Thermal and soft magnetic properties of Co40Fe22Ta8B30 glassy particles: In-situ X-ray diffraction and magnetometry studiesAmir Hossein Taghvaei, Mihai Stoica, Ivan Kaban, Jozef Bednarik, and Jürgen Eckert

Citation: Journal of Applied Physics 116, 054904 (2014); doi: 10.1063/1.4892041 View online: http://dx.doi.org/10.1063/1.4892041 View Table of Contents: http://scitation.aip.org/content/aip/journal/jap/116/5?ver=pdfcov Published by the AIP Publishing Articles you may be interested in The soft magnetic properties of ring-shaped (Co0.6Fe0.3Ni0.1)68(B0.811Si0.189)27Nb5 bulk metallic glasses J. Appl. Phys. 113, 17A336 (2013); 10.1063/1.4800737 Role of Si in high Bs and low core-loss Fe85.2B10XP4Cu0.8SiX nano-crystalline alloys J. Appl. Phys. 112, 103902 (2012); 10.1063/1.4765718 Local structure origin of higher glass forming ability in Ta doped Co65B35 amorphous alloy J. Appl. Phys. 112, 073520 (2012); 10.1063/1.4757945 Glass-forming ability and soft magnetic properties of FeCoSiAlGaPCB amorphous alloys J. Appl. Phys. 92, 2073 (2002); 10.1063/1.1494848 New bulk amorphous Fe–(Co,Ni)–M–B (M=Zr,Hf,Nb,Ta,Mo,W) alloys with good soft magnetic properties J. Appl. Phys. 83, 6326 (1998); 10.1063/1.367811

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Thermal and soft magnetic properties of Co40Fe22Ta8B30 glassy particles:In-situ X-ray diffraction and magnetometry studies

Amir Hossein Taghvaei,1,a) Mihai Stoica,2,3 Ivan Kaban,2,4 Jozef Bednarcik,5

and J€urgen Eckert2,4

1Department of Materials Science and Engineering, Shiraz University of Technology, Shiraz, Iran2IFW Dresden, Institute for Complex Materials, Helmholtzstr. 20, 01069 Dresden, Germany3POLITEHNICA University of Timisoara, P-ta Victoriei 2 Timisoara, Romania4TU Dresden, Institute of Materials Science, 01062 Dresden, Germany5Photon Science DESY, Notkestraße 85, 22603 Hamburg, Germany

(Received 2 May 2014; accepted 23 July 2014; published online 4 August 2014)

The structural evolution of Co40Fe22Ta8B30 glassy particles has been studied by in-situ high-energy

synchrotron X-ray diffraction (XRD) upon isochronal annealing. The changes in position, intensity,

and full width at half maximum (FWHM) of the first and second diffuse maxima of the XRD

patterns suggest the occurrence of irreversible structural relaxation upon the first heating up to a

temperature close to the glass transition temperature Tg. The variations in reduced pair correlation

functions upon annealing are discussed in the frame of the topological fluctuation theory for

structural relaxation. Isochronal annealing of the Co40Fe22Ta8B30 glassy particles improves their

soft magnetic properties through decreasing the coercivity and increasing the magnetic

susceptibility, saturation magnetization, and Curie temperature. VC 2014 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4892041]

I. INTRODUCTION

Metallic glasses (MGs) exhibit outstanding physical and

mechanical behavior, owing to their unique atomic structure.

Such materials are far from metastable equilibrium due to

the formation of quenched-in defects caused by rapid

quenching.1,2 The presence of defects, such as free volume,

in the glassy state can significantly affect the mechanical

behavior. For instance, these defects can decrease viscosity

or enhance plasticity of glasses.1,3 Upon a heat treatment of

MGs at sufficiently high temperature, the atomic mobility

increases and the free energy of the system decreases toward

the metastable equilibrium through a process called struc-

tural relaxation.4 Usually, structural relaxation is accompa-

nied by variations in chemical short-range order (CSRO) and

topological short-range order (TSRO). The latter involves a

long-range rearrangement of atoms associated with the redis-

tribution and reduction of the excess free volume.2 The

decrease of the free volume upon annealing results in higher

viscosity,5 density,6 and tensile strength,7 lower plasticity,7,8

and better soft magnetic properties.9 Hence, characterization

of the excess free volume is important for understanding the

relationship between the atomic structure and properties of

MGs. The evolution of the excess free volume upon isother-

mal or isochronal annealing has been widely investigated by

density measurements,6 positron annihilation spectroscopy

(PAS),10 calorimetric measurements,4 dilatometry,11 and

X-ray diffraction (XRD)2. In-situ high-energy synchrotron

XRD is a particularly useful method to study the changes in

the atomic structure and thermal expansion of the MGs at

different temperatures.2,12

Very recently, a new Co40Fe22Ta8B30 glassy alloy with

good soft magnetic properties, higher thermal stability, and

significantly longer incubation time prior to crystallization,

compared to the well-known Co43Fe20Ta5.5B31.5 MG, has

been obtained.13 It has been found that the Co40Fe22Ta8B30

bulk metallic glass (BMG) and composites with good ther-

mal stability and excellent soft magnetic properties can be

synthesized by hot consolidation of the glassy particles

obtained by ball milling of the as-quenched ribbons.14,15 In

this paper, we examine the temperature-dependent behavior

of the Co40Fe22Ta8B30 glassy particles obtained by ball mill-

ing of the as-quenched ribbons using in-situ high-energy syn-

chrotron XRD. We study the relationship between the

reciprocal space data, structural relaxation, and thermal

expansion by analyzing the first and second diffuse peaks on

the XRD patterns measured at different temperatures.

Finally, we investigate the correlation between the soft mag-

netic properties and structural relaxation of Co40Fe22Ta8B30

glassy particles upon isochronal annealing.

II. EXPERIMENTAL PROCEDURE

An alloy ingot with a nominal composition of

Co40Fe22Ta8B30 (at. %) was obtained by arc-melting of the

constituent elements with purity of 99.5% under a

Ti-gettered Ar atmosphere. Fully glassy ribbons (width of

3.5 mm, thickness of 30 lm) were prepared by a single-roller

B€uhler melt-spinner on a copper wheel at 41 m/s tangential

wheel velocity under an argon flow. Glassy Co40Fe22Ta8B30

particles were synthesized by ball milling of the melt-spun

ribbons in a planetary ball mill (Retsch PM4000) using hard-

ened steel balls with 10 mm diameter. The milling process

was conducted for 1 h at a ball-to-powder weight ratio of

15:1 and a rotation speed of 200 rpm. Due to a short milling

a)Author to whom correspondence should be addressed. Electronic mail:

amirtaghvaei@gmail.com.

0021-8979/2014/116(5)/054904/8/$30.00 VC 2014 AIP Publishing LLC116, 054904-1

JOURNAL OF APPLIED PHYSICS 116, 054904 (2014)

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time, the ribbons were fractured into particles with a flake-

like shape and size distribution between several microns to

several hundreds of microns. To minimize the temperature

rise, the milling was interrupted after each 15 min of the

work and the vials were cooled down at a bath of liquid

nitrogen for 20 min. All sample handling was carried out in a

glove box under a purified argon atmosphere (less than

1 ppm O2 and H2O).

In-situ XRD was carried out at different temperatures

using a monochromatic synchrotron radiation with a photon

energy of 100 keV (k¼ 0.0124 nm) in a transmission geome-

try at the BW5 beam-line of DORIS III electron-positron

storage ring (DESY, Hamburg, Germany). The samples were

sealed under vacuum in a quartz capillary and then heated

and cooled at a constant rate of 20 K/min in a computer-

controlled Linkam hot-stage. The XRD patterns were

recorded using a two-dimensional (2D) X-ray detector

(Perkin Elmer 1621). The background scattering was sub-

tracted directly from the 2D XRD patterns and the resulting

intensities were integrated using the FIT2D software pack-

age.16 The integrated intensities were corrected for polariza-

tion, sample absorption, fluorescence contribution and

inelastic scattering using the PDFgetX2 software.17 The total

structure factors S(Q) were determined from the normalized

elastically scattered intensities according to the Faber-Ziman

formalism18 (Q¼ 4p sin h/k, where h is the half of the scat-

tering angle and k is the wavelength). The reduced pair dis-

tribution function, G(r), was calculated by a sine Fourier

transform of S(Q) as:

G rð Þ ¼ 2

p

ðQmax

Qmin

Q S Qð Þ � 1ð Þsin Qrð ÞdQ: (1)

The thermal stability of the as-quenched and ball-milled

Co40Fe22Ta8B30 glasses was determined by a differential

scanning calorimeter (DSC, NETZSCH 404) at a heating

rate of 20 K/min under a flow of high-purity argon.

The hysteresis loops and the saturation magnetization

were recorded by a vibrating sample magnetometer (VSM)

at ambient temperature. The thermomagnetic behavior and

the Curie temperature Tc of the samples were determined

using a Faraday magnetometer at a heating rate of 10 K/min.

The coercivity was measured using a Foerster Coercimat

under an applied field sufficient to saturate the samples. In

order to avoid the rotation of the particles in the applied

magnetic field, the particles were encapsulated in silver cups

and glued. All magnetic properties were measured under DC

magnetic field.

III. RESULTS

Fig. 1 shows the room temperature structure factors S(Q)

of the as-quenched and ball-milled Co40Fe22Ta8B30 ribbons.

As it can be observed, the amorphous structure of the as-cast

ribbons is preserved after 1 h of ball milling. The DSC curves

measured at a constant heating rate are plotted in Fig. 2. The

ribbons and the particles exhibit an endothermic event corre-

sponding to the glass transition at a temperature Tg¼ 893 K.

Crystallization in both samples proceeds through three exo-

thermic peaks with the onset of the first crystallization event

at Tx¼ 967 K. Hence, the Co40Fe22Ta8B30 glassy ribbons and

particles exhibit a large supercooled liquid region

(DTx¼ Tx� Tg) of 74 K prior to the crystallization and conse-

quently a high thermal stability. Table I lists the thermal pa-

rameters of the Co40Fe22Ta8B30 glass in the as-quenched and

ball-milled state, as measured by DSC. It is seen that similar

to the crystallization temperature, the crystallization enthal-

pies did not change after ball milling. This indicates that the

amorphous phase remained completely after 1 h of milling, in

a good agreement with the XRD results (Fig. 1). Despite the

same crystallization enthalpies, the DSC plot of the ball-

milled ribbons shows a larger area under the broad exother-

mic peak appearing before the onset of Tg (see the inset of

Fig. 2). The thermal parameters of 1 h milled ribbons are very

similar to those determined recently for glassy particles

obtained by ball milling of the Co40Fe22Ta8B30 ribbons for

3 h at the same milling condition (see Table II in Ref. 14).

Fig. 3 shows the M-H hysteresis curves of the as-

quenched, ball-milled and annealed Co40Fe22Ta8B30 glassy

FIG. 1. Room temperature XRD total structure factors S(Q) of the as-

quenched and ball-milled Co40Fe22Ta8B30 glassy ribbons.

FIG. 2. DSC plots of the as-cast and ball-milled Co40Fe22Ta8B30 glassy

ribbons.

054904-2 Taghvaei et al. J. Appl. Phys. 116, 054904 (2014)

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ribbons. The annealing was performed by isochronal heating

of the Co40Fe22Ta8B30 glassy particles up to 873 K and sub-

sequent cooling of the particles to ambient temperature with

the same heating and cooling rate of 20 K/min. The as-

quenched ribbons exhibit a rectangular hysteresis curve due

to a small demagnetizing factor with a saturation magnetiza-

tion of 40 Am2/kg (saturation polarization Js¼ 0.5 T) and a

coercivity of 0.8 A/m, indicating good soft magnetic proper-

ties. The small demagnetizing factor of the ribbons origi-

nates from their small thickness compared to their width and

length.19 It has been shown that the coercivity of the

Co40Fe22Ta8B30 glassy ribbon can reach an extremely low

value of 0.3 A/m by suitable annealing.14 Such value is very

close to coercivity of the zero magnetostrictive CoFeMoSiB

amorphous ribbons (Hc� 0.4 A/m (Ref. 20)) and signifi-

cantly lower than that of conventional CoFeSiB amorphous

ribbons (Hc� 5 A/m) with a low thermal stability (DTx

� 20 K).21 According to Fig. 3, the ball milling of the

Co40Fe22Ta8B30 ribbons for 1 h does not influence the satura-

tion magnetization, while it strongly affects the hysteresis

curve through distortion of the rectangular shape.

Based on Fig. 3, the hysteresis loop of the glassy

Co40Fe22Ta8B30 particles becomes more rectangular after the

isochronal annealing. In addition, the saturation magnetization

increases about 2.5% after annealing. Table II lists the mag-

netic properties of the as-quenched Co40Fe22Ta8B30 ribbons,

as-milled and relaxed particles. It is seen that the coercivity

increases noticeably from 0.8 A/m to 70 A/m after 1 h milling.

However, the subsequent isochronal annealing decreases sig-

nificantly the coercivity of the particles to 14 A/m, indicating

the improvement of soft magnetic behavior. Moreover, it

enhances the magnetic susceptibility featured by the near-

rectangular shape of the hysteresis loop (Fig. 3).

Fig. 4 illustrates the thermomagnetic behavior of the

Co40Fe22Ta8B30 glassy alloy measured at a heating rate of

10 K/min in the as-quenched, ball-milled and subsequently

annealed states. As the figure shows, for each sample, the

magnetization drops to zero through a single inflexion point

corresponding to the Curie temperature of the amorphous

phase Tcam. In order to accurately determine the Tc

am, the

Herzer approach was used.22 Table II lists the values of Tcam

for the as-quenched ribbons and particles. The Tcam increases

about 5.8% after isochronal heating, similar to the increase

in the saturation magnetization upon annealing (Table II).

IV. DISCUSSION

As shown above, ball milling and subsequent isochronal

annealing significantly affect the magnetic properties of the

Co40Fe22Ta8B30 glassy alloy. The evolution of the magnetic

properties upon ball milling or heat treatment can be corre-

lated to the changes in the atomic arrangement and concen-

tration of the free volume. According to Table II, a

noticeable increase of the coercivity after 1 h of ball milling

can be mainly attributed to the increase of free volume or re-

sidual stress. During ball milling, deformation of the glassy

phase can be localized in narrow shear bands, which usually

FIG. 3. Hysteresis curves of the glassy Co40Fe22Ta8B30 alloy in the different

states, including the as-cast ribbons, as-milled and relaxed particles.

TABLE II. Magnetic properties of the Co40Fe22Ta8B30 glassy alloy in the

form of as-cast ribbons, 1 h milled and relaxed particles. Ms is the saturation

magnetization, Tc denotes the Curie temperature and Hc is the coercivity.

The measurement errors are within 60.5 Am2/kg, 61.5 K, and 60.1 A/m

for saturation magnetization, Curie temperature, and coercivity,

respectively.

Sample Hc (A/m) Tc (K) Ms (Am2/kg)

As-quenched ribbon 0.8 410 40

1 h milled particles 70 409 40

Relaxed particles 14 433 41

FIG. 4. Thermomagnetic behavior of the as-cast ribbons, ball-milled and

relaxed Co40Fe22Ta8B30 glassy particles.

TABLE I. Thermal stability parameters of the as-cast and milled

Co40Fe22Ta8B30 glassy ribbons measured by DSC at heating rate of 20 K/

min. DHi (i¼ 1–3) is the enthalpy of each crystallization event, Tg is the

glass transition temperature, Tx1 is the onset of the first crystallization tem-

perature and DTx is the width of the supercooled liquid region. The accuracy

of the experimental data lies within 60.5 J/g and 61.5 K for the enthalpies

and temperatures, respectively.

sample

H1

(J/g)DH2

(J/g)DH3

(J/g)DTg

(K)

Tx1

(K)

DTx¼Tx1�Tg

(K)

As-cast ribbon 48.5 14.5 6.7 893 967 74

1 h milled 48.5 14.5 6.7 894 967 73

054904-3 Taghvaei et al. J. Appl. Phys. 116, 054904 (2014)

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are characterized by a lower atomic density and conse-

quently have much more free volume, compared to non-

deformed regions.23,24 It has been suggested that the excess

free volume can produce line defects called quasi dislocation

dipoles, QDDs, which are the main source of stress in the

glassy phase.25 The QDDs may act as the pinning centers for

the movement and rotation of magnetic domain walls and

consequently increase the coercivity. However, the micro-

scopic image of the milled ribbons (not shown here) did not

reveal any shear bands on the particles surface probably due

to a very brittle nature of the Co40Fe22Ta8B30 glassy alloy,

particularly at very low temperature and high strain rate de-

formation (cryogenic ball milling). It is known that for the

MGs with a high concentration of metalloids, due to the

strong covalent bonding between the constituent elements,

the fracture usually occurs in a brittle mode and the samples

shatter apart into many small fragments without any sign of

shear bands on the lateral surface.26 The absence of shear

bands on the surface of the Co40Fe22Ta8B30 glassy particles

suggests that free volume content of the as-quenched ribbons

may not be changed noticeably upon ball milling. Hence, the

observed increase in coercivity after milling is mainly attrib-

uted to the enhanced residual stress. Our previous results

indicated that the ball milling of the Co40Fe22Ta8B30 glassy

ribbons can produce a long-range stress field in the glassy

structure.27 This effect can enlarge the area under the broad

exothermic peak designated before the onset of Tg, as shown

in the inset of Fig. 2. The appearance of this peak indicates

that the enthalpy of the glass decreases owing to structural

relaxation, decreasing in stress and annihilation of the

quenched-in free volume upon heating.

As indicated in Figs. 3 and 4, ball milling does not

change the saturation magnetization and Curie temperature

of the ribbons. This indicates that the short term milling did

not cause crystallisation of the ribbons, in a good agreement

with the XRD and DSC results (Figs. 1 and 2). The

decreased rectangular tendency of the hysteresis loop after

milling is due to a larger demagnetizing factor of the par-

ticles compared to the ribbons, as well as the stress-induced

anisotropy caused by ball milling.

The structural relaxation upon isochronal annealing

could enhance the spin-exchange interaction through decreas-

ing the average distance between magnetic atoms,28 which

improves both the saturation magnetization and Curie

temperature of the milled ribbons (Fig. 3 and 4). At the same

time, reduction of the quenched-in free volume and the

stress-induced anisotropy upon isochronal annealing decrease

significantly the coercivity of the particles to 14 A/m.

However, coercivity of the relaxed particles is still more than

one order of magnitude larger than that of the as-quenched

ribbons (Hc¼ 0.8 A/m) owing to the larger surface roughness

of the particles. The fracture of the ribbons during ball mill-

ing can increase the surface irregularities, particularly on the

fractured area.29 The increase of the surface roughness can

enhance the magnetic domain wall pinning and consequently

increase the coercivity. Moreover, the existence of air gaps

between the particles as the second non-magnetic phase

increases the stray field and consequently the coercivity.9 It is

worth noting that the values for magnetization and Curie tem-

perature of 1 h milled ribbons are comparable to those meas-

ured recently for 3 h milled Co40Fe22Ta8B30 glassy ribbons

(Ms¼ 42.4 Am2/kg and Tc¼ 412 K).14 However, a larger

coercivity was reported for 3 h milled glassy particles

(Hc¼ 300 A/m14), probably due to the enhanced residual

stress and surface roughness by increasing the milling time,

which results in stronger domain wall pinning.

The structural relaxation in the Co40Fe22Ta8B30 glassy

particles upon isochronal annealing can be investigated using

in-situ XRD technique. For this purpose, the particles were

heated up to 873 K, i.e., 20 K below the onset of the glass

transition (Tg¼ 893 K); then the temperature was decreased

to 322 K and increased again up to 870 K. The positions of

the center of mass for the first diffuse maximum (Q1) and the

second diffuse maximum (Q2) of the structure factor S(Q)

were determined by fitting the curves with a pseudo-Voigt

function.

Fig. 5 shows the temperature dependence of Q1 and Q2

during the heating-cooling cycles. It is noteworthy that both

Q1 and Q2 corresponding to the first heating lie below the re-

spective values measured during the cooling and the second

heating. The difference in the position of the diffuse maxima

is well above the determination error of the peak positions.

Thus, the temperature dependences of both Q1 and Q2 clearly

indicate the occurrence of irreversible structural changes in

the temperature interval between about 750 K and 870 K

upon the first heating. As the temperature dependences for

Q1 and Q2 remain unchanged during subsequent heating and

cooling, the changes observed during the first cooling are

FIG. 5. (a) Position of the first diffuse

maximum Q1 and (b) second diffuse

maximum Q2 of Co40Fe22Ta8B30

glassy particles upon different temper-

ature cycles.

054904-4 Taghvaei et al. J. Appl. Phys. 116, 054904 (2014)

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supposed to be related to the structural relaxation of the ball-

milled amorphous ribbons.

It has been shown that in the temperature range where

structural changes are absent or negligible, the linear coeffi-

cient of thermal expansion a of an amorphous alloy can be

determined from the slope dQ1(T)/dT.30 The best linear fit of

the temperature dependence for the Q1 measured during the

second heating of our particles gives a¼ 11.7� 10�6 K�1.

This value is very close to that of Co43Fe20Ta5.5B31.5 BMG

(a¼ 11� 10�6 K�1), which has a similar composition to our

glassy alloy.31 It is interesting that the slope dQ1(T)/dT is

almost the same for the as-milled and heat treated

Co40Fe22Ta8B30 particles (Fig. 5(a)).

The occurrence of structural relaxation upon isochronal

annealing can be further investigated according to variations

in the height and width of the first and second diffuse max-

ima in the XRD scattering intensity. As it is seen in Fig. 6,

the heights of both peaks for the glassy Co40Fe22Ta8B30 par-

ticles increase after first heating up to 873 K. During the first

heating, the observed temperature dependencies result from

the superposition of two effects: intensity increase due to the

relaxation and intensity decrease due to the enhanced ther-

mal oscillations of atoms.32,33 During the second heating, in-

tensity of the relaxed glassy particles decreases because of

the thermal oscillations, which can be described by the

Debye-Waller factor.33 Hence, the variations observed in the

height of the diffuse maxima, besides their positions, could

be related to an irreversible structural relaxation upon the

first heating cycle. Moreover, the variations of full width at

half maximum (FWHM) of the first diffuse halo during the

thermal cycles indicate the irreversible changes correspond-

ing to structural relaxation (Fig. 7). During the first heating,

the FWHM increases up to T¼ 673 K and then starts to

decrease. Such variations originate from the superposition of

thermal oscillations and irreversible structural relaxation.

The initial increase of FWHM results from thermal oscilla-

tions, while the subsequent decrease is attributed to the

occurrence of structural relaxation and the elimination of

fluctuations in the inter-atomic distance.34 During the cool-

ing and second heating cycles, the plots show lower FWHM,

compared to the first heating cycle, which reversibly changes

as a result of thermal oscillations. The FWHM at the same

temperature T¼ 322 K decreased by about 3% after the first

heating.

Fig. 8 compares the S(Q) functions of the

Co40Fe22Ta8B30 glassy particles calculated for the first and

second heating cycles at T¼ 322 K. According to this figure,

the first diffuse maximum becomes sharper and its height

increases by about 2.7% after the first heating due to the

FIG. 6. Height of the first and second diffuse maxima of the glassy

Co40Fe22Ta8B30 particles upon the different temperature cycles.

FIG. 7. Variations of the FWHM corresponding to the first diffuse maximum

of the glassy Co40Fe22Ta8B30 particles during different temperature cycles.

FIG. 8. Structure factors S(Q) of the Co40Fe22Ta8B30 glassy particles calcu-

lated at the first and second heating cycles at T¼ 322 K and the correspond-

ing difference curve, DS(Q)¼ S(Q)relaxed(322 K)� S(Q)milled(322 K).

054904-5 Taghvaei et al. J. Appl. Phys. 116, 054904 (2014)

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structural relaxation. The structural changes upon isochronal

annealing can be further assessed by calculating the differ-

ence curve DS(Q) at T¼ 322 K, which is plotted in the lower

part of Fig. 8. The difference curve obviously shows that the

annealing enhances the amplitude of the S(Q) oscillations,

manifesting the changes in the atomic structure of the

Co40Fe22Ta8B30 MG after annealing.

The structural relaxation study of the ball-milled ribbons

after isochronal annealing was further carried out in the real

space. Fig. 9(a) compares the reduced pair distribution func-

tions G(r) of the Co40Fe22Ta8B30 glassy particles calculated

for the first and second heating cycles at T¼ 322 K. In addi-

tion, the difference curve, DG(r)¼G(r)relaxed�G(r)milled, is

depicted in Fig. 9(b). The isochronal annealing increases the

intensity of the G(r) peaks, particularly the first coordination

shell, without any significant change in the shape of the peak.

For instance, the intensity of the main G(r) peak increases by

about 2.5% after annealing. Annealing sharpens also the min-

ima on the G(r) functions, suggesting that the local topological

disorder of the glassy phase decreased upon annealing. In the

first coordination shell, DG(r) is negative both at the short and

long inter-atomic distances, however, it is positive around the

center of the main G(r) peak (see Fig. 9(b)). This means that

structural relaxation in the Co40Fe22Ta8B30 glassy particles is

accompanied by elimination of short and long inter-atomic dis-

tances. In other words, annealing decreases the fluctuation for

distribution of the atomic-level hydrostatic stress.35

It has been suggested that the changes in Q1 after

annealing of a MG are in line with the variations in the

excess free volume.30 According to the X-ray scattering

theory for one-component system, the position of the first

diffuse maximum Q1 has an inverse relationship with the

interatomic distance r:36

Q1 ¼ 2kp=r; (2)

where k is a constant.36 If the structural changes in a disor-

dered alloy are sufficiently small upon annealing, the

increase in Q1 might imply the decrease of the average inter-

atomic distance and consequently the atomic volume due to

the decrease in the excess free volume.30 If we assume that

the atomic arrangement of a MG does not change signifi-

cantly during structural relaxation, the volume decrease

caused by reduction of the excess free volume can be equiva-

lent to the decrease in the volume obtained by cooling of the

MG. In other words, the changes in the atomic structure due

to decrease of the free volume should resemble those

observed upon reversible cooling for a same percentage of

the volume decrease. If k in Eq. (2) remains constant upon

structural relaxation, the volume decrease of the

Co40Fe22Ta8B30 MG between the first and the second heat-

ing cycles, according to Fig. 5(a), is around 0.25% at

T¼ 322 K. In addition, the volume shrinkage during the

cooling from 393 K to 322 K (DT¼ 71 K), considering

ath¼ 35.1� 10�6 K�1 for the Co40Fe22Ta8B30 MG, is

0.25%. Fig. 9(b) also shows the difference between the G(r)

functions of the Co40Fe22Ta8B30 glassy particles calculated

at 393 K and 322 K for the second heating cycle. As can be

observed, the difference curves corresponding to structural

relaxation and cooling are considerably different, particu-

larly beyond the first coordination shell. This result indicates

that compared to reversible thermal expansion or contrac-

tion, the configuration of atoms noticeably changes during

structural relaxation. Hence, the above assumption (constant

k) is not justified and the excess free volume of the

Co40Fe22Ta8B30 MG could not be calculated using the corre-

lation between Q1 and the atomic volume. Similar conclu-

sion has been attained recently after investigating the free

volume changes in Pd40Cu30Ni10P20 BMG upon annealing.32

The observed extensive atomic rearrangements during struc-

tural relaxation may originate from recombination of the

liquid-like atomic sites corresponding to the dilatational sites

(negative density fluctuation, n-type) and compressive sites

(positive density fluctuation, p-type) in the amorphous struc-

ture.35,37 According to the topological fluctuation theory, a

long-range stress field can be produced in the MG by the

atomic-level local density fluctuations in n-type and p-type

regions.35,38 In this case, the changes in G(r) upon annealing

are proportional to its second derivative as:35

DG � � 1

2c2@2G0 rð Þ=@r2 hP2imilled � hP2irelaxed

� �; (3)

FIG. 9. (a) Reduced pair distribution function G(r) of the Co40Fe22Ta8B30

glassy particles calculated at the first and second heating cycles at

T¼ 322 K; (b) comparison of the difference curve for structural relaxation

upon first heating cycle (DG(r)¼G(r)relaxed(322 K)�G(r)milled(322 K)) with

that for volume shrinkage (DG(r)¼G(r)relaxed(322 K)�G(r)relaxed (393 K)) by

the temperature decrease (DT¼ 71 K).

054904-6 Taghvaei et al. J. Appl. Phys. 116, 054904 (2014)

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where hP2i is the fluctuation of the atomic-level hydrostatic

pressure, G0(r) is the reduced pair correlation function of a

part with P¼ 0, and c is a materials dependent factor which is

constant beyond the first peak of G0(r). Fig. 10 compares

the experimentally calculated DG(r) at T¼ 322 K with

�@2G0ðrÞ=@r2, which was estimated by using the second de-

rivative of Gmilled(r) for G0(r).35 The two plots in Fig. 10 have

different scale factors and were scaled to agree at larger inter-

atomic distances. From Fig. 10, DG(r) changes directly with

�@2G0ðrÞ=@r2, indicating positive hP2imilled � hP2irelaxed .

Hence, the width of distribution of atomic-level hydrostatic

pressure decreases after annealing of the Co40Fe22Ta8B30

glassy particles, as mentioned above. The discrepancies

between the plots below the 0.6 nm in Fig. 10 can be attrib-

uted to the phase shift between the n-type and p-type regions,

which is usually constant for larger atomic separations.35 It

should be mentioned that the changes in G(r) due to structural

relaxation do not show a good agreement with the first deriva-

tive of G(r) (not shown here). Compared to the topological

fluctuation theory, which considers both the positive and neg-

ative local density fluctuations, the free volume theory consid-

ers only the negative density fluctuations (free volume sites).

In other words, changes in G(r) should be related to the first

derivative.39 Therefore, the structural relaxation in the

Co40Fe22Ta8B30 glassy particles upon isochronal annealing is

assumed to be better explained according to the topological

fluctuation theory.

V. CONCLUSIONS

The thermal behavior of the Co40Fe22Ta8B30 glassy par-

ticles during isochronal annealing below the glass transition

temperature Tg was studied by in-situ high-energy synchro-

tron XRD. The structural changes upon isochronal annealing

were studied in the reciprocal space through the analysis of

positions, intensities and FWHM of the first and second dif-

fuse maxima. It was demonstrated that compared to the re-

versible thermal expansion or contraction, the relative

arrangement of atoms significantly changes during structural

relaxation. As a result, the excess free volume of the

Co40Fe22Ta8B30 MG could not be determined according to

the changes in position of the first diffuse maximum and its

correspondence with the atomic volume. Analysis of the

reduced pair correlation functions indicated that structural

relaxation was accompanied by decreasing the fluctuation of

the distribution of the atomic-level hydrostatic stress.

Isochronal annealing of the Co40Fe22Ta8B30 glassy particles

below Tg noticeably improved their soft magnetic properties

through decreasing the coercivity and increasing the mag-

netic susceptibility and Curie temperature.

ACKNOWLEDGMENTS

A. H. Taghvaei is thankful to IFW Dresden for the

support of his stay and research in the frame of PhD study at

the Institute for Complex Materials. Parts of this research

were carried out at the light source DORIS III at DESY, a

member of the Helmholtz Association (HGF).

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