目录结构

详情信息展示

参考文献

1 Introduction▲
2 Experimental▲
3 Model formulation▲
4 Results and discussion▲
5 Conclusion▲
图表▲

Rare Metals2018年第5期

Texture-based magnetostriction calculation of oriented polycrystalline cobalt ferrites

Ji-Quan Wang J-Heng Li Chao Yuan Xiao-Qian Bao Xue-Xu Gao

State Key Laboratory of Advanced Metals and Materials,University of Science and Technology Beijing

收稿日期：22 October 2015

基金：financially supported by the Natural Science Foundation of Beijing Municipality (No. 2132052);

Texture-based magnetostriction calculation of oriented polycrystalline cobalt ferrites

Ji-Quan Wang J-Heng Li Chao Yuan Xiao-Qian Bao Xue-Xu Gao

State Key Laboratory of Advanced Metals and Materials,University of Science and Technology Beijing

Abstract：

Oriented polycrystalline cobalt ferrites with different alignments were prepared via a ceramic method.The maximum magnetostriction λ_s up to-270 x 10^-6 was achieved for oriented samples, when the oriented magnetic field was above 1.0 T. Textures of all samples were determined by electron back-scattered diffraction(EBSD)technique and were used to calculate magnetostriction values of oriented poly crystalline cobalt ferrite samples.Results show that a preferred <001> orientation has been obtained within oriented sample. Calculation was done by considering the magnetostriction value as the sum of the content in volume fraction-weighted single-crystal behavior along [100], [110], [210], [310], [311], [211] and [111]directions. The calculated magnetostriction values when compared with experimentally obtained values show identical behavior as a function of applied magnetization orientation field. Good consistency of change rules between calculated values and measured ones illustrates the successful application of this method in predicting magnetostriction values of polycrystalline materials.

Keyword：

Magnetostriction calculation; Oriented polycrystalline; Cobalt ferrites; Texture;

Author： Xue-Xu Gao,e-mail:gaox@skl.ustb.edu.cn;

Received： 22 October 2015

1 Introduction

Magnetostriction describes the phenomenon of dimensional changes occurring with changes in an applied magnetic field.Metal-based magnetos trictive materials have attracted significant attention as the suitable materials for applications in transducers [ 1] ,noncontact sensing of stress or torque [ 2, 3] and micro-displacement actuator [ 4, 5, 6, 7, 8, 9] ,e.g.,Terfenol-D,Galfenol.As nonmetallic magnetostrictive materials,ferrimagnetic cobalt ferrites provide low cost,high electrical resistance,easy processability and good mechanical properties [ 10] while preserving high magnetostriction coefficient and strain derivative,which may be used as ideal materials for vibration components in high frequency ultrasonic transducer.

Magnetostriction values of single-crystalline magnetostrictive materials are normally higher than those of poly crystallines.But complex process conditions and high cost limit the application of single-crystalline materials.Metal-based polycrystalline magnetos trictive materials with certain textures can be obtained by directional solidification technique,rolling technique and heat-treating process.Results show that these methods are all effective to improve magnetostriction behaviors.However,high melting point and bad deformability of cobalt ferrites make it difficult to get certain textures according to above methods.The effects of the method of synthesis,sintering and annealing parameters were studied systematically.It shows that magnetic annealing could raise the magnetostriction and strain derivative values significantly for the uniaxial anisotropic distribution of magnetic domains [ 11] .Ion doping was also studied,which could be used to decrease the anisotropy fields to improve the magnetostrictive behavior in low magnetic field [ 12, 13, 14, 15, 16] .

Several models were developed to simulate the magnetos trictive behaviors of single crystallines.In Preisach model,the effect of stress on magnetomechanical behaviors was studied by treating stress as an effective field [ 17, 18, 19] .In Armstrong model,a space-dependent fluctuation in local energy conditions and magnetization orientation was caused by the interaction of defect strain fields with magnetocrystalline and magnetoelastic anisotropy [ 20] .The probability of the magnetic moment orienting along a particular direction was assumed to be proportional to the inverse exponential of the energy (E) pided by an empirical factor (Ω).Based on the Armstrong models,Atulasimha et al. [ 21] studied the actuation and sensing behavior of polycrystalline Fe_81.6Ga_18.4 sample and magnetomechanical behavior was modeled as the sum of the contents in volume fraction-weighted single-crystal behavior along[100],[110],[210],[310],[111],[211]and[311]directions.

The main contributions of this work were in preparing oriented polycrystalline cobalt ferrites samples with fiber textures and calculating magnetostriction values from the contents in volume fraction of grains along several main directions.Calculated values were compared with measured ones,and results show a well consistency.Method applied in this work was proved to be effective to predict magnetostriction values of oriented polycrystalline samples.

2 Experimental

The CoFe₂O₄ composition was targeted due to its excellent magnetostriction behaviors.CoFe₂O₄ powder was mixed with 5 wt%polyvinyl alcohol (PVA) solution to prepare semisolid slurry.The slurry was then injected into the desired shape (cylindrical,Φ10 mm×30 mm) and oriented along the axial direction under a direct current (DC)magnetic field of 0,0.5,1.0 and 1.5 T for 30 s,respectively.Finally,molded bodies were slowly heated to 973 K to remove the PVA and then sintered at 1623 K for 6 h.

Fig.2 Experimental data ofλ-H curves of CoFe₂O₄ samples magnetized in different fields during forming process.Inset showing saturation magnetostriction (λ_s) of different samples

The cylindrical samples were polished in the transverse direction of the cylinder axis for textures analysis.Textures of polished samples were observed by electron back-scattered diffraction (EBSD) system which was equipped on a field emission scanning electron microscope(FESEM,Zeiss SUPRA^TM 55).Pole figures and orientation distribution function (ODF) plots were obtained from EBSD patterns.Inverse pole figures (IPF) were analyzed to get the contents in volume fraction (determined by the areas) of grains that lie within 18°of[100],[110],[111],[210],[211],[310]and[311]orientations.The magnetostriction values under an increasing applied field from 0 to 250 kA·m^-1 were measured at room temperature by means of resistance strain gauges,with the gauges positioned along axial direction of cylindrical samples.

Fig.1 IPF images along normal direction of CoFe₂O₄ samples magnetized in different fields during forming process (red,green and blue indicating [001],[110] and[111]grains,respectively):a 0 T,b 0.5 T,c 1.0 T and d 1.5 T

3 Model formulation

The aim of this polycrystalline modeling is to predict the magnetostriction values of oriented polycrystalline CoFe₂O₄samples from texture information and knowledge of singlecrystal behavior.While a magnetic field (H_m) is applied to the magnetostrictive materials,strain appears and increases until saturation magnetostrictive strain is reached at higher fields.Generation of the strain is attributed to the combined effects of magnetocrystalline anisotropy and spin-orbit coupling.

For the single-crystal samples,magnetic domains are usually thought to be along the easy magnetization axis after annealing processes.Original length of the sample along[α_iα₂α₃]direction is l.While a magnetic field is applied along this direction,strain (δl/l) can be expressed as the following equation [ 22] :

whereλ₁₀₀ andλ₁₁₁ are the magnetostriction values in[100]and[111]directions,respectively.

As the direction cosines[α₁α₂α₃]in Cartesian coordinates are transformed into the corresponding orientation (θ,Φ) in spherical co-ordinates,Eq.(1) can also be expressed as follows:

whereθandΦare azimuth angle and elevation angle in spherical coordinates,respectively.

For the polycrystalline sample,if effects of intergranular interactions were ignored,the macroscopical magnetostriction value can be obtained by summing strain contributionλ(θ_i,Φ_i) of all single-crystal grains in (θ_i,φ_i)direction.Actually,it is hard to get every strain of all grains.For simplicity,X-ray diffraction (XRD) and EBSD techniques were used to estimate the contents in volume fraction of grains close to[100],[110],[210],[310],[111],[211]and[311]directions (x₁₀₀,x₁₁₀,x₂₁₀,x₃₁₀,x₁₁₁,x₂₁₁and x₃₁₁),respectively [ 23] .And then the poly crystalline magnetostriction value ( ) can be calculated as:

4 Results and discussion

The texture is a key factor determining the magnetostrictive behaviors of oriented polycrystallines and can be determined by EBSD technique.The IPF images of crystal orientation for the oriented CoFe₂O₄ samples with magnetization orientation fields of 0,0.5,1.0 and 1.5 T are given in Fig.1.Obvious change in the areas covered by<001>grains is observed on IPF images.Figure la shows that grain orientation distribution of non-oriented sample is isotropic.As the magnetization orientation field increases,a preferred orientation appears and becomes stronger.While a magnetic field is applied,the single-crystal particles in the semisolid slurry will be rotated with the easymagnetization axis<001>along the direction of orientation field under the combined function of magnetostatic torque and magnetocrystalline interaction force.The higher the magnetization orientation field is,the stronger the fiber textures will be.

下载原图

Table 1 Relative angles and magnetostriction values along seven main directions in a single-crystal cobalt ferrite

Fig.3 Schematic illustration of easy axis of a grain in a spherical coordinate system a (H_m measuring field;Ωsolid angle) and magnetostriction values along different directions in a single-crystal cobalt ferrite sample b

Fig.4 EBSD maps and corresponding contents in volume fraction (determined by areas) of grains that lying within 18°of[100],[110],[111],[210],[211],[310]and[311]orientations for CoFe₂O₄ samples magnetized in different fields during forming process:a 0 T,b 0.5 T,c 1.0 T and d 1.5 T

The magnetostriction values for CoFe₂O₄ samples with different alignments are shown in Fig.2.As shown in Fig.2,the saturation magnetostriction (λ_s) of non-oriented sample is about-142×10^-6,which is similar to the previous values of CoFe₂O₄ prepared by traditional ceramic method [ 20] .The saturation magnetostriction (λ_s) increases as the magnetization orientation field becomes higher,which can be seen in the inset.When the field is above1.0 T,the maximum measured value of-270×10^-6 is obtained,where a<001>fiber texture is achieved.

Fig.5 Calculated and measured magnetostriction values of CoFe₂O₄samples with different alignments

To calculate maximum magnetostriction values of polycrystalline samples,orientation of each grain is defined by the misorientationθ(0,π) and azimuth angleΦ(0,2π)according to Fig.3a.This spherical coordinate system with texture axis [ 1] as reference axis holds for uniaxial textures with rotational symmetry,the so-called fiber texture [ 24] ,as it is the case for oriented poly crystalline CoFe₂O₄.Figure 3b shows magnetostriction values along different directions for single-crystal cobalt ferrites which are represented as Eq.(2).Relative angles (θ,Φ) and magnetostriction value (λ_ijk)of grains along[100],[110],[210],[310],[111],[211]and[311]directions are listed in Table 1,respectively.

While IPF images of all samples are obtained,the contents in volume fractions of grains close to[ijk]direction(x_ijk) can be estimated using the corresponding software program.The contents in volume fractions (determined by the areas) of grains that lie within 18°of[100],[110],[111],[210],[211],[310]and[311]orientations are counted,respectively.In mentioned seven direction types,<310>is the closest direction to<100>.Angle between<310>and<100>is almost 18°which is chosen as the standard to pide grains and insure that all grains have been taken into account.Actually,the contents in volume fraction in all these directions add up to greater than 100%.This is because of the overlap of some grains which are close to two directions [ 21] .For calculating purposes,the contents in volume fraction in all the above directions are normalized so that they add to l00%.Figure 4 indicates the normalized content in volume fraction for all samples.Color of the line under the particular curve graph represents grains with particular direction in IPF images.

When normalized contents in volume fractions (xijk) and magnetostriction values (λ_ijk)of different directions for all CoFe₂O₄ samples are obtained,the polycrystalline magnetostriction values can be calculated using Eq.(3).Calculated values are compared with measured magnetostriction in Fig.5.Results show that the change rule of calculated values is similar to that of measured ones.Magnetostriction values increase significantly as the magnetization orientation field changes from 0 to 0.5 T and get saturated as field above 1.0 T.Good consistency of change rules between calculated values and measured ones illustrates the successful application of this method in predicting magnetostriction values of polycrystalline materials.It is worth noting that calculated values are higher than measured ones.This could be due to two reasons.The first reason is that theλ₁₀₀ andλ₁₁₁ of singlecrystal Co_0.8Fe_2.2O₄ are slightly higher than those of single-crystal CoFe₂O₄ which are adopted in Eq.(2).The other is the overlap of some grains occurring in estimating the contents in volume fraction.

5 Conclusion

In this study,oriented polycrystalline CoFe₂O₄ samples with different alignments were prepared by a ceramic method.Textures of all samples were determined using EBSD technique,and results show that fiber textures are obtained in oriented samples.All grains are classified into seven kinds which lie within 18°of[100],[110],[111],[210],[211],[310]and[311]directions,respectively.Contents in volume fraction of all above orientation were estimated using the corresponding software program.Calculation was taken by considering the magnetostriction value as the sum of the contents in volume fractionweighted single-crystal behavior along above seven directions.Similar change rules are observed in calculated magnetostriction values and measured ones.Magnetostriction (λ_s) increases significantly as the magnetization orientation field changes from 0 to 0.5 T and gets saturated with field above 1.0 T.