Anisotropic thermal conductivity in epoxy-bonded magnetocaloric composites Bruno Weise, Kai Sellschopp, Marius Bierdel, Alexander Funk, Manfred Bobeth, Maria Krautz, and Anja Waske Citation: Journal of Applied Physics 120, 125103 (2016); doi: 10.1063/1.4962972 View online: http://dx.doi.org/10.1063/1.4962972 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/120/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Improvement of magnetic hysteresis loss, corrosion resistance and compressive strength through spark plasma sintering magnetocaloric LaFe11.65Si1.35/Cu core-shell powders AIP Advances 6, 055321 (2016); 10.1063/1.4952757 Enhanced thermal conductivity in off-stoichiometric La-(Fe,Co)-Si magnetocaloric alloys Appl. Phys. Lett. 107, 152403 (2015); 10.1063/1.4933261 Enhanced magnetostrictive effect in epoxy-bonded TbxDy0.9−xNd0.1(Fe0.8Co0.2)1.93 pseudo 1–3 particulate composites J. Appl. Phys. 117, 17A914 (2015); 10.1063/1.4916507 Consequences of the magnetocaloric effect on magnetometry measurements J. Appl. Phys. 108, 043923 (2010); 10.1063/1.3466977 La ( Fe , Co , Si ) 13 bulk alloys and ribbons with high temperature magnetocaloric effect J. Appl. Phys. 107, 09A953 (2010); 10.1063/1.3335892 Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 141.30.233.200 On: Mon, 14 Nov 2016 12:13:00
7
Embed
Anisotropic thermal conductivity in epoxy-bonded ...nano.tu-dresden.de/pubs/reprints/2016_JAP_Weise.pdfAnisotropic thermal conductivity in epoxy-bonded magnetocaloric composites Bruno
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Anisotropic thermal conductivity in epoxy-bonded magnetocaloric compositesBruno Weise, Kai Sellschopp, Marius Bierdel, Alexander Funk, Manfred Bobeth, Maria Krautz, and Anja Waske Citation: Journal of Applied Physics 120, 125103 (2016); doi: 10.1063/1.4962972 View online: http://dx.doi.org/10.1063/1.4962972 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/120/12?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Improvement of magnetic hysteresis loss, corrosion resistance and compressive strength through spark plasmasintering magnetocaloric LaFe11.65Si1.35/Cu core-shell powders AIP Advances 6, 055321 (2016); 10.1063/1.4952757 Enhanced thermal conductivity in off-stoichiometric La-(Fe,Co)-Si magnetocaloric alloys Appl. Phys. Lett. 107, 152403 (2015); 10.1063/1.4933261 Enhanced magnetostrictive effect in epoxy-bonded TbxDy0.9−xNd0.1(Fe0.8Co0.2)1.93 pseudo 1–3 particulatecomposites J. Appl. Phys. 117, 17A914 (2015); 10.1063/1.4916507 Consequences of the magnetocaloric effect on magnetometry measurements J. Appl. Phys. 108, 043923 (2010); 10.1063/1.3466977 La ( Fe , Co , Si ) 13 bulk alloys and ribbons with high temperature magnetocaloric effect J. Appl. Phys. 107, 09A953 (2010); 10.1063/1.3335892
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 141.30.233.200 On: Mon, 14 Nov
Anisotropic thermal conductivity in epoxy-bonded magnetocaloriccomposites
Bruno Weise,1,a) Kai Sellschopp,1,a) Marius Bierdel,1 Alexander Funk,1,a) Manfred Bobeth,2
Maria Krautz,1 and Anja Waske1,b)
1Institute for Complex Materials, IFW Dresden, P.O. Box 270116, D-01171 Dresden, Germany2Institute for Materials Science and Max Bergmann Center of Biomaterials, TU Dresden,01062 Dresden, Germany
(Received 6 July 2016; accepted 5 September 2016; published online 28 September 2016)
Thermal management is one of the crucial issues in the development of magnetocaloric refrigeration
technology for application. In order to ensure optimal exploitation of the materials “primary”
properties, such as entropy change and temperature lift, thermal properties (and other “secondary”
properties) play an important role. In magnetocaloric composites, which show an increased cycling
stability in comparison to their bulk counterparts, thermal properties are strongly determined by the
geometric arrangement of the corresponding components. In the first part of this paper, the inner
structure of a polymer-bonded La(Fe, Co, Si)13-composite was studied by X-ray computed tomogra-
phy. Based on this 3D data, a numerical study along all three spatial directions revealed anisotropic
thermal conductivity of the composite: Due to the preparation process, the long-axis of the magneto-
caloric particles is aligned along the xy plane which is why the in-plane thermal conductivity is larger
than the thermal conductivity along the z-axis. Further, the study is expanded to a second aspect
devoted to the influence of particle distribution and alignment within the polymer matrix. Based on
an equivalent ellipsoids model to describe the inner structure of the composite, numerical simulation
of the thermal conductivity in different particle arrangements and orientation distributions were per-
formed. This paper evaluates the possibilities of microstructural design for inducing and adjusting
anisotropic thermal conductivity in magnetocaloric composites. Published by AIP Publishing.[http://dx.doi.org/10.1063/1.4962972]
I. INTRODUCTION
Magnetocaloric refrigeration is believed to be a competi-
tive alternative for conventional vapour compression technol-
ogy and therefore has drawn large interest from both scientific
(a comprehensive overview can be found in Ref. 1) and indus-
trial research (see recent press-releases2,3). Instead of a gas
which is used conventionally, a solid body exhibiting a
magnetocaloric effect serves as refrigerant material for
magnetocaloric refrigeration. The material is magnetized and
demagnetized during a refrigeration cycle and thereby expels
or absorbs heat to or from the surrounding, respectively. In
the search for suitable materials, the alloys based on La(Fe,
Si)13 and Fe2P-type compounds are considered to be most
promising for room-temperature application.4 It is crucial that
these materials can withstand up to several millions of magne-
tization/demagnetization cycles, which is one of the reasons
why composites with increased mechanical stability have
been developed.5–8 Since the refrigerant material is a solid,
the generated heat has to be transferred out of the solid body
to a surrounding heat transfer fluid in order to create a hot and
cold end of the regenerator bed within a certain operating fre-
quency. This frequency scales with the cooling power of the
device; therefore, a large thermal conductivity from the solid
body to the surrounding cooling liquid is required.9 On the
contrary, lateral heat transfer within the refrigerant material is
disadvantageous since the operating thermal span and, there-
fore, the cooling power of the device are reduced. From this
technical viewpoint, the demand of an anisotropic heat con-
ductivity of the magnetocaloric material arises. Up to now,
experimental values only for isotropic thermal transport prop-
erties have been reported,10–13 and less attention has been
paid towards anisotropy. In this paper, the 3D microstructure
of an epoxy-bonded composite plate is determined by X-ray
computed tomography (XCT) in order to access potentially
preferred particle orientation. The inner structure then is
linked to the thermal properties, the thermal conductivity in
this case, which is experimentally and numerically determined
along each plate edge (x-, y-, z-direction). Based on that,
hypotheses to increase the anisotropy of the thermal conduc-
tivity are assessed by modeling different particle arrange-
ments by means of an equivalent ellipsoids model.
II. 3D MICROSTRUCTURE OF COMPOSITES
A. Preparation and characterization
Pulko et al.6 investigated a series of polymer-bonded mag-
netocaloric composites in order to assess their competitiveness
in comparison to conventionally sintered LaFe13�x�y CoxSiyplates. From these series, one sample has been chosen in order
to study its inner constitution in detail by X-ray computed
a)Also at Institute for Materials Science, TU Dresden, D-01069 Dresden,
Germany.b)Also at Institute for Materials Science, TU Dresden, D-01069 Dresden,
0021-8979/2016/120(12)/125103/6/$30.00 Published by AIP Publishing.120, 125103-1
JOURNAL OF APPLIED PHYSICS 120, 125103 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 141.30.233.200 On: Mon, 14 Nov
can also be calculated for each particle from the 3D dataset
using the substitution of the volume integral in Eq. (1). In
these equations,~r denotes the position vector, E is the iden-
tity matrix—a 3� 3 diagonal matrix where all the diagonal
elements equal 1—and the density of the particle is assumed
to be constant and set to 1 for the sake of simplicity. The
eigenvectors of the inertia tensor are regarded as the princi-
pal axes of the particle, which are used to describe the orien-
tation of the particle. The eigenvector with the lowest
eigenvalue, i.e., with the lowest principal moment of inertia,
corresponds to the direction with the largest dimension of
the particle.
C. Model of equivalent ellipsoids
In order to assess the influence of the particle orientation
on the thermal properties of the composites, the complex
geometry of the particles is translated into an equivalent
ellipsoid model. Based on the XCT-data of the composite,
the volume, the center of mass, and the inertia tensor of each
individual particle are determined. Then, each particle is
replaced by an ellipsoid with the same center of mass and
inertia tensor. This method for the simplification of particle
shape is well known in literature (see, e.g., Refs. 16–18). It
can be seen in Figure 2 that the particle orientation is con-
served by this means. Nevertheless, it has to be mentioned
that the volume of the ellipsoid is slightly bigger than that
of the initial particle. When replaced by an equivalent ellip-
soid, the orientation of the particle can be manipulated easily
with the help of a self-written MATLABVR
program in further
simulations. As a consequence, all further results on thermal
properties are based on real XCT-data sets, i.e., the orienta-
tion distribution of the equivalent ellipsoids represents the
FIG. 1. Tomographic slice of the composite including all grey values (a), binarization step to prepare the separation of individual particles (b), and separated
particles by watershed algorithm marked with individual colour code (c). On the right side, the reconstructed 3D volume with individual particles marked in
all tomographic slices is shown. The sample volume was ð2� 1:5� 0:3Þmm3.
FIG. 2. Illustration of equivalent ellipsoids model. The equivalent ellipsoid
representing the particle is defined by three half-axes corresponding to the
axes of inertia of the real particle.
125103-2 Weise et al. J. Appl. Phys. 120, 125103 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 141.30.233.200 On: Mon, 14 Nov
2016 12:13:00
arrangement of the irregularly shaped particles in the
composite.
D. Analysis of 3D microstructure
Similar to a pole figure for texture depiction in materials,
the orientation distribution of the half-axes of the equivalent
ellipsoids in the composite is shown in Figure 3. h describes
the angle between each half-axis of the particle and the global
z-axis of the composite (cf. Fig. 1). The range of h is restricted
to the interval [0�; 90�] because of the twofold symmetry of
the ellipsoids.
Obviously, the long and the middle half-axes are oriented
perpendicular to the z-axis (out-of-plane direction) of the
composite. Due to that, intuitively, the short half-axis of
the ellipsoids would be oriented parallel to the z-direction.
However, a random distribution of the short-axis is observed
which can be attributed to the statistical deviation of the orien-
tation angles of the ellipsoids within the composite. In other
words, during the preparation of the epoxy-bonded compo-
sites as described in Ref. 6, elongated irregularly shaped
La(Fe, Co, Si)13 particles align along the global xy plane (in-
plane). Note that from Fig. 3(a) mean orientation angle of the
long-axis of 70:6� was determined.
It is obvious that geometrical anisotropy will affect the
thermal properties of the composites. The influence of the
orientation texture on the thermal conductivity of the compo-
sites will be addressed in Sec. III.
III. THERMAL CONDUCTIVITY OF COMPOSITES
A. Theoretical bounds
The overall thermal conductivity in a multicomponent
system can be described in analogy to Ohm’s law:19 The lim-
iting cases are either a series or parallel arrangement of the
components, i.e., the upper and lower bound of the overall
thermal conductivity in the present composite can be deter-
mined from
kmax;parallel ¼ fkparticles þ ð1� f Þkmatrix; (4)
and
kmin;series ¼kparticleskmatrix
1� fð Þkparticles þ fkmatrix; (5)
with f¼ 58 vol. % (from XCT) as the volume fraction
of the particles in the composite and thermal conductivi-
ties kparticles ¼ 8:93 Wðm�1 K�1Þ (Ref. 6) and kmatrix
¼ 0:24 Wðm�1 K�1Þ,20 respectively. From this approach,
the thermal conductivities determined by computational
methods in Sec. III B have to be in the interval
0.55 W m�1 K�1 <k < 5.28 W m�1 K�1.
B. Measurements and finite element method (FEM)simulation
According to Equation (6), the thermal conductivity
k can be directly derived from the thermal diffusivity a,
specific heat capacity cp, and density q
k ¼ acpq: (6)
To access, the thermal conductivity of the composite measure-
ments of thermal diffusivity was performed with a NETZSCH
LFA 457 MicroFlash device in zero-field using the Cape-
Lehman model.21 Due to geometrical restrictions of the device,
only the out-of-plane thermal diffusivity, az, was accessible.
Specific heat measurements were performed in a quantum
design physical property measurement system in zero-field.
According to Pulko et al.,6 the density of the composite was
4.7 g cm�3. Figure 4 shows the measured data of azðTÞ(dashed), cpðTÞ (dashed-dotted), and the resulting curve (solid)
of the thermal conductivity kzðTÞ. At T¼ 300 K, the measured
thermal conductivity is kz ¼ 2:41 W m�1 K�1.
The binarized reconstructed volume of the XCT-scans
served for the simulation of the thermal conductivity of the
FIG. 3. Orientation distribution of the half-axes of equivalent ellipsoids.
FIG. 4. Temperature dependent thermal diffusivity az and heat capacity
cp of the composite in zero-field (right axes). The thermal conductivity
kz (left axis) was calculated from these measurements according to
Equation (6).
125103-3 Weise et al. J. Appl. Phys. 120, 125103 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 141.30.233.200 On: Mon, 14 Nov
2016 12:13:00
composite in all three directions (x-, y-, z-axis). For FEM simu-
lation, the binarized histogram as described in Section II B
was used to generate a voxel-based mesh comprising
65 847 936 elements. Following that, the thermal conductivity
of the two different phases (kparticles ¼ 8:93 W m�1 K�1,
kmatrix ¼ 0:24 W m�1 K�1) was allocated to the corresponding
phases within the mesh. Table I summarizes the results of the
numerical simulation of the thermal conductivity along the x-,
y-, and z-axis of the composites and the in-plane and isotropic
value of k that can be directly derived from kðx;y;zÞ. First, it is
to note that the experimentally and numerically determined
out-of-plane values of heat conductivity (kz) correspond very
well. Additionally, simulated kz is significantly lower than kx
and ky. Evidently, the anisotropic alignment of the La(Fe, Co,
Si)13 particles along the xy plane (as shown in Fig. 3) leads to
anisotropic thermal conductivity of the composite.
To summarize, in the presented composite, the thermal
conductivity is larger in the xy plane than along the z-axis.
This is opposite to what is desired for practical use: In a
regenerator plate-bed, thermal conductivity should be large
along the z-axis, in order to transfer heat out of the plate
body and low in xy plane to reduce parasitic heat exchange
within the refrigerant body.
It is therefore consistent to study the influence of the
degree of orientation on the thermal conductivity both in-
plane (xy plane) and out-of-plane (along z-axis) to assess the
limits of thermal conductivity that can be achieved by parti-
cle alignment across a regenerator composite-plate.
C. Influence of particle orientation on thermalconductivity
In this section, the influence of particle orientation on
thermal conductivity is studied using the aforementioned
equivalent ellipsoid model. For this purpose, the model first
is created with the self-written MATLAB program. Then, a
mesh for FEM simulation is generated using the þFE mod-
ule of the ScanIP software environment (Simpleware Ltd.,
Exeter, UK). It has to be mentioned that meshing did not
lead to satisfying results for all particle sizes in the sample.
Meshing errors occurred for particle sizes below d < 10 lm.
Due to this fact, this fraction was neglected during the
meshing process. Although the fraction of coarse particles
increases slightly with this method, the total volume fraction
of the particles (f ¼ 58 vol:%) remained approximately
constant because of the small volume of the excluded
particles. The FEM simulation for the determination of
thermal conductivity is finally performed with the software
COMSOL MultiphysicsVR
. In preliminary simulations, the
influence of mesh density was studied so that for the follow-
ing simulations the mesh density could be chosen in a way
that it does not affect the results. Furthermore, it has to be
mentioned that the absolute values of thermal conductivity
in the ellipsoid model are higher than in the original dataset
since the volumes of the equivalent ellipsoids are slightly
bigger than those of the original particles.
1. Thermal conductivity after changing the preferredorientation from in-plane to out-of-plane
It was shown in Sec. II that the long and middle half-
axis of the particles in the as-prepared composite is aligned
along the xy plane. In this section, the influence on thermal
conductivity of the particle orientation along the z-axis
will be studied by numerical simulation. As input data, the
geometric information of the equivalent ellipsoids of the as-
prepared composite is taken. The long half-axis of the equiv-
alent ellipsoids, representing the magnetocaloric particles,
is oriented in 15� steps from 0� (xy plane ¼̂ in-plane) to 90�
(z-axis ¼̂ out-of-plane).
Depending on this orientation angle, / values for the in-
plane and out-of-plane thermal conductivity can be simu-
lated as shown in Figure 5. An increasing orientation of the
long half-axis along the z-axis of the composite gives rise to
a relative enhancement of kz of about 21% to a maximum
value of 5.16 W m�1 K�1 at / � 67�, which approximately
corresponds to the mean orientation angle of the longest
half-axis in the initial distribution. Note that the change from
xy plane as preferred orientation to / � 90� along the z-axis
gives about 16% of enhancement. The in-plane thermal con-
ductivity on the other hand decreases at the same time, since
the geometrical anisotropy is increased due to the change
of the preferred particle orientation from the xy plane to the
z-axis. The orientation dependent in-plane and out-of-plane
thermal conductivity can be described as a sinusoidal
TABLE I. Anisotropic thermal conductivities determined by laser flash
method and FEM simulation. If the same temperature gradient is applied in
all directions, kin�plane is the mean value of the thermal conductivity along
the x- and y-axis. The isotropic thermal conductivity can be derived analo-
gously by the mean value of the thermal conductivity along all three axes.
Thermal conductivity (W m�1 K�1) Measured Simulated
kx … 2.67
ky … 2.65
kin�plane … 2.66
kz 2.41 2.47
kiso … 2.60 FIG. 5. Simulated thermal conductivity as function of orientation angle / of
the equivalent ellipsoids.
125103-4 Weise et al. J. Appl. Phys. 120, 125103 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 141.30.233.200 On: Mon, 14 Nov
2016 12:13:00
function of the orientation angle, i.e., due to symmetry rea-
sons values of kz and kin–plane decrease/increase again above
/ � 67� where some ellipsoids are already turned out of
z-axis again (insets Fig. 5). Due to overlapping of ellipsoids
and finite sample size, a re-orientation of the ellipsoids
results in a change of the particle-to-matrix ratio. The par-
ticles volume fraction decreases from 70% at / ¼ 0� to 60%
at / ¼ 90�. This causes a decrease of the mean (isotropic)
thermal conductivity superposing the influence of the re-
orientation of the ellipsoids (grey values in Fig. 5). In real
composites with oriented particles, equal volume fractions
can be created for all rotation angles. Therefore, it can be
assumed that the isotropic thermal conductivity will not
depend on the rotation angle in real composites. Building on
this assumption, we corrected our data to compensate the
influence of decreasing volume fraction with increasing /(blue and orange values in Fig. 5). Admittedly, the quantita-
tive values of heat conductivity are slightly overestimated in
all directions because of the slightly larger volume of the
inertia equivalent ellipsoids compared to the initial particles.
Nevertheless, the tendency of the evolution of k by reorienta-
tion is well represented.
The initial values of kz and kin–plane reflect the particle
arrangement of the as-prepared composite, where a larger
heat conductivity in the xy plane is present.
2. Thermal conductivity for different orientationdistribution functions
The above mentioned simulation is based on the ori-
entation distribution predefined by the as-prepared com-
posite (Fig. 3). A manipulation of this distribution will
have an impact on the thermal conductivity. In the follow-
ing, different orientation distributions differing in their
standard deviation r will be examined. As a condition,
the preferred orientation of the particles is already along
the z-axis. For illustration, particle arrangements with
broad (high standard deviation) and narrow (low standard
deviation) orientation distributions are schematically
shown in Fig. 6(a).
In order to evaluate the influence of r on kz as initial
scenario, a particle arrangement corresponding to reor-
iented particles along the z-axis with orientation angle
sponds to the orientation distribution determined by XCT
from the as-prepared sample (as discussed in Fig. 3). As
can be seen in Figure 6, the thermal conductivity kz
increases with decreasing standard deviation of the particle
orientation distribution r. In other words, a narrow distri-
bution leads to enhanced thermal conductivity although
kz saturates by approaching r ¼ 0�. As a result, already
a rotation of all equivalent ellipsoids along the z-axis of
/ � 10� is enough to give a larger heat conductivity. It is
to expect that kz reaches values close to kiso for increasing
r > 25:5�. However, the increase in kz is only about 5.6%.
In comparison to the effect of particle reorientation from
the xy plane along the z-axis, the increase of kz by narrow-
ing the orientation distribution is rather low.
IV. CONCLUSION
The 3D microstructure of a polymer-bonded magneto-
caloric composite (cf. Ref. 6) was studied by X-ray com-
puted tomography, and its thermal conductivity along the x-,
y-, and z-axis was determined by numerical simulation
(FEM). The simulated result of kz was experimentally con-
firmed by measuring out-of-plane thermal conductivity with
the laser flash method.
Based on the XCT-data, a texture along the global xyplane of the composite has been revealed. During the com-
paction process, plate- and rod-shaped particles align along
their long and middle half-axes of their equivalent ellipsoids.
This texture leads to an increase of the in-plane thermal con-
ductivity (kx, ky), whereas kz is decreased.
Besides the characterization of an as-prepared compos-
ite, the second aspect of the paper was devoted to the possi-
bilities of enhancing the anisotropic thermal conductivity as
it is crucial for regenerator designs. Numerical simulation of
different particle arrangements and particle orientation distri-
butions has been evaluated. To summarize, a reorientation of
particles along the axis where thermal transport is preferred
gives a considerable (16% in the present composite) increase
of the thermal conductivity in comparison to the natural
FIG. 6. Illustration of the orientation of equivalent ellipsoids in the compos-
ite with large and low standard deviation r of the distribution of the long
half-axis (red arrow) along the z-axis (a). Out-of-plane thermal conductivity
kz as function of r (b).
125103-5 Weise et al. J. Appl. Phys. 120, 125103 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 141.30.233.200 On: Mon, 14 Nov
2016 12:13:00
plane-anisotropy which is present in composites prepared by
conventional cold-pressing. Although smaller, a further
increase of the thermal conductivity can be achieved by a
narrow particle distribution function. Considering these
influences, this paper gives hints for an optimized prepara-
tion (e.g., curing in a magnetic field, optimized particle
shapes, etc.) of composite plates for regenerator beds.
ACKNOWLEDGMENTS
The authors thank Robert M€uller for supporting the
finite element calculations and the Center for Information
Services and High Performance Computing (ZIH) at TU
Dresden for computational resources. B.W. thanks the Korea
Institute of Industrial Technology (KITECH) for financial
support. A.W. would like to gratefully acknowledge funding
from the DFG SPP “Ferroic Cooling” under Grant No. WA
3294/3-2.
1A. Kitanovski, J. Tu�sek, U. Tomc, U. Plaznik, M. O�zbolt, and A. Poredos,
Magnetic Energy Conversion-From Theory to Application (Springer,
Cham, 2015), p. 456.2Haier, BASF, and Astronautics, press release in Premiere of Cutting-Edge
Cooling Appliance at CES 2015, 2015.3Cooltech Applications, press release in Premiere of Revolutionary
Medical Refrigerator with Cooltech Applications at Medica 2015, 2015.4A. Smith, C. R. Bahl, R. Bjørk, K. Engelbrecht, K. K. Nielsen, and N.
Pryds, Adv. Energy Mater. 2, 1288 (2012).5H. Zhang, Y. Sun, E. Niu, F. Hu, J. Sun, and B. Shen, Appl. Phys. Lett.
104, 062407 (2014).
6B. Pulko, J. Tu�sek, J. D. Moore, B. Weise, K. Skokov, O. Mityashkin, A.
Kitanovski, C. Favero, P. Fajfar, O. Gutfleisch, A. Waske, and A. Poredo�s,
J. Magn. Magn. Mater. 375, 65 (2015).7M. Krautz, A. Funk, K. P. Skokov, T. Gottschall, J. Eckert, O. Gutfleisch,
and A. Waske, Scr. Mater. 95, 50 (2015).8I. A. Radulov, K. P. Skokov, D. Y. Karpenkov, T. Gottschall, and O.
Gutfleisch, J. Magn. Magn. Mater. 396, 228 (2015).9K. K. Nielsen and K. Engelbrecht, J. Phys. D: Appl. Phys. 45, 145001
(2012).10S. Fujieda, Y. Hasegawa, A. Fujita, and K. Fukamichi, J. Appl. Phys. 95,
2429 (2004).11B. Rosendahl Hansen, L. Theil Kuhn, C. Bahl, M. Lundberg, C. Ancona-
Torres, and M. Katter, J. Magn. Magn. Mater. 322, 3447 (2010).12J. Lyubina, U. Hannemann, L. F. Cohen, and M. P. Ryan, Adv. Energy
Mater. 2, 1323 (2012).13G. Porcari, K. Morrison, F. Cugini, J. A. Turcaud, F. Guillou, A. Berenov,
N. H. van Dijk, E. H. Br€uck, L. F. Cohen, and M. Solzi, Int. J. Refrig. 59,
29 (2015).14J. P. Kruth, M. Bartscher, S. Carmignato, R. Schmitt, L. de Chiffre, and A.
Weckenmann, CIRP Ann.-Manuf. Technol. 60(2), 821–842 (2011).15L. Najman and M. Schmitt, Signal Process. 38, 99 (1994).16T. St€uckrath, G. V€olker, and J.-H. Meng, “Die Gestalt von nat€urlichen
Steinen und ihr Fallverhalten in Wasser,” Mitteilung/Institut f€ur
Wasserbau und Wasserwirtschaft, Technische Universit€at Berlin, Report
No. 137 (Institut f€ur Wasserbau und Wasserwirtschaft, Berlin, 2004), Vol.
137.17V. I. Kushch, I. Sevostianov, and V. S. Chernobai, Int. J. Eng. Sci. 83, 146
(2014).18A. Giraud, I. Sevostianov, F. Chen, and D. Grgic, Int. J. Rock Mech. Min.
Sci. 80, 379 (2015).19G. T.-N. Tsao, Ind. Eng. Chem. 53, 395 (1961).20H. Czichos, in H€utte: Die Grundlagen der Ingenieurwissenschaften, 29th
ed., edited by H. Czichos (Springer, Berlin, Heidelberg, 2000), p. D51.21J. Cape and G. Lehman, J. Appl. Phys. 34, 1909 (1963).
125103-6 Weise et al. J. Appl. Phys. 120, 125103 (2016)
Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Download to IP: 141.30.233.200 On: Mon, 14 Nov