- Email: [email protected]
Densification of potassium-doped tungsten during sintering
Int. Journal of Refractory Metals and Hard Materials 50 (2015) 217–220
Contents lists available at ScienceDirect
Int. Journal of Refractory Metals and Hard Materials journal homepage: www.elsevier.com/locate/IJRMHM
Densification of potassium-doped tungsten during sintering Jürgen Almanstötter OSRAM GmbH, Corporate Technology CT TSS MTS MET, Mittelstetter Weg 2, 86830 Schwabmünchen, Germany
a r t i c l e
i n f o
Article history: Received 20 October 2014 Received in revised form 21 January 2015 Accepted 27 January 2015 Available online 28 January 2015 Keywords: Potassium-doped tungsten Sintering
a b s t r a c t Tungsten is traditionally sintered at very high temperatures. The master sintering curve (MSC) for densification is a functional model that describes sintering under an arbitrary time–temperature regime of a particular material during heating. The MSC for potassium-doped tungsten (W-K) has been determined by fitting experimental relative density data results versus work of sintering data with a modified sigmoid function. Five independent parameters of the fitting function are identified by minimizing error in terms of mean residual square. For measurement of relative density during sintering, we developed a non-contact high temperature dilatometer experiment using an optical method. Densification was continuously recorded at constant heating rates of 5, 10, 20, 30 and 40 °C/min. The work presented here was carried out to predict and control densification evolution of W-K during free sintering. The results demonstrate, that the MSC model of W-K describes densification independently of selected temperature regime. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Potassium doped tungsten (W-K) is heavily used in the lighting industry e.g. for filaments in modern automotive halogen lamps and electrodes in high intensity discharge (HID) lamps. It has excellent creep properties at high temperatures resulting from the interlocking grain structure in recrystallized state due to the presence of potassium bubble rows. Besides the outstanding creep resistance, W-K exhibits high recrystallization temperature and significantly enhanced ductility at elevated temperature [1]. These excellent high temperature properties and good resistance to erosion as well as sputtering make W-K also an attractive alternative to be used as plasma facing material in future fusion reactors [2]. The processing of W-K is done via the powder metallurgical route, starting from powder synthesis followed by powder compaction, sintering and thermo-mechanical deformation. Sintering is a complex process involving microstructural evolution by densification through several different transport mechanisms. The factors that influence sintering are temperature, time, green density and bulk composition. In materials with high melting points, like tungsten, that require high sintering temperatures, it is beneficial to design sintering cycles that minimize energy consumption while attaining a certain target density and uniform microstructure. Therefore, there is a need for optimizing the sintering process parameters. The aim of this paper is to construct the master sintering curve (MSC) of W-K, which can then be further used to predict densification behavior under arbitrary thermal histories for a given processing method. Predicting the sintering deformation of compacts is very important to powder
E-mail address: [email protected].
http://dx.doi.org/10.1016/j.ijrmhm.2015.01.017 0263-4368/© 2015 Elsevier Ltd. All rights reserved.
metallurgical manufacturing. For the determination of sintering shrinkage, we developed a non-contact in situ measuring device using an optical method. 2. Master sintering curve model The concept of MSC was introduced by Su und Johnson [3] as an extension of classical sintering theory for free (pressureless) sintering to characterize densification behavior of a given powder regardless of heating procedures. It was derived from the combined stage sintering model [4] including volume and grain boundary diffusion mechanism, dρ γΩa Γ ðρÞD0 1 −k QT ðtÞ ¼ e B kB ðGðρÞÞn T ðt Þ 3ρdt with n = 3 for volume diffusion, n = 4 for grain boundary diffusion, γ is surface energy, Ωa is atomic volume, kB is Boltzmann's constant, Γ is a scaling factor, D0 is diffusion pre-exponent, G is grain size, Q is apparent activation energy for diffusion, t is time, and T is absolute temperature. The model assumes that grain growth can be described as a function of density only. The master sintering curve is derived by rearranging the equation above to gather all the constants and material-dependent parameters, except for the apparent activation energy, into a single density-dependent parameter: ΦðρÞ :¼
kB γΩa D0
Z
ρ
n
ðGðρÞÞ dρ: ρ0 3ρΓ ðρÞ
Integration is performed from green density to the sintered density. The remaining terms are collected into a parameter Θ(t,T(t)) that
218
J. Almanstötter / Int. Journal of Refractory Metals and Hard Materials 50 (2015) 217–220
Fig. 1. Setup of the optical high temperature dilatometer.
represents the thermal work done to reach sintered density. Z ΦðρÞ ¼ Θðt; T ðt ÞÞ :¼
τ 0
1 −Q=ðkB T ðtÞÞdt e T ðt Þ
Note that the work of sintering depends on the time temperature pathway and contains a unique apparent activation energy. Many materials densify through a mixture of volume and grain boundary diffusion. Because of these mixed events and their complex dependence on temperature, grain size, surface area, and curvature, the apparent activation energy Q often does not match a handbook diffusional parameter. Instead, the apparent activation energy that yields the maximum coefficient of determination through regression analysis of experimental data to a sigmoid curve is selected for the MSC: a ic ρðΘÞ ¼ ρ0 þ h 1 þ exp ln Θ−b ln Θ0 where a, b and c are constants, lnΘ0 is the abscissa coordinate of the reflection point of the curve and ρ0 is the initial relative green density. These five parameters determine the exact form of the curve. The concept of MSC has been successfully applied to different classes of materials ranging from e.g. ceramics [5] and metals [6,7] to metal oxides [8].
Fig. 2. W-K sintering sample within tungsten holder.
Fig. 3. Density evolution for different heating rates.
3. Experimental The W-K powder (Osram) used in this work has a potassium content of 140 ppm and grain size of 4.1 μm (Fisher SSS). Powder compacts are prepared by pressing 3 g of tungsten powder in a double-action press [9] to obtain nearly homogeneous density along the sample height. The relative green density obtained after compaction is about 65% of theoretical density and defines the initial condition for subsequent sintering. Fig. 1 shows our setup of the thermo-optical device, which allows in situ measurement of shrinkage during sintering. The cylindrical sample (12 mm diameter) is placed on a tungsten holder with four knife shaped edges to minimize thermal and mechanical contacts (c.f. Fig. 2). High frequency inductive heating at 620 kHz is applied through a coil that surrounds the sample. The length of the coil is chosen such that homogeneous temperature distribution of the sample is achieved. The setup is placed into a vacuum chamber. Operating pressure is less than 10− 5 mbar. Shrinkage is measured using an optical dimension measuring system with a CCD camera located outside of the vacuum
Fig. 4. Determination of apparent activation energy Q by using regression analysis.
J. Almanstötter / Int. Journal of Refractory Metals and Hard Materials 50 (2015) 217–220
219
Fig. 5. Identified MSC for W-K and individual experimental data converging close to the single curve.
chamber. It is pointing through a window to the flat surface of the cylindrical sample. Thermal expansion was corrected by scaling the dimensional measurements with the data of a final sintered sample of the same material measured at the respective temperatures. Temperature is determined by using a two-wavelength pyrometer pointing through a second window to the outer surface of the cylindrical sample. Surface emissivity effects are corrected using calibration by a sample with a blind hole in its cylindrical surface to realize a cavity-type blackbody source. A computer program with feedback loop is used to heat the sample with a predefined temporal temperature profile. Non-isothermal sintering at constant heating rates of 5, 10, 20, 30 and 40 °C/min starting from a very short pre-heating stage at 1150 °C is used to reach a desired maximum temperature of 2400 °C without subsequent holding. Different green compacts with same density are used in each sintering run.
Fig. 7. Characteristic diagram for isothermal sintering of W-K.
4. Results Sample shrinkages as a function of time collected at five heating rates are converted to corresponding relative densities. Results are shown in Fig. 3. In all the cases curves have familiar truncated sigmoid shape and are shifted to shorter times with increasing heating rates. The maximum attainable sintered density at 2400 °C reduces with increase in rate of heating, because of shorter total sintering times. The highest sintered density reaching over 90% of theoretical density under these conditions is observed using the lowest heating rate. Results for final densities are in agreement with additional measurements using Archimedes' method. To determine the MSC of W-K we use a variation of values for apparent activation energy Q and conduct nonlinear curve fitting to the union of all data sets included in Fig. 3. For this purpose we employ the nonlinear model fit capabilities of Mathematica [10]. The mean residual square of the fitted MSC and experimental data is given by,
Rða; b; c; lnΘ0 ; Q Þ ¼
Fig. 6. Evolution of sintered density of a cylindrical sample using isothermal heating at 1200 and 1800 °C for 5 h. The line represents the model prediction by MSC, dots indicate experimental recorded data.
N 1X MSC exp 2 ρ −ρi : N i¼1 i
Fig. 4 shows the results of mean residual square R obtained by the variation of values for Q. The minimum of this curve represents the point where all shrinkage data converge to a single curve. This minimum is found to be Q = 272.1 kJ/mol and is close to the experimental measured value for surface diffusion of tungsten (301 kJ/mol [11]). The other constants found with nonlinear model fitting are, a = 33.9596, b = 1.93108, c = 1.873, lnΘ0 = −15.8747 and ρ0 = 65.13%. Fig. 5 shows the related MSC together with experimental data from all heating rates. It can be seen, that the value of Θ(t,T(t)) changes in the range of experimental data to a large extend. Despite the rise of heating rates of about an order of magnitude, the individual curves converge close to a single curve. This indicates that the MSC found is independent of sintering path. For verification of concept, we predict evolution of sintered density from the identified MSC using isothermal conditions at 1200 and 1800 °C as a function of time for 5 h. Densification for cylindrical samples heated under the same conditions is recorded in the
220
J. Almanstötter / Int. Journal of Refractory Metals and Hard Materials 50 (2015) 217–220
optical dilatometer. Fig. 6 shows the results for calculated densification curve together with the collected experimental data and indicates very good agreement. An extension of this prediction of density evolution for isothermal heating is shown in Fig. 7. This diagram illustrates the influence of temperature on density of W-K during sintering for 1 h and can be used for process design. Beyond that, the MSC found allows direct calculation of sintering density evolution for any given thermal process history.
5. Conclusions The densification of potassium-doped tungsten (W-K) during sintering is successfully determined by constant heating rate experiments using a non-contact in-situ measuring device. For modeling of densification the master sintering curve (MSC) concept is used. The density continuously measured during free sintering is used in a nonlinear model fit to find the MSC parameters. It is shown, that the MSC found can be used to predict density evolution regardless of heating regime.
References [1] E. Pink, L. Bartha, The Metallurgy of Doped/Non-sag Tungsten, Elsevier, 1989. [2] G. Pintsuk, I. Uytdenhouwen, Thermo-mechanical and thermal shock characterization of potassium doped tungsten, Int. J. Refract. Met. Hard Mater. 28 (2010) 661–668. [3] H. Su, D.L. Johnson, Master sintering curve: a practical approach to sintering, J. Am. Ceram. Soc. 79 (1996) 3211–3217. [4] J.D. Hansen, R.P. Rusin, M.H. Teng, D.L. Johnson, Combined-stage sintering model, J. Am. Ceram. Soc. 75 (1992) 1129–1135. [5] R.K. Enneti, M.G. Bothara, S.J. Park, S.V. Atre, Development of master sintering curve for field-assisted sintering of HfB 2-20SiC, Ceram. Int. 38 (2012) 4369–4372. [6] K.J. An, Modeling of densification during hot pressing of Fe–Cu–Co–Ni–W–Sn powder mixture, Mater. Trans. 52 (2011) 1334–1337. [7] D.C. Blaine, J.D. Gurosik, S.J. Park, R.M. German, D.F. Heaney, Master sintering curve concepts as applied to the sintering of molybdenum, Metall. Mater. Trans. A 37 (2006) 715–720. [8] J. Banerjee, A. Ray, A. Kumar, S. Banerjee, Studies on sintering kinetics of ThO2–UO2 pellets using master sintering curve approach, J. Nucl. Mater. 443 (2013) 467–478. [9] J. Almanstötter, A modified Drucker–Prager cap model for finite element simulation of doped tungsten powder compaction, Int. J. Refract. Met. Hard Mater. (2015) (submitted for publication). [10] Wolfram Research Inc., Mathematica, Version 9.0, 2012. (Champaign, IL). [11] J.P. Barbour, F.M. Charbonnier, W.W. Dolan, W.P. Dyke, E.E. Martin, J.K. Trolan, Determination of the surface tension and surface migration constants for tungsten, Phys. Rev. 117 (1960) 1452–1459.
Contents lists available at ScienceDirect
Int. Journal of Refractory Metals and Hard Materials journal homepage: www.elsevier.com/locate/IJRMHM
Densification of potassium-doped tungsten during sintering Jürgen Almanstötter OSRAM GmbH, Corporate Technology CT TSS MTS MET, Mittelstetter Weg 2, 86830 Schwabmünchen, Germany
a r t i c l e
i n f o
Article history: Received 20 October 2014 Received in revised form 21 January 2015 Accepted 27 January 2015 Available online 28 January 2015 Keywords: Potassium-doped tungsten Sintering
a b s t r a c t Tungsten is traditionally sintered at very high temperatures. The master sintering curve (MSC) for densification is a functional model that describes sintering under an arbitrary time–temperature regime of a particular material during heating. The MSC for potassium-doped tungsten (W-K) has been determined by fitting experimental relative density data results versus work of sintering data with a modified sigmoid function. Five independent parameters of the fitting function are identified by minimizing error in terms of mean residual square. For measurement of relative density during sintering, we developed a non-contact high temperature dilatometer experiment using an optical method. Densification was continuously recorded at constant heating rates of 5, 10, 20, 30 and 40 °C/min. The work presented here was carried out to predict and control densification evolution of W-K during free sintering. The results demonstrate, that the MSC model of W-K describes densification independently of selected temperature regime. © 2015 Elsevier Ltd. All rights reserved.
1. Introduction Potassium doped tungsten (W-K) is heavily used in the lighting industry e.g. for filaments in modern automotive halogen lamps and electrodes in high intensity discharge (HID) lamps. It has excellent creep properties at high temperatures resulting from the interlocking grain structure in recrystallized state due to the presence of potassium bubble rows. Besides the outstanding creep resistance, W-K exhibits high recrystallization temperature and significantly enhanced ductility at elevated temperature [1]. These excellent high temperature properties and good resistance to erosion as well as sputtering make W-K also an attractive alternative to be used as plasma facing material in future fusion reactors [2]. The processing of W-K is done via the powder metallurgical route, starting from powder synthesis followed by powder compaction, sintering and thermo-mechanical deformation. Sintering is a complex process involving microstructural evolution by densification through several different transport mechanisms. The factors that influence sintering are temperature, time, green density and bulk composition. In materials with high melting points, like tungsten, that require high sintering temperatures, it is beneficial to design sintering cycles that minimize energy consumption while attaining a certain target density and uniform microstructure. Therefore, there is a need for optimizing the sintering process parameters. The aim of this paper is to construct the master sintering curve (MSC) of W-K, which can then be further used to predict densification behavior under arbitrary thermal histories for a given processing method. Predicting the sintering deformation of compacts is very important to powder
E-mail address: [email protected].
http://dx.doi.org/10.1016/j.ijrmhm.2015.01.017 0263-4368/© 2015 Elsevier Ltd. All rights reserved.
metallurgical manufacturing. For the determination of sintering shrinkage, we developed a non-contact in situ measuring device using an optical method. 2. Master sintering curve model The concept of MSC was introduced by Su und Johnson [3] as an extension of classical sintering theory for free (pressureless) sintering to characterize densification behavior of a given powder regardless of heating procedures. It was derived from the combined stage sintering model [4] including volume and grain boundary diffusion mechanism, dρ γΩa Γ ðρÞD0 1 −k QT ðtÞ ¼ e B kB ðGðρÞÞn T ðt Þ 3ρdt with n = 3 for volume diffusion, n = 4 for grain boundary diffusion, γ is surface energy, Ωa is atomic volume, kB is Boltzmann's constant, Γ is a scaling factor, D0 is diffusion pre-exponent, G is grain size, Q is apparent activation energy for diffusion, t is time, and T is absolute temperature. The model assumes that grain growth can be described as a function of density only. The master sintering curve is derived by rearranging the equation above to gather all the constants and material-dependent parameters, except for the apparent activation energy, into a single density-dependent parameter: ΦðρÞ :¼
kB γΩa D0
Z
ρ
n
ðGðρÞÞ dρ: ρ0 3ρΓ ðρÞ
Integration is performed from green density to the sintered density. The remaining terms are collected into a parameter Θ(t,T(t)) that
218
J. Almanstötter / Int. Journal of Refractory Metals and Hard Materials 50 (2015) 217–220
Fig. 1. Setup of the optical high temperature dilatometer.
represents the thermal work done to reach sintered density. Z ΦðρÞ ¼ Θðt; T ðt ÞÞ :¼
τ 0
1 −Q=ðkB T ðtÞÞdt e T ðt Þ
Note that the work of sintering depends on the time temperature pathway and contains a unique apparent activation energy. Many materials densify through a mixture of volume and grain boundary diffusion. Because of these mixed events and their complex dependence on temperature, grain size, surface area, and curvature, the apparent activation energy Q often does not match a handbook diffusional parameter. Instead, the apparent activation energy that yields the maximum coefficient of determination through regression analysis of experimental data to a sigmoid curve is selected for the MSC: a ic ρðΘÞ ¼ ρ0 þ h 1 þ exp ln Θ−b ln Θ0 where a, b and c are constants, lnΘ0 is the abscissa coordinate of the reflection point of the curve and ρ0 is the initial relative green density. These five parameters determine the exact form of the curve. The concept of MSC has been successfully applied to different classes of materials ranging from e.g. ceramics [5] and metals [6,7] to metal oxides [8].
Fig. 2. W-K sintering sample within tungsten holder.
Fig. 3. Density evolution for different heating rates.
3. Experimental The W-K powder (Osram) used in this work has a potassium content of 140 ppm and grain size of 4.1 μm (Fisher SSS). Powder compacts are prepared by pressing 3 g of tungsten powder in a double-action press [9] to obtain nearly homogeneous density along the sample height. The relative green density obtained after compaction is about 65% of theoretical density and defines the initial condition for subsequent sintering. Fig. 1 shows our setup of the thermo-optical device, which allows in situ measurement of shrinkage during sintering. The cylindrical sample (12 mm diameter) is placed on a tungsten holder with four knife shaped edges to minimize thermal and mechanical contacts (c.f. Fig. 2). High frequency inductive heating at 620 kHz is applied through a coil that surrounds the sample. The length of the coil is chosen such that homogeneous temperature distribution of the sample is achieved. The setup is placed into a vacuum chamber. Operating pressure is less than 10− 5 mbar. Shrinkage is measured using an optical dimension measuring system with a CCD camera located outside of the vacuum
Fig. 4. Determination of apparent activation energy Q by using regression analysis.
J. Almanstötter / Int. Journal of Refractory Metals and Hard Materials 50 (2015) 217–220
219
Fig. 5. Identified MSC for W-K and individual experimental data converging close to the single curve.
chamber. It is pointing through a window to the flat surface of the cylindrical sample. Thermal expansion was corrected by scaling the dimensional measurements with the data of a final sintered sample of the same material measured at the respective temperatures. Temperature is determined by using a two-wavelength pyrometer pointing through a second window to the outer surface of the cylindrical sample. Surface emissivity effects are corrected using calibration by a sample with a blind hole in its cylindrical surface to realize a cavity-type blackbody source. A computer program with feedback loop is used to heat the sample with a predefined temporal temperature profile. Non-isothermal sintering at constant heating rates of 5, 10, 20, 30 and 40 °C/min starting from a very short pre-heating stage at 1150 °C is used to reach a desired maximum temperature of 2400 °C without subsequent holding. Different green compacts with same density are used in each sintering run.
Fig. 7. Characteristic diagram for isothermal sintering of W-K.
4. Results Sample shrinkages as a function of time collected at five heating rates are converted to corresponding relative densities. Results are shown in Fig. 3. In all the cases curves have familiar truncated sigmoid shape and are shifted to shorter times with increasing heating rates. The maximum attainable sintered density at 2400 °C reduces with increase in rate of heating, because of shorter total sintering times. The highest sintered density reaching over 90% of theoretical density under these conditions is observed using the lowest heating rate. Results for final densities are in agreement with additional measurements using Archimedes' method. To determine the MSC of W-K we use a variation of values for apparent activation energy Q and conduct nonlinear curve fitting to the union of all data sets included in Fig. 3. For this purpose we employ the nonlinear model fit capabilities of Mathematica [10]. The mean residual square of the fitted MSC and experimental data is given by,
Rða; b; c; lnΘ0 ; Q Þ ¼
Fig. 6. Evolution of sintered density of a cylindrical sample using isothermal heating at 1200 and 1800 °C for 5 h. The line represents the model prediction by MSC, dots indicate experimental recorded data.
N 1X MSC exp 2 ρ −ρi : N i¼1 i
Fig. 4 shows the results of mean residual square R obtained by the variation of values for Q. The minimum of this curve represents the point where all shrinkage data converge to a single curve. This minimum is found to be Q = 272.1 kJ/mol and is close to the experimental measured value for surface diffusion of tungsten (301 kJ/mol [11]). The other constants found with nonlinear model fitting are, a = 33.9596, b = 1.93108, c = 1.873, lnΘ0 = −15.8747 and ρ0 = 65.13%. Fig. 5 shows the related MSC together with experimental data from all heating rates. It can be seen, that the value of Θ(t,T(t)) changes in the range of experimental data to a large extend. Despite the rise of heating rates of about an order of magnitude, the individual curves converge close to a single curve. This indicates that the MSC found is independent of sintering path. For verification of concept, we predict evolution of sintered density from the identified MSC using isothermal conditions at 1200 and 1800 °C as a function of time for 5 h. Densification for cylindrical samples heated under the same conditions is recorded in the
220
J. Almanstötter / Int. Journal of Refractory Metals and Hard Materials 50 (2015) 217–220
optical dilatometer. Fig. 6 shows the results for calculated densification curve together with the collected experimental data and indicates very good agreement. An extension of this prediction of density evolution for isothermal heating is shown in Fig. 7. This diagram illustrates the influence of temperature on density of W-K during sintering for 1 h and can be used for process design. Beyond that, the MSC found allows direct calculation of sintering density evolution for any given thermal process history.
5. Conclusions The densification of potassium-doped tungsten (W-K) during sintering is successfully determined by constant heating rate experiments using a non-contact in-situ measuring device. For modeling of densification the master sintering curve (MSC) concept is used. The density continuously measured during free sintering is used in a nonlinear model fit to find the MSC parameters. It is shown, that the MSC found can be used to predict density evolution regardless of heating regime.
References [1] E. Pink, L. Bartha, The Metallurgy of Doped/Non-sag Tungsten, Elsevier, 1989. [2] G. Pintsuk, I. Uytdenhouwen, Thermo-mechanical and thermal shock characterization of potassium doped tungsten, Int. J. Refract. Met. Hard Mater. 28 (2010) 661–668. [3] H. Su, D.L. Johnson, Master sintering curve: a practical approach to sintering, J. Am. Ceram. Soc. 79 (1996) 3211–3217. [4] J.D. Hansen, R.P. Rusin, M.H. Teng, D.L. Johnson, Combined-stage sintering model, J. Am. Ceram. Soc. 75 (1992) 1129–1135. [5] R.K. Enneti, M.G. Bothara, S.J. Park, S.V. Atre, Development of master sintering curve for field-assisted sintering of HfB 2-20SiC, Ceram. Int. 38 (2012) 4369–4372. [6] K.J. An, Modeling of densification during hot pressing of Fe–Cu–Co–Ni–W–Sn powder mixture, Mater. Trans. 52 (2011) 1334–1337. [7] D.C. Blaine, J.D. Gurosik, S.J. Park, R.M. German, D.F. Heaney, Master sintering curve concepts as applied to the sintering of molybdenum, Metall. Mater. Trans. A 37 (2006) 715–720. [8] J. Banerjee, A. Ray, A. Kumar, S. Banerjee, Studies on sintering kinetics of ThO2–UO2 pellets using master sintering curve approach, J. Nucl. Mater. 443 (2013) 467–478. [9] J. Almanstötter, A modified Drucker–Prager cap model for finite element simulation of doped tungsten powder compaction, Int. J. Refract. Met. Hard Mater. (2015) (submitted for publication). [10] Wolfram Research Inc., Mathematica, Version 9.0, 2012. (Champaign, IL). [11] J.P. Barbour, F.M. Charbonnier, W.W. Dolan, W.P. Dyke, E.E. Martin, J.K. Trolan, Determination of the surface tension and surface migration constants for tungsten, Phys. Rev. 117 (1960) 1452–1459.