PHYSICAL METALLURGY OF REFRACTORY METALS AND ALLOYS

METALLOVEDENIE TUGOPLA VKIKH METALLOV I SPLAVOV

METAJIJIOBE,lJ.EHVlE TyronJIABKVlX METAJIJIOB VI CnJIABOB

PHYSICAL MET ALLURGY OF REFRACTOR Y METALS

AND ALLOYS

E. M. Savitskii and G. S. Burkhanov A. A. Baikov Institute of Technology Academy of Sciences of the USSR

Moscow, USSR

Translated from Russian

® CONSULTANTS BUREAU· NEW YORK-LONDON· 1970

Evgenii MikhaiIovich Savitskii was born in 1912 and completed his studies at the Moscow Institute of Nonferrous Metals and Gold in 1936, specializing in physical metallurgy; from 1937 to 1953 he worked at the Institute of Gen­eral and Inorganic Chemistry, where in 1940 he was appointed director of the mechanical testing laboratory. Since 1953 he has been associated with the A. A. Baikov Institute of Metallurgy as director of the refractory and rare metal alloys laboratory. In 1953 he was awarded the degree of Doctor of Chemical Sciences, and in 1954 was appointed Professor of Physical Metallurgy. In 1966 Savitskii was elected corresponding member of the

Academy of Sciences of the USSR.

Gennadii Sergeevich Burkhanov was born in 1932 in Moscow. In 1955 he was graduated from the Moscow Steel Institute, where he specialized in physical metallurgy. After completing graduate studies at the A. A. Baikov Institute, he joined its staff, and since 1963 has been a senior scientific

assistant in the refractory and rare metal alloys laboratory.

ISBN-13: 978-1-4684-1574-2 e-ISBN-13: 978-1-4684-1572-8 DOT: 10.1007/978-1-4684-1572-8

The original Russian text, published by Nauka Press in Moscow in 1967 for the A. A. Baikov Institute of Metallurgy of the Academy of Sciences of the USSR, has been corrected by the authors for the present edition. The English translation is published under an agreement with Mezhdunarodnaya

Kniga, the Soviet book export agency.

EBzeflu(i MuXatVIOBU'i Ca8ulf1wii,

reflHaauii Cepzee8u'l Bypxaflo8

~eTannoBe~eHue TyronnaBKux MeTannOB U cnnaBOB

Library of Congress Catalog Card Number 69-12519

SBN 306-10841-0

© 1970 Consultants Bureau, New York A Division of Plenum Publishing Corporation 227 West 17th Street, New York, N. Y. 10011

United Kingdom edition published by Consultants Bureau, London A Division of Plenum Publishing Company, Ltd.

Donington House, 30 Norfolk Street, London, W.C. 2, England

All rights reserved

No part of this publication may be reproduced in any form without written permission from the publisher

PREFACE TO THE AMERICAN EDITION

The principal reasons which induced the authors to write this book and the features of the book are set forth in the preface to the Russian edition.

That section of the science of metals which in Russian is called "metallovedenie" or the "physical chemistry of metals" is generally referred to in scientific and technical literature published in the English language by the term "physical metallurgy." These concepts are much broader than the term" metallography," used in the scientific and technical literature of various countries, and applied solely to research on the interrelationships of the structure and proper­ties of metals and alloys.

Each science must have its own subject and its own method of research. Certainly, all specialists will agree that metals and alloys, including their solid solutions, mechanical mix­tures, and metallic compounds, form the subject of "physical metallurgy" or "physical chemis­try of metals." The aim of this science. is to produce a theory and to elucidate the experimental relationships which ought finally to make it possible to calculate quantitatively alloys Of given properties for any working conditions and parameters.

With regard to the methods of research on metals and alloys, we assume that "physical metallurgy" may properly employ any theoretical and experimental methods which will help to solve its basic problems. The experience of the last few decades has shown that among the experimental methods a leading position is occupied by the physicochemical analysis of metal systems developed by N. S. Kurnakov, that is to say, the systematic investigation of the phYSical properties of alloys as a function of he variation of their chemical composition and phase com­position. This method has also been employed for investigating the interrelationship of the structure and properties of alloys at different temperatures and pressures (see E. M. Savitsky, The Influence of Temperature on the Mechanical Properties of Metals and Alloys, Stanford University Press, 1961). The "physical chemistry of metals" makes extensive use of physico­chemical analysis. The science of metals and alloys absorbs all the achievements of the exact fundamental sciences, primarily physics and chemistry. It may even be said more precisely: The "physical chemistry of metals" or "physical metallurgy" is the synthesis of the physics of metals and the chemistry of metal alloys. The distribution and energy of electrons is the basic factor determining the crystal structure and all the properties of metals and alloys. The main problems which have to be solved in the framework of these sciences are the following: the electronic structure and nature of the interatomic bond in metal crystals, solid solutions of metals and metallic compounds, the development of methods for the quantitative measurement of the value of the interatomic forces with variation in the fundamental parameters of thermody­namic equilibrium (composition, temperature, pressure), by the application of electromagnetic, gravitational, and other fields, penetrating radiations, research on the interrelationship of the structure and properties of metals and alloys, the influence on them of impurities, defects and their anisotropy, as well as the influence of specific experimental, technological, or service conditions.

v

vi PREF ACE TO THE AMERICAN EDITION

It is clear from this that our science, if only in the interests of its own development, can­not live in an ivory tower of theory, shut off from the technology and the service of metal arti­cles, since these in particular finally decide the suitability of the new metallic materials devel­oped. It is no accident that many of the encyclopedic reviews published in the USA on rare and refractory metals bear the title "Progress in Science and Technology."

There may be different views among specialists regarding the content, limits, and methods of the "physical chemistry of metals" or "physical metallurgy." From the point of view of the writers of this book, in addition to what has been set forth in this preface, its readers may gain some idea after acquaintance with the contents of the book, and particularly with its "Conclusion."

The book was published in Moscow in 1967. Judging by the reviews in periodicals, the effort has been regarded as timely and successful. The Russian edition of the book was sold out in several weeks, indicating the growing demand for books on refractory metals and alloys.

The level of "physical metallurgy" is determined primarily by the requirements of engi­neering for metals and alloys possessing a definite combination of properties. Originally, there­fore,the "physical metallurgy" of iron, steel, and cast iron was first developed, then that of nonferrous and light metals, and in recent years the physical metallurgy of refractory metals and rare metals.

The scientific and technological revolution which is unfolding before our eyes, the appear­ance of new branches of industry - atomic, jet, electronic, and space technologies - is accom­panied by constantly increasing and diverse requirements for metallic materials. These de­mands may often be satisfied only by the use of rare and refractory metals and their alloys and compounds. The demands of the new technology have also resulted in the appearance of a new branch of the refractory and rare metals which produces, almost all the known elements of Mendeleev' s periodic system, and their alloys, and compounds.

The experimental data and theoretical concepts relating to refractory and rare metals have made it possible to reconsider the structure and properties of ordinary industrial ferrous and nonferrous metals and alloys. In this respect, it is possible to include concepts on purity and structural perfection, the part played by interstitial impurities, particularly carbon and oxygen, in the cold brittleness of metals and alloys, information obtained regarding single crys­tals in the construction of the phase diagrams of alloys of refractory metals, in research on superconducting alloys, the function of rare-earth metals, the" rhenium effect," and the mecha­nism of hardening by the precipitation of nonmetallic compounds in quenched niobium and mo­lybdenum alloys.

It has become an urgent problem to create a "physical metallurgy" of each refractory and rare metal, as was done earlier for iron, nickel, copper, aluminum, magnesium, and more recently for titanium. The physical metallurgy of niobium, vanadium, rare-earth metals, mo­lybdenum, rhenium, platinum, palladium, lithium, yttrium, and the radioactive metals may be regarded to be already developed, especially at the level of binary systems [see the bibliog­raphy appended to the article by E. M. Savitskii in Metallovedenie i termicheskaya obrabotka metallov, No. 10, p. 12 (1967) 1.

Russian scientists value the achievements of their foreign colleagues highly. We apolo­gize if some of the experimental work carried out in the USA or in other countries is not de­scribed in adequate detail in our book, and in connection with a proposed second Russian edition of our book, we should like to reguest our foreign colleagues to send us copies of their publica­tions in the field of the physical metallurgy of refractory metals and alloys.

Unfortunately, a lack of knowledge of the language is often one of the principal difficulties preventing a closer contact between scientists and the exchange of information regarding their

PREFACE TO THE AMERICAN EDITION vii

researches and new ideas. The translation of books and articles helps to minimize this short­coming. We are grateful to Plenum Publishing Corporation for their initiative and labor in publishing an English version of our book, and esteem this as a friendly act to the scientists of our country and to us personally.

The A. A. Baikov Institute of Metallurgy of the Academy of Sciences of the USSR, Moscow January. 1968

E. M. Savitskii G. S. Burkhanov

PREFACE TO THE RUSSIAN EDITION

New metals and alloys, new methods of producing and investigating them, new extensive experimental data and fields of application - all this has immeasurably widened the horizons of modern physical metallurgy, metal physics, and the physical chemistry of metals compared with the level of knowledge at the end of the nineteenth and the beginning of the twentieth cen­turies.

Many earlier data on the properties of metals are now out of date, having been determined on insufficiently pure metals. In recent years, all the refractory transition metals (titanium, zirconium, hafnium, vanadium, niobium, tantalum, rhenium, pure iron, manganese, chromium, molybdenum, tungsten), refractory metals of the platinum group (osmium, ruthenium, iridium, and others), lithium, beryllium, semiconductors (germanium, silicon, boron, high-purity carbon), and the radioactive metals (uranium, thorium, plutonium) have become available for research. The rare-earth metals of the cerium subgroup (lanthanum, cerium, neodymium, praseodymium), metals of the yttrium subgroup, as well as scandium and yttrium are being produced in ever­increasing quantities. They are no longer just rare laboratory specimens, but industrial metals for alloying and for application as alloy bases.

In the 50' sand 60' s of this century, scientific and production workers created a new com­bination of the media of the chemical technology of the production of pure substances and vacuum metallurgy: ion exchange chromatography, the iodide method, electrolysis, distillation, vacuum or argon-arc, electron-beam, plasma, and laser melting, vacuum zone refining using different sources of heat, pressure treatment and welding in a vacuum or in an atmosphere of inert gases, vacuum annealing, use of getters, protective envelopes, coatings, and so forth.

The temperature ceiling of physical metallurgical research in particular has been raised. Vacuum metallography, vacuum dilatometry, and the determination of electrophysical proper­ties, high-temperature thermal analysis, neutron diffraction analysis, electron, ion, and proton microscopy with magnifications of hundreds of thousands and even millions of times, all these made their appearance. In addition, research on the structure and special properties of metals and alloys close to the absolute zero of temperature in liquid helium (4.2°K) is being contin­uouslyextended, principally in connection with rapid developments in recent years in the physics of metals, physical chemistry, and physical metallurgy of superconducting materials.

This book is based primarily on the experimental work of the Refractory and Rare Metals and Alloys Laboratory of the A. A. Baikov Institute of Metallurgy of the Academy of Sciences of the USSR. Two main circumstances led to the writing of this book. They were the increasing value of refractory metals in the new technology and the complete lack of monographs and text­books on the physical metallurgy and physical chemistry of refractory metals and alloys (with the exception of titanium and niobium). In the meantime, the need for the publication of reviews of work on these materials had undoubtedly grown, since in recent years, the people who, by the very nature of their work, have to deal with the production, treatment, purification, research on electrophysical and mechanical properties, and, in particular, with the application of semi-

ix

x PREF ACE TO THE RUSSIAN EDITION

finished products and components made of refractory metals and alloys, in instruments and apparatus of the new technology (jet aircraft and rockets, satellites and spacecraft, nuclear jets, the special-purpose fleet, devices for converting thermal energy into electrical energy, superconducting magnets and other devices, electrical vacuum instruments, chemical reactors). and also as radioactive isotopes and surgical material in medicine.

Specialists in the field of the production of the devices and appratus mentioned (designers, physicists, chemists, power engineers, technologists, workers in the radioelectronic industry), and finally surgeons, unfortunately do not as a rule receive the necessary grounding in general physical metallurgy and the physical chemistry of metals, and are still less familiar with cur­rent literature on research into the structure and properties of refractory metals, published in specialized metallurgical, chemical, and physical journals. Interest in the growth of science itself also calls for periodic reviews of the accumulated experimental data.

It is the hope of the authors that the collection in one book of a considerable proportion of published data on the structure properties and application of alloys will assist the work of the group of specialists mentioned with regard to the use of refractory metals in the new tech­nology, although the authors lay no claim to having exhaustively dealt with all the available in­formation on refractory metals and alloys which, in view of the vigorous development of re­search in these fields, is constantly being published in the Russian and foreign periodical press.

The universities and technical colleges as yet have no up-to-date textbook on the physical metallurgy and physical chemistry of refractory metals and alloys, despite the fact that the expanding volume of the application of refractory metals in industry is even now calling for suitable specialization in the metallurgical faculties of our universities. In time, such a text­book will be produced, but for the time being, lecturers, graduates, and undergraduates will be able if they so Wish to use the corresponding sections of the present monograph.

The planning of the book, the choice of material, and its interpretation have been carried out by the authors from the physicochemical standpOint, since at the present time, as practice has shown, such an approach to the problem of refractory metals and alloys is the most fruitful. The physical chemistry and physical metallurgy of refractory metals have not yet been finally formulated; they are in a state of dynamic development, and a number of cardinal questions, such as the control of plastic properties, the quantitative calculation of the physical properties, and concepts regarding the optimum structure of the metals, have not yet been sol ved. This is primarily due to the lack of a quantitative theory of metals and inadequate knowledge of the distribution of the electrons in crystals, and of the interatomic bond and the methods of measur­ing it, and also of the quantitative relationships between the structure and properties of metals, their compounds, and alloys. Of course, all this has affected the contents of the present book. Unfortunately, many questions of the physical metallurgy and physical chemistry of refractory metals (as is furthermore the case with all the other metals) can be considered only on a quali­tative level.

Nevertheless, it is essential to insist on drawing the attention of workers in science and production to the need for the creation of a valid phYSicochemical theory of metals; to take these considerations into account, a special chapter is devoted to the available information on the interatomic bond in refractory metals.

In accordance with the physicochemical bias of this monograph, the main attention is directed to a consideration of the interaction of refractory metals with each other, with other metals, and with nonmetallic impurities, and to the interrelationship of structure and proper­ties in accordance with the position of the refractory metals in the periodic system, as well as to the structure, properties, and application of their alloys. Data on natural resources, methods of purification, melting, and treatment are generally presented as reference material.

PREFACE TO THE RUSSIAN EDITION xi

In the discussion of structure and properties, the information available on vacuum-melted met­als and alloys has been mainly used as being more reliable. The book contains practically no discussion of these questions for cermet materials.

Owing to the intense demand of the new technology for metallic materials, postwar physi­cal metallurgy and the physical chemistry of metals are in a process of vigorous development. A numerous group of rare metals and alloys having become of industrial interest, the range of subjects of physical metallurgy is constantly widening and the overall available knowledge is becoming increasingly difficult to cover in one book, not to mention the considerations associ­ated with publications of considerable bulk. Books are therefore now being produced on the phYSical metallurgy of individual refractory rare metals. "Nauka" Press has already published monographs on the alloys of niobium and rhenium. As knowledge Widens, books will be pub­lished on the physical metallurgy of each metal, which of course does not preclude the writing of comprehensive works. Furthermore, in contemporary physical metallurgy, quite new sec­tions are appearing and developing as the result of the discovery in entire groups of metals of special physical properties, for example, the propensity of atomic nuclei to fission under the action of neutrons, the existence of superconducting properties of metals in liquid helium, re­sulting in the creation of entirely new branches of industry, and branches of physical metallurgy, such as the physical metallurgy of fissile materials and the physical metallurgy of superconductors.

For revealing the true properties of metals, undistorted by impurities and defects, ever­increasing attention is being devoted to their production and investigation in a particularly pure and perfect state in the form of single crystals.

Yet another new branch of physical metallurgy is currently being formed, the physical metallurgy of single crystals, which has come into being through the requirements of the new technology, and a new branch of metallurgical industry has already appeared, the production and treatment of single crystals of refractory and rare metals and alloys.

Taking into consideration the special scientific and practical significance of single crys­tals of refractory metals and alloys and the rapid development of the experimental investiga­tions of their structure and properties, a specially written lengthy chapter on single crystals has been included in this book for the first time in the literature of physical metallurgy. The foregoing also applies to a considerable degree to the material of Chapter IV, where problems, specific to refractory metals having a bod~T-centered cubic lattice are discussed in connection with methods of combating their cold brittleness.

Considerable attention has also been paid to technological peculiarities, which are very important and specific for refractory metals, and also to available data on the prospects of their industrial utilization.

The authors regard their work as a first attempt to solve a very difficult problem, that of producing a comprehensive printed work on the physical metallurgy and physical chemistry of refractory metals and alloys, useful to all who have to do with the production, investigation, and application of these materials.

The authors will accept with gratitude any comments which readers may have to make on the contents of the book and will endeavor to take them into consideration in a subsequent work.

The authors thank N. V. Ageev, I. V. Burov, V. L. Girshov, K. N. Ivanova, I. A. Karyazin, A. M. Zakharov, Yu. V. Emifov, 1. M. Kop'ev, D. V. Ignatov, V. P.Polyakov,andL.F.Myzenkov for reading various chapte rs of the manusc ript and making corrections, as well as M. 1. Beloborodov, S. p. Pertsev, E. V. Ottenberg, and 1. V. Mal'tsev for assistance in formulating the manuscript.

Chapter 1.

CONTENTS

Natural Resources and Methods of Producing Refractory Metals •....... 1

Natural Resources and Principal Minerals. • • • . • • . . . . . . . . . . . . . . . . . . 1 Production Methods. . . . . . . . . . . . . . . • . . . . . . . . . . . . . . . . . . . . . . . . 3 Literature Cited. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

Chapter II. Interatomic Bond, Crystal Structure, and Principal Physical Properties of Refractory Metals ............................ . 7

Interatomic Bond in Transition Metals . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 Crystal Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 Physical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 Compatibility of Refractory Metals and Alloys with

Various Materials. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 Mechanical Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . 39 Recrystallization of Refractory Metals . . . . . . . . . . • • • • • . . . . . . . . . . 47 Effect of Irradiation on the Properties of

Refractory Metals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Literature Cited" . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

Chapter III. Physicochemical Interaction of Refractory Metals with Elements 01 the Periodic System .... 59

Present State of the Theory of Metal Alloys. . . . . . . . . . . . . . . . . . . . . . . . 60 Characteristics of the Methods of Investigating Refractory

Metal Alloys • • • • • • • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 Interaction of Refractory Metals of Groups IV-VIII

(in the Limits of Each Group) . . . . . . .. . . . . . . . . . . . . . . . . . . . . . 75 Interaction between Metals of Groups Va and VIi

and Their Interaction with Metals of Other Groups . . . . . . . . . . . . . . . 77 Interaction of Rhenium with Other Refractory Metals. . . . . . . . . . . . • . . . . . 91 Some Ternary and Multicomponent Systems of

Refractory Metals. . . . . . . . • . . . . . . . . . . . . • . • . . . . . . . . . • . • . 95 Interaction of Refractory Metals with Interstitial Impurities. . . . . . . . . . . . . 100 Literature Cited. . . . . . . . . . . . . . . • . . • . . . . . . . . . . . . . . . . . . . . . . . 109

xiii

xiv CONTENTS

Chapter IV. The Problem of Cold Brittleness of Refractory Metals and Alloys............. 119

Cold Brittleness of Metals and the Interatomic Bond. • • . . . . . • • • . . . . . . . 119 Methods of Determining the Ductile - Brittle Transition Temperature ..... 121 Factors Affecting the Ductile - Brittle Transition Temperature • • • • . . . • . . 123 Methods of Combating Cold Brittleness in Refractory Metals. . . . . . . • . . • • 139 Literature Cited. . • . . • • • • • • . . . . • . . . . • . . . . . • . . . . . . . . . . . . . . . 142

Chapter V. Single Crystals of Refractory Metals andAlloys ....................... o ••• o •• ooo 147

Methods of Growing Metal Single Crystals . . . • . . • • . . • • . • • . • . . . . • . • 148 SpecifiC Features of the Zone-Refining Process •....••.......•....• 150 Production of Molybdenum and Tungsten Single Crystals. . . . . . • • . . • . . . . 154 Estimation of Purity and Degree of Perfection of

Metal Single Crystals. . • . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155 Substructure of Refractory Metal Single Crystals 0 •••••••••••••• 0 0 • • 158 Growing of Refractory Metal Single Crystals of Given

Crystallographic Orientation. • • • . . . . . . . . • . . . . . . . . . . . . . . 163 Influence of Plastic Deformation on the Structure of Tungsten

and Molybdenum Single Crystals •...•........••....•. 0 • • • 166 Deformation of Rhenium Single Crystals. . . . . . . . . • . . • . . . . • . . • . . • • . 167 Influence of Impurities on the Substructure of Deformed

Refractory Metal Single Crystals .....••...... 0 • • • • • • • • • • 168 Mechanical and Other Properties of Metal Single Crystals •....... 0 • • • • • 169 Anisotropy of the Properties of Single Crystals of Metals

Having a Body-Centered Cubic Lattice •....•••...• 0 • • • • • • • • 176 Production and Properties of Refractory Metal Alloy Single Crystals • • . . . . 179 Production of Semifinished Products of Tungsten and

Molybdenum Single Crystals and Their Properties. . • . • • . . • • . . . 183 Literature Cited •.....••.••..•..••......••.••• 0 • • • • • • • • • • • 185

Chapter VI. Alloys of Refractory Metals ....••...••..•......• 191

Chromium-Based Alloys .•..•..............• 0 ••••••••••••• 0 • 193 Molybdenum-Based Alloys. . . . . • . • . . . . . . . . . . • • . . . . . • . . . . . • . . . 194 Tungsten-Based Alloys. . • . . . . • • . . . • • . . . . . . . • . . . • . . . . . . . . . . . 199 Rhenium Alloys . • . • • • . • . . . . . . . • • . • • . . . . . • • • • . . • . • . • . . . . . . 203 Vanadium-Based Alloys. . . . . • . . . . . . . • . . • . . . . . . . . . . . . . . . . . . • • 207 Niobium-Based Alloys ...•...••••..•••...••....•• 0 ••••••• 0 • • 207 Tantalum-Based Alloys. . . . . . . . . . . . . • . . . . . . • . • • • . . • • • . . . . . • . 215 Alloys Based on Titanium, Zirconium, and Hafnium. . . . . • . • . . . . . . . . . . 218 Alloys Based on the Noble Metals. . • . . . . . . . . . . . . . . . . . . . . . . . . . . . 219 Metallic Compounds ..............••••• 0 • • • • • • • • • • • • • • • • • • • 222 Metals of SAP Type (Metal- Metal Oxide). . • • . . . . • • . . . • . . • • . . . . . . . 223 Protection of Refractory Metals and Alloys from Oxidation ......• 0 •••• 0 225 Literature Cited. . . . . . . . • . • . . . . . . . . . • . . . . • • • . . • • • . • • • • • . . . 228

CONTENTS xv

Chapter VII. Melting and Treatment of Refractory Metals and Alloys. • . . . • • . • . • • . . • • . . • • • . • • . • 235

Melting and Casting of Refractory Metals and Alloys. • • • • • • . . . • • . . . . . 235 Pressure Working of Refractory Metals and Alloys ••.•.......•.... 251 Heat Treatment of Refractory Metals and Alloys. • . • • . . . • • • • . . . . . . . • 269 Welding and Soldering of Refractory Metals. . • • . . . • • • . . • . . . • . . . . . . 275 Literature Cited .•.••• 0 ••••• 0 • • • • • • • • • • • • • • • • • • • • • • • • • • • • 277

Conclusion. • • . • . • • . • • . . • • . . • • . . • . . • . . . . . . . • . . . • . • . • . • . . . . • . . . 285