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Applications of Polymer, Composite, and Coating Materials

Magnetic submicron mullite coatings with oriented SiC whiskersZhaoxi Chen, James Townsend, Pavel Aprelev, Yu Gu, Ruslan

Burtovyy, Igor Luzinov, Konstantin G Kornev, and Fei PengACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b16572 • Publication Date (Web): 09 Mar 2018

Downloaded from http://pubs.acs.org on March 12, 2018

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1

Magnetic submicron mullite coatings with oriented SiC whiskers

Zhaoxi Chen1, James Townsend

1, Pavel Aprelev

1, Yu Gu

2, Ruslan Burtovyy

1, Igor Luzinov

1,

Konstantin G Kornev1*†

and Fei Peng1*‡

Keywords: alignment, superparamagnetic nanorods, mullite, silicon carbide, magnetic

rotation, ceramic thin film

1 Department of Materials Science and Engineering, Clemson University

2 Institute of Optoelectronic and Nanomaterials College of Materials Science and Engineering, Nanjing

University of Science and Technology * Corresponding authors

† Email: [email protected]

‡ Email: [email protected]

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Abstract

Addressing the challenge of making ceramic thin films with the in-plane-oriented

nanorods, we propose to decorate the nanorods with magnetic nanoparticles and orient them

using the external magnetic field. As an illustration, the mullite thin films with embedded and

oriented SiC nanorods were synthesized. The SiC nanorods were decorated with the Fe3O4

nanoparticles. A two-step processing route was developed when the nanorods are first oriented in

a sacrificial polymer layer. Then, the polymer film with the aligned nanorods was removed by

heat-treatment. At the second step, a sol-gel/dip-coating method was applied to produce the

mullite composite film. The main challenge was to guarantee that all the nanorods which were

initially randomly distributed in the polymer would have time to rotate toward the field direction

before complete solidification of the sacrificial layer. Theoretical and experimental analyses of

the orientational distribution of the nanorod axes were conducted to identify a relationship

between the polymer viscosity, magnetic and processing parameters of the system. In contrast to

the ferromagnetic nanorods, the rate of rotation of paramagnetic nanorods and their time of

alignment are more sensitive to the magnetic field. This methodology allows manufacturing

different ceramic films with aligned nanorods and making non-magnetic ceramic coating

magnetic.

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1. Introduction

Ceramic thin films enjoy broad applications and especially important in applications

where the temperature is high and the environment is hazardous and chemically harsh. It is

therefore attractive to enrich these films with additional functionalities by embedding some

functional inclusions. Thin films with embedded nanoparticles, nanowhiskers, nanoplates and

nanorods are on demand by many technologies including catalysis, microwave engineering,

magnetic recording and sensing, and solar cell engineering 1-5

. The embedded anisotropic nano-

inclusions, nanorods in particular, brings to the composite the superior mechanical properties and

exclusive novel functionalities such as magneto-optic anisotropy, microwave absorbency and

controlled heat dissipation 6-14

. The most popular existing approaches to attain the nanorods

ordering in ceramic thin films are 1) the growth of nanorods in a porous template with ordered

arrays of uniform nanochannels 8-9, 15

, and 2) the deposition of a ceramic thin film on a substrate

with a pre-grown forest of nanorods 16-22

.

In the first approach, the nanoporous films with oriented pore channels serve as the

templates for nanorods grown by vapor or electrochemical deposition 8-9, 15

. However, processing

of the porous templates is often tedious and time consuming 18

. In the second approach, the

arrays of vertically aligned nanorods were grown on substrates by the template-based growth,

hydrothermal, patterned electrodeposition or laser deposition methods 16-23

. The most important

limitation of these two technologies is their inability to provide large area films with a uniform

orientation of nanorods: uniform deposition over an area exceeding several cm2 appears to be

difficult 23

. The strategy for the in-plane orientation of anisotropic nanoparticles in ceramic films

has not yet been developed and thus remains the main challenge in thin film technology 5.

The idea of using electric or magnetic fields to orient an assembly of the field responsive

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nanorods offers many exciting opportunities to fabricate large volumes of composite materials

with a desirable anisotropy 5, 24-26

. The main effort in the last decade has been directed on the

development of different strategies to manufacture polymer films with aligned nanostructures 5-6,

14, 24-28. Ceramic films with the in-plane ordering of nanorods have not been reported yet.

In many cases, the fillers of interest in the form of nanorods are diamagnetic, for example,

the Si3N4, SiC, Al2O3 particles are quite popular in applications. Extremely strong magnetic

fields have been used for many years to fabricate the bulk ceramic composites out of these

materials 29-31

. This approach combines the ceramic processing methods with electrophoretic

deposition of colloidal suspensions and slip casting of fine ceramic powders in strong magnetic

fields of greater than 10T 29-31

. It is therefore attractive to adapt this technology for film

fabrication. However, it is desirable to relax the requirements on the field strength. Making the

nanorods superparamagnetic or ferromagnetic, one can significantly decrease the applied

magnetic field 5, 14, 24-25

.

Recent studies demonstrated a robust and attractive methodology to make many desirable

fillers magnetic by decorating ceramic particles with magnetic nanoparticles responding to

sufficiently weak magnetic fields 14, 26, 32

. We will follow this methodology.

The main challenge in the nanorod ordering during the film fabrication is that the

nanorods subject to the forced rotation may not keep in pace with the applied field because of the

gradually increased viscous drag of evaporating or curing film. Thus, some nanorods from an

initially randomly distributed assembly might not have time to make the full revolution towards

the desired field direction prior to the film solidification 6, 12, 33-36

. The condition for complete

alignment of ferromagnetic nanorods in solidifying polymer films was investigated employing

the distribution function theory 28, 33, 36

. A phase diagram specifying complete and partial

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alignment of ferromagnetic nanorods was introduced; in particular, the necessary processing

conditions such as the strength of magnetic field and the rate of viscosity increase were identified

for the nanorods with the given physical properties 5. The phase diagram for paramagnetic

nanorods have not been analyzed yet which makes the experimental analysis of the in-plane

ordering of nanorods costly and tedious.

To capitalize on our understanding of physics of nanorod ordering in polymeric films, we

have chosen the sol-gel method as a versatile ceramic processing method enjoying a large library

of material compositions, yet having many common features with the processing of polymeric

films 37-40

. In this method, ceramic films are formed from the polymer-like solutions 41-42

. Post-

processing of polymeric films, however, represents a great challenge: one has to heat treat the

material to the extent when the materials composition changes significantly from being a soft

polymeric (gel) to becoming a rigid ceramic. This transformation of the matrix material affects

the nanorod ordering; without a special care, the ordering attained in a polymer film gets

completely destroyed after firing the film. The challenges in the fabrication of ceramic films

include the preservation of nanorods alignment, control of film thickness, elimination of defects

caused by the film dewetting and cracking. In this paper we develop a methodology for

fabrication of ceramic composite films carefully addressing all these challenges.

The SiC nanowhiskers decorated with the iron oxide superparamagnetic particles will be

used as the fillers. The properties of these composite fillers have been analyzed in detail in our

earlier publication14

. These SiC whiskers demonstrate excellent optical, semiconducting, field

emission, thermal and mechanical properties, hence are attractive for the high-power, high-

frequency and high-temperature applications 43-44

. Mullite (3Al2O3·2SiO2) is chosen as the

matrix material for the film. Mullite demonstrates excellent strength, creep resistance, thermal

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and chemical stability at high temperatures 45-47

. It has been widely used in ceramics engineering.

Moreover, the mullite-SiC system has been established as a gold standard in ceramics owing to

its superior thermo-mechanical properties with the damage self-healing characteristics 48-50. The

reliable processing routes for synthesis of bulk mullite-SiC nanocomposites have been developed

48. However, the mullite thin films with embedded SiC nanorods has not been produced yet. With

the developed methodology supported by the theory of magnetic alignment, these mullite-SiC

films are expected to pave the way for new exciting applications.

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2. Materials preparation and characterization

The SiC nanorods were coated with Fe3O4 nanoparticles. The detailed experimental

procedure for the nanorod functionalization can be found in our recent publication14

. A single

SiC-Fe3O4 nanorod is shown in Figure 1. As has been shown in Ref. 14

, these nanorods are

superparamagnetic.

Schematic of the processing rout for fabrication of mullite films with embedded SiC-

Fe3O4 nanorods is shown in Figure 2. The procedure assumes the two important steps: 1)

formation of a sacrificial polymeric layer with the aligned nanorods and 2) synthesizing ceramic

films covering the aligned nanorods after removal of the polymer matrix by firing.

Figure 1. SEM image of a silicon carbide nanorod decorated with Fe3O4 magnetic

nanoparticles

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Step 1. The obtained magnetic nanorods were dispersed in a methanol- polyethylene

oxide (PEO, Mw = 1,000,000 g/mol, Sigma Aldrich, St. Louis, MO) solution at a polymer

concentration of 2.1 wt. %. The obtained suspension was used to prepare a polymer thin film on

silicon wafers (1 × 4 cm rectangles) using the dip-coating method. The wafers were dip coated

with the nanorod dispersion at the withdrawing speed of 5.4 mm/sec. The dip coated wafer was

immediately transferred and dried in a glass vial between the two parallel neodymium magnets

(K&J Magnetics, Pipersville, PA). During solidification of the liquid film, the nanorods were

oriented under the static magnetic field generated by these magnets. After drying, the obtained

samples were heated to 750°C at 0.5°C/min in the air to remove the polymer films.

Step 2. Before deposition of the ceramic precursor, the samples were cleaned by plasma

(pdc-32g, Harric Plasma, NY, USA) for 5 minutes. Dip-coating the wafer with the solution

containing 2.5 wt. % mullite yield and 1.25 wt. % PVP , one forms a precursor ceramic film

deposited on top of the cleaned surface 39

. The films with different thickness obtained at different

withdrawal velocities from 0.17 to 5.4 mm/sec were examined. After deposition, the films were

dried for 24 hours at room temperature before heat treatment. The films were heated in argon at

5 °C/min and calcined at 1000°C for 2 hours. Repetitive applications of these two processing

Figure 2. Schematic showing the experimental approach

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steps led to the multilayered structures. The direction of applied magnetic field was changed (e. g.

by the 90°rotation) to alter orientations of nanorods within each layer.

For fabrication of a free-standing film, the graphite substrate was used for the polymer

film deposition following the same procedure. A ceramic precursor was directly deposited onto

the polymer film that was dried for 24 hours at 25°C. The substrate was then removed by slowly

heating (0.5°C/min) the coated substrate in the air at 750°C. The free-standing film was then

heated in argon at 5 °C/min and calcined at 1000°C for 2 hours before the magnetic

measurements.

The Atomic Force Microscope (AFM) measurements were performed in the tapping

mode on a Dimension 3100 (Veeco Instruments, Plainview, NY) microscope. Silicon probes

with a spring constant of 50 N/m were used. Imaging was carried out at the 1 to 2 Hz scanning

rates. The thickness was measured by the AFM scratch technique 51

. The polymer composites

were further investigated through imaging with a LEXT Optical Profiler (Olympus Scientific

Solutions Americas Inc. Waltham, MA). An analysis of the nanorods orientation was carried out

according to the previously reported protocol 33

. The microstructure was characterized using

scanning electron microscopy (SEM, Hitachi S4800, Hitachi, Ltd., Tokyo, Japan). The magnetic

characterization was done by using the Alternating Gradient Magnetometer (AGM 2900,

Princeton Measurements Inc., NJ, USA).

Magnetic field strength was characterized using a magnetic probe sensor (DTM-133

Digital Teslameters, GMW associates, San Carlos, CA). For the magnets with the 8cm

separation, the field varied from 0.0216 Tesla at the very center of the sample to 0.0320 Tesla at

the ends of the wafer. The magnetic field at the center decreased as the distance between the

magnets increased. The magnetic fields that were applied to study the nanorod alignment were

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0.0216, 0.0037 and 0.0006 Tesla corresponding to the magnets separation of 8, 14 and 28cm,

respectively.

Experimental histograms of the nanorods oriented in a particular direction were

constructed by counting the number of nanorods present in the 10° sectors and normalizing it by

the total number of nanorods in the field of view. To generate each diagram, the orientation

angles of more than 500 nanorods were measured.

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3. Theory of alignment of superparamagnetic nanorods in solidifying films

3.1 Model of the 2D rotation of a paramagnetic nanorod in Newtonian liquid

Alignment of magnetic nanorods in drying/curing liquid films is possible only when the

nanorods rotate quickly enough so that the film is still mobile 12, 28, 33

. The distribution of

nanorods within the given angular sector has been recently studied for ferromagnetic nanorods in

solidifying polymer films 12, 28, 33

. It remained unclear whether the theory would work for the

paramagnetic nanorods for which magnetic moment can be easily detached from the nanorod

axis.

Consider a single paramagnetic nanorod suspended in a liquid film; its motion is assumed

confined within the plane of the liquid layer. The liquid is assumed Newtonian. Schematic of

action of magnetic field and torques on a single rod is shown in Figure 3. We introduce the unit

vectors �∥ and �� , oriented parallel and perpendicular to the nanorod long axis, respectively,

with the positive �∥ pointing to the right. Magnetic field vector makes angle � with vector �∥.

An essential difference between superparamagnetic and ferromagnetic nanorods is that when

submitted to external magnetic field, the magnetic moment (��) of superparamagnetic nanorod

follows magnetic field: when the field vector deviates from the nanorod axis, the magnetic

moment follows it leaving the nanorod axis as schematically illustrated in Figure 3. The

magnetic moment of a paramagnetic nanorod is a function of the magnetic field B, angle , as

well as the bulk susceptibility � of the magnetic material. The detailed expressions for the

magnetic moment �� can be found in Supplementary material, Eq. (S1). In contrast to

ferromagnetic nanorods, for which magnetic moment does not depend on the magnitude of

applied field at weak fields, the magnitude of vector �� is proportional to the strength of the field

( ∝ �). This approximation of a uniformly distributed magnetic material over the nanorod

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volume is expected to work well for the rods with thick magnetic shells; our nanorods belong to

this case hence in our theory we will use this approximation.

An applied magnetic field exerts a torque on the nanorod. In contrast, for a ferromagnetic

nanorod in a weak magnetic field when the magnetic moment is always aligned with the long

axis of the particle (see Supplementary material, Eq. S3). Thus, the angular dependence of the

magnetic torque Γ � ��

� sin�2��for the superparamagnetic nanorods is different from

that for the ferromagnetic ones.

For a superparamagnetic nanorod the condition � � �/2 is special: at this condition the

corresponding magnetic torque is equal to zero. However, this equilibrium is unstable and a

Figure 3. As an illustration of the characteristic steps of the filed-induced alignment, the

applied field is considered perpendicular to the nanorod axis at the first moment of time.

The field direction does not change, but the nanorod tend to set their long axis parallel to

the field.

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small perturbation of the angle � leads to a non-zero torque; the nanorod rotates clockwise- or

counterclockwise, depending on the sign of the perturbation as shown in Figure 3.

The viscous drag from the polymer solution opposes the nanorod rotation. Balancing the

magnetic torque by the viscous torque, Γη � γφ! ,where γ is the drag coefficient defined

Supplementary material, one arrives at the following equation 52-54

:

�! � −$%&'sin2� (1)

where the characteristic frequency $%&'is introduced as 53-54:

$%&' �()*+�, -⁄ �/�.01-�

�234,�∙ �

�

�� (2)

where6 and 7 are the diameter and length of the nanorod, respectively, 8 is the solution viscosity, 9: is the permeability of vacuum, and � is the applied magnetic field.

Dynamics of rotation of ferromagnetic nanorods is described by the following equation 5,

55:

�! � −$%;sin� (3)

where the corresponding characteristic frequency $%; is given by

$%; � ),2,? ∙ � (4)

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The quadratic dependence of the characteristic frequency of rotation of a superparamagnetic rod

on the magnetic field makes the superparamagnetic nanorods more sensitive to small changes in

magnetic field as compared to the ferromagnetic rod. In contrast to the ferromagnetic nanorods

which are always magnetized, the superparamagnetic nanorods are not magnetized in the

absence of magnetic field. Upon application of an external magnetic field, the nanorods get

magnetized with their magnetic moment aligned in either positive or negative direction along the

long axis. This direction of magnetic moment depends on the initial orientation of the nanorod

(Fig. 3). The magnitude of magnetic moment of a single nanorod is a linear function of B, which

makes the nanorod very sensitive to the strength of applied field.

3.2. Kinetics of alignment of an assembly of superparamagnetic nanorods in

Newtonian films.

To study the kinetics of ordering of an assembly of non-interacting nanorods under an

applied magnetic field, it is convenient to introduce the orientational distribution function F(φ,t)

as where dN(φ) is the number of nanorods with the major axes oriented

within the angle φ and φ+dφ, Nt is the total number of nanorods in the film and F(φ,t) is the

distribution function. According to this definition, the distribution function describes the density

of nanorods sitting within the angle φ and φ+dφ. If the nanorods are initially randomly

distributed, the distribution function is constant, F(φ,0)=1/(2π). Detailed derivations of F can be

found in Supplementary Material, Eq. (S4). This function depends only on parameter $%&', time t

and angle φ.

The evolution of F(φ,t) as a function of dimensionless time 2$%&'@ is shown in Figure

4(a). The distribution function shows a non-monotonous behavior with time at angles φ=π/8 and

( , ) ( , ) ,tdN t N F t dϕ ϕ ϕ=

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φ=7π/8; a similar behavior was observed with the ferromagnetic nanorods 36

: the population of

nanorods at these angles first increases to reach a maximum, then decreases with time. At the

other angles, F exhibits monotonous decrease with time.

The time at which F(φ,t) reaches its maximum is determined by setting dF(φ,t)/dt=0,

which yields the following relation between dimensionless time $%&'@ and angle φ.

$%&'@ � A0 ln �A�CDE�FA/CDE�F� (5)

Since $%&'@ G 0, the maximum can be reached within (-π,-3π/4), (-π/4, π/4) and (3π/4, π).

For ferromagnetic nanorods, the corresponding maximum in distribution function F is found

within a semi-plane (-π/2, π/2).

It can be seen from Eq. (S4) that F is an even π periodic function of φ. This makes the

evolution of nanorods’ population at φ0, -φ0, π-φ0 and -π+φ0, identical, provided that the

Figure 4. (a) Dependence of F(π/8,t), F(π/4,t), F(π/2,t), F(3π/4,t) and F(7π/8,t) on

dimensionless time $%IJ@. (b) The profile of F(φ,t) at different dimensionless time moments.

(c) Dependence of K&' on viscosity under different magnetic field strength B, the drag

coefficient was calculated with A=2.4.

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inequality 0

17

To quantify the rate at which the nanorods get aligned in the field direction, it is

convenient to analyze the probability P(φ,t,∆φ) to find nanorods within angle 2]� around angle

� at time t. P(φ,t,∆φ) is defined as the percentage of nanorods oriented within the angles � ± ]�.

Expression for P(φ,t,∆φ) can be found in Supplementary material, Eq. (S5). For the initial

random orientation, _��, 0, ]�� ∆� �⁄ . As the time goes to infinity, the probability to find all

nanorods aligned parallel to the applied field, � � ±� goes to 1/2,

_�0,∞, Δ�� _�±�,∞, Δ�� → 1/2, implying that all nanorods get aligned (since the

paramagnetic nanorods oriented at � � 0 and � � � are considered identical their population in

the Δ� band around these two angle is the same, making the total probability 1). In the absence

of drying or curing, nanorods will ultimately rotate towards the field. A critical probability P0

can be introduced to specify the time K&' needed to reach a certain level of alignment of

nanorods in Newtonian films. By stating _�0, K&' , Δ�� G _:, one ensures that the total number

of nanorods outside the interval [−Δ�, Δ�] is negligibly small. One can calculate this time (K&')

for achieving the alignment of paramagnetic nanorods in fluids with constant viscosities by

substituting _: into eq. (S5) of Supplementary Material:

K&' � A�WXYZ ln def+�>'4�ef+�gF�h (7)

In order to keep the square brackets greater than zero for 0

18

oriented parallel to the direction of the applied magnetic field within the angular sector Δ� < 0 ±

10°.

The time K&' is linearly proportional to 8, and it increases by two orders of magnitude

with B increases by one. For ferromagnetic nanorods, the corresponding characteristic time

evolves at a slower rate with the change in B, K2;∝1/�, see Supplementary material, Eq. (S11)5,

55. Therefore, the dependence of time of alignment of superparamagnetic nanorods in Newtonian

film is stronger relative to that of ferromagnetic nanorods.

The derived estimates for the time of alignment of superparamagnetic nanorods can be

used to significantly shorten the process by increasing the field strength. For polymer films with

viscosities of about ~10 times of water (~0.01 Pa s), the alignment of the paramagnetic nanorods

is spontaneous (K&'

19

The nanorod rotation problem in solidifying films can be considered as a special case for

Eq. (1) and (3) when the characteristic frequencies, Eqs. (2), (4) depend on time $%&'�@� and

$%;�@� because the rheological equation of state of the liquids is time-dependent. The time-

dependent viscosity of many drying systems is described by the following equation 56-57

:

8�@� � 8:exp�@ K:⁄ � (8)

where 8: is the initial viscosity,K: is the characteristic time of polymerization. To analyze the

effect of film solidification on the kinetics of nanorod alignment, it is convenient to deal with the

following dimensionless variable33, 56, 58

:

m � m:&' ⋅ exp � [o4�, (9)

where m:&' � K2&' K:⁄ . K2&' is a characteristic time defined as K2&' ≡ 1 $%&'�0�⁄ . It is related to the

magnetic response of the nanorod to the external field and the viscous drag exerted by the liquid

at t=0, before solidification takes place. The dimensionless time m depends non-linearly on the

real time t. Similarly, we can define mq; = K2; K:⁄ for ferromagnetic nanorods to solve the

equations describing the kinetics of rotation. Derivations of kinetic equations for the rotation of a

magnetic nanorod in such a solidifying film can be found in the Supplementary material; Eq. (S9)

and (S10) are the corresponding solutions for � as a function of dimensionless variable m for

superparamagnetic (SP) and ferromagnetic (FR) nanorods, respectively. Figure 5 (a) illustrates

the difference between two kinetics with different initial �: and mq&' specified in the figure. For

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comparison, we assume the same value of m:&' = m:; � m: for ferro and superparamagnetic

nanorods implying $%&'�0� � $%;�0�.

When �: is close to but less than 90°, the ferromagnetic nanorod rotates faster than the

superparamagnetic nanorod with the same value of m: = 0.5. Indeed, as follows from Eq. (1), a

superparamagnetic nanorod initially oriented at �: � 90° experiences no magnetic torque hence

it does not move. All nanorods with the long axes situated close to �: � 90°, would experience

very weak magnetic torque, hence their rotation speed is slow.

In contrast, a ferromagnetic nanorod experiences very strong magnetic torque when its

long axis is oriented at �: � 90°. Thus, all ferromagnetic nanorods with the long axes situated

close to �: � 90°, would experience strong magnetic torque and hence rotate fast.

Figure 5. (a) Different dynamic regimes of nanorod rotation. The initial values at U =0 for

different curves are �0 = 45°, 75°, 89.1° and 135°. The arrows indicate the directions of

rotation of the FR and SP nanorods initially oriented at 89.1° and 135°. (b) distribution

functions for ferromagnetic (FR) and superparamagnetic (SP) nanorods when m0 =mq&' � mq;.

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For 60° < �: < 90°, at the beginning of rotation, superparamagnetic nanorods revolve at

a slower rate than the ferromagnetic ones, then pick up the speed to overrun the ferromagnetic

nanorods.

For 0 < �: < 60°, superparamagnetic nanorods revolve faster than the ferromagnetic

ones. Both superparamagnetic and ferromagnetic nanorods rotate towards the direction of

magnetic field (� � 0) in the anticlockwise direction, i.e. toward smaller �. However, when the

SP nanorod is placed in the sector 90° < �: < 180° , the direction of nanorod rotation flips to

the clockwise toward increase of � . As for the ferromagnetic nanorod, it always rotates

anticlockwise toward � � 0, the direction of the applied magnetic field.

3.4.Kinetics of alignment of an assembly of superparamagnetic nanorods in solidifying films.

We follow the methodology of Ref. 33

to determine the behavior of corresponding

distribution function L for superparamagnetic nanorods (see Supplementary material, eq. S12).

In the limit as time goes to infinity, @ → ∞, the distribution function for the SP nanorods in a

solidified film is given as:

L&'��,∞� � A�> ⋅A

CDEwx� y4YZ⁄ \/Ez+wx� y4YZ⁄ \CDE�F . (10)

For comparison, the equilibrium distribution function L��,∞� for ferromagnetic

nanorods is given by 33

:

L;��,∞� � A�> ⋅A

CDEwxA y4{⁄ \/Ez+wxA y|{⁄ \CDEF (11)

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The corresponding probability to find the SP nanorod in the 2]� angular sector around �

is given as:

_&'��, ]�,∞� � } L��′,∞�F�FF/F ⋅ 6� �A�> arctan dtan�

∙ exp � �y4YZ�h |F/FF�F (12)

For comparison, we show the corresponding probability for ferromagnetic nanorods 33

:

_;��, ]�,∞� � A> arctan dtanF� ∙ exp �

Ay|{�h |F/FF�F (13)

In contrast to ferromagnetic nanorods for which the directions � =0 and � = � are

distinguishable implying different directions of the sample magnetization, the probability

_��, ]�,∞� for superparamagnetic nanorods is � − periodic. That is, if a superparamagnetic

nanorod rotates over an angle � , its new orientation will be identical to the previous one.

Therefore to cover all orientations of nanorods we can multiply F or P by two with � ranging

from −�/2 to �/2.

Figure 5 (b) shows the plot of the distribution function L&'��,∞� and L;��,∞� with

m:; � m:&' � m: � 0.2 and m: � 1 . For both types of nanorods, the peak value of the

distribution function decreases as m: increases, which indicates that less nanorods are captured

by the applied field. For example, at m: � 0.2 , the peak value of L&'��,∞� increases by

approximately three orders of magnitude compared to that of m: � 1; the peak value of the peak

value of L;��,∞� increases by two orders of magnitude. The distribution function for

superparamagnetic nanorods has a narrower spiky profile and a greater peak value as compared

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to that for the ferromagnetic nanorods, indicating that more superparamagnetic nanorods can be

captured when all other parameters are the same. When m: goes to infinity, the peak values of

both functions asymptotically approach 1/2�.

3.5 Criterion of nanorod alignment in solidifying films

Following Ref. 33

, we introduce a quantitative criterion specifying the condition of

nanorod alignment in solidifying films. Assigning a desirable probability level _: for the

nanorod alignment and assuming that alignment is practically achieved when the inequality

_�0, ]�,∞� G _: holds true, a critical value of m:&'�_:� � m%&' is obtained by solving eq. (12).

The expression for m%&' is given as:

m%&' � �*+d�Z4/�� h (14)

The corresponding parameter for ferromagnetic nanorods was found in Ref. 33

:

m%; � A*+d�Z4/��/�� h (15)

As an example, we take _:=0.9 and ]� � 10° as the alignment criteria. That is to say, 90%

of the nanorods will be oriented parallel to the direction of the applied magnetic field within the

angular sector < 0 ± 10°. We analyze the nanorods decorated with ferromagnetic and

superparamagnetic nanoparticles of the same iron oxide. Saturation magnetization of the

ferromagnetic iron oxide Fe3O4 (bulk) is 4.6×105 A m

-1 59

. Susceptibility of superparamagnetic

SiC-Fe3O4 nanorods is of the order of ~5.39 (see Ref. 14

for the characterization details). Figure 6

shows the phase diagrams in terms of B vs. aspect ratio l/d , specifying the necessary conditions

to achieve complete alignment of nanorods in thin films with different rheological and

solidifying behaviors during solidification. The region of parameters above the line

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corresponding to the range of parameters where m: < m% (with the corresponding superscripts)

holds will lead to the alignment of the nanorods before complete solidification. The requisite

magnetic field for the defined complete alignment increases with the aspect ratio.

For the small ratio 8:/K: = 0.02 Pa, the ferromagnetic SiC-Fe3O4 nanorods can be

aligned more readily (B10-3

T),

provided that both types of nanorods have the same aspect ratio l/d (l/d

25

curing films with viscosity increasing with time exponentially fast. The rotation rate of

superparamagnetic nanorods is more sensitive to small changes in magnetic field due to the

quadratic B2 dependence of the torque on the field, Eqs. (2), (9). Accordingly, the B vs l/d curve

of the superparamagnetic nanorods is less steep relative to that of the ferromagnetic nanorods. As

an example, consider the ratio 8:/K: = 200Pa and the nanorods with the aspect ratio 7/6 > 64:

for the ferromagnetic nanorods, the required magnetic field is about two orders of magnitude

greater than that for the superparamagnetic ones. This makes superparamagnetic large aspect

ratio nanorods more attractive in achieving complete alignment in the highly viscous and fast

curing thin films.

4. Experimental validation of the theory

In the theory, the nanorods are assumed non-interacting. This requires that the nanorods

are well-separated in the drying solution. The measured average distance between nanorods at

the higher concentration is 41 ± 20 µm, which is 4 times larger than the average length of the

nanorod making the nanorod-to-nanorod interactions an unlikely source for disorientation.

Moreover, because of the surface treatment of nanorods according to the protocol of Refs. 60

, the

probability of their aggregation was significantly reduced.

The nanocomposite films with magnetically oriented SiC-Fe3O4 nanorods were obtained

using two different PEO concentrations 0.01 wt. % and 0.038 wt. %. The concentration of SiC-

Fe3O4 nanorods in the PEO dry matrix was estimated to be 0.5 wt. % (or ~0.16 vol. %) and 1.84

wt. % (or ~0.58 vol. %), respectively. Figure 7(a) is a stitched image of the composite film with

0.57 vol. % of SiC-Fe3O4 nanorods in the PEO film. The image is 2.4 mm long to show macro-

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scale dispersion and orientation. The center of the image is taken at the center of the applied

magnetic field. The magnetic field gradient at the edge of the image is on the order of 2×10-4

Tesla/mm. The average nanorods orientation of the entire sample with respect to the direction of

the magnetic field is 7.8°.

Figure 7(b) illustrates the distribution of nanorod orientations for the left, middle, and

right portions. The Y-axis values (percent SiCW-MagNP) are the percentage of nanorods within

10° around the selected angles (X-axis values) normalized by the total number of nanorods. The

middle of the Figure 7(a) has the highest degree of orientation, along with the lowest strength of

applied magnetic field (0.0216 Tesla). The average deviation from the direction of magnetic field

is 8.3°, 6.1°, and 8.8° for the left, middle and right portions of the stitched image.

Figure 8 shows the orientation of the SiC-Fe3O4 rods of two different concentrations.

With a magnetic field strength of 0.0216 Tesla, the composite with 0.16vol. % of SiC-Fe3O4 rods

has higher orientation with 83% of material oriented within 10o

of the direction of the field. The

Figure 7. (a) a stitched image of the composite thin film with 0.57 vol% of SiC-Fe3O4

nanorods labeled as SiCW-MagNP; (b) the distribution of orientation from section I, II and III

of the image.

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composite with 0.58vol. % of SiC-Fe3O4 rods had 75% of the material oriented within 10o

of the

direction of the field. In general, the difference in the alignment for the two concentrations is

quite small. The degree of orientation reduces as a weaker magnetic field (0.0037 Tesla) is

applied. When the magnetic field is 0.0006 Tesla, the orientation of the nanorods is almost

random. The fitting curves were generated from eq. (12) with adjustable parameter exp �− �y4YZ�.

The simulated values were exp �− �y4YZ�=0.248 and exp �−�y4YZ�=0.307 for the low- and high-

concentration samples obtained at 0.0037 Tesla. The values obtained at 0.0216 Tesla were

respectively 0.068 and 0.095 for the low- and high-concentration samples. A smaller value of

exp �− �y4YZ� corresponds to a stronger magnetic field, which is in good agreement with Eq. (S7).

5. Formation of ceramic thin films with nanorod assembly

5.1 Single and Multi-layered ceramic films

Figure 8. The percentage of aligned of SiC-Fe3O4 nanorods labeled as SiC-MagNP (a) low

concentration (0.16%vol) and (b) high concentration (0.58%vol) after removal of PEO.

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The SiC-Fe3O4 nanorods remained separated during the polymer removal, the ceramic gel

film deposition and the gel-to-ceramic film conversion. Figure 9 shows the orientational

distribution of nanorods during each of those steps. Overall, the most significant alignment was

achieved in the initial polymer films. The changes in the percentage (∆P) of nanorods within

each 10° segment with respect to the initial distribution in polymer films are shown in figure 9

(c-d). For the majority of nanorods, ∆P is less than 5%. This deviation initially appeared after the

polymer removal, which is possibly owing to the settlement of nanorods during the polymer

decomposition. To better retain the nanorod orientation, the polymer removal is desired to be

executed at a slow heating rate. The orientation remains fixed after the gel deposition and gel-to -

ceramic conversion. This indicates that the nanorods are getting less mobile after they get

sintered to the substrate. In general, the differences in nanorod orientations between those

processing stages are quite small.

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Figure 10 (a-b) shows the SEM images of a single-layered ceramic film with embedded

magnetic SiC-Fe3O4 nanorods. The embedded SiC-Fe3O4 nanorods were well-separated and

aligned. No significant segregation of nanorods was observed. The obtained mullite film with

embedded magnetic nanorods is dense and crack-free, which is the desired goal for the high-

temperature applications when the materials are exposed to the chemically aggressive

environment 61

. The mullite matrix with very low oxygen diffusivity can effectively protect the

SiC-Fe3O4 rods from chemical attack such as oxidation 62

.

Figure 9. (a)-(b) The percentage of aligned nanorods in the films with different volume

fraction of nanorods: (a) 0.16 vol. % and (b) 0.58 vol. %; (c) and (d) ∆_ – the change in the

probability P(φ) of the corresponding samples compared to the distribution in the PEO film.

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The mullite matrix obtained from the sol-gel process is nanocrystalline. In our previous

study, we demonstrated that the crystallite size of the film can be well controlled by annealing

Figure 10. The SEM micrographs showing the top view of the thin film composite: a single

layered film at low (a) and high (b) nanorod concentration; a triple layered film at low (c)

and high (d) nanorod concentration; orthotropic layers with low (e) and high (f) nanorod

concentration. (scale bar: 100µm)

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the material at 1000-1200ºC 39

. The hydrolysis and condensation reactions in the sol-gel

processing that has been carefully controlled at ambient temperature lead to the conversion of gel

to phase-pure ceramic at relatively low temperatures 38

. Hence, the ceramic thin film matrix

crystallizes at temperature below 1000 °C, which gives rise to the formation of nanocrystalline

thin film without further significant grain growth. Significant coarsening of the matrix material is

not likely desired because nanorods might segregate at the grain boundaries which compromises

the degree of orientations and the film mechanical properties 61

. A higher temperature (>1400ºC)

processing is not likely desired due to the phase instability of iron oxide nanoparticles in contact

with the oxide matrix. Either aggregation to form large particles or undergoing chemical reaction

with matrix to form Al3+

containing solid solution result in the changes of magnetic properties of

the nanoparticles 63

.

Figure 10(c-f) shows the SEM images of multilayered mullite films with embedded

nanorods. The nanorods remain well separated and aligned in the multilayered films. In Figure

10(c-d), the 3 layers (140nm×3) mullite-SiC-Fe3O4 thin films were obtained from the repetitive

deposition. Figure 10(e-f) shows the SEM image of a bi-layer mullite-SiC-Fe3O4 film with

embedded nanorods of orthotropic distribution. The distribution statistics of nanorods is shown

in Figure 11. The major populations (> ~30%) of SiC-Fe3O4 nanorods are oriented at 0-10º and

80-90º to the direction of the magnetic field.

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The layer-by-layer (LBL) assembly method offers the opportunity of creating 3D

nanocomposites through sequential ordering of nanorods inside the films 64

. Lamination of

composites with a specific orientation of inclusions within each layer is desired for many

applications 26

. For example, an orthotropic lattice structure is often desired for effective

mechanical reinforcement in all directions 26

.

5.2.Morphology of the film surface

The magnified SEM images of the films with an embedded nanorod are shown in Figure

12. By varying the film thickness (t) and keeping the same nanorod diameter (d), different

microstructures were observed. In general, mullite films are smooth, while the SiC nanorods

have rough surfaces due to the presence of Fe3O4 NPs. When the film thickness is small as

compared to the diameter of the nanorod, the coating does not mitigate the roughness of the SiC

Figure 11. The percentage of aligned nanorods in the orthotropic samples

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nanorods. The SiC-Fe3O4 nanorod was distinct from the surrounding film when the film

thickness is small (60 nm) compared to the dimension of the rod, as shown in Figure 12 (a).

With a slightly thicker ceramic film (140 nm), Figure 12 (b), the contour of the nanorod

becomes less distinct from the film matrix. The grainy feature on the nanorod was gradually

masked by the ceramic film on the top. The result indicates that nanorods could be embedded

completely inside thicker films. The microstructure of thick films (~500 nm) with embedded

nanorods is shown in Figure 12 (c). An interesting feature is the surface protuberance of the film

induced by the rod. It is observed that surface protuberance can be gradually eliminated by

depositing the films of greater thickness.

The thickness of the sol-gel processed ceramic film is often restricted by the critical

thickness, above which the materials failure occurs 39, 65

. The defect free films are typically less

than 1 µm thick, which is only slightly greater than the nanorod diameter 39, 66

. This restricts the

opportunity of building very thick films to reduce the protrusions.

We observed that the composite films without cracks can be formed by controlling the

layer thickness. Figure 13 shows the topographic profile of two types of thin films analyzed by

Figure 12. The SEM images showing the SiC-Fe3O4 nanorods embedded within mullite films.

Images (a) and (b) of the embedded nanorods are taken from the top. The film thicknesses in

(a) is 60nm and in (b) is 140 nm. (c) The protuberance observed on the film surface, the film

thickness is ~500nm.

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AFM. The nanorods are placed parallel to the substrate. The zero level of the y-axis is chosen at

the substrate surface. The center of the nanorod is positioned at x = 0. When the film thickness is

greater than the diameter of the nanorods, a flattened surface with a small protuberance was

observed as the film thickness increases. The protuberance becomes pronounced as the film

thickness decreases. When the film thickness becomes comparable or smaller than the nanorod

diameter, one observes a crack free film with the ceramic matrix conformally coating the

nanorod with a very steep profile near the nanorod center.

Comparing to the nanorod diameter, the roughness of the film itself is very low

(evidenced by the AFM profile shown in Figure 13). Therefore the roughness of the film is

determined by the relative height of the surface protuberance and its steepness. With the

controlled alignment of nanorods, the protuberances are also aligned, making this material an

Figure 13. The profiles of the film surfaces elevated above a 400 nm diameter nanorod.

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attractive candidate for applications where one needs to control the film topography, for example,

to enhance/ hinder wettability of the ceramic film by metals at high temperatures 67

.

5.3 Magnetic properties

It is difficult to characterize the magnetic properties of thin films bonded to the silicon

substrate, as the weight of the measured magnetic material is not well-defined. And the weight of

the substrate is much greater than the film, making it difficult to detect the magnetic response

from the film. In order to prove that the composite materials are highly magnetic, the free-

standing magnetic film was obtained after removal of the graphite substrate by heating it in the

air. The film can be attracted to and lifted by a permanent magnet. Figure 14 shows the

magnetization-field (M-H) plot of the free standing mullite-SiC-Fe3O4 films. It shows that the

ceramic thin film composites are superparamagnetic. The magnetization of the material is

normalized by the total mass of the composite. For superparamagnetic materials, the magnetic

moment m follows the Langevin dependence 68

:

� : dcoth�� − Ah (25)

where B is the magnitude of the external magnetic field, : � 9, and � 9 ��⁄ , 9 is the

magnetic moment of a single magnetic domain, N the total number of domains in the composite,

is the Boltzmann constant and T is the absolute temperature. The magnetic Fe3O4

nanoparticles in the film composite contribute to this superparamagnetism. From the fitting of

experimentally measured magnetization curve, one finds that the composite film with an initial

concentration of 0.58 vol.% SiC-Fe3O4 rods in PEO has saturation magnetization (Ms) of around

0.41 Am2/kg. The weight for the normalization equals to the weight of the measured free-

standing film, which includes the mullite matrix, SiC nanorods and Fe3O4 nanoparticles. Since

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the Fe3O4 nanoparticles are the only component that is magnetic in the membrane, the small Ms

is due to large weight percentage of the non-magnetic components. We assume the Ms of the

superparamagnetic Fe3O4 nanoparticles being on the same order of magnitude of the reported Ms

values, which are typically ~ 60 Am2/kg

69-70. As a rough estimate, the concentration of magnetic

materials within the free-standing film is estimated as be on the order of 0.1-1 wt.%. This

concentration can be further controlled by altering the ratio between the thicknesses of the

polymer films and ceramic gel films. From the Langevin fitting, the magnetic moment of each

domain is estimated to be on the order of 4.7×10-20

Am2.

Figure 14. The M-H curve of a free-standing mullite-SiC-Fe3O4 film.

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6 Conclusions

A novel two step protocol for fabrication of ceramic films with aligned magnetic

nanorods was developed. At the first step, the nanorods were aligned in a polymer sacrificial

layer. Then the polymer was burned out and a ceramic precursor was deposited. A sol-gel

processing was employed to synthesize mullite submicron films with embedded and aligned

nanorods.

We derived a quantitative criterion for nanorod alignment in solidifying liquid films. The

alignment of superparamagnetic nanorods was theoretically studied to reveal the process features

distinguishable from those for ferromagnetic nanorods. The characteristic time of rotation of

superparamagnetic nanorods is more sensitive to the strength of applied magnetic field (quadratic

dependence). We constructed a phase diagram identifying the process parameters when the

nanorods can be fully aligned in solidifying polymeric films. This diagram was experimentally

validated. The macroscopic alignment of superparamagnetic SiC-Fe3O4 nanorods was achieved

in solidifying Polyethylene oxide films. The measured orientation distribution after polymer

removal was compared with the theoretical predictions.

Mullite thin film composite with aligned SiC-Fe3O4 nanorods was obtained through the

sol-gel processing of a deposited ceramic precursor after removal of the polymer film. The

alignment was retained through the process. This approach was further extended to develop

multilayered structures through repetitive layer-by-layer deposition.

The layer-by-layer formation of different ordered structures provides intriguing

opportunities of making ceramic thin films and bulk composites for many advanced applications,

such as controlled heat dissipation, polarization rotation and mechanical enhancement. The

surface of ceramic films with the embedded nanorods demonstrates novel bumpy topography.

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This feature can be well controlled by varying the ratio between the film thickness and nanorod

diameter. As refractory materials, these films offer new applications for control of the film

wettability and fluid transport at high temperatures.

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Figure 1. SEM image of a silicon carbide nanorod decorated with Fe3O4 magnetic

nanoparticles

Figure 2. Schematic showing the experimental approach

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Figure 3. As an illustration of the characteristic steps of the filed-induced alignment, the

applied field is considered perpendicular to the nanorod axis at the first moment of time.

The field direction does not change, but the nanorod tend to set their long axis parallel to

the field.

Figure 4. (a) Dependence of F(π/8,t), F(π/4,t), F(π/2,t), F(3π/4,t) and F(7π/8,t) on

dimensionless time $%IJ@. (b) The profile of F(φ,t) at different dimensionless time moments. (c) Dependence of K&' on viscosity under different magnetic field strength B, the drag coefficient was calculated with A=2.4.

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Figure 5. (a) Different dynamic regimes of nanorod rotation. The initial values at U =0 for

different curves are �0 = 45°, 75°, 89.1° and 135°. The arrows indicate the directions of rotation of the FR and SP nanorods initially oriented at 89.1° and 135°. (b) distribution

functions for ferromagnetic (FR) and superparamagnetic (SP) nanorods when m0 =mq&' � mq;.

Figure 6. Phase diagrams specifying the range of parameters leading to the complete

alignment of nanorods in solidifying films: (a) 8:/K:=0.02 Pa, (b) 8:/K:=2 Pa, (c) 8:/K:=200 Pa.

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Figure 7. (a) a stitched image of the composite thin film with 0.57 vol% of SiC-Fe3O4

nanorods labeled as SiCW-MagNP; (b) the distribution of orientation from section I, II and III

of the image.

Figure 8. The percentage of aligned of SiC-Fe3O4 nanorods labeled as SiC-MagNP (a) low

concentration (0.16%vol) and (b) high concentration (0.58%vol) after removal of PEO.

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Figure 9. (a)-(b) The percentage of aligned nanorods in the films with different volume

fraction of nanorods: (a) 0.16 vol. % and (b) 0.58 vol. %; (c) and (d) ∆_ – the change in the probability P(φ) of the corresponding samples compared to the distribution in the PEO

film.

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Figure 10. The SEM micrographs showing the top view of the thin film composite: a single

layered film at low (a) and high (b) nanorod concentration; a triple layered film at low (c)

and high (d) nanorod concentration; orthotropic layers with low (e) and high (f) nanorod

concentration. (scale bar: 100µm)

Figure 11. The percentage of aligned nanorods in the orthotropic samples

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Figure 12. The SEM images showing the SiC-Fe3O4 nanorods embedded within mullite

films. Images (a) and (b) of the embedded nanorods are taken from the top. The film

thicknesses in (a) is 60nm and in (b) is 140 nm. (c) The protuberance observed on the

film surface, the film thickness is ~500nm.

Figure 13. The profiles of the film surfaces elevated above a 400 nm diameter nanorod.

Figure 14. The M-H curve of a free-standing mullite-SiC-Fe3O4 film.

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Table of Contents Graphic

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magnetic submicron mullite coatings with oriented sic whiskers · thin films with embedded...

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