Full text of DOI:10.1557/JMR.2000.0190

Microstructure and physical properties of CaF2–MgO
eutectics produced by the Bridgman method
A. Larrea, L. Contreras, and R.I. Merino
Instituto de Ciencia de Materiales de Arago´n, Consejo Superior de Investigaciones Cientificas,
Universidad de Zaragoza, E-50015 Zaragoza, Spain
J. Llorca
Departamento de Ciencia de Materiales, Universidad Polite´cnica de Madrid, Escuela Tecnica
Superior de Ingenieros de Caminos, E-28040 Madrid, Spain
V.M. Orera
Instituto de Ciencia de Materiales de Arago´n, Consejo Superior de Investigaciones Cientificas,
Universidad de Zaragoza, E-50015 Zaragoza, Spain
(Received 21 October 1999; accepted 20 March 2000)
The microstructure and crystallographic orientation relationship of CaF2–MgO eutectics
produced for the first time were characterized by electron microscopy. The eutectic
contains single-crystal MgO rods ( 0.7 ␮m in size, spaced 8 ␮m) oriented parallel to
the cubic axis of a CaF2 matrix. The rods present low-energy {100}CaF //{111}MgO
interfaces. Light guiding was experimentally proved and considered for2possible optical
applications. Crack propagation was also studied to show the potential improvement in
fracture toughness through crack deflection at the interfaces.
I. INTRODUCTION
tion than the matrix make possible light guiding and
allow the eutectic composites to have useful applications
as microchannel plates or fiber-optic faceplates.
Recently, some oxide systems have been studied for
their possible optical applications. The luminescence
properties of ZrO2–CaO eutectics activated with Er3+
ions and the planar optical waveguiding effect in this
system has been reported.6,7 The laser floating zone
method was considered necessary to grow this eutectic
because of its high melting point (2250 °C). However,
some halide eutectic systems.5,8 present a lower melting
point and can be grown using conventional melting
techniques.
For this paper, we have studied the crystallography,
microstructure, and optical and mechanical properties of
CaF2–MgO eutectics (melting point 1350 °C) grown for
the first time using the Bridgman technique. The main
physical properties of the two constituent phases are
listed in Table I. First, the microstructure, orientation re-
lationships, and interlaces between the MgO and the
CaF2 matrix have been studied. Then, the light guiding
produced by the high-refractive-index MgO fibers em-
bedded in the low-refractive CaF2 matrix was analyzed.
Finally, special attention was paid to the analysis of crack
propagation in the eutectic, because it is expected that the
reinforcement of the CaF2 matrix with MgO brittle fibers
would increase the fracture toughness and thermal shock
resistance of the material.
Eutectics are in situ grown composites of two phases
displaying microstructures with typical interparticle
spacing ␭ ≈ 0.5 to 10 ␮m. Directional solidification
growth, required to obtain ordered microstructures, can
be understood as a cooperative, diffusion-coupled proc-
ess where two different phases simultaneously solidify.1
The basic microstructure of a regular eutectic (ordered
single-crystal rods or lamellae embedded in a single-
crystal matrix) can be classified according to the inter-
facial surface area per unit volume criterion. In the
simplest model, assuming isotropic surface energy, a
hexagonal array of fibers has less energy than a lamellar
structure when the volume of the minority phase is less
than 32%. The interparticle spacing ␭ can be controlled
varying the solidification rate R (␭ × R ס constant).2
Research on nonmetallic eutectics has been promoted
in past years by their interesting practical applications.
For instance, oxide eutectic materials can be used as
anisotropic ionic conductors with a higher resistance to
thermal shock than single crystals.3,4 In addition, as the
ordered structure may have a periodicity of the order of
light wavelength, eutectic composites of wide optical gap
materials can exhibit diffraction, interference, polari-
zation, and other effects that could be exploited in the
development of optical elements.5 Furthermore, the pres-
ence of fibers or lamellae with a higher index of refrac-
1314
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A. Larrea et al.: Microstructure and physical properties of CaF2–MgO eutectics produced by the Bridgman method
TABLE I. Main physical properties of the constituent phases of the CaF2–MgO eutectic.
Weight
(%)
Melting point
(°C)
Density
(g/cm3)
Refractive index
(yellow)
Entropy of fusion
Crystal structure
space group Fm3m
(⌬S/R)
CaF2
MgO
90.0
10.0
1360
2800
3.18
3.58
1.44
1.75
2.113
3.02
Fluorite, a ס 5.415 Å
Rock salt, a ס 4.203 Å
II. EXPERIMENTAL DETAILS
Single crystals of CaF2–MgO eutectic (composition
82.2 CaF2–17.8 MgO mol%) were grown by the Bridg-
man method in a radio-frequency-heated furnace using
vitreous carbon crucibles. The powders (CaF2 Cerac
99.95% and MgO Alfa 99.5% pure) were thoroughly
mixed and then melted in an Ar inert atmsophere at
1350 °C. The crystals were pulled at a rate of 5 mm/h.
Ingots of cylindrical shape of 1.7 cm2 × 10 cm size were
produced.
The microstructure of the samples was studied by op-
tical microscopy as well as by scanning (SEM) and trans-
mission electron microscopy (TEM). The SEM
experiments were performed in a Jeol 6400 apparatus
equipped with a link analytical energy dispersive spec-
troscopy (EDS) analyzer. The TEM experiments were
carried out in a Jeol 2000FXII (Tokyo, Japan) micro-
scope also equipped with a link analytical EDS analyzer.
For the TEM experiments, the samples were cut perpen-
dicular to the growth direction (transverse cross section),
mechanically polished to 20 ␮m thickness, and ion
milled to electron transparency at low angle (12° to 9°),
low energy (4-kV Ar+ ions), the liquid nitrogen tempera-
ture to minimize differential thinning (fluorite is much
more sensitive to ion milling than MgO phase).
FIG. 1. SEM backscattering image of a transverse cross section of the
eutectic (the growth direction is perpendicular to the picture). MgO
fibers are distributed in an imperfect hexagonal arrangement in the
CaF2 matrix.
Crack propagation was studied on polished transverse
and longitudinal cross sections. Cracks were nucleated
and propagated from 500-g load indentations made with
a Matsuzawa MXT70 (Tokyo, Japan) microhardness tester.
After indentation, the samples were carbon coated and ob-
served in the backscattering image mode with the SEM.
Since there is no information in the literature about the
Ca solution into MgO, the chemical composition of the
MgO fibers has been studied by EDS in the TEM (CaF2
is a material very sensitive to radiation damage and can-
not be studied by EDS). However, due to uncertainties of
this method associated with the presence of scattered
electrons and x-rays, the low atomic percentage of Ca
found in the MgO EDS spectra ( 1.5%) cannot con-
clusively determine the presence of this cation in the
fibers.10
III. RESULTS AND DISCUSSION
A. Microstructure and orientation relationships
The eutectic contained single-crystal MgO fibers (0.5–
0.8 ␮m size) arranged in a CaF2 matrix (Fig. 1). The
volume percentage of the phases has been estimated from
SEM images using quantitative image analysis9 as
f(CaF2) ס 0.90 and f(MgO) ס 0.10, which is in good
agreement with the eutectic composition expected from
the phase equilibria diagram.5 The matrix is formed of
CaF2 grains ( 400 ␮m size) crystallographically mis-
aligned approxmately 1° to 2° from one another, whereas
the fibers ( 400 ␮m length) are distributed in a nearly
hexagonal array (fiber spacing 6–8 ␮m). The MgO fibers
were found to be discontinuous at the grain boundaries.
The growth direction, the crystallographic interfaces,
and the orientation relationship between the phases have
been determined from TEM experiments on transverse
cross sections (Fig. 2). Growth directions follow well-
defined crystallographic axes. The CaF2 matrix grows
along the [001]CaF axis, whereas the MgO fibers gener-
2
ally display two preferred growth axes: [211]MgO and
[110]MgO. In this way, crystallographic directions of the
phases are aligned according to the orientation relation-
ships (OR) represented in Table II. The fibers display in
both cases two planar interfaces corresponding to
(010)CaF //(111)MgO crystallographic planes and two
2
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A. Larrea et al.: Microstructure and physical properties of CaF2–MgO eutectics produced by the Bridgman method
curved interfaces corresponding to the perpendicular di-
sume that the planar interfaces correspond to low-energy
CaF2–MgO interfaces, whereas curved interfaces are
formed by crystallographic planes with an imperfect
atomic matching. No evidence of faceting has been found
in the curved interfaces. The entropy of fusion criterion
of Hunt and Jackson11 suggests that MgO fibers, ⌬S/R ס
3.02 (⌬S, entropy of fusion; R, gas constant), would be
faceted. However, as the eutectic growth is a cooperative
process controlled by the minimization of interfacial en-
ergy of the two component phases, the defective atomic
matching at the (100)CaF //(011)MgO and (100)CaF
rections: (100)CaF //(011)MgO or (100)CaF //(112)MgO
.
2
These orientation r2elationships are represented in Fig. 3.
The crystallographic orientation relationship of the
phases in the material results from the minimization of
the surface energy during the eutectic growth. We as-
2
2
//(112)MgO interfaces avoids the formation of facets. In
this way, the material can be considered as a semifaceted
eutectic.
Unfortunately, a high-resolution electron microscopy
(HREM) study of the CaF2–MgO interfaces has not been
performed because fluorite is a material very sensitive to
electron beam damage, as mentioned above. Although
we have not been able to study the detailed structure of
the planar (010)CaF //(111)MgO interfaces, some conse-
2
quences can be obtained from symmetry. The {111}MgO
planes have sixfold symmetry and the {100}CaF planes
2
have fourfold symmetry. As a result, we obtain the same
lattice coincidence between the planes if we rotate 30°
around the [111]MgO axis to change from OR1 to OR2
(90° ס 30° + 60°, see Fig. 3). Apparently, this coinci-
FIG. 2. (a) Transmission electron micrograph of an MgO fiber into the
CaF2 matrix (transverse cross section). (b) The crystallographic direc-
tions have been obtained from the electron diffraction pattern.
TABLE II. Three crystal axes parallelisms defining the two main
orientation relationships found in the CaF2–MgO eutectic.
I
II
III
Growth direction
Curved interface
Planar interface
CaF2
MgO
CaF2
MgO
CaF2
MgO
FIG. 3. Diagram of the two orientation relationships found in the
eutectic. OR2 is obtained from OR1 by rotating the MgO crystallo-
graphic axes 30° around the [111] axis.
OR1 [001]
OR2 [001]
//
//
[211] [100]
[110] [100]
//
//
[011] [010]
[112] [010]
//
//
[111]
[111]
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A. Larrea et al.: Microstructure and physical properties of CaF2–MgO eutectics produced by the Bridgman method
dence presents a good atomic matching. Moreover, we
have found that a large amount of MgO fibers present an
intermediate (between OR1 and OR2) crystallographic
relationship with the matrix, but they always maintain the
ing would indicate that lower energy interfaces can be
expected from {100}CaF //{111}MgO than from
2
{100}CaF //{011}MgO or {100}CaF //{112}MgO interfaces.
2
2
B. Optical properties
[010]CaF //[111]MgO parallelism. It is apparent that the
2
{100}CaF //{111}MgO matching controls the CaF2–MgO
eutectic growth.
2
Grown ingots are optically translucent due to the high-
refractive-index contrast between fibers and matrix, and
the light-guiding effects of the MgO fibers are advanced
because of this index contrast.
The coincidence of the cationic sublattices at the
planar {100}CaF //{111}MgO interface can be briefly
2
considered in a near coincidence site lattice (NCSL)
model,12 where the density of cationic coincident sites
is usually characterized by the parameter ∑ (1/∑ of
the lattice points are common to both lattices). In this
case, the coincidence lattice is characterized by values
Taking the refractive index given in Table I, we can
calculate some fiber parameters for this system. It is con-
venient to approximate the fiber shape as circular. For the
fiber sizes mentioned before, the equivalent radii are ␳ ≈
0.4 to 0.6 ␮m.
2
The fiber parameter V, defined as13
of ∑CaF ס 2 and ∑MgO ס 4, with an atomic misfit
of 5.7% along the [001]CaF –[211]MgO direction and
8.7% along the [100]CaF –[0211]MgO direction (Fig. 4).
2␲
V = ␳ n2
− n2CaF
]
,
(1)
1ր2
2
͓
MgO
2
The charge density at the interface is +0.135/
Å2−{100}CaF /−0.126/Å2−{111}MgO. Although these
values would2 not involve a very good atomic match-
␭
(n being the refractive indexes and ␭ the light wavelength
in vacuum) takes a value of 3.9 to 6.3 for ␭ ס 550 nm.
The V value determines the number of possible propa-
gating modes in the fiber. For cylindrical-shaped fibers,
if V < 2.405, only one mode propagates (“single-mode”
operation). A cut-off wavelength, ␭c, for the second
ing of the {100}CaF //{111}MgO planes, no coincidence
2
can be obtained from the study of the matching in
{100}CaF //{011}MgO or {100}CaF //{112}MgO inter-
2
faces. (M2oreover, the {011}MgO and {112}MgO planes
are neutral, whereas the {100}CaF plane is charged.)
In this way, the NCSL analysis of2 the cationic match-
mode can be defined when V(␭c) ס 2.405. For ␭ ജ ␭
c
the system behaves as “single mode.” In our case, ␭ ≈
c
1.4 to 2.2 ␮m and single-mode propagation is expected
for the wavelength region corresponding to the third op-
tical window in telecommunications (␭ ס 1.55 ␮m).
1/2
The high numerical aperture (n2MgO − nC2 aF
)
≈ 1
2
leads to the maximum value for the angle of acceptance
␴
of 90°, as given by sin ␴ ס (n2MgO − nC2 aF ).
M
M
2
These effects are illustrated in Fig. 5, where we pre-
sent a micrograph taken with an optical microscope in the
transmission mode with white light focused on the bot-
tom part of a thin slab of 300 ␮m thickness and obser-
vation through a ×100 objective lens in the upper slab
surface. To enhance the optical contrast, the sample was
placed between cross polarizes. It is evident that light is
guided by the MgO fibers, which form an optical face-
plate of about 40,000 pixel/mm2. However, potential use
of this eutectic in optical devices is tempered by the
still-small size of the eutectic grains, which impedes fab-
rication of large homogeneous areas that can be used in
small-size optoelectronic devices. Attempts to improve
grain size are under progress.
C. Crack propagation
It is today well established that the thermal shock re-
sistance of ceramics can be improved through reinforce-
ment with brittle ceramic fibers, which increase
dramatically the toughness of the material.14,15 The criti-
cal point to achieve this result lies in the crack behavior
at the matrix–fiber interface. If the matrix cracks pen-
FIG. 4. Coincidence of the cationic sublattices at the (010)CaF
2
//(111)MgO interface. The coincidence cell is represented for OR1; the
symmetrically equivalent coincidence cell for OR2 is obtained by
rotating 30° the CaF2 sublattice.
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A. Larrea et al.: Microstructure and physical properties of CaF2–MgO eutectics produced by the Bridgman method
FIG. 5. Optical micrograph of a [001] CaF2 platelet of 300 ␮m
thickness. The image has been taken between crossed polarizers in
transmission mode.
etrate into the fibers, the overall behavior of the compos-
ite is brittle as the matrix and fibers have very low
fracture resistance. On the contrary, the matrix cracks
may deflect along the fiber–matrix interface and continue
their propagation through the matrix without breaking
the fibers. The nonbroken fibers behind the crack front
bridge the crack and slide with respect to the matrix. The
elastic energy stored in the fibers, together with the en-
ergy spent pulling out the fibers that are eventually bro-
ken within the matrix, increase significantly the fracture
energy of the composite, which may be over two orders
of magnitude higher than that of the unreinforced ce-
ramic matrix.16,17
FIG. 6. ⌫i/⌫2 ratio as a function fo the Dundurs parameter ␣. The solid
symbol (representing the CaF2–MgO interfaces) lies in the crack de-
flection region.
perpendicular to the growth direction. Typical results of
the crack–fiber interaction in each section can be found
in Figs. 7(a) and 7(b). They clearly show that the matrix
cracks did not penetrate into the MgO fiber but deflected
along the fiber–matrix interface.
From the theoretical viewpoint, the ratio ⌫i/⌫2, which
leads to the transition between crack deflection and pen-
etration, can be determined from Eq. (2) for a crack
perpendicular to the interface.18 The result is plotted in
Fig. 6 as a function of the Dundurs parameter ␣, which is
given by
The behavior of a crack impinging an interface be-
tween dissimilar isotropic elastic materials was studied
by He and Hutchinson.18 The critical condition for crack
deflection at the interface is given by
E2* − E1*
␣ =
,
(3)
⌫
⌫
Gd
Gp
i
E* + e2*
2
=
,
(2)
2
where E1* and E*2 are the generalized elastic moduli,
which are equivalent to the corresponding elastic modu-
lus E in plane stress and to E* ס E/(1 − ␯2) under plane
strain conditions, ␯ being Poisson’s coefficient. The val-
ues of E and ␯ for isotropic polycrystalline CaF2 and
MgO can be found in the literature19 and they are shown
in Table III. It should be noticed that Eq. (3) was ob-
tained for isotropic elastic materials but it may be ex-
trapolated to cubic crystals, whose degree of anistropy is
limited. For instance, the elastic moduli of the MgO fi-
bers in the [110] and [211] direction are, respectively,
321 and 286 GPa, very close to the average value for
polycrystals.
where ⌫i is the fracture energy of the interface and ⌫2
stands for fracture energy of the second material (Fig. 6).
Gd and Gp are the energies available to propagate the
crack either along the interface (crack deflection) or
through the fiber (crack penetration), respectively. Their
analysis demonstrated that the worst scenario for crack
deflection (as compared to crack penetration) is found
when the crack propagates perpendicularly to the in-
terface. Thus, it may be concluded that the fracture
toughness and the thermal shock resistance of a fiber-
reinforced ceramic will improve if crack deflection at the
fiber–matrix interface takes place under such conditions.
This led to study of the micromechanisms of crack–fiber
interaction in the eutectic composite.
The only experimental data for the fracture energy of
CaF2 and MgO single crystals were reported by Kingery
et al.20 and are also shown in Table III. They correspond
to cleavage fracture induced at 77 K. Results for the frac-
Cracks were nucleated and propagated from indenta-
tions on polished sections, which were cut parallel and
1318
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A. Larrea et al.: Microstructure and physical properties of CaF2–MgO eutectics produced by the Bridgman method
IV. CONCLUSIONS
ture energy of the CaF2–MgO interface were not found
but the fracture energy of CaF2 can be taken as an upper
limit. According to these magnitudes of the elastic con-
stants and fracture energies, the matrix cracks in the eu-
tectic composite (represented by a solid symbol in Fig. 6)
should exhibit crack deflection at the fiber–matrix inter-
face, as it was experimentally observed.
Large eutectic samples of CaF2–MgO composition
have been prepared for the first time. The system consists
of small MgO fibers of 0.7 ␮m radius and 400 ␮m
length embedded in a CaF2 matrix. The shape of the
MgO fibers presents two parallel flat faces in epitaxial
relationship with the matrix and two curved surfaces. The
system can be considered as a semifaceted nearly regular
fibrous eutectic.
Light guiding by the higher-refractive-index MgO fi-
bers has been proved and a higher resistance to fracture
is expected. Moreover, the material is much more resis-
tant to cleavage damage than the component phases.
ACKNOWLEDGMENTS
Financial support from the MAT 97-0673-C02-01 and
-02 Comision Interministerial de Ciencia y Tecnologia
projects and from “Fundacio´n Domingo Mart´ınez” is
acknowledged.
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FIG. 7. SEM backscattering images showing crack propagation in (a)
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tion is clearly observed.
TABLE III. Elastic constants (elastic modulus E and Poisson’s ratio
␯)19 and fracture energies (⌫) of CaF2 and MgO.20
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E (GPa)
␯
⌫ (J/m2)
CaF2
MgO
110
310
0.30
0.18
0.5
1.5
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