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International Journal of Refractory Metals & Hard Materials 25 (2007) 16–24

Effect of die compaction pressure on densification behaviorof molybdenum powders

Pranav Garg a,*, Seong-Jin Park b, Randall M German b

a Pennsylvania State University—University Park, Engineering Science and Mechanics, PA 16802, United Statesb Mississippi State Univeristy—Starkville, Center for Advanced Vehicular Systems, MS 39759, United States

Received 29 September 2005; accepted 29 October 2005

Abstract

Two grades of commercially available ultrafine molybdenum powders are investigated for their compaction and densification behav-ior. Dilatometer studies were performed on the two powders compacted at different pressures, and the results were rationalized usingmaster sintering curve concepts. The study gave insight into the sintering mechanism of molybdenum powders. The results were usefor developing die compaction and sintering models. Accurate density prediction and design of optimum sintering cycles are outcomesfrom this study.� 2005 Elsevier Ltd. All rights reserved.

Keywords: Molybdenum; Die compaction; Master sintering curve; Activation energy; Dilatometer

1. Introduction

The unique physical, chemical, and mechanical proper-ties of molybdenum make it attractive for several high tem-perature applications [1–5]. Because of its high meltingpoint (2610 �C), powder metallurgy (P/M) has been theestablished method for the production of bulk molybde-num components [1]. However, conventional P/M process-ing of molybdenum to near full density requires long timesintering at high temperatures. But the process is costlywhile also leading to excessive grain coarsening and subse-quent loss of mechanical properties thus many of thepotential engineering applications of molybdenum havestill not been realized. Several novel powder consolidationtechniques [6–8] have been investigated as means to lowerthe sintering temperatures to compensate for grain growth.However, these techniques are still in the development

0263-4368/$ - see front matter � 2005 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijrmhm.2005.10.014

* Corresponding author. Tel.: +1 8148652121; fax: +1 8148638211.E-mail address: pxg913@psu.edu (P. Garg).

stage. Moreover, they come at a significant cost comparedto the press and sintering route and therefore not that read-ily suitable for industrial applications.

In this study the sintering behavior of molybdenum isinvestigated. A large amount of published literature isavailable on the sintering behavior of molybdenum [9–23]. The sintering of molybdenum is dominated by the vol-ume diffusion process with associated activation energy of405 kJ/mol [9–11]. This high activation energy explainsthe need for high sintering temperatures, in the range of1800–2000 �C, over long periods to sinter molybdenum todensities above 90% of theoretical density. The additionof small amounts of elements such as Ni, Pt, Pd, and Coactivate the sintering process and considerably lower thesintering temperature to 1200–1400 �C [9,12–21]. Additionof these elements leads to formation of intermetallics alongthe grain boundaries, which provides a ‘short-circuit’ diffu-sion pathway for molybdenum which aids in densification.However, the presence of an intermetallic along the grainboundaries leads to loss of ductility and poor mechanicalproperties in the sintered structure; hence this method isnot practical for the production of high temperature facing

Table 1Powder characteristics of the molybdenum powder used in this study

Vendor Alldyne Osram

Particle shape Irregular IrregularParticle size distributionD10 (lm) 2.8 ± 0.1 2.6 ± 0.1D50 (lm) 6.2 ± 0.3 6.1 ± 0.1D90 (lm) 12.0 ± 0.8 11.1 ± 0.1Dmean (lm) 7.0 ± 0.4 6.5 ± 0.1BET surface area (m2/g) 0.482 0.703BET equivalent diameter (lm) 1.2 0.8Apparent density (g/cm3) 1.86 1.47Tap density (g/cm3) 2.65 2.41Pycnometer density (g/cm3) 10.09 10.13Avg. oxygen content (ppm) 6050 2770Avg. carbon content (ppm) 17 18

P. Garg et al. / International Journal of Refractory Metals & Hard Materials 25 (2007) 16–24 17

structural components. Further research in underway tocompensate for the embrittlement effect of these activatorelements.

The use of smaller size powder has been an establishedtechnique to improve the sinterability of metal powders[22–24]. With the increasing availability of molybdenumpowders in the submicron (0.1–0.5 lm) size range [23],manufacturing molybdenum components from these smal-ler size powders may become a possible option. However,the enhanced sinterability of smaller powders also leads toenhanced grain growth and loss of mechanical propertiesduring sintering. In a recent work on press and sinteringof nanoscale tungsten, Olevsky and German [24] haveindicated the use of high compaction pressure can helpin reducing the sintering time and temperature, thus pre-venting grain coarsening. The smaller the particle size,higher is the required compaction pressure. This studyindicates the influence of compaction pressure (or greendensity) on the sintering behavior, which has not beeninvestigated in details for sintering of pure molyb-denum.

In this study, analysis is carried out on the effect ofcompaction pressure/green density on the sintering of finemolybdenum powders. The analysis is carried out in twoparts. In the first part the pressing of molybdenum pow-ders is modeled by the same process as described byKwon et al. [28]. Once the model has been compiled,the green density can be predicted as a function of com-paction pressure. The masters sintering curve (MSC) the-ory [25] is applied to model the sintering behavior of puremolybdenum compacts. The effect of compaction pressureon sintering behavior is investigated by experimentallyobtaining the MSC at different compaction pressuresusing dilatometer analysis, and consolidating the differentcurves into one masters sintering surface. Once this sur-face has been mapped, it can be used for process optimi-zation. The approach is beneficial as it enables us to mapthe processing-property relationship over a large range ofcompaction pressures based on a small number ofexperiments.

2. Experimental procedure

2.1. Powder acquisition

Two grades of commercially available ultrafine molyb-denum powders were used during this work. The powderswere acquired from Alldyne and Osram. Both grades ofpowder were of commercial purity. The powders werecharacterized for their apparent, tap and pyconometer den-sities, the particle size and size distribution, BET surfacearea and oxygen and carbon impurities. The BET equiva-lent spherical particle diameter (DBET) was calculated forthe two powders using Eq. (1), where A = Specific BETsurface area of the powder in m2/g and qp is the pycnome-ter density of the powder in g/cm3 and DBET is in lm. The

as-measured characteristics of the two powders are listed inTable 1.

DBET ¼6

qpAð1Þ

2.2. Die compaction

Die pressing was used as the method of compaction. Fordeveloping the die-compaction models, right cylindricalcompacts, approximately 12.76 mm diameter and 3 g mass,were made at compaction pressures ranging of 200–2000 MPa from the two powders. Compaction was carriedout using a Carver hand press for compaction pressuresbelow 1000 MPa, and a Gasbarre 534 kN hydraulic pressfor compaction pressures above 1000 MPa. Five sampleswere compacted at each pressure and a typical variationof 1% pycnometer density was seen in green density at eachpressure.

For developing the MSCs for the two powders, rightcylindrical compacts, approximately 12.76 mm diameterand 10 g mass, were made at compaction pressures of280, 560, and 840 MPa using a Carver hand press. Thiscorresponded to a green density of approximately 63%,73%, and 79% of the pycnometer density respectively forthe Alldyne powder, and 58%, 69%, and 76% of the pyc-nometer density respectively for the Osram powder.

2.3. Dilatometer analysis

All sintering runs using an Anter Laboratories Uni-thermTM model #1161 vertical tube dilatometer system.Dilatometer analysis was used as it greatly reduces the totalnumber of sintering runs that have to be carried out toobtain a single MSC. Three separate runs were performedfor each sample type. These runs have been identified inTable 2. All runs were performed in flowing hydrogenatmosphere to prevent oxidation and to promote theremoval of impurities. The resulting data from three runswere used to construct the MSC at a given compactionpressure. The MSC at different compaction pressures wasthen compiled to construct the MSC surface.

Table 2List of dilatometer runs performed in this study

Run # Sintering cycle profile

1 20 �C! 10 �C/min, 900 �C, 10 min! 10 �C/min, 1400�C,60 min! 10 �C/min, 20 �C

2 20 �C! 10 �C/min, 900 �C, 10 min! 3 �C/min, 1400 �C,60 min! 10 �C/min, 20 �C

3 20 �C! 10 �C/min, 1350 �C, 60 min! 10 �C/min, 1450 �C,60 min! 10 �C/min, 20 �C

18 P. Garg et al. / International Journal of Refractory Metals & Hard Materials 25 (2007) 16–24

3. Modeling of die compaction

3.1. Constitutive model

The constitutive model that predicts the densificationbehavior of a powder during die compaction is prerequisitefor this numerical analysis. Many researchers have studiedvarious constitutive models. The general trend is to con-sider the difference in the behavior against compressionand tension such as contained in the Cam-Clay [32,33]and Drucker–Prager [34] models. However, these constitu-tive models improperly treat the tensile response andpotentially overestimate the resistance to tensile stresses,resulting in an inability to properly predict green crack gen-eration. In addition, these constitutive models upset con-vergence in the finite element analysis, since the yieldsurface of these constitutive models is not smooth nearthe intersection point of the failure line and Cap surface.Thus, we elected to use a more conventional constitutivemodel proposed by Shima and Oyane based on uniaxialcompression tests [26]

F ¼ qrm

� �2

þ 6:20ð1� qÞ1:028 prm

� �2

� q5 ð2Þ

where q and p are the effective stress and hydrostatic pres-sure, q is the relative density, and rm is the flow stress of thematrix material. Many researchers have used Eq. (2) toanalyze the compaction process with various powder mate-rials. Recently, Eq. (2) has been successfully applied to diecompaction process with stainless steel powder [27]. How-ever, Eq. (1) was derived from the uniaxial compressionand tension experiments with copper powder from the fol-lowing generalized yield criteria:

F ¼ qrm

� �2

þ að1� qÞb prm

� �2

� qd ð3Þ

where a, b, and d are the material parameters. Therefore,Eq. (2) is the yield functions for only copper powder andnew material parameters in Eq. (3) have to be determinedfor other powder materials.

3.2. Determination of material parameters

In addition to the material parameters for yield criteria,the flow stress of matrix material rm and friction coefficientl need to be measured prior to numerical analysis. The

conventional procedure is to measure these parameters iscomplicated: material parameters a, b, and d, for the yieldcriteria in Eq. (3) are obtained using a triaxial test,although Shima and Oyane demonstrated alternative uni-axial compression and tension tests. Then, to measure theflow stress of the matrix material rm, a uniaxial compres-sion test is used with a bulk sample prepared by hot iso-static pressing. However, hot isostatic pressing is timeconsuming. Even more of a problem, the flow stress duringhot isostatic pressing is different from that of powders dueto the microstructural evolution during hot isostatic press-ing. Finally, for a hard material there is substantial poly-mer binder used in die compaction that is missing in thehot isostatic pressing experiments. Thus, since the frictioncoefficient l depends on the particle size, hardness, rough-ness of tool, amount of lubricant and so on, tests usinghydrostatic compression via hot isostatic pressing arerejected. Many efforts have been tried to measure the fric-tion coefficient but it is still an important research issue.Kwon et al. [27] reports a novel approach that uses theejection force with an applied pressure to measure the fric-tion coefficient.

The conventional procedure explained above is hard touse in an industrial setting, since it needs several expensivetests and access to special equipment. Further, basic datageneration can be very time consuming. To simplify theprocedure to measure the material parameters, a and bare assumed to be invariant with powders, where the valuesfound by Shima and Oyane are used as follows:

a ¼ 6:20 and b ¼ 1:028 ð4Þ

In this study, the simplified procedure proposed by Kwonet al. [28] is used by assuming that a and b are invariantto powders.

Then, the matrix material is assumed to be work-hard-ening in form of following equation:

rm ¼ am þ bmenmm ð5Þ

where am, bm, and nm are the material parameters and em isthe effective strain of matrix material. This simplified pro-cedure needs only a series of die compaction tests by singleaction pressing instead of the complications of triaxialtests, hot isostatic pressing, and uniaxial compression. Tofind material parameters d, am, bm, and nm, cylindricaldie compaction tests are carried out. For this procedure,it is very important to minimize the friction effect as muchas possible. Two treatments are used for this purpose.First, the movement of punch should is minimized byreducing the amount powders. Second, the die wall shouldbe well lubricated using a lubricant coating on the die wallsurface. Then, the relative density versus pressure data arefit to extract d, am, bm, and nm based on the least squaremethod. Then the friction effect is increased to measurethe friction coefficient l. For this procedure, the amountof powders is increased and like traditional compactionno die wall lubricant is used. By comparing the finite ele-ment simulation results using a Coulomb friction model

P. Garg et al. / International Journal of Refractory Metals & Hard Materials 25 (2007) 16–24 19

with the experimental data, an appropriate frictional coef-ficient is determined.

4. Theory of the MSC

4.1. Master sintering curve

Early research identified that diffusion plays the primaryrole in densification of a powder during sintering [29]. Forthe large majority of materials, either grain boundary orvolume diffusion is the dominant densification mechanism.Surface diffusion is active with small powders, but it doesnot contribute to densification. The following multiplemechanism model provides a means to predict densificationbehavior [25]:

1

3qdqdt¼ cXCDo

kGm

1

Texp � Q

RT

� �ð6Þ

with m is 3 for volume diffusion and m is 4 for grain bound-ary diffusion. In Eq. (6), t is the time, c is the surface en-ergy, X is the atomic volume, k is the Boltzmann’sconstant, T is the absolute temperature, C is the materialproperties, Do is the diffusivity pre-exponent, G is the grainsize, Q is the activation energy for diffusion, R is the univer-sal gas constant, respectively. This model assumes graingrowth can be described as a function of density. The mas-ter sintering curve is a direct consequence of this model[25]. Eq. (6) is rearranged to bring all of the constantsand material parameters with slight modification into a sin-gle density dependent parameter P, except for the terms re-lated to temperature

P qð Þ � 1

cXDo

Z q

qo

Gm

3qCdq ð7Þ

Integration is from the initial or green density to the targetfinal density. The remaining terms lead to a parameter thatis equivalent to the thermal work performed in reachingthe density. This parameter H is termed the work ofsintering

H t; Tð Þ �Z t

to

1

Texp � Q

RT

� �dt ð8Þ

Note the work of sintering depends on the time-tempera-ture pathway and contains one activation energy for eachphase during sintering process. While the dominant sinter-ing densification mechanism is volume or grain boundarydiffusion, most materials densify through a mixture of den-sification mechanisms, each with changing roles duringheating and as the microstructure changes. For example,grain boundary diffusion is sensitive to the grain size, sograin growth changes its contribution as the grain bound-ary area declines. Because of these mixed events and theircomplex dependence on temperature, grain size, surfacearea, and curvature, the apparent activation energy usedin Eq. (8) often does not match a handbook diffusionalparameter. Instead, the apparent activation energy is found

through iteration to minimized mean residual amongexperiment data based master curve concept.

4.2. Sigmoid function model

It has been shown [30,31] that a sigmoid function pro-vides a good fit between the densification parameter Wand the natural logarithm of the work-of-sintering, lnH.The sigmoid equation used to define the MSC is

W ¼ q� q0

1� q0

¼ h0 � hh0

¼ 1� hh0

¼ 1

1þ exp � ln H� ab

� � ð9Þ

where h is the porosity, q0 is the relative density, and h0 isthe porosity at the start of the sintering experiment, and aand b are constants defining the curve. Alternative form ofEq. (9) is

U � q� q0

1� q¼ h0 � h

h¼ h0

h� 1 ¼ H

Href

� �n

ð10Þ

or

ln U ¼ n lnH

Href

� �¼ n ln H� ln Hrefð Þ ð11Þ

with lnHref = a and n = 1/b. In Eqs. (10) and (11), U iscalled densification ratio which is defined as the ratio ofdensity difference between current density and initial den-sity to the current porosity, n is a slope, power law expo-nent or densification function, that is rate of increment oflnU during sintering process, and lnHref is natural logarith-mic of work of sintering lnHat q = ( q0 + 1 ) / 2, that ishalf way of densification or densification to parameter Wof 0.5. Note the relationship between W and U is 1/W = 1 + 1/U.

5. Results and discussion

5.1. Powder characterization

The results of the characterization of the two molybde-num powders used in this study are summarized in Table 1.A brief glance through the data indicates that the two pow-ders have very similar characteristics; however, the surfacearea of the two powders varies considerably. The differencein the surface area and hence in the apparent density can beeasily linked to the agglomeration in the two powders asseen in Fig. 1. Since the agglomeration seen in the two pow-ders can influence the particle size distribution as measuredby laser scattering, the BET equivalent diameter particlesize as calculated from the BET surface area by Eq. (1)was used as the characteristic particle size in this study.

5.2. Die compaction behavior

The die compaction behavior of the two powdersis shown in Fig. 2. At lower compaction pressures, the

Fig. 1. SEM images of molybdenum powders (a) Alldyne and (b) Osram.

pressure (MPa)

rela

tive

den

sity

Alldyne

Osram

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

0 500 1000 1500 2000

Fig. 2. Compaction behavior of the molybdenum powders.

Table 3Material properties for die compaction behavior

Powder a b d am

(MPa)bm

(MPa)nm Average

error (%)Maximumerror (%)

Alldyne 8.00 1150 950 0.250 1.29 4.306.20 1.028

Osram 6.30 1090 900 0.250 1.42 3.04

20 P. Garg et al. / International Journal of Refractory Metals & Hard Materials 25 (2007) 16–24

Alldyne molybdenum powder, due to its higher particle size(resulting in lower inter particle friction) is easier to pressthan the finer Osram powder. However, at higher compac-

tion pressures (>1200 MPa), there is very little difference inthe compaction behavior of the two powders. At highercompaction pressures, the powder undergoes the bulkdeformation stage; hence it is the material properties andnot the powder characteristics that play a significant rolein compaction at high pressures.

The calculated material properties for the die compac-tion models as described by Eq. (3) are presented in Table3. Except for d, the calculated numerical values for theother material parameters are very similar for the two pow-ders, as would be expected since they are the same material.This indicates that d is not just a material parameter, but isalso dependent powder characteristic. It is well known thatcoarser powders are easier to press than finer powder of thesame material. In order to describe this phenomenon usingEq. (3) (and assuming all other parameters to be the samefor the two powders) the coarser powder should have ahigher d value than the finer powder. The same trend isobserved for the Alldyne and the Osram powder, withthe Alldyne powder having a higher d value than theOsram powder. The parameter d represents the sensitivityof a powder to compaction pressure during the initialand intermediate stages of compaction, i.e. before the onsetof bulk deformation stage. However, the exact nature ofthe relationship between the powder particle size and d isunclear at this time. The results of this modeling are pre-sented in Table 4. As can be seen, this model is capableof predicting the green densities at various compactionswith a typical accuracy of ±1.5% relative density. Similarcompaction models can be easily developed for any powderbased on a few compaction experiments.

5.3. Densification behavior

The sintered samples were characterized for the sinteringshrinkage, sinter density and anisotropy in the sinteredsamples. It is observed that the samples exhibit shrinkageanisotropy. The anisotropy factor for the various sinteredsamples was calculated using Eq. (12). The results are tab-ulated in Table 5. The data indicates that the Alldyne sam-ples exhibit much higher anisotropic shrinkage than thesamples made from the Osram powder. Since all the pow-ders were compacted on the same press using the same diesand tooling, differences in pressing action or die geometriescannot be responsible for this observation. Moreover, therewere no obvious differences in particle shape of the twopowders that would account for this difference in shrinkagebehavior. Anisotropic shrinkage has been observed during

Table 4Green densities for dilatometry test, actual and predicted

Powder Alldyne Osram

Compaction pressure (MPa) 280 560 840 280 560 840Average density from experiment (% pycnometer) 63.06 ± 0.08 72.64 ± 0.32 79.42 ± 0.42 57.91 ± 0.17 69.29 ± 0.54 76.40 ± 0.20Density from modeling (% pycnometer) 62.25 73.21 79.77 58.92 70.50 77.53Error (%) 1.29 0.79 0.45 1.75 1.75 1.48

Table 5Anisotropy factors

Powder Alldyne Osram

Compaction pressure (MPa) 280 560 840 280 560 840Anisotropy factor 1.169 ± 0.055 1.287 ± 0.141 1.358 ± 0.080 1.012 ± 0.040 1.029 ± 0.026 1.033 ± 0.040

Table 6Summary for densification behavior for Sinter Cycle 1

Powder Alldyne Osram

Compaction pressure (MPa) 280 560 840 280 560 840Sinter density (% pycnometer) 88.93 94.92 96.25 89.24 94.16 96.07Densification parameter W (%) 70.08 81.31 82.21 74.31 81.36 83.88Maximum shrinkage rate (10�5 s�1) 3.783 3.045 2.015 5.423 3.890 2.926Temperature at maximum shrinkage rate (�C) 1362 1320 1267 1303 1260 1226

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

800 900 1000 1100 1200 1300 1400 1500

temperature (oC)

280 MPa

560 MPa

dens

ific

atio

n pa

ram

eter

,Ψ

840 MPa

temperature (oC)

stra

in r

ate

(10-5

/s)

280 MPa

560 MPa

1320 oC

1362 oC

840 MPa

1267 oC

-1

0

1

2

3

4

800 900 1000 1100 1200 1300 1400 1500

(a)

(b)

Fig. 3. In situ sintering response of the Alldyne powder for (a) sinteringcycle #2 and (b) sintering cycle #1.

P. Garg et al. / International Journal of Refractory Metals & Hard Materials 25 (2007) 16–24 21

sintering for a large number of materials, and has beenrelated to a number of phenomenons, including particleshape and particle orientation [35,36], green density [37]and porosity [38]. However, there is still no consensus inthe scientific community as to the exact cause of thisphenomenon.

anisotropy factor ¼ strain or shrinkage in radial direction

strain or shrinkage in height direction

ð12ÞThe sintering response of the two molybdenum powders atdifferent compaction pressures for sinter cycle #1 (seeTable 2) is summarized in Table 6. It can be seen that thesamples compacted from the two powders at different com-paction pressures are sintered to approximately the samedensities, under experimental error. However, the finermolybdenum powder exhibits a higher densification thanthe coarser powder at all compaction pressures. Fig. 3aplots the densification parameter versus temperature forthe Alldyne powder compacts for sinter cycle #2. Sinter cy-cle #2 was chosen for this plot as it was the lowest heatingrate cycle, thus differences in densification behavior areclearly visible. The plot show that samples pressed at high-er pressures show higher and faster densification than sam-ples pressed at lower pressures. Fig. 3b shows the in situshrinkage behavior of the Alldyne molybdenum powdercompacts at different compaction pressures during sinter-ing cycle #1. The total shrinkage as well as the maximumshrinkage rate decreases with increasing compaction pres-sure because of the increase in the starting green density.However, the temperature at which maximum shrinkage

rate occurs also decreases with increasing compaction pres-sure. Similar observations were made for all other sintering

Table 7Apparent activation energy for plotting the MSC

Powder Alldyne Osram

Compaction pressure (MPa) 280 560 840 280 560 840Activation energy (kJ/mol) 231 285 346 246 319 380Error (%) 17.6 23.7 31.0 11.6 23.2 16.3

22 P. Garg et al. / International Journal of Refractory Metals & Hard Materials 25 (2007) 16–24

cycles in both the powders. This indicates that even thoughthe apparent activation energy for the MSC increases withincreasing compaction pressure, the samples pressed athigh pressures achieve higher densification at lower temper-atures than samples pressed at low pressures. This clearlyindicates the importance of compaction pressure, andhence the green density, on the sintering of molybdenumpowders.

5.4. Master sintering curves and master sintering surface

Fig. 4a and b plot the MSC with different compactionpressures for the Alldyne powder. Data obtained fromthree separate runs at a particular compaction pressure iscollapsed onto one curve using the MSC approach. Someprevious studies [20,31] have also applied MSC approachfor molybdenum sintering. A major departure of this studyfrom past studies is the manner in which MSC are plotted.In past studies the authors performed several (>10) sinter-ing experiments to obtain points along the MSC, which istime consuming. Moreover, they still lacked sufficient datato experimentally calculate the value for the apparent acti-vation energy and had to rely on handbook values. Usingdilatometer analysis, only three runs are required to plotthe MSC at a given compaction pressure. The dilatometeralso provides us with sufficient data to calculate the appar-ent activation energy by least square principles.

The apparent energy values used for plotting the MSCsin Fig. 4 are presented is Table 7. For both the powders,

dens

ific

atio

n ra

tio,

lnΦ

lnΘ (ln[s/K])

1

a = lnΘref

-6

-4

-2

0

2

4

6

-40 -35 -30 -25 -20 -15 -10

280 MPa

560 MPa840 MPa

n = 1/b

lnΘ (ln[s/K])

dens

ific

atio

n pa

ram

eter

,Ψ

280 MPa560 MPa

840 MPa

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-40 -35 -30 -25 -20 -15 -10

(a)

(b)

Fig. 4. MSC with different compaction pressure for the Alldyne molyb-denum powder.

the apparent activation energy increases with increase incompaction pressure. It is also noteworthy that the appar-ent activation energy increases from approximately 250 kJ/mol, which is close to 263 kJ/mol (the grain boundary dif-fusion activation energy of molybdenum) to an activationenergy of 350–380 kJ/mol, which is close to 405 kJ/mol[9–11] (the volume diffusion activation energy of molybde-num). The increase in apparent activation energy shouldnot be viewed as a change in sintering mechanism. Increas-ing the compaction pressure causes several simultaneouschanges in the green structure. The number of grain-graincontacts increases, the neck size increases, more disloca-tions are introduced, the grain shape and pore morphologychanges and the contribution of various mechanisms to sin-tering changes. However, it is very difficult to quantify thecontribution of an individual mechanism to sintering. Thenet result of all these changes is seen as an increase in theapparent activation energy.

The plots in Fig. 4 clearly indicate the influence of com-paction pressure on sintering behavior. Increasing the com-paction pressure causes the MSC to shift toward the left.Thus less work of sintering is required to achieve the samedensification at higher compaction pressure than at lowercompaction pressure. This agrees with our previous conclu-sions regarding the densification behavior. However, all thecurves converge to the same value as the sampleapproaches full density, independent of the initial compac-tion pressure/green density.

Fig. 5 shows the MSS for the Alldyne molybdenumpowder. MSS is simply a compilation of the variousMSC along the compaction pressure axis, and gives ussome qualitative information on the effect of the greendensity on the MSC. Once the MSS has been obtained,the MSC at any intermediate compaction pressure canbe obtained by sectioning the MSS along that particularpressure. One way to do so would be to develop a 3-Dequation for the surface; however this approach wouldrequire extensive effort. An easier and approximate wayto do so would be to parameterize the MSS by recognizingthe fact that any MSC can be expressed in terms of threeparameters: a, b, and Q in Eq. (9) or lnHref, n and Q inEq. (11). Once the values of these three parameters havebeen found at a minimum of three points, their value atany other point can be calculated by assuming a polyno-mial relationship between the parameter and the compac-tion parameters. Using this approach and curve fitting theexperimentally obtained parameters (from Tables 7 and 8),the following relationships can be obtained for the Alldynepowder:

lnΘ

Ψ

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

-40 -35 -30 -25 -20 -15 -10

280

560

840

P (MPa)

Fig. 5. MSS for the Alldyne molybdenum powder.

Table 8Parameters for MSC

Powder Alldyne Osram

Compaction pressure (MPa) 280 560 840 280 560 840Sigmoid function parameter, n 0.5693 0.4989 0.3832 0.5413 0.3947 0.3141Sigmoid function parameter, lnHref (ln[s/K]) �19.24 �21.95 �27.47 �20.24 �25.27 �30.92R2 0.9863 0.9926 0.9841 0.9959 0.9925 0.9884

P. Garg et al. / International Journal of Refractory Metals & Hard Materials 25 (2007) 16–24 23

QðP Þ ¼ 2:85� 102 þ 2:05� 10�1ðP � 560Þþ 4:46� 10�5ðP � 560Þ2 ð13Þ

aðP Þ ¼ ln HrefðP Þ ¼ �2:20� 101 � 1:47� 10�2ðP � 560Þ� 1:79� 10�5ðP � 560Þ2 ð14Þ

bðP Þ ¼ 1=nðP Þ ¼ 2:00� 100 þ 1:52� 10�3ðP � 560Þþ 2:28� 10�6ðP � 560Þ2 ð15Þ

and for Osram powders

QðP Þ ¼ 3:19� 102 þ 2:39� 10�1ðP � 560Þ� 7:65� 10�5ðP � 560Þ2 ð16Þ

aðP Þ ¼ ln HrefðP Þ ¼ �2:53� 101 � 1:91� 10�2ðP � 560Þ� 3:95� 10�6ðP � 560Þ2 ð17Þ

bðP Þ ¼ 1=nðP Þ ¼ 2:53� 100 þ 2:39� 10�3ðP � 560Þ� 2:30� 10�7ðP � 560Þ2 ð18Þ

where P is the compaction pressure in MPa and280 6 P 6 840, Q is in kJ/mol, and a is in ln(s/K). Notethat the constants in the above equations represent an aver-age value of the parameter over the given range of compac-tion parameter, followed by the first order sensitivity topressure and second order sensitivity to pressure terms.In addition, it is noted that Osram powder has slightly

more sensitivity to pressure on all three parameters thanAlldyne powder. Both the MSC and MSS are powder spe-cific, which tends to limit their applicability. However,using the experimental technique laid out in this study,the MSC can be obtained based on a few experiments.These curves can then be used as reference guides for accu-rate prediction of sinter densities and for the design of opti-mal sintering cycles.

6. Conclusions

The die compaction of molybdenum powders was mod-eled using approach described by Kwon et al. [28]. Diecompaction model capable of predicting the green densityto within ±1% theoretical density was formulated. Theresults indicated that the parameter d in Eq. (3), previouslyconsidered a material parameter, is infact dependent onboth the material as well as the powder characteristic. Thisparameter can be easily evaluated for a given powder basedon a few die compaction experiments.

The sintering behavior of the molybdenum powders wascharacterized using the MSC approach and dilatometerstudies. The apparent activation energy for molybdenumsintering was found to increase with increasing compactionpressure. The samples pressed at higher pressures density

24 P. Garg et al. / International Journal of Refractory Metals & Hard Materials 25 (2007) 16–24

faster and to a greater extent than samples pressed at lowerpressures. Also, the temperature at which compact under-goes maximum shrinkage rate occurs decreases withincreasing compaction pressure. Therefore, the requiredsintering temperature decreases with increasing compac-tion pressure.

The dilatometer data were used to plot the MSC andwhich were then compiled to plot the MSS. The MSS pro-vides us with an approach for predicting the sinter densityat any compaction pressure and sintering route, which canthen be used for sinter density predictions and process opti-mization. This study establishes a possible template ofexperimental procedures and modeling techniques whichcan be easily adapted for future modeling efforts.

Acknowledgements

The funding for this study was provided by membercompanies in the Center for Innovative Sintered Products,The Pennsylvania State University, University Park. Pow-ders were donated by Osram Sylvania and Alldyne PowderTechnologies.

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