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Electronic and Magnetic Excitations in Correlated and Topological Materials John S. Van Dyke
Modeling Characterization and Production of Nanomaterials Electronics Photonics and Energy Applications Woodhead Publishing Series in Electronic and Optical Materials 1st Edition Tewary
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Library of Congress Cataloging-in-Publication Data
Title: Electronic, magnetic, and optical materials / Pradeep Fulay and Jung-Kun Lee
Description: Second edition | Boca Raton : Taylor & Francis, CRC Press, 2016 | Series: Advanced materials and technologies series | Includes bibliographical references and index.
Identifiers: LCCN 2016024617 | ISBN 9781498701693 (alk. paper)
Subjects: LCSH: Electronics--Materials. | Magnetic materials. | Optical materials.
LC record available at https://lccn.loc.gov/2016024617
Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com
and the CRC Press Web site at http://www.crcpress.com
Preface
Authors
Chapter 1 Introduction
1.1 Introduction
1.2 Classification of Materials
1.3 Crystalline Materials
1.4 Ceramics, Metals and Alloys, and Polymers
1.4.1 Interatomic Bonds in Materials
1.5 Functional Classification of Materials
1.6 Crystal Structures
1.7 Directions and Planes in Crystal Structures
1.7.1
1.7.2
1.7.3
Miller Indices for Directions
Miller Indices for Planes
Miller–Bravais Indices for Hexagonal Systems
1.7.4 Interplanar Spacing
1.8 Interstitial Sites or Holes in Crystal Structures
1.9 Coordination Numbers
1.10 Radius Ratio Concept
1.11 Crystal Structures of Different Materials
1.11.1 Structure of Sodium Chloride
1.11.2 Structure of Cesium Chloride
1.11.3 Diamond Cubic Structure
1.11.4 Zinc Blende Structure
1.11.5 Wurtzite Structure
1.11.6 Fluorite and Antifluorite Structure
1.11.7 Corundum Structure
1.11.8 Perovskite Crystal Structure
1.11.9 Spinel and Inverse Spinel Structures
1.12 Defects in Materials
1.13 Point Defects in Ceramic Materials
1.14 Kröger–Vink Notation for Point Defects
1.15 Dislocations
1.16 Stacking Faults and Grain Boundaries
1.17 Microstructure–Property Relationships
1.17.1 Grain Boundary Effects
1.17.2 Grain Size Effects
1.17.3 Microstructure-Insensitive Properties
1.18 Amorphous Materials
1.18.1 Atomic Arrangements in Amorphous Materials
1.18.2 Applications of Amorphous Materials
1.19 Nanostructured Materials
1.20 Defects in Materials: Good News or Bad News?
Problems
Glossary
References
Chapter 2 Electrical Conduction in Metals and Alloys
2.1 Introduction
2.2 Ohm’s Law
2.3 Sheet Resistance
2.4 Classical Theory of Electrical Conduction
2.5 Drift, Mobility, and Conductivity
2.6 Electronic and Ionic Conductors
2.7 Resistivity of Metallic Materials
2.7.1 Effect of Thermal Expansion
2.8 Joule Heating or I2R Losses
2.9 Dependence of Resistivity on Thickness
2.10 Chemical Composition–Microstructure–Conductivity Relationships in Metals
2.10.1 Influence of Atomic-Level Defects
2.10.2 Influence of Impurities
2.11 Resistivity of Metallic Alloys
2.12 Limitations of the Classical Theory of Conductivity
2.13 Quantum Mechanical Approach to the Electron Energy Levels in an Atom
2.14 Electrons in a Solid
2.15 Band Structure and Electric Conductivity of Solids
2.16 Fermi Energy and Fermi Level
2.17 Comparison of Classical Theory and the Quantum Mechanical Approach for Electrical Conduction Problems
Glossary References
Chapter 3 Fundamentals of Semiconductor Materials
3.1 Introduction
3.2 Intrinsic Semiconductors
3.3 Temperature Dependence of Carrier Concentrations
3.4 Band Structure of Semiconductors
3.5 Direct and Indirect Band Gap Semiconductors
3.6 Applications of Direct Band Gap Materials
3.7 Motions of Electrons and Holes: Electric Current
3.8 Extrinsic Semiconductors
3.9 Donor-Doped (n-Type) Semiconductors
3.10 Acceptor-Doped (p-Type) Semiconductors
3.11 Amphoteric Dopants, Compensation, and Isoelectronic Dopants
3.12 Dopant Ionization
3.13 Conductivity of Intrinsic and Extrinsic Semiconductors
3.14 Effect of Temperature on the Mobility of Carriers
3.15 Effect of Dopant Concentration on Mobility
3.16 Temperature and Dopant Concentration Dependence of Conductivity
3.17 Effect of Partial Dopant Ionization
3.18 Effect of Temperature on the Band Gap
3.19 Effect of Dopant Concentration on the Band Gap
3.20 Effect of Crystallite Size on the Band Gap
3.21 Semiconductivity in Ceramic Materials
Problems
Glossary
References
Chapter 4 Fermi Energy Levels in Semiconductors
4.1 Fermi Energy Levels in Metals
4.2 Fermi Energy Levels in Semiconductors
4.3 Electron and Hole Concentrations
4.4 Fermi Energy Levels in Intrinsic Semiconductors
4.5 Carrier Concentrations in Intrinsic Semiconductors
4.6 Fermi Energy Levels in n-Type and p-Type Semiconductors
4.7 Fermi Energy as a Function of the Temperature
4.8 Fermi Energy Positions and the Fermi–Dirac Distribution
4.9 Degenerate or Heavily Doped Semiconductors
4.10 Fermi Energy Levels Across Materials and Interfaces
Problems
Glossary
References
Chapter 5 Semiconductor p-n Junctions
5.1 Formation of a p-n Junction
5.2 Drift and Diffusion of Carriers
5.3 Constructing the Band Diagram for a p-n Junction
5.4 Calculation of Contact Potential
5.5 Space Charge at the p-n Junction
5.6 Electric Field Variation across the Depletion Region
5.7 Variation of Electric Potential
5.8 Width of the Depletion Region and Penetration Depths
5.9 Diffusion Currents in a Forward-Biased p-n Junction
5.10 Drift Current in Reverse-Biased p-n Junction
5.11 Overall I–V Characterstics in a p-n Junction
5.12 Diode Based on a p-n Junction
5.13 Reverse-Bias Breakdown
5.14 Zener Diodes Problems
Glossary References
Chapter 6 Semiconductor Devices
6.1 Metal–Semiconductor Contacts
6.2 Schottky Contacts
6.2.1 Band Diagrams
6.2.2 Surface Pinning of the Fermi Energy Level
6.2.3 Current–Voltage Characteristics for Schottky Contacts
6.2.4 Advantages of Schottky Diodes
6.3 Ohmic Contacts
6.3.1 Band Diagram
6.4 Solar Cells
6.5 Light-Emitting Diodes
6.5.1 Operating Principle
6.5.2 LED Materials
6.5.3 LEDs Based on Indirect Band Gap Materials
6.5.4 LED Emission Spectral Ranges
6.5.5 I–V Curve for LEDs
6.5.6 LED Efficiency
6.5.7 LED Packaging
6.6 Bipolar Junction Transistor
6.6.1 Principles of Operation of the Bipolar Junction Transistor
6.6.2 Bipolar Junction Transistor Action
6.6.3 Current Flows in an npn Transistor
6.6.4 Transistor Currents and Parameters
6.6.4.1 Collector Current
6.6.4.2 Emitter Current
6.6.4.3 Base Current
6.6.5 Role of Base Current
6.6.6 Transistor Operating Modes
6.6.7 Current–Voltage Characteristics of the Bipolar Junction Transistor
6.6.8 Current Flows in a pnp Transistor
6.6.9 Applications of Bipolar Junction Transistors
6.7 Field-Effect Transistors
6.8 Types of Field-Effect Transistors
6.9 Mesfet I–V Characteristics
6.9.1 MESFET with No Bias
6.9.2 MESFET with a Gate Bias
6.10 Metal Insulator Semiconductor Field-Effect Transistors
6.11 Metal Oxide Semiconductor Field-Effect Transistors
6.11.1 MOSFET in Integrated Circuits
6.11.2 Role of Materials in MOSFET
6.11.3 NMOS, PMOS, and CMOS Devices
6.11.4 Enhancement-Mode MOSFET
6.11.5 Mechanism for Enhancement MOSFET
6.11.6 Depletion-Mode MOSFET
Problems
Glossary References
Chapter 7 Linear Dielectric Materials
7.1 Dielectric Materials
7.1.1 Electrostatic Induction
7.2 Capacitance and Dielectric Constant
7.2.1 Parallel-Plate Capacitor Filled with a Vacuum
7.2.2 Parallel-Plate Capacitors with an Ideal Dielectric Material
7.3 Dielectric Polarization
7.4 Local Electric Field (Elocal)
7.5 Polarization Mechanisms Overview
7.6 Electronic or Optical Polarization
7.6.1 Electronic Polarization of Atoms
7.6.2 Electronic Polarizability of Ions and Molecules
7.7 Ionic, Atomic, or Vibrational Polarization
7.8 Shannon’s Polarizability Approach for Predicting Dielectric Constants
7.8.1 Outline of the Approach
7.8.2 Limitations of Shannon’s Approach
7.9 Dipolar or Orientational Polarization
7.10 Interfacial, Space Charge, or Maxwell–Wagner Polarization
7.11 Spontaneous or Ferroelectric Polarization
7.12 Dependence of the Dielectric Constant on Frequency
7.12.1 Connection to the Optical Properties: Lorentz–Lorenz Equation
7.13 Complex Dielectric Constant and Dielectric Losses
7.13.1 Complex Dielectric Constant
7.13.2 Real Dielectrics and Ideal Dielectrics
7.13.3 Frequency Dependence of Dielectric Losses
7.13.4 Giant Dielectric Constant Materials
7.14 Equivalent Circuit of a Real Dielectric
7.15 Impedance (Z) and Admittance (Y)
7.16 Power Loss in a Real Dielectric Material
7.16.1 Concept of tan δ
7.17 Equivalent Series Resistance and Equivalent Series Capacitance
Problems
Glossary
References
Chapter 8
Optical Properties of Materials
8.1 Description of Light as an Electromagnetic Wave and its Connection to the Physical Properties of Optical Materials
8.2 Refractive Index: A Factor Determining the Speed of an Electromagnetic Wave
8.3 Origin of the Refractive Index: Induced Polarization of a Medium
8.3.1 Response of Free Electrons to an Electromagnetic Wave: A Case of Metals
8.3.2 Response of Bound Electrons over an Electromagnetic Wave: A Case of Dielectrics
8.4 Change in Light Traveling Direction at a Material Interface: Refraction and Reflectance
8.4.1 Refraction and Reflection of an Electromagnetic Wave at a Flat Interface
8.4.2 Power Distribution Between Refracted Light and Reflected Light at a Flat Interface
8.4.2.1 ACase of Normal Incidence
8.4.2.2 ACase of Oblique Incidence
8.5 Extinction of light: scattering and absorption
8.5.1 Scattering at Rough Surface or Fine Objects
8.5.1.1 Diffuse Reflection
8.5.1.2 Rayleigh Scattering
8.5.1.3 Mie Scattering
8.5.2 Attenuation of Light by Absorption
8.5.3 Quantitative Expression of Extinction: Beer–Lambert law
8.6 Effects of Scattering, Reflectance, and Absorption of Light
8.6.1 Color of Materials
8.6.2 Results of Energy Loss of Excited Electrons by Light Absorption
8.7 Application of light–matter interaction
8.7.1 Antireflection Coating
8.7.2 Optical Fibers
8.7.3 Light-Emitting Diodes
8.7.4 Laser
Problems
References Bibliography
Chapter 9 Electrical and Optical Properties of Solar Cells
9.1 What is a Solar Cell?
9.2 Operation Principle of p-n Junction-TYPE Semiconductor Solar Cells
9.2.1 Current–Voltage Characteristics of p-n Junction-Type Semiconductor Solar Cells
9.2.2 Fill Factor, Power Conversion Efficiency, and Quantum Yield of a Solar Cell
9.3 Physical Events Underlying p-n Junction-TYPE Solar Cells
9.3.1 Changes in Fermi Energy Level under Illumination
9.3.2 Generation, Recombination, and Transport of Electrons and Holes
9.3.2.1 Continuity Equation in a Neutral Semiconductor at QuasiEquilibrium
9.3.2.2 Photogenerated Carrier Transport through Diffusion and Drift in a Neutral Semiconductor at Quasi-Equilibrium
9.3.2.3 Photogenerated Carrier Transport in a Depletion Region of the p-n Junction
9.4 Factors Limiting Power Conversion of p-n Junction-TYPE Solar Cells
9.4.1 Theoretical Limit of PCE
9.4.2 Additional Power Loss Mechanisms in Real p-n Junction-Type Solar Cells
9.4.3 Factors Influencing Solar Cell Operation
9.5 Design of High-PERFORMANCE p-n Junction-TYPE Semiconductor Solar Cells
9.5.1 Light Management for Improved Light Absorption
9.5.2 Enhanced Collection of Photogenerated Carriers
9.6 Emerging Solar Cells not Using p-n Junction of Inorganic Semiconductors
Problems
References
Chapter 10 Ferroelectrics, Piezoelectrics, and Pyroelectrics
10.1 Ferroelectric Materials
10.1.1 Ferroelectricity in Barium Titanate
10.1.2 Ferroelectric Domains
10.1.3 Dependence of the Dielectric Constant of Ferroelectrics on Temperature and Composition
10.2 Relationship of Ferroelectrics and Piezoelectrics to Crystal Symmetry
10.3 Electrostriction
10.4 Ferroelectric Hysteresis Loop
10.4.1 Trace of the Hysteresis Loop
10.5 Piezoelectricity
10.5.1 Origin of the Piezoelectric Effect in Ferroelectrics
10.6 Direct and Converse Piezoelectric Effects
10.7 Piezoelectric Behavior of Ferroelectrics
10.8 Piezoelectric Coefficients
10.9 Tensor Nature of Piezoelectric Coefficients
10.9.1 Conventions for Directions
10.9.2 General Notation for Piezoelectric Coefficients
10.9.3 Signs of Piezoelectric Coefficients
10.10 Relationship Between Piezoelectric Coefficients
10.11 Applications of Piezoelectrics
10.12 Devices Based on Piezoelectrics
10.12.1 Expander Plate
10.13 Technologically Important Piezoelectrics
10.14 Lead Zirconium Titanate
10.14.1 Piezoelectric Polymers
10.15 Applications and Properties of Hard and Soft Lead Zirconium Titanate Ceramics
10.16 Electromechanical Coupling Coefficient
10.17 Illustration of an Application: Piezoelectric Spark Igniter
10.18 Recent Developments
10.18.1 Strain-Tuned Ferroelectrics
10.18.2 Lead-Free Piezoelectrics
10.19 Piezoelectric Composites
10.20 Pyroelectric Materials and Devices
10.20.1 Pyroelectric Detectors for Infrared Detection and Imaging
Problems
Glossary
References
Chapter 11 Magnetic Materials
11.1 Introduction
11.2 Origin Of Magnetism
11.3 Magnetization (M), Flux Density (B), Magnetic Susceptibility (χm), Permeability (μ), And Relative Magnetic Permeability (μr)
11.3.1 Magnetizing Field (H), Magnetization (M), and Flux Density (B)
11.3.2 Magnetic Susceptibility (χm) and Magnetic Permeability (μ)
11.3.3 Demagnetizing Fields
11.3.4 Flux Density in Ferromagnetic and Ferrimagnetic Materials
11.4 Classification of Magnetic Materials
11.4.1 Diamagnetic Materials
11.4.2 Paramagnetic Materials
11.4.3 Superparamagnetic Materials
11.4.4 Antiferromagnetic Materials
11.4.5 Ferromagnetic and Ferrimagnetic Materials
11.5 Other Properties of Magnetic Materials
11.5.1 Curie Temperature (Tc)
11.5.2 Magnetic Permeability (μ)
11.5.3 Coercive Field (Hc)
11.5.4 Nucleation and Pinning Control of Coercivity
11.5.5 Magnetic Anisotropy
11.5.6 Magnetic Domain Walls
11.5.7 180° and Non-180° Domain Walls
11.5.8 Maximum Energy Products for Magnets
11.5.9 Magnetic Losses
11.6 Magnetostriction
11.7 Soft and Hard Magnetic Materials
11.8 Hard Magnetic Materials
11.9 Isotropic, Textured (Oriented), and Bonded Magnets
11.10 Soft Magnetic Materials
11.11 Magnetic Data Storage Materials
Problems
Glossary
References
Index
Preface
The society we live in today relies on and is built upon our ability to almost instantly communicate and share information at virtually any location. In the past 10 to 15 years, we have witnessed unprecedented advances in the areas of computer and information technology, health care, biotechnology, environmental sciences and engineering, and clean energy technologies such as solar and wind power. All of these disciplines, as well as the challenges they face and the opportunities they create, are interrelated and depend on our ability to send, store, and convert information and energy.
The amount of information that we exchange using the Internet, computers, and other personal communication devices such as smart phones, laptops, high-definition televisions, fitness and activity trackers, electronic book readers, global positioning systems, autonomous cars, and other technologies continues to increase very rapidly. At the very core of these technologies lie very important devices made using a number of materials that have unique electronic, magnetic, and optical properties. Thus, in this age of information technology, any scientist or engineer must have some knowledge of the basic science and engineering concepts that enable these technologies. This is especially important as we move to technologies that cut across many different disciplinary boundaries.
A good portion of information-related technologies developed to date can be traced to microelectronic devices based on silicon. Of course, information storage and processing has also been supported by the availability of magnetic materials for data storage, optical fibers based on ultrahigh-purity silica, and advances in sensors and detectors. However, silicon has been at the core of microelectronics-related technologies and has served us extremely well for almost 70 years since the invention of the transistor on December 16, 1947. There is no doubt that silicon-based microelectronic devices that enable the fabrication of computer chips from integrated circuits will continue to serve us well for many more years to come.
The first transistor, which was based on germanium, used a bulky crystal. Now, in 2017, state-of-the-art transistors are made at a length scale of 14 nm. Both the size and the cost associated with the manufacturing of the transistors have decreased significantly. The size reduction has followed the famous Moore’s law, which predicted that the number of chipbased transistors would double every two years (Moore 1965). This has stayed true for nearly 50 years.
We are now at a point where we are starting to explore technologies such as quantum computing that take us into regimes that span well beyond Moore’s law. This means that simply scaling down the currently dominant Si transistors and devices would no longer meet the need. There are opportunities to create novel electronic, optical, and magnetic devices that can compete with or enhance silicon-based electronics.
Similarly, new materials other than silicon, for example, carbon nanotubes (CNT), graphene, silicon carbide, and gallium nitride, are also emerging! With the advent of nanowires, quantum dots, and so on, the distinction between a “device” and a “material” has been steadily fading away. Technologies such as those related to flexible electronics, organic electronics, photovoltaics, fuel cells, biomedical implantable devices, tissue engineering, and
new sensors and actuators are evolving rapidly. Many of these technological developments have brought the fields of electrical engineering, materials science, physics, chemistry, biomedical engineering, chemical engineering, and mechanical engineering closer together perhaps more than ever before.
The increased interdisciplinarity and interdependencies of technologies mean that engineers and scientists whose primary training or specialization is in one discipline can benefit tremendously by learning some of the fundamental aspects of other disciplines. For example, it would be useful for an electrical engineering student to not only be trained in silicon semiconductor processing but also to gain some insights into other new materials, devices, and functionalities that will likely be integrated with traditional silicon-based microelectronics. In some applications, hybrid approaches can be developed in which semiconductors such as silicon are integrated with gallium arsenide and other materials such as CNT and graphene.
The primary motivation for this book stems from the need for an introductory textbook that captures the fundamentals as well as the applications of the electronic, magnetic, and optical properties of materials. The subject matter has grown significantly more interdisciplinary and is of interest to many different academic disciplines.
There are several undergraduate engineering and science textbooks devoted to specific topics such as electromagnetics, semiconductors, optoelectronics, fiber optics, microelectronic circuit design, photovoltaics, superconductors, electronic ceramics, and magnetic materials. However, most of these books are geared toward specialists. We were not able to find a single introductory textbook that takes an interdisciplinary approach that is not only critical but also of interest to students from various disciplines. This book is an attempt to fill this gap, which is important to so many disciplines but not adequately covered in any one of them.
We have written this book for typical junior (third-year) or senior (fourth-year) students of science, such as physics and chemistry, or engineering, such as materials science and electrical, chemical, and mechanical engineering, and we have used an interdisciplinary approach. The book is also appropriate for graduate students from different disciplines and for those who do not have a significant background in solid-state physics, electrical engineering, materials science and engineering, or related disciplines. This book builds upon our almost 25 years of combined experience in teaching an introductory undergraduate course on electrical, magnetic, and optical properties of materials to both engineering and engineering physics students.
We faced three major challenges. First, we had to select a few topics that are of central importance, in my opinion, to engineers and scientists interested in the electrical, magnetic, and optical properties of materials. This means that many other important topics are not addressed in detail or are left out altogether. For example, topics such as high-temperature superconductors and ionic conductors are not discussed in detail, and some are not discussed at all. We also have not discussed some of the newest and “hottest” topics such as graphene or CNT-based devices and spintronics in detail in order to maintain this as an introductory textbook. Interested instructors may develop some of the topics not covered here as needed, since the book covers the fundamental framework very well.
The second challenge was maintaining a relative balance between the fundamentals (with respect to the underlying physics-related concepts) and the technological aspects (production of devices, manufacturing, materials processing, etc.). The approach we have adopted here was to provide as many real-world and interesting technological examples as possible whenever there was an opportunity to do so. For example, while discussing piezoelectric materials, we provide many examples of technologies such as smart materials and ultrasound imaging. We have found that the inclusion of examples of real-world technologies helps maintain a high level of interest as students relate to the topics easily (e.g., how is a Blu-ray disc different from a DVD?). Students also tend to retain what they have learned for a longer period when these real-world connections are made.
The third challenge was to determine the level at which different topics are to be covered. For example, electrical engineering students who have some exposure to circuits may find the device-related problems to be rather simple, such as calculating limiting resistance for a light-emitting diode (LED). However, this may not be the case for many other students from other disciplines. Similarly, students who have had a class in introductory materials science may find some of the concepts related to materials synthesis, processing, and structure–property relationships to be somewhat straightforward. However, many other students may not have such a background and may be confused by the terminology used. We have therefore maintained an introductory level for all the topics covered and have tried to make the concepts as interesting as possible while challenging the students’ ability and piquing their curiosity.
In the second edition of this book, we have strengthened the optical materials section significantly. Two new chapters have been added to address the fundamentals of optical materials as well as their applications to technologies such as solar cells and LEDs.
We take full responsibility for any mistakes or errors this book may have. Please contact us as necessary so that they can be corrected as soon as possible. We welcome any other suggestions you may have as well.
Any book such as this is a team effort, and this book is no exception. In this regard, we appreciate the assistance of the Taylor & Francis staff who worked with us. In particular, we thank Allison Shatkin for helping us develop this textbook. We are thankful to Todd Perry and Viswanath Prasanna for their assistance and patience in working with us on this book. We are also grateful to a number of colleagues and corporations who have provided many of the illustrations.
Pradeep Fulay is thankful to his mother, Pratibha Fulay, and father, Prabhakar Fulay, for all they have done for him and the values they have taught him, and to his wife, Dr. Jyotsna Fulay, his daughter, Aarohee, and his son, Suyash, for the support, patience, understanding, and encouragement they have always provided him.
Jung-Kun Lee expresses his appreciation to his father and mother for their love and unconditional support. He is also very thankful to his wife, Heajin, his daughter, Grace, and his son, Noah. They have been a constant source of joy, strength, and encouragement, without whom nothing would have been accomplished.
Pradeep P. Fulay is a professor and associate dean for research at the Benjamin M. Statler College of Engineering, West Virginia University, Morgantown, West Virginia. Prior to joining Statler College, he was a professor in the Swanson School of Engineering at the University of Pittsburgh, Pittsburgh, Pennsylvania, from 1989 to 2012. Dr. Fulay earned his PhD degree from the University of Arizona, Tucson, Arizona. From 2008 to 2011, Dr. Fulay served as a program director in the electrical, communications, and cybersystems division in the Engineering Directorate of the National Science Foundation (NSF). At NSF, he managed the electronic, magnetic, and photonic devices program and helped initiate the BioFlex program aimed at flexible electronics-based devices for biomedical applications. Dr. Fulay has published several journal articles, holds US patents, and is an elected Fellow of the American Ceramic Society. He has authored a number of textbooks that are used around the world.
Jung-Kun Lee is an associate professor and William Kepler Whiteford Faculty Fellow in the Department of Mechanical Engineering and Materials Science at the University of Pittsburgh (Pitt), Pittsburgh, Pennsylvania. He joined Pitt in September 2007 after more than 5 years of service at Los Alamos National Laboratory as a technical staff member as well as a Director’s-funded Postdoctoral Fellow. He received his PhD degree from the Department of Materials Science and Engineering at Seoul National University, Seoul, South Korea. His research interests include material processing of electronic and optical materials, ion-beam synthesis of materials, and domain engineering of ferroic materials. Currently, he is focusing on the electronic and optical properties of semiconductor materials and their energy application with emphasis on solar energy harvesting. He was a recipient of the NSF CAREER Award in 2009 and has attracted multiple external grants from NSF, DOE, and NRC. The quality of his research is validated by more than 150 journal publications and multiple patents in various areas of functional properties of materials.
1 Introduction
KEYTOPICS
Ways to classify materials
Atomic-level bonding in materials
Crystal structures of materials
Effects of imperfections on atomic arrangements
Microstructure–property relationships
1.1 INTRODUCTION
The goal of this chapter is to recapitulate some of the basic concepts in materials science and engineering as they relate to electronic, magnetic, and optical materials and devices. We will learn the different ways in which technologically useful electronic, magnetic, or optical materials are classified. We will examine the different ways in which the atoms or ions are arranged in these materials, the imperfections they contain, and the concept of the microstructure–property relationship. You may have studied some of these and perhaps more advanced concepts in an introductory course in materials science and engineering, physics, or chemistry.
1.2 CLASSIFICATION OFMATERIALS
An important way to classify materials is to do so based on the arrangements of atoms or ions in the material (Figure 1.1). The manner in which atoms or ions are arranged in a material has a significant effect on its properties. For example, Si single crystals and amorphous Si film are made of same silicon atoms. Though their compositions are same, they exhibit very different electric and optical properties. While single crystal Si has higher electric carrier mobility, amorphous Si exhibits higher optical band gap. This is because of different Si atom arrangement. While atoms are perfectly aligned in single crystals, they are randomly distributed in amorphous film.
1.3 CRYSTALLINE MATERIALS
A crystalline material is defined as a material in which atoms or ions are arranged in a particular order that repeats itself in all three dimensions. The unit cell is the smallest group of atoms and ions that represents how atoms and ions are arranged in crystals. Repetition of a unit cell in three dimension leads to the formation of a three-dimensional crystal. The crystal structure is the specific geometrical order by which atoms and ions are arranged within the unit cell. Crystal structures can be expressed using a concept of Bravais lattices, or simply lattices. A lattice is an infinite array of points which fills space without a gap. Auguste
Bravais, a French physicist, showed that there are only 14 independent ways of repeatedly placing a basic unit of points in space without leaving a hole. Aconcept of lattice is analogous to that of a crystal consisting of unit cells (Figure 1.2).
Note that a sphere in Figure 1.2, which is called a lattice point, does not refer to the location of a single atom or ion. The lattice point is a mathematical idea that refers only to points in space, which is applied to several fields of science and engineering. In crystallography, the lattice represents the crystal and the lattice points are associated with the location of atoms and ions. Simply speaking, we can think that either a single atom/ion or a group of atoms/ions occupy a lattice point. When a group of atoms/ions take up the lattice point, their configuration exhibits a certain symmetry around the lattice point. The symmetry of atoms and ions occupying the same lattice point is called basis. A combination of the lattice and the basis determines the crystal structure. In other words:
1.1 Classification of materials based on arrangements of atoms or ions
We have only 14 Bravais lattices (Figure 1.2). However, there are many possible bases for the same Bravais lattice. The symmetry operation of bases includes angular rotation, reflection at mirror plane, center-symmetric inversion, and gliding, which in turn leads to 230 possible crystal structures out of 14 Bravais lattices. We also have many materials that exhibit the same crystal structure but have different compositions, that is, the chemical makeup of these materials. For example, silver (Ag), copper (Cu), and gold (Au) have the same crystal structure (see Section 1.6).
Similarly, materials often exhibit different crystal structures, depending upon the temperature (T) and pressure (P) to which they are subjected. In some cases, changes in
FIGURE
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LTHE marriage ceremony was fixed for the second week of the new year. All London was invited. The Childwicks liked to do things well, and however well they did them made no impact on their wealth. They were really rich people and of late years their stock had been going continually up.
Still it was generally felt that Gwendolen had done very well. She was a cut and polished jewel, but a setting was needed for her. What choicer setting could mortal girl desire than an old and distinguished marquisate and that beautiful and historical place Warlington Towers? These things would supply the essential background her millions lacked. Then, too, Bill was a popular young man. His feelings, as his sister said, might not run deep, but in his way he was immensely attractive. Everybody liked Bill. Even his fecklessness was a point in his favour. And he would be all the better for having a shrewd and clever American wife to keep him up to the mark.
Mame received an invitation from the Childwicks; her friends saw to that. It was duly accepted; yet when the day came she did not feel equal to facing the music. Lady Violet did her best to persuade her to come to the church and to the reception in Berkeley Square, until she realised that it would not be kind to persist. Good, brave little puss! Those quaint furry paws had been rather nastily trapped. She was still suffering. For all her wonderful grit, when the day came she could not help groaning a bit over the throbbing of her wounds. It went to Lady Violet’s heart to leave her behind. But there was no help for it. The child could not face the music. And it was hardly reasonable to expect that she should.
Even as Lady Violet stood in her regalia, which emphasised her fine points, and took a tender and affectionate leave of poor Mame, she could not help saying in her frank way: “I’m not going to enjoy this one bit. We’re shown up too badly. I wish now I hadn’t interfered.”
It was no more than the truth. She felt on a low plane. Compared with her friend and business partner she had a sense of inferiority which was new and decidedly unwelcome.
“You were quite right, honey.” Mame was brave and magnanimous to the end. “Had I been you I’d just have done that. It’s nature. And it’s no use trying to go against nature.”
But Mame’s eyes were so tragic, that her friend, without venturing to say another word, made a sort of bolt for the door and for the lift beyond it. No, Lady Violet did not feel that she was going to enjoy her day
The day, for Mame, was very far from being one of enjoyment either. A great deal of it was spent walking about London. Now the pinch had really come it was the go-getter who mounted to the saddle and took command. The practical side of a dual nature was not slow to inform her that she had gone back on herself. She had betrayed, at the beck of a mere whim, all that she had stood for.
Life had always been against her until a few months ago. She had had to fight so hard for bare existence that she might at least have had the sense to ensure the future when opportunity arose. But no, she had denied her luck. There was a Tide. Well, the Tide had come and she had deliberately ignored it. A great position, social security had been offered her. She had even accepted her chance and then, just for a whim, had passed it on to her enemy and rival.
The go-getter spared her nothing. It had a royal time. She had been a fool. The lot of the fool was suffering. “You’ve broken a paw, honey Always you’ll be a little mucker now. You’ll never be able to fix on anything again. No more will you be able to mark down your bird and fly at it. You’ll be unsettled for the rest of your days. Not always will you be brisk and quick; your looks, such as they are, and they’ve never been much to bank on, honey, are going already. These folks in London, England, who mocked at you and pulled your leg, you could have handed them a haymaker. But no, you must get fanciful and highfalutin.”
Yes, the go-getter with the sardonic voice and a flow of rather second-rate conversation had a royal time. He spared her nothing. She was unworthy of herself, of her breed, of her clan. Idealism. The hearty fellow landed his simp of a partner a blow on the point. If some of these honest-to-God Americans didn’t watch out, Idealism was going to be their ruin. You didn’t catch the dyed-in-the-wool Britisher playing around with flams of that kind. He was a pretty successful merchant, the Britisher, but he was content to leave idealism to other people. As a business man he was a model for the world. And why? Because with all his lip service he knew how to keep the soft stuff apart from the hard.
Poor Mame! She trudged half the day about the streets of a hostile city. With that pressure upon her spirit it was impossible to stay quiet indoors. Her very soul seemed to ache. Every syllable was true that was whispered in her overwrought ear. She had gone back on all she had ever stood for. They had put one over on her, these hardroed Britishers. Yes, she must be cuckoo. You came over to pull big stuff, whispered the relentless voice. And by cripes, Mame Durrance, you’ve pulled it!
Tired out at last with tramping the West End parks and squares, she took a little food in a restaurant in a by-street of Soho. There she was likely to meet no one she knew. She was not in a mood to face her kind. As she ate her soup a nostalgia came upon her. After all, she was in a strange land, an alien. Their ways were not her ways; they had a different viewpoint; their method of doing things was not the same. She began to long for the sight and the sound of the homely, hearty, warm-blooded folks she had known; the folks who spoke the same language as herself, in the curious drawl that lately she had been taking such pains to get rid of.
Her thoughts went back to the land where she belonged. In the bitterest hour she had known since she had started out from her home town to see life, she had a craving for the friendly easygoingness of her own kind. She had crowded a lot of experience into her European pilgrimage; in certain ways her luck had been truly remarkable. Mame Durrance had made good at her job; but this
evening with a very large size “black monkey” upon her, she had a sudden yearning for the larger and freer air of her native continent.
Miserably unhappy she returned to the flat about nine o’clock. Lady Violet had been home from the revels, had inquired for her anxiously, but had changed her dress and gone out to dinner. Evidently she was making a day of it. Mame was not sorry. She had no wish to be caught in this mood. Yet she had no desire for bed. She would not be able to sleep if she turned in. The ache in her heart was terrible. If she could not learn to subdue it, for the first time in her life she would be driven to take a drug.
Suddenly her eye lit on a package on the writing table. It bore the label of a New York publisher and was addressed to herself. Perfunctorily she tore off the wrapper. A novel in a gay jacket was revealed. It was called Prairie City; and the name of the author was Elmer Pell Dobree.
Mame’s heart leaped. Coincidence has an arm notoriously long, but nothing could have been more timely than the arrival of this book. Her thoughts rushed back to the source of its being. And as if to speed them on their way, a letter had been enclosed in the parcel.
Characteristically it ran:
D M ,
You are such a girl now, among your slick friends in London, and you are pulling such big stuff with your weekly columnising, that I daresay you have forgotten your obscure Cowbarn epoch, and the junk whose early chapters you had the honour (sic) of typing for your first and most distinguished (sic) editor, with which the boob filled in his spare hours. You used to tell him how good these opening chapters were and the boob used to believe you. The consequence is ... well, this is the consequence. By the way, it was clever you that invented the title, after we had shaken a leg—and you were always some dancer—at that dive at the top of Second Street, one wet afternoon.
Well, Mame, that title was lucky Prairie City has made good. It has, if I may say it modestly, made quite surprisingly good. ’Tis hardly six weeks since it was first issued here by Allardyce, Inc., but already it’s gone big. Early next month their London house will publish it, and if it can repeat in England what it has done in New York, the undersigned Elmer Pell Dobree is a permanent whale. So go to it, Mame, you little go-getter. Corral the big drum and get around the comic town of your adoption—worse luck! —and see if for the sake of old times—good times they were, too, I’ll tell the world—you can’t put one over, in the name of an old friend, on the doggone Britisher.
P.S. When do we see you again here? As I’ve told you more than once, this continent is a poorer place for your absence. If you’ve left us for keeps it’s a great, great shame; and there’s one young man who won’t forgive you.
When, at a decidedly late hour, or, rather, an early one, Lady Violet returned from the festivities, she invaded Mame’s bedroom. She wanted to see if the child had come back and that she was all right. In spite of the excitements of the day her thoughts had been pretty constantly with her little friend. She was a good deal concerned about Mame. And now it was something of a relief to find her propped up in bed, simply devouring a book with a red cover.
It was so good to see a smile on a countenance which a few hours ago looked as if it would never smile again, that the intruder exclaimed, “Why, why, whatever have you there?”
“Elmer’s written a book.” A glow of excitement was in Mame’s tone and in her eyes. “It’s all about Cowbarn and the folks we used to know.”
“True to life, I hope.” Mame’s friend, gazing at her furtively, sought to read what lay behind that rather hectic air.
“Better than life ever was or ever will be. It just gets you feeling good. And it keeps you feeling good all the time.”
“He must be a clever man, your friend Elmer P.”
“Clever is not the name for Elmer.” Mame spoke excitedly “A genius —that baby! All the Cowbarn folks are in it. I’m in it. And I’ll say he’s let me down light.”
“I hope he’s made you the heroine of the piece. Anyhow, he ought to have. You are fit to be the heroine of the best piece ever written.”
“Say now, honey,” expostulated Mame in the way her friend had learned to love, “that’s where you get off. Heroine-ism and that fancy jake is no use to me. I’ll never be able to get away with it. But Elmer has let me down light.”
“You must let me read it.”
Mame laughed. She actually laughed. “Why, you shall so. It’s the goods. That boy has an eye to him. He can see into things. And he knows a lot about human nature, does that boy.”
Already Lady Violet was feeling a lively sense of gratitude towards the famous and legendary Elmer P. The poor child was transformed. Her own people, for whose homely and abounding kindliness she had in her misery been longing, were alive in those magic pages. Yes, they were alive and they were dancing, Mame declared. And half America was dancing with them.
The mirth of the simple creatures she loved so well had lifted a weight from her heart. The relief might only be temporary, but Lady Violet was very willing to do homage to the wizardry of Elmer P.
“There’s his letter.” Mame tossed it excitedly across the bright green expanse of counterpane.
Lady Violet read with a smile. And then suddenly there came a mischievous little clutch at her heart. Yes, why not? It was an idea. The brilliantly clever woman of the world again glanced furtively at Mame. This intoxicating moment, which was doing so much to heal the child and to keep her sane, must, if possible, be held. But how? Like all things in time it was fleeting, transitory. With the coming of daylight it would surely pass. A pitiless January dawn would throw her back upon hard and cruel reality. Yet this moment of happiness might be extended; perhaps there was a chance of making it permanent.
She fixed her wise eyes upon those of the feverish Mame. “Yes, my dear, we’ll go round with the big drum. We’ll corral the Press all right. If Prairie City doesn’t knock London endways it shall not be our fault.”
“You can bet your life it won’t be!”
“Well, write to-morrow and tell him so.”
“I will.”
“And tell him, my dear, in a postscript, strongly underlined, that if he will do the one thing you ask you’ll guarantee the success of Prairie City this side the Atlantic.”
Mame was all ears. “What’s that, honey?”
“He must come over himself as soon as ever he can. We’ll promise the very best that can be done for him in the way of a good time. After all there is no advertisement for a book quite equal to the person who wrote it.”
Mame gave a chuckle of pleasure. Sure, it was an idea. Why had not she thought of it herself?
“Yes, hon, if Elmer comes that’ll fix it.”
But would he come? That stern question at once invaded Mame’s mind.
“We’ll make him,” said Lady Violet.
“He’s not easy to make do anything he don’t want to. And he’s pretty busy these days and rather important, too.”
“We’ll get at him somehow.” Lady Violet had an arch look. “For his own sweet sake,” she added artfully.
LITHE next day they laid their clever heads together and wrote a letter to Elmer P. It was appreciative but peremptory. He must mail his latest photograph at once. And he had better send that old green album, too, with all those snapshots in it of Cowbarn, Iowa, including some interesting views of the exterior and the interior of the office building of the good old Independent.
Mame gave a solemn undertaking to get out the big drum and to go around with it. She and her friends, in fact, would organise such a publicity campaign as would astonish even a booster like himself. But he, too, must be ready to do his bit. By the time London had the book in its hands, it would be dying to see the author. He must come over, if only for a week, he must, he must! That final imperative word was three times underscored.
The thirteen days that followed the letter’s posting were rather anxious ones. Lady Violet feared that when Mame’s excitement had time to cool a bad reaction would set in. By judicious fanning, however, she was able to keep the flame alive; sufficiently, at any rate, to provide a highly necessary distraction.
Elmer’s reply came promptly. The urgent skill of the summons had at least stirred him to that. Moreover, in the pompous language of the British House of Go-getters, which Mame had heard for herself from the Ladies’ Gallery, the answer was in the affirmative. The great man actually promised to come to London. His coming, moreover, should synchronise with the British publication of his book, which since he wrote last had sold three more editions in these United States.
“He doesn’t let the grass grow!” Mame crowed her triumph. It was disinterested triumph. She had nothing to gain, as far as she knew, by the coming of Elmer, except in the way of humble-minded ministry to his rapidly growing fame. “One of the up-and-coming ones is
Elmer, for all he’s so quiet. Tell me, Vi, what do you think of his photograph?”
“Is it like him?”
“He’s changed some, I’ll say, since I left him in the editor’s office at Cowbarn, twenty months ago to-morrow.”
“A clever face.” A good face, too, Lady Violet might have added. She certainly saw something oddly attractive in the fair, open countenance of Elmer P.
“I guess there’s something better than clever in it.” Mame gazed critically at the photograph.
“Well, dear child, I guess there is, too.”
Her friend looked at her tenderly and then laughed to herself softly.
LII
THEY lost no time in getting to work. First they went to Henrietta Street and called upon Allardyce, Inc. Taking wise men into their counsels, they started to plan a campaign whose aim was the making of Elmer Pell Dobree a household name in Britain. They infected Allardyce, Inc., with their own enthusiasm; not perhaps such a difficult process. Every mail was bringing news of breaking records across the water. Prairie City was the best in its kind since Mark Twain. Indeed some of the highbrows thought really and truly it was better.
The publishers were taken with Mame. All the natural zip of the booster-born sprang to the surface as she lightly gave off her ideas for the big drum. Very bright some of these ideas were. There was one in particular which appealed to these shrewd men. Unfortunately, to carry it out would cost money. But as smart Miss Amethyst Du Rance, a writer herself, by the way, declared, quoting from a favourite calendar that had once adorned the wall at the back of her typewriter in that identical office which soon would be famous over the breadth of two continents, If you want to make Omelettes you’ve got to break Eggs.
This boom was going to cost money. No use burking that fact in political economy. But it was going to be worth it. Lady Violet Treherne—that very distinguished-looking girl who had accompanied the corking little Miss Du Rance into the back parlour: Celimene, by the way, of the Morning News—was of that opinion, too. Prairie City was the goods. It was the big stuff. Every dime spent on boosting it would earn a dollar.
Allardyce, Inc., of the Allardyce Building, East Forty-ninth Street, New York City, U.S.A., and 1-a Henrietta Street, London, England, not to mention 16 Rue de la Paix, Paris, France; 39 Stratton Street, Johannesburg, S.A., and 105 Victoria Avenue, Melbourne, Australia;
in short, wherever the honest mother tongue is spoken, Allardyce, Inc., decided to fall for Miss Du Rance and her little campaign. Still it was going to cost money.
“It’ll be worth it all the time.” The air of Miss Du Rance was already victorious. “You do your bit and we’ll do ours. That’s all we ask.”
The head of the London branch of the well-known firm personally bowed the two ladies into their taxi. He had not been so impressed in years. Full of vim this Miss Du Rance. Portentously full of pep. No wonder they made good in cradle-rocking Britain, when they came over, these one-hundred-per-cent little ladies from the U.S. And the cunning minx kept back a few grains of the pep for her final shot. As she offered a hand in parting, at its most fashionable angle, to Allardyce, Inc., she said in her new and careful Mayfair manner: “When Elmer Pell Dobree arrives in this country, Lady Violet Treherne will give a luncheon for him at the Savoy Hotel. All the most worth-while folks in London will be invited to meet him. I tell you, sir, although you mustn’t tell the world just now, she has already arranged with her friend the Prime Minister, if he happens to be disengaged at the mo-ment, to attend the gathering and to give an ad-dress on the Value of Literary Art in International Relations.”
They left Allardyce, Inc., balanced on the extreme edge of the kerb of Henrietta Street, staring after their departing chariot. As they drove off to luncheon at the Ladies Imperium, Lady Violet said, “My child, I rather think you’ve clicked.”
Mame felt rather that she had. The happy feeling was confirmed, moreover, a little later in the week when a second letter from Elmer P. was delivered in Half Moon Street. In it, that now famous man positively undertook to be at the Savoy Hotel on February 10, always providing the Olympic in which he had booked a passage came in on time. He hoped to stay a fortnight in London. But that, he feared, must be his limit. For just now he was living a forty-eight-hour day in New York.
“You can bet your life that’s so,” was Mame’s approving comment.
LIII
ELMER came and saw London, England. And the ancient burg gave him a real good time. He went here, there and everywhere; his photograph was in all the papers; columns were written about his book. There was a brilliant luncheon at the Savoy. Lady Violet kept her promise. Big-wigs attended it, including her father’s old friend the Prime Minister, who seized the occasion to deliver a most significant address on the Value, Etc., which was cabled verbatim all over the English-speaking world.
No young author, since the art of writing was invented, ever had a more generous reception in the great metropolis. A modest, rather shy, young man, he was inclined at first to be overwhelmed by it. But the undefeated Mame, who met him at Euston, who took him to his hotel, who gave him continual advice, saw to it that he wasn’t. For the honour of Cowbarn, Iowa, he must stand right up to his job. It was her task to see that he did so without flinching and she duly performed it. She mothered him through receptions and tea parties; she toted him around; and the bewildered and breathless Elmer hardly knew whether to be more impressed by the storm his coming had aroused or by the manner in which Mame rode it.
Nothing in the whole of London astonished him quite so much as Mame’s transformation from her chrysalis Cowbarn period. Her clothes, her style, her English accent fairly tickled him to death. Then the friends she had made! She appeared to hob-nob with half the swells in Britain and to have them feeding from the hand.
Elmer had many surprises in these crowded and glorious days. But, shrewd and cool American citizen that he was, he managed to keep a perfectly level head. For the life of him he couldn’t imagine what all the fuss was about; or at least if he had an inkling of the reason for it, he could not understand how Mame had contrived it all. She had evidently had the luck to strike some very powerful backers.
Even before landing in England, he had surmised that such was the case. The mysterious Celimene, of the weekly news-letter, had proved to be so highly informed in social matters that her value had been clearly demonstrated in New York. Her name had been given him in confidence before he came over; and he was mighty keen to meet her.
They might be said to challenge each other’s curiosity. But their meeting not only fulfilled their hopes of one another; it was the beginning of a friendship. One could not help liking the author of Prairie City. He was a well-set-up young man; and behind the dry shrewdness and the determination to get there, qualities characteristic of Mame herself, were genuine kindliness and modesty. His rise to fame had been less sudden than it seemed. It had been prepared for and earned. He owned to thirty-one years of life. They had not been easy years, but they had made him the man he was.
Lady Violet was glad that Elmer answered fully to Mame’s description of him as “a regular fellow.” There was something about him that inspired confidence. Whether it was a certain slowness of speech which implied depth of mind, a vein of real grit, or the charming air of diffidence with which he wore the fame that so deservedly was his, she instinctively felt that here was what Mame called a he-man.
This was well. She had a plan in that sagacious mind of hers. But the carrying out of it depended upon Elmer P. himself. Unless he could pass the test, and a pretty severe one, that a thorough woman of the world felt bound to impose, the fine scheme was doomed from the outset. His bearing, however, in those crowded days in which they saw a good deal of each other, convinced this friend that rumour had not over-painted him. Undoubtedly the young man deserved the position his talents had won. Beneath a surface a little stiff and formal at first, and, the critic thought, none the worse for that, was a warmth of heart and a balance of nature which enabled him to pass his examination with flying colours.
As much time as Elmer could spare from his exceedingly numerous engagements was devoted to Half Moon Street. From the first afternoon he went there to drink tea, with reviewers and people of influence in the world of letters, he took a great liking to the place. For one thing he was made to feel so much at home. The presence of Mame guaranteed that. She was quite unspoiled in spite of the English accent, which to Elmer’s secret delight was apt to wear a little thin in places. He was no end of an observer, the author of Prairie City. Back in the Cowbarn days there was something in Mame that had appealed to him; and in this new orientation she was still the Mame he had liked, smiled at just a little, and yet admired. Wonderful how she had been able to get away with it; yet he was not really surprised. He had always known that his little stenographer had a lot in her.
Everybody was so friendly in Half Moon Street. They seemed to take quite a personal pride in his success; they seemed to treat it almost as a part of their own. During the hours he spent there Mame and her friend Lady Violet were always devising fresh schemes for Prairie City. The boom was growing daily. But it must get bigger and bigger. Had he been their own brother they could not have done more.
One afternoon, when Elmer had been in London a week, he came rather early and happened to catch Lady Violet alone. Mame had gone, at the call of duty, to the première of a new play. In this rather providential absence, which yet did not owe quite so much to providence as appeared on the surface, Lady Violet seized the chance to have a private talk.
“So you are leaving us a week to-day?”
Elmer confessed that was his intention.
“If you find us all as complacent as our perfectly absurd newspapers you won’t be sorry.”
Elmer had the tact to ignore the vexed question of the British newspaper. “I’ll be sorry enough,” he said with simple sincerity. “You are just giving me the time of my life.”
“Your book is so delightful. Every fresh reader is one friend more for the man who has written it.” Lady Violet yielded to none in point of tact. Over that course few could live with her. “But I do hope you realise,” she went laughingly on, “that, although you are your own best asset, as of course every true author has to be, you have also had a very clever and enthusiastic friend to pull the strings over here.”
Elmer realised that.
“One doesn’t say your success might not have been as great without her; but it could hardly have come so soon.”
Yes, Elmer was sure.
“The way that dear child has worked for you has simply been splendid. Had she written the book herself, I don’t think she could have been prouder of it. She literally bullied your publishers into boosting you—you know what even the best publishers are!—she bullied me into corralling the Prime Minister—it was a rare bit of luck getting him to come and make that speech—and it was her idea, wasn’t it, that you should come over here and let us see you?”
Elmer felt all this was true. But gallantly he wanted to include Lady Violet herself in the big bill of his gratitude.
“Please keep it all for Mame. That good child deserves every bit. She has worked for you like a demon. As good as gold, as true as steel. And she is quite cast down that you are leaving us next week.”
Unluckily there was no help for it. But Elmer P., like most people of true genius, was simple at heart. He responded to the piping. Mame Durrance—in the mouth of her former employer the accent fell upon the first syllable of her surname rather than upon the second— deserved all the luck there was in the world. She was as real as they made them; and she was able to think of others.
Lady Violet drove that right home. “I, of all people, have reason to know it. She is capable of big things, that dear child. Some day, when you come and see us again, as of course you will, I may tell you a little story about her.”
Elmer could not help a feeling of subtle flattery It is difficult for rising young men to resist such a feeling when they find themselves tête-àtête with an accomplished woman of the world. Lady Violet was quite as intriguing as any of the Fifth Avenue queens, with one or two of whom he was beginning to get acquainted. Mame had had amazing luck to put herself in so solid with this fascinating woman. It was true that Elmer personally owed a lot to Mame, a peerless little go-getter, but it was also true that Mame for her part owed much to this brilliant daughter of a famous statesman who in his day had done a great deal for the English-speaking world.
The clock ticked pleasantly on to five o’clock and then quite as pleasantly to 5:15. But no Mame. Lady Violet feigned surprise. Then she glanced at an imposing array of cards on the chimneypiece. Oh, yes, she remembered! This was the at-home day of the wife of an influential editor. Mame had evidently kept it in mind even if Lady Violet herself had forgotten. “She’s gone there to boost Prairie City,” said her friend with a smile. “Wherever she goes now she boosts Prairie City; and at night she boosts it in her dreams.”
A quarter past five already! Elmer Pell Dobree rose with a start. At 5:30—Lady Violet must really excuse him—he was due in Aldwych to orate to the Journalists’ Circle on the Coming of the American Novel. He was sorry to go, but Mame had fixed that on him at about twelve hours’ notice, and as his good fairy declared it would mean another edition, he supposed he must stand up, a hero, and face it.
“You must.” Lady Violet had what Elmer privately described as a Gioconda smile. Here was guile, here was subtlety or the author of Prairie City was not a judge of such matters. How intriguing she was. Gee! she had a power of making your blood course quicker.
“I’ve one favour to ask, Lady Violet.” Elmer was moving to the door. “Can you and Mame spare to-morrow evening to dine with me quietly at the Savoy?”
Lady Violet took up a little red book from the writing table. A glance revealed that by the courtesy of providence to-morrow night was free. She could not answer for Mame, but to the best of her
recollection there was reason to think the little go-getter would not be in action that evening.
So then it was arranged, a little dinner, just the three of them, for the next evening, which was so providentially free, at the convenient hour of eight. Unless, of course, Mame, which somehow Lady Violet felt was hardly likely, telephoned him to the contrary.
LIV
THE little dinner was capital. In every small but considered detail it could not have been nicer. Elmer P., as the world looks for in one of his eminence, was growing to be a judge of food and wine. Also the shrewd dog knew how to choose his company. On his right sat Lady Violet, on his left was Mame. Over and beyond this pair of friends and boosters was vacancy, the limitless inane, at least so far as those three minds were concerned, although at other tables sat persons not without importance in their way.
In return for delicate food and dry champagne Elmer received high entertainment from the lively tongues of his charming guests. Both were observers of the human comedy, yet they observed it in the right way. There was nothing in their talk that was spiteful or backstairs, or beneath the dignity of human nature. Their aptness, wit, and general information, their opinions upon books, plays, music and the world at large gave the host a mental punch from the hors d’œuvres to the comice pear and the crème de menthe, for which crude liqueur both ladies confessed a partiality.
Elmer had had his triumphs, in the last week or so particularly, but frankly he doubted whether he had ever enjoyed a meal like this. It was so gay. And there was the glamour of new experience. His life had suddenly been touched to newer and finer issues.
When the coffee appeared, at the end of the meal, Lady Violet drank hers quickly. Then quite unexpectedly she rose. She would have to fly. There was a musical party she had promised to attend. A stupid affair, but it was the call of duty.
Mame and Elmer were pressing in their entreaties for their amusing friend to remain, but she was not to be seduced from the true path. Besides, as she laughingly said, it was a perfect night of stars. And this being a sufficiently rare occurrence for London, she hoped that Elmer—if she might use his Christian name?—would walk with
Mame through Trafalgar Square, along Pall Mall, up the Haymarket, across the Circus and down the full length of Piccadilly. She ventured to prescribe that route, because a little bird had whispered that if Elmer duly followed it he might look for a very pleasant surprise, for which Mame was alone responsible.
This was all so enigmatic that Elmer might have been tempted to disbelieve Lady Violet. But he knew she was no trifler. Emphatically she was one of the people who did not make promises unless they were able to deliver the goods.
“We’ll go along and try it, anyway,” conceded Elmer the polite. And being something of an altruist into the bargain: “But you’ll come with us, won’t you? We can’t lose you!”
Lady Violet’s refusal was amusingly definite. She was late already; she must fly. Besides, there was an even more cogent reason. That, however, she was careful not to disclose to Elmer P. Dobree. As that homme du monde moved a bit ahead of her to the restaurant door to see her into her cloak and her taxi, she bent to Mame’s ear and whispered urgently, “My child, if you don’t put one over on him tonight I’ll never speak to you again.”
