 2 during the run. The dehydroxylation endotherms
were often asymmetric or split into two maxima; the average dehydroxylation temperature
was therefore determined by sketching in a reasonable base line and using a computer
program to calculate the weighted average.
Samples for transmission electron microscopy (TEM) were ultrasonically dispersed in
distilled water or ethanol and a drop of the suspension placed on a carbon-coated copper
grid and allowed to air dry. Micrographs were obtained with a Zeiss EM10 transmission
electron microscope operating at 80 kV.
TABLE1. Synthesisprocedures and extent of A1substitution for someof the goethites studied.
Sample
34/0-34/7,
34/0A-34/6A
35/0
DL1, DL5
30/4,30/10,30/12
38/33
Procedure
Mixtures of Fe(NO3)3and A1C13solutions stored for 14 days
under 0.3 MKOH at 70~
Ferrihydrite stored for 433 days at 24~ under 0.3 MKOH
Ferrihydrite stored for 3 years at room temperature under 1 M
and 0.3 MKOH, respectively
Ferrihydrite stored for 441 days at 24~ and pH 4, 10 and 12,
respectively (Schwertmann & Murad, 1983)
Slowoxidation of a 3 : i mixture ofFeC12and AICI3with air at
room temperature and pH 11-7
Al-substitution
(mole%)
0-10.9
0-6.5
0
0
0
32.6
Properties of Al-substituted goethites
523
Specific surface areas were determined using the ethylene glycol monoethyl ether
(EGME) method of Carter et al. (1965) as modified by Egashira & Aomine (1974).
The sum of chemisorbed and structurally bound H20 and OH was determined by weight
differences on samples dried at 150~ and then heated to 800~
in both cases until
constant weight was obtained. 150~ was chosen to assure that most of the physically
adsorbed H20 would be driven off; no conversion of goethite to hematite was noted at this
temperature. The additional OH + H20 will be represented by AOH, and was calculated
from the weight loss on heating minus the stoichiometric amount of H20 estimated from
the formula Fe,_x~AIxOOH (x = mole fraction AI) and expressed as mole/mole goethite.
RESULTS
AND
DISCUSSION
Relationships among the different sample properties were studied using statistical techniques. A matrix of Pearson correlation coefficients (Table 2) gives an overview as to
which properties are closely related. Individual coefficients will be discussed below.
TABLE 2. Pearson correlation coefficients (r) for the properties studied.*
a
Mole% A1
substitution
Aa
vOH
-0.47
(57)
0-001
Aa
0.82
(57)
0.001
0.11
(57)
0.199
vOH
3OH
yOH
Average DTA
Surface area
I110/Illl
MCDllo
Average Surface
DTA
area
0.62
0.92
0-95
0.08
(57)
(57)
(57)
(53)
0-001 0.001 0-001 0,277
0.22 - 0 , 6 4 - 0 . 2 9 - 0 - 8 5
(57)
(57)
(57)
(53)
0.048 0,001 0.014 0-001
0.84
0.63
0,88 - 0 . 4 0
(57)
(57)
(57)
(53)
0.001 0.001 0.001 0.001
0.43
0.71 --0-43
(57)
(57)
(53)
o.ool
3OH
7OH
o.ool
o.ool
0.86
(57)
0.001
0,28
(53)
0.019
--0.08
(53)
0.275
I11o/I111MCDll 0
AOH
0-54 - 0 . 4 8
0.01
(52)
(57)
(57)
0.001 0,001 0.468
0.40
0.01 - 0 . 6 2
(52)
(57)
(57)
0.002 0-470 0.001
0.85 - 0 . 5 3 --0.39
(52)
(57)
(57)
0.001 0.001 0.002
0.85 --0.63 --0.40
(52)
(57)
(57)
0.44
(42)
0.002
0.70
(42)
0-001
0-75
(42)
0-001
0.74
(42)
o.ool
o.ool
o.ool
o.ool
0.32 --0-37
0.16
0.25
(52)
(57)
(57)
(42)
0.011 0.002 0.120 0.054
0-68 --0.47 --0.11
0-53
(52)
(57)
(57)
(42)
0.001 0.001 0.211 0.001
-0.69
O. 19
0.75 --0-82
(49)
(53)
(53)
(42)
0.001 0.090 0.001 0.001
--0.53 - 0 - 6 8
0-85
(52)
(52)
(42)
0.001 0.001 0.001
0.20 -0-43
(57)
(42)
0.072 0.0O2
-0,88
(42)
0.001
* 0.00 ~ correlation coefficient; (00) = number of data pairs; 0,000 = level of significance.
524
D. G. Schulze and U. Schwertmann
The unit-cell a dimension
As mentioned in the introduction, the a dimension was usually significantly larger than
predicted from a linear relationship between goethite and diaspore (Vegard rule) (Schulze,
1984). The a dimension was not closely correlated with A1 substitution (r = -0.47,
Table 2). The difference between the observed a dimension and the a dimension predicted
by the Vegard rule will be represented by Aa and defined by the relationship:
Aa = a - (4.596 - 0.002 • %AI).
The end-members for defining the Vegard line were taken from card 17-536 (starred) for
goethite and card 5-355 (starred) for diaspore (JCPDS, 1974).
Aa showed a much better positive correlation with A1 substitution (r = 0.82) than the a
dimension itself. This correlation may, however, only be valid for Al-goethites synthesized
at temperatures <100~ (25 or 70~ in our case) and ambient pressure. Goethites
synthesized by Thiel (1963) at 155 ~ in an autoclave showed much less deviation from the
Vegard rule (Schulze, 1984, fig. 3), but they still plotted above the Vegard line. Aa was
closely related to the surface area (r -- 0.85) suggesting that the smaller the crystaUites,
the more likely a deviates from the theoretical a.
OH stretching and bending frequencies
OH stretching. The OH stretching band position (vOH) showed a general shift to
higher wavenumbers with increasing A1 substitution (Fig. 1) but the relationship was not
particularly good (r = 0.62) and even goethites with no A1 substitution showed about an
80-wavenumber spread in vOH frequency. Clearly, Al substitution is not the only factor
influencing vOH position.
The increase of the vOH band position to higher wavenumbers with increasing A1substitution is contrary to what can be expected from a comparison between goethite and
diaspore. In goethite the Oi--Oii distance is 2.757/~ and the angle O~-OH-H is 11.6 ~
(from data reported by Forsyth et al., 1968, and Sampson, 1969), while in diaspore they
are 2.650/k and 12.1 ~ (Busing & Levy, 1958). The OII-H distance is 0.990/~ in each
case. The vOH band positions are ~3130 cm -~ in goethite and ~2950 cm -1 in diaspore
(Schwarzmann & Sparr, 1969). The shorter Oi-Oi1 distance in diaspore gives rise to a
stronger H-bond in diaspore than in goethite, which is indicated by the lower wavenumber
of the vOH band. The slightly smaller O~-On-H angle in goethite should increase slightly
the strength of the H-bond (Schwarzmann & Sparr, 1969) but the increase is not enough to
compensate for the change in bond strength caused by the differences in O1-O H distances.
For increasing ionic substitution of A1 for Fe in the goethite structure one would expect a
steady, but not necessarily linear, increase in H-bond strength and a corresponding
decrease in vOH band position.
Mendelovici et al. (1979) also found a shift in vOH to higher wavenumbers with
increasing Al substitution which they attributed to a weakening of the hydrogen bond
caused by a higher screening effect in A1-O-H groups compared to similar F e - O - H
groups. Such a weakening of the H-bond by the ionic substitution of A1 for Fe is, however,
unlikely.
To see if there was a relationship between H-bond length and vOH, the Oi--Oii distance
was calculated for each sample using the formula: Oi-O n bond length = [(0.5084a) 2 +
Properties of Al-substituted goethites
525
om-1
c m .!
3240
960 +
940 -
+
3200
+
+
+
o
+
o
920
n
& Q~&
v
+
&
+
6.D +
3160
go0 -
~120
880
L
I
I
xo
Molo % A1
3240
860 -
+
+
+
840"
+
3200
+
+
+
v
820 +
+
x
3160
x
800
9
3120
'
' o.'o2
' o.'o4
J
'
,
0.'08 O.
0.06
780
1
I0
180 -
W
140Sorio6
12
I
Q
Sorio~ 28
x S o r i o ~ 31
9 Sorio~
34
O Serie~
OL
Seriem
v Othorg
3 ~
+
i
I
120
-
O
~D
IOO-I~I~+W
~-'> +
+
+
+
+
4
80
o
i'o
2'0
Mole
% AI
FIG. 1. vOH, 6OH, 7OH, and 6OH-?OH frequencies vs. mole% A1 substitution and vOH
frequency vs. Aa.
(0.1463b)2] v2. The coefficients 0.5084 and 0.1463 were calculated from position parameters taken from Forsyth et al. (1968) and were assumed to remain constant regardless
of Al substitution. For the unsubstituted goethites there was a significant relationship
between the Of-O u distance and vOH position (r --- 0.70, n = 16) but when all of the
goethites were considered together the relationship was not significant (r = 0.12, n -- 59).
There are several possible reasons for this unlikely result. The most likely one is that the
position parameters do not remain constant with increasing Al substitution. Another
possibility is that the H-bond in the Al-substituted goethites is deflected much farther away
from the Oi-O u axis than the 12 ~ in diaspore, resulting in a bent (and weaker) H-bond.
These possibilities could not be tested because they would require a structural refinement
on each individual sample.
There was, however, a significant relationship between Aa and vOH position (r = 0.84,
Fig. 1). The correlation was not increased significantly by the inclusion of additional
terms, such as A1 substitution or surface area, into the regression equation. The increase
526
D. G. Schulze and U. Schwertmann
in vOH frequency can be interpreted as an overall weakening of the H-bond. The fact that
the increase in vOH corresponds to an increase in Aa suggest that both of these properties
have a common cause.
OH bending. Both the 6OH (~900 cm -~) and yOH (~800 cm -1) OH-bending bands
shifted to higher wavenumbers with increasing A1 substitution, but the 6OH band shifted
more than the ~,OH band (Fig. 1). Fey & Dixon (1981) and J6nas & Solymhr (1971) noted
a similar difference in the shift of these two bands with AI substitution.
The 7OH band is due primarily to vibrations out of the a-b plane, i.e. along the c axis
(Schwarzmann & Sparr, 1969), and the almost linear dependency of 7OH with AI
substitution (Fig. 1) is consistent with the linear decrease in the c dimension with increasing A1 substitution (Schulze, 1984). In contrast, the fiOH band is due primarily to
vibrations in the a-b plane (Schwarzmann & Sparr, 1969), and the slightly greater
variability of 6OH for a given A1 substitution (Fig. 1) apparently reflects the variability of
the a dimension. The distance between the ~OH and the ?OH band may be interpreted as
reflecting the strength of the H-bond.
Linear regression analysis was performed using 6 O H - ~ ) H as the dependent variable
and mole% A1 and Aa as the independent variables. Of the independent variables, Aa alone
explained only a small part of the variability in fiOH-~OH ( r 2 = 0.17), while mole% A1
(r 2 = 0.60, Fig. 1) or the square of mole% A1 (r 2 = 0.65) explained much more. The best
regression was obtained with both %A12 and Aa in the equation resulting in:
6 O H - ? O H = 0.1019 (%A1) 2 -- 302.8 (Aa) - 0-9243 (Aa x %A1 z) + 103.7;
r z--0.95,
n=57,
S . D . = 2 . 1 c m -I.
The negative coefficients for Aa and the interaction terms mean that an increase in Aa
correlates with a decrease in 6 O H - y O H , which may indicate a decrease in the strength of
the H-bond with an increase in Aa. Likewise, the positive coefficient for mole% A1
substitution would suggest an increase in H-bond strength with increasing A1 substitution,
brought on, perhaps, by the contraction of the unit cell along the b and c dimensions.
Dehydroxylation characteristics
The most characteristic feature of the goethite DTA pattern is a strong endotherm
around 300~ due to dehydroxylation and concurrent conversion to hematite. For the
samples-studied, the dehydroxylation peak occurred between 220 and 360~ and was
often split into a double peak (Fig. 2), the high-temperature component usually being the
larger one of the two. When a single synthesis series of goethites (a single 'batch') was
considered, there was often a systematic relationship between average dehydroxylation
peak temperature and A1 substitution (Fig. 3), but when all of the samples were considered
together, there was no relationship (r = 0-08).
The dehydroxylation of goethite can be influenced by A1 substitution (J6n~ts & Solym/tr,
1970; Fey & Dixon, 1981), particle size, and by structural defects (Mackenzie & Berggren,
1970). Multiple linear regression analysis using mole% A1, Aa, and surface area as
independent variables, showed that two combinations, A1 substitution + Aa and AI
substitution + surface area both gave significantly higher r 2 values than surface area or
Aa alone (Table 3). Surface area and Aa are themselves linearly correlated (Table 2),
which explains why both variables are correlated with dehydroxylation peak temperature.
Properties of A 1-substituted goethites
527
At - st bstituti0n (mote %1
i
'~ ~
('3
~ 2,7
\\
372
FIG. 2. Differentialthermalanalysiscurvesof goethitesfrom Series 31.
X
V
X
~40"
x
9 X
n
X
L
m,,O
(I)
I
260
+
+
220
+
+
+
+
I
I
J
0
10
20
7. A1
Mole
,
I
30
F~G.3. Averagedehydroxylationtemperature(DTA)vs. mole%AI substitutionfor the goethites
studied (symbolsas in Fig. 1).
528
D. G. Schulze and U. Schwertmann
TABLE 3. Multiple linear regression analysis using average
dehydroxylation temperature as the dependent variable and
mole% A1, Aa, and surface area as independent variables
(n = 49).
Independent variable
%AI
Aa
Surface area
%A1, Aa
%A1, surface area
Aa, surface area
%A1, Aa, surface area
r2
0-00
0.18"**
0.48***
0.76***
0.77***
0.58***
0.81"**
Standard deviation
(o C)
34
30
24
17
16
22
14
The highest r 2 o c c u r s when all three variables are included, resulting in the equation:
Average DTA = 4-65 (%A1) -- 1814 (Aa) -- 0.330 (surface area) + 337; r 2 = 0.81 (Table
3). The positive coefficient for %A1 substitution is consistent with the increased thermal
stability of goethite as A1 substitution increases. The negative coefficients for Aa and
surface area show that both of these factors play a role in decreasing the thermal stability
of goethites.
The split dehydroxylation endotherm has been observed before (Fey & Dixon, 1981;
Jrnfis & Solymfir, 1970; van Oosterhout, 1965) and thermal gravimetric data (Schulze,
1982; Forsyth et al., 1968) show that the split endotherm corresponds to a brief decrease in
the rate of weight loss from the sample, i.e. to a momentary decrease in the dehydration
rate. Jrnfis & Solymfir (1970) attributed a shoulder on the low-temperature side of the
endotherm to gibbsite in their samples. This explanation must be rejected because the
split endotherm is most clearly expressed in the sample with no A1 substitution (Fig. 2).
Additional research has shown that the split endotherm can be attributed to the formation
of an intermediate goethite phase, with slightly modified unit-cell dimensions, which forms
when the domains of the goethite crystals are above a certain size (Schwertmann, 1984a).
Additional O H + H20
The amount of additional OH + H20 in the samples (AOH) was negatively correlated
with dehydroxylation temperature (r = - 0 . 8 2 , Table 2). In other words, the more
OH + H 2 0 in excess of the stoichiometric amount, the lower the dehydroxylation
temperature. AOH was also positively correlated with surface area, indicating that
essential parts of the additional weight loss may be due to surface hydroxyl completing
the coordination shells of surface Fe atoms and to chemisorbed H20 not driven off at
150~
Recent thermogravimetric studies with goethites of varying crystallinity have
indeed shown that the additional water is essentially driven off below 200~ (Schwertmann & Cambier, in preparation).
Properties of A l-substituted goethites
5 29
X-ray line intensities
Synthesis Series 34 was the only group for which standardized intensity data were
obtained (intensity relative to the 021 line of 50% admixed tt-Al203). I13o, I021, IH1, and
I~40 remained relatively constant with increasing A1 substitution, whereas IHo decreased
significantly (Table 4). Relative line intensities of all other samples (obtained without an
internal intensity standard) were therefore calculated relative to the 111 line (the second
strongest line) rather than the 110 line. Data for selected goethite lines (Fig. 4) show that
below 10% A1 substitution IH0 is the most variable relative to I m, followed by I~20, I130,
and 1140. In fact, I110/Ill 1 varies by a factor of 2, from a ratio of 1.5 to 3. Io20 and I02~vary
little with increasing A1 substitution.
Golden (1978) also noted a similar decrease in IH0 of synthetic Al-substituted goethites
between 0 and ~ 10 mole% A1 substitution which he explained as a decrease in preferred
orientation caused by a change in the particle morphology. Brown (1980) also explained
3
0.6
xx
x
~atix
o
----- 2
x
;
H
--
~- A o §
+
0.4
a
+
1
H
0.2
0.0
0.3
0.24 -
0.18-
I
~ 0
;
x
o
o
0.2
.o
0.12"
+
x
§
4-
+
o +
§
O. 0 6 9
0.00
9
0.0
a
a
x
o
v
1.2"
Series
Series
SeriQs
DL9 t o
G-NKI,
12
28
31
DLI2
P24
+ Series
A
a
"
o
v
+
0.4
0.3
3,4
Series
Series
Series
DL9 t o
G-NK1,
Series
12
28
31
DLI2
P24
3,4
0.8"
~eax
H
~
t
~o a ~ %
+
a+xaa
~
a
+
""
0.2
0.4'
0.1
0.0
0.0
0
5
10
15
20
Mole ~ AI
25
30
35
0
5
10
15
20
25
Hole ~ AI
FIG. 4. Intensities of selected X R D lines relative to (111) intensity for selected goethite synthesis
series.
30
35
D. G. Schulze and U. Schwertmann
530
TABLE 4. Intensities of selected diffraction lines of goethite: synthesis
Series 34.
Sample
Mole%
AI
111o*
I13o
/o21
1111
It4o
34/0
34/1
34/2
34/3
34/4
34/5
34/6
34/7~
34/0A
34/3A
34/6A
0
0.9
1.5
3-0
3.4
5.8
7-9
10-9
0
3.3
6.5
4-64
4.18
4.37
4.00
4.06
3.79
3.56
3.04
3.97
3.87
3.61
1.24
1.19
1.21
1.16
1.20
1.18
1-17
1-17
1.21
1.14
1.10
0.32
0.33
0.33
0.33
0.33
0.34
0-37
0.37
0.36
0.34
0.35
1.98
1.94
1.95
1.91
1.95
1.95
2.01
1.91
2.02
1.94
1.91
0.76
0.73
0.75
0.76
0.78
0.80
0.81
0.79
0.76
0.75
0.76
* All intensities relativeto the 021 line of admixed ct-Al203(1 : 1 mixture).
t Sample contains a trace of hematite.
differences in the relative intensities of observed and calculated goethite patterns as being
due to preferred orientation.
Orientation of the c axis in the plane of the sample surface but with random orientation
along a and b would cause all hk0 lines to increase in intensity relative to lines with l :~ 0.
This trend is not observed (Fig. 4) since, relative to I111, the variability is Ii10 > I120 >
1130 > 1140. However, additional orientation of the b--c planes parallel to the sample
surface can account for the observed intensity ehanges. The 110, 120, 130, and 140 planes
make angles of 25, 43, 54, and 62 ~ respectively, with the b-c plane, and partial orientation of the b - c planes in the plane of the sample surface would lead to a greater increase
in 110 intensity than in 120, 130, and 140. This interpretation receives support from two
further observations. As the needles become shorter, i.e. beyond ~ 10% substitution, they
are less prone to orientation on pressing, and therefore the increase in Ihko, particularly in
1110, becomes negligible. For the same reason, among the samples with zero substitution
111o/1111 decreases as crystallinity decreases because the acicular nature is less well
expressed (see Fig. 6).
Particle size and shape
X-ray diffraction. The broadening of the X-ray diffraction lines gives information which
reflects the average size and shape of the crystals, or more exactly, that of the coherently
scattering domains within the crystals. By using the Scherrer formula some of this information can be extracted. The Scherrer formula allots all line broadening to domain size and
does not take into account line broadening caused by structural defects.
The Scherrer formula gives the mean crystaUite dimension (MCDh~/) perpendicular
(_L) to a given plane hkl. MCDhk t can be decomposed into its components along the
crystallographic axes by multiplying it by cos ~, where ~, is the angle between the vector _t_
to the plane hkl and the vector defining the axis of interest. Cos ~ values for the first 10
goethite lines are tabulated in Table 5 along with M C D values along the a, b, and c axes
calculated from 9 goethite diffraction lines for a representative sample.
Properties of Al-substituted goethites
531
TABLE 5. Cosine p,, where ~ / i s the angle between the vector perpendicular to a plane with
indices hkl and either the a, b, or c axes, calculated for the first 10 goethite diffraction lines
and m e a n crystalline dimensions as determined from 9 X - r a y lines for sample 31/0.
Cosine ~,
hk I
a
b
c
020
1 10
120
130
0 2 1
10 1
0 4 0
11 1
121/210
14 0
0
0.909
0.735
0.585
0
0.548
0
0.534
n.d.
0,477
1
0.420
0.679
0.810
0.518
0
1
0.246
n.d,
0.881
0
0
0
0
0.854
0.834
0
0.812
n.d.
0
MCDhk t
MCD a
MCDo
MCD c
53.9
26.8
33-5
41.7
111.8
54.5
74.4
50.6
n.d.
55.9
-24.4
24.6
24.4
-29.9
-27.0
n.d.
26.7
53.9
11.3
22.7
33.8
57.9
-74.4
12.4
n.d.
49.2
----95.5
45.5
-41.1
n.d.
--
n.d. = not determined because two lines are coincident.
80
040
avorago partiolo
boundary
E
(-
6O
021
V
/
020
n
9
140
9
111
O~
C
o
o
40
130 "
ID
E
.X;
0
.w-I
.12
120
I
I
I
I
I
9
~- 2 0
110 9
101
i
0
TKickne88
~
"20
alon 9 a
I
40
(nm)
FIG. 5. M C D a vs. M C D b for selected goethite lines for s a m p l e 31/0.
D. G. Schulze and U. Schwertmann
532
Unless h00, 0k0, or 00l lines are available, it m a y not always be possible to determine
the thickness along all the axes directly. M C D a and M C D b values from Table 4 are plotted
in the a-b plane in Fig. 5. Note that M C D a values are about the same for all lines with
h :/: 0. In contrast, the M C D b values for the hk0 lines increase in the order 110 < 120 <
130 < 140 and all are less than the MCD~ value obtained from the 020, 021 and 040 lines.
It can be concluded, therefore, that the particles are thinner along the a axis than along the
b axis and that the average M C D a obtained from the 110, 120, 130, 140 and 111 lines is a
reasonble estimate for M C D a (the 101 line was not used in the average because it could
not be accurately measured when lines were broad). The good agreement in M C D a from
different lines indicates that line broadening is due to d o m a i n size rather than structural
defects.
The 020 and 040 lines should give the same MCD~; however, MCD040 was always
slightly larger than MCD02 o. This could be due to defect broadening also being present,
but it is m o r e likely caused by measurement errors because the 040 line is partially overlapped b y the much stronger 111 line. The 021 line, however, gives an M C D b value which is
closer to that of 020 than o f 040. The average o f M C D o obtained from the 020 and 021
lines was therefore taken as M C D b. As is shown below, this gives g o o d agreement with
particle widths measured from electron micrographs. M C D a can be thought o f as a
limiting dimension for the example given in Fig. 5 because it is M C D a, not M C D b which
limits the length o f MCDhk t for lines with h r 0.
M C D c cannot be determined from the d a t a given in Table 5 because M C D a is the
limiting dimension for M C D H I and MCDI01, and M C D b is the limiting dimension for
MCDo2 r Since the 021 line gives the greatest length for M C D c, this will be taken as a
minimum length for MCDc. The average M C D ~ and M C D b and the minimum MCD~
values determined from X R D are listed in Table 6 for most o f the goethites studied.
TABLE 6. Mean crystallite dimension (MCD) along the a, b and c axes as
calculated from XRD data, mole% A1 substitution, and EGME surface
areas.
Sample
A1
substitution
(mole%)
31/0
31/1
31/2
31/3
31/4
31/5
31/6
31/7A
31/7B
0
0.5
1.7
2.7
4.2
6.7
9.7
11.3
11.3
25+ 1
27_+1
29 _+ 1
30 _+ 1
33 _+ 1
37 _+ 1
41 _+3
41 _+5
42_+ 7
56+3
60_+5
64 _+4
68 _+ 5
71 _+2
72 _+ 1
75 _+9
70_+ 14
71 _+ 10
>96
>104
>110
>117
>119
>118
>113
>100
>105
16
23
28
26
26
23
25
39
36
12/0
12/5
12/10
12/15
12/20
0
4.7
9-0
12.4
15.7
9 _+ 1
15 _+ 1
15 _+ 1
15 _+ 1
14 _+ 1
29 _+ 1
45 _+ 1
43 _+ 3
35 _+ 1
31 _+ 1
>48
>75
>74
>57
>50
88
69
68
69
62
0
1.6
2.6
26 _+2
28 _+2
30 _+2
60 _+2
66 _+7
73 _+ 7
>102
>117
>128
30
30
30
28/0
28/1
28/2
MCD~~
(nm)
MCDbz
(nm)
MCDc 3
(nm)
surface
area
(m2/g)
Properties of A l-substituted goethites
TABLE 6. (continued)
Sample
A1
substitution
(mole%)
28/3
28/5
28/7
28/10
28/12
28/15
28/20
3.5
4.7
6-6
7.7
8.7
10.5
16.7
_+ 2
_+ 2
+ 1
_+ 1
+ 1
_ 1
22 _+ 2
73
63
49
43
39
41
49
34/04
34/14
34/24
34/34
34/44
34/54
34/64
34/74
34/0A 4
34/3A 4
34/6A 4
0
0.9
1.5
3.0
3.4
5.8
7.9
10.9
0
3.3
6.5
23
24
27
31
33
36
40
38
21
21
28
69
63
77
83
94
66
59
48
60
64
72
DL/9
DL/10
DL/ll
0
5.9
10-6
19 + 1
32 + 3
46 _+ 3
3/0
3/5
4/10
4/15
4/20
4/25
4/30
4/33
0
5.1
9.7
13.9
18.6
22.1
24.9
31-0
35/04
DL14
DL54
P24
P146
P150
30/44
30/104
30/124
G2B34
38/33'
0
0
0
0
0
0
0
0
0
33.3
32.6
MCD~ ~
(nm)
27
22
16
14
14
16
MCD~ 2
(nm)
Surface
area
(m:/g)
>126
>106
>82
>71
>64
>68
>85
34
45
58
64
72
56
42
> 114
>103
>126
>137
>155
>109
>98
>79
>99
>106
>120
22
23
34
32
21
21
14
25
49
38
34
60 _+ 3
96 + 1
106 + 14
>95
>157
>158
67
n.d.
n.d.
9+ 1
7+ 1
6.+2
7 _+ 2
5 _+ 2
5 _+ 2
5 .+ 2
4 _+ 2
20 + 3
11 + 2
7+1
8+ 1
4 -+ 1
3 _+ 2
3+ 2
2+ 1
>29
>16
>11
>11
>6
>3
>3
>3
103
138
191
180
228
207
253
211
16 + 1
I0 + 1
14 + 1
12 -+ 1
5 _+ 1
6+1
30 _+ 3
37 + 5
23 + 2
14 _+ 7
32 + 14
48
34
50
35 +_ I
8+ 1
10-+1
66
178
105
7
20
+_ 2
_+ 1
_+ 2
_+ 2
+_ 3
+ 3
_+ 4
_+ 9
_+ 1
_+ 1
_+ 2
_+ 5
+ 2
_+ 1
_+ 1
+ 1
_+ 1
+ 4
MCDc3
(nm)
533
>80
>56
>82
>57
>12
>16
> 108
>294
>173
>12
>34
57
65
65
n.d.
136
68
27
37
126
35
~Average and standard deviation from 110, 120, 130, 111 and 140 lines
except for samples 34/0 through 34/6A and G2B3 & 38/33 which are the
average of the 110, 130, 111 and 140 lines, and samples 35/0, DL1, DL5,
30/4, 30/10, and 30/12 which are the average from the 110, 130, and 111
lines.
2 Average and standard deviation from 020 and 021 lines except for
samples containing a-Al20 a which are the values from the 021 line alone.
3 Minimum value derived from 021 fine.
4 Sample contained a-Al203 as an internal standard.
534
D. G. Schulze and U. Schwertmann
l~m
J
ZZ:
0.1jJm
FIG. 6. Transmission electron micrographs of selected samples from Series 31 and 12.
L
Properties of Al-substituted goethites
535
Transmission electron microscopy. Transmission electron microscopy (TEM) gives
independent data on particle size and shape which complements the data obtained from
XRD. Particle size and shape varied greatly among the different synthesis series.
For Series 31, the least substituted samples consist of large (1-2 #m long), lath-shaped
particles with jagged ends (Fig. 6; Table 7). This morphology suggests that different parts
of a crystal grew at different rates in the c direction from one nucleus. Many dark bending
contours appear perpendicular to the long axis of the particles (Fig. 6, arrows; Schwertmann, 1984b). The bending contours are interrupted within the crystals, suggesting that
the crystals consist of domains separated from each other by disrupted zones.
With increasing A1 substitution the goethite laths become shorter, narrower, and thicker
(Tables 6 and 7, Fig. 6). The increase in thickness is mainly responsible for the specific
surface (Table 6) not increasing as much as might be expected. This is because for a
lath-shaped particle the specific surface is mainly determined by the thickness of the laths.
The particles of the most Al-substituted samples appear to be single laths with angular
ends (Fig. 6) and bending contours are rare.
If the laths are assumed to be lying with their a axis perpendicular to the grid surface,
then their width as measured from the micrographs should represent the length along the
b axis. For the lowest A1 substitutions this width is much larger than MCD o determined
from XRD (Table 7). As A1 substitution increases, MCD b approaches the width obtained
from TEM, and for samples 31/6, 31/7A and 31/7B it is the same. This agreement shows
that for these samples the particles observed in the micrographs act as one coherently
scattering domain for X-rays along the b axis. In contrast, the unsubstituted and least
substituted goethite particles are made up of several coherently scattering domains parallel
to the b axis. The lengths along the c axis show a similar trend (Table 7), but because
MDC c is only a minimum length along c, complete agreement cannot be expected. The
multi-domainic nature of the unsubstituted and least substituted goethite crystals of this
synthesis series is also shown by their dissolution in 6 M HC1, which in the beginning of the
dissolution process preferentially proceeds between the domains (Schwertmann, 1984b).
TABLE 7. Average lengths and widths of particles from Series 31 as measured from electron micrographs and
ratios of lengths and widths from XRD and TEM.
Length (nm)
Sample
Average
31/0
31/1
31/2
31/3
31/4
31/5
31/6
31/7A
31/7B
1246
950
103 l
846
781
493
358
284
303
S.D.*
496
441
426
417
336
255
149
130
170
Width (nm)
Average
142
128
142
122
124
94
76
69
67
Length XRD (MCDc) Width XRD (MCDb)
S.D.*
nt
Length TEM
Width TEM
51
59
55
59
51
45
38
32
30
59
58
74
74
64
70
81
78
90
>0.07
>0-!0
>0.10
>0.13
>0.15
>0.23
>0-31
>0.35
>0.35
0-39
0.46
0.45
0.55
0.57
0.76
0.98
1.01
1.05
* S.D. = standard deviation.
~"n = number of particles measured on the micrographs.
536
D. G. Schulze and U. Schwertmann
TABLE8. Summary of the effectsof A1 substitution and structural defects on goethite properties.
Effect of
Property
Unit-cell dimensions
vOH frequency
AI substitution
all dimensions decrease
decreases
(stronger H-bonds)
~OH-),OH
increases
Temperature of dehydroxylation
increases
AOH
decreases
Crystal size
laths become shorter and
narrower, but thicker
Dissolution rate in acid (Schwertmann, 1984b) decreases
structural defects
a dimensiondilates
increases
(overall weaker H-bonds)
decreases
decreases
increases
decreases
increases
Particle size and morphology of Series 28 and 34 are similar to those of Series 31.
Particle width and length decrease continuously with increasing A1 substitution but this does
not agree with X R D data which predicts that the M C D values (except M c D a for Series
34) show maxima at intermediate A1 substitution (Table 6). In Series 28 a second
maximum occurs at high substitution. Part of this heterogenous behaviour in Series 28 can
be explained by irregularities during synthesis, in which some K o H was added before AI
addition and some was added after, influencing nucleation in different ways (Schwertmann, 1984b).
The particles in Series 12 (Fig. 6) are considerably smaller than those of Series 28, 31,
and 34, in line with a surface area approximately twice as large. They do not show the dark
bending contours. As A1 increases the particles become shorter and more plate-like, and
crystals with irregular edges appear in addition to acicular ones. X R D indicates larger
MCDa and M C D b values than for 12/0, which causes the surface area to decrease slightly.
Electron diffraction has shown that the monodomainic acicular crystals fall on the 110
faces rather than on [1001 (Mann et al., 1984).
The goethites prepared from the Fe(II) system (Series 3 and 4) are much less crystalline
than those of the other series, which were made from ferrihydrite under alkaline conditions.
The acicular nature of the crystals is still clearly expressed at zero A1 substitution although
the particles are highly serrated. As A1 substitution increases the acicular shape is less and
less obvious, in agreement with results of Fey & Dixon (1981, fig. 4). This situation is
clearly reflected in the very low M C D values (Table 6).
The overall relationship between crystal size and specific surface area as measured by
E G M E adsorption cannot be expected to be a simple one. The lath-shaped nature of the
crystals makes it likely, however, that the thickness of the laths should determine much of
the surface area because the lath thickness determines the contribution of the largest partial
surface of the crystal to the overall surface, namely the b - c planes. If the crystal shape
remains essentially constant, then there should be a linear relationship between surface
area and the reciprocal of the lath thickness (1/MCD~) because surface area increases as
the square of thickness, whereas particle volume increases as the cube of thickness. This is
indeed the case as shown by Fig. 7.
Properties of A l-substituted goethites
537
300
9
S=IO4g
( I I M C D a) -5. 14
C~J
E
v
200
O
0
L
(3
0
O
qI_
3
t0
+
V
i00
0
I
o
o. io
I/MCO
I
'
0.20
(nm-1)
FIG. 7. S u r f a c e a r e a vs. 1 / M C D a ( s y m b o l s as in Fig. 1).
GENERAL
DISCUSSION
From the data presented, it is clear that the ionic substitution of A1 for Fe in goethite does
not account for many of the differences in goethite properties. Another factor, which we
believe to be structural defects of some kind, is necessary to account for the remaining
variation. Aa appears to be a good measure of the relative concentration or severity of the
defects. The effects of structural defects on some goethite properties are often opposite to
those of A1 substitution (Table 8).
The type of structural defect is still obscure. Among the two possibilities--0) point
defects randomly distributed in the crystal and (ii) defects separating coherent zones
(domains) arranged in a more or less ordered fashion within the c r y s t a l l m O s t of the
information obtained favours the latter possibility. Recent H R T E M work on goethites
(Smith & Eggleton, 1983; Cornell et aL, 1983; Schwertmann, 1984b; Mann et al., 1984)
has clearly demonstrated the existence of domains and perfect structural order within the
domains. The domains usually run along the c-direction. The zones between the domains
may be micropores or partly filled with disordered material (cf. Turner & Buseck (1983)
for nsutite, y-MnO2). They are zones of prefered proton attack (Schwertmann, 1984b) and
may be accessible to sorbate molecules as well. It is probably the thickness of the domains
rather than the overall thickness of the crystal which determines X R D line broadening.
The reasonable agreement between domain size as measured from TEM and from XRD
line broadening also favours the idea of this kind of structural defect.
Some of the factors determining the extent of structural defects can be determined from
the data presented above. If larger Aa values and vOH stretching frequencies and smaller
5 O H - 7 O H values are taken as indicators of structural defects (domain size), then there is
a general correlation between the synthesis temperature and Aa, 7OH, and 6 O H - ? O H .
In the temperature range used for synthesis of the goethites described here (25-70~
the
higher the synthesis temperature, the lower Aa and vOH and the higher ~OH-7OH, and,
therefore, the less defective the crystals. Even higher temperatures, such as the 155~
538
D. G. Schulze and U. Schwertmann
hydrothermal synthesis procedure used by Thiel (1963), seem to produce goethites with
still fewer defects as indicated by smaller Aa values (Schulze, 1984). Synthesis o f goethites
over a wide temperature range ( 4 - 9 0 ~
and h y d r o t h e r m a l treatment o f defect goethites
fully support these conclusions (Schwertmann & Cambier, in preparation).
A second factor influencing structural defects is the O H concentration. Series 12, 28, 31
and 34 were all synthesized at 70~ but at different O H concentrations. Series 12 was
synthesized in 2 M K O H while 28, 31 and 34 were synthesized in 0 . 3 - 0 . 4 M K O H . Series
12 had larger A a (Schulze, 1984) and vOH values and smaller 6 O H - ? O H values (Fig. 1)
than Series 28, 31 and 34, indicating more structural defects in Series 12 than in 28, 31
and 34. This is p r o b a b l y the result of the increase in crystallization rate with increasing
K O H concentration because increasing [OH] results in higher supersaturation with
respect to goethite.
As a third factor, [AI] in the system decreases structural defects b y decreasing the
crystallization rate (Schwertmann, 1984b).
In F e ( I I ) systems such as Series 3 and 4, a fourth factor appears important, namely the
oxidation rate. Increasing the rate leads to faster crystallization and thus to more
structural defects.
ACKNOWLEDGMENTS
This project was supported in part by a grant from the Deutsche Forschungsgemeinschaft, Project Schw
90/33-1. Thanks are due to Dr D. Lewis, Waite Agricultural Research Institute, University of Adelaide, Glen
Osmond, South Australia; to Dr N. K~impf, Departamento De Solos, Faculdade Agronomia-UFRGS,
Porto Alegre, Brazil, who synthesized some of the goethite samples; to Dr H-Ch. Bartscherer, Lehrstuhl fiir
Physik, Weihenstephan, for carrying out the EM work; and to Birgit Gallitscher, Christine Wagner, Ulrike
Maul, and Ellen Schneider for carrying out chemical analysis and obtaining the IR spectra and DTA curves.
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