Microstructure evolution in eutectic alloys under directional solidification conditions
Directionally solidified binary eutectics exhibit a wide array of two-phase microstructures ranging from rods to lamellae. They are interesting as self-organized composite materials with tunable microstructural size and shape distribution. The principal objective of this work is to initiate an extensive study of the microstructure evolution in eutectic alloys. Directional solidification is a convenient way to investigate the microstructure formation as it can accurately impose the process parameters such as temperature gradient and solidification speed. It also allows the evaluation of experimental results with theory and simulation more accurately. We have primarily chosen Sn-Te and Mg-Zn eutectic alloys for our studies. As confirmed from previous literature study, the Sn-Te alloy displays a wide range of morphologies upon employing suitable conditions. Thermoelectric properties of Sn-Te depend on spacing and morphology of the eutectic structure. Mg-Zn displays a unique morphology due to a mixture of faceted and non-faceted components. The binary alloys are directionally solidified at different interfacial velocities to study the morphological evolution. Samples are characterized using SEM and Optical Microscopy. Resulting morphologies that were observed displayed a transition from mixed morphology to rod-like structures. Eutectic spacing is calculated from the SEM images for different velocities using the ImageJ software.
|SEM||Scanning Electron Microscope|
|FFT||Fast Fourier Transform|
|M||Mega (106 units)|
|wt. %||Weight Percent|
|at. %||Atomic Percent|
The study of the morphology of any material and understanding the pattern formation of various structures that together make up the material microstructure is critical to the understanding of the fundamental properties characterizing that material. The type of microstructure that a material exhibits help us in determining an accurate relationship between its structure and properties. A complete and comprehensive study on the microstructure of materials is, therefore, a critical requirement. Such studies prove to be extremely useful when fabricating methods to introduce new properties in a material or modify existing properties in a material of interest.
Eutectic alloys possess a wide range of properties that are distinct from non-eutectic systems. Many of these properties depend upon the microstructure of the eutectic. We have, therefore, undertaken this research to study the microstructures of these directionally solidified eutectic alloys as a function of the growth velocity.
Objective of the Research
The principal objective of this research is to study and describe the formation and development of microstructures in directionally solidified binary eutectic alloys, namely, Sn-Te and Mg-Zn, at various growth velocities.
- An attempt to explain the morphological patterns in binary alloys.
- Examination of morphological growth in these alloys as a function of growth velocity.
- Determination of eutectic spacing of Sn-Te.
The work that we have carried out pertains to a relatively new area of research which, at the moment, is under further exploration. Therefore, very little relevant literature is available regarding the related works that were carried out prior to our research. We have thus provided a brief outline of the key concepts and theories which serve as fundamental ingredients to our work. These may also serve as prerequisites to give a general understanding of the content of the research that we have initiated, and are described in detail below.
Alloys, their properties, and the phase diagram
It is widely known that an alloy is a homogeneous mixture of two or more elements, of which at least one of those elements must be a metal. Since there exists a mixture of different elements in an alloy, it is appropriate to state that an alloy does not have a fixed melting and freezing point, but rather exhibits a range of melting and freezing temperatures at different compositions of the solute material. Much of the information about the control of the phase structure of a particular system is conveniently and concisely displayed in what is called a phase diagram, also termed an equilibrium diagram. The phase diagram of a given system displays the phases present in that system, along with the range of compositions and temperatures for the given phase to exist at thermodynamic equilibrium. A typical phase diagram for the Tin-Tellurium system is shown below.
The familiarity of a few terms pertaining to the concept of the phase diagram is necessary in order to obtain a general understanding of the same. These terms are defined below:
1. Liquidus Line: The line separating the liquid phase (Liq.) from the liquid (Liq.) and solid phases (SnTe and Te, respectively). A point on this line at a particular composition represents the freezing point of the alloy at that composition.
2. Solidus Line: The line that separates the pure solid phases from the liquid and solid phases, respectively, is called the Solidus Line. The melting point of the alloy at a particular composition can be determined from the solidus line.
3. Solvus Line: The line separating one solid phase from a mixture of solid phases is called the solvus line.
Eutectic System and its properties
As can be observed in the alloy system shown in Fig 1, there exists a particular point in the phase diagram where both the liquidus lines meet at the isotherm. This point is known as the eutectic point, and such systems are also called Eutectic Systems. As can be seen, a eutectic point is characterized by a fixed composition and temperature at which the transformation from the liquid to solid phases (and vice versa) can be achieved.
The Sn-Te System
The Sn-Te alloy is characterized by two eutectic points. The specifics of these eutectics are given below:
a) At TE = 504.5 K, CE = 0.01 at. % Te:
b) At TE = 674 K, CE = 85 at. % Te:
Our study is primarily focused on microstructure evolution in the second case (b).
The Mg-Zn System
The phase diagram for the Mg-Zn system is shown below.
The eutectic composition that we have chosen for our studies is, namely, Zn- 3 wt. % Mg, at a eutectic temperature of 369oC.
Eutectic alloys are a fascination to many scientists and researchers alike and are undergoing extensive research, primarily due to their remarkable properties over pure materials and non-eutectic systems. They have a low melting point compared to pure components and their composite microstructures procure them superior mechanical properties. Uniform and distinct microstructures upon solidification are a general characteristic of eutectic alloys.
We obtained mixed microstructures of Sn-Te (rod-like + lamellar morphology) and spiral structures of Mg-Zn in our experiments. These anomalous spirals were reported to arise due to the anisotropy of the solidifying solid/liquid interface. This anisotropy is expected to originate due to the high kinetic undercooling, which is associated with the high entropy of melting of similar alloys . Directionally solidified Zn-3 wt. % Mg was prepared by Fullman and Wood , who reported complex-regular structures originating from the components Mg and MgZn2. A concise theory of the formation of such structures has also been illustrated in their work. Croker et al  had directionally solidified Mg2Zn11-Zn eutectic at various growth velocities. A transition from complex-regular fish-spine structures to complex-regular trigonal structures was reported at increasing growth velocities.
Solidification is a type of phase transition which is characterized by the transformation of a material from a pure liquid phase to the solid phase. The process is widely employed in various metals as well as alloys. In all these cases, the primary reason for the influx of solidification is, simply, the extraction of heat. The generation of an external heat flux around the solidifying material facilitates heat transfer from a high temperature zone to a low temperature zone.
Solidification occurs when the temperature of the liquid phase drops below the equilibrium melting temperature. This is characterized by the generation and growth of a single stable nucleus from the molten pool, under appropriate conditions. The process of formation of a stable nucleus from a melt is known as nucleation.
This nucleus, and later subsequent nuclei, can only be created when sufficient driving force is provided to the melt. This driving force appears in the form of undercooling. Undercooling is defined as the lowering of the temperature of the alloy or metal below the liquidus temperature. It is expressed as:
where ΔT is the undercooling, TL is the temperature at liquidus, and T* is the temperature of the solid/liquid interface of the solidifying material.
The figure shown below depicts a typical setup of directional solidification.
Here, the sample is being pulled down at an extremely small velocity (v) between two regions. The velocity (v') depicts the velocity of the moving solid/liquid interface, which is close to v for extremely small values. The external heat flux imposed by the two temperature zones is chosen to be qe. The top region consists of a heater used to melt the sample while the middle region is a thin adiabatic zone, which helps to establish the required thermal gradient. The bottom part consists of a cooler for slow cooling of the melt as it approaches the bottom.
The Modified Bridgman-type Directional Solidification Furnace
We have used a Modified Bridgman-type Directional Solidification Furnace in our experiments in order to achieve the desired microstructures. The DS apparatus is shown below:
The schematic of the Bridgman-type Directional Solidification Furnace is as follows:
The quartz tube containing our alloy is placed on the sample holder. The sample holder is now placed under the furnace in such a way that the top view of the furnace clearly displays the top portion of the quartz tube. Care must be taken that neither the sample holder nor the quartz tube touches the inner sides of the furnace, both at rest and in motion. The bottom zone of the furnace is connected to a cooling system that provides a steady flow of cooled water to the walls of the lower zone, thus helping to establish a low-temperature region. The desired thermal gradient, growth velocity, and direction of solidification can be fed into the apparatus via a computer which is connected to the same.
After the desired growth rate and temperature gradient are entered into the system, the necessary temperature zones are established. The crucible starts moving upwards or downwards with a constant velocity (v) through the generated temperature profile. As the crucible is set in motion, solidification proceeds in a direction opposite to that of the motion of the crucible. In this way, the entire melt in the quartz tube is solidified from one terminal to the other.
The Vacuum System
A Vacuum System is a device used to create a zone of vacuum around a given sample. This is achieved by extracting all the atmospheric gases present around the sample and venting them out into the atmosphere. The quartz tube which contains the components to be melted for alloy formation must be devoid of all air and atmospheric elements in order to prevent accidental side reactions of the components, which may degrade the alloy formed. This is where the vacuum system comes into play. The vacuum system that we have operated in our experiments is shown below.
This vacuum system consists of two main components. These are:
- The Rotary Pump
- The Diffusion Pump
A concise description of the theory and working of these pumps is given below.
1. The Rotary Pump:
The rotary pump comes under the category of Roughing Pumps, which are typical in almost all vacuum systems. The rotary pump serves two functions:
1. Pumping the chamber which is at atmospheric pressure to a low pressure level so that the high-vacuum pump can subsequently operate.
2. Revert to a secondary position where it can support the high-vacuum pump by providing a low enough pressure at its outlet. A typical sketch of the rotary pump is shown in Fig 8 below.
The rotary pump utilizes a set of rolling parts to attain vacuum. These rotating parts take a certain volume of air which is at low atmospheric pressure from the inlet; they compress the volume via rolling to a pressure just above atmospheric pressure and finally vent it out into the atmosphere through an outlet valve.
2. The Diffusion Pump
A diagram of the Diffusion Pump is shown in Fig 9.
This pump consists of an inner cylinder called pumping stack. The bottom of the pump contains a heater and an oil of high purity. The heater heats the oil at the bottom to a temperature of about 250oC until it evaporates. The evaporated oil flows up inside the stack until it reaches the top. After reaching the top, the oil starts moving downwards. As it does so, it collides with the gas molecules and drives them towards the bottom of the pump. Vaporized oil traps the gas molecules by diffusion action. When this trapped gas reaches the bottom, high pressure is developed. The pressure at the bottom is high enough to allow the rotary pump to remove gas to the atmosphere. The jets at the sides of the stack serve to deflect the hot oil vapors at the walls of the pump. The oil that gets in contact with the pump walls is condensed by water-cooling lines. This condensed liquid then falls back to the bottom to be reheated.
Metallographic Sample Preparation Techniques
The study of microstructures of all types of metals and alloys is termed Metallography. It consists of a complete analysis of the chemistry and atomic structure of metals and alloys along with the spatial distribution of their constituents and phases. Certain metallographic sample preparation methods are employed in order to undertake a thorough and accurate microstructural analysis, failure of which to incorporate will lead to the observation of an incorrect microstructure, further resulting in inaccurate data and results. Employing appropriate sample preparation methods help in ensuring that a true microstructure is obtained with minimal deviations from the expected observations. Various equipment are used for determining the microstructure of different materials. For metals and alloys, Optical Microscopes and Electron Microscopes are generally used. The type of microscope to be employed depends primarily on the nature of microstructural features which are to be examined, and the appropriate sample preparation method is employed for observation under that particular microscope.
Sample Preparation for Optical Microscopy
Optical microscopic studies require the sample surface under observation to possess a smooth and flat face completely devoid of any scratches or marks. This is achieved through some sample preparation steps, which are described below:
1. Cutting: A sample of specified dimensions is cut from the bulk material. Various cutting techniques such as hand sawing, abrasive cutting with proper cooling, chemical or electrochemical sectioning, etc. can be used for the cutting process. It must be ensured that, during the process of cutting, the microstructure is not altered due to the generation of excessive heat. For this purpose, cutting is accompanied by the use of cool water sprays in order to prevent the generation of heat or stress which can affect the microstructure of the sample.
2. Mounting: This is the process of embedding the sample in resin. We used cold mounting to prepare our samples. In cold mounting, a homogeneous liquid mixture of resin (monomer) and catalyst is poured into a metallic or phenolic ring placed surrounding the sample on a glass slide . The catalyst reacts with the resin at room temperature, and the mixture solidifies, thus embedding the sample. This process is usually carried out if the sample has high porosity or contains cracks.
3. Grinding: Grinding is carried out to remove the deformed materials and reduce the surface roughness caused due to cutting. It also serves to reduce the number of coarse scratches that are present on the specimen surface. This is carried out by placing the sample surface on a rotating platform backed with an abrasive paper of a certain grade. Lubricant or water is continuously poured onto the grinding surface to reduce the chances of embedding of abrasive particles with the specimen surface. Grit sizes of increasing magnitude are used upon subsequent grinding operations until a completely flat surface with fine scratches is obtained. A 90o change in the direction of grinding is recommended each time all the scratches become oriented in the direction of grinding.
Polishing processes are employed for the removal of residual fine scratches. It is achieved by placing the ground surface on a cloth-covered rotating platform coated with minuscule particles. In our experiments, we have used 1 µm and 0.5 µm Alumina (Al2O3) suspension over wet cloth as the polishing surface. These abrasive particles serve to eliminate the finer scratches and produce a smooth and fine surface completely free of any deformations. Surface features such as cracks, inclusions, pits, pores, etc. become visible after proper polishing of a sample.
5. Etching: This is the final step in the sample preparation process. The sample surface is coated with a chemical called etch. This coating helps to make visible the intricate microstructural details such as grain boundaries and precipitates. After this step is complete, the sample is suitable for observation under the optical microscope.
The Optical Microscope
The Optical Microscope is an apparatus used to study the microstructure of most metals and alloys, more specifically, the grains, grain sizes, and nature of inclusions present in the material. It can also be called a compound microscope since it uses two primary lenses to study the object. These two lenses are known as Objective and Eyepiece. The objective is placed close to the object to be studied. The eye of the observer is placed near the eyepiece for viewing the final image. In our study, various objectives of magnifications 2.5X, 10X, 30X, 50X, and 100X were employed for observing the resulting microstructure. The magnification of the eyepiece was 10X. The device mostly operates in the range of the visible spectrum of light, which is around 400-650 nm. In some cases, light of shorter wavelength is used in order to improve resolution.
We have utilized an inverted optical microscope in our experiments.
The optical microscope utilizes the principle of Reflected Light Microscopy. Explicitly, it uses light rays reflected from the specimen for displaying the final image. It is this reflected light that ultimately passes through the eyepiece and reaches the eye of the observer. Since the materials used here are almost always opaque, only a minuscule amount of light is absorbed by the sample. Most of the light rays are reflected from the material, due to which a sharp and clear microstructure can be obtained.
The Scanning Electron Microscope
The Scanning Electron Microscope is used to obtain microstructures with resolutions of the order of about 5 nm. A wonderful feature of this instrument is the ability to analyze not only the microstructure, but also the elemental composition and crystallographic, electric and magnetic properties of the sample material. Another characteristic of SEM is its high depth of field (about 300 times that of the optical microscope), which enables it to generate three-dimensional images of specimens along with better topographical data than other microscopes. Due to their unique versatility, SEMs find extensive use in numerous fields ranging from materials science to biological sciences and chemistry.
Sample preparation for SEM:
The SEM cannot generate images of non-conducting samples as the incident electrons would get embedded within the material, thus producting an inaccurate image. Therefore, it must be ensured that the specimen is made both conductive and dry prior to SEM analyses. For non-conducting samples, a conductive coating is applied on the surface of the specimen. Conducting samples need no such coating and only have to be ensured dry before mounting on the sample stage.
In our experiments, carbon tape was applied between the samples in order to make the setup conducting. Aluminum foil was added along the edges of the sample mount before placing it on the sample stage.
Unlike other microscopes, the SEM generates images by scanning a beam of electrons on the specimen and capturing the microstructural data from the scanned surface. The device consists of an Electron Gun, Magnetic Lenses, a Column, Electron Detectors, Specimen Chamber, and the Sample Stage.
The electron gun generates a beam of electrons; these electrons are accelerated by an anode and travel through the column. There are two types of electron guns:
1. Thermionic gun: This gun consists of a tungsten (W) filament which, when heated to extremely high temperatures, generates high-energy electrons above the threshold energy.
2. Field Emission gun: In this type, the gun consists of a pointed W filament from which electrons are pulled out by an extremely high electrostatic field. This voltage is also called extraction voltage.
The column through which the electron probe travels contains an array of magnetic lenses. These are actually a set of electromagnetic lenses which serve to reduce the electron beam to a spot of a certain size. The spot size can be adjusted in order to ensure a brighter or darker image, also taking into consideration the extent of details which can be recorded in each case. A higher spot size will increase brightness but will result in lesser detail in the microstructure. A lower spot size will decrease brightness but will result in better details recorded in the specimen. The column also contains scan coils. With the action of magnetic fields set up around these coils, the scan coils help to deflect the electron probe in the X and Y-directions. In this way, the electron spot “scans” across the surface of the specimen. The viewing screen is scanned in synchrony with the beam falling on the specimen, thus generating a clear and resolved image on the screen. The magnification of the image can be adjusted by varying the rectangular scanning area. The magnification increases as the area of the raster decreases and vice versa.
The morphological, topographical, and compositional data of the specimen is obtained from three different types of electrons which are generated when the electron probe strikes the sample surface. These are, namely:
1. Backscattered electrons (BSE): These are initially the electrons from the incident electron probe which get elastically scattered after coming close to the atoms of the specimen. Since these are high-energy electrons, they penetrate up to a certain extent inside the specimen and thus carry with them a lot of microstructural data. This is the reason why we obtain three-dimensional images in SEM micrographs. The image resulting from these electrons can be observed by operating the SEM in BSE mode
2. Secondary electrons (SE): These are electrons that are ejected out from the surface atoms of the specimen when an incident electron, whose energy is greater than the threshold energy, strikes the atom. As these electrons are ejected from the surface of the material, they mostly carry the surface features (or topographical data) of the specimen. The topography of the sample can be generated by operating the device in SE mode.
3. X-rays: X-rays are also generated from the specimens. These provide data on elemental composition and crystallographic properties of the specimen. Energy Dispersive X-ray Analyses utilize these X-rays in order to obtain information on various elements present in the specimen.
Introduction to ImageJ
ImageJ is a Java-based open source software, originally developed by Wayne Rasband at the Macintosh-based National Institutes of Health. This software is primarily an image processing program serving various functions such as editing, analyzing, and displaying of different image types ranging from 8-bit, 16-bit and 32-bit to RGB color type.
The various functions that can be executed using this software are:
- Measurement of distances, angles, distance between two points, etc.
- Calculation of area and pixel-value statistics from user-defined selections .
- Generation of density histograms, line profile plots, surface plots, etc.
- Geometric transformations such as scaling, rotation, translation, and flipping of images.
- Basic image processing operations such as contrasting, sharpening, thresholding, smoothening of images, detection and highlighting of edges, and median filtering.
Determination of Eutectic Spacing using ImageJ
1. Adjustment of Image settings: The image to be studied is opened in the ImageJ window. Shortly after opening the image, the image type is changed to 8-bit.
2. Calibration: Before executing subsequent operations on our selected image, we must first set the scale for any measurements which are to be followed. This is done by calibration in order to fit the scale as mentioned in the micrograph, viz. 50 µm.
3. Contrasting and related operations: Contrasting operations are performed in order to obtain greater clarity between dark and bright shades of the micrograph. Two contrasting operations are performed here:
- Enhance Contrast: Enhancing saturation of pixels by 50%
- Threshold: The threshold command is used to form a binary image. This is done by specifying a particular threshold value, so that pixels only above or below that value are shown. We can even specify two threshold values in order to find a range of pixels falling between those values.
4. Fast Fourier Transform: The FFT command generates an FFT spectrum of the image.
As can be observed in Fig 18, the FFT spectrum consists of a series of periodically appearing bright and dark spots from the centre of the box. The average eutectic spacing is determined by moving the cursor to the first bright spot from the centre, which is oriented in the direction of the row of rods, and noting the r-value specified in the status bar. In our study, the average eutectic spacing was found to be 7.50 µm.
Placing the cursor to the first bright spot of the series oriented along the direction of the row of rods gives the average distance between two consecutive rods. This was found to be about 6.43 µm.
Synthesis of Sn-Te
High purity Tin (99.99+% purity) and high purity Tellurium (99.999% purity) were used. Appropriate amounts of 85.89 wt. % Te and 14.10 wt. % Sn were delivered in a quartz tube. We have chosen the total weight of the sample as 20 g. The quartz tube was sealed and vacuumed to 10-5 mbar. To ensure homogenization of the contents in the quartz tube, the sample was placed in a furnace. The temperature was set at 700oC for 2 hours. The synthesized alloy was divided into five samples for directional solidification experiments. Each of the four samples was consecutively placed in a Modified Bridgman-type Directional Solidification Furnace. A temperature gradient of 10oC/mm was set for each sample with growth velocities at 0.5 µm/s, 2 µm/s, 8 µm/s, 16 µm/s, and 32 µm/s, respectively.
Synthesis of Mg-Zn
Appropriate amounts of Zinc pellets (99.999% purity) were mixed with Magnesium balls and the entire mixture was sealed in a quartz tube. A vacuum upto 10-6 mbar was achieved in the quartz tube, since magnesium is very reactive with atmospheric oxygen. The vacuumed sample was homogenized using a high-temperature furnace and subsequently sent for directional solidification.
Samples of the directionally solidified eutectics were prepared for Optical Microscopy. Different samples were cut, mounted, and prepared for metallographic analysis by grinding using abrasive SiC papers of grit sizes 800, 1500 and 2500, respectively, in succession. Ground specimens were polished using 1 µm and 0.5 µm Alumina powder suspension over wet cloth. Polished samples were examined using Axiovert 200M MAT Optical Microscope equipped with HBO 100 Microscope Illuminating System. Samples were also analysed using FEI Quanta Thermionic Scanning Electron Microscope.
RESULTS AND DISCUSSION
Microstructures of eutectic Sn-Te
Resultant microstructures display a mixed morphology consisting of rods and lamellae. It was observed that an increase in the growth velocity facilitates the formation of additional rods, leading to a transition from a mixed morphology to more rod-like structures at increased growth rates.
Microstructures of eutectic Mg-Zn
We had attempted to study the microstructures of eutectic Mg-Zn using Optical Microscopy. However, due to the inability to resolve the fine eutectic spacings, the samples were directly sent for SEM analysis.
The figure below displays the SEM micrographs of Zn- 3 wt. % Mg..
These microstructures illustrate the formation of spiral structures. These spirals are expected to arise due to a difference in growth rates between the two phases. As a result, it is expected that the phase of higher growth rate will tend to grow around the phase of lower growth rate, thus forming a spiral . These structures are, however, not completely as regular as those reported by Fullman and Wood, who synthesized completely hexagonal-faceted spirals. This irregularity may be associated with the side-reaction of magnesium with silica in the quartz tube. Attempts to completely impede the interaction between these two elements are currently in progress so that a fully complex-regular microstructure can be obtained and required properties can be determined.
CONCLUSION AND RECOMMENDATIONS
We have synthesized two eutectic alloys in our experiments, viz. Sn-Te and Mg-Zn, via directional solidification and reported the resultant microstructures for the same. Sn-Te showed mixed morphologies, viz. lamellar + rod-like structures, at low growth rates which evolved to rod-like structures at higher growth rates. Mg-Zn showed spiral growth of the two phases, which is expected to occur due to a significant difference in growth rates of the two solidifying phases. These spirals were not shown to have regular hexagonal faceting as was reported from previous studies, most expectedly due to the reaction of magnesium with the silica in the quartz tube. The utilization of less-reactive graphite crucibles is recommended as a substitute for the quartz tube in order to prevent such side-reactions.
A further study of the various properties resulting from these microstructures is yet to be attempted. Future works can include initiating different elemental impurities in such binary alloys and recording the microstructures obtained in each case. Thermoelectric properties of Sn-Te as a function of growth velocity must also be explored. Apart from growth velocity as a process parameter, numerous temperature gradients can also be imposed on such alloys in order to study the resultant microstructures.
I would like to express my deepest gratitude to my guide, Dr. Abhik Choudhury, for the constant support and guidance provided during the entire course of this Fellowship. This project would not have been completed without his consistent supervision and encouragement.
I extend my deepest thanks to my mentors, Mr. Aramanda Shanmukha Kiran and Mr. Saikiran Salapaka, for imparting in me the indispensable knowledge and skills that were required for the development and successful culmination of this project.
I offer my special thanks to Ph.D. students Mr. Srivatsan S. and Ms. Sireesha Panithi, for engaging me in our regular scientific debates and exchanges which enabled me to procure within myself the imperative mindset critical for a competent researcher.
I also express my greatest gratitude to the Computational Materials Science group members Mr. Sumeet Khanna, Mr. Fiyanshu Kaka, and Mr. Bhalchandra Bhadak for the constant help and advice which they provided during my time at IISc.
I thank the coordinator of the Summer Research Fellowship Programme, Mr. C.S. Ravi Kumar, and the Indian Academy of Sciences, for giving me the opportunity to work as a Summer Research Fellow at this prestigious institute.
I also extend my thanks to AuthorCafe for providing a wonderful and elegant platform which enabled me to compose this work in a perfectly structured manner requiring minimum efforts.
I wish to give my greatest thanks to Prof. Ravi Kumar, Head of Department, Department of Materials Science and Engineering, NIT Hamirpur, for recommending me as a summer research fellow for this distinguished programme
Finally, I would like to express my deepest gratitude to my parents for their constant and unparalleled love, support, and motivation.
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