水解塔設(shè)計(全套CAD圖+說明書+開題報告+翻譯)
水解塔設(shè)計(全套CAD圖+說明書+開題報告+翻譯),水解,設(shè)計,全套,cad,說明書,仿單,開題,報告,講演,呈文,翻譯
英文文獻(xiàn)
1英文原文
Stress Corrosion Cracking of Pressure Vessel Steels in High-Temperature Caustic Aluminate Solutions
SU'E LIU, ZIYONG ZHU, HUI GUAN, and WEI KE
Stress corrosion cracking (SCC) behavior of three kinds of low alloy pressure vessel steels in high temperature (200 ℃ to 300℃ ) caustic aluminate (AlO2-) solutions has been studied by slow strain rate tests (SSRT). The results indicate that these pressure vessel steels are susceptible to SCC in caustic alnminate solution and that the SCC susceptibility increases with increasing temperature between 200 ℃ to 300 ℃ Sulfide content and stringered sulfide inclusions severely and anisotropically affect the caustic SCC of these low alloy steels. The inclusions in the rare-earth-treated steel are predominantly globular rare-earth sulfides or oxysulfides, resulting in improved transverse properties. The effect of inclusions on SCC behavior correlates with the projected area of inclusions per unit volume at the crack tip, Av, on the plane perpendicular to the tensile direction. The susceptibility to SCC increases with increasing A v.
I. INTRODUCTION
LOW alloy pressure vessel steels are the common structural materials for welded reaction vessels (e.g., digesters, precipitators, and evaporators) in the Bayer process for extraction of alumina from hydrated oxide ores (e.g., bauxite). These low alloy reaction vessels are in contact with high temperature concentrated caustic alnminate solutions and frequently suffer from stress corrosion cracking (SCC) during service. 1,2 Although SCC of steels in simple NaOH solutions has been the subject of numerous studies, f3,41 little work has been done in caustic aluminate solutions at 92 oc.t5,61 To purify alumina from lower quality ores, the extracting temperature has been elevated. However, there are no data on SCC susceptibility of steels used in the alumina industry at higher temperatures. The objective of the present work is to study the SCC behavior of low alloy pressure vessel steels with different sulfur contents in an imitative Bayer process at 200 ℃ to 300℃ Over the past few years, a number of research works 7,8,9 have shown that nonmetallic sulfide inclusions can cause environmentally assisted cracking to occur in high-temperature water related primarily to Boiling Water Reactor (BWR) and Pressurized Water Reactor (PWR) environments. The effect of MnS inclusions on caustic SCC property is also discussed in this article to give recommendations for improving SCC resistance of materials used in the alumina industry.
II. EXPERIMENTAL PROCEDURE
Studies were conducted on three kinds of low alloy steels: 16MnR, A48CPR, and rare-earth-treated 16MnRE. The pressure vessel quality rolling steel plates used in this work were 50-mm thick and were annealed at 650 ℃ The chemical compositions and mechanical properties of these steels were similar (Tables I and II), although the sulfur contents were very different. The cylindrical tensile specimens were 24 mm in gage length and 5 mm in diameter with threads at each end to fit tensile grips. Two kinds of tensile test pieces were sectioned from the steel plates parallel (L specimen) and perpendicular (T specimen) to the rolling direction to investigate specimen orientation effects. All specimens were polished with a 1000 grit emery paper and then cleaned with alcohol and acetone before testing. The test environment imitated the industrial Bayer process, and the temperature was varied from 200℃ to 300℃ The initial molal (M) concentration (Table III) in imitative Bayer solutions (IBS) was 7.42M NaOH, 1.32M A1203 3H20, and some impurities: carbonate, sulfate, and chloride. The test solution was prepared from distilled water and analytical grade chemicals. The resulting concentrations of anions are based on stoichiometric formation of aluminate species (AlOe-) according to Eq. 1:
The slow strain rate tests were performed on an SERT-5000DP-9L machine in a static autoclave at an initial strain rate of 3.3*10-6/s. To protect the autoclave from caustic
solution, a loose-fitting nickel liner, which held the corrosive media, was placed within it. A small amount of water was injected into the crevice between the autoclave and the liner to improve heat transfer and to prevent the formation of a concentrated caustic solution in this crevice. After sealing, the system was overpressured with 2.0 MPa nitrogen to prevent boiling and to minimize the transfer of corrosive media to the crevice. At the start of each test, specimens were initially loaded to 50 MPa and then strained to fracture. The tensile specimens were at the natural corrosion potential during straining. The results obtained in IBS were compared with those in an inert environment of 2.0 MPa nitrogen. The time to failure (TTF), the percent reduction of crosssectional area (pet ROA), and the elongation (E) were the main parameters used to evaluate SCC susceptibility. One-half of the specimen was mounted with epoxy resin, ground, and given a final metallographic polish to observe the secondary cracks along the gage length by optical microscopy.
Table I. Analyses of Composition (Weight Percent)
Steels
C
Si
Mn
P
S
Al
Cu
Mo
Ni
RE
16MnR
0.16
0.47
1.53
0.014
0.018
--
0.055
--
--
--
A48CPR
0.175
0.34
1.35
0.012
0.006
--
--
0.045
0.058
--
16MnRE
0.16
0.40
1.38
0.018
0.009
--
-
--
--
0.020
Table II. Mechanical Properties of Steels
Steels
Ultimate
Strengt( MPA )
Yield
Strength( MPA )
Elongation (Pct)
Impact Strength(J/cm , by Charpy Test)
25℃
260℃
L Specimen
T Specimen
L Specimen
T Specimen
16MnR
530.0
350.0
32.0
159
—
172
77
75
97
142
—
169
85
81
76
A48CPR
528.9
316.1
31.6
209
—
240
187
—
233
298
—
317
231
258
272
16MnRE
535.0
338.0
32.5
169
172
172
156
129
122
—
—
—
—
—
—
Table III. Composition of IBS (M)
NaOH
Al2O33H2O
Na2CO3
Na2SO4
NaCl
7.42
1.32
0.3
0.14
0.14
Ill. RESULTS
A. The Effect of Temperature on Caustic SCC Behavior Figure 1 shows the effect of temperature on SCC behavior for L specimens of 16MnR steel in IBS at 260 ℃ The pct ROA is reduced by the corrosive solution as compared with that in nitrogen. Also the TTF, pct ROA, and E of specimens in IBS decrease with increasing test temperature. The results indicate that 16MnR steel is susceptible to SCC in IBS and that the susceptibility increases with an increase in temperature from 200 ℃ to 300 ℃
B. Comparison of SCC Susceptibility between 16MnR, A48CPR, and 16MnRE Steels
The pet ROA data of L specimens for both steels shown in Figure 2 are the average values of duplicate specimens in each test condition, and the results can be reproduced as follows. For A48CPR steel, the pct ROA data are 66.0 and 64.2 at 260 ℃ and 63.6 and 61.1 at 280 ℃ For 16MnR steel, the pct ROA data (as shown in Figure 1) are 57.2
and 55.0 at 260 ℃ and 49.6 and 47.0 at 280 ℃ The results (Figure 2) of L specimens for both steels indicate that A48CPR steel is also susceptible to SCC under the test conditions and that the susceptibility may increase slightly with increasing temperature from 260 ℃ to 280℃ The L specimens of 16MnR steel are inferior to those of A48CPR steel.
The effects of specimen orientation on SCC behavior ar shown in Figure 3. The T specimens of 16MnR steel ar obviously more susceptible to SCC than its L specimens
However, the SCC behavior for A48CPR steel of T specmens is similar to the L specimens. The SCC resistanc for the T specimen of rare-earth-treated steel 16MnRE improved, and the extent of anisotropy of 16MnRE decreases as compared with 16MnR.
The large number of cracks observed on an L specimen of 16MnR steel after testing in IBS at 280 ℃ is shown in Figure 4. The cracking path of a typical specimen is shown in Figure 5. The cracks predominantly propagated in intergranular path, but there are also some transgranular cracks.
IV. DISCUSSION
Caustic SCC of low alloy pressure vessel steels in IBS at elevated temperatures is predominately intergranular (Figure 5) as at 92 ℃ The SCC susceptibility increases at high temperatures between 200 ℃ and 300 ℃ (Figures1 and 2). In comparison to the conventional (25 ℃ Pourbaix diagram, the most noticeable change at higher temperature diagrams is the larger area of stability for the HFeOi ion. An association between caustic cracking and the formation of HFeO2 ion has been previously suggested, vq Simultaneously, the reaction rate of the anodic and cathodic reactions increases at the elevated temperature.
The orientation effect on SCC behavior (Figure 3) is considered to be related to inclusions in the steels. The volume fraction, shape, and distribution of manganese sulfide inclusions in 16MnR and A48CPR steels are very different,as shown in Figures 6(a) and (b). The volume fraction of
inclusions in 16MnR steel is greater than in A48CPR steel because the sulfur content is higher. The inclusions in A48CPR steel are globular and well distributed, whereas those in 16MnR steel are predominantly elongated and in bands parallel to the rolling direction.
The SCC process is the brittle or quasibrittle fracture of a material under the conjoint actions of stress and corrosive environments. The detrimental effects of nonmetallic inclusions on the mechanical properties of steels are now well established, tg] Considering the mechanical fracture aspect during the SCC process, the effect of inclusion on SCC behavior correlates with the total projected area, Aw, of inclusions per unit volume at the crack tip on the plane perpendicular to the tensile direction, i. The crack propagation rate is accelerated by cracking in or around the inclusions near the crack tip and is more severe with increasing A w. If the shape of inclusion is assumed to be triaxial ellipsoids (Figure 7), it is possible to calculate the magnitude of A vi in the following equation:
Avi=6Vv/(Πdi) [2]
where Vv is the volume fraction of inclusion and di is the average dimensions of inclusion in the tensile direction, i.There are more inclusions in 16MnR steel than in A48CPR steel. The value of Vv for 16MnR steel is therefore larger. But the average dimension of the elongated inclusions on the longitudinal section, for L specimens of 16MnR steel is also larger. However, the value of Aw on the plane perpendicular to the tensile direction, for the L specimen, is similar for both steels. So the difference in SCC susceptibility of L specimens between 16MnR and A48CPR steels is slight (Figure 2). The results indicate that the amount and shape of inclusion have no significant effect on the SCC behavior for L specimens.
However, the shape and distribution of inclusion in steels severely affect the transverse properties such as the impact strength of Charpy tests (Table II) and SCC susceptibility (Figure 3). Even though a steel contains the same amount of inclusion, in a given steel, the volume fracture of inclusion should be the same, but the inclusion length dimension di and A w on the different fracture plane may be different according to the shape of inclusion. Because inclusions in 16MnR steel are stringered bands parallel to the rolling direction, the average length dimension of inclusions in the longitudinal direction, is much larger than that in the transverse direction, d2, and the average projected area on the transverse plane for the longitudinal specimen, Aw, is correspondingly smaller than that on the longitudinal plane for the transverse specimen, A v2. The elongated inclusionsin the 16MnR steel cause anisotropy in its SCC resistance(Figure 3). In comparison with the 16MnR steel, the value of Art is equal to that of At2 for globular inclusions in the A48CPR steel, so the SCC behavior is isotropic.
On the other hand, SCC is also an electrochemical process. The pre-existing active-path theories tl31 have been applied primarily to intergranular cracking of ductile alloys in
aqueous environments and relate the propagation process to the preferential dissolution of chemically active regions in the grain boundaries. The recent investigations indicate that
the MnS inclusions dissolve readily in high-temperature water, presumably forming HS- and H2S. These species strongly affect the crack growth rate during SCC or corrosion fatigue processesYl In areas containing a dense distribution of elongated MnS inclusions, the crack tip can propagate much faster than in the surrounding area. So inclusions in steels have an influence on SCC behavior.
The results of rare-earth-treated steel 16MnRE under the same test conditions further confirmed the inclusion effect. The inclusions in 16MnRE steels are predominately globular rare-earth sulfides or oxysulfides (Figure 6(c)) which are hard particles and difficult to be deformed and elon-
gated. The SCC results shown in Figures 3 and 8 indicate that the ratio of pct ROA for T specimens, ROA(T), to that for L specimens, ROA(L), increases in comparison with that for 16MnR steel. The transverse SCC resistance obviously improves with inclusion shape, controlled by adding rare-earth elements in the low alloy steel 16MnR. But there are still a few stringered inclusions (Figure 6(c)) in 16MnRE, so the transverse SCC resistance of 16MnRE is not as good as that of A48CPR. Nevertheless, it is hoped that 16MnRE steel can have the same SCC resistance as that of A48CPR used in the alumina industry by controlling the amount of rare-earth elements added and the rolling process.
V. CONCLUSIONS
1. Both 16MnR and A48CPR steels exhibit caustic SCC susceptibility in the IBS. The SCC susceptibility of 16MnR steel increases with increasing temperature from 200 ℃ to 300℃
2. The volume fraction, shape, and distribution of inclusions in steels affect the caustic SCC of low alloy pressure vessel steels, especially in steels with stringered sulfide inclusions where the transverse SCC resistance is severely reduced. Adding rare-earth elements to the steel improves transverse SCC resistance by controlling the shape and dis tribution of inclusions.
3. The effects of inclusion on SCC behavior correlate with the projected area of inclusions at the crack tip, Av, on the plane perpendicular to the tensile direction. The SCC susceptibility increases with A v.
ACKNOWLEDGMENTS
This work was supported by the National Natural Science Foundation of China (Contract No. 59271049) and the State Key Laboratory of Corrosion and Protection, Academia Sinica.
REFERENCES
1. Caustic Stress Corrosion Symposium, Alcan Jamaica Company (Aljam), Mandeville, Jamaica, Mar. 1982.
2. V.I. Artem'ev, V.I. Seregin, E.P. Zholoboya, and V.P. Belyaev: Zashch. Met., 1979, vol. 15, p. 62-65.
3. M.F. Maday, A. Mignone, and A. Borello: Corrosion, 1989, vol. 45, pp. 273-82.
4. D. Singbeil and D. Tromans: Metall. Trans. A, 1982, vol. 13A, pp. 1091-98.
5. Huy Ha Le and Edward Ghali: Corros. Sci., 1990, vol. 30, pp. 117- 34.
6. R. Sriram and D. Tromans: Corrosion, 1985, vol. 41, pp. 381-85.
7. F.P. Ford: Proc. 2nd Int. Atomic Energy Agency Specialists Meeting on Subcritical Crack Growth, Sendai, Japan, May 15-17, 1985, W.H. Cullen, ed., NUREG CP-0067, vol. 2, pp. 3-72.
8. H. Hanninen, K. Torronen, M. Kemppainen, and S. Salonen: Corros. Sci., 1983, vol. 23 (6), pp. 663-79.
9. J.H. Bulloch: Proc. 3rd lnt. Symp. on Environmental Degradation of Materials in Nuclear Power Systems-Water Reactors, TMS, Warrendale, PA, 1988, pp. 261-68.
10. H.E. Townsend: Corros. Sci., 1970, vol. 10, pp. 343-58.
11. M.J. Humphries and R.N. Parkins: Syrup. Fundamental Aspects of Stress-Corrosion Cracking, The Ohio State University, Columbus, OH, Sept. 11 15, 1967, R.W. Stache, A.J. Forty, and D. Van Rooyen, eds., NACE, Houston, TX, 1969, pp. 384-95.
12. W.A. Spitzig: Metall. Trans. A, 1984, vol. 15A, pp. 1259-64.
13. Shinobu Matsushima, Yasuyuki Katada, Shunji Sato, and Norio Nagata: Corrosion Control, Proc. 7th Asian-Pacific Corrosion Control Conf., International Academic Publisher, Beijing, 1991, pp. 112-17
2譯文
鋼制壓力容器在高溫腐蝕性鋁酸溶液中的應(yīng)力腐蝕裂紋研究
劉舒 朱自勇 關(guān)慧 魏柯
通過慢應(yīng)變速率(SSRT)的測試,對三種低合金壓力容器用鋼在高溫( 200 ℃-300℃)腐蝕性鋁酸(AlO2-)溶液中的應(yīng)力腐蝕開裂(SCC)情況進(jìn)行了研究。結(jié)果表明,這類壓力容器鋼在該類溶液中SCC較敏感,并隨溫度升高SCC會加劇。另外,硫化物及其它雜質(zhì)的混入也會引起鋼的腐蝕。稀土處理過的鋼中主要含球狀的硫化稀土和硫氧化合稀土,這就導(dǎo)致其加大了橫向斷裂特性,包括在延伸區(qū)域應(yīng)力腐蝕斷裂點Av,也就是在垂直與平面的伸長方向,隨著Av值的變大,應(yīng)力腐蝕特性較為明顯。
一.引言
低合金鋼是比較常見的焊接反應(yīng)容器的材料(例如沼氣池, 除塵器,蒸發(fā)器等) ,通過貝爾反應(yīng)從含氧的水合物中將AlO2-提取出來。這類低合金反應(yīng)容器與具腐蝕性的高溫鋁酸溶液接觸并立刻出現(xiàn)腐蝕現(xiàn)象。在此期間,鋼材在純NaOH溶液中的應(yīng)力腐蝕已經(jīng)有過大量的研究,在92℃腐蝕性鋁酸溶液中也做了小規(guī)模的實驗。為了將氧化鋁從雜質(zhì)礦石中提取出來,提取時的溫度大大高于92℃。然而,很難預(yù)知SCC的敏感性在更高溫度下的鋁酸鹽工業(yè)中的情況。目前的主要工作就是研究低合金壓力容器用鋼與不同硫化物模擬在200 ℃- 300℃時的貝爾反應(yīng)情形下的應(yīng)力腐蝕斷裂。在過去的幾年里,大量的研究工作表明,能引起非金屬硫化物在沸水中對容器的腐蝕,主要與反應(yīng)器和壓水器的環(huán)境有關(guān),包括含腐蝕性的MnS的影響,這一點在本文也將提到,并介紹抗SCC材料在鋁酸鹽工業(yè)中的應(yīng)用。
二.實驗步驟
三種低合金鋼處理方式的研究:16MnR鋼, A48CPR ,稀土處理過的16MnRE 。進(jìn)行試驗的壓力容器軋制鋼板厚50毫米, 650 ℃退火處理。這類鋼材的化學(xué)成分和力學(xué)性能(表一和表二)較為相似,但硫的含量大不相同。取可伸長的圓柱形樣本原長24毫米,直徑5毫米,且均帶螺紋便于裝緊。從鋼材的橫斷面和縱斷面方向分別切割,這種張力實驗研究樣本的向性能力,所有樣本用硬度為1000的砂輪拋光并且測試前用酒精和丙酮液清洗。
測試環(huán)境模仿工業(yè)上的貝爾過程,溫度持續(xù)在200 ℃到 300℃之間 。初始摩爾(M)濃度(表三)類似貝爾溶液:7.42M的NaOH, 1.32M的Al2O3 3H2O,并含有雜質(zhì)碳酸鹽、硫酸鹽、氯化物。待測液由蒸餾水和分析化學(xué)藥物組成。此化學(xué)反應(yīng)根據(jù)反應(yīng)前后負(fù)離子(AlO2-)濃度相等得到公式:
在一個SERT- 5000DP-9L型機(jī)器中進(jìn)行試驗,應(yīng)變速率為3.3 *10-6 /秒。為避免腐蝕性溶液腐蝕反應(yīng)容器,內(nèi)置一個裝有抗腐蝕介質(zhì)的密合式鎳墊片。將少量的水注入反應(yīng)容器和墊片之間的縫隙,以提高傳熱和防止縫隙中形成腐蝕性的濃堿溶液。密封后,該系統(tǒng)充入2.0 MPa氮,以防止沸騰并最大限度地減小縫隙的腐蝕。在每次試驗之前,樣本先被加壓到50MPa,然后將裂縫張緊。受拉樣本在被拉時處于自然腐蝕的狀態(tài)。在IBS情況下獲得的結(jié)果與在2.0 MPa氮的情況下作比較。其失效期(TTF) ,伸縮率(pct ROA) ,伸長率( E )是用來評價SCC敏感性的主要參數(shù)。其中一半的樣本加上環(huán)氧樹脂,并做最后的磨光處理,使其有金屬光澤,觀察沿斷面方向的二次斷裂。
表一 分析成分(重量百分比)
鋼材
C
Si
Mn
P
S
Al
Cu
Mo
Ni
RE
16MnR
0.16
0.47
1.53
0.014
0.018
--
0.055
--
--
--
A48CPR
0.175
0.34
1.35
0.012
0.006
--
--
0.045
0.058
--
16MnRE
0.16
0.40
1.38
0.018
0.009
--
--
--
--
0.020
表二 鋼的力學(xué)性能
鋼材
極限強(qiáng)度( MPA )
屈服強(qiáng)度( MPA )
伸縮率 (Pct)
沖擊強(qiáng)度(焦耳/厘米2 ,貝爾試驗)
25℃
260℃
L樣本
T樣本
L樣本
T樣本
16MnR
530.0
350.0
32.0
159
—
172
77
75
97
142
—
169
85
81
76
A48CPR
528.9
316.1
31.6
209
—
240
187
—
233
298
—
317
231
258
272
16MnRE
535.0
338.0
32.5
169
172
172
156
129
122
—
—
—
—
—
—
表三. 組成IBS的成分(摩爾)
NaOH
Al2O33H2O
Na2CO3
Na2SO4
NaCl
7.42
1.32
0.3
0.14
0.14
三.實驗結(jié)果
A.溫度對SCC性能的影響。
圖1表明溫度為260 ℃時,在IBS中16MnR鋼的SCC狀況。在腐蝕性溶液中其收縮率與在氮氣中相比較而言變小了。樣本在IBS中,其失效率、伸縮率、伸長率隨測試溫度的升高也減小了。結(jié)果表明,在IBS中,16MnR鋼極易發(fā)生應(yīng)力腐蝕斷裂,而且隨著溫度的升高,SCC也變的更為明顯。
圖1 圖2
B.16MnR、A48CPR、16MnRE之間SCC敏感性對比。
圖2表示同種鋼材L樣本的伸縮率在同一條件下其數(shù)據(jù)的平均值,以下可重復(fù)利用此結(jié)果。對于A48CPR鋼材,伸縮率在260 ℃時是66.0和64.2 ,在280℃ 時是63.6和61.1。對于16MnR鋼材,伸縮率在260℃時是(如圖1所示)57.2和55.0,在 280℃時是49.6和47.0 ,其結(jié)果和圖2 相吻合。表明A48CPR鋼材在測試條件下也極易發(fā)生SCC現(xiàn)象。隨著溫度的升高,從260 ℃到280 ℃,其SCC現(xiàn)象更為明顯,不難看出, 16MnR鋼的L樣本性能比A48CPR鋼的性能差。
圖3表示樣本對SCC特性的影響。由圖可知,16MnR鋼材的T樣本比L樣本更易出現(xiàn)SCC現(xiàn)象。然而, A48CPR鋼材的T樣本與L樣本SCC程度是一樣的。稀土處理過的16MnRE鋼材的T樣本抗SCC能力強(qiáng)些,同16MnR鋼材相比,16MnRE的性能較低。
圖4表示經(jīng)280 ℃的IBS測試后,16MnR鋼的L樣本有大量的裂痕。圖5表示的是一個典型的樣本裂口,裂縫多出現(xiàn)在樣本中間,粒狀,也有穿晶裂紋。
圖3 圖4
圖5
四.討論
在低合金壓力容器用鋼的SCC圖中,隨著溫度的升高,在92℃時,腐蝕性較明顯(圖5)。在高溫200℃ ? 300 ℃之間,SCC不斷增加(圖1和2) 。與常溫(25 ℃) 相比較,高溫下最顯著的變化是HFeO2-離子大面積是穩(wěn)定的。腐蝕性裂紋與HFeO2-離子間關(guān)系在前文已述。同時,陽極的反應(yīng)速率隨溫度的升高而加快。
鋼中的雜質(zhì)會影響應(yīng)力腐蝕開裂的方向。16MnR鋼和A48CPR鋼的體積、外形、錳硫化物的含量均不同,如圖6( a )和( b )所示 。同體積的兩種鋼材,16MnR鋼雜質(zhì)含量大于A48CPR鋼,因為16MnR鋼材硫含量較高。雜質(zhì)在A48CPR鋼中呈球形且均勻分布,在16MnR鋼中主要是延伸的纖維狀,平行于軋制方向。
在SCC過程中,應(yīng)力活動結(jié)點和腐蝕環(huán)境在材料脆性和偽脆性部分,鋼中非金屬雜質(zhì)對其機(jī)械性能的影響是有害的,目前已進(jìn)行了很詳細(xì)的研究。雜質(zhì)對SCC性能的影響是與整個設(shè)計面積Avi(即在裂紋尖端與延伸方向相垂直的每單元體積)是相關(guān)聯(lián)的。在裂紋尖端的雜質(zhì)周圍,裂紋的生長速度增加,若增加Avi,裂紋會加快生長。
如果假定雜質(zhì)的外形是三維橢球形(圖7) ,即可通過公式:
Avi=6V
收藏