Diamond and Other Carbon Materials for Solar-Thermionic Energy Conversion Timothy Fisher tsfisher@purdue.edu School of Mechanical Engineering, and Birck Nanotechnology Center Purdue University October 19, 2004 Stanford GCEP Solar Energy Workshop 1
Outline General overview Sunlight Thermionic emission spectroscopy Solar-thermal collector design Ongoing work Concentrator Solar Receiver Summary and conclusions Direct Energy Conversion Device [Not to Scale] 2
Thermionic Emission Involves release of electrons from solids, usually heated to high temperature Bulk material current density described by Richardson- Dushmann equation: J Φ = AT 2 exp kt B Brief Background µ 1 ε ν (1,1) Emitted electrons φ 1 E=0 cathode, T 1 Thermal-field emission effect of space charge Φ 1 Φ 2 E vac vacuum or vapor φ 2 anode, T 2 Electron motive diagram for a thermionic power generation diode, with T 1 > T 2. µ 2 3
Electron Emission Spectroscopy with Vance Robinson, grad student Hemispherical energy analyzer measures electron count rate at a given energy (±0.04eV) Heater in vacuum chamber is electrically and thermally isolated. Vacuum pressure: ~10-7 torr Temperature measured by infrared pyrometer (±20K) 4
Analyzer Calibration Calibration Measure work function of tungsten (100) with analyzer (φ = 4.56 ev) Adjust analyzer work function accordingly Analyzer Work Function 4.38 ev 4.142 ev Run Measured Work Function 1 4.798 ev 2 4.791 ev 1 4.557 ev Intensity (arb units) 2 4.554 ev Electron Energy (ev) 5
TEEDs from H-terminated Diamond Approximate EWF (effective work function) corresponding to lowenergy peak: 3.5eV High-energy peak corresponds to EWF = 4.62eV, approximately that of graphite Shift of maximum intensity to high-energy peak after heating to 781 C demonstrates permanent change in surface chemistry Intensity (a. u.) 1 0.8 0.6 0.4 0.2 0 606C before max temp 781C max temp 606C after max temp 3 3.5 4 4.5 5 5.5 6 6.5 Energy (ev) With G. Swain (Michigan State); Robinson et al., in review, Diamond Rel. Matls, 2004 6
Partial Pressure, Nitrogen Equivalent (torr) 3.00E-06 606C before max temp 781 C max temp interest: 2.50E-06 1 (+H), 2 (H 2 ) and 16 606 C after max temp Residual Gas Analyzer Mass-to-charge ratios of (CH 4 ) H2.00E-06 2 occupied a greater percentage of the vacuum chamber gas after the heating cycle 1.50E-06 than it did before. contrary to the general trend of diminishing partial pressures witnessed in the other species. 1.00E-06 unique response may indicate that H 2 has been supplied to the vacuum chamber from the hydrogen-terminated film through a desorption process. 5.00E-07 0.00E+00 1 3 5 7 911 13 1517 Partial Pressure, Nitrogen Equivalent (torr) 19 2123 1.20E-07 1.00E-07 8.00E-08 6.00E-08 4.00E-08 2.00E-08 0.00E+00 25 2729 31 3335 Mass-to-Charge Ratio 1 2 16 (m/z) Charge-to-Mass Ratio (m/z) Mass-to-Charge Ratio 37 3941 43 4547 49 7
Mat of Herringbone Graphitic Carbon Nanofibers (GCNFs) GCNFs grown by pyrolysis of CO over catalysts Produce a mat of fibers of ~50nm diameter with C. Lukehart (Vanderbilt); Robinson et al., in review Nano Letters, 2004. 8
Intercalation of Potassium in GCNFs (004) C 8 K Herringbone (101) (008) (116) 5 15 25 35 45 55 65 75 85 95 2 theta Powder XRD Scan (Cu Ka radiation) of a Stage 1 C8K Potassium Metal/Herringbone GCNF Intercalate line pattern = bulk C8K potassium metal/bulk graphite intercalate CCDC standard 9
TEEDs of GCNFs Experiments on arrays of graphitic carbon nanofibers with and without potassium intercalation Intensity (a. u.) 1 0.8 0.6 0.4 0.2 0 600C w/ K 700C w/ K 750 C w/o K intercalation 1.5 2.5 3.5 4.5 5.5 Energy (ev) 10
Integrated Thermionic-Solar Concentrator Modeling with Paul Majsztrik, grad student Concentrator and receiver design Sketches of parabolic dish concentrator and cavity receiver with coordinate systems. The solar collector system, consisting of receiver and concentrator, shows the relative size and orientation of the components. 11
Conical Cavity Receiver Reduces radiation losses caused by reemission and reflection Efficiency depends on relative dimensions and surface properties 12
Solar Collection Modeling Schematic Network 13
Concentrator Flux Profiles Solar flux in Focal Plane Concentration Factor (AM0) 35000 30000 25000 20000 15000 10000 5000 0 f=5 f=4 f=6 0 10 20 30 40 Radial distance (mm) Flux profile in different planes 25,000 focal plane h=25mm f = focal length in m Concentration factor 20,000 15,000 10,000 5,000 h=50mm h=75mm h=100mm 0 0 20 40 60 80 100 120 Radial distance(mm) 14
Model Assumptions Source Sun treated as uniformly radiating disk with an angular radius of θ S = 4.7 mrad. Solar irradiation G = 1350 W/m 2 at concentrator aperture. Concentrator Perfectly smooth and specularly reflective surface with reflectivity ρ c = 0.9 (all absorbed radiation is lost) Rim radius r c = 1.5m Focal length f = 1.5m No losses due to tracking errors Includes loss due to shading of incoming solar radiation by receiver Receiver Perfectly smooth and specularly reflective walls with reflectivity ρ r = 0.95 (all absorbed radiation is lost) Gray absorber with emissivity ε = 0.95 and diffuse reflection/ radiation (material properties of carbon) Uniform temperature distribution over absorber surface Absorber radius r ab = 0.15 m Cavity height h and aperture radius r ap ; variable 15
Simulated Receiver Efficiency Efficiency defined as fraction of incident solar radiation on concentrator retained by receiver Solar collector efficiency for different receiver dimensions. h is the receiver height. 16
Integrated Thermionic-Solar Concentrator Modeling Emission occurs from cathode to anode and anode to cathode. Current densities given by Richardson s equation: J H 2 φ C + V = ATH exp kt B H J C 2 φc = ATC exp KT B H Hot electrode (cathode) Cold electrode (anode) Where A = constant, φ = work function, V = voltage, and T = temperature of Anode (C) and Cathode (H). 17
Simulated System Efficiency Efficiency of the solar collector and entire system as a function of output voltage. Results for two work functions are given. Majsztrik et al., AIAA Thermophys. Conf., 2002 18
Ongoing Work: Thermionic Emission Motivation from a Quantum Wire with Yang Liu, grad student Quantum-confined materials may allow higher thermionic current densities and thus higher energy conversion capacities Non-equilibrium Green s Function (NEGF) formalism provides a means of modeling interfacial transport between bulk (3D) and confined regions 19
Quantum Confinement Effects L z L y 3D Emitted electrons a 1D a L x Confinement influences energy states of electrons ε ε 2 h = + + 2m ( 2 2 2 k k k ) 3 D * x y z hπ h 2m 2m = W + ε ν ( a) 2 2 ( 2) a 2 2 * 1 D = k ( ), * x + n * y + nz ny, z = integer L * Square-wire approximation after Sun et al., Appl. Phys. Lett., 74, 4005 (1999) 20
Electron Supply Function Supply function gives number of electrons striking the emitting surface per unit time, area, and energy Noticeable increase in highenergy supply function for 1 nm quantum wire Larger wires are similar to bulk Supply Function (s -1 m -2 ev -1 ) N 10 34 10 33 10 32 10 31 10 30 10 29 10 28 10 27 10 26 10 25 10 24 10 23 10 22 10 21 10 20 10 19 10 18 10 17 10 16 10 15 10 14 10 13 10 12 10 11 1D 10 33 2 4 10 32 2 4 10 31 2 4 10 30 2 4 10 29 2 ( W) -1-0.5 0 0.5-1 0 1 2 3 4 Reduced Energy, W' (ev) a = 1 nm a = 2 nm a = 4 nm bulk (3D) 1 W +εν( a) E F = 1+ exp πh kt B 1 21
Model for Thermionic Emission from a Quantum Wire Bulk1 Quantum Wire [ H ] Vacuum Bulk2 [ (E)] 1 [ (E)] 2 Quantum wire and vacuum are discretized with a one-band effective mass model and the energy levels are described by a Hamiltonian matrix Coupling at interfaces is described by self-energy matrices [ (E)] 2 [ (E)] 1 22
Handling of Boundaries [ H + iδ ] R [ H ] [ H + iδ ] R [ H ] [ τ ] { Φ R } Device { Φ } + { χ } Reservoir R Reservoir Device { ψ } Reservoir Device Reservoir Device + EI R 0 R H R + iδ τ Φ + χ = τ EI H ψ 0 [ EI ( H + )]{ ψ } = { S} 23
Discretized Model (1D) Contact1 T 1, µ 1 Quantum Wire (Cathode) Vacuum Contact2 (Anode) T, µ 2 2 Emission Current from QW: Fermi Function: f ( E) Transmission Function: = + e 1,2 ( E µ )/ k T 2q I = T( E)[ f1( E) f2( E)] de h 1 1,2 B 1,2 1 T( E) = Trace( ΓGΓ G + ) 1 2 Current flows because of different Fermi functions: Thermionic emission Field emission T T 1 2 µ 1 µ 2 Non-equilibrium 24
Emitted Energy Distribution (3D) µ = 4.5eV Φ = 2.0eV 25
Quantum Confinement Size Effects From 3D to 1D: For a wire with a finite cross section, total current is calculated by summation of contributions from each subband 26
Conclusions Thermionic solar converters will require materials with low work functions Ideally φ 1eV Nanoscale material synthesis offers some promise of customizing properties Concentrated solar collection can achieve temperatures required for thermionic operation Quantum confinement may improve conversion capacity and thus improve prospects for moderate-temperature operation 27