Magnetic susceptibility of Al-Co-Ce alloys
at high temperatures
S. Uporov, N. Uporova, V. Sidorov, K. Shunyaev*
Ural State Pedagogical University, Ekaterinburg, Russia
*Institute of Metallurgy UD RAS, Ekaterinburg, Russia
Abstract. In this work magnetic susceptibility of Al91-xCo9Cex (1<x<11 at.%) and Al91-xCoxCe7 (1<x<11 at.%) alloys was investigated by Faraday’s method in the wide temperature (T=300-2000K) and field (B=0.6-1.2T) ranges. The abnormal behavior of susceptibility above melting point of Al2R compound is discovered. The magnetic susceptibility concentration curves for quasybinary systems Al-Ce (XCo = 9 at.%) and Al-Co (XCe = 7 at.%) were plotted. It was found that χ=f(Ce) dependences have oscillating form similar both in solid and liquid states; while for χ=f(Co) susceptibility practically does not depend on Co content. The existence of Al2REM quasimoleculars is highly probable in these alloys and their destruction starts only above melting point of Al2REM compound. Magnetic properties of the alloys depend on behavior of such quasimoleculars – creation of chains, nets etc. The estimation of some parameters for such chains and nets, as well as for electronic characteristics of the alloys is given.
Introduction
Aluminum alloys with cobalt and cerium are of permanent interest due to their unique physical properties, especially in amorphous and nano-crystalline states (amorphous samples can be prepared by rapid quenching the melt with rather low cooling rates of 104-105 K/s [1]). However, the mechanism of glass formation in these alloys differs from those for alloys with deep eutectic – the concentration region of high glass-forming ability is shifted from eutectic composition to the first intermetallic compounds with high melting points [2].
Using DSC it was shown that Al-TM-REM amorphous alloys overcome 2-step crystallization, as a rule [2,3]. In crystal state such phases as α-Al, Al11REM3, Al3TMand a small part of some ternary compounds were identified by X-rays [2,3]. These facts can be taken as an evidence of microheterogeneous melts states before quenching. This idea is confirmed by viscosity measurements made in [4]. It was stated, in particular, that homogenization processes in Al-TM-REM melts take place at high overheating above liquidus and long-time isothermal expositions only.
Magnetic studies at low temperatures demonstrate rather complicated electronic structure of these objects [5]. As for high temperatures, magnetic properties of Al-Co-Ce alloys are practically unknown. Thus the aim of the work was the investigation of magnetic susceptibility behavior for glass forming Al91-xCo9Cex (1<x<11 at.%) andAl93-xCoxCe7 (0<x<13 at.%) alloys in wide temperature and field ranges including solid and liquid states.
Experiment
The crystal samples for susceptibility investigation were prepared from pure aluminum (99,999%) and certificated Al11Ce3 and AlCo compounds by re-melting in vacuum at 2000 K for one hour. Phase control wasmade by X-rays and chemical composition was analyzed using atom emission ICP spectrometer. Oxygencontent before and after experiments was determined also. Cobalt and cerium concentration ranges correspond to high glass forming ability of alloys, according to [6,7].
Magnetic susceptibility χ was measured by Faraday’s method in BeO crucibles at the equipmentdescribed in [8]. The chamber was firstly de-gazed to 10-3 Pa and then filled in with helium of high purity up to 1,2*105Pa. The experiments were made during heating and subsequent cooling in the temperature range 300 to 2000 K and magnetic fields B = 0,6 – 1,3 T. The temperature was changed in steps of10 to 15 degrees and with an isothermal exposition during 5-10 min at each temperature. Both liquid and crystalline phases were studied with an accuracy of 1.5 %.
Results
Typical temperature dependences of magnetic susceptibility for Al-Co-Ce alloys are presented in Figs. 1–2.
Fig. 1. Temperature dependencies of magnetic susceptibility for quasibynary alloys Al-Ce(XCo = 9 at.%): 1 at.% Ce (●, ○); 2 at.% Ce (▲, ∆); 3 at.% Ce (♦, ◊). (+3; +1.5 – curves shift along vertical axis). (●,▲,♦) – heating, (○, ∆, ◊) – cooling.It was found that in the range T = 300-800 K magnetic susceptibility decreases follow Curie-Weiss law and after that remains practically constant up to 1550 Kfor all quasibynary Al-Ce (XCo=9 at.% ) and Al-Co (XCe=7 at.%) alloys. Above 1600 K the drastic abnormal increase of susceptibility was discovered (see Figs. 1, 2). At the same time, the cooling curve coincides with heating one for all the compositions, i.e. no hysteresis was fixed.
Fig. 2. Temperature dependencies of magnetic susceptibility for quasibynary alloys Al-Co(XCe= 7 at.%): 0 at.% Co (●, ○); 1 at.% Co (▲, ∆); 2 at.% Co (♦,◊). (+2; +4 - curves shift along vertical axis). (●,▲,♦) – (●,▲,♦) – heating, (○, ∆, ◊) – cooling.Susceptibility concentration curves have similar forms both in solid and liquid states: nonmonotonous in case of χ = f(%Ce) (Fig. 3) and practically constant in case of χ = f(%Co) (Fig. 4).
Fig. 3. The influence of cerium on magnetic susceptibility for quasybinary Al-Ce (X =9 at.%) alloys: “Δ” – (T = 300 K); “ж” – (T = 500 K); “”– (T=1100K); “o” – (T=1500K).Fig. 4. The influence of cobalt on magnetic susceptibility for quasybinary Al-Co (X =7 at.%) alloys: “Δ” – (T = 300 K); “ж” – (T = 500 K); “+”– (T=1100K); “o” – (T=1500K).
This fact allows us to make a conclusion that cobalt exists in nonmagnetic state in all investigated Al-Co-Ce alloys and its contribution into total magnetic susceptibility of alloys is negligible. The similar nonmagnetic state for 3d-transition metals in aluminum were observed previously in papers [9, 10].
Let us mention also the existence of susceptibility field dependences χ = f(B) at all investigated temperatures (Figs. 5, 6).
Fig. 5. The dependencies of magnetic susceptibility vs applied magnetic field for some alloys of quasybinary system Al-Ce.Fig. 6. The dependencies of magnetic susceptibility vs applied magnetic field for some alloys of quasibinary system Al-Co.
Discussion
According to the results obtained, the structure of the samples can be represented asparamagnetic aluminum matrix with the inclusions of microparticles consisting of AlxREMyquasymolecules. Thus microparticles are characterized by specific magnetic ordering, the total susceptibility of the alloys can be approximated by
(1)
In eq. (1) N is the number of particles per mass unit and Mo is the average magnetic moment ofone particle. The first term corresponds to superparamagnetic particlesand the second describesthe susceptibility of the remaining paramagnetic matrix.
The so-called “generalized” Curie-Weiss law can be used for the second term
(2)
here C is the Curie constant, Θ- the paramagnetic Curie temperature and χ0 - the temperatureindependentsusceptibility depending mainly on density of electrons states at the Fermi level.
The function f (x) in eq. (1) is the derivative of Langevin function [12]:
, (3)
From measurements at the fields B1, B2 and at two temperatures T1, T2 one can according to eq.(1) obtainthequantity
(4)
where
,,,(5)
Since the value of a is determined from the experimental data, x1 can be deduced from eq. (5).For investigated Al-Co-Ce alloys the solution arrives forx1 = 3.8-4.3. The value of x1 depends slightly onT2 and B2. From eq. (5) one can obtain the average magnetic moment per superparamagnetic particle Mo = 2000-2125 µB. Knowing Moit becomes possible to estimatetheeffective number of “noncompensated” magnetic moments in the particle n using equationMo = n * μeff, where μeff is the effective magnetic moment per molecular (atom) in superparamagnetic particle. The structure and composition of superparamagnetic particles are unknown, however, the existence of Al2Ce, Al3CeorAl11Ce3 compounds is highly probable. Supposing that the magnetic moment of AlxREMy quasimolecular is close to μeff≅2.5 μB, one gets n1≅800-850. If µeff≅1.1 µB (like in case of Al11Ce3) n2=1820-1930. But without knowing the dimension of the particle and structure of itscore, it is not possible to estimate linear sizes of superparamagnetic particles correctly.
The stability of the solution (4) means that magnetic moment per particle Modoes not depend ontemperature and applied field. Thus the mass density N of superparamagnetic particles can be determinedthrough
(6)
TheobtainedvalueN≅ 2,3815g-1seems to be very smallandthatiswhysuchsuperparamagneticparticlescannotberegisteredusing standard X-ray diffraction method.
To calculate some electronic characteristics for Al-Co-Ce alloys, the experimental χ(T) curves were fitted by “generalized” Curie-Weiss law (2) in the rangeT = 300-800 K. It was possible because χ(T) curves were obtained in magnetic field B = 1 T, when the first term in eq. (1) issmallerthanthesecondterminanorder
Density of states at Fermi level N(EF)can be derived from temperature independent term χ0 in eq. (2)
here NA– Avogadro number, M – molar mass, ξ – exchange amplification factor (for rare earth metals ξ = 1.5 [11, 12]).
Thus aluminum is a very weak paramagnetic material and cobalt atoms exist here in nonmagnetic state, the effective magnetic moment per cerium atom was calculated using
herek – Boltsmanconstant, µB – Bohr magneton,α – cerium atomic concentration.
The results of calculations (density of electron states at Fermi level - N(EF), paramagnetic Curie temperature - Θ, effective magnetic moment per cerium atom - µeff) for Al-Co-Ce alloys are given in Tables 1, 2.
Table 1. Some parameters of electron structure for quasybinary Al-Ce alloys(XCo = 9 at.%)
Cerium, at.% / 0*106, emu/g / N(EF), eV-1 / , К / C*105, emu*K/g / eff, B
1 / 0,708 / 0,226 / 110 / 9,100 / 1,01
2 / 0,903 / 0,298 / 105 / 19,297 / 1,04
3 / 1,146 / 0,392 / 100 / 28,945 / 1,04
4 / 1,167 / 0,412 / 95 / 36,400 / 1,01
5 / 1,313 / 0,479 / 90 / 55,950 / 1,12
6 / 1,333 / 0,502 / 80 / 55,686 / 1,02
7 / 1,361 / 0,528 / 75 / 67,540 / 1,04
8 / 1,396 / 0,558 / 70 / 83,240 / 1,08
9 / 1,417 / 0,583 / 65 / 100,711 / 1,12
10 / 1,403 / 0,594 / 55 / 91,000 / 1,01
11 / 1,493 / 0,649 / 52 / 118,734 / 1,1
Table 2. Some parameters of electron structure for quasybinary Al-Co alloys
(XCe = 7 at.%)
Cobalt, aт.% / 0*106, emu/g / N(EF), eV-1 / , К / C*105, emu*K/g / eff, B
0 / 1,445 / 0,518 / 105 / 68,845 / 1,05
1 / 1,507 / 0,545 / 100 / 74,190 / 1,09
2 / 1,493 / 0,545 / 98 / 74,190 / 1,09
3 / 1,493 / 0,550 / 95 / 72,835 / 1,08
4 / 1,479 / 0,550 / 90 / 70,163 / 1,06
5 / 1,472 / 0,552 / 85 / 67,540 / 1,04
6 / 1,514 / 0,573 / 82 / 76,938 / 1,11
7 / 1,514 / 0,578 / 80 / 75,558 / 1,10
8 / 1,507 / 0,580 / 78 / 64,967 / 1,02
9 / 1,493 / 0,580 / 75 / 64,967 / 1,02
10 / 1,493 / 0,585 / 70 / 67,540 / 1,04
11 / 1,493 / 0,589 / 65 / 72,835 / 1,08
12 / 1,493 / 0,594 / 60 / 72,835 / 1,08
13 / 1,445 / 0,580 / 55 / 63,700 / 1,01
One can see that density of states at Fermi level grows up from 0.226 to 0.649 eV-1 with the increase of cerium content from 1 to 11 at.% in quasybinaryAl-Ce series, whereas for quasybinaryAl-Co alloys it changes from 0,518 to 0,580 eV-1 when cobalt concentration enlarges from 1 to 13 at.%. Paramagnetic Curie temperature decreases monotonously from 110 to 55 K with the increase of doped element (TM or REM) content. As for effective magnetic moment per cerium atom, it was found to be equal 1.0 – 1.1 B independently on alloys composition for all investigated samples.
The small values of effective magnetic moment per cerium atom are the evidence of the fact that in investigated concentration range rare earth atoms exist not in R3+ state, as it was considered before [1], but create directed bonds with aluminum atoms (this idea was generated in our previous papers [14-16]). This situation takes place both in liquid and solid states. 4f-electrons located earlier on REM ions are involved now into directed bonds formation, i.e. some part of them become delocalized. Because of that effective magnetic moment on REM atom decreases and becomes lower than for R3+ ion. We think that in Al-Co-Ce alloys the probability of Al2Ce quasymolecules existence is rather high (this situation was described in details in [14-16]). When the melt is overheated above melting point of Al2Ce compound, the destruction of mentioned directed bonds in quasymolecules starts; 4f-electrons come back to cerium atoms, i.e. become localized again; magnetic moment per REM atom begins to grow up and total susceptibility of the alloy increases as well. This fact was confirmed in our experiments (see fig.1,2). The existence of Al2Ce quasymolecules in Al-Co-Ce alloys and their interaction can explain nonmonotonous behavior of magnetic susceptibility vs cerium concentration, like it was done in [16].
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