Arash Karimbakhsh Asli

Mentor: Shahin Shafiee Department of Mechanical Engineering

Introduction: With measuring the effects on scattering rates before and after applying the magnetic field, the thermal control and improvement in thermal performance in solid materials is anticipated to disclosure interesting data. In this work, it will be considered to utilize either traditional or new materials or magnetite (Fe3O4) and iron filings (random composition of iron oxides). Four phases and procedures can be considered for measurement and evaluation which are included to be in natural conditions of scattering of our solid and without exposing in heat elements as phase one. As a second phase, heat will be released, and the scattering rate of phonons in nanoscale measurement will be recorded. By exposing the sample to a magnetic field, nanoscale magnetic sensing will be applied with electron spin of magnetic material under ambient conditions, which would be the third phase of measurements. Electromagnetic field is a manifestation of changes, and the electron has a charge or its own magnetic field changes in one directly influence the other to scatter the phones and this rate of scattering will be measured. In the final step, heat will be directed to the solid and data will be collected. The conclusion can be reached by determination of constant boundary conditions, sample, insulation, room temperature and recording the heat flux in each step. In a broad view the nanoscale measurements of heat transfer are considered to be the next generation of heat transfer study and the result of this paper aim to develop the nanoscale study to monitor the thermal management strategies with comparison conditions.

Model Equation

The start of our work began with understanding basics of thermal energy concepts. In order to find the heat flow, various models can be utilized, such as Debye model using the Callaway method for calculating the thermal conductivity with a combined scattering time constant. One of the model equation is Qph = C ∞ (D)ħD6(D)[E0i(T1)- E 0i(T2)]dω. This model

∫ illustrates that heat flow can be 0 measured by having transmission function as T when energy is transposing for the carrier ħD in differential of carrier contribution functions at two different temperatures known as function of the Fermi energy or chemical potential, D represents surrogate of energy. In this study, we analyzed the harmonic approximation of lattice vibration that normally doesn’t have very large displacement. Then, we studied electronic bonding; which two main factors of this study are the strength of the bonds and interest in the electronic contribution to thermal energy transport. Further, we categorized the potential atomic amount and the knowledge of quantization of electronic states according to a set of four quantum numbers as 1- Principal (Energy) 2- Magnetic (Zcomponent of orbital angular momentum) 3- Angular momentum (Magnitude of angular momentum) 3- Spin (Up or down). This study gave us the excellence knowledge about the strength of each bonding in terms of atomic phase. By looking forward to the mathematical description of the lattice, we considered the one-dimensional atomic chain lattice for our evaluation. We made a comparison of simplest shape of bonding with spring to simulate the classic physic energy equation with this bonding in order to simplifying the bonding model. In 2-dimensional lattice, we chose graphene due to have good thermal and electrical properties for more study concerns. Graphene comprised of all carbon atoms, so every atoms you see in carbon lattice is carbon, and it’s arranged in honeycomb pattern, group of hexagons that are linked together in two dimensional arrays. In order to finding the best model, we studied the crystal structure lattice to simplifying 3D modeling and crystallography. We chose just one cubic lattice, and we pulled that out of entire crystal lattice. Cubic lattice including Body centered (bcc), Face centered (fcc) and, Diamond (dia).

In terms of lattice study, we found out that materials can be categorized in different classes. One of the most common material is Polycrystalline. Each crystal gain has a repeated lattice structure. The gains are important cause influence mechanical strength and thermal transport properties. We acknowledged that a crystal can be constructed by essentially mapping a bunch of points in a systematic way throughout whatever dimensionality of space that is interested, and it called Bravais lattice. Basically, Bravais lattice is an infinite array of distance points whose position vectors can be describes as :⃑ =n1 G 1 + n2 G 2 + n3 G 3 In this equation, ai and ni represent primitive translation vectors and integer respectively, and i can be varies from zero to infinity. We enhanced our study by covering primitive unit cell. Privative unite cell is a volume of space that, when translated through all possible R, just fits all space, without overlap or voids. This cell contains one lattice point. As we talked about graphene, we studied that graphene is an example of monatomic lattice that still requires a basis atom, a 2D crystal lattice, strong and with tight bond ã=1.42 angstroms. Graphene requires two atoms per point. The Translation vectors can be written as: G 1 = 3 ̃H + √3 GI ; G 2 = 3 GH √3 GI. Each primary atoms are connected by translation vectors a1 and

2 2 2 2 a2. In infinity lattice, we continued with heavy mathematical summation and integrals. So, to avoid that it is going to transform the lattice from real space to reciprocal space. We onsidered the mass density J(x) of a 1D atomic lattice, lattice periodicity dictates to J(x + ma) = J(x) in Chain of atoms. The Fourier series form of density is: J(x) =∑" Jn exp{iGnx} = J(x + ma) = ∑" Jn exp{iGn(x+ma)} =∑" Jn exp {iGnx} exp {iGnma} exp {iGnma} = 1 Gnma = 2π * integer. By Generalizing to 3D: Gn . Rm = 2π * integer Which vector G is in reciprocal space vector and R is represented in real space. In terms of Reciprocal Lattice, it is more convenient to express spatial dependencies in terms of wave-vectors instead of wavelength. Reciprocal lattice (RL) is like the inverse of a Bravais lattice G is the wave vector and satisfies K =k1 L⃑ 1 + k2 L⃑ 2 + k3 L⃑ 3. Ki represent integers as: L⃑ i = 2π G⃑ j × G⃑ k In this equation, b is translation in reciprocal space in reciprocal space and wave-vector

G⃑ 1 .( G⃑ 2 × G⃑ 3)

instead of Wavelength # wave-vector (inversely proportional) and “a” is represented in translation in

M real space.

Summary

Our intention of this study is to find the best possible way of understanding thermal energy at nanoscale regards to fulfill the abstract that was written before by us. We are going to continue this study in order to perform either simulation model equation or academic lab work. The completion of this study will enlighten the chosen way, and it aimed to be worked on an article paper in order to be submitted in form of conference or journal.

Refrences:

[1] Jin, H., Restrepo, O., Antolin, N. et al. Phonon-induced diamagnetic force and its effect on the lattice thermal conductivity. Nature Mater 14, 601–606 (2015). [2] Fundamentals of Nanotransistors, By (author): Mark Lundstrom (Purdue University, USA), ISBN: 978981-121-298-7 [3] Applied Thermal Measurements at the Nanoscale: A Beginner's Guide to Electrothermal Methods, By (author): Zhen Chen (Southeast University, China) and Chris Dames (University of California, Berkeley,

USA), ISBN: 978-981-3271-10-4