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«STUDENT RESEARCH PAPERS SUMMER 2011 VOLUME 22 REU DIRECTOR UMESH GARG, PH.D. REU Student Research Papers – Summer 2011 University of Notre Dame – ...»

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Antiferromagnetism is like ferromagnetism where instead the magnetic moments line up antiparallel to each other.

If we begin by assuming separate Curie constants CA and CB for ions at two different sites A and B, we will have two interactions as BA=-μMB and BB=-μMA; μ is a positive mean field constant. With the mean field approximation we would have

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here, the Ba is the applied field. We solve this system of equations using a matrix, by assuming the applied field is zero. The susceptibility to at TTC

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where θ is TTN. A summary of all of the magnetizations is shown in the figure below. Note that at TC for a ferromagnet the magnetization is a singularity, whereas at TN of an antiferromagnet the magnetization peaks.

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For this experiment, we used the SQUID (superconducting quantum interference device), which uses Josephson junctions to measure magnetic fields in samples of La0.7Sr0.3Mn1-xNixO3. Small samples were obtained from pellets of bulk material of different Ni contents (x= 0, 0.05, 0.1, 0.2, 0.3). The samples were prepared via solid-state reaction methods. 100 mg bars were cut using a diamond bladed saw. The sample was mounted with cotton into a pill capsule to protect it from moving around. After that, we sewed the capsule into place inside a straw, three-quarters of the way down. We inserted the straw into the SQUID.

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varying field at constant temperatures. This data is plotted in two graphs for each sample composition:

magnetic susceptibility[χ] vs. Temperature [T], and magnetization[M] vs. applied field[H]. The applied field was in the range of 0-70 KOe. Three sweeps were performed consecutively in the susceptibility measurements: Zero-field cooled (ZFC) where the sample is cooled in 0 field then warmed in a field while taking measurements, field cooled (FC) where the sample is then cooled in the same field while taking measurements, and field cooled warming (FCW) where the field is then turned off and measurements are taken as the sample warms.

As shown in Figures 1, 3, 5, 7 and 9, the transition temperature of the x= 0 composition is approximately 375K, while for x=0.05 it is 330K, for x=0.1 it is 350K, for x=0.2 it is 300K and for x=0.3 it is 300K.

If we look at Figures 2, 4, 6, 8 and 10, we see that there is saturation at the x=0 state (at both 5K and 300K), at x=0.05 (at 5K, but not at 300K), at x=0.1 (at both 5K and 300K), and at x=0.2 (at 5K, but not at 300K).

Figure 4 shows a mixture of phases, at the higher temperatures, which can be seen through the combination of saturation and flatness. One point of interest, is that at the x= 0.2 state, the 300K measurement was the only one we took above the transition temperature. Another point of interest, is at the x= 0.3 state, there is no saturation at either temperature, even up to 70 KOe. All of the M vs T graphs seem have have comparably similar shapes, however by the time we have 30 percent doping, we see it has a different shape. The properties begin to change and there is a great suppression of the order of magnitude of magnetization, which can be seen on the y-axis, due to doping.

Based off Figure 11, it seems like there is no strong correlation between doping and transition temperature, however it does trend towards TC supression as Ni-doping increases.

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Figure 9: Temperature10: Field dependence of susceptibility for x=0.3 Figure dependence of susceptibility for x=0.3 measured in a 10 Oe a 10 Oe field measured in field

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Kittel, Charles, Introduction to Solid State Physics 7th ed., John Wiley & Sons, Inc., New York 1996 Thomas F. Creel, Jinbo B. Yang, Mehmet Kahveci, Jagat Lamsal, Satish K. Malik, S.

Quezado, B. W. Benapfl, H. Blackstead, O. A. Pringle, William B. Yelon and William J. James, Structural and Magnetic Properties of La0.7Sr0.3Mn1-xNixO3 (x ≤ 0.4), not published

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There are many different phases of Ice, which exist in different pressure and temperature combinations. The effort of my research is to study the phase transition between Ice VI and Ice VII, building upon the research done on previous REU student, Dawn King. I use the lattice framework of Ice VI-VII transition created by Dawn King and apply a Stillinger – Weber model of Monoatomic water as developed by Molinero and Moore. Taking a King’s lattice as a unit cell containing 512 sites, I simulate 3×3×3 unit cells and take the central unit cell to calculate the energy. The central unit cell is chosen because it is surrounded by other unit cells and we do not have to apply periodic boundary conditions. Further work needs to be done on applying the periodic boundary conditions and develop the Monte Carlo simulations, in order to be able to do statistical calculations.

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understand the processes involved in the phase transition of Ice VI to Ice VII. Ice VI and Ice VII both are self clathrate crystal structures, which means that these structures consist of interpenetrating sub-lattices. The effort of my research is to study the phase transition between Ice VI and Ice VII, building upon the research done on previous REU student, Dawn King[1]. I use the lattice framework of Ice VI-VII transition created by Dawn King and apply a Stillinger – Weber model of Monatomic water as developed by Molinero and Moore[2]. We use King’s lattice and assume that atoms can only occupy discrete locations in the lattice. Also we use the idea of water being modeled as an intermediate element between carbon and silicon to understand the energy distribution in the lattice[2]. We try to understand the different kind of energetics that occur in the process of phase transition in order to create a Monte Carlo simulation that would explain the processes involved.





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King’s lattice framework for ice VI consists of 20 atoms, ten from each sub-lattice. The entire lattice consists of 512 discrete sites. Ice VI is shown in the second figure.

The numbers associated with each atom the height of each atom on the z-axis. The pattern follows in all x,y and z directions for a bigger lattice. The dimensions of the lattice are (√2/8)a× (√2/8)a × (1/8)c, where a and c are 6.27 Å and 5.79 Å.

Molinero and Moore[2] consider water as a monatomic substance that consists only oxygen. They compare the properties of water to other monatomic materials like silicon and germanium. These materials also form tetrahedral structures like Ice. Similar to Ice, their crystalline forms are also less dense than their liquid forms. The energy function used is called a Stillinger- Weber silicon potential and it is given by

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the pairwise interaction between the atoms in the lattice. The second part of the energy is due to the angle formed by triplets of atoms in the tetrahedral units. The parameter λ determines how tetragonal the structure is. For water the value of λ is 23.15,which is higher than silicon (21) and germanium (20). We only consider interactions within a cutoff distance of 4.306 Å. The value of energy for both part of energy beyond this cutoff is zero.

3. Energy Calculation Initially, for testing the programming of the energies we compared it with the results produced in [3]. For developing a Monte Carlo simulation, we need to apply periodic boundary conditions to the lattice. The periodic boundary condition is applied so that all atoms have a bulk environment. There are basically two different environments for the atoms in the sublattice. One in which the atom is bonded to another chain in the same sub-lattice, another in which the atom is bonded to only atoms in the same chain. The atoms on each faces other than the faces formed by z-plane require one more atom to complete the set of four atoms bonded to it. When the atom is on the faces formed by the z-plane, two atoms are required to

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we require two more atoms to complete the set of four atoms. All other edges and corners would need one more atom to complete the set of four. Atoms on edges that are parallel to x and y axis are bounded to the corresponding parallel edge on the same plane while the edges that are parallel to z-axis are bounded to diagonal edges. The figure below shows the chains of the two sub-lattices extending in the z direction. Connecting bonds to other chains are not shown.

We do a static energy calculation on a unit cell. We create a 3×3×3 unit, where each unit is King’s lattice. For energetics, the central unit cell is chosen because we don’t have to apply periodic boundary conditions to it. All atoms in it are bounded to a set of other four atoms.

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height values, keeping a2c constant. The plot of the energy with respect to decreasing c-value is shown below For constant volume the plot shows that there exists other configurations of atoms for which the energy of the unit cell is lower. The values for c and a at the lowest energy configuration are 7.69 Å and 5.44 Å respectively, the lattice is more cubic in this configuration.

The second c and a value for which the energy is lower are 2.88 Å and 8.89 Å. The lattice is compressed in the z direction for this configuration.

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with varying a and c with constant a/c is given below.

We can see that there is a better configuration of atoms for which a/c is constant. The value of c for which the energy is lower is around 4.79 Å. If we increase the value of c instead of decreasing, then the energy reaches zero since atoms become further apart from each other and there are no interactions or bonds.

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More work need to be done in applying the periodic boundary condition to the lattice.

Once periodic boundary condition is applied we could apply the Monte Carlo Metropolis algorithm. We should be able to check the Monte Carlo trajectories and see how the Ice VI structure changes to Ice VII. Or if it does not transition to Ice VII, we could conclude that the Stillinger-Weber model would not be sufficient to simulate the transition of Ice VI to Ice VII.

5. References [1] http://physics.nd.edu/assets/25212/king_dawn_modeling_phase_trans.pdf [2] V. Molinero and E.B. Moore, “Water Modeled As an Intermediate Element between Carbon and Silicon,” J.Phys. Chem B113, 4008-4016 (2009).

[3] M. Laradji and D.P. Landau,” Structural Properties of Si, Ge alloys: A Monte Carlo simulation with the Stillinger-Weber potential,” Phy. Rev. B 51,8 (1995).

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To Table of Contents

Abstract

The star CSS 081231:071126+440405 is a variable star located in the constellation Auriga. The star system is composed of a main sequence star and a denser white dwarf that accretes mass from the main sequence star. While in most cases the infalling matter forms an accretion disk surrounding the white dwarf, the high magnetic field of this star instead causes the ionized gas to fall through the Lagrangian point and follows the magnetic field lines of the white dwarf, creating a stream of particles. This stream, in addition to stabilizing the period of the system, impacts the surface of the white dwarf, creating a hot-spot that dominates the emission from the star.

Observations taken by members of the AAVSO (American Association of Variable Star Observers), as well as data acquired by the VATT telescope in Arizona, allowed us to track the magnitude changes of CSS 081231 across a multitude of periods spanning months. Using this data, we calculated an average orbital period for the star of approximately 117.18279 minutes, with eclipse averaging around around 5.776 minutes. Additionally, we determined what relationship the hot-spot had on stars’ orbit. Furthermore, the magnitude of the system experiences a large change outside of the eclipse that appears to be wavelength dependent, and we determine the effect of this on the star’s orbit. Using data obtained with the 4 meter telescope at KPNO, we then performed spectral analysis on the star to determine how the emission varies between eclipses, focusing the Hα, Hβ, and He II lines. Finally, we used the total flux in various filters to determine color variations.

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To Table of Contents

2 Procedure

2.1 Period and eclipse width determination Using light-curve and spectroscopic data provided After obtaining an average period, we next deby the AAVSO, VATT (Vatican Advanced Technol- cided to see how this period varied over time. To ogy Telescope), and the KPNO (Kitt Peak National do this we first found the base magnitude of the sysObservatory),we set out to determine how the period tem (magnitude outside of eclipse). The hot-spot is and the base magnitude of the system has changed the dominant source of light for the system, and the over time. We started by finding an average orbital brightness of the hot-spot increases as the amount of period for the star, using a list of 23270 observation matter falling onto it increases. Thus the base bagtimes and magnitudes provided by the AAVSO. Af- nitude gives us information about the accretion rate.

ter changing the observation times into Julian dates, By subtracting this base magnitude, we ssubtracted we then used the IDL program “helio jd” to convert off the base magnitude and put all the eclipses in to the heliocentric Julian date to remove any vari- the same phase and plotted the results. We then ations caused by light travel time. Finally, we sub- examined the graph to see if there was any signifitracted off a constant so that the data began on day cant changes over time. In addition we determined zero, corresponding to the Julian day 2454833. the relationship between the accretion rate and the period of the star using the base magnitudes.

In order to get an average period, we first created a program which identifies local maxima in the magnitude and then plotted area around the maximum.



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