On the existence of solid solutions based on magnesium diboride

Article abstract of DOI:10.1023/A:1026163230359

Dense samples of pure magnesium boride and of the compositions Mg _(1-x) A_xB₂ (A = Na, K, Ca, Sr, Ba, Sn, Ti; 0. 05 < x < 0.15) were prepared by sintering and using high temperature - high pressure treatment. The lattice parameters of most of the doped MgB ₂ samples vary only slightly as compared to those of the pure MgB₂ irrespective of the sample preparation procedure, high temperature-high pressure treatment conditions, and the amount of dopant, thus indicating the absence of extended solid solution regions. The superconducting transition temperatures of all the samples did not exceed the value characteristic of MgB₂ (39±1 K). The results obtained for the dense MgB₂ samples using the Andreev reflection and tunneling spectroscopies confirm the two-gap nature of superconductivity in magnesium diboride and point to analogy between the superconductivity mechanisms in this compound and in cuprates.

Full text of DOI:10.1023/A:1026163230359

1674
Russian Chemical Bulletin, International Edition, Vol. 52, No. 8, pp. 1674—1680, August, 2003
On the existence of solid solutions based on magnesium diboride
L. G. Sevast´yanova,a P. E. Kazin,a O. V. Kravchenko,a S. A. Kuz´michev,b
a
Ya. G. Ponomarev,b K. P. Burdina,a and B. M. Bulychev
ꢀ
aDepartment of Chemistry, M. V. Lomonosov Moscow State University,
Leninskie Gory, 119992 Moscow, Russian Federation.
Fax: +7 (095) 932 8846. Eꢀmail: burdina@highp.chem.msu.ru
bDepartment of Physics, M. V. Lomonosov Moscow State University,
Leninskie Gory, 119992 Moscow, Russian Federation.
Fax: +7 (095) 932 8876. Eꢀmail: svet@mig.phys.msu.ru
Dense samples of pure magnesium boride and of the compositions Mg(1–x)AxB2 (A = Na,
K, Ca, Sr, Ba, Sn, Ti; 0.05 < x < 0.15) were prepared by sintering and using high temperaꢀ
ture—high pressure treatment. The lattice parameters of most of the doped MgB2 samples vary
only slightly as compared to those of the pure MgB2 irrespective of the sample preparation
procedure, high temperature—high pressure treatment conditions, and the amount of dopant,
thus indicating the absence of extended solid solution regions. The superconducting transition
temperatures of all the samples did not exceed the value characteristic of MgB2 (39 1 K). The
results obtained for the dense MgB2 samples using the Andreev reflection and tunneling
spectroscopies confirm the twoꢀgap nature of superconductivity in magnesium diboride and
point to analogy between the superconductivity mechanisms in this compound and in cuprates.
Key words: magnesium, borides, alkali metals, solid solutions, doping, superconductivity.
The discovery1 of superconductivity in magnesium
ture and composition using experimental techniques deꢀ
veloped for copper oxide based superconductors. Indeed,
it was shown15—19 that, similarly to cuprates, the transiꢀ
tion temperature of MgB2 should be most sensitive to
changes in both the electronic configuration of charge
carriers and the crystal lattice parameters. In other words,
the nature and number of chemical elements whose atꢀ
oms replace the magnesium or boron atoms can strongly
affect the Tc value. FLMTO (Full Linearized MuffinꢀTin
Orbital) calculations20 revealed that Be impurity in the
boron sublattice (as well as Li, Na, and Cu impurities in
the Mg sublattice) and the formation of both types of
lattice vacancies favor an increase in Tc. At the same
time, the effect of isovalent substitution of Be, Ca, Ba,
and Sr for magnesium is still unclear, though an increase
in the unit cell volume, which should occur in these cases
(except for beryllium), also favors an increase in Tc.
From the standpoint of crystal chemistry, the existꢀ
ence of hexagonal CaB2, SrB2, and BaB2 (isovalent anaꢀ
logs of superconducting MgB2) is thought to be imposꢀ
sible21 despite indirect data16 indicating that CaB2 can be
synthesized. However, analysis of the experimental data
available thus far shows that replacement of magnesium
atoms by those of other elements or doping responsible
for the appearance of lattice defects either cause a deꢀ
crease in Tc (Al, C, Fe, Co, Ni, Mn) or have virtually no
effect on this parameter (Si, Zn and Li).22 Here, we will
diboride, MgB2, a compound with simple composition
and structure (hexagonal lattice; AlB2 structure type), was
as unexpected and unpredictable as the discovery of
cuprateꢀbased superconductors. Magnesium diboride has
been known for more than six decades2 and over forty
years it has been used as a catalyst of the transformation of
hexagonal boron nitride into its cubic modification.3 The
superconducting transition temperature, Tc, of MgB2
(39 K) lies at boundary between the highest Tc values for
the classical Bardeen—Cooper—Schrieffer (BCS) superꢀ
conductors4 and the lowest Tc values for copperꢀoxide
ceramics.5 Magnesium diboride also possesses some propꢀ
erties typical of both the true BCS superconductors and
cuprates. Taken altogether, these findings make the probꢀ
lem of determining the nature and mechanism of superꢀ
conductivity in magnesium diboride topical.
For instance, studies6—12 of the effect of pressure on
the superconducting transition temperature of MgB2 reꢀ
vealed that the action of hydrostatic pressure on the sample
always causes a decrease in Tc, which is typical of the
BCS superconductors. Large boron isotope effect13 clearly
indicates that the superconductivity in MgB2 is due to
phononꢀmediated pairing of charge carriers.
At the same time the discovery of cuprateꢀlike physiꢀ
cal properties of this compound14 gives an impetus to
search for methods of increasing Tc by modifying its strucꢀ
Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1587—1592, August, 2003.
1066ꢀ5285/03/5208ꢀ1674 $25.00 © 2003 Plenum Publishing Corporation

Solid solutions based on magnesium diboride
Russ.Chem.Bull., Int.Ed., Vol. 52, No. 8, August, 2003
1675
not dwell on consideration of such evident reasons for the
samples thus obtained have a highly porous structure and
are therefore unsuitable for performing wellꢀreproducible
physical and electrophysical experiments. Preparation of
more dense samples by substantially increasing the sinterꢀ
ing temperature is precluded by relatively low thermal
stability of MgB2.32—33 In this case it is more appropriate
to apply high temperature—high pressure treatment;34—38
however, the process can be accompanied by formation
of secondary phases, namely, MgB6 and MgB12, because
the higher the temperature, the higher the formation probꢀ
ability of these phases.32
In this work the procedure for preparation of highly
ordered, pure, and dense samples of both stoichiometric
and doped MgB2 was divided into some stages. The necꢀ
essary amounts of magnesium, boron, and a metal dopant
were specified prior to sintering stage (stages), while
compaction and additional homogenization of the
samples were performed under conditions of high temꢀ
perature—high pressure treatment of ceramics.
23—25
decrease in Tc
as the effect of impurities, low denꢀ
sity of diboride samples, and nonstoichiometry of sample
compositions. Two experimental studies26,27 on the dopꢀ
ing of magnesium diboride with Zn atoms revealed a deꢀ
crease in Tc upon doping, the reduction magnitude being
not in proportion to the Zn concentration. The lattice
parameters of the doped MgB2 increase linearly with an
increase in the doping level.
By and large, despite negative results of the experiꢀ
ments on replacement of magnesium atoms by other metal
atoms we cannot say that the potentialities of the methods
of heterovalent and isovalent substitution are exhausted.
Probably, in doing so researchers are on the right track.
In this work we report on the synthesis, Xꢀray phase
analysis, and electrophysical studies of dense magnesium
diboride and mixed Mg(1–x)AxB2 (A = Na, K, Ca, Sr, Ba,
Sn, Ti; 0.05 < x ≤ 0.15) samples.
Results and Discussion
The sintering conditions, Tc values, and lattice paꢀ
rameters of the Mg(1–x)AxB2 samples are listed in Table 1,
while a number of Xꢀray diffraction patterns are presented
in Fig. 1. As can be seen in Table 1, the lattice parameters
of all the MgB2 samples coincide, within the limits of
experimental error, with the published data39 irrespective
of the sample preparation procedure. The lattice paramꢀ
A widely used method for the preparation of MgB2 at
atmospheric pressure is based on the reaction between
magnesium powder and amorphous or crystalline boron
at temperatures above 920 K in closed tantalum or moꢀ
lybdenum tubes.28—31 Polycrystalline magnesium diboride
I/I0 (rel. units)
101
0.4
0.2
a
100
110
002
201
112
*
102
*
103
*
*
*
*
20
40
40
40
60
80
2θ/deg
2θ/deg
2θ/deg
I/I0 (rel. units)
0.4
0.2
b
o
o
o
o
o
o
o
o
20
60
80
I/I0 (rel. units)
0.4
0.2
#
c
#
#
#
#
#
#
#
20
60
80
Fig. 1. XꢀRay diffraction patterns of MgB2 doped with Ca (a), Sr (b), and Ba (a). Shown are the MgB2 (indicated "hkl"),
CaB6 (asterisked; sample No. 10), SrB6 (symbolized "o"; sample No. 13), and BaB6 lines (symbolized "#"; sample No. 16).

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Sevast´yanova et al.
Table 1. Sintering conditions and properties of pure MgB2 and doped magnesium diboride samples
Run
Mixture composition
Sintering conditions
Tc/K
MgB2 lattice parameters
P/kbar
T/K
t/min
a
c
a
1
2
3
4
5
6
7
8
3.0864
3.084 b
3.5215
3.521 b
Mg + B2
Mg + B2
Mg + B2
MgB2
MgB2
MgB2
MgB2
970
1020
1320
970
480
60
120
3
5
5
39
39
40
39
40.5
40
3.085(1)
3.085
3.086
3.086
3.520(1)
3.521
3.522
3.525
3.526
3.525(3)
3.523
3.524
3.523(2)
3.523
3.523
3.522
3.521
3.523(2)
3.523
3.524(2)
3.524
3.521
3.522
3.521
3.519
3.520
3.520
3.518
3.522
3.519
40
40
40
80
1020
1470
1470
1270
1270
1270
1270
1270
1270
1270
1270
1270
1470
1470
1470
1470
1470
1470
1470
1270
1270
1470
1470
1470
1270
1270
5
38.5
40
3.086
3.088(2)
3.085
3.088
3.087(2)
3.085
3.089
3.085
3.086
3.088(2)
3.085
3.088(3)
3.084
3.083
3.082
3.084
3.085
3.085
3.085
3.086
3.085
3.084
3.084
3.084
9
Mg0.95 + Ca0.05 + B2
Mg0.9 + Ca0.1 + B2
Mg0.85 + Ca0.15 + B2
Mg0.95 + Sr0.05 + B2
Mg0.9 + Sr0.1 + B2
Mg0.85 + Sr0.15 + B2
Mg0.95 + Ba0.05 + B2
Mg0.9 + Ba0.1 + B2
Mg0.85 + Ba0.15 + B2
Mg0.95 + Ca0.05 + B2
Mg0.95 + Ca0.05 + B2
Mg0.9 + Ca0.1 + B2
Mg0.95 + Sr0.05 + B2
Mg0.9 + Sr0.1 + B2
Mg0.95 + Ba0.05 + B2
Mg0.9 + Ba0.1 + B2
Mg0.95 + Na0.05 + B2
Mg0.9 + Na0.1 + B2
Mg0.95 + Na0.05 + B2
Mg0.95 + Sn 0.05 + B2
Mg0.95 + Sn 0.05 + B2
Mg0.95 + Ti 0.05 + B2
Mg0.9 + Ti 0.1 + B2
180
180
180
180
180
180
180
180
180
5
5
3
5
3
5
3
180
180
5
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
40
39
40
39
40
40
39.5
39
40
40
80
40
40
40
40
40
39
40
40
40
40
40
80
3
5
210
210
40
3.519
3.519
a JCPDS No. 38ꢀ1369.39
b The lattice parameters were determined with an accuracy of (0.001—0.003) Å.
eters of most of the mixed samples prepared by sintering
also vary only slightly and remain very close to those of
the pure magnesium diboride. This indicates a low soluꢀ
bility of impurities under sintering conditions.
Figure 1 shows that replacement of Mg by isovalent
Ca, Sr, and Ba or doping magnesium diboride with these
elements result in twoꢀphase mixtures. The major phase is
MgB2, while the secondary phases are apparently hexaꢀ
borides CaB6, SrB6 or BaB6 with faceꢀcentered cubic latꢀ
increase in the reflection intensities of the hexaboride
phases MB6 (M = Ca, Sr, Ba, Mg) and magnesium metal
in the Xꢀray diffraction patterns. The process is accompaꢀ
nied by gradual decrease in the Tc values of the samples
and by broadening of the transition temperature interval.
Because of this, all other boride ceramic samples were
prepared by high temperature—high pressure treatment at
temperatures at most 1470 K, a pressure of 40 kbar, and a
treatment duration of at most 5 min.
Figures 2—4 present the magnetic susceptibility vs.
temperature plots for a number of pure and doped magneꢀ
sium boride samples prepared under different sintering
conditions and high temperature—high pressure treatment
regimes. The superconducting transition temperatures of
all the samples did not exceed the value characteristic of
MgB2 (39 1 K), while a marked decrease in Tc was usuꢀ
ally observed only for the heavily doped (>0.15 at.%)
samples.
40
tices (space group Fm3m). Data on the existence of BaB2
and CaB2 16 were not confirmed. Analyses of the samples
doped with other elements (Sn, Ti, Na) also revealed the
presence of MgB2 and some impurity phases.
Sequential increases in the temperature (>1470 K),
pressure (>50 kbar), and duration (>5 min) of high temꢀ
perature—high pressure treatment cause a progressing deꢀ
composition of magnesium diboride according to the reꢀ
action 3 MgB2 = 2 Mg + MgB6 and a corresponding

Solid solutions based on magnesium diboride
Russ.Chem.Bull., Int.Ed., Vol. 52, No. 8, August, 2003
1677
χ
m (rel. units)
High temperature—high pressure treatment of the
samples at a pressure of 40 kbar and at temperatures below
970 K for at least 3 min causes narrowing of the transition
temperature interval, which is consistent with the availꢀ
able data on the positive effect of the sample density on
the electrophysical characteristics. These results were obꢀ
tained for both the pure and calciumꢀdoped diboride
samples (see Figs. 2 and 3, respectively). At the same
time, the electrophysical properties of the samples obꢀ
tained after high temperature—high pressure treatment at
80 kbar approach those of the less dense samples prepared
by sintering (see Figs. 2 and 3). Thus, the best results were
obtained for the ceramic samples sintered at a pressure of
40 kbar. Substantial compaction of ceramics achieved by
high temperature—high pressure treatment under optiꢀ
mum conditions and the addition of alkaliꢀearth metals
or sodium to the starting materials (nearly 0.05 at.%) staꢀ
bilize magnesium diboride, thus making it more stable
toward external conditions. Because of this, the transition
to the superconducting state becomes much more sharp
and narrow and the corresponding electrophysical charꢀ
acteristics of differently doped samples approach one anꢀ
other (see Fig. 4).
According to calculations,41,42 two weakly interacting
superconducting condensates (σꢀband and πꢀband) coexꢀ
ist in MgB2 at temperatures below Tc. The relatively high
Tc value (nearly 39 K) is due to quasiꢀtwoꢀdimensional
σꢀbands, the superconductivity in which arises from
strong electron—phonon interaction. Calculations for the
superconducting gap corresponding to these bands gave
∆L ≈ 7—8 meV (T → 0). For the threeꢀdimensional charge
carriers in the πꢀbands (weak superconductivity), the gap,
∆S, is about 2 to 3 meV. Both gaps simultaneously vanish
(close) at Т = Тс due to intrinsic proximity effect. These
theoretical results were confirmed in our experiments.
Using the MgB2 samples prepared at P = 40 kbar, T =
1020 K, and t = 5 min. (run 6, see Table 1), we measured
the currentꢀvs.ꢀvoltage curves in the temperature range
4.2 K ≤ T ≤ Tc for more than 150 point contacts obtained
by break junction technique. The gap structures correꢀ
sponding to both the large twoꢀdimensional ∆L (σꢀband)
and small threeꢀdimensional ∆S (πꢀband) superconductꢀ
ing gaps in the normalized conductance spectra of the
MgB2 junctions are shown in Fig. 5. The subharmonic
gap structure in the conductance spectrum of the Andreev
junction (Fig. 6, curve 2) exhibits a number of dips whose
positions coincide with those of the features of the point
contact obtained using the same sample by mechanically
adjusting the junction (Fig. 6, curve 1´). Our variableꢀ
temperature study of the behavior of both superconductꢀ
ing gaps showed that the large gap, ∆L, decreases obeying
a BCS type dependence as the temperature increases.
However, the 2∆L/kTc ratio is as high as nearly 5 to 6,
being typical of superconducting cuprates and much higher
than the BCS theoretical value (3.5). We found that the
0
–0.01
–0.02
–0.03
–0.04
–0.05
–0.06
H = 1 T
1
2
3
20
30
40
50
T/K
Fig. 2. Magnetic susceptibility vs. temperature plots for pure
magnesium diboride prepared at a pressure of 0 (1), 40 (2), and
80 kbar (3) (sample Nos. 4, 6, and 8, respectively).
χ
m (rel. units)
0
–0.01
–0.02
–0.03
–0.04
H = 1 T
1
2
3
24
32
40
48
T/K
Fig. 3. Magnetic susceptibility vs. temperature plots for Caꢀdoped
magnesium diboride prepared at a pressure of 0 (1), 40 (2), and
80 kbar (3) (sample Nos. 11, 18, and 19, respectively).
χ
m (rel. units)
0
–0.01
–0.02
–0.03
–0.04
–0.05
H = 1 T
1
2
3
4
24
32
40
48
T/K
Fig. 4. Magnetic susceptibility vs. temperature plots for magneꢀ
sium diboride doped with 0.05 at.% of Na (1), Ca (2), Sr (3),
and Ba (4) after high temperature—high pressure treatment
(40 kbar, 1470 °C) (sample Nos. 27, 18, 21, and 23, respecꢀ
tively).

1678
Russ.Chem.Bull., Int.Ed., Vol. 52, No. 8, August, 2003
Sevast´yanova et al.
dI/dV (rel. units)
I/mA; dI/dV (rel. units)
1.2
4
3
2
4 ∆
L
1.0
0.8
0.6
0.4
0.2
3
2
1
0
4 ∆
S
nS = 2
4
1´
–1
–2
–3
–4
nL = 2
nL = 1
2
1
1
nS = 1
–20
–12
–4
4
12
V/mV
Fig. 6. Currentꢀvs.ꢀvoltage curve (1) and conductance specꢀ
trum (1´) of a SꢀIꢀSꢀIꢀ... tunnel junction and the conductance
spectrum of the Andreev SꢀnꢀSꢀn junction (2). Positions of the
dips in the subharmonic gap structure in the conductance specꢀ
trum of the Andreev junction (2) coincide with positions of the
features of the point contact (1´) obtained using the same sample
–20
–10
0
10
Vnorm/mV
Fig. 5. Conductance spectra of SꢀIꢀSꢀIꢀ... tunnel junctions in
MgB2 at 4.2 K normalized to point contact: fiveꢀjunction
stack (1), fiveꢀjunction stack (2), twoꢀjunction stack (3), and
single junction (4). All spectra exhibit twoꢀgap structures with
∆ = 8 meV and ∆ = 1.7 meV (sample No. 6).
by mechanically adjusting the junction. ∆ = 8 0.5 meV and
L
S
L
∆ = 1.9 meV, T = 4.2 K.
S
characteristic values of the large superconducting gap, ∆L,
lie between 7 and 11 meV, which is apparently deterꢀ
mined by the method employed to obtain point contacts
at helium temperatures (this prevents the surface from
poisoning with oxygen and other substances). The smaller
∆L gaps correlate with the lower Tc values; therefore, the
2∆L/kTc ratio remains nearly constant for different gaps.
Measurements for the small gap, ∆S, gave 1 to 3 meV at
T = 4.2 K. At T > Tc/2, the temperature dependence
∆S(T ) is typical of induced superconductivity.
The characteristic voltages, Vc = IcRn, of the Josephꢀ
son junctions studied in this work lie between 3.0 and
6.0 meV, which is in good agreement with the predictions
made using the twoꢀgap model.43
The results obtained confirmed correctness of the asꢀ
sumption of twoꢀgap superconductivity in MgB2.44 In carꢀ
rying out this work we have repeatedly observed the specꢀ
tra of SꢀIꢀSꢀIꢀ... (internal Josephson effect, see curve 1 in
Fig. 5) and SꢀnꢀSꢀnꢀ... junctions (effect of intrinsic mulꢀ
tiple Andreev reflections, see curve 2 in Fig. 5). The lastꢀ
mentioned phenomenon is due to the layered structure of
MgB2 and, along with the value of the 2∆L/kTc ratio
(2∆L/kTc ≈ 5—6), points to analogy between the nature of
superconductivity in this compound and in cuprates.
Experimental
Starting materials were sintered from elemental Mg and B
and dopants (when necessary). Magnesium flakes or powder
(both of 99.8% purity) were used. Amorphous boron of reagent
purity (99.7% purity) was preꢀheated in dynamic vacuum at
600—650 K over a period of 1 to 1.5 h. A tube (8 mm in diameter
and 80 mm long) made of "12X18H10T" stainless steel was filled
with the reaction mixture in a dry box under nitrogen, welded at
both ends, and sintered at T = 1170—1200 K and P = 1 atm. for
periods between 3 and 6 h. In the second stage (in some cases
this stage was omitted) the tube was opened in the dry box, the
samples were ground in an agate mortar, the powders were
pressed in pellets at some excess pressure, and then sintered
again under the firstꢀstage conditions. The third stage involved a
high temperature—high pressure treatment of the samples at
P = 3—8 GPa and T = 1070—1870 K in highꢀpressure chambers
of the recessed anvils type. For comparison, a number of samples
were obtained from elemental magnesium and boron by high

Solid solutions based on magnesium diboride
Russ.Chem.Bull., Int.Ed., Vol. 52, No. 8, August, 2003
1679
temperature—high pressure treatment under conditions of the
third stage of the multistage process. The results obtained for
these samples were the same as those reported for the samples
prepared using the first method.
In all stages the number of phases and the phase composiꢀ
tions were monitored by Xꢀray phase analysis (XRD) (URDꢀ6
instrument and a Guinier chamber) (CuKα radiation, with Si as
internal reference). According to quantitative XRD data, the
MgO content in the finished samples was at most 0.5% by mass.
Magnesium oxide was detected only in the samples synthesized
using magnesium flakes as the starting material.
The superconducting properties were studied by dynamic
magnetic susceptibility (in rel. u.) measurements (inductance
measurements) in an alternating magnetic field (1 Oe, 27 Hz) in
the temperature range from 15 to 290 K. An original setup using
an APD Cryogenics closedꢀcycle cryostat was designed at the
Inorganic Chemistry Chair, Department of Chemistry, M. V.
Lomonosov Moscow State University.
Tunnel junctions for investigating the currentꢀvs.ꢀvoltage
curves of MgB2 polycrystals were produced by cracking the
samples at helium temperatures. The junctions were measured
using the Josephson, tunneling, and Andreev reflection specꢀ
troscopies. The break junctions were driven into different meaꢀ
surement regimes by mechanically adjusting the point contacts
at liquid helium temperatures. This allowed obtaining both the
SꢀIꢀS (superconductor—insulator—superconductor) and SꢀnꢀS
(superconductor—normal metal—superconductor) junctions usꢀ
ing the same sample and permitted comparison of the results
obtained by different methods. The experimental data were found
to be selfꢀconsistent and well reproducible.
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00ꢀ15ꢀ97457 and 02ꢀ02ꢀ17915) and the R. F. State Target
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