Diffusion in Ceramics

464 Pages·2016·17.04 MB·English

by  Joshua Pelleg (auth.)

Solid Mechanics and Its Applications
Joshua Pelleg
Diffusion in
Ceramics
Solid Mechanics and Its Applications
Volume 221
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Joshua Pelleg
Diffusion in Ceramics
123
JoshuaPelleg
Department ofMaterials Engineering
Ben-Gurion University of the Negev
Beer Sheva
Israel
ISSN 0925-0042 ISSN 2214-7764 (electronic)
Solid MechanicsandIts Applications
ISBN978-3-319-18436-4 ISBN978-3-319-18437-1 (eBook)
DOI 10.1007/978-3-319-18437-1
LibraryofCongressControlNumber:2015939163
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Ever since the beginning, the wheels of
random transport have been moving the
Universe in the spirit of Genesis.
To my wife Ada and my children Deenah
and her late husband, Gidon Barak, Ruth
and Christer Kallevag, Shlomit and Asher
Pelleg and their families.
Preface
This textbook is unique at present, since no other book on this subject currently
exists. It is composed of two parts: Part I on the Fundamentals of Diffusion and
Part II on Diffusion in Ceramics (Experimental).
Part I is quite general, explaining the basics of diffusion as first presented in a
scholarlymannerbyAdolfFick,inwhosestepsdiffusionresearcherstheworldover
have been walking for decades. Following his fundamental laws of diffusion,
progress has been made in the field by internationally distinguished theoreticians
and experimentalists. Undoubtedly, the current stage in understanding of diffusion
was reached as the result of precise measurements of diffusion coefficients in
corroboration of basic theories. Although most of the experiments were initially
performed on ‘well-behaved’ metals, such as the noble metals, later diffusion
coefficientmeasurementsextendedtoothermetalsandalloysandthentoallsolids,
including ceramics. In order to understand lattice diffusion and to avoid the con-
tributionofshort-circuitdiffusion(mainlyingrainboundaries),singlecrystalswere
used alongside polycrystalline solids.
Part I contains 10 chapters. Chapter 1 considers macroscopic diffusion, the
backboneofFick’slawsandsolutionstovariouscasesencounteredinexperimental
diffusion. Microscopic (or atomic) diffusion is dealt with in Chap. 2. The basis of
atomic transport is the random walk, which is believed to be the cornerstone of
atomic diffusion.Often, thewalkofa‘drunken sailor’exemplifiestherandomness
ofdiffusion.Diffusionismainlytheexchangeofanatomwithsomedefectarriving
at its vicinity. Vacancy-dominated diffusion is the basic entity exchanging places
with an atom, unless an interstitial mechanism of small atoms regulates the diffu-
sion process. In Chap. 3, the Schottky and Frenkel defectsinvolved indiffusion in
ceramicsarediscussed.Interstitialdiffusionisalsoincludedinthischapter,sinceit
may be an important method of transport in ceramics. The thermodynamics of
defect formation is illustrated for vacancies. Chapter 4 focuses on a discussion of
diffusion mainly by vacancy and interstitial mechanisms. Self-diffusion, solute
diffusion, and correlation effects in ionic crystals (some ceramics are ionic in nat-
ure) are the subject of Chap. 5. The relation between diffusion and conductivity is
discussed. Integral parts of this chapter are binding, enhanced diffusion, and the
ix
x Preface
isotopeeffect.InterdiffusionandDarken’sequationarethemaintopicsinChap.6.
Grain-boundary diffusion is considered in Chap. 7, which also discusses self- and
solute diffusion in grain boundaries, as well as diffusion in nano-materials. Self-
diffusion and solute diffusion in dislocations are presented in Chap. 8, while
Chap. 9 considers some important and commonly used experimental techniques,
suchastracertechnique,SIMS,andconductivitymethods.Part1closeswithsome
empirical rules for evaluating diffusion coefficients and activation energies in
Chap. 10.
Part II is focused on the experimental observation of diffusion in ceramics, and
selectively discusses five of the most technically important ceramics, examples of
monolithic and single-phased ceramics: alumina (Al O ), silicon carbide (SiC),
2 3
magnesia (MgO), zirconia (ZrO ), or yttria-stabilized zirconia (YSZ), and silicon
2
nitride(Si N ),representingthenitrideceramics.Asfaraspossible,thediscussion
3 4
on diffusion for each of these ceramics follows the same pattern; thus, each dis-
cussion starts withself-diffusion of a certain ceramiccomponent and then presents
its solute (impurity) diffusion in single crystals, followed by its self- and solute
diffusion in polycrystalline ceramics. Separate sections deal with the self-diffusion
of each component and its solutes in grain boundaries, and then its self- and
impurity (solute) diffusion in dislocations. Finally, each chapter summarizes the
diffusionequationsaccordingtotheoutlinedpattern,sothatonecanquicklyfinda
diffusionequation relatingthediffusioncoefficienttotheinversetemperature inan
Arrhenius-type relation.
Actual problems are not presented for solution; lecturers may devise their own
problems to challenge their students. Other books on diffusion may include such
exercises, but this author encourages the readers to seek practical problems and
their probable solutions in the field.
I would like to express my gratitude to all the publishers and authors for their
permission to use and reproduce some of their illustrations and microstructures.
Last but not least, without the tireless devotion, help, understanding, and
unlimitedpatienceofmywifeAda,Icouldneverhavecompletedthisbook;despite
my decades of teaching in this field, her encouragement was essential and her
helpfulattitudeinstrumentalininspiringmetowritethisbook.Freeingmefromall
domestic chores enabled me to devote my time to writing and to concentrate my
energy on accomplishing my goal. Also, my heartfelt thanks to Ethelea Katzenell,
at the Ben-Gurion University of the Negev, for improving the English.
Contents
Part I Fundamentals of Diffusion
1 Macroscopic Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.1 Fick’s First Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Fick’s Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Some Most Common Solutions for Eq. (1.5) . . . . . . . . . . . . 6
1.3.1 Thin-Film Solution . . . . . . . . . . . . . . . . . . . . . . 7
1.3.2 Short Bar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.3.3 Diffusion in a Pair of Semi-infinite Solids
(The Extended Initial Distribution
of the Diffusant) . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.4 Diffusant Confined in a Region, −h < x < +h. . . . 10
1.3.5 Separation of Variables: A Method
for Solving the Diffusion Equation . . . . . . . . . . . 12
1.3.6 Diffusion Out of a Slab . . . . . . . . . . . . . . . . . . . 13
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Further Reading. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 Microscopic (or Atomic) Diffusion. . . . . . . . . . . . . . . . . . . . . . . . 15
2.1 Random Motion of Atoms . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2 Random Walk. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Defects in Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 Schematic Illustration of Point Defects. . . . . . . . . . . . . . . . . 22
3.1.1 Vacancies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.1.2 Interstitials . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.1.3 Point Defects of Mixed Character . . . . . . . . . . . . 23
3.1.4 Point Defects in a Crystal. . . . . . . . . . . . . . . . . . 25
xi