Sintering behavior and mechanical properties of nano-sized
Cr
3
C
2
/Al
2
O
3
composites prepared by MOCVI process
Chih-Lung Chen, Wen-Cheng J. Wei*
Department of Materials Science and Engineering, National Taiwan University, 1 Roosevelt Rd, Section 4, Taipei 106, Taiwan, ROC Received 9 October 2001; received in revised form 15 March 2002; accepted 24 March 2002
Abstract
A process using metal-organic chemical vapor infiltration (MOCVI) conducted in fluidized bed was employed for the preparation of nano-sized ceramic composites. The Cr-species was infiltrated into Al2O3 granules by the pyrolysis of chromium carbonyl
(Cr(CO)6) at 300–450C. The granulated powder was pressureless sintered or hot-pressed to achieve high density. The results
showed that the dominant factors influencing the Cr-carbide phases formation, either Cr3C2or Cr7C3, in the composite powders
during the sintering process were the temperature and oxygen partial pressure in the furnace. The coated Cr-phase either in agglomerated or dispersive condition was controlled by the use of colloidal dispersion. The microstructures showed that fine (20 – 600 nm) CrxCygrains ( 8 vol.%) located at Al2O3grain boundaries hardly retarded the densification of Al2O3matrix in sintering
process. The tests on hardness, strength and toughness appeared that the composites with the inclusions (Cr3C2) had gained the
advantages over those by the rule of mixture. Even 8 vol.% ultrafine inclusions have greatly improved the mechanical properties. The strengthening and toughening mechanisms of the composites were due to grain-size reduction, homogenous dispersion of hard inclusions, and crack deflection. # 2002 Published by Elsevier Science Ltd.
Keywords:Al2O3; Composites; Cr3C2; Cr7C3; MOCVI; Sintering behavior; Mechanical properties
1. Introduction
Ceramic matrix composites have recently come into prominence for structural applications because of their fascinating mechanical properties at room as well as higher temperature. A composite material consisting of Al2O3as a matrix phase and Cr3C2as the second dis-persive phase was prepared by Fu and coworkers.13 The composite with 10–40 vol.% Cr3C2 particulates demonstrated superior mechanical properties better than those of the matrix phase. Due to the high mod-ulus of Cr3C2 and its outstanding high-temperature erosion resistance up to 1100 C, Cr
3C2-based compo-site has been reported ideally suitable for hot extrusion die. Furthermore, its high electrical conductivity is bet-ter than the lowest limit (102 1-cm1) allowed for EDM (electrical discharge machine).3 Those qualities make the composite more favorable for low cost appli-cations.
A number of authors have studied the coating of metal layer by pyrolysis of metal organic precursors.411 Ultrafine nano-composite powder can be synthesized from the molecular precursor by gas reaction technique. Metal-organic chemical vapor deposition (MOCVD) was developed in previous works911and successfully applied in gas-reaction processes of Cr(CO)6and Mo(CO)6. Fur-thermore, the MOCVD process was recently applied for the infiltration of Mo-species in Al2O3matrix for the pre-paration of nano Mo/Al2O3composites.12
The advantages of the addition of ultrafine inclusions have been reported by Niihara and Nakahira in several aspects,1315 namely the reduction of grain size of the matrix grain, the strengthening, and fracture toughening advantages. In this study, a fluidized powder reactor was used for MOCVI processes. The crystalline struc-tures of the Cr-species might show several phases, including pure-Cr, Cr2O3, Cr3C2, CrO2, and CrCO, etc.711The addition of Cr-carbides could have homo-genous Cr distribution and nano-sized inclusions in Al2O3matrix. The implementation of a fluidized powder bed for the preparation of CrO2/Cr2O3 nanopowder/ ceramic composite powders is presented. Besides, this 0955-2219/02/$ - see front matter # 2002 Published by Elsevier Science Ltd.
P I I : S 0 9 5 5 - 2 2 1 9 ( 0 2 ) 0 0 0 5 8 - 4
www.elsevier.com/locate/jeurceramsoc
* Corresponding author. Tel.: 2363-2684; fax: +886-2-2363-4562.
study also used colloidal process to prepare well-dis-persed Cr3C2/Al2O3 mixture before sintering. A small amount ( < 8 vol.%) of Cr3C2 inclusions is enough to significantly improve the strength of the composites.
2. Experimental
2.1. Powder and sample preparation
Chromium hexacarbonyl (Cr(CO)6, 99.7%, Alta
Aesar, Johnson Matthey Company, USA) was used as a source powder. The carbonyl vapor was carried by N2 gas (99.9% pure) into the fluidized powder reactor for MOCVI process.12 Based on Lander’s results, Cr(CO)
6 evaporates readily at ambient temperature under vacuum with a saturation pressure P:4
log P ¼ 11:832 3755:2=T ð1Þ
where T is the reaction temperature in Kelvin. The cal-culated saturation pressure of the carbonyl is 10 Torr at 75 C. The source chamber was maintained at a
con-stant temperature (75C) under vacuum (10 Torr) using
a water bath. A schematic diagram of the apparatus is shown in Fig. 1. The fluidization column made of quartz, had an inside diameter of 75 mm and a length of 500 mm. The pressure drop in the column was measured with a pressure sensor located between the top and bottom of the column. A rotary vacuum pump (R.P.) was installed with cold trap systems. Besides, there was
a vacuum gauge (G) to detect the pressure in front of the pump. The temperature inside the powder bed was measured with a thermocouple. The temperature con-troller (T.C.) connected to an electrical heating system allowed the operation to maintain a constant tempera-ture in the hot-wall reactor.
Because the temperature in the reactor dominated the reactions and the saturation pressure of the carbonyl species, the resulted microstructure and characteristic of Cr-products were greatly affected. One of the para-meters is the yield of the Cr-species by MOCVI process. Precursor would evaporate and partially deposit on the wall of reactors to cause various yields. Yield (Y) of Cr-product was evaluated from the following relationship: Y ¼ Wf 1Wf 0
WS1WS0
ð2Þ
where Wf1 and Wf0 represent the mass of infiltrated composite and alumina powders, respectively, and WS1 and WS0 is the mass of Cr(CO)6 precursor and the remainder after gas reaction.
The carbonyl vapor flowed through the lowest part of the fluidized powder bed and infiltrated into or depos-ited on fluidizing alumina agglomerates1 (AKP-50, Sumitomo Chemical Co., Tokyo, Japan) in a N2stream, as shown in Fig. 1. The deposited agglomerates was analyzed by XRD and showed a Cr2O3/CrO2/Al2O3 mixture. Then, the mixture (Cr2O3/CrO2/Al2O3) was put in aqueous solution with 1.0 mass% dispersant (Darvan C, Vanderbilt Co., Norwalk, USA) based on
Fig. 1. Schematic diagram of the fluidized powder reactor and equipments for MOCVI.
1 The Al
powder and ball-milled for 24 h. The well-dispersed suspension with 30 vol.% powder loading was pressure-casting by an air pressure of 10 kg/cm2 (980 kPa) to form a green compact. After drying, the compact was ground and sieved through a 150-mesh screen for hot-pressing, or made ready for pressureless sintering. 2.2. Densification
Either pressureless sintering or hot-pressing methods were applied for the densification of powder mixture. The 150 mesh mixtures were die-pressed at first, then put into a BN-coated graphite die and hot-pressed at a pressure of 25 MPa for 1 h in a HP furnace (High-multi 5000, Fujidempa Kogyo Co., LTD, Japan) at 1400 C
under vacuum (5104Torr). The pressureless sintering were conducted at temperatures between 1100 and 1600C.
2.3. Characterization of properties
2.3.1. Analyses of phases and microstructure observation The phases of sintered composites were identified by an X-ray diffractometer (Philips PW1710, Philips Co., Netherlands). The morphologies of polished and frac-tured surfaces of composites were analyzed by scanning electron microscopy (SEM, Philips XL30, Philips Co., USA) equipped with an X-ray energy dispersive spec-troscopy (EDS, DX-4, EDAX Co., USA). The TEM samples were cut to thin layers by Isomet (Buehler Ltd., USA) and a 3 mm diameter disc was prepared by using an ultrasonic disc cutter (model 601, Gatan Co., USA). The thickness of the sample was ground and reduced to <100 mm by using Minimet polisher (Buehler Ltd., USA). Afterward, the sample was dimpled to a thick-ness of < 25 mm by a dimple grinder (model 656, Gatan Co., USA) and ion milled by an ion miller (Gatan Co., USA). The transmission electron microscopes (TEM,
100CXII, Jeol Co., or Hitachi Model HF-2000
FETEM, Japan) were employed to observe the micro-structure of the sample previously coated with a thin carbon layer.
2.3.2. Thermal shrinkage analysis
The sintering behaviors and shrinkage of the compo-sites were tested by a thermal mechanical analyzer (TMA, SETSYS TMA16/18, SETARAM Co., France). The operation conditions were conducted usually from room temperature to 1400C under vacuum condition
with a heating rate of 10C/min.
2.3.3. Mechanical tests
The sintered or HP composite disks were cut and ground to the dimensions of 3435 mm3. All surfaces of the test bars were polished with various diamond pastes with sizes from 30, 6 to 1 mm. The flexural
strength was conducted following a four-point bending test method according to ASTM C1161 standard. Hardness and toughness were measured by a Vickers indentor (AKASHl, AVK-A, Japan). The toughness values were calculated following the equation proposed by Evans.16These mechanical properties were measured at room temperature.
3. Results and discussion
3.1. Effects of temperature and atmosphere
The yield of Cr(CO)6decomposition at various reac-tion temperatures in a N2 flow rate of 1.5 l/m and a constant pressure of 10 Torr is shown in Fig. 2. The yield increases with the reaction temperature, and reaches a maximum at 400C. When the reaction
tem-perature is 400 C during the MOCVI process, the
highest conversion ratio shows 60% yield. The residual products are lost by two ways. Part of the residue was adhered on the wall of fluidization column and the rest was sucked away by the mechanical pump. The Cr-spe-cies were stuck on the cold trap tubes during the MOCVI process.
The deposited composites were analyzed by XRD. A series of the spectra of the composites treated in vacuum (5102Torr) is shown in Fig. 3. At low temperature, i.e. 600C, the spectra show that Cr
2O3phase is the as-deposited Cr-species. According to our previous analy-sis,11a few per cent of carbon can form a solid solution in the oxide. At higher temperature, Cr3C2 appears above 700C, but it is replaced by Cr7C3above 1100
C. The formation of the carbides from Cr2O3in reducing atmosphere can be:
Fig. 2. Plot of the decomposition yield of Cr(CO)6at various coating
3=2Cr2O3ðSÞþ2COðgÞ¼Cr3C2ðSÞþ13=4O2ðgÞ
G ¼ 1800765 þ 234:9T
ð3Þ
The Cr3C2 (orthorhombic phase) likely transforms into Cr2O3in the O2-rich atmosphere. The above reac-tion was proven by XRD analysis.
There are several Cr-carbide phases in Cr–C system, such as Cr3C2, Cr7C3and Cr23C6. The Cr3C2is unstable in O2-rich atmosphere compared to the others. It is easily oxidized at high temperature and even at very low partial pressure of oxygen in accordance with the ther-modynamic results, suggesting the following oxidation reaction of Cr3C2:
Cr3C2ðSÞþ5=14O2ðgÞ¼3=7Cr7C3ðSÞþ5=7COðgÞ
G¼ 63284:766:78T ð4Þ
and the carbon and oxygen reaction in graphite furnace can be
CðSÞþ1=2O2ðgÞ¼COðgÞ G¼ 11170087:65T ð5Þ
By means of Eqs. (4) and (5), we can draw an Elling-ham diagram as shown in Fig. 4 which shows the var-iation of the Gibbs free energy with temperature at 1 atm. The Gibbs free energy of CO(g) formation (258 kJ/mol) is lower than that of Cr7C3(S)formation (175 kJ/mol) at 1400C. Because of the heating element, the insulation and mold in the furnace were made of gra-phite, the graphite easily reacts with oxygen if it is an impurity in flowing N2(g), to form CO(g) during HP
sintering at 5104Torr. In other words, the CO gas is more stable than Cr7C3 in oxygen-contained atmo-sphere. Besides, Eq. (4) can be confirmed by the appearance of Cr-carbide samples which turn to a pur-ple color (i.e. Cr7C3). The formation of Cr3C2 during HP (hot-pressing) at a vacuum condition of 5104 Torr is easily differentiated from the formation of Cr7C3 during pressureless sintering at a poor vacuum condi-tion of 5102Torr. The Cr
3C2will react with oxygen gas and form Cr2O3or Cr7C3in a poor vacuum condi-tion. Moreover, a high-density matrix will restrict the CO producing diffusing out from the interior of matrix. Fig. 3. XRD patterns of Cr7C3/Al2O3composites heated at different
temperatures for 1 h in vacuum condition.
Fig. 4. Free energy versus temperatures of two oxidation reactions. Note that CO(g)is more stable than Cr7C3(s)in an oxygen-containing
atmosphere.
Fig. 5. Bulk densities of Cr-carbide PLsintered and HP at various temperatues for 1 h in vacuum condition of 5102 Torr (PL) or
5104Torr (HP). The green density of the composites was 2.07 g/
cm3, the density of HPed Al
As a result, the interior of the densified sample shows a mixture of Cr3C2/Al2O3phases.
Fig. 5 shows bulk densities of several sintered com-posites. The initial stage of shrinkage obviously occurs above 1200C. Although the product phases are
differ-ent,2 colloidal process in association with PLsintering or HP can indeed get density (4.03 g/cm3) very close to the theoretical density (T.D.) of the composite. Besides, by means of the high pressure bearing on the composite during sintering can reach the final density at 1400 C,
either with 3 or 8 vol.% Cr3C2. The final density of hot pressed 3 vol.% Cr3C2/Al2O3 composite is similar to that of 8 vol.% Cr3C2/Al2O3composite.
3.2. Microstructural development and sintering behavior A small amount of hard agglomerates which are lar-ger than 20 mm may exist if without colloidal dispersion, as shown in Fig. 6(a). In order to improve the homo-geneity of Cr-carbide dispersion, dispersing, ball mil-ling, and slip casting techniques were adapted. The average grain size of Cr-carbide in sintered composite is
below 1.0 mm and the phase is well dispersed within the Al2O3matrix [Fig. 6(b)]. The agglomerated or micron-sized carbide grains in colloidal-processed composites are hardly observed in the matrix [Figs. 6(b) and 7(a)]. The TEM micrographs [Figs. 6(c) and 7(b)] appear that Cr-carbide grains may have the sizes as small as 20 nm. Most of the intergranular Cr7C3and Cr3C2 grains are larger than 50 nm, and the intragranular Cr7C3 and Cr3C2 grains are in the range of 20 10 nm and are spherical in shape. Only a few Cr-carbide inclusions are larger than 1 mm [Figs. 6(b) and 7(a)].
The size of Al2O3 matrix grains in the composites is smaller with the addition of Cr3C2. The size of most Al2O3grains is restrained to less than 1.2 mm, essentially predicted by the following equation, which relates the matrix grain size (G) to the volume fraction (f) of the second phases, and the grain size (r) of inclusions: G ¼ Kt
r ’pf
1=3 ð6Þ
where Kt is a constant, ’p is the volume fraction of inclusions which is able to restrain the motion of matrix grain boundaries. The topological relation emphasizes the strong pinning effect of a second phases to the matrix grain. Nevertheless, ultra-fine inclusions are Fig. 6. SEM and TEM of Cr7C3/Al2O3composites (a) as-prepared by MOCVI, (b) and (c) followed by colloidal processing. The sintering
condi-tions were PLsintered at 1600C for 1 h in vacuum. Note that Cr
7C3phase was formed in those sintering conditions.
2 The theoretical density (T.D.) of Cr
3C2and Cr7C3is 6.92 and 6.68
unable to be observed in Al2O3matrix due to the reso-lution of SEM. But these carbide grains can be clearly observed by TEM. Ultra-fine, nano-sized Cr-carbide can be fabricated by the gas reaction process.
Several studies reported the sintering behavior and phase transformation during the process of Cr3C2/ Al2O3 composite at high temperature.1,2,18,19 Most of their results showed that the relative density and flexural strength of Cr3C2/Al2O3sintered in vacuum were better than that of argon. Besides, it was proven in previous research that the phase stability of Cr3C2phase was quite sensitive to the temperature and sintering environment.
The die-pressed pure Al2O3, 3 vol.% Cr-carbide/ Al2O3, and 8 vol.% Cr-carbide/Al2O3were examined by TMA in vacuum condition. The results are shown in Fig. 8(a). All three curves start to shrink at ca. 900C,
and show maximal densification rate at ca. 1300 C.
Total 18% linear shrinkage is resulted after holding at 1400 C for 1 h. The pure Al
2O3 was densified nearly identical to that of Cr-carbide composites. But the sin-tering temperature of the composites for full densifica-tion is higher than that of pure Al2O3 which needs temperatures 51500 C for 1 h. There are two reasons
for this. One is the impeding effect of Al2O3 grains by
the inclusions. The other is the back-stress that results from the difference of sintering rate between the carbide phase and Al2O3matrix.
The linear shrinkage of colloidal-processed 8 vol.% Cr-carbide/Al2O3composite sintered at 1600C for 1 h is about 23.5% [Fig. 8(b)] which is larger than that sin-tered at 1400 C. The bulk density of the 8 vol.%
Cr-composite can reach 4.03 g/cm3if PLsintered at 1600C
(Fig. 5).
3.3. Mechanical properties
It is expected that the hardness of Al2O3will increase by the addition of Cr3C2 inclusions because the hard-ness of Cr3C2(27 GPa) is much higher than the hard-ness 18.6 GPa of pure Al2O3. The Vickers hardness of the composites is shown in Fig. 9(a) as a function of inclusion content. The data represent the measured values of 6–8 specimens. The standard deviation is also shown in the figure. Based on the Soroka’s study,20 the Fig. 7. (a) SEM and (b) TEM micrograph of granular 8 vol.% Cr3C2/
Al2O3composites prepared by colloidal processing. The samples were
HP at 1400C in 1 h in vacuum. Note that Cr
3C2phase was formed.
Fig. 8. Dilatometric curves showing the shrinkage behaviours of two composites: (a) sintering of die-pressed powder mixture at 1400C; (b) sintering of colloidal-processed powder mixture at 1600C for 1 h in vacuum condition.
more the porosity, the smaller the hardness of ceramic materials. The influence of porosity to hardness was neglected in this investigation. First, a Cr3C2/Al2O3 composite was fabricated by colloidal processing and hot-pressing. We consider that the composite has reached its final densification. The dotted line in Fig. 9(a) means the hardness plotted according to the rule of mixture. The hardness of the composites is indeed greater than the values calculated by the rule of mixture. Fig. 9(b) shows the four-point flexural strength of Al2O3-based composites as a function of Cr3C2content. Obviously, the flexural strengths of 3 and 8 vol.% Cr3C2 composites are improved from 380 MPa of pure Al2O3
to 600 MPa. The strength increases with increasing Cr3C2content, and shows a maximal value of 546 MPa of 8 vol.% Cr3C2 composite. The strength shows 44% improvement with the addition of 8 vol.% Cr3C2. Based on the Petch relation,21 the finer the grain sizes, the better the strength of materials. This relation suggests that an increasing amount of Cr3C2 could further reduce the size of Al2O3 matrix, thus improving the strength of the composite. More important, the Cr3C2 was synthesized and colloidal processed to achieve a well-dispersive condition. Therefore, the flexural strength is optimized by means of the uniform distribu-tion of the fine Cr3C2inclusions.
Fig. 9. (a) Vickers hardness, (b) four-point bending strength, and (c) fracture toughness of Cr3C2/Al2O3composite plotted against content of Cr3C2.
The toughness of the Cr3C2/Al2O3composites is illu-strated in Fig. 9(c). The toughness of the composites increases with increasing inclusion content. The average value of toughness of 3 and 8 vol.% Cr3C2composites are 5.8 and 6.3 MPa m1/2, respectively.
The SEM morphologies of the fracture surfaces of Cr3C2/Al2O3 composites are shown in Fig. 10. Fine inclusions pointed out in Fig. 10(b) show sphere shape
and have Cr3C2 composition as confirmed by EDS
analysis. The fracture mode of the Al2O3and 3 vol.% Cr-composites apparently exhibit a mixture of trans-granular and intertrans-granular modes. However, the sam-ples with large grains show higher possibility of transgranular fracture mode, and intergranular fracture on smaller grains.
The transgranular fracture seems to happen along the slip plane of Al2O3, as shown in the right-hand corner of Fig. 10(a). The stepwise cleavage features shown on the surface of larger Al2O3 grains is as conspicuous as the occurrence of transgranular fracture. Since the transgranular fracture greatly depends upon the matrix grain size and the contents of Cr3C2 inclusions, the 8
vol.% Cr3C2composites show more intergranular frac-ture, and should have better toughening behavior than that of pure Al2O3and 3 vol.% Cr3C2composite.
Besides, residual stresses may exist on the interface between Cr3C2 and Al2O3. The mismatch of CTE ( =2.8106/C) during the cooling process may
result in a tensile force in the matrix along the radial direction and a compressive force along the tangential direction. The larger the inclusion, the greater the stres-ses. If a crack is approaching the inclusion, the analysis shows that the crack will be deflected thus leading to an increase of the fracture surface area. With regard to the toughening mechanism, one microstructure of the crack/inclusion interaction induced by the Vicker’s indentation is revealed in Fig. 11. A significant feature is observed that the crack propagated along the particle/ matrix interfaces. The crack pattern apparently reveals that the primary toughening mechanism is crack deflec-tion. Based on Evans’ model of crack deflection,22 the toughness increases is mainly due to the increase of total fracture surface area and the change of the fracture mode. Accordingly, the toughness increases as the Fig. 10. SEM micrographs of the fracture surfaces of Cr3C2/Al2O3
composites with (a) 3 vol.% Cr3C2, or (b) 8 vol.% Cr3C2content.
Cr-phase is indicated by arrows in the figure.
Fig. 11. (a) SEM (back scattering image) and (b) TEM micrographs of the interaction of inclusions with crack formed by Vickers indenta-tion on Cr3C2/Al2O3composites. The samples were HP at 1400C for
crack-tip region is subjected to the local compressive stress to decrease the stress intensity while the cracks are propagating within the Al2O3matrix. The crack deflec-tion through the nearest particles induced by residual thermal tension is effectively caused by accounting the number of inclusions available on the crack paths. We believe that 8 vol.% of ultra-fine Cr3C2inclusions can lead to appropriate crack deflection in Al2O3, thereby improving the toughness of the composites.
Nevertheless, there are no other conspicuous tough-ening effects in the composite reinforced by ultra-fine
(450 nm) Cr3C2 inclusion. One TEM observation
shown in Fig. 11(b) indicates that the crack does not propagate straightly in Al2O3matrix, but rather around the Cr3C2 inclusion, as pointed out in Fig. 11(b). That means that even a small Cr3C2 inclusions also have a toughening effect in Al2O3matrix.
4. Conclusion
Nano-sized Cr3C2on Al2O3granules were synthesized by MOCVI. A maximum deposition yield of 60% is obtained at the optimal deposition temperature 400C.
Well-dispersed inclusions (Cr3C2 or Cr7C3) either in agglomeration or dispersive condition in the Al2O3 matrix can be controlled.
The sintering temperature and oxygen partial pressure are the dominant and sensitive factors which affect the phase transformation of Cr-carbide during sintering process. The dense Cr3C2/Al2O3composite can be pre-pared by hot-pressing sintered at 1400C for 1 h at 25
MPa in vacuum. Otherwise, Cr7C3/Al2O3 composites can be obtained in poor vacuum condition. Besides, the shrinkage behaviors between pure Al2O3 and low (48 vol.%) Cr-carbide composites are hardly differentiated.
Based on the microstructural observation, the inter-granular and intrainter-granular Cr-carbide grains are larger than 50 nm and in the sizes of 20 nm, respectively. The Al2O3matrix grains can be controlled to sizes less than 1.2 mm. Two effects were introduced by the fine particles in the composites, less constrain of densification and greater inhibition of matrix grain growth. However, the microstructure of the composite has significantly influ-enced the mechanical properties. The strength and toughness of Al2O3can be improved by the addition of 8 vol.% Cr3C2hard inclusions. Grain size reduction and homogenous distribution of the inclusions in the Al2O3 matrix are the primary strengthening mechanisms. In addition, the major toughening mechanism for Cr3C2/ Al2O3 composite generated by fine Cr3C2 particles is crack deflection. The hardness and strength improve-ment of the composites are similar, and show up to 44% increase. On the other hand, the contribution of tough-ness by 8 vol.% Cr3C2is nearly 40%.
Uncited reference
Ref 17 is not cited in the text
Acknowledgements
The authors like to thank the research funding sup-ported by National Science Council in Taiwan (NSC89– 2216-E-002–001) and helpful discussion with Dr. C.M. Wu in CSIST.
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