Journal of Materials Science and Chemical Engineering, 2013, 1, 7-10 Published Online October 2013 (
Copyright © 2013 SciRes. MSCE
Mechanical Properties of Micro- and Nanostructured
Copper Films
N. Kosarev, M. Khazin, R. Apakashev, N. Valiev
The Ural State Mining University, Ekaterinburg, Russia
Received June 2013
Mechanical properties of electrodeposited and electroless copper with nano- and crystalline structure are considered.
Grain diameters in films ranged from 0.06 to 8 μm. A model is described which takes into account the grain bou ndary
hardeni ng and den sity of dislocation.
Keywords: Nano- and Microcrystalline Materials; Hall-Petch Relation; Yield Point Stress; Grain Boundary Hardening
Coefficient; Nonequilibrium Grain Boundaries
1. Introduction
Structural features of nanomaterials determine their uni-
que properties. Properties of nanomaterials strongly de-
pend from type of distribution, form, size and chemical
composition of crystallites. Nanomaterials are used in
practice due to their mechanical properties: resilience,
plasticity, strength etc. The identification of regularities
of influence of size effects to forming of nanomaterials’
properties is one of the most important problems of na-
nostructural materials science.
In this paper copper films received by electroless and
electrodeposit precipitation to metallic and dielectric
substrates are researched. Thin structure of copper was
studied by the method of transmission electron micros-
copy on the electronic microscope TESLA BS 500. Cov-
erings are thinned by two-sided electrodeposite etching
with using the method of “window” in 50% water solu-
tion of ort hophosphoric acid.
2. Experiment
The studying of structure is conducted from the broad-
ening of the lines on received polycrystalline X-ray pic-
tures. The record of intensity distribution curves of mod-
el and samples is conducted on diffract meter “DRON-3”
with use of nickel-filtered characteristic Кα iron emis-
sion. For calculation of characteristics of thin structure
we us ed seven Fo urier co efficien ts (t = 0, 1, ···, 6). Stud-
ying of elemental composition of the conductors is con-
ducted by atomic adsorption method on the spectro-
photometer “Perkin Elmer” model 403. For researching
of mechanical properties the copper films is separated
from the substrate. Mechanical properties of free copper
films were determined at tensile tests on the breaking
machine with record of strain diagrams.
In polycrystalline metals the change in the flow stress
(σт) from the grain diameters (d) is described by Hall-
Petch relation:
ту okd
= +
σо: tension which characterizes plastic deformation re-
sistance, kу: coefficient which characterizes the influ-
ence of gra i n b oundaries on harde ning.
Received experimental results of research of depend-
ence of flow stress of electroless and electrodeposited
precipitated copper from the grain diameters (according
to d1/2) averaged by linear dependence (Figure 1).
Extrapolation of dependence
ε = 0
allowed to estimate the value of shear stress σƒ. Results
for electroless and electrodeposited precipitated copper
are concordant with data for the copper which got by
casting method and vacuum deposition method [1-3]. A
Table 1 shows coefficients of the Equation (1) which
adequate to samples received by various methods.
Value σƒ or σo depends from the presence of obstacles
for promotion of dislocations in sliding places: friction
forces of Peierls, cluster of dislocations, impurity atoms
and other defects). Coefficient ky characterizes a diffi-
culty of transmission of strains from grain to grain [4].
Elemental composition of precipitated conductors deter-
mined y atomic adsorption method similar to copper
grade М2 (mass fraction of the copper 99.70%). At the
same time the samples considered in works [2,3] similar
Copyright © 2013 SciRes. MSCE
, MPa
, μm
Figure 1. The dependence of the flow stress of copper from
the grain diameters: 1. electroless precipitated films, 2.
electrodeposited precipitated films.
Table 1. Values of Hall-Petch coefficients for copper re-
ceived by various methods.
Method of
producing Range of grain
diameters, μm σf, MPa σ0, MPa kу, MPa m1/2
Casted [5] 500 - 1000 - 26.10 0.11
Casted [4] 0.8 - 3.4 3.5 - 0.14
in vacuum [3] 0.056 - 8.4 6.4 - 0.15
electrolyte 1 0.5 - 5 6.2 37.31 0.17
electrolyte 2 0.8 - 8 6.1 32.74 0.15
liquor 1 0.06 - 2 6.5 27.21 0.16
liquor 2 0.10 - 2 6.4 25.16 0.15
liquor 3 0.06 - 1,5 6.5 36.23 0.18
liquor 4 0.04 - 2 6.7 28.14 0.16
Casted [6] 1 - 10 0.1 - 0.13
Casted [6] 0,1 0.06
Casted [6] 0.07 0.05
Casted [7] 50 0.12
Casted and
deformed [7] 0.18 0.09
Casted [8] 50 70 0.28
Casted and
deformed [8] 0.30 25 0.19
to the copper grade МОО (mass fraction of the copper
99.99%) [5].
Increasing of coefficient σƒ with vacuum condensates
may be connected with high concentration of point de-
fects formed at condensation of copper, i.e. due to the
method of receiving and also entering of the evaporator
material to the condensate [3].
Electroless precipitating of copper foil was conducted
at 310 - 320 К. Density properties of received samples
after annealing are exceeding values for massive copper.
Therefore we propose decrease in purity of copper 99,99
to 99.95%, i.e. the presence of impurities determines
observable increasing of coefficients’ meanings σƒ and ky.
This proposal confirmed by the data about electrodepos-
ited copper (Table 1). Injection of some organic addi-
tives led to conversion from equiaxed structure to co-
lumnar structure, thereafter temporary tensile strength
and yield point stress plasticity have reduced, and elec-
trical resistivity has increased.
3. Result
Estimation of density of dislocations at experimental
values of flow stress is consistent with data received
from broadening of the diffraction peaks. Increasing of
film thickness and copper grain diameters is lead to re-
ducing of density of dislocations, thereafter flow stress
and temporary tensile strength have reduced and plastic-
ity has increased.
Theory of the strain hardening is connect flow stress
and density of dislocations with relation [4,8]
σσρ fGb
= +
σf: shear stress, G: shear modulus, b: Burgers vector, ρ:
density of dislocations, α: constant close to 1.
Basis of this model is proposal about the path length of
dislocation l s proportionally to average grain diameter.
As far as plastic deformation and density of dislocations
are connected by relation [8]
ε = ρlb
, (3)
so density of dislocations is
ρ = ε/,a bd
(4 )
а1 is a constant.
Placing relation (4) in (2), we get
1/2 1/2
= +
Equation (5) is similar to Hall-Petch relation, if we
(ε).k aGb=
From (6) it is follows that value of coefficient ky must
to increase with increasing of the deformation degree.
Such dependence is observed well at 77 К, but almost no
at the room temperature.
4. Discussion
In our time there are some theories explain ing the change
of value of yield point stress after injection of non-in-
teracting second-phase particles to the matrix. Two cases
of interaction of dislocations with particles are po ssi ble:
а) dislocations cut the particles on early stages of de-
formation—Ansell-Lenel model [6];
Copyright © 2013 SciRes. MSCE
b) dislocations bend and then follow between particles
leaving concentric dislocation loops around them—Oro-
van model [4,8].
Most theoretical justification and experimental con-
firmation are gotten by Orovan model specified by Ash-
by [9].
Releases of the second phase follow to significant in-
creasing of flow stress and deformation hardening, re-
sulting in the first stage suppression on the hardening
curve. In polycrystalline except direct interaction of dis-
locations with par ticles grain boundary hardening effects
due to the grinding of structure are essential. Acting as
barriers for movement of dislocations grain boundaries is
providing additional hardening [8], which add to harden-
ing by Orovan. At the same time indirect effect of sec-
ond-phase through the grinding of structure can signifi-
cantly exceed its direct str engthening effect, i.e. the main
effect created by second phase is the grinding of struc-
Thus in film systems the main result of hardening is
determined by indirect effect of second-phase particles:
high dispersion of particles and grinding of structure
when a small volume fraction of particles. In a theory
about plastic def ormation of inhomogeneous material the
density of dislocations is connected with solid flat parti-
cles at Ashby [8] as
= +
ρс: density of statistically distributed dislocations, ρg:
density of geometrically needed dislocations.
In polycrystalline grain boundaries may be considered
as analogy of flat particles as almost impassable barriers
for dislocations. In common case it is known that the way
of influence grain diameters to physical and mechanical
properties is in the barrier effect of grain boundaries at a
slip [4]. In fine-grained materials the most likely way of
plastic deformation is a slip.
Usually common density of dislocations in a material
is proportional to degree of plastic deformation [4,8]. In
this case the tension иbecause of dislocations and dislo-
cation loops circling particles obstructs further move-
ment of the slide and has an influence to issues of dislo-
cations. Because of this in the early stages of deforma-
tion yet the strain hardening rate dσ/dε will strongly
higher than for massive alloys. As a result there is inten-
sive increase of dislocation density with increase of de-
gree of deformation. Then we may get the equality for
dispersion-hardened material provided that geometrically
necessary dislocat i ons a re distrib ut e d h omogeneo us l y:
gn bd=
and c,ρε o
=+ (7 )
Г: shear deformation.
Replacing Г through mε (m: Tailor factor) and mark-
ing value 4 mn/b through В, we get
ρ = ρ( 1)ε,A Bdn++ −
ρо: density of dislocations in the infinitely large grain .
Solving (2) and (8) in common, we get equation
σσ(ρfaGbA n
Let’s consider possible special cases.
1) When n = 1, we ignore value ρо 0, this equality
transfers to equation got by Van der Beikel [9] for plas-
tically deforming metals.
2) In case of fine-grained material А < Вd – 1. If we
ignore value ρо 0 and mark
( )(ε)aGbB nk=
, then
we get Hall-Petch equation.
3) In case of hard-grained material А > Вd1 and ρо
0 we get
σσ( )(ρfaGbA n
Analysis of Equation (9) shows that observed strength
properties of electroless precipitated copper caused by
high density of dislocations and ultrafine structure. Be-
cause of this, a metal possess of low plasticity was also
watched by experiments for various materials and alloys.
So Equation (9) may be used in a wide range of grains
diameters and density of dislocations.
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