Negative Magnetostrictive Paper Formed by Dispersing CoFe 2 O 4 Particles in Cellulose Nanofibers

doi:10.21203/rs.3.rs-2219766/v1

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Negative Magnetostrictive Paper Formed by Dispersing CoFe 2 O 4 Particles in Cellulose Nanofibers

https://doi.org/10.21203/rs.3.rs-2219766/v1

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published 15 Apr, 2023

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Polymers are often combined with magnetostrictive materials to enhance their toughness. This study reports a cellulose nanofiber (CNF)-based composite paper containing dispersed CoFe₂O₄ particles (CNF–CoFe₂O₄). Besides imparting magnetization and magnetostriction, the CoFe₂O₄ particles increase the fracture elongation of the CNF–CoFe₂O₄ composite paper, although the ultimate tensile strength of the composite paper decreases with increasing CNF content. As strength and toughness are usually inversely proportional, it was inferred that the magnetostrictive CNF–CoFe₂O₄ composite paper has good toughness.

Physical sciences/Engineering/Mechanical engineering

Physical sciences/Materials science/Materials for energy and catalysis

Physical sciences/Materials science/Soft materials

cellulose nanofiber

composite

magnetic properties

magnetostrictive properties

tensile properties

To alleviate the global energy crisis and environmental pollution, many researchers are exploring alternative energy technologies that harvest energy from the ambient environment (e.g., mechanical vibrations) [1–3]. When the ambient energy supply is limited, piezoelectric-energy harvesting devices generate sufficient power for targeted devices such as Internet of things sensors [4]. For this purpose, piezoelectric materials, composites, and devices have been actively researched [5–11] and their vibration-energy harvesting performances have been evaluated.

Magnetostrictive materials can deform under an external magnetic field [12]. The magnetostrictive effect was first described by James Prescott Joule in 1842 [13]. He reported that iron, a ferromagnetic material, changes its dimension in response to a magnetic field. Since that time, researchers have developed various magnetostrictive materials such as Tb–Dy–Fe alloys (Terfenol-D), Fe–Ga alloys (Galfenol), Fe–Co alloys, and CoFe₂O₄ (cobalt ferrites) [14–18]. Magnetostrictive materials, composites, and devices are also attracting attention in the energy harvesting field [19–24]. Terfenol-D and Galfenol are well-known giant magnetostrictive alloys showing huge magnetostriction at room temperature, but are brittle and expensive [1, 16].

To overcome the brittleness of magnetostrictive materials, many researchers have dispersed magnetostrictive particles through a polymer matrix, forming magnetostrictive polymer composites (MPCs) [25]. Under an external magnetic field, the magnetostrictive particles deform and exert a force on the polymer matrix, deforming the whole composite. Equilibrium is achieved by balancing the stresses generated in the magnetostrictive particles and the polymer matrix, resulting in overall deformation of the MPC. MPCs are potentially applicable to current and stress sensing, vibration damping, actuation, health monitoring, and biomedical applications. In addition, they are easier to manufacture to the required geometry than the above-mentioned giant magnetostrictive alloys. Previous studies on MPCs have reported Terfenol-D particles [26] and Galfenol particles [27] dispersed through an epoxy resin matrix (Terfenol-D/epoxy and Galfenol/epoxy composites, respectively), Fe–Co alloy particles dispersed through a polyurethane matrix (Fe–Co/PU composites) [28] and various others. Positive magnetostriction values of 1600, 360, and 70 ppm been reported in Terfenol-D/epoxy, Galfenol/epoxy, and Fe–Co/PU, respectively. However, MPCs with negative magnetostriction have been rarely investigated. Nersessian et al. [29] reported saturation magnetostrictions of − 24 and − 28 ppm in hollow and solid nickel composites, respectively. Similarly, Ren et al. [30] reported negative magnetostriction in polymer-bonded Sm_0.88Dy_0.12Fe_1.93 pseudo-1-3 composites.

Recently, the growth of paper-based devices has gained attention [31] because paper is low cost (~ 0.005 $/m²), biocompatible, environmentally friendly, 100% recyclable, frivolous, and more stretchable than other polymer-based flexible devices [32]. Cellulose fiber is inexpensive, bio-based, biodegradable, non-hazardous, recyclable, and low- density [33]. Cellulose nanofibers (CNFs) in particular shows outstanding strength, stiffness, and toughness [34] and are expected to be utilized as reinforcing fibers [35–38]. Yermakov et al. [39] fabricated magnetostrictive nanocellulose membranes by embedding Terfenol-D particles into CNFs. After evaluating the magnetostrictive properties of the membranes, they found that various orientations of the Terfenol-D particles were induced in the membranes, and that particles with in-plane alignment showed the strongest magnetostrictive effect.

In the present study, CoFe₂O₄ particles were dispersed through CNF to form a CNF–CoFe₂O₄ composite paper. This paper reports the magnetic, magnetostrictive, and tensile properties of the paper. The microstructure of the CNF–CoFe₂O₄ composite paper was observed using a scanning electron microscope (SEM) and an X-ray diffraction (XRD) system.

2.1 Specimen preparation

Figure 1 is a schematic of the fabrication process of the CNF–CoFe₂O₄ composite paper. The starting materials were CoFe₂O₄ particles (Kojundo Chemical Laboratory Co., Ltd., Japan) and a 2 wt.% CNF slurry (IMA-10002, Sugino Machine, Japan). The CoFe₂O₄ particle size distribution was measured by a laser diffraction particle size analyzer (MASTERSIZER 3000, Malvern Panalytical, Spectris, UK). The CoFe₂O₄ particles and CNF slurry were manually mixed for 5 minutes with different weight ratios of CoFe₂O₄ particles: CNF slurry $=x:100-x$ $(x=$ 5, 20, 35 wt.%; total weight = 20 g). The solutions were sandwiched between two mesh sheets sized (100 $\times$ 100) mm². The samples were compressed and dehydrated under an ultra-compact manual hydraulic heating press (Model IMC-195A-E, Imoto Mfg. Co., Ltd., Japan) operated at 120°C for 30 sec. After peeling off the mesh sheets, the dehydrated CNF–CoFe₂O₄ composite paper was further compressed and dried using a 2500-g weight for 24 hours. The circular CoFe₂O₄ plate ($\varphi$15 $\times$ 2.25 mm³) was then consolidated by spark plasma sintering (SPS, SPS-1050, Fuji Electric Industrial Co., Ltd., Japan), under a compressive stress of 20 MPa at 1000°C for 10 minutes in a vacuum. A reference CoFe₂O₄ plate was cut to a size of (10 $\times$ 10 $\times$ 2.25) mm³ and reserved for further measurements.

2.2 Density

To obtain the densities of the CoFe₂O₄ composite paper and CoFe₂O₄ sintered plate, the lengths and thicknesses of the samples were measured using an electronic digital caliper (SDV-150, Fujiwara Industrial Co., Ltd., Japan) and a digital thickness gauge (MDC-SX, Mitutoyo, Japan), respectively, and the weights of the samples were measured on a digital scale (ALE223R, Sinko Denshi Co., Ltd., Japan).

2.3 Microstructure analysis

The microstructures of the CNF–CoFe₂O₄ composite paper and CoFe₂O₄ particles were investigated in a multipurpose XRD system (Ultima IV, Rigaku Co., Japan). The XRD patterns were obtained under CuK${\alpha }$ radiation with a counting time of 1.67/s, a step size of 0.02°, a voltage of 40 kV, and a current of 40 mA. The scanning range was determined to be between 10° and 70°. The microstructure of the CNF–CoFe₂O₄ composite paper was observed using a field emission SEM (FE-SEM) (SU-70, Hitachi High-Tech Co., Ltd., Japan), with an acceleration voltage of 5 kV and a working distance of 10 mm. In preparation for FE-SEM, the surface of the CNF–CoFe₂O₄ composite paper was sputtered for 30 seconds using an ion sputtering device (E-1045, Hitachi High-Tech Co., Ltd., Japan) with a discharge current of 15 mA at 15 Pa to provide electrical conductivity to the composite paper. Furthermore, the FE-SEM was equipped with an energy dispersed X-ray spectrometer (EDX) for measuring the carbon (C), oxygen (O), Co, and Fe concentrations in the CNF–CoFe₂O₄ composite paper. The EDX was operated at an acceleration voltage of 5 kV and a working distance of 15 mm.

2.4 Magnetic and magnetostrictive properties

The magnetic properties of the CNF–CoFe₂O₄ composite paper were evaluated using a vibrating sample magnetometer (VSM) (BHV-50H, Riken Denshi Co., Ltd., Japan) calibrated to 4.931 emu. The VSM was calibrated on a pure nickel (Ni) plate sized (10 $\times$ 10 $\times$ 0.1) mm³. The applied magnetic field range was ± 759 kA/m. The magnetostrictive properties of the CNF–CoFe₂O₄ composite paper were evaluated under the VSM electromagnets. The electromagnets were separated by 50 mm. The applied magnetic field was measured with a gauss meter (GM-4002, Denshijiki Industry Co., Ltd., Japan). The strain of the CNF–CoFe₂O₄ composite paper was measured by an orthogonal strain gage (JFGS-1-120-D16-16 L3M2S, Kyowa Electronic Instruments Co., Ltd., Japan) positioned on the sample surface under an applied magnetic field range of ± 733 kA/m. The data were collected by data loggers (NR-ST04 and NR-HA08, Keyence, Japan) [28].

2.5 Tensile properties

The tensile properties of CNF–CoFe₂O₄ composite paper sized (30 $\times$ 15) mm² were investigated on a compact tabletop tester (EZ-SX, Shimazu Co., Ltd., Japan) with a 500-N load cell (Shimazu Co., Ltd., Japan). The tensile grips were separated by 15 mm. #600-grit sandpaper was inserted between the CNF–CoFe₂O₄ composite paper and the tensile grips to prevent slipping.

This section formulates the problem of predicting the effective magneto-mechanical properties of the CNF–CoFe₂O₄ composite paper. In rectangular Cartesian coordinates x_i (O-x₁, x₂, x₃), the constitutive equations of the heterogeneous magnetostrictive composite material are given by

$$<{\epsilon }_{ij}>={s}_{ijkl}^{\text{*}\text{H}}{<\sigma }_{kl}>+{d}_{kij}^{*}{<H}_{k}>$$

$$<{B}_{i}>={d}_{ikl}^{*}{<\sigma }_{kl}>+{\mu }_{ik}^{\text{*}\text{T}}{<H}_{k}>,$$

where $<{\epsilon }_{ij}>,{<\sigma }_{kl}>,<{B}_{i}>$ and ${<H}_{k}>$ are the average components of the strain tensor, stress tensor, magnetic flux density vector, and magnetic field intensity vector, respectively, and ${s}_{ijkl}^{\text{*}\text{H}}$, ${d}_{kij}^{*}$ and ${\mu }_{ik}^{\text{*}\text{T}}$ are the elastic compliances under a constant magnetic field, the piezomagnetic constant, and the magnetic permittivity under constant stress, respectively. Hereafter, the asterisk (*) will denote the effective average properties of the magnetostrictive composite material. This formulation adopts the compressed matrix notation, which is more useful than the extended tensor notation when discussing symmetry. In this matrix notation, ij or kl (i, j, k, l = 1, 2, 3) is replaced with p, q (valued from 1 to 6). Equations (1) and (2) are then rewritten as

$$<{\epsilon }_{p}>={s}_{pq}^{\text{*}\text{H}}{<\sigma }_{q}>+{d}_{kp}^{*}{<H}_{k}>$$

$$<{B}_{i}>={d}_{iq}^{*}{<\sigma }_{q}>+{\mu }_{ik}^{\text{*}\text{T}}{<H}_{k}>$$

To demonstrate the effective properties of the CNF-CoFe₂O₄ composite paper, we consider the longitudinal magnetostrictive effect, meaning that the external field (either mechanical stress or a magnetic field) acts along the x₃-direction (the easy magnetization axis of the composite paper). The magneto-mechanical coupling factor is given by

$${k}_{33}^{2}=\frac{{d}_{33}^{\text{*}2}}{{s}_{33}^{\text{*}\text{H}}{\mu }_{33}^{\text{*}\text{T}}}=\frac{{E}_{}^{\text{*}}{d}_{33}^{\text{*}2}}{{\mu }_{33}^{\text{*}\text{T}}}$$

where ${E}_{}^{\text{*}}$ is the Young’s modulus (slope of the stress–strain plot) of the CNF–CoFe₂O₄ composite paper. Note that the material properties ${E}_{}^{\text{*}}$, ${d}_{33}^{*}$ and ${\mu }_{33}^{\text{*}\text{T}}$are functions of the volume fractions ${V}_{\text{c}\text{f}\text{o}}$of the CoFe₂O₄ particles, ${V}_{\text{p}} \text{o}\text{f} \text{t}\text{h}\text{e}$pores, and $1-({V}_{\text{c}\text{f}\text{o}}+{V}_{\text{p}})$ of the CNF matrix, respectively:

${E}_{}^{\text{*}}={E}_{}^{\text{*}}\left({\text{V}}_{\text{c}\text{f}\text{o}}, {V}_{\text{p}},{V}_{\text{m}}\right),$

${d}_{33}^{\text{*}}={d}_{33}^{\text{*}}\left({V}_{\text{c}\text{f}\text{o}}, {V}_{\text{p}},{V}_{\text{m}}\right),$

${\mu }_{33}^{\text{*}\text{T}}={\mu }_{33}^{\text{*}\text{T}}({V}_{\text{c}\text{f}\text{o}}, {V}_{\text{p}},{V}_{\text{m}})$,

where $\text{t}\text{h}\text{e}$ subscripts cfo, p, and m represent the CoFe₂O₄ particles, pores, and matrix (i.e., CNF), respectively.

The real densities of the CNF–CoFe₂O₄ composite papers were 0.7983 g/cm³ (x = 5), 1.1967 g/cm³ (x = 20), and 1.5058 g/cm³ (x = 35). Assuming that all water was evaporated from the dried CNF–CoFe₂O₄ composite paper and taking the theoretical densities of CoFe₂O₄ and cellulose (5.29 [40] and 1.50 g/cm³, respectively), the volume fractions of the CoFe₂O₄ particles dosed at x = 5, 20, and 35 were calculated as 10.9, 21.0, and 27.5 vol.%, respectively, in the final CNF–CoFe₂O₄ composite paper (see Table 1). The average thicknesses of the CNF–CoFe₂O₄ composite paper containing 10.9, 21.0, and 27.5 vol.% CoFe₂O₄ were 0.25, 0.49, and 0.92 mm, respectively. The real density of the CoFe₂O₄ sintered plate was 4.298 g/cm³. The relative density of the CoFe₂O₄ sintered plate was calculated as 81.2% of the theoretical density of 5.29 g/cm³.

Table 1

Parametric values of the CNF–CoFe₂O₄ composite papers
CoFe₂O₄ content	10.9 vol.%	21.0 vol.%	27.5 vol.%
${\text{V}}_{\text{c}\text{f}\text{o}}$	0.109	0.210	0.275
${V}_{\text{p}}$	0.744	0.731	0.689
${V}_{\text{m}}$	0.147	0.059	0.036
Apparent${E}_{}^{\text{*}}$	0.523 GPa	0.269 GPa	0.195 GPa
${d}_{33}^{\text{*}}$	–8.95$\times$10⁻¹² m/A	–66.5$\times$10⁻¹² m/A	–166$\times$10⁻¹² m/A
$\text{A}\text{p}\text{p}\text{a}\text{r}\text{e}\text{n}\text{t} {\mu }_{33}^{\text{*}\text{T}}$	0.0769$\times$10⁻⁶ H/m	0.127$\times$10⁻⁶ H/m	0.228$\times$10⁻⁶ H/m
Apparent${k}_{33}^{2}$	5.45$\times$10⁻¹⁶	9.37$\times$10⁻¹⁵	2.36$\times$10⁻¹⁴

Figure 2 shows the size distributions of the CoFe₂O₄ particles. The average particle size was 56 µm. The CoFe₂O₄ powder comprised small and large particle populations with approximate diameters of 10 and 150 µm, respectively. As shown in Fig. 3, the XRD patterns of the 10.9 vol.% CNF–CoFe₂O₄ composite paper matched those of the CoFe₂O₄ particles. Therefore, the CoFe₂O₄ was stable against chemical transformations during the fabrication process. Figure 4 shows the SEM images of the CNF–CoFe₂O₄ composite paper. Although the CoFe₂O₄ particles were dispersed through the CNF matrix, they were agglomerated by the hand mixing process. The size distribution peak at 150 µm in Fig. 2 was probably contributed by large agglomerates of CoFe₂O₄ particles. Figure 5 shows the EDX mapping of the 27.5 vol.% CNF–CoFe₂O₄ composite paper (the micrograph is shown in Fig. 4(c)). The EDX detected C, O, Co, and Fe on the surface of the CNF–CoFe₂O₄ composite paper and implied that CoFe₂O₄ was stable during the fabrication process, reconfirming the XRD results. Note that no characteristic intensities of the X-rays appeared in the shadow of the EDX detector because they were attenuated by the uneven surface of the CNF–CoFe2O4 composite paper surface.

Figure 6 shows the magnetic properties of the CNF–CoFe₂O₄ composite paper and CoFe₂O₄ plate. The CoFe₂O₄ additives magnetized the CNF paper. The maximum magnetization of the CNF–CoFe₂O₄ composite paper linearly increased with increasing proportion of CoFe₂O₄ particles. Consistent with the present results, Williams et al. [41] reported that the magnetic properties of magnetizing cellulose fibers depend on the volume percentage of the implemented magnetic filler in the fiber matter. The magnetic curve of the CNF–CoFe₂O₄ composite paper reached saturation more slowly than the CoFe₂O₄ sintered plate. In Eq. (4), the effective magnetic permittivity ${\mu }_{33}^{\text{*}\text{T}}$ of the CNF–CoFe₂O₄ composite paper under stress-free conditions was given by

$${\mu }_{33}^{\text{*}\text{T}}=\frac{{B}_{3}}{{H}_{3}}$$

The apparent effective magnetic permittivities ${\mu }_{33}^{\text{*}\text{T}}$ of CNF–CoFe₂O₄ with CoFe₂O₄ contents of 10.9, 21.0, and 27.5 vol.% were evaluated as 0.0769$\times$10⁻⁶, 0.127$\times$10⁻⁶, and 0.228$\times$10⁻⁶ H/m, respectively (see Table 1).

Figure 7 shows the magnetostrictive properties of the CNF–CoFe₂O₄ composite paper and CoFe₂O₄ plate. In the CNF–CoFe₂O₄ composite paper, the magnetostriction was negative and positive in the directions parallel and perpendicular to the magnetic field, respectively, as expected. The magnetostriction of the CoFe₂O₄ plate was − 90 ppm under a magnetic field of 217 kA/m. The maximum negative magnetostriction of the CNF–CoFe₂O₄ composite paper deviated from the fitting line [see Fig. 7(e)]. Note that the 10.9 and 21.0 vol.% CNF–CoFe₂O₄ composite papers failed to achieve magnetostrictive saturation under a magnetic field of ${H}_{3}=\pm$733 kA/m. These results imply that the CNFs between the CoFe₂O₄ particles deformed with magnetostriction of the CoFe₂O₄ particles and facilitated linear magnetostriction of the whole CNF–CoFe₂O₄ composite paper. In Eq. (3), the effective piezomagnetic constant ${d}_{33}^{\text{*}}$ of the CNF–CoFe₂O₄ composite paper under stress-free conditions was calculated as

${d}_{33}^{\text{*}}=\frac{{\epsilon }_{3}}{{H}_{3}}$.

After straight-line fitting of the linear portions of the curves in Fig. 7(a)–(c), the ${d}_{33}^{\text{*}}$ values of the CNF–CoFe₂O₄ composite papers containing 10.9, 21.0, and 27.5 vol.% CoFe₂O₄ were calculated as − 8.95$\times$10⁻¹², − 66.5$\times$10⁻¹², and − 166$\times$10⁻¹² m/A, respectively (see Table 1). Clearly, the ${d}_{33}^{\text{*}}$ of the CNF–CoFe₂O₄ composite paper increased with increasing CoFe₂O₄ particle addition. From Eq. (3), the effective piezomagnetic constant ${d}_{31}^{\text{*}}$ of the CNF–CoFe₂O₄ composite paper under stress-free conditions was also obtained as

$${d}_{31}^{\text{*}}=\frac{{\epsilon }_{1}}{{H}_{3}}$$

Similarly, the ${d}_{31}^{\text{*}}$ values of the CNF–CoFe₂O₄ composite paper containing 10.9, 21.0, and 27.5 vol.% CoFe₂O₄ were calculated as 0.391$\times$10⁻¹², 18.8$\times$10⁻¹², and 27.1$\times$10⁻¹² m/A, respectively.

Figure 8(a) shows the stress–elongation curves of the CNF–CoFe₂O₄ composite papers. Here, the elongation was estimated from the displacement of a universal testing machine crosshead. Between 0 and 0.2% elongation, the slopes of the stress–elongation curves of the 10.9, 21.0, and 27.5 vol.% CNF–CoFe₂O₄ composite papers were determined as 0.523, 0.269, and 0.195 GPa, respectively (see Table 1). These values were taken as the apparent effective Young's moduli. Panels (b) and (c) of Fig. (8) plot the ultimate tensile strengths (UTSs) and fracture elongations versus CNF volume fraction in the CNF–CoFe₂O₄ composite papers. The CNF volume fractions in the 10.9, 21.0, and 27.5 vol.% composite papers were 14.7, 5.9, and 3.6 vol.%, respectively. The UTS of the CNF–Fe₂O₄ composite paper was increased by the connection between the CoFe₂O₄ particles via the CNFs. On the downside, the CoFe₂O₄ additives decreased the UTS. As strength and toughness are usually considered to be inversely proportional, the CNF–CoFe₂O₄ composite paper probably has good toughness, and further experiments will reveal its durability as a vibration-energy harvesting device. The apparent ${k}_{33}^{2}$ values of the 10.9, 21.0, and 27.5 vol.% CNF–CoFe₂O₄ composite paper were 5.45$\times$10⁻¹⁶, 9.37$\times$10⁻¹⁵, and 2.36$\times$10⁻¹⁴, respectively (see Table 1). The improved magneto-mechanical coupling factor after adding CoFe₂O₄ implies that the CNF–CoFe₂O₄ composite paper is a promising candidate for energy harvesting applications.

This study evaluated the magnetic, magnetostrictive, and tensile properties of CNF–CoFe₂O₄ composite paper with different volume fractions of CoFe₂O₄. The XRD and EDX analyses revealed that CoFe₂O₄ remained stable during the fabrication process. The SEM images confirmed that CoFe₂O₄ particles were dispersed through the CNF matrix but were sometimes agglomerated. The CoFe₂O₄ particles imparted magnetization to the CNF paper and the maximum magnetization of the CNF–CoFe₂O₄ composite paper was a linearly increasing function of CoFe₂O₄ content. The magnetostriction of the CNF–CoFe₂O₄ composite paper was negative and positive in the directions parallel and perpendicular to the magnetic field, respectively. However, the apparent effective Young’s modulus and UTS of the CNF–CoFe₂O₄ composite paper decreased with increasing CoFe₂O₄ content because the CoFe₂O₄ particles increased the CNF volume fraction of the composite paper. As strength and toughness are inversely proportional, the magnetostrictive CNF–CoFe₂O₄ composite paper is expected to achieve high toughness. Overall, the CoFe₂O₄ additives impart magnetic and magnetostrictive properties to the CNF paper and may increase its toughness in exchange for decreasing its tensile properties. The magneto-mechanical coupling factor of the paper was improved by adding CoFe₂O₄ particles; therefore, the CNF–CoFe₂O₄ composite paper is expected to be available for energy harvesting applications.

Data Availability

The materials described in the manuscript, including all relevant raw data, will be freely available to any researcher wishing to use them for non-commercial purposes from the corresponding author on reasonable request.

Acknowledgments

This work was supported by the Japan Society for the Promotion of Science (JSPS) KAKENHI Grant-in-Aid for Scientific Research (A) (Grant Numbers 22H00183) and Grant-in-Aid for Early-Career Scientists (Grant Numbers 19K14836).

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published 15 Apr, 2023

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Negative Magnetostrictive Paper Formed by Dispersing CoFe 2 O 4 Particles in Cellulose Nanofibers

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Abstract

Figures

1. Introduction

2. Experimental Procedure

2.1 Specimen preparation

2.2 Density

2.3 Microstructure analysis

2.4 Magnetic and magnetostrictive properties

2.5 Tensile properties

3. Theory

4. Results And Discussion

5. Conclusion

Declarations

References

Additional Declarations

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Journal Publication

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CoFe₂O₄ content	10.9 vol.%	21.0 vol.%	27.5 vol.%
\({\text{V}}_{\text{c}\text{f}\text{o}}\)	0.109	0.210	0.275
\({V}_{\text{p}}\)	0.744	0.731	0.689
\({V}_{\text{m}}\)	0.147	0.059	0.036
Apparent\({E}_{}^{\text{*}}\)	0.523 GPa	0.269 GPa	0.195 GPa
\({d}_{33}^{\text{*}}\)	–8.95\(\times\)10⁻¹² m/A	–66.5\(\times\)10⁻¹² m/A	–166\(\times\)10⁻¹² m/A
\(\text{A}\text{p}\text{p}\text{a}\text{r}\text{e}\text{n}\text{t} {\mu }_{33}^{\text{*}\text{T}}\)	0.0769\(\times\)10⁻⁶ H/m	0.127\(\times\)10⁻⁶ H/m	0.228\(\times\)10⁻⁶ H/m
Apparent\({k}_{33}^{2}\)	5.45\(\times\)10⁻¹⁶	9.37\(\times\)10⁻¹⁵	2.36\(\times\)10⁻¹⁴