Supercooling of In2Bi and InBi melts

Article abstract of DOI:10.1023/B:INMA.0000020519.80274.2f

The effect of melt overheating ΔT⁺ on the critical supercooling ΔT^- of liquid In₂Bi and InBi is studied by cyclic thermal analysis. It is shown that, the ΔT^- for In₂Bi is ?2.0 K, independent of the me

Full text of DOI:10.1023/B:INMA.0000020519.80274.2f

Inorganic Materials, Vol. 40, No. 3, 2004, pp. 227–230. Translated from Neorganicheskie Materialy, Vol. 40, No. 3, 2004, pp. 278–281.
Original Russian Text Copyright © 2004 by Aleksandrov, Frolova.
Supercooling of In2Bi and InBi Melts
V. D. Aleksandrov and S. A. Frolova
Donbass State Academy of Civil Engineering and Architecture,
ul. Derzhavina 2, Makeevka, Donetsk oblast, 86023 Ukraine
e-mail: yugov@donace.dn.ua
Received January 15, 2003
Abstract—The effect of melt overheating ∆T+ on the critical supercooling ∆T– of liquid In2Bi and InBi is stud-
ied by cyclic thermal analysis. It is shown that, the ∆T– for In2Bi is Ӎ2.0 K, independent of the melt preheating
temperature. In contrast, the ∆T– for InBi varies jumpwise with ∆T+: ∆T– Ӎ 1.0–1.6 K at ∆T+ < 5 K, and ∆T− Ӎ
16 K at ∆T+ = 5–300 K, independent of the cooling rate (varied from 0.002 to 8.0 K/s). The solidification behav-
iors of In2Bi and InBi are shown to correlate with the structures of their liquid and solid phases.
INTRODUCTION
The melting and solidification of In2Bi and InBi
were studied using thermal cycling, as described in
detail elsewhere [1–4]. The temperature was monitored
with Chromel–Alumel thermocouples. Temperature
versus time curves were recorded on a KSP-4 chart
recorder (2- to 5-mV scale). The samples were heated
and cooled in the range 303–673 K in a purpose-
designed “zero-gradient” resistance furnace. The lower
In earlier studies [1, 2], thermal cycling was used to
assess the solidification kinetics of elemental sub-
stances, bismuth and indium, at ordinary cooling rates,
from 0.002 to 8 K/s. It was found that, depending on the
difference between the melt preheating temperature
and melting point, ∆T + = T – Tm (T > Tm), the solidifi-
cation behavior of bismuth may change sharply: from boundary (303 K) was not varied, while the upper
boundary was incremented by 1–2 K from cycle to
cycle. The heating/cooling rate was 0.03–0.05 K/s. In
assessing the effect of the cooling rate on critical
supercooling, the scanning rate was varied from 0.002
to 8 K/s. Each of the six In2Bi and six InBi samples
was subjected to 80–90 thermal cycles in the specified
temperature range. The accuracy in the temperature
measurements was 0.2 K. The reproducibility of the
results was checked by repeated measurements on
each sample.
equilibrium solidification, without supercooling, to
nonequilibrium (explosive) solidification, with appre-
ciable supercooling ∆T – = Tm – T (T < Tm). Indium
solidification under such conditions was found to be a
near equilibrium process, with supercooling values in
the range Ӎ1–2 K, independent of ∆T +.
The purpose of this work was to study the effect of
melt overheating (∆T +) on the critical supercooling
(∆T –) of In2Bi and InBi. These compounds are com-
monly prepared via melting of elemental mixtures. It is,
therefore, reasonable to expect that the thermal history
of In2Bi and InBi melts has a significant effect on their
solidification behaviors.
RESULTS AND DISCUSSION
At melt preheating temperatures of up to 673 K
(with isothermal holding for 5 min to 4 h or without),
we observed equilibrium In2Bi solidification at 362 K,
with ∆T – Ӎ 2.0 K (Fig. 1, curves 1, 2). The critical
supercooling value remained unchanged as the cooling
rate was varied by several orders of magnitude, from
EXPERIMENTAL
In2Bi and InBi were prepared from 99.99%-pure
bismuth and 99.97%-pure indium. Stoichiometric mix- 0.002 to 8 K/s. This type of solidification behavior was
tures (4-g samples) of In and Bi (In + 47.7 wt % Bi and observed earlier for pure indium under similar experi-
In + 64.6 wt % Bi, respectively) sealed in Stepanov mental conditions [2].
vessels of fused silica under a vacuum of Ӎ1 Pa were
InBi exhibited a different solidification behavior. At
melted at 623 K and held there for 2 h with constant
relatively low melt overheating values, below ∆Tc+
=
vibration stirring. The formation of In2Bi and InBi
was checked by thermal analysis (melting points) and 4−5 K, InBi showed equilibrium solidification, with
x-ray diffraction (DRON-4-07 powder diffracto-
meter).
insignificant supercooling (Fig. 2, curve 1), just as
In2Bi. At the same time, after melt preheating to
0020-1685/04/4003-0227 © 2004 MAIK “Nauka/Interperiodica”

228
T, K
ALEKSANDROV, FROLOVA
T, K
400
400
∆Tc+
380
360
340
2
1
380
360
2
1
340
τ
τ
Fig. 2. Temperature vs. time curves for InBi illustrating the
+
Fig. 1. Temperature vs. time curves illustrating equilibrium
+
transition from (1) equilibrium solidification at ∆T < ∆Tc
In Bi solidification (insignificant supercooling) at (1) low
2
+
+
+
to (2) explosive solidification at ∆T > ∆Tc .
and (2) high values of ∆T .
387−388 K (Tm = 383 K) InBi exhibited explosive
solidification (Fig. 2, curve 2), with a critical supercool-
ing of Ӎ16 ± 2 K, as determined by repeated thermal
cycling. Thus, the transition from equilibrium to explo-
sive solidification is very sharp, as illustrated by the
plot of ∆T – versus ∆T + in Fig. 3. The same mean value
∆T – = 16 ± 2 K was obtained after heating the melt to
673 K (∆T + = 311 K), after isothermal holds for up to
several hours, and at cooling rates from 0.002 to 8 K/s.
The variation of ∆T – with ∆T + for InBi is similar to
that for bismuth.
The reflections from InBi corresponded to d = 0.373,
0.303, 0.264, 0.225, 0.211, 0.184, 0.178, 0.168, 0.163,
0.155, 0.133, and 0.122 nm. From these d spacings, we
obtained a = 0.5496 nm and c = 0.6579 nm (c/a =
1.197) for In2Bi and a = 0.5005 nm and c = 0.4771 nm
(c/a = 0.953) for InBi, in agreement with earlier data
[6]. Solid In2Bi is a Laves phase with a hexagonal struc-
∆T–, K
In [2]
In2Bi
[5]
In Bi
It can be seen from the data in Fig. 3 that the solidifi-
cation behavior of In2Bi is similar to that of In, with insig-
nificant supercooling under the conditions in question.
∆T – versus ∆T + data for In2Bi and InBi are not avail-
able in the literature. It is of interest to compare our
∆T –(∆T +) data for InBi and Bi [1] with those reported
for Bi in [5]. According to Danilov, ∆T – varies mono-
tonically with ∆T +, without sharp changes. The likely
reason is that no systematic data were obtained in [5]
for low ∆T –.
32
24
16
8
Bi [1]
+
(∆T = 90 K)
To interpret the present experimental data, consider
the structures of solid and liquid In2Bi and InBi. In this
work, the crystal structures of In2Bi and InBi were stud-
ied on an x-ray diffractometer (CuKα and FeKα radia-
tion). The x-ray pattern of In2Bi showed reflections
with d = 0.384, 0.327, 0.274, 0.269, 0.223, 0.211,
0.198, 0.192, 0.164, 0.158, 0.157, 0.141, and 0.137 nm.
0
5
15
25
35
300
∆T+, K
–
+
Fig. 3. Plots of ∆T versus ∆T for In Bi, InBi, Bi, and In.
2
INORGANIC MATERIALS Vol. 40 No. 3 2004

SUPERCOOLING OF In2Bi AND InBi MELTS
Characteristics of In, In2Bi, InBi, and Bi near their melting points
229
Substance
In
Bi
In2Bi
InBi
Structure
Tetragonal
Rhombohedral
Hexagonal
Tetragonal
Lattice parameters at 298 K, nm:
a
0.4583
0.4936
1.07
0.4746
0.5498
0.3291
0.598
0.5015
0.4781
0.953
c
c/a
Atomic radius, nm
Electronic configuration
Oxidation state
0.166
5s25p1
0.182
6s26p3
1+, 2+, 3+
3–, 1+, 2+, 3+, 4+, 5+
Coordination number:
solid phase
8 + 4
11.6
3 + 3
10
10
liquid phase
7.5 (7 in a supercooled state)
9.9
9.2
8.4
7.7
Mean supercooling ∆T–, K
1–3
30
2
16
α
0.04
0.71
0.05
0.706
ture, and InBi has a tetragonal structure. The table lists liquid and crystalline InBi differ markedly: liquid In2Bi
the lattice parameters and structures of the substances
under consideration and the relevant coordination num-
bers, atomic radii, electronic configurations, mean
supercooling values ∆T –, and fractions of crystal-like
clusters α.
The structures of liquid In2Bi and InBi between Tm
and 693 K have been studied in great detail [7].
At temperatures of up to 320 K above Tm, liquid
In2Bi retains a short-range order similar to the nearest
neighbor environment in the structure of crystalline
In2Bi. The arrangement of the In and Bi atoms in liquid
has a quasi-eutectic structure.
The crystal-like clusters in liquid InBi are assumed
to persist at ∆T + ≤ ∆Tc+ Ӎ 4–5 K. Cooling from such
temperatures leads to a sort of self-seeded crystalliza-
tion at Tm or after a slight supercooling (Ӎ1.0–1.6 K).
At higher ∆T +, the clusters break down. During subse-
quent cooling, an induction time (τi) is needed for ran-
domly arranged atoms to form crystal-like clusters
(nuclei). During the induction period, the system is in a
metastable, supercooled state.
In2Bi is very similar to that in solid In2Bi [7]. At ∆T + ≤
130 K, 30–40% of the atoms in liquid In2Bi form
groups similar in coordination to crystalline In2Bi,
while the rest of the atoms form microregions consist-
ing entirely of In or Bi atoms (“quasi-eutectic” struc-
ture). At higher temperatures, these microregions break
down, and the quasi-eutectic melt structure gives way
to a random distribution of atoms with a dense packing.
The nearest neighbor environments of atoms in liquid
and crystalline In2Bi differ very little.
The cooling curves in Figs. 1 and 2 can be used to
evaluate the volume fractions of crystal-like clusters
(seed material for melt crystallization) and quasi-
eutectic regions at the beginning of crystallization.
The total solidification time τΣ is the sum of induction
(nucleation) time τ1 , the nucleus coagulation time τ2
at the initial stage of solidification, and the crystal
growth time τ3: τΣ = τ1 + τ2 + τ3. The volume fraction
of the quasi-eutectic melt, incapable of crystallizing at
Tm , can be found as α = τ2/τΣ, and the volume fraction
of crystal-like clusters, crystallizing at Tm , is β =
τ3/τΣ. According to our estimates, α Ӎ 0.05 for In2Bi
and 0.706 for InBi.
It seems likely that, during cooling from a tempera-
ture between Tm and 673 K, liquid In2Bi contains crys-
tal-like clusters, or such clusters form above the melt-
ing point. For this reason, In2Bi solidification is a near
equilibrium process.
In the x-ray scattering curve of liquid InBi, the first
peak corresponds to In–In and Bi–Bi nearest neighbors,
while that for crystalline InBi corresponds to dissimilar
atoms. The nearest neighbor environments of atoms in
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INORGANIC MATERIALS Vol. 40 No. 3 2004