100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH 1. Atomic Force Microscopy (AFM)
Introduction
The atomic force microscope (AFM), also known as scanning force microscope
(SFM) is a very high-resolution type of scanning probe microscopy (SPM), which can
achieve resolution of fractions of a nanometre, more than 1000 times better than the
optical diffraction limit.
Atomic Force Microscope was developed to overcome a basic drawback with Scanning
Tunnelling Microscopy (STM) - that it can only image conducting or semiconducting
surfaces. The former, however, has the advantage of imaging almost any type of
surface, including polymers, ceramics, composites, glass, and even biological samples.
This technique was invented by Binnig, Quate, and Gerber in 1985.
AFM operates by allowing an extremely fine sharp tip to either come in contact or in
very close proximity to the sample that is being imaged. This tip is usually a couple of
microns long and often less than 100Å in diameter. The tip is located at the free end of a
cantilever that is 100 to 200 µm long (see figure 1). The sample is then scanned beneath
the tip. Force between the tip and the sample (either attractive or repulsive) causes the
deflection of the cantilever. These deflections are recorded and processed using imaging
software; the resulting image is a topographical representation of the sample. Moreover,
AFM can measure other properties of the sample (i.e. mechanical properties) that other
forms of microscopy cannot reproduce.
Figure 1. SEM images of a typical cantilever used in
AFM experiments. The inset shows a pyramidal tip at the
end of the cantilever.
Today, most AFMs use a laser beam deflection system where a laser is reflected onto a
position-sensitive detector as represented in figure 2. AFM tips and cantilevers are
microfabricated from Si or Si3N4.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Figure 2. Beam deflection system,
using a laser and photodector to
measure the beam position.
Measuring forces
In AFM, as the name suggests, interactive forces between the sample and the tip are
measured, concretely, interatomic Van der Waals forces. The relation between this force
and distance is shown in Figure 3. The force is not measured directly, but calculated by
measuring the deflection of the lever, and knowing the stiffness of the cantilever.
Hook’s law gives F = -kz, where F is the force, k is the stiffness of the lever, and z is the
distance the lever is bent.
Figure 3. Van der Vaals force versus distance curve.
It is easier to understand this curve considering the tip like a group of atoms interacting
with the surface which is essentially another group of atoms. At the right side of the
curve, the atoms are separated by a large distance. As the atoms are gradually brought
together, they first weakly attract each other. This attraction increases until the atoms
are so close together that their electron clouds begin to repel each other electrostatically.
This electrostatic repulsion progressively weakens the attractive force as the distance
decreases. Following the graph, the force goes to zero when the distance reaches a
couple of angstroms. Anything closer than this, the total Van der Waals force becomes
positive (repulsive). This distance will not change, therefore any more attempt to force
the sample and tip closer will result in deformation or damage either the sample or the
tip. Different scanning modes operate in different regions of this curve: Non–contact in
the attractive region (tip held on the order of tens to hundreds of angstroms from the
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH sample surface), contact mode in the repulsive region (tip-sample distance less than a
few angstroms (10-10 m)) and intermittent or tapping mode fluctuates between the two.
The principles of each mode are:
- Contact Mode: The contact mode where the tip scans the sample in close contact with
the surface is the common mode used in the force microscope. The force on the tip is
repulsive with a mean value of 10-9 N. This force is set by pushing the cantilever against
the sample surface with a piezoelectric positioning element. In contact mode AFM the
deflection of the cantilever is sensed and compared in a DC feedback amplifier to some
desired value of deflection. If the measured deflection is different from the desired value
the feedback amplifier applies a voltage to the piezo to raise or lower the sample
relative to the cantilever to restore the desired value of deflection. The voltage that the
feedback amplifier applies to the piezo is a measure of the height of features on the
sample surface. It is displayed as a function of the lateral position of the sample.
Problems with contact mode are caused by excessive tracking forces applied by the
probe to the sample. The effects can be reduced by minimizing tracking force of the
probe on the sample, but there are practical limits to the magnitude of the force that can
be controlled by the user during operation in ambient environments. An attempt to
avoid this problem is the Non-contact Mode.
- Noncontact mode: belongs to a family of modes which refers to the use of an
oscillating cantilever. A stiff cantilever is oscillated in the attractive regime, meaning
that the tip is quite close to the sample (50 - 150 Angstrom above the sample surface),
but not touching it (hence, “noncontact”). The forces between the tip and sample are
quite low, on the order of pN (10-12 N). The detection scheme is based on measuring
changes to the resonant frequency or amplitude of the cantilever due to its interaction
with the sample. The principal disadvantage is than for highest resolution, it is
necessary to measure force gradients from Van der Waals forces which may extend only
few nanometres from the sample surface, so it should be difficult to obtain high
resolution topographic images with this mode.
- Dynamic Force / Intermittent-contact / “tapping mode” AFM: Tapping mode is a key
advance in AFM. This potent technique allows high resolution topographic imaging of
sample surfaces that are easily damaged, loosely hold to their substrate, or difficult to
image by other AFM techniques. Tapping mode overcomes problems associated with
friction, adhesion, electrostatic forces, and other difficulties commented above by
alternately placing the tip in contact with the surface to provide high resolution and then
lifting the tip off the surface to avoid dragging the tip across the surface. Tapping mode
imaging is implemented in ambient air by oscillating the cantilever assembly at or near
the cantilever's resonant frequency using a piezoelectric crystal. The piezo motion
causes the cantilever to oscillate with a high amplitude (typically greater than 20nm)
when the tip is not in contact with the surface. The oscillating tip is then moved toward
the surface until it begins to lightly touch, or tap the surface. During scanning, the
vertically oscillating tip alternately contacts the surface and lifts off, generally at a
frequency between 50 and 500 kHz. As the oscillating cantilever begins to
intermittently contact the surface, the cantilever oscillation is necessarily reduced due to
energy loss caused by the tip contacting the surface. The reduction in oscillation
amplitude is used to identify and measure surface features.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH During tapping mode operation, the cantilever oscillation amplitude is maintained
constant by a feedback loop. Selection of the optimal oscillation frequency is softwareassisted and the force on the sample is automatically set and maintained at the lowest
possible level. When the tip passes over a bump in the surface, the cantilever has less
distance to oscillate and the amplitude of oscillation decreases. Conversely, when the tip
passes over a depression, the cantilever has more distance to oscillate and the amplitude
increases (approaching the maximum free air amplitude). The oscillation amplitude of
the tip is measured by the detector and input to the controller electronics. The digital
feedback loop then adjusts the tip-sample separation to maintain constant amplitude and
so force on the sample.
Tapping Mode inherently prevents the tip from sticking to the surface and causing
damage during scanning. Unlike contact and non-contact modes, when the tip contacts
the surface, it has sufficient oscillation amplitude to overcome the tip-sample adhesion
forces.
Most AFM modes can work perfectly well in ambient air or even in a liquid
environment. This makes it possible to study biological macromolecules and even living
organisms provided by the employment of fluid cells. It consists of a glass cantilever
holder and silicon o-ring to form an enclosed fluid environment with the ability to
exchange liquids. The latter allows contact mode and tapping mode AFM imaging in
fluid environments. Tapping mode operation in fluid has the same advantages as in the
air or vacuum. However imaging in a fluid medium tends to damp the cantilever's
normal resonant frequency. In this case, the entire fluid cell can be oscillated to drive
the cantilever into oscillation. This is different from the tapping or non-contact
operation in air or vacuum where the cantilever itself is oscillating. When an appropriate
frequency is selected (usually in the range of 5 to 40 kHz), the amplitude of the
cantilever will decrease when the tip begins to tap the sample, similar to Tapping Mode
operation in air. Alternatively, very soft cantilevers should be used to get proper results
in fluid. The spring constant is typically 0.1 N/m compared to the tapping mode in air
where the cantilever may be in the range of 1-100 N/m.
Description of the Lab
Objectives
The lab introduces atomic force microscopy (AFM) and provides a general overview of
its applications in crystallography and crystallization. The lab will encompass both
theoretical and practical aspects of handling and possible applications of AFM
depending on the individual interest of students.
At the end of the course, the students will acquire a basic knowledge on how to run an
AFM emphasizing on sample preparation, probes manipulation, data
acquisition/electronics, modes of operation and practical applications.
Procedure of the Lab
The lab encompasses a first block dedicated to a theoretical introduction of the
technique including a wide explanation of the software that controls the AFM system.
In this part, basic concepts related to atomic force microscopy as sample and tip
preparation, data acquisition, modes of operation and images treatment will be revised.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH In the second block, before starting with the experimental section, a calibration
measurement will be performed. With this aim, a standard sample will be used in order
to check piezoscanner movements in XYZ directions. Afterward, the surface of
different solid samples will be studied in air environment. The images obtained will be
treated using the software which controls the AFM system.
Finally, it will be carried out an experiment in liquid environment employing a fluid
cell. Gypsum samples will be analyzed in order to study the in-situ gypsum dissolution
in water solutions.
At the end of the course, a report with the obtained results will be presented following
the next scheme: i) introduction; ii) experimental details, iii) results and discussion and,
iv) conclusions.
Final report
At the end of the course, a detailed description of the results will be presented as a
report following the next scheme:
i)
introduction
ii)
experimental details
iii)
results
iv)
conclusions
v)
references and/or bibliography
Recommended Books and WebPages:
1) Wiesendanger, R. Scanning probe microscopy and spectroscopy: methods and
applications. Cambridge University Press. 1994.
2) http://www.chembio.uoguelph.ca/educmat/chm729/afm/firstpag.htm
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH 2. In situ observation of crystal growth with Laser confocal
differential interference contrast microscopy (LCM-DIM)
Setup
Laser confocal differential interference contrast microscopy (hereafter referred to as
LCM-DIM) is a technique developed by Sazaki and co-workers for noninvasive in situ
observation of crystal growth [1]. Figure 1.1 shows a schematic drawing of a typical
LCM-DIM setup which consists in a confocal system (FV300, Olympus Optical Co.
Ltd.) attached to an inverted optical microscope (IX71, Olympus Optical Co. Ltd.), and
a Nomarski prism (UDICTHC: large shear length type) inserted into the optical path to
utilize differential interference contrast (DIC). In order to obtain a sufficient DIC
effect, an analyzer is inserted in front of the photomultiplier such that the orientation of
the analyzer and the polarized laser light are perpendicular.
The strength of this
experimental configuration resides in the combination of the main advantages of two,
already well known, microscopy techniques; laser confocal microscopy (LCM)
providing high resolution, and differential interference contrast microscopy (DICM)
providing excellent contrast. In this optical microscope illumination is provided by a
SLD light source with a wave length of 680 nm and images of growing crystal surfaces
can be obtained with different high resolution objective lenses (10x, 20x, 40x, 60x).
Next, the main parts of this experimental setup will be explained in detail.
Figure 1.1 Schematic drawing of optical components integrated in the experimental
setup of a LCM–DIM system.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Laser confocal microscopy
A modern laser scanning confocal microscope incorporates two basic principles: point
by point illumination of the sample and rejection of out of focus light. Confocal imaging
relies upon the sequential collection of light from spatially filtered individual specimen
points, followed by electronic signal processing and the visual display as corresponding
image points. In this way images are taken point by point and then reconstructed via
computer to the 2D image plane one pixel at a time rather than projecting it through an
eyepiece. The key feature of confocal microscopy is its ability to produce blur-free
images providing a significant improvement in lateral resolution. In the LCM-DIM
setup a reflection type laser confocal microscope is integrated (Figure 1.1).
Image generation
The generation of a 2D image from the focal plane (i.e. object plane) of a confocal
microscope is essentially comprised of three process steps:
§
Line by line scanning of the specimen with a focused laser beam deflected
in the X and Y directions by means of two galvanometric mirrors or .
§
Pixel by pixel detection of the reflected light from the scanned specimen
with a photosensitive detector (e.g. photomultiplier tube, PMT).
§
Digitization of the object information contained in the electrical signal
provided by the PMT, i.e. image data is displayed, pixel by pixel, from a
digital matrix memory to a monitor screen.
Confocal beam path
The term “confocal” refers to the condition where two lenses are arranged to focus on
the same point. The major optical difference between a conventional microscope and a
confocal microscope is the presence of the confocal pinhole. The pinhole allows only
light from the plane of focus to reach the detector (Figure 2.2). The confocal principle is
combined with a scanning system utilizing a laser source to scan a point of laser light
across the sample in both X and Y directions.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Figure 2.2 A schematic representation of beam paths in a confocal microscope. A
microscope objective is used to focus a laser beam onto the specimen. The reflected
light is collected by the objective and efficiently directed onto the detector via a dichroic
beam splitter. The pinhole is arranged in front of the detector, on a plane conjugate to
the focal plane of the objective. Light coming from planes above or below the focal
plane is out of focus (green lines), and most of it will not pass the pinhole and therefore
does not contribute to forming the image.
The light path of a typical confocal microscope is shown in Figure 2.2. Coherent light
emitted by the laser system is first expanded and reflected by a dichromatic mirror to
completely fill the objective rear aperture (a critical requirement in confocal
microscopy). The light beam is then focused by the lens system to a very small spot and
scanned across the specimen (X-Y plane) in a defined focal plane. Reflected light
coming from points on the specimen, in the same focal plane, pass back through the
dichromatic mirror and are focused, as a confocal point, on the detector pinhole
aperture. A significant amount of reflected light that comes from points above and
below the objective focal plane are not “confocal” with the pinhole (i.e. out of focus
light rays) and will not pass through the pinhole aperture. This extraneous light is not
detected by the photosensitive detector and will not contribute to the resulting image.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH The filtering of out of focus light leads to a sharper image compared to conventional
microscopy techniques.
Confocal Pinhole
One of the most important components of the scanning unit is the pinhole aperture,
which acts as a spatial filter at the conjugate image plane positioned directly in front of
the photosensitive detector and will determine the sharpness of the image. The pinhole
diameter is variable (ideally infinitely small) and the confocal microscope can be
understood as an inherently depth discriminating optical system. By varying the pinhole
diameter the degree of confocality can be adapted to practical requirements. With the
aperture fully open, the image is nonconfocal (or completely visible) and will act as a
conventional widefield microscope. In addition the pinhole suppresses also stray light,
which helps to improve image contrast.
Scanning unit
The scan unit is responsible for rasterizing the emitted laser light, as well as collecting
the reflected light from the sample surface that is required to assemble the final image.
The classification of confocal microscope designs is usually done on the basis of the
method by which the specimens are scanned. In the case of LSCM a single-beam
scanning method is used. The scanning of the beam is achieved by the use of computer
controlled mirrors driven by galvanometers. One of the mirrors moves the beam from
left to right along the lateral X axis, while the other translates the beam in the Y
direction. After each single scan along the X axis, the beam is rapidly transported back
to the starting point and shifted along the Y axis to begin a new scan in a process termed
flyback. During the flyback operation no image information is collected. The speed of
the confocal microscope is limited by the rate at which the mirrors can scan the entire
sample plane.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Differential interference contrast microscopy
Reflected DICM is one of the most common techniques used to enhance the contrast
of opaque specimens. Slopes, valleys, and other discontinuities on the surface of the
specimen create optical path differences, which are transformed by reflected light DIC
microscopy into amplitude or intensity variations that reveal the topographic profile.
The image created in reflected light DIC can often be interpreted as a true three
dimensional representation of the surface geometry, provided a clear distinction can be
made between raised and lowered regions in the specimen. However, this technique is
not suitable for accurate measurements of physical heights and depths.
DICM is a beam shearing interference system in which the reference beam is sheared
by a minuscule amount. This technique produces a monochromatic shadow cast image
which effectively displays the gradient of optical paths for both high and low spatial
frequencies present in the specimen. The regions of the specimen where the optical
paths increase along a reference direction appear brighter (or darker), while regions
where path differences decrease appears in reverse contrast. Pixel intensity is
proportional to the local optical path gradient and thus, when the gradient grows steeper
image contrast will be dramatically increased.
The light path and optical components of a DIC microscope
In Figure 2.1 the key optical train components forming part of the reflected light
differential interference contrast microscope integrated in the LCM-DIM are shown.
Linearly polarized light (East-West direction) exiting the laser is reflected from the
surface of a 20/80 mirror placed at a 45 degree angle to the incident beam. The
reflected light waves are deflected by an optical pass selector and are now travelling
along the optical axis of the inverted microscope. The light waves enter a Nomarski
prism (Figure 2.3a), housed below the objective, and are separated into two polarized
orthogonal components and sheared according to the geometry of the birefringent prism
(Figure 2.3b). Acting in the capacity of a high numerical aperture, perfectly aligned,
and optically corrected illumination condenser, the microscope objective focuses the
sheared orthogonal wave fronts, produced by the Nomarski prism, onto the surface of a
reflecting specimen. The two beams travel parallel and extremely close to each other
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH with a slight path difference. However, they are vibrating perpendicular to each other
and therefore are unable to cause interference. The distance between the rays, called the
shear, is so minute that it is less than the resolving ability of the objective.
Reflection of the incoming light beams is produced at the crystal-solution interface
because of the difference in refractive index. Reflected wave fronts, which experience
varying optical path differences as a function of specimen surface topography, are
gathered by the objective and focused on the interference plane of the Nomarski prism.
When entering the prism they are recombined, eliminating shear and the original path
difference between the beam pairs, and will generate elliptically polarized light. Upon
exiting the Nomarski prism the elliptical wave fronts are deflected by the OPS and enter
the confocal unit where they pass through a 20/80 mirror on a straight trajectory and
finally encounter, in front of the photomultiplier, an analyzer positioned with the
transmission axis oriented in a North-South direction. Components of the elliptical
wave fronts that are parallel to the analyzer transmission vector are able to pass through
in a common azimuth, in contrast to linearly polarized light, and subsequently undergo
interference in the plane of the photomultiplier to generate amplitude fluctuations and
form the DIC image.
Figure 2.3 (a) Schematically representation of a typical light path in a reflection DIC
microscope. (b) Schematic drawing of a Nomarski prism used in DIC microscopy.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Nomarski prism
The Nomarski prism employed in reflected light DIC microscopy is composed of two
precisely ground and polished wedge-shaped slabs of optical quartz that are identical in
shape, but have differing orientations of the optical axes (Figure 2.3b). The axis of one
wedge is parallel to the flat surface, while the axis of the other wedge is oriented
obliquely. The Nomarski prism interference plane is positioned at a remote location in
space, outside the prism itself. Incident linearly-polarized light waves (parallel to the
optical axis of the microscope) that enter a Nomarski prism are divided into two
mutually perpendicular (orthogonal) components, termed the ordinary and extraordinary
wave, which have identical amplitudes (70.7 percent of the original polarized wave) and
are coherent (provided, of course, that the illumination source is coherent). In order to
produce orthogonal components having equal amplitudes, the linearly polarized light
entering a Nomarski prism is oriented with the direction of the electric vector at a 45degree angle with respect to the principal optical axis in the upper wedge of the prism.
The wedge having an oblique optical axis produces wave front shear at the quartz air
interface, and is responsible for defining the shear axis.
The Nomarski prism (Figure 2.3b) not only separates linearly polarized light into two
orthogonal components, it also produces a relative phase shift (often termed an optical
path difference) in each wave front relative to the other. The degree of phase shift
between the wave fronts varies linearly with the location of the input light beam in
relation to the shear direction. In the LCM-DIM setup, the prism can be laterally
translated along the optical axis of the microscope in the shear direction (a process
known as introduction of bias retardation) to enable adjustment of the optical path
difference introduced between the orthogonal wave components. In this manner, finetuning of the relative intensity in the image can be manipulated to produce the
distinctive shadow cast appearance typically produced by DIC microscopy. Images
appear as if they were illuminated from a highly oblique light source originated from a
single azimuth. A clear example is shown in Figure 2.4.
Once the wave fronts exit the prism, they enter the objective lens system (acting as a
condenser) from the rear, and are focused into a parallel trajectory before being
projected onto the specimen. Reflection of the orthogonal wave fronts from a
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH horizontal, opaque specimen returns them to the objective, but on the opposite side of
the front lens and at an equal distance from the optical axis. The waves gathered by the
objective are focused on the Nomarski prism interference plane (again on the opposite
side from their journey down, see Figure 2.3a), which results in a phase shift that
exactly offsets the original difference produced before the waves entered the objective.
The positional exchange of incident and reflected waves results in cancellation of
relative phase shifts across the entire microscope aperture. A system of this type is
referred to as being self compensating, and the produced image has a uniform intensity.
Figure 2.4 Orientation specific imaging of a cuboid in DIC.
In reflection DIC microscopy only a single birefringent Nomarski prism is required
and the objective serves as both condenser and image forming optical system. As
shown in Figure 2.1, in the LCM-DIM setup there is only an analyzer, and no polarizer,
because laser light is already linearly polarized in a certain direction. The correct
aligned of the laser polarization direction and direction of the analyzer (90º) is crucial in
the setup of the LCM-DIM. Input waves also have to be parallel (or nearly so) to the
optical axis. A poorly collimated input beam will result in nonuniform compensation
across the prism (and the resulting image), destroying the unique phase relationship
between orthogonal components at each image point.
The image
The image is generated from two identical bright field images being overlaid slightly
offset from each other. The subsequent interference, due to phase difference, converts
changes in phase (and so optical path length) to a visible change in darkness. This
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH interference may be either constructive or destructive giving rise to the characteristic
appearance of three dimensions.
Because of this characteristic the image has the
appearance of a three dimensional object under very oblique illumination, causing
strong light and dark shadows on the corresponding faces (Figure 2.4). The direction of
apparent illumination is defined by the orientation of the Nomarski prism. The sheared
orthogonal wave front components are separated by only fractions of a micrometer
(usually between 0.15 and 0.6 µm), which is less than the resolution of the used
objectives. To the observer, it is not apparent that the resulting image visualized in the
eyepieces is composed of these two superimposed components because their separation
is too minute to be resolved by the microscope. Surface features become distinguishable
because shadow directions are reversed for specimen details that posses either a higher
or lower topographical profile than the surrounding surface.
Orientation Effects on Reflected Light DIC Images
Since reflected light DIC images are inherently bestowed with a pronounced azimuthal
effect, many reflecting specimens imaged in differential interference contrast have a
prerequisite orientation limitation in order to achieve maximum contrast (either parallel
or perpendicular to the shear axis) that restricts freedom of specimen rotation. By
rotating the specimen with respect to the shear axis, the contrast effects for selected
specimen features can be maximized or minimized.
SLD light source
A super luminescent diode (Amonics 680nm SLD) is used as light source to illuminate
the crystal surface.
A super luminescent diode (SLD) is an edge-emitting
semiconductor light source that combines high power and brightness of laser diodes
with low coherence of Edge Emitting Light Emitting Diode (ELED). The main
advantage of this illumination system is the short coherence length, typically less than
10µm. This short coherence length ensures that all unnecessary interference will be
eliminated from the light path and only relevant information from the crystal surface
will reach the photomultiplier (PMT). The SLD source is connected to the confocal unit
of the experimental setup with a fiber optic coupler followed by a beam expander that
enables the thin laser beam wrist to completely fill the objective rear aperture. Expanded
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH laser light that passes through the microscope objective forms an intense diffraction
limited spot which is scanned by the coupled galvanometer mirrors in a raster specimen
plane.
Objective lenses
An overview of lenses that can be used with the LCM-DIM setup are listed in Table
2.1. Low magnification lenses (4x and 10x) are used for locating crystals inside of an
observation cell and high magnification lenses (20x and 40x) are used for observing in
situ crystal growth processes on a crystal surface.
Table 2.1 Summary of the most relevant characteristic of the objective lenses used for
LCM-DIM observations.
Type
Magnif
cation
UPlanFL
UPlanFL
LUCPlan FL
LUCPlan FL
PlanApo
4x
10x
20x
40x
60x
Numerical
Aperture
0.13 P
0.30 P
0.45 P
0.60
1.45
Working distance
(mm)
13.0
3.1
6.9
3.4
0.15
Lateral resolution
(mm)
3.2
1.4
0.92
0.68
0.28
Company
Olympus
Olympus
Olympus
Olympus
Olympus
U: Universal lens type; Plan: “plain” lens, aberration for different wavelengths is corrected (color
aberration); Fl: lens for Fluorescent light; P: lens for Polarized light.
In Figure 2.5 a typical high magnification objective lens is shown. High magnification
objectives are prone to aberration artefacts due to variations in cover glass thickness and
dispersion. Most objectives are designed to be used with a cover glass that has a
standard thickness of 0.17 millimetres and a refractive index of 1.515, which is
satisfactory when the objective numerical aperture is 0.4 or less. However, when using
high numerical aperture dry objectives (numerical aperture of 0.8 or greater), variations
of only a few micrometers of the cover glass thickness result in dramatic image
degradation due to aberration, which gets worse with increasing cover glass thickness.
In order to compensate for this error the objectives are equipped with a correction collar
that allows adjustment of the central lens group position to coincide with fluctuations of
the cover glass thickness. The correction collar is the key feature of these lenses and is
very important for obtaining sharp images with a good contrast. In the LCM-DIM setup
the correction collar was mainly used for precisely focusing the focal plan on the
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH crystal-solution interface. The correct use of a correction collar requires a considerable
amount of practice and careful attention.
Figure 2.5 Front view and transversal section of a typical high performance Confocal
Microscope Objective.
The maximum obtainable resolution with these lenses (see table 2.1) can be calculated
from Abbe´s formula,
d " 0.61
!
!
= 0.61
NA
n(sin µ )
(2.1)
where d is the minimum distance separating two objects, λ is the wavelength of the light
source, NA the numerical aperture, n the index of refraction and µ one half of the
angular aperture of the lens. Abbe’s theory describes the interaction of the parameters
that can be modified to improve lateral resolution, including decreasing the wavelength
of the incident light, increasing the refractive index of the specimen medium or
increasing the numerical aperture of the optical system.
Image acquisition
The Fluoview program, the standard tool for image acquisition of confocal
microscopes of Olympus, is used for capturing photomicrographs of 1024x1024 pixels.
Acquisition time for each image is 9.6 s, and can be recorded at 10 to 300 sec intervals
depending on the experimental requirements.
Temperature control
The observation cell is placed on a temperature controlled stage. In this way the
temperature of the solution inside the growth cell can be adjusted in the range of 10.0–
35.0ºC. Peltier elements are used for heating and cooling. For the calibration of the
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH system, a test cell with a thermocouple inside is implemented to measure the
temperature at the position of the seed crystals. The obtained calibration curve is used
to calculate the temperature inside the cell for each experimental condition. The room
temperature is kept constant during the experiment to improve the accuracy of the
temperature controlled stage.
Figure 2.6 Photograph of the Laser Confocal Differential interference contrast
microscope.
Observation cell
One type of observation cell is made out of two glass plates (0.17 mm thickness) and
polystyrene spacers of 1.0 mm thickness: all of these parts are glued together by silicone
adhesive (see Figure 2.10). Before introducing the seed crystal and after solidification
of the adhesive, the cell was carefully washed by ultrasonic cleaning with pure (MilliQ) water. Once the seed crystals are introduced in the cell the top cover glass is fixed
and sealed with silicone adhesive to avoid evaporation. Growth cells sealed in such a
way provided stable conditions for several weeks, and sometimes even months.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH A second type of observation cell is available made out of two sandwiched glass plates
of 0.17 mm thickness separated by a 3mm thick Teflon spacer fixed to each glass plate
with high vacuum silicon grease (Figure 1c).
Figure 2.10 Materials necessary for the preparation of an observation cell.
The arrow in Figure 2.11a indicates the crystal–solution interface on which surface
microtopography is observed by the LCM–DIM system. The observed crystal surface
has to be completely parallel to the bottom glass plate and perpendicular to the
incoming laser beam. All observation cells are handmade which allows a great
flexibility in the design as a function of the specific requirements of each experiment.
For example, the volume of the cell can be significantly reduced if only a small amount
of samples is available. This design also allowed the use of needles coupled to a
peristaltic pump so that the solution inside the observation cell can be easily changed.
[1] Sazaki G., Matsui T., Tsukamoto K., Usami N., Ujihara T., Fujiwara K.,
Nakajima K. J. Cryst. Growth 2004, 262, 536-542.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Protocol of a typical crystal growth experiment
Solution preparation
Protein example
Seikagaku lysozyme is dissolved in a 50mM Na-acetate buffer (pH 4.5) and
dialyzed against the same buffer at 4ºC to remove the excess salts present in commercial
lysozyme. The solution is filtered (0.2µm) and the lysozyme concentration is
determined by measuring the absorbance at 280 nm using an extinction coefficient of
2.65 ml/mg cm. Stock solutions of approximately 180mg/ml are stored at 4ºC for
further usage, also stock solution of 200 mg/ml NaCl are prepared in a 50mM Naacetate buffer (pH 4.5) and filtered (0.2µm).
Inorganic example
Supersaturated CaSO4 solutions are prepared by dissolving reagent grade
Na2SO4 in two times distilled water and CaCl2 in two times distilled water. The pH of
the stock solutions should be adjusted to pH 7.0 by adding small amounts of NaOH or
HCl. Solutions are filtered (0.2 µm) before usage.
4 g/l(solution)
CaSO
Solubility curve:
10
Lysozyme solubility
30 mg/ml NaCl
40 mg/ml NaCl
50 mg/ml NaCl
70 mg/ml NaCl
2,1
2,0
1,9
5
1,8
1,7
1,6
0
0
5
10
15
Temperature
20
25
0
20
40
60
Temperature (ºC)
80
100
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Seed crystals
Protein example
The batch crystallization method is used to grown tetragonal crystals of the
model protein hen egg-white lysozyme at 20.0 ± 0.1°C from a solution containing 70
mg/ml Seikagaku lysozyme, 25 mg/ml NaCl and 50 mM sodium acetate (pH 4.5)
buffer. Volumes of 200 µl crystallization solution are stored in 250 µl Eppendorf
containers. At these solution conditions approximately 50 to 100 crystals are obtained
after 2 -3 days.
A schematic overview is given of the transfer of crystals from an eppendorf
container to an observation cell. Once crystals reach a desirable size an eppendorf tube
containing crystals is filled until the rim with a “washing solution”, this is a slightly
supersaturated solution (20 mg/ml lysozyme, 25 mg/ml NaCl and 50 mM sodium
acetate (pH 4.5)). Crystals are detached from the eppendorf walls by locally increasing
the temperature, and thus increasing solubility, by using the fingertips. After a desirable
amount of crystals are detached, the eppendorf container is turned around and detached
crystals sediment to the air-solution interface. This interface is brought into contact with
a drop of washing solution placed on a siliconized cover slip. This way, crystals gently
pass from the eppendorf tube to the drop. When enough crystals are inside the drop a
pipet is used to transfer “optically perfect” crystals to drops with washing solution.
Finally a few (4-5) crystals are placed, with the help of a pipet, on the bottom glass plate
of the observation cell were a drop of slightly supersaturated solution is present. When
necessary, crystals can be orientated properly by using a pipet. Finally, the observation
cell is sealed off with a top cover slip and made air tight using silicon glue.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Schematic representation of the transfer process of crystals from an eppendorf
container to an observation cell.
After the transfer of the crystals, the observation is sealed and stored at 20ºC.
After 24 h crystals are fixed to the bottom glass plate and the solution inside the
observation cell can be changed with a freshly prepared solution of desired
concentration before starting an experiment.
Inorganic example
Gypsum growth is best observed on {010} faces of fragments cleaved from
natural, very transparent, natural gypsum crystals. The fragments are handled with
tweezers to avoid surface contamination and can be cleaned with reagent grade ethanol.
Samples are fixed onto a cover-glass (0.17 mm) using high vacuum silicone grease.
Image acquisition and analyses
Images, 1024x1024 pixels, are captured by the Fluoview program of the
Olympus confocal microscope. The image acquisition is typically time-lapsed in the
order of 10–300 s, depending on the supersaturation and the growth velocity. Image J
and AVI2JPG, freeware programs, are used for data analysis of the obtained images.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH In situ observation of crystal growth with LCM-DIM
A. Preparation of an observation cell with a seed crystal
The first step in performing an experiment of in situ observation of crystal
growth with LCM-DIM is the preparation of an observation cell as described
above and the selection of a seed crystal. In this laboratory practice the
student can choose between using protein crystals or inorganic crystals. In
both cases seed crystals are necessary.
Protein crystals: set up a couple of batch crystallization experiments as
described above to obtain seed crystals.
Inorganic crystals: set up crystallization experiments or use a piece of
natural gypsum crystal by cleaving a small piece of the large gypsum
sample available in the laboratory.
Note 1: Students can study their own crystals if they like to!
B. Determination of experimental conditions
Before starting the observation the experimental conditions (T, solubility,
[C], additives, etc…) should be chosen. First of all the solubility should be
studied from literature, if no previous data are available the first task
during the in situ observation should be to determine the solubility at
different temperatures or precipitant concentrations.
If the solubility is know, the growth solution should be prepared as function
of supersaturation. A good approach is to start observation at low
supersaturation. If the solubility is dependent on temperature, temperature
can be used to alter the supersaturation during the experiment. If the
solubility is independent on temperature then the concentration of the
solute, pH or additive concentration should be changed.
C. Determination of solubility as a function of solute Conc./T
This should be done when the solubility is not known. A protocol on how to
measure solubility with LCM-DIM can be found in following reference:
Journal of Crystal Growth, 311, 2009, 3479-3484.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH D. Observation of growth mechanism as a function of supersaturation
As a general rule it is accepted that the dominant growth mechanism will
change with supersaturation. This should be tested by observing the crystal
surface at three different supersaturations: low, middle and high
superstation levels.
E. Measuring growth kinetics (I): step velocities
Step dynamics can be studied in situ by LCM-DIM. If we want to study the
growth kinetics of our crystal, we should measure the step velocity as
function of supersaturation. Important is that we know the exact
supersaturation for each measurement. Hence, we need to know the
concentration of our solute, precipitant (when present) and temperature. (or
any other component present in the solution that has an effect on the
solubility).
Step
velocities
should
be
measured
at
four
different
supersaturations.
F. Measuring growth kinetics (II): 2D nucleation rate
If the crystal face grows by 2D nucleation than the 2D nucleation rate can
be measured as a function of supersaturation.
G. Analysis of the obtained data
Once finished the in situ observations, the obtained data should be analyzed
and step velocities and 2D nucleation rates should be represented as a
function of supersaturation. From this type of graphics it is possible to
determine the step kinetic coefficient and/or the step free energy.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Questionnaire
Question 1: Why is the observation of single steps on a protein surface
easier then on the surface of inorganic crystals?
______________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Question
2:
What
is
the
dominant
growth
mechanism
at
low
supersaturation and at high supersaturation?
______________________________________________________________________
_____________________________________________________________________
____________________________________________________________________
Question 3: How can the step kinetic coefficient and the step (ledge) free
energy be determined from in situ observation with LCM-DIM?
______________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Question 4: Which growth mechanism cannot be observed by LCM-DIM?
(explain why)
______________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
Question 5: Give an example of what type of surface process you would
observe using AFM and another example where you would use LCM-DIM,
pointing out the advantages of both methods?
______________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
______________________________________________________________________
_____________________________________________________________________
_____________________________________________________________________
______________________________________________________________________
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH 3. Mach‐Zehnder Phase Shift Interferometry applied to Mass
Transport Characterization in Crystallisation Solutions
OBJECTIVE
Provide students with a basic background upon Mach-Zehnder Phase Shift
Interferometry, including the technique principles, instrument description, data
processing for estimation of concentration maps in solutions.
Students will perform an experiment with an evaporating microdrop slightly
undersaturaded with NaCl, in order to follow mass transport during nucleation and
growth of a NaCl crystal.
INTRODUCTION
Mach-Zehnder Interferometry (MZI) is a technique extensively used in fields as diverse
as Optical Communications, Fluid Science, Heat and Mass Transport, Digital
Holographic Microscopy, Microgravity Research. This document deals with MZI in a
refraction index mapping application.
Let’s describe MZI principle: A laser beam is divided in the reference and the sample
(test) beams by means of a beamsplitter. The sample beam propagates through the
experimental volume before being recombined with the reference beam. The result of
the recombination is the generation of interference fringes (Interferogram) at imaging
plane. The interferogram carry the information of the variation of the optical path
between the object and the reference beam. A schematic view of a Mach-Zehnder
interferometer is shown in figure 1.
Fig. 3.1 Mach-Zehnder Interferometer setup
The intensity fringes resulting from the interference between the reference beam and the
object beam is expressed as:
! !, ! = !! 1 + ! !, ! !"# ! !, !
(1.1)
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Where I0 is the sum of the reference and sample beam intensities, γ is the fringe
modulation and x,y are spatial coordinates. Fringe modulation is proportional to the
ratio between the reference and sample intensities, according to: ! ∝ 2 !
!!!!
!! !!
, but depends
also on the illumination beam coherence.
Ψ(x,y) is the integration of the phase difference between the reference and sample
beams along the optical path z:
! !, ! =
2!
!
!!
!!
! !, !, ! − !! !"
(1.2)
Where λ is the illumination wavelength, z2-z1 is the sample volume thickness along the
laser propagation path, n(x,y,z) is the local refractive index inside the sample volume
and nr is a reference refraction index.
Phase Shifting Interferometry
Phase cannot be directly extracted from a single interferogram (Eq. 1.1). Phase shifting
interferometry (PSI) allows extracting the real phase for each pixel of the image. It
consists in acquiring a minimum of 3 phase-shifted images of the same fluid status and
in calculating the phase of each pixel with a phase shifting algorithm. The method
consists in introducing in the reference beam a small (controlled) phase delay between
the recorded images. The intensity distribution on the acquired images (j is the number
of the image) is given by:
!! !, ! = !! 1 + ! !, ! !"# ! !, ! + !" !, !
(1.3)
Generally, the phase step is calibrated to be α = π/2 in such way that the set of images
can be seen as a set of equations to be solved easily. Several methods are possible to
introduce the phase shift. Phase shifting can be performed mechanically, by modulation
of reference arm refraction index or by changes on illumination wavelength.
The most familiar method consists in introducing an optical path modification in the
reference arm by displacing a mirror. This mirror is either mounted on a piezoelectric
transducer (PZT) or on a stepper motor. IN refraction index modulation methods, the
delay is introduced by means of liquid-crystal variable retarders (LCVR) and pockels
cells. Such approaches provide satisfactory performances, but have some drawbacks; cost and time constants- that might limit its use depending on the application
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH An alternative way to achieve the phase shift is introducing very slight changes in the
illumination wavelength. No moving parts or additional optical elements are then
necessary for introducing the phase shift in this case.
Lec’s mach-zehnder interferometer
In our laboratory, we have developed a Phase-Shift Mach-Zehnder Interferometer based
on wavelength modulation. Figure 3.2 shows a schematic view of our instrument.
The interferometer follows an unbalanced Mach-Zehnder configuration. Indeed, the
reference arm is longer than the sample arm, in an amount of 2U. This unbalance allows
reducing the bias current range necessary to scan the phase shift range, as further
explained in section 3. The laser diode temperature and bias current is controlled with a
composite driver. Emitted light pass first through a Faraday isolator, so as to avoid any
back-reflection toward the semiconductor laser cavity. A movable short focal length
lens L1 and a rotating ground glass diffuser allow tuning the spatial coherence of the
beam. L2 is a collimating lens. A half-wave plate is placed before a polarizing beam
splitter PBS, the plate can be manually rotated in order to equilibrate the laser intensity
between the interferometer arms. The sample beam is transmitted by the PBS whereas
the reference beam is reflected and follows the reference path through the mirrors M1
and M2. As the reference and sample beams polarizations are orthogonal, another halfwave plate is placed on the reference beam path. Both beams are recombined by a nonpolarizing beam splitter NPBS. Imaging of the sample and the interference is performed
by a long working distance microscope and a CCD camera. The whole system is
controlled and automated through a PC running Labview based scripts, developed adhoc for the instrument.
For the unbalanced interferometer setup, the set of equations 1.3 is defined as follows:
!! !, ! = !! + !Δ! 1 + ! !, ! !"# ! + Δ!!
(1.4)
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Where:
! + Δ!! ≅
2!
!
2! + Δ! !, !
−!
Δ!
2! + Δ! !, !
!
(1.5)
Where ΔS(x,y) is the contribution of the simple to the phase between the reference and
the simple arm.
In practice, the interferometer unbalance is several orders of magnitude greater than
variations in the optical path along the sample volume. The assumption ΔS(x,y)<<2U is
therefore valid. Set (1.5) can be rewritten:
!! !, ! = !! + !Δ!
1
+ ! !, ! !"#
2!
2! + Δ! !, !
!
−!
2πΔ!
2! !!
(1.6)
The phase step is then:
!! = !
2πΔ!
2!
!!
(1.7)
!"
!"
!"
Δ! = !Δ! with ! =
!"
Δ! = !Δ! with ! =
(1.8)
(1.9)
Where i is the laser bias current , C and D stand for the linear dependencies of the Laser
Diode Wavelength and Intensity on the bias current. Equation (1.7) illustrates the
versatility of the unbalanced setup and wavelength tunability. Indeed, adjusting
unbalance U, -which varies within a tens of cm range-, allows limiting the current
variation necessary to scan the phase shift within a 0-2π range. This advantage is nonnegligible as the current scan range should be as small as necessary to avoid undesirable
laser mode hopes.
Therefore, for N phase steps and a scan from 0-2π, the current step and unbalance are
fixed according to:
!Δ! < !!" , !!" > 2! ≫ !
!!
!!!
(1.10)
Where εMH and is the laser diode current range between consecutive mode hopes and
LLD is the laser diode coherence length. Optionally, Intensity variation could be
minimized according to the third inequality (in red).
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH Phase calculation algorithm
Accounting for power variations
Varying laser bias currents leads unavoidably to laser intensity variations (Eq. 1.9). It is
reasonable to minimise these variations, to an extent high enough to ignore them (Eq.
1.10) or kept them small so as to preserve the common background and noise
cancellation advantages of PSI.
When intensity variations cannot be ignored i.e. the third inequality in Eq. 1.10 is not
fulfilled, there are two ways to proceed: One is correcting acquired images Ij intensity
according to:
!!"##,! = !!
!!
(1.11)
!! + !!Δ!
DΔi can be measured for each set of phase-shifted images with the laser diode internal
photodiode.
The second one is using an algorithm that takes into account intensity variations.
Hariharan algorithm
For phase estimation purposes N can be varied from 3 to infinity. However, for only 3
images, there is not explicit feedback concerning the phase-step calibration. There’s a
multiplicity of algorithms, but Hariharan’s algoritms (N=5) is one of the most used, as it
provides a minimised phase error for a phase step of π/2. Phase map, fringe modulation
and phase step can be estimated from the set of 5 phase-shifted interferograms:
! !, ! = !"!#
γ !, ! =
3
cos ! !, !
2 !2 !, ! − !4 !, !
2!3 !, ! −!1 !, ! −!5 !, !
!! − !! ! + !! +!! −2!!
2 !! +!! +2!! +!! +!!
=
!! !, ! − !! !, !
!! !, ! − !! !, !
!
(1.12)
(1.13)
(1.14)
Phase unwrapping
The phase map is obtained by means of an expression involving the arctangent function
(Eq. 1.12). This mathematical function returns values that are known between the limits
π and ‐π. Hence the result is given modulo 2π and discontinuities with values near to 2π
appear in the phase distribution. Unwrapping is the procedure by which these
discontinuities are resolved; the result is converted into the desired continuous phase
function.
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH In the LEC laboratory setup, phase is unwrapped according to the algorithm PUMA,
developed by Bioucas-Dias and coworkers from the Instituto de Telecomunicações,
Lisboa.
From phase to Concentration maps
When working with a time series experiment with assumed known starting conditions, it
is possible to either subtract a starting reference plane fit or the first acquired phase
image to all subsequent phase images in the series, hence, the phase variation is given:
Δ! !, !, ! =
2!
!
!
!
Δ! !, !, !, ! !" − ! !, !, !!
(1.15)
Where W is the sample volume thickness. The average index variation along the
observation axis (z) is:
Δ! !, !, !, ! =
!
Δ! !, !, !
2!"
(1.16)
From equation Eq. 1.16 and a known refraction index concentration coefficient
Δ!
Δ! obtained
from calibration, the concentration map variations Δ! !, !, !, ! time
series can be obtained:
Δ! !, !, !, ! =
!
Δ! !, !, !
Δ!
2!"
Δ!
(1.17)
100386: IN SITU CHARACTERIZATION OF CRYSTAL GROWTH MZ-PSI LAB: CHARACTERIZATION OF MASS TRANSPORT IN A NaCl
EVAPORATING MICRODROP BY MZ-PSI.
In this lab, the student will characterize mass transport in a crystallization solution of
NaCl in distilled water. The nucleation triggering mechanism will be evaporation.
Indeed, as the drop evaporates, concentration increases, and nucleation occurs followed
by crystal growth. Characteristic mass transport regimes dominated by convective
transport will take place. The student will manage the acquired data in order to extract
growth rate and supersaturation maps within the drop volume. Conclusions concerning
the relationship between these magnitudes shall be provided by students.
LAB DESCRIPTION
1. Prepare Interferometer for acquisition
2. Prepare a slightly undersaturaded NaCl solution in distilled water
3. Place a 10 µL drop inside the crystallization cell
4. Place the cell inside the sample interferometer arm
5. Launch acquisition. Nucleation and growth of the crystal should occur within
10-20 min
6. Stop acquisition when the crystal stop growing
7. Save results
8. Calculate phase, Fringe modulation, Phase and Phase step images from the time
series of 5 phase-shifted images (Eqs. 1.12-1.14)
9. Unwrap the phase images
10. Estimate concentration (Eq. 1.17)
11. Generate Growth rate and Supersaturation profiles in the crystal vicinity.