YOUNG’S MODULUS OF SINGLE PHASE CEMENTITE

H. Mizubayashi*, S.J. Li**, H. Yumoto** and M. Shimotomai****Institute of Materials Science, University of Tsukuba, Tsukuba, Ibaraki 305-8573, Japan

**Department of Materials Science and Technology, Science University of Tokyo, Noda, Chiba278-8510, Japan ***Technical Research Laboratories, Kawasaki Steel Corporation, Chiba,

Chiba 260-0835, Japan

(Received November 24, 1998)(Accepted in revised form January 3, 1999)

Introduction

The Young’s modulus of cementite, Fe3C, is one of the physical quantities which are inevitably requiredto understand the mechanical properties of the high strength steels. Thus, efforts have been devoted toestimate the Young’s modulus of cementite from the mechanical tests on cast iron containing cementite(1–3). Very recently, the electron-shower-assisted physical vapor deposition (ES-PVD, hereafter) hasbeen applied to prepare single phase cementite films (4–6), and their Young’s modulus and Poisson’sratio have been evaluated using the surface wave method (6). On the other hand, the vibrating reedmethod to measure the Young’s modulus of a thin film deposited on a reed-substrate has beenestablished recently (7). In the present paper, we applied the vibrating reed method to the single phasecementite films deposited on silicon reed-substrates to determine the Young’s modulus of cementite.

Experimental

Figure 1(a) is a schematic drawing of a silicon reed-substrate which has been cut out from a FZ-Si singlecrystal and polished into a vibrating reed with a thick end for clamping. The surface-1 scheduled for thedeposition of a cementite-film is a mirror surface, and the surface-2 for the deposition of a silver-film-electrode is a smooth surface with small undulations, where the homogeneity of thickness along thelong axis is within 2%. Firstly, the silicon reed-substrates were ultrasonically cleaned and then, asilver-film-electrode was deposited on the surface-2 of the silicon reed-substrate by means of vapordeposition in 1025 Pa. It is found that the contamination of the surface-1 by silver vapor spoiled thesuccessive deposition of a cementite film on the surface-1. Therefore, the surface-2 was covered by amask to pattern with the electrode and also to avoid the contamination of the surface-1 by silver vaporduring deposition. Figure 1(b) is a schematic drawing of a measurement setup, where the resonantflexural vibration of a silicon reed-substrate with strain amplitude of 1026 was electrostatically excitedand detected through one electrode, and the temperature was kept at, nominally, 300.000 K within60.005 K during measurements for the resonant frequency (7–9). Firstly, the resonant frequency,f0, ofa silicon reed-substrate with the silver-film-electrode on the surface-2 was measured, and then thesilicon reed-substrate was detached from the clamp. The weight of the silicon reed-substrate wasmeasured and then it was subjected to the deposition of a cementite film by ES-PVD (4–6). It is noted

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that the reproducibility off0 is within about 10 ppm for handling for the detachment from and theattachment to the clamp. This experimental accuracy inf0 corresponds to about 1% of the change in theresonant frequency found after the deposition of a cementite film. The weight of the silicon reed-substrate is about 120 mg, which mainly reflects the weight of the thick end for clamping. In theES-PVD chamber, the silicon reed-substrate is placed on the stainless steel mask to minimize thecontamination of the surface-2 by cementite. The size of the window in the mask is 3321.7 mm2 anda thin beam with 0.3 mm wide locates nearby one end of the window. The silicon reed-substrate withthe total length of 22.2 mm is supported by the mask at the thick end and by the thin beam nearby thefree end of the reed.

A cementite film was deposited on the whole surface of the surface-1 except the slit-1 and -2 asschematically depicted in Figure 1(c). After the deposition, the weight of the silicon reed-substrate wasagain measured. The thickness of the cementite film was measured at the slit-1 using a stylus after thevibrating reed measurements. For a silicon reed-substrate used to check the distribution of a cementitefilm, the thin reed was weighted to minimize a gap between the reed and the thin beam in the stainlesssteel window and then the deposition of a cementite film was done. Then, we measured the cementitefilm thickness at the slit-1 and 2, where the film thickness showed good agreement within a fewpercents. For a silicon reed-substrate intended to evaluate the Young’s modulus of a cementite film, thethin reed was not weighted to avoid a mechanical damage on it, and therefore cementite was depositedin the slit-2 in some extent. After the deposition of the cementite film, the silicon reed-substrate is againclamped to the measurement bed. In the present work, we measured on four specimens, the specimen-Ato D listed in Table 1. For the specimen-B, an increase in the weight after the deposition is 124mg,suggesting that the density of the cementite film is 7.2 g/cm3 which is almost the same to the theoreticaldensity of cementite, and that the film thickness is homogeneous. On the other hand, for thespecimen-A, C and D, since part of the thick end of the silicon reed-substrate had broken off due tohandling, an increase in the weight found for these specimens is smaller by several tensmg than thatexpected from the theoretical density and the film thickness.

In Table 1, we list the chemical composition of the cementite films measured by the electron probemicroanalyzer (EPMA) and the thickness of the films determined by the stylus measurements. Thechemical composition is almost the same to the theoretical composition of cementite for the speci-men-B, slightly iron-deficient for the specimen-A and considerably iron-deficient for the specimen-C,respectively. The X-ray diffraction for a specimen whose chemical composition was almost the same

Figure 1. (a) A schematic drawing of a silicon reed-substrate. (b) The set up for the vibrating reed measurements. (c) A schematicdrawing for the silicon reed-substrate after the deposition of a cementite film.

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to the theoretical composition showed reflections from cementite alone as well as the observation in thetransmission electron microscope (TEM). The depth profile measured by the X-ray photoelectronspectroscopy (XPS) showed no oxygen peak in the specimens (10). These observations suggest that thefilm is a single phase cementite film. It is reported that the probable deviation from the stoichiometryis less than 1% for cementite in equilibrium with ferrite at room temperature (11). These results andreport suggest that the specimen-B is a single phase cementite film, the specimen-A is nearly singlephase cementite, and somewhat graphite may be contained in the specimen-C, respectively. This issuewill be mentioned later. The surface morphology of the film was observed by the field-emissionscanning electron microscope (FE-SEM), indicating that it is a flat and smooth film and the mean grainsize is about 90 nm.

Results and Discussion

From a change in the resonant frequency,Df, observed after the deposition of a cementite film, theapparent Young’s modulus,Ef9, of the cementite film can be determined using the following equation,

E9f 5 ~Es/3!@2~Df/f0!/~d/b! 1 ~rf /rs!# (1)

whereEs andrs denote the Young’s modulus and the density of silicon,b is the thickness of the siliconreed-substrate, andd andrf are the thickness and the density of the cementite film (see (7) for details).In Equation (1), a constrained film is assumed to deform with the Poisson’s ratio of the substrate. Theproper Young’s modulus,Ef, of the film may be given by

Ef 5 E9f~1 2 vf2!/~1 2 vfvs!, (2)

wherenf andns denote the Poisson’s ratio of the film and that of the substrate, respectively (12).The change in the resonant frequency observed after the deposition of a cementite film was, for

example,Df 5 11.773 Hz fromf0 5 751.843 Hz for the specimen-A withd 5 780 nm andb 5 112.4mm, andDf 5 10.600 Hz fromf0 5 731.252 Hz for the specimen-B withd 5 230 nm andb 5 95.8mm. From the observed quantities and Equation (1), we found the apparent Young’s modulus (Ef9) ofthe specimen-A to D which is listed in Table 1 and shown in Figure 2, where the density of thecementite film is assumed to be the theoretical density of cementite, 7.2 g/cm3. In Fig. 2, somedispersion in the data can be seen, which will be discussed at first. Equation (1) is valid when adhesionbetween a film and a substrate is strong enough. We observed that the cementite film does not peel offfrom the silicon reed-substrate even after it has broken off, suggesting that adhesion between them isstrong enough. In Equation (1) the film thickness is assumed to be homogeneous along the long axisof the reed. For example, an increase in the film thickness towards the free end of the reed gives a

TABLE 1The Properties of the Cementite Films

specimen

chemical composition ofcementite film (at. %) thickness of

cementite film(nm)

apparent Young’smodulus of

cementite film(1010 Pa)Fe C O

specimen-A 72.9 26.1 1.0 780 16.8specimen-B 75.4 24.0 0.6 230 16.9specimen-C 70.3 28.5 1.2 265 14.4specimen-D not measured 210 17.7

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deviatory decrease in the experimental value ofEf9 and the opposite case, a deviatory increase inEf9.As already mentioned, for the specimen-B, the chemical composition and the density of the film arealmost the same to the theoretical values of cementite and the film thickness is homogeneous. For thespecimen-A, the chemical composition is slightly iron-deficient. For the specimen-A and B, theexperimental value ofEf9 shows good agreement with each other. In Fig. 2, the dashed line 1 is drawnas the mean value found for the specimen-A and B. On the other hand, the data found for thespecimen-C and D show the considerable deviation from the mean value. The deviation found for thespecimen-D can be explained when the film thickness in the specimen-D is assumed to decrease byabout several percent toward the free end of the reed-substrate. For the specimen-C, however, thedeviatory decrease inEf9 is too large to be explained by an increase in the film thickness by severalpercent toward the free end of the reed-substrate. As mentioned in Table 1, some graphite may becontained in the specimen-C, suggesting that it is responsible for the strong decrease inEf9 observed inthe specimen-C. Thus, we adopt the mean value found for the specimen-A and B asEf9 of the cementitefilms. Equation (2) withnSi 5 0.44 andnFe3C5 0.26 (6) within the experimental accuracy givesEf 517.76 1 3 1010 Pa. Table 2 compiles the Young’s modulus of cementite found here and reported inthe Ref. (1–3,6), where the present value shows good agreement with the mean value of the reporteddata. The combination ofEf 5 17.73 1010 Pa andnFe3C5 0.26 yields the shear modulus of 7.03 1010

Pa under the assumption of isotropic elasticity.

Conclusion

To a single phase cementite film deposited on a silicon reed-substrate by ES-PVD, we applied thevibrating reed method and found the Young’s modulus of cementite as 17.76131010 Pa, which showsgood agreement with the mean value of those reported previously.

Figure 2. The apparent Young’s modulus,Ef9, found in the specimen-1 to 4.

TABLE 2The Young’s Modulus of Cementite

Young’s modulusof cementite film

(1010 Pa) material used for evaluation remarks

17.761*1 single phase cementite film present16.0 single phase cementite film (6)17 cast iron containing cementite (1, 2)20 cast iron containing cementite (3)

*1 The value estimated from E9f516.85 3 1010 Pa found in Fig. 2 and Equation (2) withvsi 5 0.44 andvFe3C 5 0.26 (6).

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Acknowledgment

This work is partly supported by Ferrous Super Metal Consortium of Japan under the auspices ofNEDO.

References

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