American Mineralogist, Volume 77, pages 904-910, 1992
An atomic force microscope(AFM) study of the calcite cleavageplane:
Image averagingin Fourier space
Ar,lN L. Rlcnr,ru,
GuNr
S. HnNoBnsoN
Department of Geology, University of Toronto, Toronto, Ontario M5S 38l, Canada
M. CvNrnn Gorr
Department of Chemistry, University of Toronto, Toronto, Ontario M5S 1Al, Canada
Ansrntcr
The cleavageplane of calcite (in equilibrium with HrO) has been examined at nearly
atomic resolution using an atomic force microscope (AFM). The images obtained suggest
that there is minimal reconstruction of the surface.The cleavageplane exhibits a rectangular unit cell 0.74(5) nm by 0.48(2) nm, which is in generalagreementwith both the unit
cell calculated from the bulk structure and that derived from low-energy electron diffraction (LEED) images. Individual AFM images were too noisy to resolve atoms, and the
surfacepattern appearedto vary. Conversion of the images into Fourier spaceshowed a
consistentpattern of periodicities similar to that observedin previously published LEED
images, but the individual peak locations and intensities varied slightly from image to
image. For periodic surfaces,averagingof imagesin Fourier spaceimproves image quality
without loss of information.
INrnooucrroNr
Calcite is one of the most ubiquitous materials at the
Earth's surface.It occurs in geologicalsettingsas diverse
as near shore marine muds and carbonatites (Reeder.
1983).However, although it is a simple salt and has been
studied extensively, the geochemistry of calcite is complex and remains imperfectly understood.
Many studies have examined the bulk interaction between calcite and various aqueousimpurities (cf. Kitano
etal.,1975,1979a,1979b;Reddyand Wang, 1980;Sdhnel and Mullin, 1982; Mucci and Morse, 1983). More
recently, interactions at the mineral's surfacehave been
studied using X-ray photoelectron spectroscopy(XPS),
Auger electron spectroscopy(AES), or low-energy electron diffraction (LEED) (cf. Bancroft et al., 1977a, 1977b,
I 979;Brown, I 978;Mucci et al., I 985; Mucci and Morse,
1985; Fulghum et al., 1988:'Zacharaet al., 1989; Stipp
and Hochella, l99l). However, thesemethods are technically demanding, as they require that the sample be
under vacuum.
The atomic force microscope (AFM) was developedin
1985 (Binnig st al., 1986) as an extensionof scanning
tunneling microscope (STM) technology. Samplescan be
imaged under ambient conditions, in contact with solutions or in a vacuum. Sample preparation is relatively
simple, and the AFM can be used to image both conducting and nonconducting materials. AFM technology
is still young and has only recently been applied to earth
scienceproblems. It has been used to image muscovite
(Drake et al., 1989),illite and montmorillonite (Hartman
et a1.,1990),clinoptilolite (Weisenhornet al., 1990),hematite (Johnssonet al., l99l), graphite (Binnig et al.,
0003-004x/92109
l 0-0904$02.00
1986),sodium chloride (Meyer and Amer, 1990),albite
(Drake and Hellmann, l99l), and lizardite (Wicks et al.,
1992\.
To date, atomic resolution AFM imageshave been difficult to obtain becausethe images could not be reproduced. This study attempts to characterizethe unit cell
of the calcite cleavageplane by performing a statistical
analysis of the periodicities exhibited by multiple AFM
images in Fourier space.
C,tr-crrr STRUCTURE
Calcite (CaCOr) is hexagonal, space group R3c, with
hexagonalunit-cell parametersa : 0.4990nm, c : 1.700
nm, Z: 6, as determined by X-ray diffraction (Chessin
et al., 1965).As seenfrom Figure l, the structureconsists
of alternating layers of Ca" and COI groups oriented
perpendicular to the c axis, with interionic bonding between layers. Carbonate groups within a layer are all coplanar and have identical orientations, and alternate layers are rotated 180'with respectto the layers above and
below. Calcite has perfect rhombohedral cleavage{1014},
which intersectsthe alternatinglayers at 4437'. lf Ihe
conformation of a cleavagesurfaceis consistentwith the
mineral's bulk structure, then it should consist of alternating rows of Ca2* and CO3-. The carbonate goups
should all be inclined with respectto the plane such that
one O atom lies above it. one in it. and one below it.
ExpnnrunNtarImages were obtained using a Digital Instruments Inc.
Nanoscope II AFM equipped with a standard A head.
This equipment has been previously describedby Hoch-
904
905
RACHLIN ET AL.: AFM STUDY OF CALCITE CLEAVAGE
TaBLE1. MeasuredR (nm),d ("),and o of periodicitiesin Fourier
space in the 16 best imagesobtainedin this study
Peak
b
d
(o0o1)
l
s
@ calciun
A
carbonate
No. obs.
16
15
13
16
I
14
h
2
n
p
4
c
hm
0.48
0.40
o.74
0.41
0.29
0.36
0.30
0.24
0.25
0.18
n
180.39
148.59
93.28
34.33
13031
92.28
57.87
181.46
97.27
49.05
0.02
0.02
0.05
0.02
0.02
0.02
0.01
0.00
0.02
0.01
2.44
2.31
4.68
'1.47
2.28
4.92
4.58
4.21
3.55
3.97
atom
group
shows the 2DFFT image of each of the imagesin Figure
2. Figure 4 is a schematic illustration of the averageobserved 2DFFI pattern, basedon examination of I l9 images.The most frequently observed peaks have been arella et al. (1990). A si3Nowide-legged100-pm rriangular bitrarily labeled for easeof reference.By measuringR, d,
cantilever was used throughout this study. Colorlessand and 1 for each of the frequently observed peaks, it betransparent material ("iceland spar") from an unknown comes possible to calculate mean values and standard
locality was cleavedinto platesapproximately2 mm thick. deviations for the observedperiodicities. Table I lists the
A fluid cell was filled with Aldrich HPLC H,O (glassdis- measuredR, d, and o of periodicities in Fourier spacein
tilled and filtered through 0.5-pm filters) and was allowed the l6 best imagesobtained from samplesin orientations
to equilibrate for at least 2 h. Becausethe cantilever is
I and 3, with various applied rotations. Intensity (f is
triangular and contacts the surface to be scanned at an omitted to simplify the illustration. The variability in R
angle, its mechanical properties vary depending on the and d is causedin part by determinate error arising from
scandirection. In addition, ifthe cleavageplane contains the quantization of cursor movement. The quality of iminclined CO. groups, then the orientation of the sample ages obtained in orientation 2 was consistently poorer
with respectto the tip may also affect image quality. For than that of the other orientations, and therefore images
this study the cleavageplate was placedin the microscope in that orientation were not used. As set out in Table 1,
head in three different orientations. Orientation I was the cleavagesurfacein equilibrium with HrO exhibits a
such that the projection of the positive c axis onto the rectangularunit cell of 0.74(5)nm by 0.48(2)nm. This is
cleavageplane (c') was approximately parallel to the pos- in generalagreementwith the calculatedunit cell of 0.808
itive scan direction of the y-piezo. Orientation 2 placed + 0.001 nm by 0.4990 + 0.0002 nm using the cell pathe projection parallel to negative x-piezo scandirection, rametersof Chessinet al. (1965).
and orientation 3 placed it parallel to the positive x-piezo
Figure 5a showsthe best unfiltered image of the calcite
scan direction.
cleavageplane obtained in this study. In Figure 5b the
image has been filtered using the 2DFFT algorithm to
Rrsur,rs AND DrscussroN
retain all observedperiodic maxima in Fourier space(13
When the cleavagesurfacewas examined in equilibri- unique peaks).In both Figures 5a and 5b the alternating
um with HrO, periodic structureswere observed,but their rows of Ca2* and COI- can be clearly seen. Finally, in
shapeappearedto vary from image to image. The signal Figure 5c we have applied a hard filter consistingofthree
to noise ratio remained poor. No atomic or molecular lowpassfrlters,an algorithm to eliminate image bow, and
scaleresolution was obtained when the sample was equil- a 2DFFT filter to remove noise. The essentialfeaturesof
ibrated for less than lth h, presumably becausecalcite the original image can still be resolved. A projection of
was still dissolving. Equilibration for as long as 72 h re- the cleavageplane was drawn using fractional atomic cosulted in no discernible changein image quality. Figure ordinates from Chessin et al. (1965) and the observed
2 is a representativesample of raw images,captured in a unit cell; it has been superimposedon Figures 5b and 5c.
variety oforientations. For clarity, they have been rotat- Ionic radii have beenreducedto make the structure easier
ed so that c' is vertical in each image in the figure.
to visualize. There is a good correlation between the obWhen the imageswere transformed into Fourier space served image and the projection; indeed, it appearsthat
using a two-dimensional fast Fourier transform (2DFFT) the carbonate O that projects out of the plane is somealgorithm, a consistent pattern of periodicities was ob- what better visualized than the O that should, in theory,
served. However, when measured using polar coordi- lie in the crystal.
The Fourier transform of a crystalline surface should
nates, the radial (R), angular (d), and intensity (4 components of each periodicity varied slightly from image to be the same as the LEED image of that surface.The LEED
image.This appearsto be the reasonthat different images image of the calcite cleavageplane cleavedin air and after
of the same surfaceappear to be quite different. Figure 3 dissolution in HrO has recently been examined by Stipp
Fig. l. Calcirestructure,projectionparallelto [1210].
906
RACHLIN ET AL.: AFM STUDY OF CALCITE CLEAVAGE
F\9. 2. Unfiltered imagesofthe calcite cleavageplane: (a) orientation 3 rotated I 80", (b) orientation 3 rotated I 35', (c) orientation
rotated 135o,(d) orientation I rotated 135', (e) orientation 1 rotated 30', (0 orientation I rotated 60'.
RACHLIN ET AL.: AFM STUDY OF CALCITE CLEAVAGE
Fig. 3. The 2DFFT imagesof imagesin Figure 2a-2f.
907
908
RACHLIN ET AL.: AFM STUDY OF CALCITE CLEAVAGE
ac
++*nt+P++
'x
I
c,
+
P+
o+
Ca
9+
f' +
->
h
D*
Fig. 4. Schematicillustrationof the averageobserved2DFFT
plane,basedon 119images.The
imageof the calcitecleavage
peakshavebeenarbitrarilylabeledfor
mostfrequentlyobserved
easeof reference.
and Hochella (1991). They report a rectangular unit cell
of dimensions0.811(25)by 0.497(14)nm for material
cleavedin air and 0.816(23)bV 0.505(la) nm after dissolution, in general agreementwith the results reported
here. Stipp and Hochella (1991) also report diffuse €xtra
reflections that effectively double the periodicity in the
=0.5 nm direction, and they suggestthat theseadditional
reflectionsmay representslightly different orientations of
some surface CO, groups. Analogous peaks are not observedin this study. If the additional observedreflections
were causedby the CO, groups, that would imply that
the CO. groups along the rows take two different but alternating orientations with respectto the cleavageplane.
We suggestthat a more plausible explanation of these
reflectionsis simply small domains of ordering of cationic
impurities as describedby Reksten (1990).
Friedbacher et al. (1991) report having imaged the
{0001} plane of commercially available powdered calcite
and ofbiogenic calcite from the seaurchin Strongylocentrotuspurpuratus at atomic resolution. In view of calcite's
perfect rhombohedral cleavageand, more importantly,
the relative rarity of {000 I }, we suspectthat the reported
imagesare in fact of the cleavage{10T4} and not {0001}.
The images presented by Friedbacher et al. (1991) are
generally similar to the images observed in this study.
Examination of the 2DFFT image's peak pattern should
resolve the identity of the plane imaged.
Examination of Figure 4 and Table I suggeststhat o
for R and 0 are proportionally larger for those peaks lying
along c' in Fourier space(c'*) (c, f, and n in Fig. 4). This
corresponds to the periodicity between the alternating
rows of Ca and CO. if the cleavagesurfaceis represented
by a section through the bulk structure. The general
-)
Fig. 5. Best image obtained ofthe calcite cleavageplane. (a)
Unfiltered image, (b) filtered using 2DFFT algorithm to retain
all observedperiodic maxima (13 unique peaks),(c) hard filter
using three lowpassfilters, an algorithm to eliminate image bow,
and a 2DFFT filter to remove noise.
RACHLIN ET AL.: AFM STUDY OF CALCITE CLEAVAGE
909
Fig. 6. A 2DFFT image showing splitting of every other peak. We suggestthat this may be causedby a slightly misaligned
superstructureof some sort.
agreementbetweenthe calculatedand observedunit cells
confirms that the cleavageplane is similar to a section
through the bulk structure and that little reconstruction
takes place. We sr ggestthat the larger o for periodicities
along c'* may be causedby slight random variation in
the inclination of the carbonate groups with respect to
the surface.
Finally, some of the imagesobtained during this study
showed consistent periodic splitting of peaks in Fourier
spaceas shown in Figure 6. Becausenot every peak is
split, we believe that the splitting is not causedby twinning or some sort of dislocation. This splitting is difficult
to interpret. By analogy to single-crystalX-ray crystallographic relations, it appearsto imply a slightly misaligned
superstructureof some sort.
SuNlNrlny AND coNcLUSroN
In this study the AFM has been used to obtain near
atomic resolution of the surface of the calcite cleavage
plane in equilibrium with HrO. The observedsurfacepattern is variable, but examination of the imagesin Fourier
spacedisclosesa consistent pattern ofperiodicities, with
slight variations in the R and d of the peaks from image
to image. Measurement of R and d for peaks in Fourier
space of multiple images allows a mean observed rectangularunit cell of0.74(5) bV 0.a8(2)nm to be derived.
Filtering by means of averagingimages in Fourier space
may allow unit-cell dimensions to be extractedfrom otherwise noisy and unusableimages of periodic surfaces.
A comparison of AFM and LEED resultsfor the calcite
cleavageplane suggeststhat similar surface information
can be obtained with both techniques. For many applications the AFM's relative simplicity of instrumental set-
up and sample preparation will make it the instrument
of choice.
AcxNowr,nncMENTS
The authors thank Digital Instruments for advice on instrumental settings, K. Gona for photographic assistance,and M.F. Hochella, Jr. for
his careful review ofan earlier draft. This study was supportedby a Natural Sciencesand Engineering ResearchCouncil of Canada operating grant
to G.S.H.
RrrnnrNcns crrno
Bancroft, G.M., Brown, J.R., and Fyfe, W.S. (1977a) Calibration studies
for quantitative X-ray photoelectron spectroscopy of ions. Analltical
Chemistry, 49, 1044-1048.
(1977b) Quantitative X-ray photoelectron spectroscopy(ESCA):
StudiesofBa,* sorption on calcite. Chemical Geology, 19, l3l-144.
-(1979)
Advances in, and applications of, X-ray photoelectron
spectroscopy(ESCA) in mineralogy and geochernistry.Chemical Geo l o g y , 2 5 ,2 2 7 - 2 4 3 .
Binnig, G., Quate, C.F., and Gerber, C. (1986) Atomic force microscope
Physical Review L.etters,56, 930-933.
Brown, J.R. (1978) Adsorption ofmetal ions by calcite and iron sulfides:
A quantitative X-ray photoelectron spectroscopystudy. Ph.D. dissertation, University of Western Ontario, I-ondon, Ontario. Canada.
Chessin,H., Hamilton, W.C., and Post, B. (1965) Position and thermal
parametersofoxygen atoms in calcite.Acta Crystallographica,18, 689693.
Drake, 8., and Hellmann, R. (1991) Atomic force microscopy imaging of
the albite (010) surface.American Mineralogist, 76, 1773-1776.
Drake, B., Prater,C.B., Weisenhorn,A.L., Gould, S.A.C.,Allbrecht, T.R.,
Quate,C.F., Connell,D.S., Hansma,H.G., and Hansma,P K. (1989)
Imaging crystals, polyrners, and processes in water with the atomic
forcemicroscope.Science,243, 1586-1589.
Friedbacher,G., Hansma, P.K., Ramli, E., and Stucky, G.D. (1991) Imaging powderswith the atomic force microscope:From biominerals to
commercial materials. Science.253. 1261-1263.
Fulghum, J.E., Bryan, S.R., Linton, R.W., Bauer, C.F., and Griffis, D.p.
(1988) Discrirnination betweenadso4rtion and coprecipitation in aquatic
910
RACHLIN ET AL.: AFM STUDY OF CALCITE CLEAVAGE
particle standardsby surfaceanalysistechniques:Lead distributions in
calcium carbonates.Environmental Scienceand Technology,22,463467.
Hartman,H, Sposito,G., Yang,A, Manne,S.,Gould, S A C, and Hansma, P.K. (1990) Molecular scaleimaging of clay mineral surfaceswith
the atomic force microscope.Clays and Clay Minerals, 38,331-342.
Hochella,M.F., Jr., Eggleston,
C.M., Elings,V.B., and Thompson,M S.
(1990) Atomic structure and morphology of the albite {010} surface:
An atomic-force microscopeand electron diffraction study. American
Mineralogist, 7 5, 723-730
C.M , and Hochella,M.F., Jr. (1991)Imaging
Johnsson,P A., Eggleston,
molecular-scalestructure and microtopography of hematite with the
atomic force microscope.American Mineralogist, 76, 1442-1445.
Kitano, Y., Okumura, M., and Idogaki, M. (1975) Incorporation of sodium, chloride and sulfatewith calcium carbonate GeochemicalJournal. 9. 75-84.
-(1979a)
Influence of borate-boron on crystal form of calcium carbonate GeochemicalJournal, 13, 223-224.
-(1979b)
Behaviour of dissolved silica in parent solution at the
formation ofcalcium carbonate.GeochemicalJournal, 13, 253-260
Meyer, G., and Amer, N.M. (1990) Optical-beam deflectionatomic force
microscopy:The NaCl (001) surface.Applied Physicsktters, 56, 21002tol.
Mucci, A., and Morse,J.W. (1983)The incorporationof Mg'* and Sr'?*
into calcite overgrowths:Influencesof growth rate and solution composition. Geochimica et Cosmochimica Acta, 47, 217-233.
-(1985)
Auger spectroscopydetermination of the surfacemost adsorbedlayer composition on aragonite,calcite,dolomite and magnesite
in syntheticseawater.AmericanJoumal ofScience,285, 306-317.
Mucci, A., Morse,J W, and Kaminsky,M.S (1985)Auger spectroscopy
analysisof magnesiancalcite overgrowlhs precipitated from seawater
and solutions of similar composition. American Joumal of Science,
285,289-305.
Reddy, M M., and Wang, K.K. (1980) Crystallization of calcium carbonate in the presenceof metal ions. Joumal of Crystal Grouth, 50, 470480.
Reeder,R.J. (1983)Carbonates:Mineralogy and chemistry. Mineralogrcal
Societyof America Reviews in Mineralogy, 11, 394 p.
Reksten,K. (1990) Superstructuresin calcite.American Mineralogist, 75,
8 0 7 - 8I 2 .
Sdhnel, O., and Mullin, J (1982) Precipitation of calcium carbonate.
Joumal of Crystal Growth, 60, 239-250.
Stipp, S L., and Hochella,M.F., Jr. (1991)Strucrureand bondingenvironments at the calcite surfaceas observed with X-ray photoelectron
spectroscopy(XPS) and low energyelectron diffraction (LEED). Geochimica et CosmochimicaActa, 55, 1723-17 36
Weisenhorn,A.L., Macdougall,J.E., Gould, S A.C., Cox, S.D., Wise, W.S.,
Massie,J., Maivald, P., Elings, V P., Stucky, G.D., and Hansma, P.K
(l 990) Imaging and manipulating moleculeson a zeolite surfacewith
an atomic forcemicroscope.Science,247,1330-1333.
Wicks, F.J , Kjoller, K., and Henderson,G.S. (1992)Imaging the hydroxvl
surfaceof lizardite at atomic resolution with the atomic force mrcroscope.Canadian Mineralogist, 30, 83-92.
Zachara,I M., Kittrick, J.A., Dake, L S., and Harsh, J B. (1989) Solubilitv
and surfacespectroscopyofzinc precipitateson calcite Geochimica et
CosmochimicaActa. 53. 9-19.
Novevstn 6, l99l
MeNuscnrpr REcEIvED
Mev 18, 1992
M.cNuscmPrACcEPTED