Abinitha's Blog - Crystallography at Princeton University (Partners in Science Program)

Hi everyone! My name is Abinitha Gourabathina, and I am a rising junior. This summer, I will be working at the PRISM (Princeton Institute for the Science and Technology of Materials) center at Princeton University through the Partners in Science program. I am working under Professor Nan Yao, who is the director of PRISM, and will be working on different types of microscopy and crystallography.

The Andlinger Building for Energy and the Environment

So far, I have worked on simulating crystals and have read about atomic force microscopy (AFM), scanning electron microscopy (SEM), transmission electron microscopy (TEM), and x-ray diffraction.

XRDS SEM AFM Diagram

I have simulated NaCl crystals, as a basic template to run the code and verify the ionic radii database, and then simulated PMN-PT crystals in monoclinic-A and monoclinic-B crystals (I attached a video of the simulations!). PMN-PT single crystals are formed from lead magnesium niobate-lead titanate solid solution, (1-x)[Pb(Mg1/3Nb2/3)O3]-x[PbTiO3]. PMN-PT is being studied for its piezoelectric properties. Piezoelectricity is when mechanical stress applied to an object results in electric currents.

With the help of other researchers in the department, I have received training using the SEM and AFM! The SEM works by shooting a beam of electrons onto the surface of a material. The electrons from the electron gun are sped up going from an anode to the magnetic lens. The applied electromagnetic force is carried out through the scanning coils (as seen in the diagram below). The secondary electrons that are produced by the electron-surface sample collisions are studied to analyze the chemical structure of the substance and gain knowledge on other aspects of the sample, such as thickness, lattice, and roughness.

Shortly after training with the SEM, I was able to image a butterfly wing using the SEM.

The Original Sample

Low Zoom Image

Mid Zoom Image

AFM requires more hands-on work to operate as compared to the technological pursuits to focus the image in the SEM. The AFM has a stylus, or tip as it is more commonly referred to, which is at the edge of a cantilever. The optical lever of the AFM operates by reflecting a laser beam off the cantilever. The reflected laser beam strikes a photodiode which consists of a four-segment photo-detector. The differences between the segments of photo-detector of signals indicate the position of the laser spot on the detector and thus the angular deflections of the cantilever. Unlike the SEM, the AFM can make 3D models of the sample's surface.

Atomic Force Microscope (right)

Montgomery's very own, Junlan Lu (Class of 2015), can be seen collecting data using the AFM to study an NbSi film. Here is an example of how the AFM can make 3D models of sample surfaces:

The single crystal of lead magnesium niobate-lead titanate solid solution, (1-x)[Pb(Mg1/3Nb2/3)O3]-x[PbTiO3] (PMN-PT), is a piezoelectric material. PMN-PT exhibits very large electromechanical coupling coefficients, high piezoelectric coefficients, high dielectric constants and low dielectric losses that results in improving bandwidth, sensitivity and source level in applications.

PMN–PT has a perovskite crystal structure. The crystal that we have modeled is monoclinic with space group P 1 m 1.

A transmission electron microscope (TEM) comprises of an electron gun, electromagnetic lenses, and apertures. The electron gun, often referred to as a thermionic electron gun, emits electrons from a heated filament. The electrons are then accelerated towards an anode. The electron beam must be generated and used in a high vacuum of 10-4 mbars or less. This ensures that the electrons are not deflected by gas molecules and that the filament and specimen are not contaminated. Similar to an optical microscope that has glass lenses, a TEM has electron lenses, which are magnetic. These electron lenses either take all the rays emanating from a point in an object and recreate a point in an image or focus parallel rays to a point in the focal plane of the lens.

In the TEM, electrons are scattered by the sample. Electrons scattered in the same direction are focused in the back focal plane, which is where diffraction patterns are formed. Electrons coming from the same point of the object are focused in the image plane. In the bright field (BF) mode, an aperture is placed in the back focal plane of the objective lens which allows only the direct beam to pass. In this case, the image results from weakening of the direct beam through its interaction with the sample. Therefore, mass-thickness and diffraction contrast contribute to image formation: thick areas, areas in which heavy atoms are enriched, and crystalline areas appear with dark contrast. It should be mentioned that the interpretation of images is often impeded by the simultaneous occurrence of the contrast-forming phenomena. In dark field (DF) images, the direct beam is blocked by the aperture while one or more diffracted beams are allowed to pass the objective aperture. Since diffracted beams have strongly interacted with the specimen, very useful information is present in DF images, about planar defects, stacking faults or particle size.

Atomic radius periodic trend shows that every atom has a unique atomic radius. The elements in PMN-PT are lead (Pb), magnesium (Mg), niobium (Nb), titanium (Ti), and oxygen (O).

Radii of Elements in PMN-PT

The “crystal” radius is used in crystallography databases, such as the CDC, from which the CIF file was imported to make the PMN-PT crystal on CrystalMaker. The PMN-PT crystal has a perovskite structure where the central “atom,” which is actually a conglomeration of atoms, of the crystal is composed of niobium, magnesium, and titanium. The central atom, however, is predominantly niobium, making the radii of Mg and Ti irrelevant and not included in the crystal structure.

Finding the Separation Between the Lead and Oxygen Column

Using Crystal Maker:

X Value of Oxygen = 0.971

X Value of Lead = 1

Difference in X Values = 1-0.971= 0.029Distance Between Lead and Oxygen Column = 0.029*4.0055 Å = 0.116 Å

3x3x3 PMN-PT