Hume-Rothery Rules for Structurally Complex Alloy Phases: 1st Edition (Hardback) book cover

Hume-Rothery Rules for Structurally Complex Alloy Phases

1st Edition

By Uichiro Mizutani

CRC Press

356 pages | 142 B/W Illus.

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Hardback: 9781420090581
pub: 2010-11-15
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With a history that reaches back some 90 years, the Hume-Rothery rules were developed to provide guiding principles in the search for new alloys. Ultimately, the rules bridged metallurgy, crystallography, and physics in a way that led to the emergence of a physics of the solid state in 1930s, although the physical implications of the rules were never fully resolved. Even today, despite a revived interest brought about by the 1984 discovery of quasicrystals, much about the rules remains an enigma.

Now almost a century after the rules were put forward, Hume-Rothery Rules for Structurally Complex Alloy Phases provides researchers with an insightful and applicable interpretation of the Hume-Rothery electron concentration rule. Invoking first-principle band calculations, the book emphasizes the stability of structurally complex metallic alloys (CMAs).Written by Uichiro Mizutani, long considered the most knowledgeable expert on both the history and science of Hume-Rothery, this seminal work —

  • Offers a unified interpretation of phase stabilization mechanism of CMAs in different classes
  • Explains how to determine the effective valency of transition metal elements
  • Details establishment of d-states-mediated-FsBz interactions in strongly orbital-hybridizing systems
  • Covers the contrast between e/a and VEC, two notions of electron concentration parameters and includes a way to differentiate between them in designing new alloys
  • Explores strengths and shortcomings for the theory on alloy phase stability
  • Discusses the latest take on electron concentration for gamma-brass

This work summarizes the ongoing history of Hume-Rothery and reflects the theoretical studies that Professor Mizutani embarked upon to gain deeper understanding of the basic physics behind stabilizing effects related to electron concentration. It describes how metallic and covalent bonding styles can be harmonized to stabilize a given phase in relation to electron concentration and electrochemical effect as defined by the rules. Beyond theory, the approaches presented in these pages will prove of great value to researchers developing new functional metals and alloys.


… overall, the present book is an excellent update on complex alloy phases in metallic systems : both crystalline and quasicrystalline , which shall find place in major libraries of science and technology.

—G.S. Upadhyaya

Table of Contents


What is the Definition of the Hume-Rothery Rules?

Historical Survey of Chemistry and Metallurgy

Historical Survey of Crystallography

Historical Survey of Physics

Chemical Bonding and Phase Diagrams in Alloy Phase Stability

Cohesive Energy of a Solid

Free Energy of Formation and Enthalpy of Formation

Kinetic Energy of Electrons and the Role of the Pseudogap

Early Theories of Alloy-Phase Stability

Mott-Jones Model for Alpha-, Beta-, and Gamma-Brasses

The Model of Jones (I)

The Model of Jones (II)

First-Principles Band Calculations Using the Muffin-Tin Potential

First-Principles Band Calculations versus the Hume-Rothery Electron Concentration Rule

Origin of the Pseudogap: Orbital Hybridizations versus FsBz interactions

What Are First-Principles Band Calculations?

All-Electron Band Calculations Within the Muffin-Ti n Approximation

Wave Functions Inside and Outside the MT Sphere

Orthogonality Condition with Core Electron States

KKR-ASA Equation

Linearization Method

LMTO -ASA Method

Extraction of spd-d Orbital Hybridizations in the LMTO -ASA Method

AP W Method

LAP W Method

Hume-Rothery Electron Concentration Rule Concerning the α/β Phase Transformation in Cu-X (X = Zn, Ga, Ge, etc.) Alloy Systems

Stable fcc-Cu versus Metastable bcc-Cu

Fir st-Pri nciples Band Calculations for fccand bcc-Cu in Literature

FLAP W Electronic Structure Calculations for fcc- and bcc-Cu

Total-Energy and Valence-Band Structure Energy

Subject Categories

BISAC Subject Codes/Headings:
SCIENCE / Chemistry / General
SCIENCE / Solid State Physics