J. GONDRO et al.: INFLUENCE OF STRUCTURAL DEFECTS ON THE MAGNETIC PROPERTIES ... 559–564 INFLUENCE OF STRUCTURAL DEFECTS ON THE MAGNETIC PROPERTIES OF MASSIVE AMORPHOUS Fe60Co10Mo2WxY8B20-x (x = 1, 2) ALLOYS PRODUCED WITH THE INJECTION CASTING METHOD VPLIV STRUKTURNIH NAPAK NA MAGNETNE LASTNOSTI MASIVNE AMORFNE ZLITINE Fe60Co10Mo2WxY8B20-x (x = 1, 2), IZDELANE Z METODO LITJA Z VBRIZGAVANJEM Joanna Gondro, Katarzyna B³och, Marcin Nabia³ek, Sebastian Garus Institute of Physics, Faculty of Production Engineering and Materials Technology, Czestochowa University of Technology, Al. Armii Krajowej 19, 42-200 Czestochowa, Poland j.gondro@wp.pl Prejem rokopisa – received: 2015-06-30; sprejem za objavo – accepted for publication: 2015-07-29 doi:10.17222/mit.2015.148 This paper presents the results of research pertaining to high-field magnetic properties, in relation to the theory of H. Kronmüller. Studies were performed on bulk amorphous alloys featuring composition Fe60Co10Mo2WxY8B20-x (x = 1, 2). Samples were produced in the form of plates with a thickness of 0.5 mm; they were prepared by injecting the molten alloy into a water-cooled copper mould. The influence of structural defects on the magnetization process was investigated within high magnetic fields known as the area of the approach to ferromagnetic saturation. For the investigated samples, the studies showed that, in the process of magnetization in high magnetic fields, rotation of the magnetization vector was mainly due to the presence of linear defects in the structure, i.e., quasidislocational dipoles. The density of quasidislocational dipoles in a sample with an addition of 1 % W was nearly twice as high as that of an alternative alloy. Keywords: bulk amorphous alloy, metallic glasses, high magnetic fields, magnetization, structural defects, relaxation ^lanek predstavlja rezultate raziskav, ki se nana{ajo na visokomagnetne lastnosti, v povezavi s teorijo H. Kronmüllerja. [tudije so bile izvedene na masivni amorfni zlitini s sestavo Fe60Co10Mo2WxY8B20-x (x = 1, 2). Vzorci so bili izdelani v obliki plo{~ic debeline 0,5 mm, izdelane z vbrizgavanjem staljene zlitine v vodno hlajeno bakreno kokilo. Preiskovan je bil vpliv napak v strukturi na proces magnetizacije v visokomagnetnih poljih, poznanih kot podro~je pribli`ka k feromagnetnemu nasi~enju. Za preiskovane vzorce so raziskave pokazale, da pri procesu magnetizacije v visoko magnetnih poljih pride do rotacije magnetnega vektorja predvsem zaradi prisotnosti linearnih napak v strukturi: to so kvazidislokacijski dipoli. Gostota dislokacijskih dipolov v vzorcu, z dodatkom 1 % W, je bila skoraj dvakrat vi{ja kot pa pri drugi zlitini. Klju~ne besede: masivna amorfna zlitina, kovinska stekla, visokomagnetno polje, magnetizacija, napake v strukturi, relaksacija 1 INTRODUCTION Within the past decade, a group of materials known as šbulk amorphous alloys’ have been studied inten- sely;1–4 This interest is associated with their excellent soft-magnetic and mechanical properties, which facilitate their application. The amorphous alloys can be classified into two categories: classic (in the form of thin ribbons with a thickness of up to 100 μm) and bulk amorphous alloys (with a thickness greater than 100 μm). The bulk amorphous alloys are characterised by properties, which are very difficult or even impossible to achieve in the classic, ribbon-shaped, amorphous alloys.5,6 The group of bulk amorphous alloys includes: ribbons with a thick- nesses of approximately 100 μm, plates and rods with diameters of a few millimetres, and cores that can feature complex shapes.7 Although the finished amorphous alloys are in the solid state, the constituent particles are distributed in a chaotic way; their configuration is closer to that of the liquid state.8 These alloys are characterised by a lack of a long-range order and they exist in a metastable state. If a sufficient quantity of energy is delivered to these meta- stable materials, the crystallisation process will be activated; therefore, this value of energy is called the activation energy. The barriers to their crystallisation, during the rapid-quenching process from the liquid state (104–106 K/s), are mainly their high viscosity and the presence of inclusions within their volumes. The bulk amorphous alloys consist of more than three elements and they are based mostly on Pd, Zr, Ti, Al, Mg, Fe or Cu. The group with the highest prospects for applications is based on Fe. Given an appropriate com- position of this type of alloy, it is possible to obtain a material with a stable structure and excellent magnetic properties – both hard and soft. These properties are often determined by local stresses in the structure, resulting from the existence of structural defects. In the case of crystalline materials, these irregularities are point and linear defects; their counterparts in the amorphous Materiali in tehnologije / Materials and technology 50 (2016) 4, 559–564 559 UDK 67.017:669.018.25:621.74.04 ISSN 1580-2949 Original scientific article/Izvirni znanstveni ~lanek MTAEC9, 50(4)559(2016) materials are free volumes and quasidislocational di- poles. Defects are usually the result of the production pro- cess itself, being a by-product of the rapid solidification, "freezing" the structure. The resulting free volumes faci- litate short- and long-distance movement of the atoms within the systems of atomic pairs.8,9 The free volumes created in a relatively slow solidification process, below the glass transition temperature, have the ability to create cluster systems. These clusters are systems with a low stability and, as a result of the atomic movement, they disintegrate into simpler, two-dimensional systems called quasidislocational dipoles.10,11 A direct observation of the structural defects of an amorphous structure is very diffi- cult; therefore, the indirect method is used. This method involves observation and analysis of the initial magneti- sation curve, according to the H. Kronmüller theorem.12 On the basis of the modified Brown micromagnetism theorem13, H. Kronmüller showed that structural defects in the ferromagnetic materials with soft magnetic proper- ties are the source of internal stresses, causing a locally inhomogeneous distribution of the magnetisation vector. The presence of these stresses in an amorphous material prevents the achievement of the state of ferromagnetic saturation, even under the influence of a strong magnetic field.12 The magnetisation of the amorphous alloys within high magnetic fields, in the so-called "approach to the ferromagnetic saturation" region, could be described using the following Equation (1):9    0 0 1 2 0 1 2 1 0 1 2 0 21M H M a H a H a Hs ( ) ) ) ) / /= − − − ⎡ ⎣⎢ ⎤ ⎦⎥ + +b H( ) / 0 1 2 (1) where: Ms – spontaneous magnetization; μ0 – magnetic per- meability of a vacuum; H – magnetic field; ai – direc- tional coefficients of the linear fit (free volumes and linear defects i = 1/2, 1, 2); b – directional coefficient of the linear fit. The b coefficient is calculated on the basis of the spin-wave theorem and connected with the spin-wave stiffness parameter (Dsp) with the following relation: 14–16 b g D k T g= ⎛ ⎝ ⎜ ⎞ ⎠ ⎟354 1 40 3 2 1 2. ( ) / / B sp B Bπ (2) where: μB – Bohr magneton, kB – Boltzmann constant, g – gyro- magnetic coefficient, T – temperature. The strongest influence on the stresses, connected with the existence of free volumes, is observed for the a1/2 coefficient: a H A r r G V N A 1 2 0 1 2 0 2 2 2 3 20 1 1 2 / /) ( )   = + − ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ ⋅ ⋅ ex s Δ ex s 0 1 2 0 1 2 1 M H ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ / /( ) (3) where: N – volume density of point defects, V – volume change caused by point defects, Aex – exchange constant, r – Poisson number, G – transverse elasticity modulus, s – saturation magnetostriction. The elements a1/μ0H and a2/(μ0H)2 are connected with the linear, elongated agglomerates of free volumes, in which the internal stress field is equivalent to the field created by linear dislocation dipoles with a width of Ddip, the effective Burgers vector beff and the surface density of N. The stresses related to these defects cause a non-collinear distribution of the magnetic moments in their vicinity:17 a H G V Nb M D H 1 0 0 2 2 2 2 0 211 1 1    ) . ( ) ) = − s eff s dip (4) This situation exists, when l DH dip − <1 1, and lH is the exchange distance given with the following equation:18,19 l A HMH = ⎛ ⎝ ⎜ ⎞ ⎠ ⎟ 2 0 1 2 ex s / (5) In the case where l DH dip − >1 1, the dominant element influencing the magnetisation process, according to Equation (1), is a2/(μ0H)2; this is described with Equation (6): a H G V Nb M D H 2 0 0 2 2 2 2 0 20 456 1 1    ) . ( ) ) = − s eff s dip (6) In Equation (1), each separate element exerts a major influence on the magnetisation process in the approach to the ferromagnetic saturation region, in strictly defined ranges of the magnetic field. Therefore, it is possible to define the influence of structural defects, inherent in amorphous materials, on the magnetisation process within high magnetic fields. On the basis of "defined" defects, their packing density within the alloy volume can be calculated using Equations (3), (4) and (6).20 2 MATERIALS AND METHODS In this paper, results of investigations are presented for the samples obtained by injecting liquid alloy into a water-cooled copper die under a protective atmosphere of inert gas (Ar). The manufactured samples were in the form of plates with an approximate width of 10 mm and a thickness of 0.5 mm. The nominal compositions of the investigated alloys, Fe60Co10Mo2WxY8B20-x (x = 1, 2), were obtained by weighing high-purity (99.9 %) compo- nents. J. GONDRO et al.: INFLUENCE OF STRUCTURAL DEFECTS ON THE MAGNETIC PROPERTIES ... 560 Materiali in tehnologije / Materials and technology 50 (2016) 4, 559–564 The structure of the resulting alloys was investigated by means of an X-ray diffractometer. The BRUKER "ADVANCE D8" X-ray diffractometer was equipped with a Cu-K radiation source. The samples were studied within a 2 range of 30–120° with a measurement step size of 0.02° and an exposure time of 5 s per step. Measurements of magnetization were performed over a magnetic field range of 0–2 T using a vibrating sample magnetometer (VSM). 3 RESULTS AND DISCUSSION X-ray diffraction (XRD) curves for the investigated alloys are presented in Figure 1. These curves feature only one broad maximum, as characteristic of amor- phous materials. Static hysteresis loops were found to exhibit shapes typical for ferromagnetic materials, which exhibit soft magnetic properties (Figure 2). The value of the coercive field was obtained from an analysis of the static hysteresis loops, being 8705.57 A/m for the Fe60Co10W1Mo2Y8B19 alloy and 4610.88 A/m for Fe60Co10W2Mo2Y8B18 (Figure 3). From an analysis of the magnetisation as a function of magnetic-field induction curves, it was found that the magnetisation process in the Fe60Co10W1Mo2Y8B19 alloy (Figures 4 to 6), where the domain structure is not J. GONDRO et al.: INFLUENCE OF STRUCTURAL DEFECTS ON THE MAGNETIC PROPERTIES ... Materiali in tehnologije / Materials and technology 50 (2016) 4, 559–564 561 Figure 5: Curves of high-field magnetisation as a function of (μ0H)–1, for a plate-shaped sample of Fe60Co10W1Mo2Y8B19 alloy Slika 5: Krivulje visokopoljske magnetizacije kot funkcija (μ0H)–1 pri plo{~atih vzorch iz zlitine Fe60Co10W1Mo2Y8B19 Figure 2: Static hysteresis loops obtained for the investigated alloys Slika 2: Stati~ne histerezne zanke, dobljene pri preiskovanih zlitinah Figure 1: X-ray diffraction patterns for powdered as-quenched sam- ples: a) Fe60Co10W1Mo2Y8B19 and b) Fe60Co10W2Mo2Y8B18 Slika 1: Rentgenska difrakcija kaljenih vzorcev prahu: a) Fe60Co10W1Mo2Y8B19 in b) Fe60Co10W2Mo2Y8B18 Figure 4: Curves of high-field magnetization as a function of (μ0H)–½, for a plate-shaped sample of Fe60Co10W1Mo2Y8B19 alloy Slika 4: Krivulje visokopoljske magnetizacije kot funkcija (μ0H)–½ pri plo{~atih vzorch iz zlitine Fe60Co10W1Mo2Y8B19 Figure 3: Coercive filed obtained from the analysis of the static hysteresis loops for the investigated alloys Slika 3: Koercitivno polje, dobljeno iz analize stati~nih histereznih zank pri preiskovanih zlitinah present, is influenced by two types of defect: point defects, indicated, in Figure 4, by the linear relationship of magnetisation as a function of (μ0H)–1/2 over a mag- netic field range of 0.039–35 T and linear defects (called quasidislocational dipoles), indicated, in Figure 5, by the linear relationship of magnetisation as a function of (μ0H)–1) over a magnetic field range of 0.35–1.2 T. In a strong magnetic field, i.e., greater than 1.2 T, a small increase in the magnetisation is connected with the dumping of thermally induced spin waves by the strong magnetic field (Figure 6). The high-field magnetisation curves for the Fe60Co10W2Mo2Y8B18 alloy are presented in Figures 7 to 9. Similarly, in the case of this alloy, the magnetisation process is connected with the rotation of magnetic moments around the point defects (Figure 7) and linear defects (Figure 8), for which the relationship l DH dip − <1 1 was fulfilled. The further increase in the magnetisation is J. GONDRO et al.: INFLUENCE OF STRUCTURAL DEFECTS ON THE MAGNETIC PROPERTIES ... 562 Materiali in tehnologije / Materials and technology 50 (2016) 4, 559–564 Table 1: Results of the analysis of magnetisation as a function of magnetic field to the powers of –½, –1 and ½; spin-wave stiffness parameter Dspf and Ndip – density of quasidislocational dipoles Tabela 1: Rezultati preizkusa magnetizacije kot funkcije magnetnega polja na potenco –½, –1 in ½; parametra vrtilno-valovne togosti Dspf in gostote kvazidislokacijskih dipolov Ndip Composition a1/2 (T–1/2) a1 (T–1) b (T–1/2) Dspf (meVnm2) Ndip (1016m–2) Fe60Co10W1Mo2Y8B19 0.166 0.089 0.108 29 51 Fe60Co10W2Mo2Y8B18 0.611 0.040 0.085 34 30 Figure 9: Curves of high-field magnetisation as a function of (μ0H)–½, for a plate-shaped sample of Fe60Co10W2Mo2Y8B18 alloy Slika 9: Krivulje visokopoljske magnetizacije, kot funkcija (μ0H)–½ pri plo{~atih vzorch iz zlitine Fe60Co10W2Mo2Y8B18 Figure 7: Curves of high-field magnetisation as a function of (μ0H)½, for a plate-shaped sample of Fe60Co10W2Mo2Y8B18 alloy Slika 7: Krivulje visokopoljske magnetizacije, kot funkcija (μ0H)½ pri plo{~atih vzorch iz zlitine Fe60Co10W2Mo2Y8B18 Figure 6: Curves of high-field magnetisation as a function of (μ0H)½, for a plate-shaped sample of Fe60Co10W1Mo2Y8B19 alloy Slika 6: Krivulje visokopoljske magnetizacije, kot funkcija (μ0H)½ pri plo{~atih vzorch iz zlitine Fe60Co10W1Mo2Y8B19 Figure 8: Curves of high-field magnetisation as a function of (μ0H)–1, for a plate-shaped sample of Fe60Co10W2Mo2Y8B18 alloy Slika 8: Krivulje visokopoljske magnetizacije, kot funkcija (μ0H)–1 pri plo{~atih vzorch iz zlitine Fe60Co10W2Mo2Y8B18 related with the existence of the Holstein-Primakoff paraprocess (Figure 9).21,22 The parameters obtained from the analysis of the high-field magnetization curves, obtained for both alloys, are presented in Table 1. 4 CONCLUSIONS During the production process involving bulk amorphous alloys, structural relaxations occur, leading to a more stable structure. This process influences both topological (TSRO) and chemical (CSRO) short-range ordering. Changes in TSRO are irreversible and con- nected with the decreases in the volume and redistribu- tion of free volumes.23 As a result, the average distance between the atoms decreases and this, in turn, causes an increase in the atomic packing density. On the basis of the obtained results of the current investigations, it could be stated that the investigated alloys are amorphous. The value of the coercivity for Fe60Co10W2Mo2Y8B18 is half the value for the other alloy. On the basis of the magnetisation studies, carried out in strong magnetic fields, it was found that for both alloys the magnetisation process was influenced by the presence of point defects and quasidislocational dipoles. Also, the dumping of thermally induced spin waves by the magnetic field (Holstein-Primakoff paraprocess) has an influence on the magnetisation process. In the case of the Fe60Co10W2Mo2Y8B18 alloy, both the a1/2, and a1 coefficients are half the equivalent values found for the Fe60Co10W1Mo2Y8B19 alloy. Also, the value of the den- sity of the quasidislocational dipoles Ndip is almost halved for the alloy with a higher tungsten content. These values indicate a higher atomic packing density in the Fe60Co10W2Mo2Y8B18 alloy. The analysis of the high-field magnetisation curves facilitated the calcul- ation of the spin-wave stiffness parameter, Dspf, which is connected with the changes in the chemical and topo- logical atomic ordering. The higher value of this para- meter for the sample of the Fe60Co10W2Mo2Y8B18 alloy indicates a high concentration of magnetic atoms in a given volume and confirms that the alloy has a higher atomic packing density. 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