simulation capabilities that are proving to
be very useful in this effort. For example,
atomistic-scale calculations can be used to
determine the strength of a dislocation–
dislocation interaction when one dislocation
cuts through another, and a dislocation-
dynamics calculation can be used to incor-
porate the results into a large-scale model
including the configuration of hundreds
or even thousands of dislocations. This
could be further tied into a finite element
simulation that would couple this disloca-
tion motion with external stresses and
strains. Unfortunately, experiments, ana-
lytical models, and simulations often “pass
in the night,” in that, although they are
intended to study the same phenomena
with the same goals, they often are con-
ducted at incompatible time or length scales.
As a result, it is difficult to compare them.
In the following articles, the general
theme of mechanical behavior in small di-
mensions has been divided into five areas:
intrinsic stress generation, elastic defor-
mation, dislocation-mediated plasticity,
diffusion-mediated plasticity, and fracture
and adhesion. For each topic, a team of
experts has been assembled representing
a range of viewpoints. Experimentalists,
analytical modelers, and simulators have
contributed their views on these topics in
an attempt to provide an overview of what
is known, what remains to be done, and
how different approaches might be com-
bined to most effectively solve problems.
In some cases, combinations of experiment,
continuum modeling, and simulations have
been very successful; in other cases, they
are still far apart.
The first article, by Floro et al., is unique
in that it is the only one in this issue that is
not about deformation per se. A common
feature of many nanoscale materials is that
they are manufactured and used on rela-
tively massive substrates. Due to differen-
tial thermal expansion or microstructural
evolution, high stresses may arise. Stresses
may also arise as a result of microstructure
evolution during film growth. Recent un-
derstanding of this problem has grown
considerably as results from sensitive real-
time measurements of stress evolution are
combined with continuum modeling and
atomistic simulation. These studies have
revealed a generic compressive–tensile–
compressive sequence that correlates with
island nucleation and growth, island coa-
lescence, and postcoalescence film growth.
Compressive stresses can be attributed to
surface stress effects and to the flux-driven
incorporation of excess atoms within grain
boundaries. Tensile stresses result from is-
land coalescence and grain growth.
Mechanical
Properties in
Small Dimensions
Richard P.Vinci and Shefford P. Baker,
Guest Editors
Abstract
This brief article describes the content of the January 2002 issue of MRS Bulletin
focusing on Mechanical Properties in Small Dimensions. Articles discuss the current
understanding of stress evolution during thin-film growth, elastic and anelastic behavior,
dislocation-mediated plasticity, creep deformation, and fracture. Emphasis is placed on
explaining the mechanisms that underlie the well-known fact that length scale can play
a significant role in mechanical behavior.
Keywords: mechanical properties, thin films.
Like many other properties, the mechani-
cal properties of materials begin to deviate
from bulk scaling laws when characteristic
dimensions become small. Such deviations
may occur when either microstructural
features (e.g., grain size) or object dimen-
sions approach the length scales of defects,
defect interactions, or processes that con-
trol deformation. Unlike other physical
properties, which deviate from continuum
models only at atomistic length scales,
mechanical properties are often found to
deviate from bulk scaling behavior at sur-
prisingly large length scales. In many cases,
deviations are clearly apparent when the
smallest relevant features are in the micro-
meter regime. A common example is the
fact that micrometer-scale thin films are
often found to support much higher stresses
than bulk samples of the same material.
This has been attributed to constraints on
dislocation motion or diffusion imposed
by the interfaces with the surrounding
layers and to the smaller grain size that is
often found in films.
behavior (e.g., blocking of dislocations at
grain boundaries, diffusion along inter-
faces) that is thought to be controlling and
build a model around that behavior. Some
attempts have been made to combine
mechanisms, but since the appropriate
means for summing the effects of different
mechanisms are not clear, such approaches
are limited.
Further complications arise due to ex-
perimental difficulties. Restricted volumes
and geometries may preclude the typical
approach of geometrically confining de-
formation to a well-defined gage section
in a “dog-bone”-shaped sample in uni-
axial loading. Furthermore, small strains
in small volumes translate into extremely
small displacements that must be imposed
and measured, and controlled at bound-
aries. A great deal of effort has gone into
developing tests that allow one to meas-
ure small samples, films, and patterned
structures by a variety of means with
good resolution.
One promising path for the future is
to combine experiments with theory and
simulations that can incorporate the effects
of many defects, provide details of defect
behavior that are not amenable to analyti-
cal approaches, and give information about
stress/strain distributions and boundary
conditions in complex sample geometries.
Increases in computational power and im-
provements in methods have resulted in
The combination of a tremendous tech-
nological driving force and a wealth of un-
familiar behavior has led to much interest
and work in this area. However, progress
has been slow. With few exceptions, me-
chanical behavior is determined by the
ensemble behavior of defects (vacancies,
grain boundaries, dislocations, cracks). A
typical approach is to select a single defect
In the second article, recoverable elastic
and anelastic deformation are discussed
12
MRS BULLETIN/JANUARY 2002
Ziegler
