Advanced Energy Materials

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Advanced Energy Materials

Edited by

Ashutosh Tiwari and Sergiy Valyukh

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ISBN 978-1-118-68629-4

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10 9 8 7 6 5 4 3 2 1

v

Contents

Preface xv

1 Non-imaging Focusing Heliostat 1Kok-Keong Chong1.1 Introduction 11.2 The Principle of Non-imaging Focusing

Heliostat (NIFH) 31.2.1 Primary Tracking (Global Movement for

Heliostat Frame) 31.2.2 Secondary Tracking (Local Movement

for Slave Mirrors) 91.3 Residual Aberration 10

1.3.1 Methodology 121.3.2 Optical Analysis of Residual Aberration 19

1.4 Optimization of Flux Distribution Pattern for Wide Range of Incident Angle 29

1.5 First Prototype of Non-imaging Focusing Heliostat (NIFH) 351.5.1 Heliostat Structure 361.5.2 Heliostat Arm 381.5.3 Pedestal 391.5.4 Mirror and Unit Frame 401.5.5 Hardware and Software Control System 401.5.6 Optical Alignment of Prototype Heliostat 411.5.7 High Temperature Solar Furnace System 46

1.6 Second Prototype of Non-imaging Focusing Heliostat (NIFH) 521.6.1 Introduction 521.6.2 Mechanical Design and Control System

of Second Prototype 53

vi Contents

1.6.3 High Temperature Potato Skin Vaporization Experiment 56

1.7 Conclusion 64Acknowledgement 65References 65

2 State-of-the-Art of Nanostructures in Solar Energy Research 69Suresh Sagadevan2.1 Introduction 702.2 Motivations for Solar Energy 71

2.2.1 Importance of Solar Energy 712.2.2 Solar Energy and Its Economy 742.2.3 Technologies Based on Solar Energy 752.2.4 Photovoltaic Systems 76

2.3 Nanostructures and Different Synthesis Techniques 772.3.1 Classifi cation of Nanomaterials 782.3.2 Synthesis and Processing of Nanomaterials 79

2.4 Nanomaterials for Solar Cells Applications 812.4.1 CdTe, CdSe and CdS Thin-Film PV Devices 822.4.2 Nanoparticles/Quantum Dot Solar Cells

and PV Devices 822.4.3 Iron Disulfi de Pyrite, CuInS

2 and Cu

2ZnSnS

4 84

2.4.4 Organic Solar Cells and Nanowire Solar Cells 852.4.5 Polycrystalline Thin-Film Solar Cells 86

2.5 Advanced Nanostructures for Technological Applications 872.5.1 Nanocones Used as Inexpensive Solar Cells 882.5.2 Core/Shell Nanoparticles towards PV

Applications 892.5.3 Silicon PV Devices 902.5.4 III-V Semiconductors 91

2.6 Theory and Future Trends in Solar Cells 922.6.1 Theoretical Formulation of the Solar Cell 932.6.2 The Third Generation Solar Cells 96

2.7 Conclusion 97References 97

Contents vii

3 Metal Oxide Semiconductors and Their Nanocomposites Application towards Photovoltaic and Photocatalytic 105Sadia Ameen, M. Shaheer Akhtar, Hyung-Kee Seo and Hyung Shik Shin3.1 Introduction 1063.2 Metal Oxide Nanostructures for Photovoltaic

Applications 1083.3 TiO

2Nanomaterials and Nanocomposites for the

Application of DSSC and Heterostructure Devices 1093.3.1 Fabrication of DSSCs with TiO

2 Nanorods

(NRs) Based Photoanode 1093.3.2 Fabrication of DSSCs with TiO

2 Nanocomposite

Based Photoanode 1163.3.3 TiO

2 Nanocomposite for the Heterostructure

Devices 1183.4 ZnO Nanomaterials and Nanocomposites

for the Application of DSSC and Heterostructure Devices 1213.4.1 Fabrication of DSSCs with ZnO Nanotubes

(NTs) Based Photoanode 1213.4.2 Fabrication of DSSCs with Nanospikes

Decorated ZnO Sheets Based Photoanode 1253.4.3 Fabrication of DSSCs with ZnO Nanorods

(NRs) and Nanoballs (NBs) Nanomaterial Based Photoanode 129

3.4.4 Fabrication of DSSCs with Spindle Shaped Sn-Doped ZnO Nanostructures Based Photoanode 132

3.4.5 Fabrication of DSSCs with Vertically Aligned ZnO Nanorods (NRs) and Graphene Oxide Nanocomposite Based Photoanode 135

3.4.6 ZnO Nanocomposite for the Heterostructures Devices 139

3.4.7 Fabrication of Heterostructure Device with Doped ZnO Nanocomposite 141

3.8 Metal Oxide Nanostructures and Nanocomposites for Photocatalytic Application 1443.8.1 ZnO Flower Nanostructures for Photocatalytic

Degradation of Crystal Violet (Cv)Dye 1443.8.2 Advanced ZnO-Graphene Oxide Nanohybrid

for the Photocatalytic Degradation of Crystal Violet (Cv)Dye 147

viii Contents

3.8.3 Effective Nanocomposite of Polyaniline (PANI) and ZnO for the Photocatalytic Degradation of Methylene Blue (MB) Dye 150

3.8.4 Novel Poly(1-naphthylamine)/Zinc Oxide Nanocomposite for the Photocatalytic Degradation of Methylene Blue (MB) Dye 152

3.8.5 Nanocomposites of Poly(1-naphthylamine)/SiO

2 and Poly(1-Naphthylamine)/TiO

2 for the

Photocatalytic Degradation of Methylene Blue (MB) Dye 155

3.9 Conclusions 1573.10 Future Directions 158References 159

4 Superionic Solids in Energy Device Applications 167Angesh Chandra and Archana Chandra4.1 Introduction 1674.2 Classifi cation of Superionic Solids 1704.3 Ion Conduction in Superionic Solids 1714.4 Important Models 173

4.4.1 Models for Crystalline/Polycrystalline Superionic Solids 173

4.4.2 Models for Glassy Superionic Solids 1784.4.3 Models for Composite Superionic Solids 1864.4.4 Models for Polymeric Superionic Solids 194

4.5 Applications 1994.5.1 Solid-State Batteries 2004.5.2 Fuel Cells 2014.5.3 Super Capacitors 202

4.6 Conclusion 203References 204

5 Polymer Nanocomposites: New Advanced Dielectric Materials for Energy Storage Applications 207Vijay Kumar Thakur and Michael R. Kessler5.1 Introduction 2085.2 Dielectric Mechanism 209

5.2.1 Dielectric Permittivity, Loss and Breakdown 2095.2.2 Polarization 212

Contents ix

5.3 Dielectric Materials 2135.4 Demand for New Materials: Polymer Composites 2145.5 Polymer Nanocomposites: Concept and Electrical

Properties 216

5.5.1 Polymer Nanocomposites for Dielectric Applications 217

5.6 Conclusion and Future Perspectives 245References 247

6 Solid Electrolytes: Principles and Applications 259S.W. Anwane6.1 Introduction 2606.2 Ionic Solids 262

6.2.1 Bonds in Ionic Solids 2626.2.2 Structure of Ionic Solids 264

6.3 Classifi cation of Solid Electrolytes 2656.4 Criteria for High Ionic Conductivity and Mobility 2666.5 Electrical Characterization of Solid Electrolyte 267

6.5.1 DC Polarization 2676.5.2 Impedance Spectroscopy 269

6.6 Ionic Conductivity and Temperature 2716.7 Concentration-Dependent Conductivity 2746.8 Ionic Conductivity in Composite SE 2756.9 Thermodynamics of Electrochemical System 2786.10 Applications 280

6.10.1 Solid-State Batteries 2806.10.2 Sensors 2846.10.3 SO

2 Sensor Kinetics and Thermodynamics 286

6.12 Conclusion 291References 291

7 Advanced Electronics: Looking beyond Silicon 295Surender Duhan and Vijay Tomer7.1 Introduction 296

7.1.1 Silicon Era 2967.1.2 Moore’s Law 298

7.2 Limitations of Silicon-Based Technology 2997.2.1 Speed, Density and Design Complexity 2997.2.2 Power Consumption and Heat Dissipation 2997.2.3 Cost Concern 300

x Contents

7.3 Need for Carbon-Based Electronics Technology 3007.4 Carbon Family 303

7.4.1 Carbon Nanotube 3047.4.2 Graphene 307

7.5 Electronic Structure of Graphene and CNT 3097.6 Synthesis of CNTs 311

7.6.1 Arc Discharge Method 3117.6.2 Pyrolysis of Hydrocarbons 3117.6.3 Laser Vaporization 3127.6.4 Electrolysis 3127.6.5 Solar Vaporization 312

7.7 Carbon Nanotube Devices 3137.7.1 Nanotube-Based FET Transistors CNTFET 3137.7.2 CNT Interconnect 3147.7.3 Carbon Nanotube Sensor of Polar Molecules 3157.7.4 Carbon Nanotube Crossbar Arrays for

Random Access Memory 3167.8 Advantages of CNT-Based Devices 317

7.8.1 Ballistic Transport 3177.8.2 Flexible Device 3177.8.3 Low Power Dissipation 3187.8.4 Low Cost 318

7.9 Issues with Carbon-Based Electronics 3197.10 Conclusion 322References 323

8 Ab-Initio Determination of Pressure-Dependent Electronic and Optical Properties of Lead Sulfi de for Energy Applications 327Pooja B and G. Sharma8.1 Introduction 3278.2 Computational Details 3288.3 Results and Discussion 329

8.3.1 Phase Transition and Structural Parameters 3298.3.2 Pressure Dependent Electronic Properties 3338.3.3 Pressure-Dependent Dielectric Constant 340

8.4 Conclusions 340Acknowledgements 342References 342

Contents xi

9 Radiation Damage in GaN-Based Materials and Devices 345S.J. Pearton, Richard Deist, Alexander Y. Polyakov, Fan Ren, Lu Liu and Jihyun Kim9.1 Introduction 3469.2 Fundamental Studies of Radiation Defects in

GaN and Related Materials 3479.2.1 Threshold Displacement Energy: Theory

and Experiment 3479.2.2 Radiation Defects in GaN: Defects Levels,

Effects on Charge Carriers Concentration, Mobility, Lifetime of Charge Carriers, Thermal Stability of Defects 349

9.3 Radiation Effects in Other III-Nitrides 3669.4 Radiation Effects in GaN Schottky Diodes, in

AlGaN/GaN and GaN/InGaN Heterojunctions and Quantum Wells 370

9.5 Radiation Effects in GaN-Based Devices 3749.6 Prospects of Radiation Technology for GaN 3769.7 Summary and Conclusions 379Acknowledgments 380References 380

10 Antiferroelectric Liquid Crystals: Smart Materials for Future Displays 389Manoj Bhushan Pandey, Roman Dabrowski and Ravindra Dhar10.1 Introduction 390

10.1.1 Molecular Packing in Liquid Crystalline Phases 391

10.2 Theories of Antiferroelectricity in Liquid Crystals 39810.3 Molecular Structure Design/Synthesis of AFLC

Materials 40210.4 Macroscopic Characterization and Physical

Properties of AFLCs 40410.4.1 Experimental Techniques 40410.4.2 Dielectric Parameters of AFLCs 41010.4.3 Switching and Electro-Optic Parameters 419

10.5 Conclusion and Future Scope 425Acknowledgements 426References 426

xii Contents

11 Polyetheretherketone (PEEK) Membrane for Fuel Cell Applications 433Tungabidya Maharana, Alekha Kumar Sutar, Nibedita Nath, Anita Routaray, Yuvraj Singh Negi and Bikash Mohanty11.1 Introduction 434

11.1.1 What is Fuel Cell? 43611.2 PEEK Overview 442

11.2.1 Applications of PEEK 443 11.2.2 Why PEEK is Used as Fuel Cell Membrane 445

11.3 PEEK as Fuel Cell Membrane 44611.4 Modifi ed PEEK as Fuel Cell Membrane 452

11.4.1 Sulphonated PEEK as Fuel Cell Membrane 45311.5 Evaluation of Cell Performance 45911.6 Market Size 45911.7 Conclusion and Future Prospects 460Acknowledgement 461References 461

12 Vanadate Phosphors for Energy Effi cient Lighting 465K. N. Shinde and Roshani Singh12.1 Introduction 46512.2 Some Well-Known Vanadate Phosphors 46612.3 Our Approach 46912.4 Experimental Details 46912.5 Results and Discussion of

M3–3x/2

(VO4)

2:xEu (0.01 ≤ x ≤ 0.09 for M = Ca

and 0 ≤ x ≤ 0.3 for M = Sr,Ba) Phosphors 470 12.5.1 X-ray Diffraction Pattern of

M3–3x/2

(VO4)

2:xEu Phosphor 470

12.5.2 Surface Morphology of M

3–3x/2(VO

4)

2:xEu Phosphor 474

12.5.3 Photoluminescence Properties of M

3–3x/2(VO

4)

2: Phosphor 476

12.6 Effect of Annealing Temperature on M

3–3x/2(VO

4)

2:xEu (x = 0.05 for M = Ca, x = 0.1 for

M = Sr and x = 0.3 for M = Ba) Phosphors 484 12.6.1 X-ray Diffraction Pattern of

M3–3x/2

(VO4)

2:xEu phosphor 484

Contents xiii

12.6.2 Surface Morphology of M3–3x/2

(VO4)

2:xEu

phosphor 486 12.6.3 Photoluminescence Properties of

M3–3x/2

(VO4)

2:xEu phosphor 488

12.7 Conclusions 494References 496

13 Molecular Computation on Functionalized Solid Substrates 499Prakash Chandra Mondal13.1 Introduction 50013.2 Molecular Logic Gate on 3D Substrates 50413.3 Molecular Logic Gates and Circuits on

2D Substrates 507 13.3.1 Monolayer-Based System 507

13.4 Combinatorial and Sequential Logic Gates and Circuits using Os-polypyridyl Complex on SiO

× Substrates 514

13.5 Multiple Redox States and Logic Devices 52013.6 Concluding Remarks 523Acknowledgements 523References 525

14 Ionic Liquid Stabilized Metal NPs and Their Role as Potent Catalyst 529Kamlesh Kumari, Prashant Singh and Gopal K.Mehrotra14.1 Introduction 53014.2 Applications of Metal Nanoparticles 53114.3 Shape of Particles 53214.4 Aggregation of Particles 53314.5 Synthesis of Metal Nanoparticles 53314.6 Stability against Oxidation 53414.7 Stabilization of Metal Nanoparticles in Ionic Liquid 53514.8 Applications of Metal NPs as Potent Catalyst

in Organic Synthesis 54014.8 Conclusion 544References 544

xiv Contents

15 There’s Plenty of Room in the Field of Zeolite-Y Enslaved Nanohybrid Materials as Eco-Friendly Catalysts: Selected Catalytic Reactions 555C.K. Modi and Parthiv M. Trivedi15.1 Introduction 55615.2 Types of Zeolites 55715.3 Methodology 55915.4 Characterization Techniques 56115.5 Exploration of Zeolite-Y Enslaved Nanohybrid

Materials 562 15.5.1 Catalytic Liquid-Phase Hydroxylation

of Phenol 565 15.5.2 Catalytic Liquid-Phase Oxidation of

Cyclohexane 57115.6 Conclusions 576References 579

Index 585

xv

Preface

Energy plays a critical role in the developmental progression of an emerging society. A high standard of living and an increasing world population require more and more amounts of energy. At the same time, the standard energy sources based on fossil fuels are limited and pollute th e environment, leading to climate change on a global scale. In order to avoid an energy crisis, the research efforts of many scientifi c centers around the globe are being directed towards searching for new solutions and improving those already existing in the energy sector. In parallel with the growth rate of renewable energy, essential attention is being paid to the develop-ment of advanced methods and materials for effective utilization of energy resources. Technological advantages will help to overcome energy-related diffi culties. Among the main criteria for the viability of new energetic techniques are effi ciency, cost, usability and envi-ronmental infl uence.

This book summarizes the current status of know-how in the fi elds of advanced materials for energy-associated applications, in particular, photovoltaics, effi cient light sources, fuel cells, energy saving technologies, nanostructured materials, etc. Tendencies for future development are also discussed. A good understanding of the excited state reactivity of photoactive materials would help to prepare new materials and molecules capable of absorbing light over a given wavelength range for use in driving electron trans-fer. There has been scientifi cally and technologically well-equipped materials science exploration into the possibility of developing and optimizing charge separation in light-harvesting architectures. However, it has yet to bear fruit due to the diffi culty of transport-ing electrons and holes to corresponding electrodes. Modeling charge mobility in semiconductors is complicated due to the pres-ence of bulk heterogeneity in the structure. The understanding of

xvi Preface

the interface between the metal electrode and the active materials, where charge collection takes place, is even more intriguing.

The design and fabrication of molecular-based information pro-cessing devices on conducting substrates have been key areas of research in materials science. One particularly attractive applica-tion in this area is the conversion of solar energy into fuel, which is currently being proposed as a cheaper alternative for energy conversion. Energy storage technologies are dealt with in some chapters. High energy density capacitors are of particular signifi -cance, for example, in defense-related applications, where tasks in remote areas without traditional energy resources demand novel approaches to energy storage. Polymer nanocomposites offer attractive, low-cost potential storage systems for high-energy den-sity capacitors. Their tailored characteristics offer unique combina-tions of properties which are expected to play a vital role in the development of new technologies for energy storage applications.

Other chapters consider the aspects of solar energy. Rapid prog-ress in photovoltaic science and technology during the last decades is a reason that solar cells came out of the laboratories and are becom-ing a part of our everyday life. And this is only the beginning of the era of solar energy. The number of reports about new approaches in this fi eld is increasing dramatically. Among the reported topics are nanostructure compositions, transparent conductors, inclusion of metal oxide as well as metal-based thin fi lms, light-trapping schemes that enable increased conversation effi ciency, various con-centrators and solar tracking systems, etc. Chapters two through ten are devoted to consideration of innovative materials and tech-niques for future nanoscale electronics. Two allotropic forms of carbon, carbon nanotubes and graphene, are able to replace con-ducting channels and silicon in elements of integrated circuits, thereby opening a new era of carbon-based electronics which will lead to denser, faster and more power-effi cient circuitry. A possible attractive alternative to the semiconductor components in digital processing devices is chip-based molecular logic gates—molecules possessing the property to perform logical operations where a chemical or physical binary input to the molecules causes a binary output. Surface-confi ned materials showing switching behavior along with changes in physical properties (i.e., optical, orientation, magnetism) make it possible to create integrated complex circuits for massive networking systems. Signifi cant attention is being paid to the development of fuel cells—devices that convert chemical

Preface xvii

energy from a fuel into electricity through a chemical reaction with oxygen or another oxidizing agent. Because there is no combustion in the energy conversion process, fuel cells are effi cient and envi-ronmentally friendly. The fuel cell market is also growing at a fast pace, and according to Pike Research, the stationary fuel cell market is predicted to reach 50 GW by 2020. There is a chapter describing the problems related to energy effi cient lighting, In particular, van-adate phosphors are considered—luminescent materials that have excellent thermal and chemical stability. Phosphor layers provide most of the light produced by fl uorescent lamps, and are also used to improve the balance of light produced by metal halide lamps.

Also discussed in the book is the role of materials engineering in providing much needed support in the development of pho-tovoltaic devices with new and fundamental research on novel energy materials with tailor-made photonic properties. This book is written for a large readership, including university students and researchers from diverse backgrounds such as chemistry, materials science, physics, pharmacy, medical science and engineering. It can be used not only as a textbook for both undergraduate and gradu-ate students, but also as a review and reference book for researchers in materials science, nanotechnology, photovoltaic device technol-ogy and non-conventional energy. We hope the chapters herein will provide readers with valuable insight into the state-of-the-art of advanced and functional materials and cutting-edge energy technologies. The main credit for this book must go to the authors of the chapters who have summarized information in the fi eld of advanced energy-related materials.

EditorsAshutosh Tiwari, Docent, PhD

Sergiy Valyukh, Docent, PhD

1

Ashutosh Tiwari and Sergiy Valyukh (eds.) Advanced Energy Materials, (1–68) 2014 © Scrivener Publishing LLC

1

Non-imaging Focusing Heliostat

Kok-Keong Chong

Faculty of Engineering and Science, Universiti Tunku Abdul Rahman, Kuala Lumpur, Malaysia

AbstractOvercoming astigmatism has always been a great challenge in designing a heliostat capable of focusing the sunlight on a small receiver throughout the year. In this chapter, a non-imaging focusing heliostat with dynamic adjustment of facet mirrors in a group manner is presented for optimizing the astigmatic correction in a wide range of incident angles. Non-imaging focusing heliostat that consists of m × n facet mirrors can carry out contin-uous astigmatic correction during sun-tracking with the use of only (m + n – 2) controllers. A further simplifi ed astigmatic correction of non-imaging focusing heliostat is also discussed which reduces the number of control-lers from (m + n – 2) to only two. A detailed optical analysis is carried out and the simulated result has shown that the two-controller system can perform comparably well in astigmatic correction with a much simpler and more cost effective design. The new heliostat is not only designed to serve the purpose of concentrating sunlight to several hundreds of suns, but also to signifi cantly reduce the variation of solar fl ux distribution with incident angle.

Keywords: Non-imaging focusing heliostat, new heliostat, optical analy-sis, solar fl ux

1.1 Introduction

There are two fundamental designs of solar concentrator technolo-gies for harnessing high concentration solar energy: on-axis and

*Corresponding author: chongkk@utar.edu.my, kokkeong_c@yahoo.com

2 Advanced Energy Materials

off-axis focusing techniques. The most popular devices for on-axis focusing include parabolic dish, parabolic trough, spherical bowl (or so-called Fixed Mirror Distributed Focus), Fresnel lens, etc. [1, 2]. The off-axis focusing device involves the use of heliostat to focus sunlight onto a fi xed receiver in the systems such as the cen-tral power tower, the solar furnace, etc. [2–7]. The on-axis focusing devices are usually used for distributed and smaller scale power generation (in the range from several kW to tens of kW) compared to that of off-axis focusing devices in the application of a central receiver system. For the central power tower, the concave mirrors used for the heliostat encounter a serious deterioration in focused image due to the off-axis aberration.

Off-axis aberration or astigmatism is a key factor in limiting the solar concentration ratio, especially for the central tower system that consists of a stationary receiver located in a fi eld of focusing heliostats [8]. Full correction of the astigmatism requires a continu-ous adjustment in the local curvature of the refl ector in both space and time. Although this method has been implemented in extremely large telescopes, it is obviously impractical for solar energy applica-tion because it would impose a very expensive and complicated con-trol system with a total of 2 × m × n motors to orient each facet to its own unique direction for the heliostat composed of m × n facets. As a result, a new non-imaging focusing heliostat, that employs a clever approach to maneuver the facets in group manner for astigmatic cor-rection has been proposed. Many research works on non-imaging focusing heliostat have been carried out by Chen et al. [9–15], Chong et al. [16–22] and Lim et al. [23] to establish the principle and technol-ogy of the new heliostat. Overall, there are two major advancements achieved in the new heliostat compared to the conventional helio-stat that has remained unchanged for many decades [24]. One is the fi rst mathematical derivation of the new spinning-elevation tracking formula to replace the commonly used azimuth-elevation tracking. Even the principle of spinning-elevation or target-aligned tracking method was fi rst discussed by Ries et al. [25] and Zaibel et al. [26], but they did not propose any method of implementation in their papers such as derivation of new sun-tracking formula or construction of a prototype to implement the new tracking method. The second advancement is the correction of the fi rst order astigmatism with the innovative line movements of the facets instead of trivial individual movements that would lead to complex and expensive mechanics.

Non-imaging Focusing Heliostat 3

1.2 The Principle of Non-imaging Focusing Heliostat (NIFH)

In the design of the non-imaging focusing heliostat (NIFH), mir-rors are arranged into rows and columns. The central column is maintained in the optical plane by rotating the frame. The mas-ter mirror is fi xed at the center with slave mirrors surrounding it, they share the same frame but the slave mirrors have two extra moving freedoms about their pivot points. To focus all the mirror images into one fi xed target, each slave mirror is angularly moved about its pivot point to refl ect sunrays onto the same target as the master mirror. The result at the target is the superposition of indi-vidual mirror images. As the sunlight is not coherent, the result is the algebra sum of the energy of the beams without a specifi c optical image.

1.2.1 Primary Tracking (Global Movement for Heliostat Frame)

The purpose of primary tracking is to target the solar image of the master mirror into a stationary receiver. Then, this image acts as a reference for secondary tracking where all the slave mirror images will be projected on it. In Figure 1.1(a), we defi ne ON

�����as the vec-

tor normal to the refl ector surface; OS����

as the vector that points to

the sun;

OS����

as the vector that points to a fi xed target. Figure 1.1(b) shows the rotation of the plane of refl ection, that plane which con-tains the three vectors ( OS

����, ON�����

and OT����

), during primary tracking. In Figure 1.1(b), the vector

OS����

points to the new position of the sun and the vector ON ′

������

is the refl ector normal of the new orientation

so that the sunlight is still refl ected towards the target. The track-ing movement can be studied by two independent components (Figure 1.2):

a. Spinning movement: The heliostat has to rotate about the TT′ axis so that

the plane of refl ection can follow the rotation of the vector

OS����

. Therefore, as the sun moves through the sky from the morning to solar noon, the plane will rotate starting from horizontal and turning to vertical.

4 Advanced Energy Materials

Sun

Normal

Target

Heliostat

N

S

OT

(a)

N'θ

S'

OT

(b)

Figure 1.1 Rotation modes of non-imaging focusing heliostat. (a) ON�����

is defi ned as the normal vector of the heliostat surface; OS

���� is the vector that points to the

sun; OT����

is the vector that points to a fi xed target. (b) The plane that contains the three vectors is rotated about the vector OT

����during primary tracking. The new

vectors OS′�����

and ON ′������

shown in the fi gure indicate the new position of the sun and the heliostat frame so that the sunlight is still refl ected towards the target.

F

Pivot point

Heliostat

Target

T'F'

T

Figure 1.2 Diagram showing the mounting of non-imaging focusing heliostat. The heliostat has two tracking axes that are perpendicular to each other, as does the conventional mount. The fi rst rotational axis is pointing toward the target and it is indicated by TT’ axis; the second axis is the elevation axis (attached parallel to the refl ector) and it is shown as FF’ axis.

Non-imaging Focusing Heliostat 5

The angular movement about this spinning axis is denoted as θ.

b. Elevation movement: The rotation of the heliostat about the FF′ axis (per-

pendicular to the plane) will adjust the refl ector nor-mal position within the plane until it bisects the angle between ~OS and ~OT . As a result, the sunlight will be refl ected onto the target. This angular movement depends on the incidence angle of the sun relative to the heliostat surface normal and it is denoted as θ.

The formulas for ρ and θ can be derived by transformation study of two different coordinate systems: one attached to the center of the earth and the other attached to the local heliostat.

In Figure 1.3(a), by defi ning a coordinate system with the ori-gin, C, set at the center of the earth, the CM axis is a line from the origin to the intersection point between the equator and the merid-ian of the observer at Q. The CE (east) axis in the equatorial plane is perpendicular to the CM axis. The third orthogonal axis, CP, is the rotation axis of the earth. Vector ~CS pointing to the sun can be described in terms of its direction cosines, Sm, Se and Sp to the CM, CE, and CP axes, respectively. Given the direction cosines of ~CS in terms of declination angle (δ) and hour angle (ω), we have a set of coordinates in matrix form

cos cos

cos sin

sin

SmSeSp

d w

d w

d

= −

⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥= ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥⎣ ⎦⎣ ⎦

S

(1.1)

Figure 1.3(b) illustrates another coordinate system, which is attached to the local heliostat. The local heliostat reference frame is referred to only when the heliostat frame is oriented in such a way that the normal of the master mirror becomes parallel with the spin-ning axis. The origin of the coordinate system is defi ned at the cen-ter of the master mirror and is denoted as O. The OR axis is parallel with the array of mirrors arranged in the vertical direction of the heliostat frame. The second axis, OU axis, is parallel with the array of mirrors arranged in the horizontal direction. The third orthogo-nal axis, OT axis, is a line pointing out from the origin towards the target direction. Similar to the case of ~CS , vector ~OS pointing to the

6 Advanced Energy Materials

Polaris

Solar noonmeridianSun

Observermeridian

Equatorial plane

E (east)

R

U

Heliostat

(b)

(a)

Hu

ρ

βθ

θ

Ht

Hr

H

N

O

T

Target

Sun

P (polar axis)

S

Q

M

C

(Observer)

Sp

Sm

Seω Φ

δ

Figure 1.3 (a) Coordinate system attached to earth reference frame. (b) Coordinate system attached to heliostat reference frame.

Non-imaging Focusing Heliostat 7

sun can be described in terms of its direction cosines, Hr, Hu and Ht to the OR, OU, and OT axes, respectively. In daily sun tracking, the elevation axis (FF′) is rotated about the OT axis from the morning to the evening, but the OR and OU axes remain static all the time. The angle between the OU axis and the FF′ axis is ρ and these two axes coincide with each other at solar noon.

Given the direction cosines of ~OS in terms of the angles β and ρ, we have a set of coordinates in matrix form

cos coscos sin

sin

f

r

t

H

H

H

b rb r

b

⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥= = −⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦

H

(1.2)

where b is the angle between the vector ~OS and its projection on the plane that contains the OR and OU axes. From the law of refl ection, Figure 1.1 and Figure 1.3 show that θ is obviously:

12 2

pq b⎛ ⎞= −⎜ ⎟⎝ ⎠ (1.3)

The new set of coordinates, H, can be interrelated to the earth-frame-based coordinates, S, by three successive rotation transformations.

The fi rst transformation is effected by a rotation about the CE axis through the latitude angle Φ (see Fig. 3[a]). In matrix notation, it takes the form

Φ Φ⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥− Φ Φ⎣ ⎦

cos 0 sin0 1 0

sin 0 cosF

(1.4)

In the NIFH, the spinning axis (TT′ axis) has to be aligned point-ing towards the target, and the elevation axis (FF′ axis) is perpen-dicular to the fi rst axis and attached parallel to the refl ector. If more than one heliostat shares a common target, each heliostat has its own orientation of the spinning axis relative to the earth surface. Taking into account the orientation angles of the spinning axis,

8 Advanced Energy Materials

which are facing angle f and target angle l, it is necessary to have two transformations. The facing angle, f, is the rotation angle about the Zenith made by the spinning axis (OT) when it rotates from the direction pointing towards north to the direction pointing towards a fi xed target (assuming that the fi xed target and central point of the master mirror are at the same horizontal level). Hence, f=0° if the heliostat is placed due south of the target; f=90° if the heliostat is located due west of the target. The transformation matrix for the angle f about the Zenith is

⎡ ⎤⎢ ⎥= −⎢ ⎥⎢ ⎥⎣ ⎦

1 0 00 cos sin0 sin cos

F f ff f

(1.5)

In general, the central point of the master mirror is not at the same horizontal level with the focusing target. Therefore, a rotation transformation through the angle l about the OU axis is required; l=0° means the central point of master mirror is at the same hori-zontal level as the target; l=10° means the OT axis is at the position 10° clockwise from horizontal line, i.e., the target is below the helio-stat. The transformation matrix is then

l l

l l

⎡ ⎤⎢ ⎥= ⎢ ⎥⎢ ⎥−⎣ ⎦

cos 0 sin0 1 0

sin 0 cosl

(1.6)

Finally, H is the product of l, f, Φ and S as follows:

H = l f F S (1.7)

b r l l F F d wb r d w

b l l F F d

⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤ ⎡ ⎤⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥− = − −⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥− −⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦ ⎣ ⎦

cos cos cos 0 sin 1 0 0 cos 0 sin cos coscos sin 0 1 0 0 cos sin 0 1 0 cos sin

sin sin 0 cos 0 sin cos sin 0 cos sinf ff f

(1.8)

From the solutions of the matrix, we obtain β and ρ as

( )( )

d w l F l F d w lb

d l F F l

⎧ ⎫− + −⎪ ⎪= ⎨ ⎬+ −⎪ ⎪⎩ ⎭

cos cos sin cos cos cos sin cos sin cos sinarcsin

sin cos cos cos sin sin

f ff

(1.9)

Non-imaging Focusing Heliostat 9

d w F d w d Frb

⎧ ⎫− + += ⎨ ⎬⎩ ⎭

cos cos sin sin cos sin cos sin sin cosarcsin

cosf f f (1.10)

Substituting the Eq. 1.9 into Eq. 1.3, we have

( )( )

d w l F l F d w lpqd l F F l

⎧ ⎫− + −⎪ ⎪= − ⎨ ⎬+ −⎪ ⎪⎩ ⎭

cos cos sin cos cos cos sin cos sin cos sin1arcsin

4 2 sin cos cos cos sin sin

f ff

(1.11)

The formulas of Eq. 1.10 and Eq. 1.11 represent a spinning-ele-vation tracking mode. We used this mode to perform sun tracking by using a prototype and it has been proven successful. However, with the movement of the sun tracking of the central master mir-ror, the images of the slave mirrors will be inevitably aberrant. To achieve a high concentration, the slave mirrors need to be adjusted accordingly to overcome this aberration. This adjustment is rather minor, particularly if the target is far away from the heliostat. The principle of this secondary order tracking is illustrated below.

1.2.2 Secondary Tracking (Local Movement for Slave Mirrors)

The new tracking mode encourages the arrangement of the slave mirrors to be grouped into rows and columns, as under this mode, the mirrors in the same row or column will have the same move-ment. Figure 1.4 shows the side view of a 25-mirror heliostat with P representing the heliostat frame and the central row (row 3) con-taining the master mirror. The elevation axis FF′ is out of the page and the spinning axis, OT, points towards the target. The slave mir-rors of rows 1, 2, 4 and 5 are attached to the heliostat frame in such a way that they can turn about their own pivot point P1, P2, P4 and P5, respectively. To superpose 4 rows of solar images onto the cen-tral image, each row of slave mirrors has to be rotated through an angle, σ,

cos1arctan

2 sinx

x

HH L

qs

q⎛ ⎞

= ⎜ ⎟+⎝ ⎠ (1.12)

where L is the distance between the central point of master mir-ror at O and the target point at T (refer to Fig. 1.4); Hx (positive

10 Advanced Energy Materials

Figure 1.4 The side view of a 25-mirror heliostat with P representing the heliostat frame and the central row (row 3) containing the master mirror. The slave mirrors of row 1, 2, 4 and 5 are attached to the heliostat frame in such a way that they can turn about their own pivot point P1, P2, P4 and P5, respectively.

for rows above the master mirror and negative for rows below the master mirror) is the perpendicular distance between the center of the heliostat and the central line of the row where the slave mirror concerned is located.

Referring to Figure 1.5, to superpose 4 columns of slave images onto the central master image, each column has to be moved through an angle,

1arctan

2 cosyH

Lg

q⎛ ⎞

= ⎜ ⎟⎝ ⎠ (1.13)

where the defi nition of L and θ remain the same, while Hy is the per-pendicular distance between the center of the heliostat and the cen-tral line of the column where the slave mirror concerned is located.

1.3 Residual Aberration

In the above section, we described a variable focusing method via secondary tracking to correct the off-axis aberration. A natural