mixing enthalpies in liquid alloys of manganese with the lanthanides

Michael Ivanova, Vadim Berezutskia, Nathalia Usenkob

a I. Frantsevich Institute for Problems of Materials Science, National Academy of Sciences, Kyiv, Ukraineb Taras Shevchenko National University, Department of Chemistry, Kyiv, Ukraine

Mixing enthalpies in liquid alloys of manganesewith the lanthanides

The enthalpies of mixing in binary liquid alloys of manganesewith the lanthanides (Nd, Gd, Tb, Dy, Tm and Lu) were deter-mined over a wide range of composition by isoperibolic calo-rimetry. The heats of mixing in the systems were found tochange gradually across the lanthanides row from the Mn–Nd system (DHmin = –0.40 � 0.26 kJ mol – 1 at xNd = 0.14;DHmax = 1.99 � 0.65 kJ mol – 1 at xNd = 0.60; T = 1600 K)to the Mn–Lu system (DHmin = –6.76 � 0.93 kJ mol – 1 atxLu = 0.40; T = 1 700 K)

Keywords: Manganese; Lanthanides; Calorimetry; Enthal-py of mixing

1. Introduction

Binary alloys of manganese with the lanthanides (Ln) areknown to display interesting physical properties and areused as permanent magnets and materials for hydrogenstorage. Thermodynamic data for Mn–Ln alloys may yieldimportant information for the calculation of phase equili-bria in multicomponent alloys with the aim of finding thecompositions with the best technological efficiency.

The alloying behaviour of Mn with the trivalent lantha-nides from Nd to Lu is characterised by the occurrence ofintermetallic compounds (which are formed by peritecticreaction) and by a narrow range of solid solubility [1].There is no experimental information on the enthalpies offormation of the reported compounds. Thermodynamic datafor the liquid Mn–Ln alloys are also rather scarce. The firstresults of calorimetric investigation of the mixing enthal-pies in binary liquid alloys of Mn with several trivalentlanthanides at 1 600 K have been reported previously [2].However, that paper does not contain any enthalpy data forthe alloys of Mn with Nd, Sm, Tb and Tm. For the liquid al-loys of Mn with Dy, Ho, Er and Lu, the mixing enthalpieswere measured only at a low concentration of lanthanidemetals. Recent calorimetric measurements of the mixingenthalpies for the liquid Mn–Sm alloys at 1 600 K acrossthe whole concentration region indicated a change in DHfrom small positive to small negative values [3]. The limit-ing values of the partial enthalpies of mixing at infinite di-lution were found to be D �H0

Sm = –5.1 � 1.6 kJ mol – 1 andD �H0

Mn = 6.8 � 1.6 kJ mol – 1 at 1 600 K. The resulting equa-tion for the integral enthalpy of mixing (kJ mol – 1) was re-presented as follows: DH = x(1– x)(6.76 + 2.39x– 45.14x2 +30.25x3) where x = xMn.

Recently there has been renewed interest in the thermo-dynamic description of some Mn–Ln systems by using thecalculation of phase diagrams (CALPHAD) method [4].This method deals with the experimental thermodynamicdata on binary systems including the mixing enthalpy datafor corresponding liquid alloys.

In the present investigation the enthalpies of mixing of theliquid alloys of Mn with Nd, Gd, Tb and Dy were measuredacross the whole composition region. For the Mn–Tm andMn–Lu liquid alloys the enthalpies of mixing were measuredup to 70 at.% of lanthanide metal because of experimentaldifficulties.

2. Experimental

The experiments were carried out in a high temperature solu-tion calorimeter working up to 1850 K in purified helium at-mosphere under a pressure of 105 Pa at 1550 –1723 K. The ap-paratus and experimental technique were similar to thoseemployed in previous investigations [5, 6]. The purity of metalswas 99.95% for Mn, 99.85% for Nd, 99.98% for Gd, 99.96%for Tb, Dy, Tm and Lu. The pieces of manganese (Mn was re-melted in vacuum in alumina crucibles at 1600 K) werewashed in dilute HNO3 solution and cleaned with pure ethanol.The lanthanides were mechanically treated and stored in petro-leum ether to prevent oxidation. Additionally, neodymiumsamples were prepared and stored in a helium filled glove box.

The partial heats of mixing in the binary melts were mea-sured in the process of successive introduction of metal sam-ples taken at 298 K into the liquid metal bath. During eachexperimental series small samples of metals (masses within0.01– 0.03 g) were dropped into the calorimetric bath (a liq-uid metal or an alloy, placed in a crucible of alumina, zirco-nia or molybdenum and their use depended on the alloyscomposition). The initial mass of a metal in the bath wasabout 3 g. The change in the alloy concentration after eachaddition was less than 1.5 at.%. Consequently, we can deter-mine the partial molar enthalpies with sufficient accuracy.

In the course of the experiments, the calculation of theweight loss of the alloy showed a certain evaporation ofmelts in the cases of the Mn–Nd and Mn–Tm systems (lessthan 5 % of the mass of an alloy) due to the high vapourpressure of these lanthanides. The vapour pressure of liquidNd (about 0.5 Pa at 1 550 K [7]) and Tm (about 102 Pa at1 400 K [7]) is higher than that of the other metals used inthe experiments. Therefore, the weight loss has been attrib-uted to the volatile components and taken into accountwhile computing alloys compositions.

M. Ivanov: Mixing enthalpies in liquid alloys of manganese with the lanthanides

Int. J. Mat. Res. (formerly Z. Metallkd.) 102 (2011) 3 277

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The experimental method is based on the measurementof the temperature difference DT (temperature measure-ments were carried out with WRe5/WRe20 thermocouples)between the sample and the reference specimen (cruciblecontained Mo or W), plotted as a function of temperaturerelaxation time (t). The heat effects were calculated fromDT vs. t curve by numerical integration [2, 5]. The thermaleffect of the process of dissolution of a sample is composedof two terms:1. the enthalpy change DHT

298 for a sample heating (per1 mole of metal dropped into the bath) from 298 K tothe temperature of liquid bath, taken from Refs. [8, 9];

2. the unknown partial molar heat (enthalpy) of mixing,D �Hi of component i.

The resulting heat balance for the endothermic effect is:

k

ZDTðtÞdt ¼ DHT

i;298 þ D �Hi ð1Þ

where k is the molar thermal equivalent of the calorimeter,which was determined in calibration additions at the begin-ning of each experimental series by using the same compo-nent as that in the bath (we can compute k from Eq. (1) put-ting D �Hi ¼ 0). Otherwise, at the end of each experimentalseries we computed k according to the iteration procedure de-scribed in Ref. [10]. In the case of manganese-rich melts kcannot be measured directly because traditional calibrationmetals (Mo, W) might react with the molten components.

The standard values of DHTi;298 for the metals used in the

experiments may also contain a contribution from the en-thalpy of fusion of a component (Tm, Lu) when its meltingtemperature was higher than that of the experiments. Liquidcomponents have been taken as the standard state.

Numerical values of the partial enthalpies of mixing ofboth the components were obtained from Eqs. (2) and (3):

D �HMn;i ¼ kMMns

m

� �Mn;i�DHT

Mn;298 ð2Þ

D �HLn;i ¼ kMLns

m

� �Ln;i�DHT

Ln;298 ð3Þ

where s = kRDTðtÞdt, m is the mass of dropping metal, MMn

and MLn are the atomic masses of Mn and Ln, respectively.Following Refs. [5, 10], the values of k were adjustedthrough computer simulation to yield consistent values ofboth the partial enthalpies via Eqs. (2) and (3) throughoutthe concentration intervals studied.

The sum of the experimental D �Hi data points for each com-ponent, computed from the mentioned procedure, was treatedstatistically (in the form of partial �-function defined as�i ¼ D �Hið1� xiÞ�2) by a least-squares analysis using For-sythe orthogonal polynomials [11]. The calculation proce-dure based on the Gibbs–Duhem equation gives the smoothedvalues of both the partial enthalpies of mixing of the compo-nents and the integral enthalpy of mixing with confidence in-tervals equal to twice the standard deviation of the corre-sponding approximating �-function [2, 5]. In order to obtaina coherent expression for the measured partial enthalpiesacross the whole composition region the two branches of theintegral �-function (� ¼ DH � x�1ð1� xÞ�1) computed fromboth the sides of pure components were treated simulta-neously to produce the best fitted least-squares smoothingcurve.

3. Results

3.1. The Mn–Nd system

Experimental data on the mixing enthalpies were measuredfor the liquid Mn–Nd alloys within the whole concentrationregion. The partial enthalpies of Nd were measured usingalumina crucibles only for dilute alloys (Nd content wasless than 10 at.%) and then up to 28 at.% Nd using zirconiacrucibles at 1550 K. The partial enthalpies of Mn weremeasured from the Nd-rich end using molybdenum cruci-bles (Mn content was less than 10 at.%) and zirconia cruci-bles for concentrated melts (up to 58 at.% Mn) at 1 600 K.

The resulting equation for the integral enthalpy of mixing(kJ mol – 1) at 1 600 K, computed from the smoothed inte-gral �-functions over the total composition region, is deter-mined as follows (x = xNd):

DH = x(1 – x)(– 3.75– 13.37x + 99.72x2 + 309.08x3– 1 613.14x4 +2503.16x5 – 1 741.26x6 + 466.88x7)

The partial and integral enthalpies of mixing for the Mn–Ndliquid alloys are listed in Table 1. The concentration depen-dence of the enthalpies is shown in Fig. 1. The integral en-thalpy is observed to be negative at around 14 at.% Nd


278 Int. J. Mat. Res. (formerly Z. Metallkd.) 102 (2011) 3

Table 1. Mixing enthalpies of the Mn–Nd liquid alloys at 1 600 K(kJ mol – 1) computed from the smoothed �-function.

xNd DH D �HNd D �HMn

0.0 0 – 3.75 � 1.82 00.1 – 0.35 � 0.15 – 2.32 � 1.30 – 0.13 � 0.020.2 – 0.30 � 0.26 2.52 � 1.03 – 1.00 � 0.060.3 0.30 � 0.69 5.70 � 1.62 – 2.02 � 0.300.4 1.11 � 0.97 5.78 � 1.46 – 2.01 � 0.650.5 1.74 � 0.98 4.04 � 0.98 – 0.56 � 0.980.6 1.99 � 0.95 2.14 � 0.64 1.77 � 1.440.7 1.84 � 0.89 0.85 � 0.39 4.15 � 2.100.8 1.37 � 0.58 0.20 � 0.16 6.04 � 2.240.9 0.72 � 0.27 0.01 � 0.04 7.05 � 2.301.0 0 0 7.32 � 2.28

Fig. 1. Mixing enthalpies in Mn–Nd liquid alloys at 1600 K: full curves– calculated self-consistent values (1 – D �HNd; 2 – D �HMn; 3 – DH); blackand white dots indicate the experimental partial enthalpies data points.

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(DHmin = – 0.40 � 0.17 kJ mol – 1), whereas it shows a maxi-mum at around 59 at.% Nd (DHmax = 1.99 � 0.95 kJ mol – 1).

3.2. The Mn–Gd, Mn–Tb and Mn–Dy systems

The enthalpies of mixing in the liquid Mn–Gd, Mn–Tb andMn–Dy alloys were measured in the total concentration re-gion at 1 650 K, 1 700 K and 1 723 K, respectively. The ex-perimental technique was similar to that described for theMn–Nd system. Zirconia crucibles were used as melt con-tainers. Molybdenum crucibles were also used when deal-ing with either liquid lanthanides or melts of high lantha-nide content.

The resulting equations for the integral enthalpy of mix-ing (kJ mol – 1), computed from the smoothed integral�-functions over the total composition region are deter-mined as follows:

for the Mn–Gd system:DH = x(1 –x)(–7.55– 6.41x –12.64x2 + 95.24x3 – 104.23x4 +

31.90x5), (x = xGd)

for the Mn–Tb system:DH = x(1 –x)(–10.00 –9.38x + 33.44x2 – 18.75x3), (x = xTb);

for the Mn–Dy system:DH = x(1 –x)(–16.84–16.00x– 5.75x2 + 323.10x3 –548.10x4 +

258.50x5), (x = xDy).

The partial and integral enthalpies of mixing for the Mn–Gd, Mn–Tb and Mn–Dy liquid alloys are negative; thecomplete set of the data is listed in Tables 2, 3 and 4, re-

spectively. The concentration dependence of the mixing en-thalpies in Mn–Gd is shown in Fig. 2 and reflects the char-acteristic features of the three mentioned systems. Theminimum values of the integral enthalpies are determinedas follows: DHmin = – 2.01 � 0.40 kJ mol – 1 at xGd = 0.40(the Mn–Gd system); DHmin = – 2.30 � 0.50 kJ mol – 1 atxTb = 0.40 (the Mn–Tb system) and DHmin = – 3.68 �0.65 kJ mol – 1 at xDy = 0.35 (the Mn–Dy system).

3.3. The Mn–Tm and Mn–Lu systems

The enthalpies of mixing in the liquid Mn–Tm and Mn–Lualloys were measured within a large composition region (upto 70 at.% Ln) at 1700 K. The experimental technique wassimilar to that described above for the other Mn–Ln systems.Zirconium dioxide crucibles were used as melt containers.For both the systems we failed to obtain the enthalpy datafor the lanthanide-rich composition region due to experimen-tal difficulties (high vapour pressure of Tm and high meltingtemperature of Lu). The missing enthalpy data were evaluat-ed by extrapolation of the �-functions of Mn according to theiteration procedure, described in Section 2.

The resulting equations for the integral enthalpy of mix-ing (kJ mol – 1), computed from the smoothed integral



Table 2. Mixing enthalpies of the Mn–Gd liquid alloys at 1 650 K(kJ mol – 1) computed from smoothed �-function.

xGd DH D �HGd D �HMn

0.0 0 – 7.55 � 1.70 00.1 – 0.74 � 0.10 – 7.19 � 0.98 – 0.020.2 – 1.40 � 0.22 – 5.99 � 0.70 – 0.25 � 0.100.3 – 1.85 � 0.34 – 4.06 � 0.72 – 0.90 � 0.180.4 – 2.01 � 0.40 – 2.07 � 0.49 – 1.97 � 0.330.5 – 1.88 � 0.39 – 0.60 � 0.30 – 3.16 � 0.390.6 – 1.54 � 0.36 0.12 � 0.11 – 4.02 � 0.740.7 – 1.10 � 0.29 0.24 � 0.05 – 4.20 � 0.870.8 – 0.68 � 0.16 0.09 � 0.02 – 3.75 � 0.690.9 – 0.33 � 0.08 0.01 – 3.22 � 0.791.0 0 0 – 3.69 � 1.40

Table 3. Mixing enthalpies of the Mn–Tb liquid alloys at 1 700 K(kJ mol – 1) computed from smoothed �-function.

xTb DH D �HTb D �HMn

0.0 0 – 10.00 � 2.33 00.1 – 0.96 � 0.21 – 8.87 � 1.85 – 0.08 � 0.020.2 – 1.71 � 0.37 – 6.62 � 1.45 – 0.48 � 0.090.3 – 2.16 � 0.49 – 4.22 � 1.14 – 1.28 � 0.210.4 – 2.30 � 0.50 – 2.25 � 0.75 – 2.34 � 0.340.5 – 2.17 � 0.49 – 0.92 � 0.49 – 3.42 � 0.490.6 – 1.83 � 0.50 – 0.21 � 0.33 – 4.26 � 0.760.7 – 1.39 � 0.49 – 0.03 � 0.20 – 4.69 � 1.130.8 – 0.91 � 0.37 – 0.03 � 0.09 – 4.69 � 1.460.9 – 0.45 � 0.20 0.00 � 0.02 – 4.49 � 1.801.0 0 0 – 4.68 � 2.00

Table 4. Mixing enthalpies of the Mn–Dy liquid alloys at 1 723 K(kJ mol – 1) computed from smoothed �-function.

xDy DH D �HDy D �HMn

0.0 0 – 16.84 � 3.15 00.1 – 1.64 � 0.34 – 15.58 � 3.02 – 0.10 � 0.040.2 – 2.96 � 0.48 – 11.18 � 1.93 – 0.91 � 0.120.3 – 3.62 � 0.62 – 5.63 � 1.44 – 2.77 � 0.260.4 – 3.57 � 0.70 – 1.42 � 1.06 – 5.00 � 0.470.5 – 3.02 � 0.67 0.39 � 0.67 – 6.42 � 0.670.6 – 2.32 � 0.71 0.36 � 0.47 – 6.35 � 1.060.7 – 1.72 � 0.61 – 0.15 � 0.26 – 5.38 � 1.430.8 – 1.23 � 0.32 – 0.24 � 0.10 – 5.21 � 1.500.9 – 0.66 � 0.16 0.01 – 6.63 � 1.601.0 0 0 – 5.09 � 1.79

Fig. 2. Mixing enthalpies in Mn–Gd liquid alloys at 1650 K: full curves– calculated self-consistent values (1 – D �HGd; 2 – D �HMn; 3 – DH); blackand white dots are the experimental partial enthalpies data points.

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�-functions over the total composition region are deter-mined as follows:

for the Mn–Tm system:DH = x(1–x)(–23.70– 39.67x + 161.60x2 – 168.09x3 + 58.20x4),(x = xTm);

for the Mn–Lu system:DH = x(1 –x)(–27.69–33.29x + 102.58x2 –55.74x3), (x = xLu).

The partial and integral enthalpies of mixing for the Mn–Tm and Mn–Lu liquid alloys are listed in Tables 5 and 6, re-spectively. The concentration dependence of the mixing en-thalpies in Mn–Lu system is shown in Fig. 3 and reflects thecharacteristic features of both the systems. The minimumvalues of the integral enthalpies at 1700 K are determinedas follows: DHmin = – 5.52 � 0.79 kJ mol – 1 at xTm = 0.38(the Mn–Tm system) and DHmin = – 6.76 � 0.93 kJ mol – 1

at xLu = 0.40 (the Mn–Lu system).

4. Discussion

The enthalpies of mixing in the studied liquid Mn–Ln al-loys demonstrate small exothermic effects (in the Mn–Ndsystem partially endothermic), reflecting a weak chemicalinteraction between the components, which gradually in-crease along the row of the lanthanides (Fig. 4). The mini-mum values of DH in these systems are located in the man-ganese-rich region and correlate with the existence of theintermetallic compounds Mn12Ln, Mn23Ln6 and Mn2Ln(in the Mn–Lu system Mn5Lu exists rather than theMn12Lu) [1, 12]. Previously the CALPHAD method hasbeen employed for the calculation of the standard enthal-pies of formation for the solid phases in the Mn–Gd system[13] and showed more exothermic values than our data forthe corresponding liquid alloys. The mixing enthalpy datafor the Mn–Dy and Mn–Lu melts, reported in Ref. [2], arealso more exothermic than our data for these systems.

The enthalpies of formation of the alloys of lanthanideswith 3d transition metals are known to be related to the elec-tronic characteristics of the elements [14]. Usually, it is sug-gested that the (3d, 4s)-bands of a transition metal overlapwith the (5d, 6s)-bands of a lanthanide by alloying and form-ing a hybridised sd-band, which depends on the Fermi energy,the electronic density of states and the bandwidth of the com-ponents [14, 15]. In the particular case of Mn–Ln systems,there is a certain difference between the Fermi energies ofthe components, which can be estimated by the electronicemission energies [15] (uMn ¼ 3:8 eV, uLn & 3.1 –3.2 eV).


280 Int. J. Mat. Res. (formerly Z. Metallkd.) 102 (2011) 3

Table 5. Mixing enthalpies of the Mn–Tm liquid alloys at1 700 K (kJ mol – 1) computed from smoothed �-function.

xTm DH D �HTm D �HMn

0.0 0 – 23.70 � 3.23 00.1 – 2.36 � 0.21 – 22.22 � 1.87 – 0.15 � 0.020.2 – 4.23 � 0.53 – 16.06 � 2.12 – 1.27 � 0.130.3 – 5.28 � 0.76 – 9.64 � 1.78 – 3.41 � 0.330.4 – 5.52 � 0.79 – 4.84 � 1.19 – 5.96 � 0.530.5 – 5.13 � 0.77 – 2.01 � 0.77 – 8.25 � 0.770.6 – 4.34 � 0.82 – 0.69 � 0.54 – 9.82 � 1.220.7 – 3.35 � 0.83 – 0.22 � 0.35 – 10.66 � 1.930.8* – 2.30 � 0.70 – 0.10 � 0.20 – 11.10 � 2.800.9* – 1.20 � 0.50 – 0.02 – 11.40 � 4.401.0* 0 0 – 11.70 � 5.00

* the extrapolated enthalpy data

Table 6. Mixing enthalpies of the Mn–Lu liquid alloys at 1 700 K(kJ mol – 1) computed from smoothed �-function.

xLu DH D �HLu D �HMn

0.0 0 – 27.69 � 2.18 00.1 – 2.70 � 0.11 – 25.50 � 1.01 – 0.17 � 0.010.2 – 4.91 � 0.24 – 19.50 � 0.95 – 1.26 � 0.060.3 – 6.29 � 0.32 – 12.73 � 0.75 – 3.53 � 0.140.4 – 6.76 � 0.93 – 6.97 � 1.40 – 6.62 � 0.730.5 – 6.41 � 0.67 – 2.98 � 0.67 – 9.85 � 0.670.6 – 5.46 � 0.56 – 0.80 � 0.38 – 12.46 � 0.850.7 – 4.17 � 0.85 0.002 � 0.36 – 13.89 � 1.970.8* – 2.8 � 0.5 0.10 � 0.02 – 14.10 � 2.500.9* – 1.4 � 0.3 – 0.01 � 0.02 – 13.60 � 2.501.0* 0 0 – 14.10 � 2.50

* the extrapolated enthalpy data

Fig. 3. Mixing enthalpies in Mn–Lu liquid alloys at 1700 K: fullcurves are the calculated self-consistent values (1 – D �HLu; 2 – D �HMn;3 – DH); dashed curves are the extrapolated values; black and whitedots – experimental data points.

Fig. 4. Variation in D �H0Mn and D �H0

Ln vs. atomic number of the lantha-nides (ZLn ) for the studied Mn–Ln liquid alloys: black dots – D �H0

Ln;white dots – D �H0

Mn. The data for the Mn–Sm system were taken fromRef. [3].

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Therefore, the Mn–Ln alloys are expected to be formed withan exothermic effect, which, however, should be small due tothe significant atomic volume differences of the components(V0

Mn = 7.35 cm3 mol – 1, whereas V0Nd = 20.58 cm3 mol – 1 and

V0Lu = 17.77 cm3 mol – 1 [16]). As shown in Fig. 4, there is a

tendency for increasing absolute values of the limiting partialmixing enthalpies of Mn–Ln alloys through the lanthaniderow. This fact correlates with the increasing of the electronicdensity of states of the lanthanides at the Fermi level fromlanthanum (about 0.58 · 1023 eV – 1 cm – 3) to lutetium (about0.73 · 1023 eV1 cm – 3) [14]. Such a variation of the mixing en-thalpies can also be attributed to the decrease in atomic vol-ume difference (the lanthanide contraction), which leads tomore effective band overlapping in the case of the heavylanthanides.

In summary, it is of current interest to compare the enthal-py values obtained experimentally with the values computedaccording to Miedema’s model [16, 17]. The calculated en-thalpies for the liquid alloys of manganese with the lantha-nides do not agree with the experimental data being signifi-cantly more negative. Moreover, standard Miedema’smodel cannot predict in principle the enthalpy data for theMn–Nd and Mn–Sm systems, for which DH values werefound to be negative at certain compositions while positiveat other compositions.

Nowadays, it is generally accepted that first-principlescalculations can provide more reliable enthalpy data thanthe semi-empirical models. Attempts in this direction havealready been reported for series of transition metal binaryalloys in solid state [18, 19]. However, we have found noinformation concerning first-principles (ab-initio) calcula-tions of the formation enthalpies for the Mn–Ln solid al-loys.

In this connection, direct calorimetric measurements forliquid alloys seem to be important to establish the completeset of thermodynamic data for the liquid alloys of manga-nese with the rare earth metals, including the Mn–Sc andMn–Y systems, which still remain unexplored over thewhole range of concentration.

References

[1] A. Saccone, S. Delfino, R. Ferro: Z. Metallkd. 84 (1993) 563 –568.[2] I. Nikolaenko: J. Alloys Comp. 225 (1995) 474 –479.

DOI:10.1016/0925-8388(94)07076-8[3] V.V. Berezutski, M.I. Ivanov: Powder Metallurg. Metal Ceramics.

48 (2009) 454 –461. DOI:10.1007/s11106-009-9144-5[4] C.P. Wang, Z. Lin, X.J. Liu: J. Alloys Comp. 469 (2008) 123 –128.

DOI:10.1016/j.jallcom.2008.01.092[5] M.I. Ivanov, V.T. Witusiewicz: J. Alloys Comp. 223 (1992) 265–

266.

[6] N.I. Usenko, M.I. Ivanov, V.M. Petiuh, V.T. Witusiewicz: J. AlloysComp. 190 (1993) 149–155. DOI:10.1016/0925-8388(93)90391-Y

[7] C.B. Alcock, V.P. Itkin, M.K. Horrigan: Canad. Metall. Quart. 23(1984) 309–315.

[8] R. Hultgren, P.D. Desai, T.D. Hawkins, M. Gleiser, K.K. Kelley,D.D. Wagman: Selected Values of the Thermodynamic Propertiesof the Elements. ASM International, Metals Park, OH, (1973).

[9] A.T. Dinsdale: Calphad 15 (1991) 317–425.DOI:10.1016/0364-5916(91)90030-N

[10] V.T. Witusiewicz, M.I. Ivanov: J. Alloys Comp. 200 (1993) 177–180. DOI:10.1016/0925-8388(93)90490-E

[11] C.W. Bale, A.D Pelton: Metall. Trans. 5 (1974) 2323 –2337.DOI:10.1007/BF02644013

[12] T.B. Massalski (Ed.): Binary Alloy Phase Diagrams, 1st ed., ASMInternational, Metals Park, OH, (1986).

[13] J. Gröbner, A. Pisch, R. Schmid-Fetzer: J. Alloys Comp. 317 –318(2001) 433 –437. DOI:10.1016/S0925-8388(00)01364-5

[14] W.A. Harrison: Electronic Structure and the Properties of Solids,Freeman and Comp., San-Francisco, (1982).

[15] I.V. Nikolaenko, M.A. Turchanin, N.I. Usenko (Beloborodova):Izv. Acad. Nauk USSR Neorg. Mater. 26 (1990) 2309 –2315 (inRussian).

[16] F.R. de Boer, R. Boom, W.C.M. Mattens, A.R. Miedema, A.K. Nies-sen: Cohesion in Metals, North Holland, Amsterdam (1988).

[17] C. Colinet: J. Alloys Comp. 225 (1995) 409–422.DOI:10.1016/0925-8388(94)07087-3

[18] X.Q. Chen, V.T. Witusiewicz, R. Podloucky, P. Rogl, F. Sommer:Acta Materialia 51 (2003) 1239 –1247.DOI:10.1016/S1359-6454(02)00497-4

[19] Yu. Wu, W. Hu, Sh. Han: J. Alloys Comp. 420 (2006) 83–93.DOI:10.1016/j.jallcom.2005.10.020

(Received November 18, 2009; accepted December 13, 2010)

Bibliography

DOI 10.3139/146.110474Int. J. Mat. Res. (formerly Z. Metallkd.)102 (2011) 3; page 277–281# Carl Hanser Verlag GmbH & Co. KGISSN 1862-5282

Correspondence address

Dr. Nathalia UsenkoTaras Shevchenko National University, Department of Chemistry64, Volodymirska St., 01601 Kyiv, UkraineTel.: +380 44 239 3370E-mail: [email protected]

You will find the article and additional material by enter-ing the document number MK110474 on our website atwww.ijmr.de



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mixing enthalpies in liquid alloys of manganese with the lanthanides

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