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Particle size characterization of ultrafine tungsten powder
International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99 www.elsevier.nl/locate/ijrmhm
Particle size characterization of ultra®ne tungsten powder Liao Jiqiao *, Huang Baiyun National Key Laboratory for Powder Metallurgy, Central South University, Changsha 410083, People's Republic of China Received 25 September 2000; accepted 4 December 2000
Abstract The aim of this research was to investigate the particle size measurement of as-supplied and lab-milled ultra®ne tungsten powders. The ultra®ne tungsten powder derived from X-ray diraction pure WO3 by hydrogen reduction process under ``dry'' reduction conditions was milled for 1, 2 and 4 h, respectively. Then the as-supplied and lab-milled tungsten powders were used to perform particle size measurement by laser diraction method and Fisher sub-sieve sizer (FSSS) method and BET method through adsorption isotherms. Results show that the mean particle size values of as-supplied and lab-milled powders measured by laser diraction method and FSSS method were misleading because of the defects of the measurement system or unsuitability of measurement theory. And the calculated particle size of dBET values from the formula 6= SBET density were smaller than that of by SEM method, which was resulted from the neglect of the eect of surface roughness and pore area on dBET calculation. The fractal dimension D of surface roughness and external surface area St of pores were obtained from adsorption isotherms, which were used to modify dBET calculation formula. The modi®ed formula was dBET M k D=2 6= SBET density), where coecient k was a constant, it was a function of pores area, D was fractal dimension value of surface roughness. As to the ultra®ne tungsten powders in this investigation, k was de®ned as SBET =St , so modi®ed dBET M may be expressed as 3D/(St density). By the modi®ed formula, the calculated dBET M values of four powders in this study were in good agreement with the SEM sizes. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Ultra®ne tungsten powder; Particle size measurement; Modi®ed dBET M calculation formula
1. Introduction Ultra®ne tungsten powders are of special interest today due to their ability to produce hardmetals with superior hardness and wear resistance and the researchers focused on ultra®ne tungsten powder production and characterization have been performed for decades [1±8]. Recent study [3] described the production mechanism of ultra®ne tungsten powder, and Zeiler [3] pointed out that each ultra®ne tungsten carbide grain was obtained from each ultra®ne tungsten grain and the ®neness of ultra®ne tungsten carbide particle was determined by the conventional manufacturing process, and is not produced by milling or classi®cation process. At the same time, the particle size characterization of ultra®ne tungsten powder had been characterized in the above-mentioned literatures. Schubert [6] pointed out that BET-surface area measurement can give some idea about the ultra®ne tungsten carbide powder and Zeiler *
Tel.: +86-731-8876204; fax: +86-731-8825755. E-mail address: [email protected] (L. Jiqiao).
[3] pointed out that due to the high sensitivity of BETmethod to particle roughness and ``sponge-like'' structure of ultra®ne powder, correlations and comparisons of dierent products can be absolutely misleading. With regard to ultra®ne powder, Bock [9] pointed out that the results of conventional particle size and particle size distribution measurements by conventional particle size measurement methods (FSSS, sedimentation, laser diffraction) are erroneous due to the high degree of particle agglomeration and insucient particle dispersion, giving misleading high values for median particle size and inaccurate distribution. The purpose of this investigation was to discuss the particle size characterization of ultra®ne tungsten powder. 2. Experimental 2.1. Production of ultra®ne tungsten powder X-ray diracted pure yellow tungsten oxide WO3 was prepared for hydrogen reduction. Reduction
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experiment was performed in a multitube push-type furnace, under ``dry'' reduction conditions, using cocurrent hydrogen ¯ow, temperature and humidity were kept low to provide unfavorable condition for the formation of WO2 OH2 in order to obtain ultra®ne tungsten powder [10]. 2.2. Milling of ultra®ne tungsten powder According to ASTM standard B430 (90) [11], reduced tungsten powder was milled in a 250 ml capacity, 140 mm high, 60 mm diameter wide-mouth ¯at-bottom centrifuge bottle at 145 rpm for 1, 2, 4 h, respectively. 2.3. Physical characterization measurements 2.3.1. Mean particle size measurements The mean particle sizes of as-supplied and labmilled ultra®ne tungsten powders were obtained by Fisher sub-sieve sizer (FSSS) [12]. Particle size distributions and volume (or mass) mean sizes of tungsten powders were evaluated by laser diraction method [13]. 2.3.2. Measurement of the gas-phase adsorption±desorption isotherms Nitrogen isotherms at 77.35 K were obtained in an Autosorb-1 instrument from Quantachrome. Approximately 5 g of material was weighed in a pellet tube and evacuated at 5 mTorr at 250°C for 10 h. After back®lling with Helium gas, the sample tube was brie¯y exposed to air prior to analysis. The static physisorption experiments were conducted using the Autosorb-1 instrument to determine the amount of liquid nitrogen LN2 adsorbing to or desorbing from the material as a function of pressure P =P0 0:025±0:999. Data were obtained by admitting or removing a known quantity of adsorbate gas into or out of a sample cell containing the solid adsorbent maintained at a constant temperature (77.35 K) below the critical temperature of adsorbate. As adsorption or desorption occurs, the pressure in the sample cell changes until equilibrium is established. The quantity of adsorbed or desorbed at the equilibrium pressure is equal to the dierence between the amount of gas admitted or removed and the amount required to ®ll the space around the adsorbent. 2.3.3. Measurements of BET surface areas and calculation of particle diameter dBET of powders BET model was used to estimate the speci®c surface area SBET through isotherms [14,15]. By SBET a calcu-
lated particle diameter dBET was derived from the formula 6= SBET density. 2.3.4. Application of the Frenkel±Halsey±Hill (FHH) model In order to identify a ``roughness exponent'' of a real surface, fractal dimension D were analyzed by the Frenkel±Halsey±Hill (FHH) model [16±18]. The BET model incorporates the assumption that the energy of adsorption is the same for all surface sites and does not depend on the degree of coverage. Another approach, which takes into account the heterogeneity of adsorption sites, is the Polanyi adsorption potential theory [19,20]. The FHH adsorption isotherm applies the Polanyi adsorption potential theory and is expressed as lg V constant s lg E;
1
where V is the amount adsorbed, and E is the adsorption potential de®ned as: E RT lg 1=X ;
2
where R is the universal gas constant, T is the absolute temperature, and X is the relative pressure, P =P0 . For a smooth surface, s is assumed to be equal to )1/3 [21], while for a fractal surface, s is a function of the fractal dimension, D. If the van der Waals attractive forces are dominant between adsorbent±adsorbate, the s is equal to D 3=3 [22]. For higher surface coverage where the adsorbent±adsorbate interface is controlled by the gas/ liquid surface tension, s would be equal to (D)3) [23,24]. According to the FHH model, on a lg V versus lg E plot, the slop of the straight-line part should be equal to s. In this paper (D 3) values were used to evaluate fractal dimensions. So, surface characterization methods based on fractal geometry describe the topography of real surface in terms of a roughness exponent known as fractal dimension D. Ideal surface, being relativity smooth, can be modeled using simple geometric concepts (e.g., 6L2 for cubes, 4pR2 for spheres, etc.) For such surface D 2, because the surface area is proportional to X 2 , where X is some characteristic dimension of the adsorbent (e.g, X L for squares, R for circles, etc.). In contrast, real surface are generally rough because of atom packing arrangement and defects, kinks and dislocations and pores themselves, depending on the scale considered. Many real surfaces present surface irregularities that appear to be similar at dierent scales. These surface are referred to as fractal because their magnitude is proportion to X D , where D is a fractional exponent that generally assumes values between D 2 (for smooth surface) and D 3 (for surface so rough that they essentially occupy all available volume). The fractal dimension D
L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
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can be thus used to quantify the roughness of real surface. 2.3.5. Application of Barrett±Joyner±Halenda (BJH) model [25] Assuming that the initial relative pressure P =P0 1 is close to unity, all pores are ®lled with liquid. The largest pore of radius rp1 has a physically adsorbed layer of nitrogen molecules of thickness t1 . Inside this thickness is an inner capillary with radius rk from which evaporation takes place as P =P0 is lowered. The relationship between the pore volume Vp1 and the inner capillary (Kelvin) volume Vk is given by 2 2 Vp1 Vk1 rp1 =rk1 :
3
When the relative pressure is lowered from P =P0 1 to P =P0 2 a volume V1 will desorb from the surface. This liquid volume V1 represents not only emptying of the largest pore of its condensate but also a reduction in the thickness of its physically adsorbed layer by an amount Dt1 =2. The pore volume of the largest pore may now be expressed as 2
Vp1 V1 rp1 = rk1 Dt1 =2 :
4
When the relative pressure is again lowered to P =P0 3 the volume of liquid desorbed includes not only the condensate from the next larger size pores but the volume a second thinning of the physically adsorbed layer left behind in the pores of the largest size. The volume Vp2 desorbed from pores of the smaller size is given by Vp2 V2
2
VDt2 rp2 = rk2 Dt2 =2 :
Fig. 1. As-supplied tungsten powder W (a) 1000; (b) 15,000.
5
An expression for VDt2 is VDt2 Dt2 Ac1 ;
6
where Ac1 is the area exposed by the previously emptied pores from which the physically adsorbed gas is desorbed. Eq. (6) can be generalized to represent any step of a stepwise desorption by writing it in the form X Ac j; j 1; . . . ; n 1: VDtn Dtn 7 Table 1 Measured mean particle sizes of as-supplied and lab-milled tungsten powders
The summation in Eq. (7) is the sum of the average area in un®lled pores down to, but not including, the pore that was emptied in the desorption. Substituting the general value for VDt2 into Eq. (5) results in an exact expression for calculating pore volumes at various relative pressure, that is Vpn Vn
Dtn
j 1; . . . ; n
X
Ac j rpn = rkn Dtn =22 ;
1:
8
The area of each pore Ap is a constant and can be calculated from the pore volume, assuming cylindrical pore geometry, that is
Samples
Status
Laser diraction method mean size (lm)
FSSS (lm)
Ap 2Vp =rp :
W W1 W2 W4
As-supplied Lab-milled 1 h Lab-milled 2 h Lab-milled 4 h
16.59 0.85 0.39 0.30
0.54 0.37 0.38 0.45
Then the pore areas can be cumulatively summed so that for any step in the desorption process Ap is known. The Barrett±Joyner±Halenda (BJH) method oers a means P of computing Ac j from Ap for each relative pressure decrement as follows.
9
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3. Results and discussion 3.1. Measured mean particle sizes of as-supplied and labmilled tungsten powders Measured mean particle sizes of four tungsten powders are shown in Table 1. The laser diraction mean particle sizes of four powders were obtained in a Microplus Mastersizer instrument (0.05±550 lm) from Malvern. It's evident that
the laser diraction volume mean particle size of assupplied tungsten powder was much larger than that of lab-milled powders. It's easy to understand that assupplied tungsten powder is the pseudomorphology of the metal powder to the starting material, which were formed into rather stable and coarse agglomerates, as Figs. 1(a,b). After milled for 1, 2 and 4 h, respectively, the mean particle sizes of lab-milled W1 ; W2 and W4 powders decreased with the increasing of milling time. But W1 ; W2 and W4 still kept rather much ``milled new
Fig. 2. Lab-milled tungsten powders: (a) W1 1000; (b) W1 15; 000; (c) W2 1000; (d) W2 15; 000; (e) W4 1000; (f) W4 15; 000.
L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
agglomerates'', as Figs. 2(a,c,e). Even though laser diffraction method gave a look ``reasonable'' particle size distributions as Fig. 3, and though it is possible to disperse the coarse and loose milled new agglomerates (Fig. 2) by strong ultrasonic dispersion unit (in this study, the ultrasonic dispersion power was 250 W) and suitable dispersion medium, but it is almost impossible to disperse the tense and small agglomerates (Figs. 2(b,d,f)) into extremely ®ne grains because of the existence of strong intergranular and interparticular forces(chemical and physical bondings) [6]. So laser diraction method gave a look reasonable but misleading and inaccurate mean particle size values and distributions of W, W1 ; W2 and W4: However, the extremely ®ne tungsten grains should be the measurement goal because each ultra®ne tungsten carbide grain was formed from each ®ne tungsten grain [3]. As to the FSSS particle size values of four powders (Table 1), the given values of mean particle size were much higher than those of in SEM graphs as shown in Figs. 1 and 2. And with the increasing of the milling time, the FSSS sizes increased too, which seemed ``unreasonable''. It's well known to all, the gas permeating method for measurement particle size and speci®c surface area is a quite ideal method to measure coarse particle, which mean particle size is above 10 lm. However, when FSSS method was used to measure mean particle size of ultra®ne powder, especially when the mean particle size is below 0.2 lm, the molecular ¯ow eect should be taken into account [26,27], and in this case the FSSS equation is not suitable any more.
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3.2. Calculated mean particle sizes of ultra®ne tungsten powders How to obtain gas adsorption isotherm was discussed in some papers [14,28,29]. In this investigation, nitrogen adsorption/desorption isotherms of four tungsten powders were obtained in an Autosorb-1 instrument, as Fig. 4. Calculated speci®c surface areas (SBET ) of four powders were derived from BET model [14,15]. SBET and dBET 6= SBET density values were shown in Table 2. With the increasing of milling time, the speci®c surface areas decreased gradually, which may be explained through the BJH cumulative adsorption pore areas of four powders calculated by BJH model [25] as in Fig. 5 and Table 2, which re¯ected the dierent adsorption capacity of four powders, and these plots were in good agreement with the four isotherms. It could be imaged that with the increasing of milling time, the bonding strength and tendency between the grain and the particle increased because of the strong intergranular and interpaticular forces, which made the grain coarsen, and consequently, calculated dBET values showed a slight increase with the increase in milling time. 3.3. Analysis of fractal dimensions and modi®cation of dBET formula To identify the fractal dimensions of surface roughness, FHH model [16±18] was adopted to analyze the four isotherms. The topography of real surface in term of a roughness exponent known as fractal dimension D
Fig. 3. Laser diraction particle size distributions of four powders.
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Fig. 4. Adsorption isotherms of four powders.
Table 2 SBET and dBET and BJH cumulative pore areas values of four powders Samples
Status
SBET (m2 /g)
dBET (lm)
BJH cumulative pore areas (m2 /g)
W W1 W2 W4
As-supplied Lab-milled 1 h Lab-milled 2 h Lab-milled 4 h
5.46 5.24 5.16 4.72
0.057 0.059 0.060 0.066
2.22 2.05 1.94 1.74
had been discussed in literature [29]. The FHH plots derived from isotherms and calculated fractal dimension D values of four powders were shown in Fig. 6 and
Table 3. The D values were calculated for the relative pressure P =P0 of 0.0±0.4 (where micropore ®lling is assumed to be completed).
L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
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Fig. 5. BJH cumulative adsorption pore areas of four powders.
(1) Eect to dBET of fractal dimension D An ideal assumption of all particles consisted of smooth spherical particles lead to the calculation formula of dBET is dBET 6= SBET density:
10
As to smooth surface, fractal dimension D equals to 2, the shape factor is 6, but to a real rough surface, D is between 2 and 3. So, Eq. (10) should be modi®ed by a factor of D/2, that is 0 dBET D=2 6= SBET density;
where 2 6 D < 3.
11
(2) Eect to dBET of pores area From the above analysis, speci®c surface area was linked with the micropore area or volume. Dierent adsorption capacity (Fig. 4) re¯ected dierent pores area (Fig. 5), and with the decrease of adsorption capacity, SBET value decreased, which would lead to dBET value increased. In order to eliminate the eect of pore area on dBET , Eq. (11) should be modi®ed again by another coecient k, that is dBET M k D=2 6= SBET density;
12
where k was a function of pores area.As to ultra®ne tungsten powder, the author proposed a de®nition of k
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Fig. 6. FHH plots of four powders.
where Vads is the volume of nitrogen gas adsorbed corrected to standard conditions of temperature and pressure and the constant 15.47 represents the conversion of the gas volume to liquid volume, t is the statistical thickness of adsorbed ®lm. Calculation of t is a function of the relative pressure using deBore equation [30]
Table 3 Calculated fractal dimension D values of four powders Samples
Status
D
W W1 W2 W4
As-supplied Lab-milled 1 h Lab-milled 2 h Lab-milled 4 h
2.584 2.582 2.581 2.578
k SBET =St ;
13:99= lg P0 =P 0:034 t A
1=2
13
where St is the external surface area of pores [24], that is St Vads 15:47=t;
14
:
15
So, the t-plots and St can be obtained from adsorption isotherm by Eqs. (14) and (15). In this study, the t-plots were obtained when P =P0 was 0.1±0.7 (where t-plots were approximately linear plots), as Fig. 7. So, Eq. (12) may be written as
L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
97
Fig. 7. t-plots of four powders.
dBET M SBET =St D=2 6= SBET density 3D= St density:
16
(3) The physical meaning of coecient k SBET =St The linear BET region for microporous materials generally occurs at relative pressures lower than 0.2. The linear t-plot range will be found at higher relative pressures and is dependent on the size distribution of micropores. The micropore surface area, SMP , then is the dierence between the SBET and the external surface area from the t-plot, that is SMP St SBET :
17
So, SMP has a contribution to SBET at lower relative pressure range (where BET equation is used). When the SBET of one powder was a certain value, a low SMP value showed that micropore had a small contribution to SBET at low relative pressure region, then a high St value led to a low coecient k SBET =St , it also meant that a low k should be compensated to dBET calculation. In this study, the SBET values, external surface area St obtained by Eq. (14) from t-plots (Fig. 7), fractal dimension D values, dBET values and dBET M values from Eqs. (10) and (16), respectively, of four powders are shown in Table 4.
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Table 4 Calculated SBET ; St ; dBET ; k; D, and dBET M values of four powders Samples
SBET (m2 /g)
St (m2 /g)
dBET lm)
k
D
dBET M (lm)
W W1 W2 W4
5.46 5.24 5.16 4.72
3.71 3.51 3.38 3.15
0.057 0.059 0.060 0.066
1.5 1.5 1.5 1.5
2.584 2.582 2.581 2.578
0.11 0.12 0.12 0.13
Obviously, the modi®ed dBET M values were in good agreement with the SEM sizes (SEM size of ultra®ne tungsten grain was about 0.10±0.15 lm), and the modi®ed dBET M value of as-supplied W powder was approximately equal to the dBET M value of lab-milled powders which meant the using of modi®ed dBET M value could approximately re¯ect the modi®ed dBET M value of lab-milled powder, although the powders were sponge-like but the roughness exponents of particle real surface were approximately same, which indicated that it was not necessary to perform the milling process if the particle size measurement aim was only to know how high or low of ultra®ne tungsten metal grain size.
4. Conclusions 1. As to as-supplied or lab-milled ultra®ne tungsten powders, laser diraction method and FSSS method both gave misleading size values because of the defects of the measurement system or measurement theory. 2. Because of neglect of eect of real surface roughness and the contribution of pore area to SBET on dBET calculation, the dBET values from formula of dBET 6/(SBET density) were smaller than that of SEM sizes. 3. A modi®ed calculation formula dBET M was proposed: dBET M k D=2 6= SBET density, where coecient k was a function of pores area, D was fractal dimension by FHH model from adsorption isotherm. As to ultra®ne tungsten powers in this study, k was de®ned as SBET =St , where St was external surface area of pores by deBore equation through t-plot. The calculated modi®cation dBET M values of four powders were in good agreement with the SEM sizes.
Acknowledgements The author gratefully acknowledges the ®nancial support for the present work by the China National Key
Laboratory for P/M (located in Powder Metallurgy Research Institute, Central South University).
References [1] Schubert WD, Lassner E. Int J Refract Met Hard Mater 1991;10:133±41. [2] Schubert WD, Lassner E. Int J Refract Met Hard Mater 1991;10:171±83. [3] Zeiler B. In: Proceedings of the 14th plansee-Seminar, Reutte, Austria 1997;1(4):265±76. [4] Zhengji T. J Refract Met Hard Mater 1986;5(2):108±12. [5] Zhengji T. J Refract Met Hard Mater 1989;8(3):179±84. [6] Schubert WD, Bock A, Lux B. Int J Refract Met Hard Mater 1995;13:281±96. [7] Lardner E, Iggstrom S. In: Proceedings of the 10th PlanseeSeminar, Reutte, Austria 1981;1:549±79. [8] Almond EA, Roebuck B. J Refract Met Hard Mater 1987;6:137± 44. [9] Bock A. In: Proceedings of the 14th Plansee- Seminar, Reutte, Austria 1997;4:437±349. [10] Schubert WD. In: Proceedings of the 12th Plansee-Seminar, Reutte, Austria 1990;4:41±78. [11] ASTM standards for nonferrous metal products. Designation:B430±1995. [12] ASTM standards for nonferrous metal products. Designation:B330-1988(93). [13] ISO13320:1997. Particle size measurement-laser diraction method guide. [14] ISO9277:1995. Determination of the speci®c surface area of solids by gas adsorption using BET method. [15] Greg SJ, Sing KSW. Adsorption, surface area and porosity. New York: Academic press; 1982 [chapter 2]. [16] Pfeifer P, David A. J Chem Phys 1983;79(7):3558±65. [17] Pfeifer P, David A. J Chem Phys 1983;79(7):3566±77. [18] Pfeifer P, Wu YJ, Core MW, Krim J. Phys Rev Lett 1989;62:1997. [19] Montgomery JM. In: Water treatment principles and design. New York:Wiley, 1985. pp. 177±9. [20] Manes M, Hofer JE. Application of the Polanyi adsorption potential theory to adsorption from solution on activated carbon. J Phys Chem 1969;73(3):584±90. [21] Drake JM, Yacullo LN, Levita P, Klafter J. Nitrogen adsorption on porous silica:model-dependent analysis. J Phys Chem 1994;98(2):380±2. [22] Avnir D, Farin D, Pfeifer P. Molecular fractal surfaces. Nature 1984;308:261±3. [23] Avnir D, Jaroniec M. An isotherm equation for adsorption on fractal surfaces of heterogeneous porous materials. Langmuir 1989;5(6):1431±3. [24] Yin Y. Adsorption isotherm on fractal porous materials. Langmuir 1991;7(2):216±7.
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[28] Jiqiao L, Shaoyi C, Zhiqiang Z, Haibo L, Baiyun H. Int J Refract Met Hard Mater 1999;17:423±9. [29] Jiqiao L, Baiyun H, Zhiqiang Z. Determination of physical characterization of tungsten oxide. Int J Refract Met Hard Mater 2001;19:79±84. [30] De Bore JH, Linsen BG, Thvander Plas GJ. J Catal 1965;4:649.
Particle size characterization of ultra®ne tungsten powder Liao Jiqiao *, Huang Baiyun National Key Laboratory for Powder Metallurgy, Central South University, Changsha 410083, People's Republic of China Received 25 September 2000; accepted 4 December 2000
Abstract The aim of this research was to investigate the particle size measurement of as-supplied and lab-milled ultra®ne tungsten powders. The ultra®ne tungsten powder derived from X-ray diraction pure WO3 by hydrogen reduction process under ``dry'' reduction conditions was milled for 1, 2 and 4 h, respectively. Then the as-supplied and lab-milled tungsten powders were used to perform particle size measurement by laser diraction method and Fisher sub-sieve sizer (FSSS) method and BET method through adsorption isotherms. Results show that the mean particle size values of as-supplied and lab-milled powders measured by laser diraction method and FSSS method were misleading because of the defects of the measurement system or unsuitability of measurement theory. And the calculated particle size of dBET values from the formula 6= SBET density were smaller than that of by SEM method, which was resulted from the neglect of the eect of surface roughness and pore area on dBET calculation. The fractal dimension D of surface roughness and external surface area St of pores were obtained from adsorption isotherms, which were used to modify dBET calculation formula. The modi®ed formula was dBET M k D=2 6= SBET density), where coecient k was a constant, it was a function of pores area, D was fractal dimension value of surface roughness. As to the ultra®ne tungsten powders in this investigation, k was de®ned as SBET =St , so modi®ed dBET M may be expressed as 3D/(St density). By the modi®ed formula, the calculated dBET M values of four powders in this study were in good agreement with the SEM sizes. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Ultra®ne tungsten powder; Particle size measurement; Modi®ed dBET M calculation formula
1. Introduction Ultra®ne tungsten powders are of special interest today due to their ability to produce hardmetals with superior hardness and wear resistance and the researchers focused on ultra®ne tungsten powder production and characterization have been performed for decades [1±8]. Recent study [3] described the production mechanism of ultra®ne tungsten powder, and Zeiler [3] pointed out that each ultra®ne tungsten carbide grain was obtained from each ultra®ne tungsten grain and the ®neness of ultra®ne tungsten carbide particle was determined by the conventional manufacturing process, and is not produced by milling or classi®cation process. At the same time, the particle size characterization of ultra®ne tungsten powder had been characterized in the above-mentioned literatures. Schubert [6] pointed out that BET-surface area measurement can give some idea about the ultra®ne tungsten carbide powder and Zeiler *
Tel.: +86-731-8876204; fax: +86-731-8825755. E-mail address: [email protected] (L. Jiqiao).
[3] pointed out that due to the high sensitivity of BETmethod to particle roughness and ``sponge-like'' structure of ultra®ne powder, correlations and comparisons of dierent products can be absolutely misleading. With regard to ultra®ne powder, Bock [9] pointed out that the results of conventional particle size and particle size distribution measurements by conventional particle size measurement methods (FSSS, sedimentation, laser diffraction) are erroneous due to the high degree of particle agglomeration and insucient particle dispersion, giving misleading high values for median particle size and inaccurate distribution. The purpose of this investigation was to discuss the particle size characterization of ultra®ne tungsten powder. 2. Experimental 2.1. Production of ultra®ne tungsten powder X-ray diracted pure yellow tungsten oxide WO3 was prepared for hydrogen reduction. Reduction
0263-4368/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 3 - 4 3 6 8 ( 0 0 ) 0 0 0 5 1 - 2
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L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
experiment was performed in a multitube push-type furnace, under ``dry'' reduction conditions, using cocurrent hydrogen ¯ow, temperature and humidity were kept low to provide unfavorable condition for the formation of WO2 OH2 in order to obtain ultra®ne tungsten powder [10]. 2.2. Milling of ultra®ne tungsten powder According to ASTM standard B430 (90) [11], reduced tungsten powder was milled in a 250 ml capacity, 140 mm high, 60 mm diameter wide-mouth ¯at-bottom centrifuge bottle at 145 rpm for 1, 2, 4 h, respectively. 2.3. Physical characterization measurements 2.3.1. Mean particle size measurements The mean particle sizes of as-supplied and labmilled ultra®ne tungsten powders were obtained by Fisher sub-sieve sizer (FSSS) [12]. Particle size distributions and volume (or mass) mean sizes of tungsten powders were evaluated by laser diraction method [13]. 2.3.2. Measurement of the gas-phase adsorption±desorption isotherms Nitrogen isotherms at 77.35 K were obtained in an Autosorb-1 instrument from Quantachrome. Approximately 5 g of material was weighed in a pellet tube and evacuated at 5 mTorr at 250°C for 10 h. After back®lling with Helium gas, the sample tube was brie¯y exposed to air prior to analysis. The static physisorption experiments were conducted using the Autosorb-1 instrument to determine the amount of liquid nitrogen LN2 adsorbing to or desorbing from the material as a function of pressure P =P0 0:025±0:999. Data were obtained by admitting or removing a known quantity of adsorbate gas into or out of a sample cell containing the solid adsorbent maintained at a constant temperature (77.35 K) below the critical temperature of adsorbate. As adsorption or desorption occurs, the pressure in the sample cell changes until equilibrium is established. The quantity of adsorbed or desorbed at the equilibrium pressure is equal to the dierence between the amount of gas admitted or removed and the amount required to ®ll the space around the adsorbent. 2.3.3. Measurements of BET surface areas and calculation of particle diameter dBET of powders BET model was used to estimate the speci®c surface area SBET through isotherms [14,15]. By SBET a calcu-
lated particle diameter dBET was derived from the formula 6= SBET density. 2.3.4. Application of the Frenkel±Halsey±Hill (FHH) model In order to identify a ``roughness exponent'' of a real surface, fractal dimension D were analyzed by the Frenkel±Halsey±Hill (FHH) model [16±18]. The BET model incorporates the assumption that the energy of adsorption is the same for all surface sites and does not depend on the degree of coverage. Another approach, which takes into account the heterogeneity of adsorption sites, is the Polanyi adsorption potential theory [19,20]. The FHH adsorption isotherm applies the Polanyi adsorption potential theory and is expressed as lg V constant s lg E;
1
where V is the amount adsorbed, and E is the adsorption potential de®ned as: E RT lg 1=X ;
2
where R is the universal gas constant, T is the absolute temperature, and X is the relative pressure, P =P0 . For a smooth surface, s is assumed to be equal to )1/3 [21], while for a fractal surface, s is a function of the fractal dimension, D. If the van der Waals attractive forces are dominant between adsorbent±adsorbate, the s is equal to D 3=3 [22]. For higher surface coverage where the adsorbent±adsorbate interface is controlled by the gas/ liquid surface tension, s would be equal to (D)3) [23,24]. According to the FHH model, on a lg V versus lg E plot, the slop of the straight-line part should be equal to s. In this paper (D 3) values were used to evaluate fractal dimensions. So, surface characterization methods based on fractal geometry describe the topography of real surface in terms of a roughness exponent known as fractal dimension D. Ideal surface, being relativity smooth, can be modeled using simple geometric concepts (e.g., 6L2 for cubes, 4pR2 for spheres, etc.) For such surface D 2, because the surface area is proportional to X 2 , where X is some characteristic dimension of the adsorbent (e.g, X L for squares, R for circles, etc.). In contrast, real surface are generally rough because of atom packing arrangement and defects, kinks and dislocations and pores themselves, depending on the scale considered. Many real surfaces present surface irregularities that appear to be similar at dierent scales. These surface are referred to as fractal because their magnitude is proportion to X D , where D is a fractional exponent that generally assumes values between D 2 (for smooth surface) and D 3 (for surface so rough that they essentially occupy all available volume). The fractal dimension D
L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
91
can be thus used to quantify the roughness of real surface. 2.3.5. Application of Barrett±Joyner±Halenda (BJH) model [25] Assuming that the initial relative pressure P =P0 1 is close to unity, all pores are ®lled with liquid. The largest pore of radius rp1 has a physically adsorbed layer of nitrogen molecules of thickness t1 . Inside this thickness is an inner capillary with radius rk from which evaporation takes place as P =P0 is lowered. The relationship between the pore volume Vp1 and the inner capillary (Kelvin) volume Vk is given by 2 2 Vp1 Vk1 rp1 =rk1 :
3
When the relative pressure is lowered from P =P0 1 to P =P0 2 a volume V1 will desorb from the surface. This liquid volume V1 represents not only emptying of the largest pore of its condensate but also a reduction in the thickness of its physically adsorbed layer by an amount Dt1 =2. The pore volume of the largest pore may now be expressed as 2
Vp1 V1 rp1 = rk1 Dt1 =2 :
4
When the relative pressure is again lowered to P =P0 3 the volume of liquid desorbed includes not only the condensate from the next larger size pores but the volume a second thinning of the physically adsorbed layer left behind in the pores of the largest size. The volume Vp2 desorbed from pores of the smaller size is given by Vp2 V2
2
VDt2 rp2 = rk2 Dt2 =2 :
Fig. 1. As-supplied tungsten powder W (a) 1000; (b) 15,000.
5
An expression for VDt2 is VDt2 Dt2 Ac1 ;
6
where Ac1 is the area exposed by the previously emptied pores from which the physically adsorbed gas is desorbed. Eq. (6) can be generalized to represent any step of a stepwise desorption by writing it in the form X Ac j; j 1; . . . ; n 1: VDtn Dtn 7 Table 1 Measured mean particle sizes of as-supplied and lab-milled tungsten powders
The summation in Eq. (7) is the sum of the average area in un®lled pores down to, but not including, the pore that was emptied in the desorption. Substituting the general value for VDt2 into Eq. (5) results in an exact expression for calculating pore volumes at various relative pressure, that is Vpn Vn
Dtn
j 1; . . . ; n
X
Ac j rpn = rkn Dtn =22 ;
1:
8
The area of each pore Ap is a constant and can be calculated from the pore volume, assuming cylindrical pore geometry, that is
Samples
Status
Laser diraction method mean size (lm)
FSSS (lm)
Ap 2Vp =rp :
W W1 W2 W4
As-supplied Lab-milled 1 h Lab-milled 2 h Lab-milled 4 h
16.59 0.85 0.39 0.30
0.54 0.37 0.38 0.45
Then the pore areas can be cumulatively summed so that for any step in the desorption process Ap is known. The Barrett±Joyner±Halenda (BJH) method oers a means P of computing Ac j from Ap for each relative pressure decrement as follows.
9
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3. Results and discussion 3.1. Measured mean particle sizes of as-supplied and labmilled tungsten powders Measured mean particle sizes of four tungsten powders are shown in Table 1. The laser diraction mean particle sizes of four powders were obtained in a Microplus Mastersizer instrument (0.05±550 lm) from Malvern. It's evident that
the laser diraction volume mean particle size of assupplied tungsten powder was much larger than that of lab-milled powders. It's easy to understand that assupplied tungsten powder is the pseudomorphology of the metal powder to the starting material, which were formed into rather stable and coarse agglomerates, as Figs. 1(a,b). After milled for 1, 2 and 4 h, respectively, the mean particle sizes of lab-milled W1 ; W2 and W4 powders decreased with the increasing of milling time. But W1 ; W2 and W4 still kept rather much ``milled new
Fig. 2. Lab-milled tungsten powders: (a) W1 1000; (b) W1 15; 000; (c) W2 1000; (d) W2 15; 000; (e) W4 1000; (f) W4 15; 000.
L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
agglomerates'', as Figs. 2(a,c,e). Even though laser diffraction method gave a look ``reasonable'' particle size distributions as Fig. 3, and though it is possible to disperse the coarse and loose milled new agglomerates (Fig. 2) by strong ultrasonic dispersion unit (in this study, the ultrasonic dispersion power was 250 W) and suitable dispersion medium, but it is almost impossible to disperse the tense and small agglomerates (Figs. 2(b,d,f)) into extremely ®ne grains because of the existence of strong intergranular and interparticular forces(chemical and physical bondings) [6]. So laser diraction method gave a look reasonable but misleading and inaccurate mean particle size values and distributions of W, W1 ; W2 and W4: However, the extremely ®ne tungsten grains should be the measurement goal because each ultra®ne tungsten carbide grain was formed from each ®ne tungsten grain [3]. As to the FSSS particle size values of four powders (Table 1), the given values of mean particle size were much higher than those of in SEM graphs as shown in Figs. 1 and 2. And with the increasing of the milling time, the FSSS sizes increased too, which seemed ``unreasonable''. It's well known to all, the gas permeating method for measurement particle size and speci®c surface area is a quite ideal method to measure coarse particle, which mean particle size is above 10 lm. However, when FSSS method was used to measure mean particle size of ultra®ne powder, especially when the mean particle size is below 0.2 lm, the molecular ¯ow eect should be taken into account [26,27], and in this case the FSSS equation is not suitable any more.
93
3.2. Calculated mean particle sizes of ultra®ne tungsten powders How to obtain gas adsorption isotherm was discussed in some papers [14,28,29]. In this investigation, nitrogen adsorption/desorption isotherms of four tungsten powders were obtained in an Autosorb-1 instrument, as Fig. 4. Calculated speci®c surface areas (SBET ) of four powders were derived from BET model [14,15]. SBET and dBET 6= SBET density values were shown in Table 2. With the increasing of milling time, the speci®c surface areas decreased gradually, which may be explained through the BJH cumulative adsorption pore areas of four powders calculated by BJH model [25] as in Fig. 5 and Table 2, which re¯ected the dierent adsorption capacity of four powders, and these plots were in good agreement with the four isotherms. It could be imaged that with the increasing of milling time, the bonding strength and tendency between the grain and the particle increased because of the strong intergranular and interpaticular forces, which made the grain coarsen, and consequently, calculated dBET values showed a slight increase with the increase in milling time. 3.3. Analysis of fractal dimensions and modi®cation of dBET formula To identify the fractal dimensions of surface roughness, FHH model [16±18] was adopted to analyze the four isotherms. The topography of real surface in term of a roughness exponent known as fractal dimension D
Fig. 3. Laser diraction particle size distributions of four powders.
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L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
Fig. 4. Adsorption isotherms of four powders.
Table 2 SBET and dBET and BJH cumulative pore areas values of four powders Samples
Status
SBET (m2 /g)
dBET (lm)
BJH cumulative pore areas (m2 /g)
W W1 W2 W4
As-supplied Lab-milled 1 h Lab-milled 2 h Lab-milled 4 h
5.46 5.24 5.16 4.72
0.057 0.059 0.060 0.066
2.22 2.05 1.94 1.74
had been discussed in literature [29]. The FHH plots derived from isotherms and calculated fractal dimension D values of four powders were shown in Fig. 6 and
Table 3. The D values were calculated for the relative pressure P =P0 of 0.0±0.4 (where micropore ®lling is assumed to be completed).
L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
95
Fig. 5. BJH cumulative adsorption pore areas of four powders.
(1) Eect to dBET of fractal dimension D An ideal assumption of all particles consisted of smooth spherical particles lead to the calculation formula of dBET is dBET 6= SBET density:
10
As to smooth surface, fractal dimension D equals to 2, the shape factor is 6, but to a real rough surface, D is between 2 and 3. So, Eq. (10) should be modi®ed by a factor of D/2, that is 0 dBET D=2 6= SBET density;
where 2 6 D < 3.
11
(2) Eect to dBET of pores area From the above analysis, speci®c surface area was linked with the micropore area or volume. Dierent adsorption capacity (Fig. 4) re¯ected dierent pores area (Fig. 5), and with the decrease of adsorption capacity, SBET value decreased, which would lead to dBET value increased. In order to eliminate the eect of pore area on dBET , Eq. (11) should be modi®ed again by another coecient k, that is dBET M k D=2 6= SBET density;
12
where k was a function of pores area.As to ultra®ne tungsten powder, the author proposed a de®nition of k
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L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
Fig. 6. FHH plots of four powders.
where Vads is the volume of nitrogen gas adsorbed corrected to standard conditions of temperature and pressure and the constant 15.47 represents the conversion of the gas volume to liquid volume, t is the statistical thickness of adsorbed ®lm. Calculation of t is a function of the relative pressure using deBore equation [30]
Table 3 Calculated fractal dimension D values of four powders Samples
Status
D
W W1 W2 W4
As-supplied Lab-milled 1 h Lab-milled 2 h Lab-milled 4 h
2.584 2.582 2.581 2.578
k SBET =St ;
13:99= lg P0 =P 0:034 t A
1=2
13
where St is the external surface area of pores [24], that is St Vads 15:47=t;
14
:
15
So, the t-plots and St can be obtained from adsorption isotherm by Eqs. (14) and (15). In this study, the t-plots were obtained when P =P0 was 0.1±0.7 (where t-plots were approximately linear plots), as Fig. 7. So, Eq. (12) may be written as
L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
97
Fig. 7. t-plots of four powders.
dBET M SBET =St D=2 6= SBET density 3D= St density:
16
(3) The physical meaning of coecient k SBET =St The linear BET region for microporous materials generally occurs at relative pressures lower than 0.2. The linear t-plot range will be found at higher relative pressures and is dependent on the size distribution of micropores. The micropore surface area, SMP , then is the dierence between the SBET and the external surface area from the t-plot, that is SMP St SBET :
17
So, SMP has a contribution to SBET at lower relative pressure range (where BET equation is used). When the SBET of one powder was a certain value, a low SMP value showed that micropore had a small contribution to SBET at low relative pressure region, then a high St value led to a low coecient k SBET =St , it also meant that a low k should be compensated to dBET calculation. In this study, the SBET values, external surface area St obtained by Eq. (14) from t-plots (Fig. 7), fractal dimension D values, dBET values and dBET M values from Eqs. (10) and (16), respectively, of four powders are shown in Table 4.
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L. Jiqiao, H. Baiyun / International Journal of Refractory Metals & Hard Materials 19 (2001) 89±99
Table 4 Calculated SBET ; St ; dBET ; k; D, and dBET M values of four powders Samples
SBET (m2 /g)
St (m2 /g)
dBET lm)
k
D
dBET M (lm)
W W1 W2 W4
5.46 5.24 5.16 4.72
3.71 3.51 3.38 3.15
0.057 0.059 0.060 0.066
1.5 1.5 1.5 1.5
2.584 2.582 2.581 2.578
0.11 0.12 0.12 0.13
Obviously, the modi®ed dBET M values were in good agreement with the SEM sizes (SEM size of ultra®ne tungsten grain was about 0.10±0.15 lm), and the modi®ed dBET M value of as-supplied W powder was approximately equal to the dBET M value of lab-milled powders which meant the using of modi®ed dBET M value could approximately re¯ect the modi®ed dBET M value of lab-milled powder, although the powders were sponge-like but the roughness exponents of particle real surface were approximately same, which indicated that it was not necessary to perform the milling process if the particle size measurement aim was only to know how high or low of ultra®ne tungsten metal grain size.
4. Conclusions 1. As to as-supplied or lab-milled ultra®ne tungsten powders, laser diraction method and FSSS method both gave misleading size values because of the defects of the measurement system or measurement theory. 2. Because of neglect of eect of real surface roughness and the contribution of pore area to SBET on dBET calculation, the dBET values from formula of dBET 6/(SBET density) were smaller than that of SEM sizes. 3. A modi®ed calculation formula dBET M was proposed: dBET M k D=2 6= SBET density, where coecient k was a function of pores area, D was fractal dimension by FHH model from adsorption isotherm. As to ultra®ne tungsten powers in this study, k was de®ned as SBET =St , where St was external surface area of pores by deBore equation through t-plot. The calculated modi®cation dBET M values of four powders were in good agreement with the SEM sizes.
Acknowledgements The author gratefully acknowledges the ®nancial support for the present work by the China National Key
Laboratory for P/M (located in Powder Metallurgy Research Institute, Central South University).
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