Shock Waves (1999) 9: 201 207
Numerical analysis in the shock synthesis of EuBa2Cu3Oy
Hideaki Hikosaka1, Keiji Kusaba1, Yasuhiko Syono1, Langdon S. Bennett2, Katsumi Tanaka3, Masahide Katayama4
1
Institute for Materials Research, Tohoku University, Katahira 2-1-1, Sendai 980-8577, Japan
2
Los Alamos National Laboratory, Los Alamos, NM 87545, USA
3
National Institute of Materials and Chemical Research, Tsukuba 305-8565, Japan
4
CRC Research Institute Inc., Koto-ku, Tokyo 136-8581, Japan
Received 2 August 1998 / Accepted 10 November 1998
Abstract. Numerical calculations using two material models, a P-Ä… model and the VIR model with and
without reaction, were applied for the shock synthesis of EuBa2Cu3Oy. The shock wave was reflected
from the back rim of the sample due to a faster shock wave velocity in the container than in the sample,
achieving very high pressure. The temperature calculated in the outer area of the 3-mm-thick sample was
higher than that of the center region because of single compression due to Mach reflection. The calculated
temperature distribution in the 1-mm-thick samples was less remarkable than in the 3-mm-thick samples.
The temperature calculated using the VIR model with reaction was higher than that of the P-Ä… model
without reaction due to the occurrence of exothermic reaction. The result of a shock recovery experiment
from a 3-mm-thick sample indicated that the yield of EuBa2Cu3Oy phase in the outer area of the sample
was larger than that of the central area. The large yield in the outer area was consistent with the result
of numerical calculation. A more-homogeneous temperature distribution achieved in a 1-mm-thick sample
than in a 3 mmthick sample indicated that the aspect ratio of the sample room is important for shock
synthesis experiments.
Key words: Shock synthesis, Shock recovery experiments, High Tc oxides, EuBa2Cu3Oy, Numerical calcu-
lation, Mach reflection
1 Introduction so on have been reported so far. Numerical calculation for
the shock synthesis of the oxides has not been reported
Shock compression of powder mixtures is an emerging
yet. In this study, we carried out numerical calculations to
method for novel material synthesis. Extraordinarily rapid
be applied for the shock synthesis of EuBa2Cu3Oy, which
chemical reactions may occur during shock compression
were reported previously (Hikosaka et al. 1995). Two kinds
of the powder specimen via particle fractures and near
of material models of the powder specimen, a P-Ä… model
instantaneous temperature increase. Metastable as well
and the VIR (void-inert-reactive) model were used (Her-
as stable phases can be synthesized due to this highly
mann 1950, Horie et al. 1993, Bennett et al. 1994). The
nonequilibrium process. However, these processes are not
latter model includes a chemical reaction which itself af-
fully understood, because in-situ observation is difficult
fects the temperature evolution along the passage of shock
due to the short time durations. In recovery experiments it
waves. Calculations for different specimen thickness, i.e. 1
is not clear whether reaction takes place during the shock
and 3 mm, were also done to see the effect of the aspect
compression (shock-induced reaction) or is caused by the
ratio of the sample room. Shock recovery experiments of
residual temperature after the pressure release (shock- EuBa2Cu3Oy were carried out for comparison with the
assisted reaction). Numerical simulation of the shock his- numerical calculations.
tory may yield some understanding of the process. There
have been many reports of numerical analysis of shock
synthesis of intermetallic compounds such as Ti-Al, Ni-
2 Experimental
Al, Ti-Si, Mo-Si and Nb-Si, along with comparisons to
the results of shock recovery experiments (Thadhani et
Numerical calculations were performed using a two-dimen-
al. 1992, Bennett et al. 1992; 1997, Yu et al. 1991, Vecchio
sional finite difference program  AUTODYN-2D (1991).
et al. 1994). On the other hand, only a few shock synthe-
Schematic illustrations of the recovery system for numer-
sis experiments in oxides such as zinc ferrite (ZnO-Fe2O3)
ical calculation and experiment are shown in Fig. 1. The
(Kimura 1963), La2-xSrxCuO4 (Graham et al. 1995) and
whole recovery system was described using a Lagrangian
Correspondence to: Y. Syono coordinate system with 0.2- and 0.5-mm-wide meshes. A
202 H. Hikosaka et al.: Numerical analysis in the shock synthesis of EuBa2Cu3Oy
Fig. 1. Schematic of the shock recovery system used for cal-
culation a and experiment b
Fig. 2a,b. Pressure distribution in the container and 3-mm-
thick sample calculated using P-Ä… model: a 2.0 µs after the
flyer impact; b 2.8 µs after the flyer impact
24-mm-diameter and 3-mm-thick SUS 304 stainless steel
flyer plastic plate attached to a plastic projectile impacted
a SUS304 stainless steel container. The 13-mm-diameter
3 Results and discussion
and 3-mm-thick powder specimen was placed at a depth
of 5 mm from the surface of the container. Four target
3.1 P-Ä… model
points to output calculated pressure and temperature his-
tories were marked in the sample, as illustrated in Fig.1a.
A calculation of the sample with 1 mm thickness was also First, the calculation using the P-Ä… model was carried out.
carried out. The initial density of the sample was 60% of Parameters of the P-Ä… model are listed in Table 1. The
the theoretical density of 1/2Eu2O3-2BaCuO2-CuO pow- material parameters of BaTiO3 (Marsh 1980, Touloukian
der mixture. The flyer impact velocity was taken to be and Buyco 1970, Touloukian et al. 1977) with the same
1.15 km/s. perovskite structure, were used instead of those of EuBa2
Shock recovery experiments were carried out using a Cu3Oy, because the Hugoniot of EuBa2Cu3Oy was not
single stage propellant gun with a 25 mm bore (Goto et available. Figure 2 shows the calculated pressure distribu-
al. 1984). The flyer velocity was measured using a mag- tion in the container and 3-mm-thick sample at 2.0 and 2.8
netoflyer method. The component oxides, 1/2Eu2O3, µs after the flyer impact. The shock velocity in the con-
BaCuO2 and CuO, were weighed for stoichiometric tainer surrounding the sample was faster than that in the
EuBa2Cu3O6.5 and thoroughly mixed by ball-milling for porous sample resulting in Mach reflection in the outer
3 hours. The powder specimen was shaped into a 13- area of the sample. The incident shock pressure in the
mm-diameter and 3-mm-thick pellet by cold pressing. The outer back rim of the sample was the highest. The high
62.1% theoretical density pellet was encapsulated in a pressure region swept from the outer to the inner back sur-
SUS304 stainless steel container and impacted with the face with the lapse of time, and finally cylindrically con-
SUS304 flyer at 1.08 km/s. The recovered container was verged in the central area of the back face of the sample
cut perpendicular to the impact plane. Four parts of the where the highest pressure state (80 GPa) was achieved.
specimen were taken from the container and examined by Figure 3 shows the pressure distribution in the 1-mm-
X-ray powder diffraction analysis. thick sample at 1.4 and 2.2 µs after the flyer impact. Mach
H. Hikosaka et al.: Numerical analysis in the shock synthesis of EuBa2Cu3Oy 203
Fig. 4. Calculated temperature distribution in the 3 mm
thick a and 1 mm thick b samples
Table 1. Parameters of P-Ä… model
P-Ä… model 1/2Eu2O3-2BaCuO2-CuO
power mixture
Initial density (Á0/g.cm-3) 3.729
Fig. 3a,b. Pressure distribution in the container and 1-mm-
Bulk sound speed (C0/km.s-1) 3.34
thick sample calculated using P-Ä… model: a 1.4 µs after the
flyer impact; b 2.2 µs after the flyer impact
Us - up slope (s) 1.79
Isothermal bulk modulus
(²t0/GPa) 69.33
,
Pressure derivative of ²t0(²t0) 6.16
reflection occurred in the outer area of the sample, as it did
Grüneisen parameter (Å‚) 0.48
in the 3-mm-thick sample. The high-pressure region swept
across the whole area of the sample from the outside to the
Specific heat (C½/J.g-1.K-1) 0.439
center. The highest pressure was achieved by convergence
Pore collapse pressure (ps/GPa) 5
of the shock wave in the central area of the back face of
Elastic limit (pe/GPa) 0
the sample, as in the case of the 3-mm-thick sample. These
figures indicate how the initial planar loading is converted
to a radial loading in a recovery fixture (Graham, 1992).
Figure 4 shows temperature distributions of the 3-mm- synthesis experiments indicated that the heterogeneity in
(a) and 1-mm-thick (b) samples when the temperature
the recovered 1 mm thick sample was less than that of
reached the highest value. The highest temperature was
the 3-mm-thick sample. Results of the calculation with
caused by the highest incident shock pressure in the back
the 1-mm-thick sample were consistent with the results of
rim of the sample. Because the jump of the internal en- the recovery experiment. The shock-recovered 3-mm-thick
ergy is caused by single compression due to Mach reflec- specimen showed remarkable heterogeneity.
tion in the outer rim region, the temperature increase is
markedly enhanced in comparison with the central region
where only a small temperature increase is expected with 3.2 VIR model
double or multiple shock reflection. It was clear that the
temperature dispersion in the 1-mm-thick sample was less The calculation using the VIR model was carried out for
remarkable than that of the 3-mm-thick sample. Shock the 3 mm thick sample and compared with results from
204 H. Hikosaka et al.: Numerical analysis in the shock synthesis of EuBa2Cu3Oy
Table 2. Parameters of VIR model
VIR model Eu2O3 BaCuO2 CuO EuBa2Cu3O6.5
Weight ratio 0.244 0.646 0.110 
Initial density (Á0/g.cm-3) 7.286 5.845 6.509 6.891
Bulk sound speed (C0/km.s-1) 4.07 3.34* 5.50 4.90
Us - up slope (s) 1.12 1.79* 1.10 1.79*
Isothermal bulk modulus (²t0/GPa) 120.0 65.2 196.6 165.5
,
Pressure derivative of ²t0(²t0) 3.48 6.16* 3.40 6.16*
Grüneisen parameter (Å‚) 1.24 0.48* 1.71 2.56
Specific heat (C½/J.g-1.K-1) 0.354 0.439* 0.531 0.429
Formation enthalpy 1/2Eu2O3+2BaCuO2+CuO EuBa2Cu3O6.5
´Hf = -746.6 J/g (-551.49 kJ/mol)
Tinitiation= 1200 K
Pore collapse pressure (ps/GPa) 5
Elastic limit (pe/GPa) 0
"
These values were taken from the properties of BaTiO3.
The formation enthalpy, "Hf = -746.6 J/g, was obtained
from the value of the combustion synthesis of YBa2Cu3O6.5
(Li et al. 1994). The threshold of the chemical reaction was
set at 1200 K. Figure 5 shows the temperature distribu-
tions in the sample calculated using the P-Ä… model and the
VIR model. In the rim of the sample, the temperature cal-
culated using the VIR model was higher than that of the
P-Ä… model because of exothermic reaction. Figures 6 and
7 show pressure and temperature profiles for the 3-mm-
thick specimen calculated using the P-Ä… model and the
VIR model. The pressure profile calculated using the VIR
model was not so different from that of the P-Ä… model.
However, the temperature profile of the P-Ä… model was
different from that of the VIR model. In the case of the
VIR model, exothermic reaction occurred when the tem-
perature reached a threshold temperature where reaction
began to occur. In the present calculation, the threshold
temperature was set at 1200 K. The chemical reaction
was shown to occur when the incident shock wave passed
through the position of target A (outer area of the front of
the sample). Mach reflection caused a higher initial tem-
perature at target point A than at the central area to
Fig. 5. Temperature distribution in the 3-mm-thick sample
the front of the sample (target C). In the central area at
2.8 µs after the flyer impact calculated using P-Ä… model (left)
the front of the sample, the incident shock wave was not
and VIR model (right)
convergent, so the temperature increase was too low to ini-
tiate the reaction. The outer area of the back face of the
sample (target B) experienced the highest incident pres-
the P-Ä… model. The parameters used for the VIR model
calculation are listed in Table 2. The parameters for Eu2O3 sure and temperature due to Mach reflection. Reaction
were estimated from the shock compression data for Gd2O3 also took place there as soon as the incident shock wave
passed through. On the other hand, in the central area at
and Sc2O3 (Atou et al. 1994; 1992), while those for CuO
the back face of the sample (target D), the reaction did
were assumed on the basis of the transition metal monox-
not take place when the incident shock wave passed, but
ides, MnO, FeO and NiO (Noguchi 1996; 1998, Yagi 1988).
the reaction occurred when the reflected shock wave ar-
The material parameters of BaTiO3 (Marsh 1980, Toulou-
rived. The reaction was also shown to occur in the central
kian and Buyco 1970, Touloukian et al. 1977) were also
area at the front of the sample due to the shock wave con-
used for BaCuO2 and EuBa2Cu3Oy.
vergence. These results suggest that exothermic reaction
The following irreversible chemical reaction was as-
has a large effect on the calculation.
sumed based on results of the recovery experiments:
1/2Eu2O3+ 2BaCuO2+ CuO EuBa2Cu3O6.5.
H. Hikosaka et al.: Numerical analysis in the shock synthesis of EuBa2Cu3Oy 205
Fig. 6. Pressure (thin line) and temperature (bold
line) profile for 3-mm-thick sample calculated using
P-Ä… model. See Fig. 1a for target point A D
Fig. 7. Pressure (thin line) and temperature (bold
line) profile calculated for 3 mm thick sample using
VIR model. See Fig. 1a for target point A D
3.3 Comparison with experiments However, the yield in the central area was small despite
a high calculated temperature. The numerical calculation
The numerical calculation using the VIR model with this showed that reaction took place in the central area of the
reaction was compared with the results of the recovery sample by temperature increase due to convergent shock
experiment. Figure 8 shows X-ray powder diffraction pat- wave. The difference between the result of the numerical
terns of the recovered specimen impacted with a flyer ve- calculation and that of the recovery experiment suggests
locity of 1.08 km/s. The yield of the EuBa2Cu3Oy phase that chemical reaction could be diminished by removal of
in the outer area of the sample was larger than that of the pores due to plane wave pre-compression before the ar-
central area. A large yield in the outer area of the sample rival of the convergent shock wave. The actual chemical
is consistent with the result of the numerical calculation. reaction would probably be enhanced by local tempera-
206 H. Hikosaka et al.: Numerical analysis in the shock synthesis of EuBa2Cu3Oy
Fig. 8. X-ray powder diffraction pat-
terns of shock recovery specimen us-
ing the SUS304 container. The shock
yield of EuBa2Cu3Oy is indicated in
the figure of the cross section of the re-
covered specimen. Open circles indicate
the EuBa2Cu3Oy phase
ture and pressure increase due to collapse of microscopic References
pores.
The fact that the yield at the outer area of the sample
Atou T, Kikuchi M, Fukuoka K, Syono Y (1994) Shock-induced
was larger than that at the central area also suggests that
phase transition of scandium sesquioxide: Geometric factor
larger deformation in the outer area of the sample would
governing high pressure transitions on rare earth sesquiox-
promote the chemical reaction. It was supposed that defor- ide. In: Schmidt SC, Shaner JW, Samara GA, Ross M (eds)
mation of the container, which might cause particle frac- High-Pressure Science and Technology 1993. AIP Press,
New York, pp 331-334
tures, is related to the reaction. Unfortunately, the VIR
model does not account for the possibility of shear initia- Atou T, Kusaba K, Syono Y, Kikegawa T, Iwasaki H (1992)
Pressure-induced phase transition in rare earth sesquiox-
tion.
ides. In: Syono Y, Manghnani MH (eds) High-Pressure Re-
search: Application to Earth and Planetary Science. Terra
Pub, Tokyo/AGU, Washington DC, pp 469-475
AUTODYN Users Manual, Version 2.4, (1991). Century Dy-
4 Summary namics Inc., Oakland, CA
Bennett LS, Horie Y, Hwang MH (1994) Constitutive model
of shock-induced chemical reactions in inorganic powder
mixtures. J. Appl. Phys. 76:3394
The results of numerical calculation indicate that Mach
Bennett LS, Tanaka K, Katayama M (1997) Numerical analysis
reflection occurred in the outer area of the sample due to
of explosively generated shocks in a Ti-Al powder mixture.
a shock velocity in the container faster than that in the
Kayaku Gakkaishi 58:9 15
powder sample. A higher temperature state in the outer
Goto T and Syono Y (1984) Technical aspect of shock com-
area of the sample than that in the central area was caused
pression experiments using the gun method. In: Sunagawa
by single compression due to Mach reflection. A more-
I (ed) Materials Science of Earth s Interior. Terra, Tokyo,
homogeneous temperature distribution in the 1-mm-thick
pp 605 619
sample than the 3-mm-thick sample was consistent with
Graham RA (1992) Solids under High-Pressure Shock Com-
the result of shock recovery experiments. By comparing
pression. Springer, New York, pp 148 159
the temperature in the sample calculated using the P-Ä… Graham RA, Venturini EL, Morosin B, Ginley DS (1987)
model and that of the VIR model, it was clear that the Shock-induced chemical synthesis of a lanthanum-
effect of exothermic reaction was remarkable. The larger strontium-copper oxide in the K2NiF4 structure type.
Phys. Lett. A 123:87-90
yield obtained in the outer area of the recovered specimen
Herrmann W (1969) Constitutive equation for the dynamic
is consistent with the result of numerical calculations. The
compaction of ductile porous materials. J. Appl. Phys.
difference between experiments and the numerical calcu-
40:2490
lation for the central area of the sample suggests suppres-
Hikosaka H, Atou T, Kusaba K, Suzuki T, Fukuoka K, Kikuchi
sion of chemical reaction due to pore removal by plane-
M, Syono Y (1995) Characterization of EuBa2Cu3Oy syn-
wave pre-compression before the arrival of the convergent
thesized in shock processes. Jpn. J. Appl. Phys. 34:1506
shock wave. It also suggests that deformation of the con-
1509
tainer, which may cause particle fractures, influence the
Horie Y, Sawaoka AB (1993) Shock Compression Chemistry of
reaction.
Materials. KTK Scientific Publishers, Tokyo
Kimura Y (1963) Formation of zinc ferrite by explosive com-
Acknowledgements. The authors are grateful to Drs. M. Kiku- pression. Jpn. J. Appl. Phys. 2:312
chi and T. Atou, IMR, Tohoku University, for useful discussion,
Lin SC, Richardson JT, Luss D (1994) YBa2Cu3O6+x synthesis
and to Mr. K. Fukuoka, IMR, Tohoku University, for technical
using vertical self-propagating high-temperature synthesis.
support with the shock recovery experiment.
Physica C 233:281
H. Hikosaka et al.: Numerical analysis in the shock synthesis of EuBa2Cu3Oy 207
Marsh SP (1980) LASL Shock Hugoniot Data. University of Touloukian YS, Kirby RK, Taylor RE, Lee TYR (eds) (1977)
California Press, Berkeley, CA Thermal Expansion Nonmetallic Solids. IFI/Plenum, New
Noguchi Y, Kusaba K, Fukuoka K, Syono Y (1996) Shock- York
induced phase transition of MnO around 90 GPa. Geophys. Vecchio KS, Yu LH, Meyers MA (1994) Shock synthesis of
Res. Lett. 23:1469 1472 silicides-I. Experimentation and microstructural evolution.
Noguchi Y, Uchino M, Hikosaka H, Kusaba K, Mashimo T, Acta Metall. Mater. 42:701 714
Syono Y (1998) Shock compression of NiO to 130 GPa. Rev. Yagi T, Fukuoka K, Takei H, Syono Y (1988) Shock compres-
High Pressure Sci. Technol. 7:832 834 sion of wüstite. Geophys. Res. Lett. 15:816 819
Thadhani NN, Work S, Graham RA, Hammetter WF (1992) Yu LH, Meyers MA (1991) Shock synthesis and synthesis-
Shock-induced reaction synthesis (SRS) of nickel alu- assisted shock consolidation of silicides. J. Mater. Sci.
minides. J. Mater. Res. 7:1063 26:601
Touloukian YS, Buyco E H (1970) Specific Heat Nonmetallic
Solids. IFI/Plenum, New York