Production of silicon carbide nanowires by induction heating
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PRODUCTION OF SILICON CARBIDE NANOWIRES BY INDUCTION HEATING. Kendra L. Wallis June 2006. Overview. Introduction SiC and Chemical Kinetics Induction Heating Testing and Use of Equipment Reaction Kinetics of SiC Nanowires Elimination of Excess Reactants Conclusions. Introduction.

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Kendra L. Wallis

June 2006


  • Introduction

  • SiC and Chemical Kinetics

  • Induction Heating

  • Testing and Use of Equipment

  • Reaction Kinetics of SiC Nanowires

  • Elimination of Excess Reactants

  • Conclusions


Nano-structure Research

  • Hot topic today—nanostructured materials research

  • Improved physical properties

  • Flexibility of designing materials from nanoblocks

  • Nanocomposites—combination of 2 or more phases, 1 or more is nano-size


  • Need for low-cost, hard materials for use at high temperature

  • SiC: ceramic composite

  • Nanostructured SiC demonstrates improved high temperature mechanical properties

  • Carbon MWNTs demonstrate high hardness and fracture toughness

What to do?

  • Make SiC nanowires

  • Study reaction

  • Study structure

  • Measure hardness and toughness

  • Correlate properties with structure

  • New uses may include hard fibers for armor

SiC and Chemical Kinetics


  • Moissanite—found in meteorites, rare

  • Synthetic SiC

    • Many ways to make it

    • Many uses

  • High melting point (2700°C) and highly inert

  • High thermal conductivity

  • High E-field breakdown and max current density

  • Hardness 9.25 (diamond is 10)

Reaction Kinetics in Solids

  • Product forms between reactants

  • One reactant passes through product barrier phase

  • Product layer grows, diffusion takes longer

  • Reaction at interface

    • Diffusion controlled

    • Nucleation controlled




Si diffuses through SiC product barrier phase

Reaction Rate

  • Chemical reaction

  • Rate of increase of product

  • Measure reaction rate for several temperatures

  • Fit to theoretical model to find reaction mechanism

General Rate Law

 = fractional remains of reactant; k = rate constant

Summary of ModelsExpected Values of n

Activation Energy

  • Energy required to initiate process

  • Arrhenius equation

    Rate constant k at temperature T

    R = universal gas constant

    E = activation energy

    A = constant

  • Plot ln k vs. 1/T to find E

Parameters in Reaction Kinetics of Solids

  • Reactants: Si and C MWNT

    Various molar ratios

  • Particle sizes: Si APS 30 nm (98%)

    C MWNT (95%) OD 60-100 nm, L 5-15 m

  • Mixing – ultrasonic mix in acetone

    Consider other methods

  • Products: SiC nanowires

    Look for formation of anything else

  • Temperature – effects on all parameters

Nano-particle Reactants

  • Particle size affects:

    • Reaction rate

    • Physical properties

    • Mechanical properties

  • Decrease particle size—increases surface area, which may explain enhanced hardness

  • Create product with small grain size

Carbon MWNT

  • One-dimensional system

  • Carbon (1s22s22p2) has 4 valence electrons

  • In 2-D, sp2 hybridization forms graphite

  • Nanotubes exhibit sp2 hybridization – but cylindrical not planar

  • Graphene sheet of 6-member C rings in honeycomb lattice

  • Multiple concentric cylindrical shells with common axis

  • Each shell is cylindrical graphene sheet, d = 1 to 10 nm

Induction Heating

Induction Heating

Faraday’s law

Joule’s law

Inductoheat Statipower BSP12

  • 480 V, 60 Hz, 3f AC current

  • Solid state inverter

    • Converts current to DC

    • Then to high frequency AC (30 kHz)

  • Variable ratio isolation transformer—feedback loop to adjust V and P for set I

  • Tuning capacitor—impedance matching

  • Coil

Induction Furnace

Current through a coil produces nearly uniform magnetic field down the center

Alternating current  Changing magnetic field Current flows around cylindrical shellSame frequency, opposite direction

 = 30 kHz max

End View of Cylindrical Shell

  • R = inner radius

  • d = wall thickness

  •  = skin depth

  • d0 = screening depth

Skin Effect

Faraday’s law

Current flowing in a conductor flows only near the surface

Ampere-Maxwell law

Electromagnetic wave equation for E-field

Complex wave number k

Substitute solution into wave equation

For a good conductor

Plane wave includes periodicity in time and space plus damping term in space

attenuation factor

Skin depth

For a wave traveling in the z-direction:

e-folding distance

skin depth

Cylindrical Shell inside Coil

  • External magnetic field B0 along z-axis

  • Frequency 

  • Faraday’s law

  • Current around shell induces magnetic field BC, screening inside of shell

  • Field inside BI = B0 + BC

Screening Depth

  • Derived by Fahy, et al.1

  • Screening factor – ratio of field at inner wall to applied field

  • Induced current falls off toward center as function of wall thickness

  • Interior screened when d > d0 where

1Fahy S., Kittel, C., Louie, S., Am. J. Phys. 56 (11) 1998 989

Screening of external field Bout by cylindrical shell, radius R, wall thickness d in units of 2 / R, where  is skin depth

d = d0 Bin = 0.7 Bout

d =2 d0 Bin < ½ Bout

Heat Generated by Resistive Losses

Joule’s law

Current density

Current flows around shell,  area element dr dz

Total current

Resistive Heat Generated

  • RE electrical resistance

  • RE =  L / A, L = 2R, A = d L

  • Resistivity varies with temperature

  • Conductivity  = 1 / 

  • Heat per unit length of cylindrical shell

  • Q proportional to R2 d 

Testing andUse of Equipment

Testing and Use of Equipment

  • Induction furnace

    • 25 kW maximum power

    • 30 kHz frequency

  • Repeatable and consistent heating pattern

  • Heats quickly—measure accurate reaction time

  • Safe and efficient

  • Non-polluting, environmentally friendly

  • Non-conducting material not affected

Graphite Crucible at 1400C

Equilibrium Temperature

  • 2 min to equilibrium

  • Increases with input power

Graphite Crucible

  • Graphite aged with repeated use

  • Possible explanations graphitization oxidation


  • Heated in nitrogen

  • Change in equilibrium temperature reduced-not eliminated

  • Rate of heating reduced

Stainless Steel Crucible

  • Heated in N2

    • no graphitization

    • no oxidation

  • Repeatable

  • Temperature increases with input power

  • Heats faster

3 Stainless Steel Crucibles

STn – small radius, thin wall

LTk – large radius, thick wall

STk – small radius, thick wall

Q = R2dQ0

  • Skin effect insignificant

  • Screening may be related to unexpected temperature of STk

Reaction Kineticsof SiC Nanowires

Reaction Kinetics

  • Requires knowledge of quantity of product and/or quantity of reactant remaining as function of time

  • Determine mass concentration of SiC product to remaining Si + SiC

  • Correlation between XRD peak intensity and mass concentration determined experimentally by Pantea and confirmed here

y = 0.36x2 + 0.64x

Reaction TimeFast heating and cooling reduce error

uncertainty (20s)

uncertainty (10s)

Reaction time

Reaction Rate

  • General Rate Law

  • Find rate constant k and parameter n for different temperatures

  • Calculate SiC concentration  from measured XRD peak intensities

  • Measure sintering time

Concentration v TimeFit to General Reaction Rate Law= 1 – exp [ - (kt)n]

k and n

  • k = 7.6 x 10-6+/- 5 x 10-6

  • n = 0.46 +/- 0.05

  • Refer to Table of Rate Laws

    • Suggests diffusion-controlled 1-dimensional growth with decelerating nucleation rate

  • Data at more temperatures will give better understanding of reaction mechanism

Elimination of Excess Reactants

X-ray Diffraction – Mixture

XRD Characteristic Peaks

Identity 2 

  • C MWNT26.28

  • Si (111)28.44

  • SiC (111)35.74

  • Si (220)47.35

  • SiC (220)60.02

X-ray Diffraction – Sintered 2 min at 1200°C

X-ray Diffraction – Burned 2 hr at 700°C

X-ray Diffraction – Washed in KOH



  • Induction heating—safe and efficient method of producing nanostructured SiC

  • Oxygen-free environment preferred

  • Material and geometry of crucible should be considered

  • Reaction rate constant at 1040 °C suggests diffusion-controlled 1-dimensional growth with decelerating nucleation rate

  • Burning in air, washing with KOH—safe and efficient method of purification

Future Work

  • Activation energy—explain reaction mechanism

  • Nanostructure of SiC nanowires

    • X-ray (grain size and strain)

    • Raman (grain size and strain)

    • TEM (nanowires)

  • Mechanical properties

  • Correlation between mechanical properties and structure

  • SiC nanograss

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