Anomalous thermal expansion of MnN

Article abstract of DOI:10.1016/S0925-8388(03)00334-7

The MnN compound is prepared as a single phase by d.c. reactive sputtering. The crystal structure of MnN is tetragonally distorted NaCl type (fct) one. The temperature variation of lattice constants for MnN is measured by X-ray diffraction experiments in the temperature range from 289 to 803 K. It is found that the MnN compound shows anomalous thermal expansion and the crystal structure of MnN has changed from fct structure to fcc one at about 650 K. On the other hand, we found formerly that MnN was an antiferromagnetic compound with a Néel temperature of 650 K. The tetragonal distortion below about 650 K is well explained by the strain dependence of the exchange interaction on the basis of molecular field theory.

Full text of DOI:10.1016/S0925-8388(03)00334-7

Journal of Alloys and Compounds 360 (2003) 34–40
L
www.elsevier.com/locate/jallcom
Anomalous thermal expansion of MnN
a ,
b
c
c
c
c
d
*
K. Suzuki , T. Suzuki , Y. Fujinaga , T. Kaneko , H. Yoshida , Y. Obi , S. Tomiyoshi
a
Tsuruoka National College of Technology, Tsuruoka 997-8511, Japan
b
Faculty of Engineering, Tohoku Gakuin University, Tagajo 985-8537, Japan
c
Institute for Materials Research, Tohoku University, Sendai 980-8577, Japan
d
Faculty of Engineering, Ehime University, Matsuyama 790-8577, Japan
Received 24 January 2003; received in revised form 25 February 2003; accepted 25 February 2003
Abstract
The MnN compound is prepared as a single phase by d.c. reactive sputtering. The crystal structure of MnN is tetragonally distorted
NaCl type (fct) one. The temperature variation of lattice constants for MnN is measured by X-ray diffraction experiments in the
temperature range from 289 to 803 K. It is found that the MnN compound shows anomalous thermal expansion and the crystal structure
of MnN has changed from fct structure to fcc one at about 650 K. On the other hand, we found formerly that MnN was an
antiferromagnetic compound with a N e´ el temperature of 650 K. The tetragonal distortion below about 650 K is well explained by the
strain dependence of the exchange interaction on the basis of molecular field theory.

2003 Elsevier B.V. All rights reserved.
Keywords: Exchange striction; MnN; Magnetically ordered materials; Gas–solid reactions; Thermal expansion
1
. Introduction
ture variation shows a peculiar behavior where the lattice
constant decreases with increasing temperature. Besides,
Nishiyama and Iwanaga reported that they prepared Mn
nitrides by nitriding Mn powder with ammonium [8].
Among the prepared samples, they found a MnN com-
pound which was not an fct structure but an fcc one with a
It has been known that there are four phases (´, z, h, u)
in the Mn–N system [1–10]. MnN which contains the
most nitrogen among these compounds belongs to the
u-phase. Lihl et al. prepared a series of Mn–N compounds
with 20.9–47.9 at.%N by reacting N or NH with Mn
˚
large lattice constant a54.435 A (651 at.%N).
2
3
amalgams [1]. The most N-rich phase has an fct crystal
We prepared the MnN compound as a single phase by
d.c. reactive sputtering whose crystal structure was an fct
one [11]. According to the results of magnetic measure-
ments, the magnetic susceptibility of MnN showed a
maximum around 650 K [11]. We also showed by powder
neutron diffraction studies that the values of the magnetic
˚
structure with the lattice constants a54.221 A, c54.113 or
˚ ˚ ˚
.115 A (45.8 at.%N) and a54.214 A, c54.148 A (47.9
4
at.%N). Otsuka et al. prepared Mn–N films by nitriding
vacuum-evaporated Mn films with NH gas at 300 8C [9].
3
The nitride film has an fct structure with the lattice
˚
˚
constants a54.214 A, c54.144 A. The specimen com-
moment of the Mn ion in MnN was found to be 3.3 m at
B
position is Mn N5.32. They investigated the temperature
16 K, 3.2 m at 295 K and 2.1 m at 450 K, respectively
8
B
B
variation of the lattice constants for the compound by
means of electron diffraction. They reported that its
tetragonal structure turned to an fcc one at about 680 K.
They concluded that the observed phase transition is of the
second order or of the first order very close to the second
order because thermal hysteresis was not observed at the
transition. Above the transition temperature the tempera-
[12]. The magnetic structure of MnN was determined to
correspond to the first kind of antiferromagnetic structure
of the fcc structure. Therefore, we concluded that MnN is
an antiferromagnetic compound with a N e´ el temperature of
650 K.
On the other hand, Leineweber et al. performed neutron
diffraction measurements on h-Mn N and u-Mn N
5.26
3
2
6
[
13]. Both phases show an antiferromagnetic ordering of
the first kind with magnetic moments between 3.3 and 3.8
m . u-Mn N has an fct structure with the lattice
*
Corresponding author. Tel.: 181-235-25-9148; fax: 181-235-24-
840.
E-mail address: suzuki@tsuruoka-nct.ac.jp (K. Suzuki).
1
0
B
6
5.26
˚
˚
constants a54.2193 A, c54.1287 A. Moreover, they
925-8388/03/$ – see front matter
 2003 Elsevier B.V. All rights reserved.
doi:10.1016/S0925-8388(03)00334-7

K. Suzuki et al. / Journal of Alloys and Compounds 360 (2003) 34–40
35
2
2
22
reported that the collinear magnetic moments in u-
Mn N were tilted by 238 relative to the tetragonal
3.0310 Torr; N partial gas pressure, 0.80310 Torr;
2
27
residual gas pressure, 1.70310 Torr; and target-substrate
distance, 23 mm. A manganese disk of 99.9% purity was
used as a target, and a water-cooled Cu plate was used as a
substrate. The thickness of the deposited Mn–N film was
about 170 mm and it was stripped off from the substrate
mechanically, and then this stripped film was powdered.
Finally, the powder sample was annealed at 510 K for 4 h
in vacuum in order to relieve stress.
According to the result of the chemical analysis, the
nitrogen content in the prepared MnN compound is
estimated to be larger than 48 at.% N. Therefore, the
atomic ratio of manganese to nitrogen in the sample is
almost 1:1. Fig. 1 shows the X-ray diffraction pattern using
Cu Ka at room temperature for the annealed powder
sample of MnN. Its crystal structure was determined to be
an fct one. The lattice constants of the fct structure are
a54.256 A and c54.189 A with c/a50.9843 at room
temperature [11]. The values of the lattice constants are a
little larger than those obtained by Lihl et al. [1], Otsuka et
al. [9] and Leineweber et al. [13], but the value of c/a is
almost the same.
In order to investigate the temperature variation of the
lattice constants of MnN, the X-ray diffraction measure-
ments were carried out in a flow of He gas. The measure-
ment was carried out at 289 K, and then carried out
successively at every 20–30 K in the temperature range
from 323 to 803 K with increasing temperature. But when
the X-ray diffraction measurements were performed in the
range of higher temperatures, there was a possibility that
nitrogen atoms escaped from the MnN sample. Therefore,
6
5.26
c-axis at ambient temperatures, and at about 550 K the
magnetic moments aligned parallel to the c-axis, and up to
the critical temperature of 660 K they decreased continu-
ously to zero. The tetragonal distortion of the unit cell
decreases and finally approaches an fcc structure.
Furthermore, as seen in the results of our experiments,
the lattice constants a and c which were measured at room
temperature for the samples annealed in vacuum for 2 h
became smaller with increasing the annealing temperature
above about 650 K because of the escape of nitrogen from
the sample [11]. These results are consistent with the fact
reported by Otsuka et al. [9] that the lattice constant a is
smaller with increasing temperature above about 670 K,
while the crystal structure is of fcc type above this
temperature.
˚
˚
In this paper, in order to investigate the tetragonal
distortion of MnN below about 650 K in more detail, the
temperature variation of lattice constants of MnN is
investigated. The results are discussed on the basis of a
model taking account of the strain dependence of the
exchange interaction.
2
. Experimental procedure
The MnN sample was prepared by a high rate-type
triode d.c. reactive sputtering in a mixture gas of Ar1N2
11]. The sputtering conditions were as follows: target
voltage, 0.22 kV; target current, 60 mA; total gas pressure,
[
Fig. 1. X-ray diffraction pattern of the powdered MnN compound at room temperature.

3
6
K. Suzuki et al. / Journal of Alloys and Compounds 360 (2003) 34–40
the X-ray diffraction measurements were also carried out
under high pressure of 3.0 GPa at several temperatures to
prevent the nitrogen escape from the sample, where the
sample was air tightly enclosed in a capsule of h-BN.
3
. Experimental results
3
.1. Temperature variation of lattice constants
Fig. 2 shows the X-ray diffraction pattern for the MnN
sample in the range of 2u from 308 to 558 and Fig. 3 from
58 to 808 at various temperatures, respectively. In the
figure, the indices of diffraction lines are shown with hkl
hkl) related to the tetragonal structure of MnN. As shown
in the figure, the lines of 200 (002), 220 (202) and 311
113) split into two lines at temperatures from 289 K up to
43 K. These lines indicate that the crystal structure is a
tetragonal one below 643 K. But these lines come close to
each other with increasing temperature and merge together
into one line above 668 K. The lines above 668 K are well
indexed as an fcc structure whose lattice constant de-
creases with increasing temperature as seen in the figures.
However, whether it is the NaCl type structure or the ZnS
type one is ambiguous from the relative intensities of the
5
(
(
6
Fig. 3. X-ray diffraction pattern of the powdered MnN compound in the
temperature range from 289 to 803 K (II) 2u555|808.
ture. It is considered that the structure of this compound is
like a NaCl type one, because the intensity of [111] line is
a little smaller than that of the [200] one. From the figures,
it is found that the relative amounts of this compound is
growing gradually with increasing temperature. It is noted
that the lattice constant of this new compound is almost the
1
11 line and the 200 line.
On the other hand, as seen in Figs. 2 and 3, another
˚
Mn–N compound which has quite a different lattice
constant appears above 693 K. In the figure, the lines of
this compound are designated by the index [hkl]. The lines
of this compound are well indexed as an fcc structure. The
same as the lattice constant a54.435 A of the MnN
compound reported by Nishiyama and Iwanaga [8].
The temperature variations of the lattice constants of
MnN are shown in Fig. 4. In the figure, an open circle
represents the lattice constant a and an open triangle the
lattice constant c of MnN whose structure is tetragonal,
where a is derived from 200 line and c from 002 line. An
˚
lattice constant of this compound is a64.47 A (at 803 K)
and does not change considerably with increasing tempera-
1
/ 3
open square represents V
which is the cubic root of the
unit cell volume of MnN in the tetragonal phase. A closed
circle represents the lattice constant a of the compound
which has changed from the tetragonal structure to the fcc
structure, where a is derived from the 200 line. As seen in
the figure, with increase of the temperature, the lattice
Fig. 4. Temperature variations of the lattice constants of MnN: an open
1
/ 3
circle represents a, an open triangle c and an open square V
(V is unit
Fig. 2. X-ray diffraction pattern of the powdered MnN compound in the
cell volume) of MnN. A closed circle represents a of the fcc compound
temperature range from 289 to 803 K (I) 2u530–558.
which has changed from the tetragonal MnN.

K. Suzuki et al. / Journal of Alloys and Compounds 360 (2003) 34–40
37
constant a (s) increases at first and decreases above about
50 K, and c (^) increases gradually at first and increases
rapidly above 600 K. The lattice constants a (s) and c
^) coincide at 668 K, where the tetragonal structure of
The calculation procedure is as follows:
5
First, the bulk modulus B is derived from the difference
of the lattice constants a under normal pressure and a high
pressure of 3.0 GPa at room temperature. B is obtained to
(
1
1
2
MnN changes into the fcc one with the lattice constant
be 1.66310 N/m . Next, the Gr u¨ neisen parameter g is
derived. g is given as
˚
a54.260 A (d). Above 668 K the lattice constant a (d)
decreases remarkably with increasing temperature, and
then approaches 4.212 A at 803 K. Such negative thermal
expansion is considered to be unreasonable in usual normal
˚
3Ba
Cv
g 5
]
(1)
thermal expansion behaviour above T . It is considered
N
where a represents the linear expansion coefficient and Cv
represents the specific heat at constant volume. The value
of g is determined to be 2.21 from Eq. (1), where a is
that the observed negative thermal expansion is caused by
the nitrogen escape from the sample in the high tempera-
ture range in this experiment.
Such contraction was also observed for MnN annealed
at 738 K for 2 h, where it was found by chemical analysis
that nitrogen escape from the sample actually occurred
although the crystal structure of MnN still remained up to
2
5
6
3
1
1
.878310 (1/K), C is 4.24310 J/m ?K and B 1.663
v
11 2
0
N/m as obtained above. The value of a is obtained
by using the least-squares method for the lattice constants
a which are derived from the 220 line at 675, 700, 725 and
7
50 K. C is the lattice specific heat at 690 K, supposing
v
7
53 K [11]. Thus it is considered that the MnN compound
that the Debye temperature of MnN is 530 K [14].
Assuming that g and B are almost independent of tempera-
ture within the whole range of temperature, they can be
taken as constant. The value of a in non-magnetic state
below 650 K can be calculated by the following expression
does not change into another compound even in the present
experiment and only the crystal structure changes at about
6
50 K. It is considered that the tetragonal structure of MnN
in the range from room temperature to about 650 K is
caused by exchange striction due to the Mn–Mn distance
dependence of the exchange interactions. The result shown
in Fig. 4 is very similar to that obtained by Otsuka et al.
gCv
a 5
]
(2)
3
B
[9].
The lattice constants a for the non-magnetic state at
temperatures below the transition temperature are derived
by using a at each temperature, as obtained from Eq. (2).
3
.2. X-ray diffraction under high pressure
In this calculation, C is the value at each temperature. The
v
As seen in Section 3.1, the crystal structure of MnN has
results are shown in Fig. 5. In this figure, the solid line
below the transition temperature represents the calculated
lattice constant a for the non-magnetic state. The open
squares above 675 K are derived from the experimental
data obtained in the X-ray diffraction measurements under
a high pressure of 3.0 GPa, where the values at each
temperature fluctuate somewhat. The solid line above the
transition temperature is derived by using a least-squares
changed from the fct structure into the fcc one at about 650
K. The lattice constant of the fcc structure decreases with
increasing temperature, which is considered to be caused
by nitrogen escape from the sample. Therefore, in order to
investigate the temperature variation of the lattice constant
of MnN when the nitrogen escape from the sample is
prevented, X-ray diffraction measurements under a high
pressure of 3.0 GPa were carried out where the sample was
air tightly enclosed in the h-BN compound.
The experiments were performed at the temperatures
6
75, 700, 725 and 750 K. The diffraction patterns show an
fcc structure. It is found that the lattice constant a of MnN
increases with increasing temperature in the region of high
temperatures above 650 K, as seen in normal thermal
expansion. This is considered as being due to the preven-
tion of the nitrogen atom to escape from the sample.
As mentioned above, it is considered that the tetragonal
structure of MnN below the transition temperature is
caused by exchange striction. Therefore, if MnN would not
be in a magnetically ordered state, the crystal structure of
MnN would be of the fcc type in the whole temperature
range. So the temperature variation of the lattice constant a
of MnN in the non-magnetic state below the transition
temperature was determined by using the linear expansion
coefficient above the transition temperature.
Fig. 5. Temperature variations of the lattice constants of MnN. An open
circle represents a and an open triangle c of MnN. A solid line represents
the calculated lattice constant a in non-magnetic state. An open square
represents a which is obtained from the X-ray diffraction measurements
under high pressure of 3.0 GPa.

3
8
K. Suzuki et al. / Journal of Alloys and Compounds 360 (2003) 34–40
method from the experimental data. Open circles (tri-
angles) represent the experimental values of the lattice
constant a (c) of MnN, as already shown in Fig. 4.
nearest neighboring Mn-ions. Four of them are in the same
(001) plane, and two of them are in the c-direction. All of
these neighbors couple ferromagnetically with the central
Mn-ion.
The exchange interaction J between the first nearest
1
4
. Discussion
neighboring Mn-ions and J between the second nearest
2
neighboring Mn-ions are estimated on the basis of molecu-
lar field approximation for the first kind antiferromagnetic
ordering in the fcc structure as proposed by Smart [19]. We
obtained that J and J are 229 and 24 K, respectively, by
Bean et al. studied a first-order magnetic transition and
pressure variation of Tc of a ferromagnetic compound
MnAs, considering the volume dependence of a single
exchange interaction [15]. On the other hand, Adachi et al.
1
2
using T 5650 K, the magnetic susceptibility value x 5
N
g
2
5
[
16] and Abe et al. [17] discussed the magnetic properties
2.3310 emu/g at 650 K obtained experimentally and
S53/2 [12]. If J and J are, respectively, the 908 and
of CrSb, considering two kinds of strain dependent ex-
change interactions. The present results of MnN are
discussed in a way similar to those of Refs. [16,17].
We reported that the magnetic structure of MnN is an
antiferromagnetic one, as shown in Fig. 6 based on neutron
diffraction studies [12]. The magnetic moment of the
1
2
1808 superexchange interactions proceeding via N-ions, the
signs of the exchange interactions in MnN are contradic-
3
tory to those of d (Mn) in the model of Goodenough and
Kanamori [20–22].
Here, J1 d is defined as J related to the eight ions in the
1
Mn-ion extrapolated to 0 K was found to be 3.3 m and to
adjacent (001) planes and J1 a as J related to the four ions
B
1
lie in the (001) plane. This is known as the first kind
antiferromagnetic ordering of the fcc lattice. The direction
of the magnetic moment within the (001) plane cannot be
determined by a powder neutron diffraction measurement
in the same (001) plane as shown in Fig. 6. So, J is J or
1
1 d
J . The number of Mn-ions related to J is six. All these
1
a
2
ions are coupled ferromagnetically and can be separated
into four which are in the same (001) plane and two which
are in the direction of the c-axis. Therefore, J2 a is defined
[18]. In the magnetic structure shown in Fig. 6, a Mn-ion
has 12 first nearest neighboring Mn-ions. Four of them are
in the same (001) plane, and couple ferromagnetically with
the central Mn-ion. And eight of them are in the adjacent
as J related to the four ions in the same (001) plane and
2
J2 c as J related to the two ions in the direction of c-axis.
2
So, J is J or J .
2
2 a
2 c
(
001) planes, and couple antiferromagnetically with the
Hence, exchange energy per unit volume of MnN can be
described in the following way:
central Mn-ion. A given Mn-ion has also six second
1
]
2
1
]
2
2
2
2
2
2
2
N ? 8J S ?
s
2 s
d
2
N ? 4J S s
1
d
1a
1
]
2
1
2
2
2
2
N ? 4J S s 2
]
N ? 2J S s
(3)
2
a
2c
2
where N is the number of Mn-ions per unit volume, S the
spin quantum number and s the relative magnetic moment.
Therefore, the Gibbs-free energy per unit volume of the
system including striction energy in addition to the ex-
change energy can be expressed as
2
2
2
2
2
G 5 2 NS
s
2 4J s 1 2J s 1 2J s 1 J s
d
1
d
1a
2a
2c
2
2
1
e
e
a
]
c
]
1
]
S
2
1
D
1 p
s
2e 1 ecd 2 T
s
f 1 fsd
(4)
a
l
2
K
K
where e and e are strain components in the direction of
a
c
the a- and c-axes, K the compressibility, P the pressure, T
the temperature and f and f the lattice and spin parts of
l
s
the entropy.
The Mn–Mn distance for J1 d is almost the same in both
the antiferromagnetic state and the paramagnetic state,
since in the antiferromagnetic state the lattice constant a is
larger and c is smaller than those in the non-magnetic
state. It is assumed that the atomic distance dependence of
J1 d needs not to be taken into consideration within a first
approximation. Thus, only J1 a depending on ea on the
Fig. 6. Antiferromagnetic structure of the MnN compound. Magnetic
moments lie in the (001) plane. J1 d is defined as J related to the eight
1
ions in the adjacent (001) planes and J1 a as J related to the four ions in
1
the same (001) plane, where J1 represents the exchange interaction
between the first nearest neighboring Mn-ions. J represents the exchange
2
interaction between the second nearest neighboring Mn-ions.

K. Suzuki et al. / Journal of Alloys and Compounds 360 (2003) 34–40
39
same (001) plane is taken into consideration. Therefore,
functions of the strain coefficients of the exchange interac-
the strain dependencies of J1 d and J1 a can be expressed as
tions b . The deviation of the lattice constants a and c from
i
that of the cubic structure in the non-magnetic state below
J 5 J
10
1
d
6
50 K is derived.
(
5)
J 5 J10s1 1 b1ead
1
a
The b values are determined for the difference between
i
the experimental values and the calculated ones to be the
where J10 represents the value of the exchange interaction
J in the unstrained state, b is coefficient which relates
least in the whole range of temperature below T . The
N
1
1
calculation is performed by using the following data for N,
S, K, J , J and taking b as fitting parameters: N5
the strain component e to J . J can be separated into J
a
1
2
2 a
and J . Since J depends on e only and J on e only,
10
20
i
2
c
2 a
a
2 c
c
2
2
3
213
2
5
.27310 (1/cm ), S53/2, K56.02310
J10 5229 K (240.0310
(cm /dyn),
respectively, the strain dependencies of J2 a and J2 c can be
expressed as
2
16
216
erg), J 524 K (33.1310
20
erg), where the value of N is approximated as constant in
the whole range of temperature and K is the inverse of the
bulk modulus B obtained in Section 3.2 and J , J
J 5 J20s1 1 b2ead
2
a
(
6)
J 5 J20s1 1 b2ecd
2
c
1
0
20
correspond to J , J in the unstrained state [12]. A
reasonable fit is obtained by taking
1
2
where J20 represents the value of the exchange interaction
J in the unstrained state, b is coefficient which relates
2
2
the strain component e and e to J .
b1 5 2 65.9 and b2 5 2 42.4
(15)
a
c
2
Substituting Eqs. (5) and (6) into Eq. (4) and using
respectively.
≠
G
≠G
≠ec
The results are shown in Fig. 7, together with the
experimental values. In the figure, an open circle and an
open triangle are the experimental values of the lattice
constants a and c which are shown in Fig. 4. The upper
solid line below 650 K represents the calculated values of
a, and the lower solid line below 650 K represents those of
c. The transition temperature is set at 650 K, so a and c
have the same value at this temperature. The middle solid
line below 650 K represents the lattice constant a of the
5
0
5 0
(7)
≠
ea
the value of e and e that minimize the Gibbs-free energy
are determined. The expression for the magnetic strain
components e and e are obtained as
a
c
a
c
2
2
e 5 NS s K
s
J b 1 J b2d
a
10
1
20
(
8)
2
2
e 5 NS s KJ b
2
c
20
cubic structure in the non-magnetic state which is shown in
by taking P50 and neglecting fl.
1 / 3
Fig. 5. The open diamonds represent V
(V is volume)
s(T) is given by the Brillouin function,
derived from the experimental values. The open squares
represent the lattice constant a obtained in the X-ray
diffraction measurements under high pressure as shown in
s
T
s d
5 BS
s
x
d
(9)
2
s
2 8J 1 4J 1 4J 1 2J2cd
K
S S
L
1
d
1a
2a
x 5
(10)
kT
where kSl5Ss, k is Boltzmann constant. Putting Eqs. (5),
(
6) and (8) into Eq. (10), we obtain
2
4
S
3
x 5
s
ps 1 qs
d
(11)
(12)
kT
where
p 5 2 2J 1 3J
1
0
20
2
2
2
2
20
2
2
q 5 NS K
s
2J b 1 4J b J b 1 3J b
d
1
0
1
10
1
20
2
The N e´ el point TN is given as
Fig. 7. Temperature variations of the lattice constants of MnN. An open
2
S
s
S 1 1 2 8J 1 4J 1 4J 1 2J
d
s
d
2c
]
1
d
1a
2a
circle and triangle represent the experimental values of the lattice
TN 5
(13)
1 / 3
3
k
constants a and c. An open diamond represents V
(V is unit cell
volume) derived from the experimental values. The upper solid line below
50 K represents the calculated value of a and the lower solid line below
Putting Eqs. (5) and (6) into Eq. (13), and then using
6
e 5e 50 ({s50), T is expressed as
650 K represents that of c. The middle solid line below 650 K represents
the lattice constant a of the cubic structure in the non-magnetic state. An
open square represents the lattice constant a obtained in the X-ray
diffraction measurements under high pressure of 3.0 GPa and the solid
line above 650 K is derived by using a least-squares method from these
experimental values.
a
c
N
2
S
S 1 1
s d
s
2 4J 1 6J20d
1
0
TN 5
(14)
3
k
As shown above, the magnetic strains are expressed as

4
0
K. Suzuki et al. / Journal of Alloys and Compounds 360 (2003) 34–40
at temperatures between 643 and 668 K, which corre-
sponds to the above transition temperature of MnN. The
anomalous thermal expansion of MnN was discussed by
taking into account the anisotropic strain dependence of
the exchange interactions on the basis of molecular field
theory.
Acknowledgements
This work was performed under the inter-university
cooperative research program of the Institute for Materials
Research, Tohoku University. We are grateful to Dr. H.
Shimizu of the Faculty of Science, Shinsyu University for
providing us with the results of band calculations and
useful discussions and Professor H. Morita of the Faculty
of Engineering, Yamagata University for his useful discus-
sions and encouragement.
Fig. 8. Strain components, ea and ec versus temperature curves. The
lattice constant a of the cubic structure in the non-magnetic state is used
as a base line. The upper solid line below 650 K (1) shows the curve for
the calculated value of e , and the lower solid line below 650 K (2) is the
a
curve calculated for e . An open circle and triangle represent the strain
c
components derived from the experimental values of the lattice constants
1
/ 3
a and c. An open diamond represents the strain component of V
(V is
unit cell volume) derived from the experimental values.
References
Section 3.2 and the solid line above 650 K is derived by
using a least-squares method from these experimental
values. The results of the temperature variations of strain
[
[
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a
c
[3] U. Zwicker, Z. Metallk. 42 (1951) 274.
in Fig. 8, together with the experimental values.
[4] O. Prelinger, Monatsh. Chem. 15 (1894) 391.
[
[
[
[
5] M. Mekata, J. Haruna, H. Takei, J. Phys. Soc. Jpn. 25 (1968) 234.
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In Fig. 7, the overall agreement between the calculated
and the experimental values appears to be reasonable,
although the calculated value of c deviates from the
experimental values in the temperature range from about
(
1945) 1.
[9] N. Otsuka, Y. Hanawa, S. Nagakura, Phys. Stat. Sol. (a) 43 (1977)
27.
1
/ 3
5
00 to 650 K. As is found in Fig. 7, the value of V
(ȣ)
1
is a little larger than that of the lattice constant a in the
non-magnetic state (middle solid line). It is concluded that
the volume striction is positive. A study of the pressure
dependence of TN is now in progress in our laboratory in
order to further clarify the atomic distance dependence of
exchange interaction.
[
[
10] W.J. Takei, G. Shirane, B.C. Frazer, Phys. Rev. 119 (1960) 112.
11] K. Suzuki, T. Kaneko, H. Yoshida, Y. Obi, H. Fujimori, H. Morita, J.
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[
13] A. Leineweber, R. Niewa, H. Jacobs, W. Kockelmann, J. Mater.
Chem. 10 (2000) 2827.
[14] The value of the Debye temperature obtained by us (to be published
elsewhere).
5
. Conclusion
[
[
15] C.P. Bean, D.S. Rodbell, Phys. Rev. 126 (1962) 104.
16] K. Adachi, K. Sato, K. Ohomori, T. Ido, Toyota Kenkyu Hokoku [in
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The MnN compound has been prepared as a single
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phase by d.c. reactive sputtering. The crystal structure of
MnN is of a tetragonally distorted NaCl type (fct) at room
temperature. The MnN compound shows antiferromag-
netism with a N e´ el temperature of 650 K. In this paper, the
temperature variation of the lattice constants of MnN was
investigated. The results showed that the crystal structure
of MnN has transformed from an fct structure to an fcc one
Soc. Jpn. 53 (1984) 2703.
[
[
18] G. Shirane, Acta Crystallogr. 12 (1959) 282.
19] J.S. Smart, in: G.T. Rado, X. Suhl (Eds.), Magnetism, Vol. 3,
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[
[
[