1. Atomic Force Microscopy (AFM)lafactoria.lec.csic.es/mcc/attachments/article/41/100386... ·...

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.


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


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.


During tapping mode operation, the cantilever oscillation amplitude is maintained constant by a feedback loop. Selection of the optimal oscillation frequency is software-assisted 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.


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


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.


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.


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.


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.


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


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.


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 45-

degree 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, fine-

tuning 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


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


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


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

Numerical Aperture

Working distance (mm)

Lateral resolution (mm)

Company

UPlanFL 4x 0.13 P 13.0 3.2 Olympus UPlanFL 10x 0.30 P 3.1 1.4 Olympus

LUCPlan FL 20x 0.45 P 6.9 0.92 Olympus LUCPlan FL 40x 0.60 3.4 0.68 Olympus

PlanApo 60x 1.45 0.15 0.28 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


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,

)(sin61.061.0

µ!!

nNAd =" (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


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 (Milli-

Q) 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.


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).

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.

Figure 2.10 Materials necessary for the preparation of an observation cell.


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 Na-

acetate 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.

Solubility curve:

0 5 10 15 20 250

5

10

30 mg/ml NaCl 40 mg/ml NaCl 50 mg/ml NaCl 70 mg/ml NaCl

Lyso

zym

e so

lubi

lity

Temperature

0 20 40 60 80 100

1,6

1,7

1,8

1,9

2,0

2,1

C

aSO4

g/l(

solu

tion)

Temperature (ºC)


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.


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.


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.


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.


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?

______________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

______________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

______________________________________________________________________


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)


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


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 half-

wave plate is placed on the reference beam path. Both beams are recombined by a non-

polarizing 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 ad-

hoc for the instrument.

For the unbalanced interferometer setup, the set of equations 1.3 is defined as follows:

!! !, ! = !! + !Δ! 1 + ! !, ! !"# ! + Δ!! (1.4)


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 ! =!"!"

(1.8)

Δ! = !Δ! with ! =!"!"

(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 non-

negligible 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).


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:

!!"##,! = !!!!

!! + !!Δ! (1.11)

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:

! !, ! = !"!#2 !2 !, ! − !4 !, !

2!3 !, ! −!1 !, ! −!5 !, ! (1.12)

γ !, ! =3 !! − !! ! + !!+!!−2!! !

2 !!+!!+2!!+!!+!! (1.13)

cos ! !, ! =!! !, ! − !! !, !!! !, ! − !! !, !

(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.


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! !, !, !, ! =!2!"

Δ! !, !, ! (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! !, !, !, ! =!

2!" Δ!Δ!

Δ! !, !, ! (1.17)


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.

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