Hematite Cubes

Abstract

The methods of synthesis of hematite particles with different shapes are reviewed. Several experimental settings with suspensions of hematite particles are described considering their rolling, spinning in rotating (in vertical or horizontal plane) magnetic field. Gravity plays an important role since the hematite density is larger than the one of the carrier liquid. Equilibrium configurations of hematite cubes under the action of magnetic field and gravity are described. The change of morphology of chains of hematite cubes with increasing applied magnetic field and the formation of kinks are explained. Various regimes of hematite particle chains are observed in a rotating (in horizontal plane) magnetic field, more specifically synchronous with a field rotation, back-and-forth rotation in the plane of the rotating field, out of plane and periodic breaking and reassembly regimes.

1 Introduction

Iron(III) oxide $\textrm{Fe}_2\textrm{O}_3$ at ambient conditions has four crystalline polymorphic forms: $\alpha$-$\textrm{Fe}_2\textrm{O}_3$ (hematite), $\beta$-$\textrm{Fe}_2\textrm{O}_3$, $\gamma$-$\textrm{Fe}_2\textrm{O}_3$ (maghemite), and $\epsilon$-$\textrm{Fe}_2\textrm{O}_3$. These forms have distinctly different structural and magnetic properties. The most common of them is hematite.

Hematite has a rhombohedral crystal structure isostructural with corundum ($\alpha$-$\textrm{Al}_2\textrm{O}_3$). Below the Morin temperature [1], for bulk hematite $T_M\approx 260\,\textrm{k}$ [2], hematite is an antiferromagnetic material. Spins reorientate under increasing temperature and, due to the Dzyaloshinsky-Moriya mechanism [3, 4], hematite becomes a weak ferromagnetic material. It remains a weak ferromagnetic material up to the Néel temperature, which for bulk hematite is $T_N\approx 950\,\textrm{K}$ [5].

Another interesting property of hematite is that hematite particles maintain a permanent dipole moment even at large sizes (up to 15 $\mu$m) [6, 7]. Thus, it allows at room temperature to create magnetic colloids (made of single domain magnetic particles) which can be directly observed with an optical microscope [8,9,10,11,12]. These colloids allow to investigate an interesting physical regime where magnetic forces, hydrodynamic forces, steric forces, and thermal fluctuations are comparable quantities and thus important to describe dynamics. Moreover, the colloidal particles can be synthesized in different shapes: cubes, disks, ellipsoids, peanuts, needles, ...[8, 13,14,15].

In this paper we mainly focus our discussion on colloids made of hematite cubes, as cubic-shaped hematite particles have an unorthodox magnetization orientation. The magnetic moment with a cube’s diagonal makes an angle 12$^\circ$ (see Fig. 6.1) in the plane defined by two diagonals [6, 11].

Fig. 6.1

The magnetic moment orientation in a hematite cube. The angle $\phi =12^\circ$ is in the plane defined by two diagonals and the magnetic moment $\boldsymbol{\mu }$ points to the face

In the scientific literature several very interesting experiments with hematite colloids formed by cubic particles can be found. Recently Chen et al. [16] investigated the medical application of cubic-shaped hematite microrobots. The main goal was the sweep of microblocks and impurities in blood vessels. There authors demonstrated that approximately $2\,\mathrm {\mu m}$ large cube-shaped hematite particles can be guided by a rotating magnetic field. In the xz (vertical) plane rotating magnetic field introduced a rolling motion and the cube moved along the x axis. In such a way cubes were able to overcome obstacles and push small objects. Similarly the motile structures formed by microrollers which were created by micron sized polymer colloids with embedded hematite cubes were demonstrated in [17].

Soni et al. [18] showed that a two-dimensional chiral fluid can be created using hematite colloids. The densely packed ensemble of hematite cubes in a horizontal plane rotating magnetic field behave like a two-dimensional fluid showing characteristic instabilities. In the article [19], authors demonstrated targeted assembly and synchronization of self-spinning microgears or rotors made of hematite cubes and chemically inert polymer beads. In [20], a potential application of hematite colloidal cubes for the enhanced degradation of organic dyes was investigated. In [21], the formations of light activated two-dimensional “living crystals” was examined.

In this article we summarize the synthesis processes of hematite cubes and results of experiments on particle structures in hematite colloids based on our experiments [6, 12, 22, 23] and the work done by the group of Albert P. Philipse from Utrecht University and their collaborators [8, 11, 15, 18, 24,25,26].

The content of this paper is divided into four sections. The Sect. 6.1 is an introduction followed by a Sect. 6.2 where synthesis methods for hematite cube are described. The particle structures in hematite colloids are summarized in Sect.6.3 and conclusions in Sect. 6.4.

2 Synthesis

The fabrication of the hematite, $\alpha$-$\mathrm Fe_{2}O_{3}$ nanosized particles with desired morphologies attracts attention due to their interesting optical, chemical and magnetic properties [27, 28]. A large number of micrometer particles of metal oxides have been developed as models for research colloid science and advanced materials [29].

Böhm in 1925 first found that freshly precipitated amorphous $\mathrm Fe^{3+}$ hydroxide turns into goethite if kept for 2 h under 2M KOH at $150\,^{\circ }$C, whereas hematite is the dominant end-product if material is heated in the water [30].

Matijević and co-workers [31] have developed and described in detail the preparation of ferric hydrous oxide sols consisting of colloidal hematite particles uniform in shape. They reported the preparation of cubic, ellipsoidal, pyramidal, rod-like, and spherical hematite particles. Matijević and Scheiner demonstrated that minor changes in the reaction environment could produce significant changes in the morphology of iron oxide particles. The importance of this work was due to the fact that for the first time well-defined monodisperse colloids of general metal hydrous oxides were developed and described. However, hematite particles were obtained from dilute homogeneous solutions of concentrations of concentration of the order of $10^{-2}$ M or less.

The gel-sol method proposed by Sugimoto has shown the possibility to prepare monodispersed hematite particles precisely controlled in shape and size, from highly condensed ferric hydroxide gel. The advantage of this method compared to the dilution solution method is the high productivity and the high yield of hematite without any solid byproduct such as $\beta$-$\mathrm FeOOH$ [29, 32].

Commonly, $\alpha$-$\mathrm Fe_{2}O_{3}$ particles can be prepared by controlled hydrolysis of ferric salts and hydroxides carried out via solvothermal/hydrothermal techniques:

• forced hydrolysis of diluted $\mathrm{FeCl_3}$ aqueous solutions which are kept for a certain time (from 3 to 192 h) [27, 33] at elevated temperatures.

• a diluted solution method applying low concentration solutions of ferric salts and alkali hydroxides used as initial reactants [31];

• a gel-sol method which allows preparing monodispersed hematite particles precisely controlled in shape and size from highly condensed ferric hydroxide gel [32, 34, 35].

The formation of hematite proceeds by transformations of iron hydroxide ($\mathrm Fe(OH)_{3}$ through akaganeite ($\beta$-$\mathrm FeOOH$) to hematite ($\alpha$-$\mathrm Fe_{2}O_{3}$) [33, 34].

Solvothermal/hydrothermal techniques are popular methods for hematite particles production with varying size and morphology, by changing the growth parameters such as different solvent combination for precursor solution [28, 36], and by varying the excess concentration of $\mathrm Fe^{3+}$ ions relative to that of hydroxide (OH)$^{-}$ ions. Their size is increasing with $\mathrm Fe^{3+}$ ions concentration [31, 37], which is in agreement with [33], where the particles growth in ferric chloride solutions was investigated under forced hydrolysis conditions. It was found that, depending upon the initial $\mathrm FeCl_{3}$ concentration, either small single crystal hematite nanocubes or larger pseudocubic polycrystalline hematite particles form.

Park et al. [29] investigated morphology and internal structure of monodispersed pseudocubic hematite particles produced by the gel-sol method through high-resolution electron microscopy. It was found that sub-crystals of cubic-shaped hematite particles are radially developed from the center of a particle in all directions, but most preferentially in the directions of the longest diagonal axis of a particle. The longest diagonal of a pseudocubic particle corresponds to the c-axis.

The $\alpha$-$\mathrm Fe_{2}O_{3}$ micro-sized particles presented in the Figs. 6.2 and 6.3 were prepared via the standard gel-sol method of Sugimoto et al. [32, 34] with template method small adjustment [8] by the following procedure:

Fig. 6.2

Images of cubic-shaped hematite particles obtained by SEM. The mean particle size is $1.28 \pm 0.38\,\mathrm {\mu m}$. The scale bar is $10\,\mathrm {\mu m}$

• A sodium hydroxide aqueous solution (21.64 g NaOH/ 100 ml $\mathrm H_{2}O$) at rate of 5 ml/min was gradually added into an iron chloride hexahydrate aqueous solution (54 g ${\mathrm {FeCl_{3}\cdot 6H_{2}O}}$/100 ml $\mathrm H_{2}O$). This solution was under vigorous magnetic stirring. The resulting dark brown gel was stirred additionally for 5 min.

• Obtained precursor was hermetically closed in a Pyrex bottle and placed into a laboratory oven at 100$\,^{\circ }$C for aging and left undisturbed for 7 d.

• The resulting precipitated solids were washed by distilled water through centrifugal separation and ultrasonic re-dispersion in water until reddish-brown color hematite particles were obtained.

• The hematite particles were dispersed in the distilled water, stabilized with sodium dodecylsulfate ($\mathrm NaC_{12}H_{25}SO_{4}$, SDS) (0.11 g SDS/80 ml $\mathrm H_{2}O$) and finally adjusted by tetramethylammonium hydroxide ($\mathrm (CH_{3})_{4}NOH$, TMAOH) aqueous solution to 8.5–9.5 values. This procedure prevents hematite particles from irreversible sticking onto the glass surface induced by attractive Van der Vaalse interactions [12, 38].

The preparation of ellipsoid and peanuts-shape hematite particles shown in Fig. 6.3 was similar to the procedure described above for cubes except that for $\mathrm NaOH$ and $\mathrm Na_{2}SO_{4}$ amounts. Conditions for preparation of different shape hematite particles are presented in the Table 6.1.

The obtained hematite particles were characterized using scanning electron microscopy (SEM) Hitachi S4800 to investigate their size. Magnetic properties for dried cubic-shaped hematite particles were determined by a vibrating sample magnetometer Lake Shore Cryotronics, Inc. 7400 VSM. The magnetization curve shown in Fig. 6.4 indicates a clear hysteresis and notable coercivity $B_{c}=250\,\textrm{mT}$. Remanent magnetization is around $M=1.9\,\mathrm {kA/m}$.

Fig. 6.3

SEM images of $\alpha$-$\mathrm Fe_{2}O_{3}$ particles of different shape prepared under the standard Sugimoto’ gel-sol route for cubic-shaped particles but with addition of $\mathrm SO_{4}^{2-}$ ions to the precursor mixture (see Table 6.1). a ellipsoids, the mean particles size is 2.10$\,\times \,$1.34 $\mu$m. b big ellipsoids, the mean particles size is 2.23$\,\times \,$1.15 $\mu$m. c “peanuts”, the mean particles size is 1.68$\,\times \,$0.48 $\mu$m. The scale bar is $5\,\mathrm {\mu m}$

In [34, 37] it was reported that the morphology of cubic-shaped hematite particles of the order of 1 $\mu$m in size obtained by aging a condensed ferric hydroxide gel at 100$\,^{\circ }$C for 7–8 d (see Fig. 6.2) can be modified from cubic via ellipsoidal to peanut-shape by introducing increasing amounts sulfate ions into the ferric hydroxide gel.

Table 6.1 Precursors composition for different shaped hematite particles (see Figs. 6.2 and 6.3) prepared by the gel-sol method

Fig. 6.4

Cubic-shaped hematite sample magnetization curve

It was found that sulfate ions restrain the growth in all directions normal to the c-axis. The anisotropy was explained in terms of specific adsorption of sulfate ions onto the sub-crystals of each hematite particle, retarding the surface reaction of ferric complexes such as $\mathrm Fe(OH)^{2+}$ on the planes perpendicular to their c-axis [29, 34].

3 Results

In colloids, hematite has a density $\rho _{h}=5.25$ g/cm$^{3}$ significantly larger than the solvent (usually water $\rho _{s}=1.00$ g/cm$^{3}$). Thus, micron-sized hematite particles sediment [6]. If there is no external magnetic field after the sedimentation process, hematite cubes lie on a face. However, under horizontal magnetic field $B>15 \,\mathrm {\mu T}$ after the sedimentation process, cubes stand on their edges [22]. For an individual cube there are two alignments (see Fig. 6.5) how it can lie [6]. The second alignment can be obtained from the first one by rotating the cube by $180^\circ$ around an axis parallel to the magnetic field (x axis in Fig. 6.5).

Fig. 6.5

Two alignments how the cube can lie on a surface after sedimentation. The green and blue arrow shows the orientation the magnetic moment and the direction of the magnetic field respectively

In a weekly concentrated colloid under a static horizontal external magnetic field, the hematite particles form chains [6, 8, 11]. Depending on the strength of the external magnetic field, two chain configurations are observed. Below the critical magnetic field $B_c\approx 0.1\,\textrm{mT}$ [6], which is typically larger but comparable with the Earth magnetic field, the first configuration is observed. In this case cubes arrange in straight chains (Fig. 6.6) and magnetic moments form zig-zag structures. The second configuration is observable for $B>B_c$ and the magnetic moment of every cube is parallel to the external magnetic field. The short chains are predominantly straight, however, longer chains contain kinks (Fig. 6.6). The kinks are formed during the assembly process when two cubes (two chains, a cube and a chain) with different alignments attach. For the short chains no kinks are experimentally observed as the thermal energy is sufficient for rotation of a single cube (changing cubes alignment) and a straight chain is formed. However, the thermal energy is not sufficient to change alignment of two or more cube chain, thus longer chains contain kinks [6].

Fig. 6.6

Chain with kinks (top) versus straight chain above $B_c$ (middle) versus straight chain below $B_c$ (bottom). The top chain has two kinks. The blue arrow shows magnetic filed direction and little green arrows show magnetic moment orientation (zig-zag structure) in the bottom chain. For all other chains in this figure magnetic moments are along magnetic field

Therefore, in a static external magnetic field, three chain types are observed which are shown in Fig. 6.6. For magnetic fields below $B_c$ straight chains with magnetic moments arranged in a zig-zag structure are observed. Due to thermal effects the chain fluctuates (more pronounced for shorter chains), but the average angle between chain direction and the external magnetic field $\theta =0^\circ$ [6]. For magnetic fields above $B_c$ chains with magnetic moments parallel to the external field are found. Short chains (less than five cubes) are usually straight and longer chains have kinks. For straight chains cubes are shifted against each other. These chains also fluctuate due to thermal effects, however, fluctuations are less pronounced as the magnetic field strength is larger. Also the average angle $\theta$ changes and reaches $\theta \approx \pm 18^\circ$[6]. For the chain with kinks the angle $\theta$ depends on the arrangement of the chain. However, for the straight parts of the chain one finds that average $\theta _i\approx 16.3^\circ$ [11], which is close to the short chain value [6].

If a rotating magnetic field is applied, individual cubes and chains rotate [22] or roll [16]. The rotation and rolling motion are observed if the magnetic field is applied in the xy (horizontal) or xz (vertical) plane respectively. If the magnetic field is applied in the xz plane, then rolling motion of the first chain configuration ( Fig. 6.6) is observed. If the rotating magnetic field is applied xy plane, then all three types of chains can rotate, however, kinked chains are very fragile and easily break and straight chains with magnetic moments orientated in zig-zag structure are stable only for small magnetic fields. Thus, in experiments mostly short chains with aligned magnetic moments are found [22].

Two scenarios of cube rotation depending on the frequency of the rotating magnetic field are possible. For a frequency smaller than the critical frequency $f_c$, the cube rotates synchronously with the magnetic field. Depending on the strength of the magnetic field and initial conditions the cube with rounded corners rotates on an edge, corner, or a face [22]. The corresponding motion of the cube can be seen in Video1, Video2, and Video3 [39]. For magnetic field frequency $f>f_c$, an asynchronous motion of a cube is observed. The critical frequency $f_c\propto 1/B$ and for $1.5 \,\mathrm {\mu m}$ large hematite cubes at $B=1\,\textrm{mT}$ one finds that $f_c\approx 10 \,\textrm{Hz}$.

For large enough rotating magnetic fields, depending on the initial conditions, either precession of the magnetic moment or back-and-forth rotation are observed (see Video4 and Video5 [39]). In the last case, the cube rotates more slowly than the magnetic field and, in order to catch up with the magnetic field, the cube for a short time rotates in the opposite direction. When gravitational effects start to dominate, precession is not observed any more. Instead, a combination of back-and-forth and precession is observed (see Video6 [39]). Initially a cube rotates on its face. The lag increases, but instead of back motion to catch up with the magnetic field, the cube rolls, the magnetic moment goes out of the plane of the rotation magnetic field and through this rolling motion catches up with the magnetic field [22]. For a single cube, the magnetic moment usually goes out of the plane of the rotation magnetic field. The magnetic moment is in the plane of the magnetic field only for synchronous rotation on an edge (see Video1 [39]), where the edge slides on the bottom surface of a capillary [22].

For chains of cubes, depending on the frequency of the rotating magnetic field, the two scenarios of synchronous and asynchronous rotation with the magnetic field are possible. The critical frequency $f_c$ depends on the chain length (number of cubes in chain), decreasing for increasing chain length. In the synchronous motion, the cubes forming chains rotate on an edge or a face (see Video7 and Video8 [39]). No motion on a corner is possible due to geometric restriction. In the asynchronous case back-and-forth rotation, periodic disassembly and reassembly of chain, and out of plane rotation are observed [22]. The corresponding motion of the two-cube chain can be seen in Video9, Video10, and Video11 [39]. The precession of the magnetic moment for a chain is not observed due to the same geometric restrictions. Instead, the out of plane rotation was observed. For out of plane motion, one finds the similar dynamics as for a single cube when the precession of the magnetic moment become impossible. To catch up with the magnetic field, the chain rolls and catches up with the magnetic field through rolling motion where the magnetic moment goes out of the plane of the rotating magnetic field and then returns. Unlike, for a single cube, magnetic moments of cubes in a chain are usually in the plane of the rotation magnetic field. The magnetic moment goes out of the plane of the rotating magnetic field only in one case, called the out of plane rotation, which is a combination of precession and back-and-forth motion. [22].

Interestingly, the dynamics of an individual chains depend on the clockwise or anticlockwise rotation direction of the magnetic field [22]. However, there is no more trend when averaging over many chains. The reason for this is that, similarly to single cube (see Fig. 6.5), also two alignments are possible for straight chains in a static magnetic field. In a large sample there are approximately equal number of chains in each alignment. Particles in each alignment behave differently at a given clockwise and anticlockwise rotation direction of the magnetic field. But the first alignment’s dynamics in a clockwise rotating magnetic field is equal to the second alignment’s dynamics in an anticlockwise rotating magnetic field. Thus, they balance out this effect and on average there are no differences [22].

Hematite particles agglomerate when their concentration is increased in a static magnetic field [8, 12]. In a slowly rotating magnetic field (in xy plane) agglomerates rotate as a solid body with the frequency of the rotating magnetic field. If the frequency is increased $f\in (3,30)\,\textrm{Hz}$ the swarms are formed [12, 18]. Swarms of circular shape consist of individual rotating cubes and short chains (mostly two-cube and three-cube chains) [12]. Chains and individual cubes forming swarms rotate with the frequency of the rotating magnetic field [18]. Swarms exhibit a smaller rotation frequency than the rotating magnetic field. For large swarms (consisting off more than $10^5$ cubes) only the outer particles rotate as the rotation speed is an exponential function from the distance to the center of the swarm [18]. For smaller swarms ($10^3$–$10^4$), however, particles in the center rotate with almost angular constant velocity which agrees with the results of model [23], which incorporates lubrication forces and magnetic dipole-dipole interactions. For small frequencies (up to $15\,\textrm{Hz}$) the rotation frequency of the swarm is proportional to the frequency of the rotating magnetic field [12, 18]. The large swarms behave like a two-dimensional chiral fluid [18].

4 Conclusions

After summarizing the literature of hematite synthesis methods, particular attention was paid to the methods for the production of cubic-shaped hematite particles. Solvothermal methods in particular the diluted solution method and Sugimoto gel-sol method were identified as the most suitable ones. It has been proved that the size of hematite particles strongly depends on the $\mathrm Fe^{3+}$ ions concentration in the initial solution.

We also summarized the richness of the possible structures that cubic-shaped hematite particles may form in magnetic colloids. In weakly concentrated colloids, particles arrange in chains of types that depend on the strength of the external magnetic field: straight chains with magnetic moments arranged in zig-zag structures, short straight chains with magnetic moments aligned with the external magnetic field, and longer chains with kinks, while keeping the individual particles magnetic moments aligned with the external magnetic field. In a rotating magnetic field chains and individual cubes rotate or roll. Rolling motion and rotation are observed when the magnetic field is rotating in the xz (vertical) and xy (horizontal) plane respectively. Both for rolling and rotation synchronous and asynchronous motion with the external rotating field is observed. In the case of rotation, the chain can go out of the plane of the rotating magnetic field.

For magnetic colloids with higher concentration, particles arrange and form aggregates. These aggregates rotate as a solid-body in a very slowly rotating magnetic field. If the frequency is increased the circular shaped swarms of particles are formed. These swarms consist of individual cubes and short chains which rotate with the frequency of the external magnetic field.

Suspension of hematite particles is interesting, in particular, by unusual competition of magnetic and steric interactions due to the non-trivial orientation of the magnetic moment in the particle. The size of the hematite particles makes it possible to observe them easily in the optical microscope. Since their magnetization is rather small then new situations arise where magnetic interactions compete with other interactions in the system, for example, due to the viscous lubrication forces. The present investigation was motivated by the goal to develop quantitative models of unusual behavior of hematite particle suspensions seen in experiments.