Green-Function Theory of Chemisorption

222 Pages·2006·2.373 MB·English

by  Sydney George Davison, K.W. Sulston (auth.)

GREEN-FUNCTION THEORY OF CHEMISORPTION
Green-Function Theory of
Chemisorption
by
SYDNEY GEORGE DAVISON
University of W aterloo, ON, Canada
and
K.W. SULSTON
University of Prince Edward Island, Charlottetown, Canada
A C.I.P. Catalogue record for this book is available from the Library of Congress.
ISBN-10 1-4020-4404-6 (HB)
ISBN-13 978-1-4020-4404-5 (HB)
ISBN-10 1-4020-4405-4 (e-books)
ISBN-13 978-1-4020-4405-2 (e-books)
Published by Springer,
P.O. Box 17, 3300 AADordrecht, The Netherlands.
www.springer.com
Printed on acid-free paper
All Rights Reserved
© 2006 Springer
No part of this work may be reproduced, stored in a retrieval system, or transmitted
in any form or by any means, electronic, mechanical, photocopying, microfilming, recording
or otherwise, without written permission from the Publisher, with the exception
of any material supplied specifically for the purpose of being entered
and executed on a computer system, for exclusive use by the purchaser of the work.
To our first teachers – our parents:
Sarah and Wilfrid Davison
Madalene and Ward Sulston
Howcanitbethatmathematics,beingafterallaproductofhuman
thought independent of experience, is so admirably adapted to the
objects of reality?
— Albert Einstein
Contents
Knowledgeisone. Itsdivisionintosubjects
is a concession to human weakness.
— Halford J. Mackinder
Preface xiii
Acronyms xvii
George Green (1793-1841) xix
1 Molecular-Orbital Picture 1
1.1 Adatom-Substrate Interaction . . . . . . . . . . . . . . . . . . 2
1.1.1 P-states . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.1.2 N-states . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Adbond Character . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.1 Homopolar bond . . . . . . . . . . . . . . . . . . . . . 12
1.2.2 Ionic bond . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.3 Metallic-like bond . . . . . . . . . . . . . . . . . . . . . 16
2 Resolvent Technique 23
2.1 Projection Operators . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Perturbation Formulation . . . . . . . . . . . . . . . . . . . . 25
2.3 Chemisorption on Cyclic Crystal . . . . . . . . . . . . . . . . 27
2.3.1 Cyclic crystal . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.2 Cyclic Green function . . . . . . . . . . . . . . . . . . 28
2.3.3 Model representation . . . . . . . . . . . . . . . . . . . 30
3 Dyson-Equation Approach 35
3.1 Dyson Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.2 Density of States . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.3 Chemisorption on Monatomic Substrate . . . . . . . . . . . . 38
3.3.1 Adatom Green function . . . . . . . . . . . . . . . . . 39
x CONTENTS
3.3.2 Adatom self-energy and density of states . . . . . . . . 40
4 Anderson-Newns-Grimley Model 45
4.1 Second Quantization Formalism . . . . . . . . . . . . . . . . . 46
4.1.1 Creation and annihilation operators . . . . . . . . . . . 46
4.1.2 Hamiltonian in c-operator form . . . . . . . . . . . . . 48
4.2 ANG Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . 50
4.3 Hartree-Fock Treatment . . . . . . . . . . . . . . . . . . . . . 52
4.3.1 Perturbed energy . . . . . . . . . . . . . . . . . . . . . 52
4.3.2 Adatom Green function and density of states . . . . . . 55
4.3.3 Adoccupancy and self-consistency . . . . . . . . . . . . 58
4.3.4 Chemisorption energy and charge transfer . . . . . . . 61
4.4 Oxygen on III-V Semiconductors . . . . . . . . . . . . . . . . 65
4.4.1 Electronic properties of AB-type semiconductor . . . . 66
4.4.2 Chemisorption functions . . . . . . . . . . . . . . . . . 69
4.4.3 Results and discussion . . . . . . . . . . . . . . . . . . 74
5 Supported-Metal Catalysts 75
5.1 Metal-Support Greenian . . . . . . . . . . . . . . . . . . . . . 75
5.2 Substrate Surface Green Function . . . . . . . . . . . . . . . . 79
5.3 Chemisorption Properties . . . . . . . . . . . . . . . . . . . . 82
5.4 H-Ni/ZnO System . . . . . . . . . . . . . . . . . . . . . . . . 86
6 Disordered Binary Alloys 91
6.1 Coherent-Potential Approximation . . . . . . . . . . . . . . . 92
6.2 Alloy Surface Green Function . . . . . . . . . . . . . . . . . . 99
6.3 Adatom Green Function . . . . . . . . . . . . . . . . . . . . . 102
6.4 Chemisorption Properties . . . . . . . . . . . . . . . . . . . . 105
6.5 H-Cu/Ni and H-Au/Pt Systems . . . . . . . . . . . . . . . . . 109
7 Electrified Substrates 117
7.1 Wannier-Stark Ladders . . . . . . . . . . . . . . . . . . . . . . 117
7.2 Recursive-Green-Function Treatment . . . . . . . . . . . . . . 123
7.3 Electrochemisorption . . . . . . . . . . . . . . . . . . . . . . . 129
7.4 H-Ti and H-Cr Systems . . . . . . . . . . . . . . . . . . . . . 133
CONTENTS xi
8 Indirect Adatom Interactions 139
8.1 Adatom Green Function . . . . . . . . . . . . . . . . . . . . . 139
8.2 Chemisorption Functions . . . . . . . . . . . . . . . . . . . . . 144
8.3 Self-consistency and Charge Transfer . . . . . . . . . . . . . . 148
8.4 Change in Density of States . . . . . . . . . . . . . . . . . . . 148
8.5 Chemisorption and Interaction Energies. . . . . . . . . . . . . 152
8.5.1 Chemisorption energy . . . . . . . . . . . . . . . . . . 152
8.5.2 Interaction energy. . . . . . . . . . . . . . . . . . . . . 153
8.6 2H-{ Ti, Cr, Ni, Cu } Systems . . . . . . . . . . . . . . . . . . 155
Appendices 165
A. Evaluation of J (b) . . . . . . . . . . . . . . . . . . . . . . 165
n
B. Slater Determinant . . . . . . . . . . . . . . . . . . . . . . 167
C. Anticommutation Relations . . . . . . . . . . . . . . . . . . 168
D. Plemelj Formula . . . . . . . . . . . . . . . . . . . . . . . . 171
E. Residues of g(ε) . . . . . . . . . . . . . . . . . . . . . . . . 172
F. Logarithmic Function . . . . . . . . . . . . . . . . . . . . . 173
G. Range of tan−1 . . . . . . . . . . . . . . . . . . . . . . . . . 173
H. Electronic States of Binary Chain . . . . . . . . . . . . . . 175
I. Normalization Factor . . . . . . . . . . . . . . . . . . . . . . 177
J. Green Function of Infinite Monatomic Chain . . . . . . . . 178
K. Green Function of Infinite Semiconductor . . . . . . . . . . 180
L. Alternate Expression for ∆E . . . . . . . . . . . . . . . . . 187
M. Analytic Green Function for Electrified Atomic Chain . . . 188
Bibliography 193
Author Index 203
Subject Index 205
Preface
Prefaces are like speeches before the cur-
tain; they make even the most self-forgetful
performers seem self-conscious.
— William Allen Neilson
The study of phenomena and processes at the phase boundaries of mat-
ter is the realm of the surface scientist. The tools of his trade are drawn
from across the spectrum of the various scientific disciplines. It is therefore
interesting that, in investigating the properties of such boundaries, the sur-
facist must transcend the interdisciplinary boundaries between the subjects
themselves. In this respect, he harkens back to the days of renaissance man,
when knowledge knew no boundaries, and was pursued simply for its own
sake, in the spirit of enlightenment.
Chemisorption is a gas-solid interface problem, involving the interac-
tion of a gas atom with a solid surface via a charge-transfer process, during
which a chemical bond is formed. Because of its importance in such areas as
catalysis and electronic-device fabrication, the subject of chemisorption is of
interest to a wide range of surfacists in physics, chemistry, materials science,
as well as chemical and electronic engineering. As a result, a vast litera-
ture has been created, though, despite this situation, there is a surprising
scarcity of books on the subject. Moreover, those that are available tend to
be experimentally oriented, such as, Chemisorption: An Experimental Ap-
proach (Wedler 1976). On the theoretical side, The Chemisorption Bond
(Clark 1974) provides a good introduction, but is limited in not describing
the more advanced techniques presently in use. Other treatments confine
the discussion of chemisorption to chapters or sections in works of a more
xiii