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Dissolution rates and solubility of some metals inliquid gallium and aluminumTo cite this article S P Yatsenko et al 2008 J Phys Conf Ser 98 062032

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Dissolution rates and solubility of some metals in liquidgallium and aluminum

S P Yatsenko N A Sabirzyanov and A S YatsenkoInstitute of Solid State Chemistry Ural Branch of Russian Academy of Sciences 91Pervomayskaya str Ekaterinburg 620041 Russia

E-mail yatsenkoihimuranru

Abstract The effect of liquid gallium and aluminum on some hard metals leading todissolution and formation of intermetallic compounds (IMC) under static conditions androtation of a specimen is studied The solubility parameters from the Clapeyron-Clausiusequation were considered to estimate the stability of still not studied metals The presentedexperimental data on solubility and corrosion in a wide temperature range allow to calculate anumber of parameters useful in manufacturing and application of master-alloys

The breakdown of materials as a result of interaction with liquid metals is determined mainly but notexclusively by solubility If the decisive stage is diffusion of atoms through a layer of an intermetalliccompound (IMC) formed an increase of the liquid metal flow rate (without cavitation) does not resultin an increase of a dissolution rate For transition metals in liquid aluminum in the laminar flow areathe experimental and theoretical effective widths of the boundary layer differ several tens times [1]

During corrosion a melt interacts with hard metal granules (pieces) without forced mixing Thesestudies [2] were performed to compare results of industrial melting of master-alloys with availabledata on solubility and dissolution kinetics

The dilution in liquid Ga and Al was carried out by isothermal exposure of a fine-disperse hardmetal discharge of the melt from a crucible to a porous plate and filtration in inert atmosphere withsubsequent selection of specimens for analysis Experimental values of solubility up to several atomicpercents are shown as straight lines in semilogarithmic coordinates (figure 1) Values of coefficients Aand B for some metals in the equation

lgC = A ndash BT (1)and their solubility (С in at ) are given in table 1

The solubility of IV-group metals in gallium is presented in figure 2 for three temperaturesManganese displaying much higher solubility than its nearest neighbors chromium and iron falls outfrom the general series of solubility decrease for IV-group metals in gallium The solubility formula(1) agrees with the thermodynamic expression for equilibrium between solid and liquid phasesdeduced from equal activity of dissolved and solid components relative to the same chosen standardstate and also from some other simplifications If a pure solid component B is in equilibrium with aliquid phase melting is the only phase transition and the heat capacity of the solid and overcooledliquid components is almost equal the partial Gibbs energy is

ΔG = RTlnаВ l = (ΔSmelt + ΔSВ)Т ndash (ΔНmelt + ΔНВ) (2)

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

ccopy 2008 IOP Publishing Ltd 1

Figure 1 Temperature dependence of solubility of thefourth group metals zirconium and hafnium in gallium

Table 1 Solubility of some metals in liquid gallium and aluminum

lgC=AminusBT С atMetal IMC IntervalТ К А minusВ 103 673 К 773 К

In galliumCopper CuGa2 500ndash700 352 161 150 28Calcium CaGa4 500ndash700 325 230 062 17Scandium ScGa3 623ndash973 399 365 35middot10minus2 020Titanium TiGa3 600ndash800 260 312 95middot10minus3 39middot10minus2Germanium Ge 400ndash600 360 178 89 198Vanadium VGa4 600ndash800 320 40 20middot10minus3 10middot10minus2Chromium CrGa4 600ndash800 270 310 12middot10minus2 49middot10minus2Manganese MnGa6 500ndash700 540 390 040 23Iron FeGa3 500ndash700 400 385 19middot10minus2 011Cobalt CoGa3 500ndash700 350 310 78middot10minus2 031Nickel NiGa3 500ndash700 252 185 059 135Zirconium ZrGa3 500ndash800 305 422 60middot10minus4 39middot10minus3Hafnium HfGa3 500ndash800 656 725 61middot10minus5 15middot10minus3

In aluminumScandium ScAl3 960ndash1200 736 728 12 196Titanium TiAl3 960ndash1200 303 394 012 056Vanadium VAl10 960ndash1000 440 488 033 210Chromium CrAl7 970ndash1170 500 526 055 410Zirconium ZrAl3 960ndash1200 660 758 010 190Hafnium HfAl3 960ndash1150 690 750 025 450

With certain assumptions the concentration C of a dissolved substance (in at ) may be used insteadof activity a For binary systems having no IMC estimated values and values determined fromcalorimetric measurements are in satisfactory agreement if the concentration of a dissolved substanceis smaller than 2 at Equation 2 takes the form

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

2

TT

HHSSC B-A=23R

Δ+Δ-32ΔΔ2=lg Bmeltdivide

oslashouml

ccedilegraveaelig +

+R

Bmelt (3)

where ΔНB = 23RB ndash ΔНmelt and DSB = 23RA - DSmelt are determined from experimental values of Aand B

Figure 2 Solubility of the fourth groupmetals in gallium at1 ndash 573 K 2 ndash 673 K 3 ndash 773 K

For systems of compounds the ΔHB value characterizes the enthalpy of displacement of a compoundrather than of an initial pure metal

The reverse problem ie determination of solubility from individual properties of metals can besolved on the base of melting temperature and heat with the use of the Clapeyron-Clausius equation orsolubility parameters [3] Estimation of solubility from parameters of two nearest neighbors givesbetter results Thus estimated and experimental (in brackets) solubility values for middle elements ofthe eighth group triads at 773 K are as follows at 036 (035) for cobalt 127 (127) for rhodium011 (0053) for iridium Hence satisfactory results may be obtained even quantitatively

When there is no interaction the dissolution consists in breakdown of metallic bonds holdingatoms on the surface of metal and their replacement by bonds between atoms of different kindsCorrosion resistance of a metal in this case is proportional to binding energy of atoms in the solidstate The second stage is the removal of reaction products from surface into the depth of the liquid-metal solution Diffusion through the solution layer adjacent to a hard metal acts often as a limitingprocess Considering the dependence between the dissolution rate and the mixing rate a motive forcehere is the diffusion gradient The dissolution rate in this case is determined by the Fick law ie it isdirectly proportional to the difference of concentrations (СНminusС) of a dissolved substance on theboundary with a solid state and in the bulk and is inversely proportional to the width of the diffusionlayer The rate of corrosion decreases with time according to equation

СCH = 1 ndash exp(ndashaSτV) (4)

where S is the surface area of dissolution V is the volume of a liquid metal a is the dissolution rateconstant and τ is time

The rates of corrosion of substances are compared at similar SV values Corrosion for a timeinterval is determined by the equation

Q = dCH(VS)[1 ndash exp(ndashaSτV)] (5)

where d is a specific mass of a liquid-metal solutionThe mass loss as a result of corrosion depends on the properties of the medium and the specimen

and the SV ratio

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

3

The duration of exposure of specimens till complete breakdown versus inverse temperature ispresented in semilogarithmic coordinates in figure 3 For convenient comparison of corrosionresistance of various metals the values are calculated for a reference thickness (15 μm) Provided thatupon dissolution of a specimen the solubility is still far from saturation a direct dependence betweenthe exposure time and the specimen thickness was assumed (table 2)

Figure 3 Temperature dependence of complete corrosion time (lgt) of hard metalspecimens in gallium left ndash metals of the first long period right ndash other metals

Table 2 Effect of the specimen plate thickness on the duration ofcomplete corrosion in gallium

Ratio of specimen exposuretimesMetal Specimen thickness

(μm) and their ratio 673К 773КScandium 3018 17 21 18Iron 3519 18 22 19Cobalt 4020 20 24 205Nickel 3015 20 22 19

The specimens were treated similarlyOver a wide temperature range the values of corrosion exhibit a linear dependence

lgτ = A + BT (6)

where τ is time s T is temperature К А and В are constantsThe coefficients from (6) determined from plots in figure 3 are listed in table 3 along with the

temperature rangesIt is seen from the plots in figure 3 that the exposure time till specimen breakdown increases

abruptly at a certain temperature different for each metal Consequently each metal may becharacterized by a temperature below which the first stage of the corrosion process is limiting Abovethis temperature the process is limited by the second stage namely diffusion It also explains almostidentical inclination angles of the corresponding lines on the plots for different metals The values ofthe coefficient B do not differ more than twice from the average value for the whole group of metals

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

4

Table 3 Corrosion of pure metals in gallium

Coefficients from equation (6)Metal minusА В 103Temperature

range КCorrosion at 673К

mgcm2middothScandium 050 297 593ndash873 110Titanium 115 381 773ndash1073 20middot10minus2Zirconium 140 323 573ndash873 73Hafnium 145 330 623ndash873 143Iron 075 285 573ndash973 71Cobalt 185 346 773ndash973 23Nickel 200 277 573ndash873 20middot102

Metals can be arranged according to the minimum temperatures at which their stability in galliumbecomes linear This sequence characterizes the change in the MendashMe bond strength as compared withMendashGa If the atomic bond energies differ slightly their detachment from the surface and ldquosolvationrdquoby a solvent obeys a statistical law The strength of atomic bonds in a hard metal correlates withmelting sublimation and evaporation heats (see figure 4) Metals with small ΔН values have weakerstability Elements with covalent bonding (Si Ge) require greater energies for detachment of atomscomparing with long-range order breakdown in metals On the lgτ ndash ΔНmelt plot (figure 4а) theseelements are displaced to the right However for the ΔН sublimation (figure 4b) the deviations for Siand Ge fit into the general scatter of points Analysis of corrosion versus the ratio of surface tension ofa metal σМе to the surface tension of gallium (figure 5) shows that metals with a face-centered cubic(FCC) lattice are below the curve plotted in the system of coordinates lgτ ndash σМеσGa Metals with abody-centered cubic (BCC) and hexagonal (hexag) lattice are in the vicinity of the smooth linewhereas those with a diamond-type (diam) structure are located much higher Figure 6 displays therelationship between physical and chemical properties of elements and the periodical character of theircorrosion stability This allows to predict the corrosion stability of metals for which the experimentaldata are not available

The corrosion of specimens in a liquid metal as a function of the medium motion rate is alsodescribed by equations (4) and (5) where only the dissolution rate constant (a) is changed Thefunctional dependence on the liquid metal motion rate υ was established as the power function amot =bmiddotυn The exponent (n) is 05 for a laminar flow and 02 for a turbulent flow [5] However whencorrosion decreases substantially (10 times) the constant a is better described by the lineardependence amot = a0 + bmiddotυ If initial sections of the dissolved transition metal dependences are used

the dissolution rate constants are calculated from plots in semilogarithmic coordinatesC-C

C

H

Hln vs

SmiddotτV The corrosion of Sc Ti Zr Hf in liquid aluminum was studied at temperatures 1073 and 1173Kand the specimen rotation rate equals to 1 and 2 rps Their dissolution rates are listed in table 4

Table 4 Dissolution rates n of Sc Ti Zr Hf in aluminum melt 10minus3gcm2middots

Dissolution temperature and rotation rate1073 K 1123 KMetal

Time ofexperiment

10minus3 s 1 rps 2 rps 1 rps 2 rpsScandium 36ndash108 24 43 56 70Titanium 36ndash108 39 58 78 86Zirconium 36ndash72 43 66 81 89Hafnium 36ndash72 41 63 75 92

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

5

Figure 4 Dependence of lgt of hard metals in gallium at 773 K on atomic melting (a)and sublimation (b) heat Values for Li and Pb are given for their melting temperatures

Figure 5 Dependence of lgt of metals in gallium at 773 K onrelative surface tension of metals

The leading stage of the process is established from the character of breakdown When thedissolution surface is uniform diffusion plays a main role Intermetallic compounds MeAl3 are formedin the considered systems and therefore the values refer to the phases in equilibrium with the meltsThe rates of formation of these phases under chosen conditions are higher than the rates of theirdissolution For zirconium this was earlier established by Eremenko et al [6] Diffusion mobility ofthese complexes is small Therefore the process of dissolution will involve the following stagesdiffusion of refractory metal atoms in the intermetallic layer and their transition to the melt and onlyafter that refractory metal atoms will diffuse in the diffusion boundary layer The assumed specimenrotation rates (1 and 2 rps) are comparable with free convection

These results show that saturation of melts with alloying components may be accelerated by usingof an alloying metal in a disperse form and also by intensive mixing The dissolution rate increasesappreciably when the temperature is raised from 800 to 900degС However even at 1000minus1100degС largepieces of metals are dissolved for several hours if mixing is weak The results obtained can be used to

b

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

6

calculate diffusion coefficients effective radii of diffusing particles and their dependences ontemperature and activation energy in liquid aluminum Inaccurate values of kinematic viscosity onlyslightly affect the calculations whereas solubility data give the main error

Figure 6 Characteristic of corrosion stability of elements (in points and mgcm2middoth)in gallium at 673 K as a function of atomic number

References[1] Darby F B Gugle D B and Kleppa O J 1963 The rate of solution of some transition elements in

liquid aluminum Trans Metal Soc AIME 227 179-185[2] Yatsenko S P 2007 Rare elements in aluminum alloys Metally Evrazii 2 66-67[3] Yatsenko S P and Khayak V G 1997 Composite solders based on fusible alloys (Ekaterinburg

UB RAS)[4] Yatsenko S P 1974 Gallium Interaction with metals (Moscow Nauka)[5] Nikitin V I 1967 Physico-chemical phenomena in the interaction between liquid and hard

metals (Moscow Atomizdat)[6] Eremenko V N Natanzon YaV and Titov V P 1998 Kinetics of dissolution of the ZrAl3

compound in liquid aluminum Izvestiya AN SSSR Metally 1 211-215

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

7

TT

HHSSC B-A=23R

Δ+Δ-32ΔΔ2=lg Bmeltdivide

oslashouml

ccedilegraveaelig +

+R

Bmelt (3)

where ΔНB = 23RB ndash ΔНmelt and DSB = 23RA - DSmelt are determined from experimental values of Aand B

Figure 2 Solubility of the fourth groupmetals in gallium at1 ndash 573 K 2 ndash 673 K 3 ndash 773 K

For systems of compounds the ΔHB value characterizes the enthalpy of displacement of a compoundrather than of an initial pure metal

The reverse problem ie determination of solubility from individual properties of metals can besolved on the base of melting temperature and heat with the use of the Clapeyron-Clausius equation orsolubility parameters [3] Estimation of solubility from parameters of two nearest neighbors givesbetter results Thus estimated and experimental (in brackets) solubility values for middle elements ofthe eighth group triads at 773 K are as follows at 036 (035) for cobalt 127 (127) for rhodium011 (0053) for iridium Hence satisfactory results may be obtained even quantitatively

When there is no interaction the dissolution consists in breakdown of metallic bonds holdingatoms on the surface of metal and their replacement by bonds between atoms of different kindsCorrosion resistance of a metal in this case is proportional to binding energy of atoms in the solidstate The second stage is the removal of reaction products from surface into the depth of the liquid-metal solution Diffusion through the solution layer adjacent to a hard metal acts often as a limitingprocess Considering the dependence between the dissolution rate and the mixing rate a motive forcehere is the diffusion gradient The dissolution rate in this case is determined by the Fick law ie it isdirectly proportional to the difference of concentrations (СНminusС) of a dissolved substance on theboundary with a solid state and in the bulk and is inversely proportional to the width of the diffusionlayer The rate of corrosion decreases with time according to equation

СCH = 1 ndash exp(ndashaSτV) (4)

where S is the surface area of dissolution V is the volume of a liquid metal a is the dissolution rateconstant and τ is time

The rates of corrosion of substances are compared at similar SV values Corrosion for a timeinterval is determined by the equation

Q = dCH(VS)[1 ndash exp(ndashaSτV)] (5)

where d is a specific mass of a liquid-metal solutionThe mass loss as a result of corrosion depends on the properties of the medium and the specimen

and the SV ratio

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

3

The duration of exposure of specimens till complete breakdown versus inverse temperature ispresented in semilogarithmic coordinates in figure 3 For convenient comparison of corrosionresistance of various metals the values are calculated for a reference thickness (15 μm) Provided thatupon dissolution of a specimen the solubility is still far from saturation a direct dependence betweenthe exposure time and the specimen thickness was assumed (table 2)

Figure 3 Temperature dependence of complete corrosion time (lgt) of hard metalspecimens in gallium left ndash metals of the first long period right ndash other metals

Table 2 Effect of the specimen plate thickness on the duration ofcomplete corrosion in gallium

Ratio of specimen exposuretimesMetal Specimen thickness

(μm) and their ratio 673К 773КScandium 3018 17 21 18Iron 3519 18 22 19Cobalt 4020 20 24 205Nickel 3015 20 22 19

The specimens were treated similarlyOver a wide temperature range the values of corrosion exhibit a linear dependence

lgτ = A + BT (6)

where τ is time s T is temperature К А and В are constantsThe coefficients from (6) determined from plots in figure 3 are listed in table 3 along with the

temperature rangesIt is seen from the plots in figure 3 that the exposure time till specimen breakdown increases

abruptly at a certain temperature different for each metal Consequently each metal may becharacterized by a temperature below which the first stage of the corrosion process is limiting Abovethis temperature the process is limited by the second stage namely diffusion It also explains almostidentical inclination angles of the corresponding lines on the plots for different metals The values ofthe coefficient B do not differ more than twice from the average value for the whole group of metals

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

4

Table 3 Corrosion of pure metals in gallium

Coefficients from equation (6)Metal minusА В 103Temperature

range КCorrosion at 673К

mgcm2middothScandium 050 297 593ndash873 110Titanium 115 381 773ndash1073 20middot10minus2Zirconium 140 323 573ndash873 73Hafnium 145 330 623ndash873 143Iron 075 285 573ndash973 71Cobalt 185 346 773ndash973 23Nickel 200 277 573ndash873 20middot102

Metals can be arranged according to the minimum temperatures at which their stability in galliumbecomes linear This sequence characterizes the change in the MendashMe bond strength as compared withMendashGa If the atomic bond energies differ slightly their detachment from the surface and ldquosolvationrdquoby a solvent obeys a statistical law The strength of atomic bonds in a hard metal correlates withmelting sublimation and evaporation heats (see figure 4) Metals with small ΔН values have weakerstability Elements with covalent bonding (Si Ge) require greater energies for detachment of atomscomparing with long-range order breakdown in metals On the lgτ ndash ΔНmelt plot (figure 4а) theseelements are displaced to the right However for the ΔН sublimation (figure 4b) the deviations for Siand Ge fit into the general scatter of points Analysis of corrosion versus the ratio of surface tension ofa metal σМе to the surface tension of gallium (figure 5) shows that metals with a face-centered cubic(FCC) lattice are below the curve plotted in the system of coordinates lgτ ndash σМеσGa Metals with abody-centered cubic (BCC) and hexagonal (hexag) lattice are in the vicinity of the smooth linewhereas those with a diamond-type (diam) structure are located much higher Figure 6 displays therelationship between physical and chemical properties of elements and the periodical character of theircorrosion stability This allows to predict the corrosion stability of metals for which the experimentaldata are not available

The corrosion of specimens in a liquid metal as a function of the medium motion rate is alsodescribed by equations (4) and (5) where only the dissolution rate constant (a) is changed Thefunctional dependence on the liquid metal motion rate υ was established as the power function amot =bmiddotυn The exponent (n) is 05 for a laminar flow and 02 for a turbulent flow [5] However whencorrosion decreases substantially (10 times) the constant a is better described by the lineardependence amot = a0 + bmiddotυ If initial sections of the dissolved transition metal dependences are used

the dissolution rate constants are calculated from plots in semilogarithmic coordinatesC-C

C

H

Hln vs

SmiddotτV The corrosion of Sc Ti Zr Hf in liquid aluminum was studied at temperatures 1073 and 1173Kand the specimen rotation rate equals to 1 and 2 rps Their dissolution rates are listed in table 4

Table 4 Dissolution rates n of Sc Ti Zr Hf in aluminum melt 10minus3gcm2middots

Dissolution temperature and rotation rate1073 K 1123 KMetal

Time ofexperiment

10minus3 s 1 rps 2 rps 1 rps 2 rpsScandium 36ndash108 24 43 56 70Titanium 36ndash108 39 58 78 86Zirconium 36ndash72 43 66 81 89Hafnium 36ndash72 41 63 75 92

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

5

Figure 4 Dependence of lgt of hard metals in gallium at 773 K on atomic melting (a)and sublimation (b) heat Values for Li and Pb are given for their melting temperatures

Figure 5 Dependence of lgt of metals in gallium at 773 K onrelative surface tension of metals

The leading stage of the process is established from the character of breakdown When thedissolution surface is uniform diffusion plays a main role Intermetallic compounds MeAl3 are formedin the considered systems and therefore the values refer to the phases in equilibrium with the meltsThe rates of formation of these phases under chosen conditions are higher than the rates of theirdissolution For zirconium this was earlier established by Eremenko et al [6] Diffusion mobility ofthese complexes is small Therefore the process of dissolution will involve the following stagesdiffusion of refractory metal atoms in the intermetallic layer and their transition to the melt and onlyafter that refractory metal atoms will diffuse in the diffusion boundary layer The assumed specimenrotation rates (1 and 2 rps) are comparable with free convection

These results show that saturation of melts with alloying components may be accelerated by usingof an alloying metal in a disperse form and also by intensive mixing The dissolution rate increasesappreciably when the temperature is raised from 800 to 900degС However even at 1000minus1100degС largepieces of metals are dissolved for several hours if mixing is weak The results obtained can be used to

b

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

6

calculate diffusion coefficients effective radii of diffusing particles and their dependences ontemperature and activation energy in liquid aluminum Inaccurate values of kinematic viscosity onlyslightly affect the calculations whereas solubility data give the main error

Figure 6 Characteristic of corrosion stability of elements (in points and mgcm2middoth)in gallium at 673 K as a function of atomic number

References[1] Darby F B Gugle D B and Kleppa O J 1963 The rate of solution of some transition elements in

liquid aluminum Trans Metal Soc AIME 227 179-185[2] Yatsenko S P 2007 Rare elements in aluminum alloys Metally Evrazii 2 66-67[3] Yatsenko S P and Khayak V G 1997 Composite solders based on fusible alloys (Ekaterinburg

UB RAS)[4] Yatsenko S P 1974 Gallium Interaction with metals (Moscow Nauka)[5] Nikitin V I 1967 Physico-chemical phenomena in the interaction between liquid and hard

metals (Moscow Atomizdat)[6] Eremenko V N Natanzon YaV and Titov V P 1998 Kinetics of dissolution of the ZrAl3

compound in liquid aluminum Izvestiya AN SSSR Metally 1 211-215

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

7

The duration of exposure of specimens till complete breakdown versus inverse temperature ispresented in semilogarithmic coordinates in figure 3 For convenient comparison of corrosionresistance of various metals the values are calculated for a reference thickness (15 μm) Provided thatupon dissolution of a specimen the solubility is still far from saturation a direct dependence betweenthe exposure time and the specimen thickness was assumed (table 2)

Figure 3 Temperature dependence of complete corrosion time (lgt) of hard metalspecimens in gallium left ndash metals of the first long period right ndash other metals

Table 2 Effect of the specimen plate thickness on the duration ofcomplete corrosion in gallium

Ratio of specimen exposuretimesMetal Specimen thickness

(μm) and their ratio 673К 773КScandium 3018 17 21 18Iron 3519 18 22 19Cobalt 4020 20 24 205Nickel 3015 20 22 19

The specimens were treated similarlyOver a wide temperature range the values of corrosion exhibit a linear dependence

lgτ = A + BT (6)

where τ is time s T is temperature К А and В are constantsThe coefficients from (6) determined from plots in figure 3 are listed in table 3 along with the

temperature rangesIt is seen from the plots in figure 3 that the exposure time till specimen breakdown increases

abruptly at a certain temperature different for each metal Consequently each metal may becharacterized by a temperature below which the first stage of the corrosion process is limiting Abovethis temperature the process is limited by the second stage namely diffusion It also explains almostidentical inclination angles of the corresponding lines on the plots for different metals The values ofthe coefficient B do not differ more than twice from the average value for the whole group of metals

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

4

Table 3 Corrosion of pure metals in gallium

Coefficients from equation (6)Metal minusА В 103Temperature

range КCorrosion at 673К

mgcm2middothScandium 050 297 593ndash873 110Titanium 115 381 773ndash1073 20middot10minus2Zirconium 140 323 573ndash873 73Hafnium 145 330 623ndash873 143Iron 075 285 573ndash973 71Cobalt 185 346 773ndash973 23Nickel 200 277 573ndash873 20middot102

Metals can be arranged according to the minimum temperatures at which their stability in galliumbecomes linear This sequence characterizes the change in the MendashMe bond strength as compared withMendashGa If the atomic bond energies differ slightly their detachment from the surface and ldquosolvationrdquoby a solvent obeys a statistical law The strength of atomic bonds in a hard metal correlates withmelting sublimation and evaporation heats (see figure 4) Metals with small ΔН values have weakerstability Elements with covalent bonding (Si Ge) require greater energies for detachment of atomscomparing with long-range order breakdown in metals On the lgτ ndash ΔНmelt plot (figure 4а) theseelements are displaced to the right However for the ΔН sublimation (figure 4b) the deviations for Siand Ge fit into the general scatter of points Analysis of corrosion versus the ratio of surface tension ofa metal σМе to the surface tension of gallium (figure 5) shows that metals with a face-centered cubic(FCC) lattice are below the curve plotted in the system of coordinates lgτ ndash σМеσGa Metals with abody-centered cubic (BCC) and hexagonal (hexag) lattice are in the vicinity of the smooth linewhereas those with a diamond-type (diam) structure are located much higher Figure 6 displays therelationship between physical and chemical properties of elements and the periodical character of theircorrosion stability This allows to predict the corrosion stability of metals for which the experimentaldata are not available

The corrosion of specimens in a liquid metal as a function of the medium motion rate is alsodescribed by equations (4) and (5) where only the dissolution rate constant (a) is changed Thefunctional dependence on the liquid metal motion rate υ was established as the power function amot =bmiddotυn The exponent (n) is 05 for a laminar flow and 02 for a turbulent flow [5] However whencorrosion decreases substantially (10 times) the constant a is better described by the lineardependence amot = a0 + bmiddotυ If initial sections of the dissolved transition metal dependences are used

the dissolution rate constants are calculated from plots in semilogarithmic coordinatesC-C

C

H

Hln vs

SmiddotτV The corrosion of Sc Ti Zr Hf in liquid aluminum was studied at temperatures 1073 and 1173Kand the specimen rotation rate equals to 1 and 2 rps Their dissolution rates are listed in table 4

Table 4 Dissolution rates n of Sc Ti Zr Hf in aluminum melt 10minus3gcm2middots

Dissolution temperature and rotation rate1073 K 1123 KMetal

Time ofexperiment

10minus3 s 1 rps 2 rps 1 rps 2 rpsScandium 36ndash108 24 43 56 70Titanium 36ndash108 39 58 78 86Zirconium 36ndash72 43 66 81 89Hafnium 36ndash72 41 63 75 92

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

5

Figure 4 Dependence of lgt of hard metals in gallium at 773 K on atomic melting (a)and sublimation (b) heat Values for Li and Pb are given for their melting temperatures

Figure 5 Dependence of lgt of metals in gallium at 773 K onrelative surface tension of metals

The leading stage of the process is established from the character of breakdown When thedissolution surface is uniform diffusion plays a main role Intermetallic compounds MeAl3 are formedin the considered systems and therefore the values refer to the phases in equilibrium with the meltsThe rates of formation of these phases under chosen conditions are higher than the rates of theirdissolution For zirconium this was earlier established by Eremenko et al [6] Diffusion mobility ofthese complexes is small Therefore the process of dissolution will involve the following stagesdiffusion of refractory metal atoms in the intermetallic layer and their transition to the melt and onlyafter that refractory metal atoms will diffuse in the diffusion boundary layer The assumed specimenrotation rates (1 and 2 rps) are comparable with free convection

These results show that saturation of melts with alloying components may be accelerated by usingof an alloying metal in a disperse form and also by intensive mixing The dissolution rate increasesappreciably when the temperature is raised from 800 to 900degС However even at 1000minus1100degС largepieces of metals are dissolved for several hours if mixing is weak The results obtained can be used to

b

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

6

calculate diffusion coefficients effective radii of diffusing particles and their dependences ontemperature and activation energy in liquid aluminum Inaccurate values of kinematic viscosity onlyslightly affect the calculations whereas solubility data give the main error

Figure 6 Characteristic of corrosion stability of elements (in points and mgcm2middoth)in gallium at 673 K as a function of atomic number

References[1] Darby F B Gugle D B and Kleppa O J 1963 The rate of solution of some transition elements in

liquid aluminum Trans Metal Soc AIME 227 179-185[2] Yatsenko S P 2007 Rare elements in aluminum alloys Metally Evrazii 2 66-67[3] Yatsenko S P and Khayak V G 1997 Composite solders based on fusible alloys (Ekaterinburg

UB RAS)[4] Yatsenko S P 1974 Gallium Interaction with metals (Moscow Nauka)[5] Nikitin V I 1967 Physico-chemical phenomena in the interaction between liquid and hard

metals (Moscow Atomizdat)[6] Eremenko V N Natanzon YaV and Titov V P 1998 Kinetics of dissolution of the ZrAl3

compound in liquid aluminum Izvestiya AN SSSR Metally 1 211-215

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

7

Table 3 Corrosion of pure metals in gallium

Coefficients from equation (6)Metal minusА В 103Temperature

range КCorrosion at 673К

mgcm2middothScandium 050 297 593ndash873 110Titanium 115 381 773ndash1073 20middot10minus2Zirconium 140 323 573ndash873 73Hafnium 145 330 623ndash873 143Iron 075 285 573ndash973 71Cobalt 185 346 773ndash973 23Nickel 200 277 573ndash873 20middot102

Metals can be arranged according to the minimum temperatures at which their stability in galliumbecomes linear This sequence characterizes the change in the MendashMe bond strength as compared withMendashGa If the atomic bond energies differ slightly their detachment from the surface and ldquosolvationrdquoby a solvent obeys a statistical law The strength of atomic bonds in a hard metal correlates withmelting sublimation and evaporation heats (see figure 4) Metals with small ΔН values have weakerstability Elements with covalent bonding (Si Ge) require greater energies for detachment of atomscomparing with long-range order breakdown in metals On the lgτ ndash ΔНmelt plot (figure 4а) theseelements are displaced to the right However for the ΔН sublimation (figure 4b) the deviations for Siand Ge fit into the general scatter of points Analysis of corrosion versus the ratio of surface tension ofa metal σМе to the surface tension of gallium (figure 5) shows that metals with a face-centered cubic(FCC) lattice are below the curve plotted in the system of coordinates lgτ ndash σМеσGa Metals with abody-centered cubic (BCC) and hexagonal (hexag) lattice are in the vicinity of the smooth linewhereas those with a diamond-type (diam) structure are located much higher Figure 6 displays therelationship between physical and chemical properties of elements and the periodical character of theircorrosion stability This allows to predict the corrosion stability of metals for which the experimentaldata are not available

The corrosion of specimens in a liquid metal as a function of the medium motion rate is alsodescribed by equations (4) and (5) where only the dissolution rate constant (a) is changed Thefunctional dependence on the liquid metal motion rate υ was established as the power function amot =bmiddotυn The exponent (n) is 05 for a laminar flow and 02 for a turbulent flow [5] However whencorrosion decreases substantially (10 times) the constant a is better described by the lineardependence amot = a0 + bmiddotυ If initial sections of the dissolved transition metal dependences are used

the dissolution rate constants are calculated from plots in semilogarithmic coordinatesC-C

C

H

Hln vs

SmiddotτV The corrosion of Sc Ti Zr Hf in liquid aluminum was studied at temperatures 1073 and 1173Kand the specimen rotation rate equals to 1 and 2 rps Their dissolution rates are listed in table 4

Table 4 Dissolution rates n of Sc Ti Zr Hf in aluminum melt 10minus3gcm2middots

Dissolution temperature and rotation rate1073 K 1123 KMetal

Time ofexperiment

10minus3 s 1 rps 2 rps 1 rps 2 rpsScandium 36ndash108 24 43 56 70Titanium 36ndash108 39 58 78 86Zirconium 36ndash72 43 66 81 89Hafnium 36ndash72 41 63 75 92

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

5

Figure 4 Dependence of lgt of hard metals in gallium at 773 K on atomic melting (a)and sublimation (b) heat Values for Li and Pb are given for their melting temperatures

Figure 5 Dependence of lgt of metals in gallium at 773 K onrelative surface tension of metals

The leading stage of the process is established from the character of breakdown When thedissolution surface is uniform diffusion plays a main role Intermetallic compounds MeAl3 are formedin the considered systems and therefore the values refer to the phases in equilibrium with the meltsThe rates of formation of these phases under chosen conditions are higher than the rates of theirdissolution For zirconium this was earlier established by Eremenko et al [6] Diffusion mobility ofthese complexes is small Therefore the process of dissolution will involve the following stagesdiffusion of refractory metal atoms in the intermetallic layer and their transition to the melt and onlyafter that refractory metal atoms will diffuse in the diffusion boundary layer The assumed specimenrotation rates (1 and 2 rps) are comparable with free convection

These results show that saturation of melts with alloying components may be accelerated by usingof an alloying metal in a disperse form and also by intensive mixing The dissolution rate increasesappreciably when the temperature is raised from 800 to 900degС However even at 1000minus1100degС largepieces of metals are dissolved for several hours if mixing is weak The results obtained can be used to

b

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

6

calculate diffusion coefficients effective radii of diffusing particles and their dependences ontemperature and activation energy in liquid aluminum Inaccurate values of kinematic viscosity onlyslightly affect the calculations whereas solubility data give the main error

Figure 6 Characteristic of corrosion stability of elements (in points and mgcm2middoth)in gallium at 673 K as a function of atomic number

References[1] Darby F B Gugle D B and Kleppa O J 1963 The rate of solution of some transition elements in

liquid aluminum Trans Metal Soc AIME 227 179-185[2] Yatsenko S P 2007 Rare elements in aluminum alloys Metally Evrazii 2 66-67[3] Yatsenko S P and Khayak V G 1997 Composite solders based on fusible alloys (Ekaterinburg

UB RAS)[4] Yatsenko S P 1974 Gallium Interaction with metals (Moscow Nauka)[5] Nikitin V I 1967 Physico-chemical phenomena in the interaction between liquid and hard

metals (Moscow Atomizdat)[6] Eremenko V N Natanzon YaV and Titov V P 1998 Kinetics of dissolution of the ZrAl3

compound in liquid aluminum Izvestiya AN SSSR Metally 1 211-215

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

7

Figure 4 Dependence of lgt of hard metals in gallium at 773 K on atomic melting (a)and sublimation (b) heat Values for Li and Pb are given for their melting temperatures

Figure 5 Dependence of lgt of metals in gallium at 773 K onrelative surface tension of metals

The leading stage of the process is established from the character of breakdown When thedissolution surface is uniform diffusion plays a main role Intermetallic compounds MeAl3 are formedin the considered systems and therefore the values refer to the phases in equilibrium with the meltsThe rates of formation of these phases under chosen conditions are higher than the rates of theirdissolution For zirconium this was earlier established by Eremenko et al [6] Diffusion mobility ofthese complexes is small Therefore the process of dissolution will involve the following stagesdiffusion of refractory metal atoms in the intermetallic layer and their transition to the melt and onlyafter that refractory metal atoms will diffuse in the diffusion boundary layer The assumed specimenrotation rates (1 and 2 rps) are comparable with free convection

These results show that saturation of melts with alloying components may be accelerated by usingof an alloying metal in a disperse form and also by intensive mixing The dissolution rate increasesappreciably when the temperature is raised from 800 to 900degС However even at 1000minus1100degС largepieces of metals are dissolved for several hours if mixing is weak The results obtained can be used to

b

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

6

calculate diffusion coefficients effective radii of diffusing particles and their dependences ontemperature and activation energy in liquid aluminum Inaccurate values of kinematic viscosity onlyslightly affect the calculations whereas solubility data give the main error

Figure 6 Characteristic of corrosion stability of elements (in points and mgcm2middoth)in gallium at 673 K as a function of atomic number

References[1] Darby F B Gugle D B and Kleppa O J 1963 The rate of solution of some transition elements in

liquid aluminum Trans Metal Soc AIME 227 179-185[2] Yatsenko S P 2007 Rare elements in aluminum alloys Metally Evrazii 2 66-67[3] Yatsenko S P and Khayak V G 1997 Composite solders based on fusible alloys (Ekaterinburg

UB RAS)[4] Yatsenko S P 1974 Gallium Interaction with metals (Moscow Nauka)[5] Nikitin V I 1967 Physico-chemical phenomena in the interaction between liquid and hard

metals (Moscow Atomizdat)[6] Eremenko V N Natanzon YaV and Titov V P 1998 Kinetics of dissolution of the ZrAl3

compound in liquid aluminum Izvestiya AN SSSR Metally 1 211-215

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

7

calculate diffusion coefficients effective radii of diffusing particles and their dependences ontemperature and activation energy in liquid aluminum Inaccurate values of kinematic viscosity onlyslightly affect the calculations whereas solubility data give the main error

Figure 6 Characteristic of corrosion stability of elements (in points and mgcm2middoth)in gallium at 673 K as a function of atomic number

References[1] Darby F B Gugle D B and Kleppa O J 1963 The rate of solution of some transition elements in

liquid aluminum Trans Metal Soc AIME 227 179-185[2] Yatsenko S P 2007 Rare elements in aluminum alloys Metally Evrazii 2 66-67[3] Yatsenko S P and Khayak V G 1997 Composite solders based on fusible alloys (Ekaterinburg

UB RAS)[4] Yatsenko S P 1974 Gallium Interaction with metals (Moscow Nauka)[5] Nikitin V I 1967 Physico-chemical phenomena in the interaction between liquid and hard

metals (Moscow Atomizdat)[6] Eremenko V N Natanzon YaV and Titov V P 1998 Kinetics of dissolution of the ZrAl3

compound in liquid aluminum Izvestiya AN SSSR Metally 1 211-215

13th International Conference on Liquid and Amorphous Metals IOP PublishingJournal of Physics Conference Series 98 (2008) 062032 doi1010881742-6596986062032

7