Thermal stability of double-ceramic-layer thermal barrier coatings

Materials Science and Engineering A433(2006)

1–7

Thermal stability of double-ceramic-layer thermal barrier coatings

with various coating thickness

Hui Dai a,b,Xinghua Zhong a,b,Jiayan Li a,b,Yanfei Zhang a,b,Jian Meng a,Xueqiang Cao a,?

a Key La

b of Rare Earth Chemistry&Physics,Changchun Institute of Applied Chemistry,Chinese Academy of Sciences,Changchun130022,Jilin,China

b Graduate School of The Chinese Academy of Sciences,Beijing100049,China

Received23January2006;received in revised form12April2006;accepted21April2006

Abstract

Double-ceramic-layer(DCL)coatings with various thickness ratios composed of YSZ(6–8wt.%Y2O3+ZrO2)and lanthanum zirconate(LZ, La2Zr2O7)were produced by the atmospheric plasma spraying.Chemical stability of LZ in contact with YSZ in DCL coatings was investigated by calcining powder blends at different temperatures.No obvious reaction was observed when the calcination temperature was lower than1250?C, implying that LZ and YSZ had good chemical applicability for producing DCL coating.The thermal cycling test indicate that the cycling lives of the DCL coatings are strongly dependent on the thickness ratio of LZ and YSZ,and the coatings with YSZ thickness between150and200?m have even longer lives than the single-layer YSZ coating.When the YSZ layer is thinner than100?m,the DCL coatings failed in the LZ layer close to the interface of YSZ layer and LZ layer.For the coatings with the YSZ thickness above150?m,the failure mainly occurs at the interface of the YSZ layer and the bond coat.

?2006Published by Elsevier B.V.

Keywords:Thermal cycling;Plasma spraying;Thermal barrier coatings

1.Introduction

During the last decade,research efforts were devoted to the development and manufacturing of ceramic TBCs on turbine parts because the traditional turbine materials have reached the limits of their temperature capabilities.TBCs have been widely used in hot-section metal components in gas turbines either to increase the inlet temperature with a consequent improvement of the ef?ciency or to reduce the requirements for the cooling air[1–3].

The typical TBC used in gas turbines consists of a bond coat produced by the vacuum or low pressure plasma-sprayed MCrAlY(M=Ni,Co)and a top coat of yttria partially stabilized zirconia made by the atmospheric plasma spraying or electron beam-physical vapor deposition(EB-PVD)[4,5].A major disad-vantage of YSZ is the limited operation temperature(1200?C) for the long-term application.At higher temperatures,the t -phase transforms into the t-phase and c-phase.During cooling the t-phase will further transform into the m-phase,giving rise to ?Corresponding author.Tel.:+864315262285;fax:+864315262285.

E-mail address:xcao@https://www.wendangku.net/doc/9b2520129.html,(X.Cao).the formation of microcracks in the coating[6,7].Furthermore, due to the sintering of the coating at elevated temperatures,the porosity of the coating is reduced combined with the increase of Young’s modulus and tensile stress,which will lead to a reduced life under thermal cycling load.

To overcome the disadvantages of YSZ,the search for can-didate materials that can withstand higher gas-inlet temperature has been intensi?ed in the past.Since the physical properties such as lower thermal conductivity than YSZ and high thermal stability up to its melting point,LZ was proposed as a promising material[6,8].However,the low thermal expansion coef?cient of LZ leads to high thermal stress between the LZ coating and the metallic bond coat,resulting in a short thermal cycling life [9].The multilayer and graded structures have been produced to overcome this shortcoming[10,11].As reported by the authors, the thermal cycling lives of multilayer coatings are two or three times longer than those of the single ceramic layer coatings [11].However,the effect of the coating thickness ratio of LZ and YSZ of the DCL coating on the thermal cycling life has not been investigated.In the present work,the thermal stabil-ity of DCL coatings with various coating thickness ratios of LZ and YSZ were examined and the failure mechanisms were studied.

0921-5093/$–see front matter?2006Published by Elsevier B.V. doi:10.1016/j.msea.2006.04.075

2H.Dai et al./Materials Science and Engineering A433(2006)

1–7

Fig.1.Spray-dried powder for plasma spraying.

2.Experimental

The main chemicals used in this work were La2O3(99.99%, Chenghai Chemicals of Guangdong),ZrO2(99.5%,Chenghai Chemicals of Guangdong),and YSZ(Sulzer Metco204NS). The LZ powder for plasma spraying was synthesized by the solid-state reaction followed by spray drying as described in detail in a previous paper[12].This powder has a good?owa-bility,a high density,and a particle size between50and100?m. The morphology of LZ powder used in this work is shown in Fig.1.

Sulzer Metco Vacuum Plasma Spray Unit with a F4gun was used to deposit a120?m NiCoCrAlY bond coat(Ni192-8 powder by Praxair Surface Technologies Inc.)on disk shaped Ni-base surperalloy substrates(supported by Beijing University of Aeronautics and Astronautics).The disk-shaped substrate has a bevelled edge to minimize the effect of stresses originated at the free edge of the specimen.The diameter and thickness of the substrate are30and3mm,respectively.

The ceramic coatings with various thickness were produced by the atmospheric plasma spraying using Praxair-Tafa5500-2000Plasma-Spray Unit with a SG-100gun.During the prepa-ration of the samples for thermal cycling,steel substrates were also coated simultaneously.These coatings were used for the characterization of the spraying condition.The plasma spraying parameters are listed in Table1.

The thermal cycling was performed with a gas burner test facility operated with coal gas and oxygen.The substrate was cooled by the compressed air from the back.The surface temper-ature was measured with a pyrometer and that of the substrate Table1

Plasma spraying parameters for DCL coatings

Current(A)900

V oltage(V)29

Coating distance(mm)80

Plasma gas(Ar/He,SLM/min)33/14 Powder feeding gas(Ar,SLM/min)

5.2Fig.2.Thermal cycling procedure for DCL coatings.T Surf and T Sub are for the surface and substrate temperatures,respectively.

was measured by a thermocouple located at the center of the sub-strate.During thermal cycling,the temperatures of the surface and substrate are T Surf=1250±30?C and T Sub=965±15?C, respectively.When5%area of the ceramic coating was lost,the cycling was manually stopped and the cycling number was then the life of the coating.The cycling procedure is shown in Fig.2.

Powder blend of50mol%LZ and50mol%YSZ was mixed in the de-ionized water followed by ball-milling for24h using zirconia-balls.The slurry was then dried and subjected to heat-treatment in a furnace in air at1250or1400?C for different time.The X-ray powder diffraction patterns were collected at room temperature using Rigaku D/Max2500diffractometers with graphite monochromators(Cu K?radiation,2θangle range from10?to90?,step0.02?).The microstructures of the coat-ings were analyzed using a XL30ESEM FEG scanning electron microscope.The cross-sectional samples were embedded in a transparent cold-setting epoxy and polished with diamond pastes down to1?m.

3.Results and discussion

For DCL coatings,the YSZ layers?rstly deposited on the bond coat have thickness of50,100,150and200?m.The LZ layers with thickness of250,200,150and100?m were then coated on top of the YSZ layer,and the total ceramic coating thickness was about300?m.For comparison,the single ceramic layer coatings of both YSZ and LZ were also produced.Fig.3 shows the microstructures of the cross-sections of DCL coat-ings with various coating thickness before thermal cycling.All coatings have a porous microstructure,which is popular for the plasma-sprayed coatings.The porosity levels of YSZ and LZ coatings are similar even though the former has a higher melt-ing point than the latter(2700?C for YSZ and2300?C for LZ) [8].

It is noted that the weakest location in typical YSZ-TBCs is the interface of the top-coat and bond coat,where the crack or spallation usually occurs because of either the thermal and elastic mismatch between the top-coat and bond coat or the

H.Dai et al./Materials Science and Engineering A 433(2006)1–73

Fig.3.Microstructures of the cross-sections of DLC coatings:(A)LZ/YSZ 250/50?m,(B)LZ/YSZ 200/100?m,(C)LZ/YSZ 150/150?m,(D)LZ/YSZ 100/200?m,(E)YSZ 310?m,central part of the coating before thermal cycling.

growth stresses due to the formation of thermally-grown oxide (TGO)[13].Moreover,at high temperatures,the chemical reac-tion between the top-coat and the TGO will dramatically reduce the performance of TBCs [14].In the DCL coatings,the inter-

face of LZ and YSZ is another weak location except that of YSZ and bond-coat.Chemical stability of LZ in contact with YSZ in DCL coatings was investigated by calcining powder blend at different temperatures.To maximize the interface area between the two ceramics,sub-micron powder blends of LZ and YSZ are used to evaluate the chemical stability of LZ in contact with YSZ.This simulates severe reaction condition,because in actual TBCs only a planar interface exits between the two ceramic layers.The chemical stability is studied at 1250?C,which is the target service temperature of next generation TBCs,and the reaction temperature of 1400?C represents a very severe testing condition.

Fig.4shows the XRD patterns for the powder blend of 50mol%LZ and 50mol%YSZ:as-prepared,heat-treated at 1400?C for 12,36and 72h.For comparison,the XRD patterns of original powders are also shown.Their lattice parameters are listed in Table 2.For blend with 12h heat-treatment,the

lattice parameter of LZ is 10.7955?A,

which is almost 0.02?A smaller than that of the LZ starting powder.After heat-treatment

Fig.4.X-ray diffraction patterns of 50mol%LZ powder and 50mol%YSZ powder blends with different heat-treatment at 1400?C.

4H.Dai et al./Materials Science and Engineering A 433(2006)1–7

Table 2

Lattice parameters of 50mol%LZ powder and 50mol%YSZ powder blends with different heat treatments Annealing time at.1250?C (h)Lattice

parameter (?A)Annealing time at 1400?C (h)Lattice

parameter (?A)2410.8101±0.0003

1210.7955±0.0004

72

10.8101±0.00063610.7733±0.000472

10.7734±0.0003

Starting blend

10.8101±

0.0007

Fig.5.X-ray diffraction patterns of 50mol%LZ powder and 50mol%YSZ powder blends with different heat-treatment at 1250?C.

at 1400?C for 36h,the XRD peaks of LZ also shift towards the lower d -value,indicating that another solid solution phase with high ZrO 2concentration appears.This is the solid solution of LZ and ZrO 2with pyrochlore structure.The La 2O 3–ZrO 2phase diagram shows a considerable solubility range for LZ from 0.87La 2O 3·2ZrO 2to 1.15La 2O 3·2ZrO 2whereby the crys-tal structure remains unchanged [9].

Fig.5shows the XRD patterns for the powder blend 50mol%LZ and 50mol%YSZ:as-prepared,heat-treated at 1250?C for 24and 72h.No obvious changes were observed after

differ-

Fig.7.Thermal cycling lives of LZ/YSZ DCL coatings as a function of the thickness of YSZ layer.Dashed line for view guide.

ent heat treatments,implying that no reaction between the LZ and YSZ powder take places.As a result,reaction between the LZ and YSZ would not be expected since the temperature of the ceramic layer interface (below 1150?C)is much lower than 1250?C during the operation,indicating that LZ and YSZ have good chemical applicability for producing DCL coating.

The surfaces of single-layer LZ coatings before and after thermal cycling are shown in Fig.6.Almost 1/6of the LZ coating spalls off the substrate after only a few cycles.Thermal cycling lives of DCL coatings with various thickness ratios are shown in Fig.7.The cycling number is plotted as a function of the thickness of YSZ.Except the coatings with YSZ thickness of 50and 150?m,each point in Fig.7was obtained by testing two specimens.Fig.8shows the microstructures of the cross-sections of DCL coatings after thermal cycling.In the typical YSZ coating,the additional stress associated with the growth of the TGO is the main factor for the crack growth [15].The micrograph of YSZ coating after thermal cycling is shown in Fig.8D,the black scale between the bond coat and YSZ is TGO layer with thickness of about 4?

m.

Fig.6.Surface photograghs of LZ coating before (A)and after (B)thermal cycling.

H.Dai et al./Materials Science and Engineering A433(2006)1–75

As shown in Fig.5,the cycling life of the DCL coating is strongly dependent on the thickness of YSZ.The life of the DCL coating with YSZ thickness smaller than100?m is short.Also, as shown in Fig.8A,the coating with YSZ thickness of100?m fails in the LZ layer close to the interface of YSZ and LZ.With the increase of the thickness of YSZ layer from100to150?m, the thermal cycling lives of the DCL coatings also increased, implying that the YSZ interlayer has reduced the severe stress condition.When the thickness of YSZ layer is150?m,the DCL coating has even longer thermal cycling life than the single-layer YSZ https://www.wendangku.net/doc/9b2520129.html,pared to the DCL coating with YSZ thickness of150?m,the DCL coating with YSZ thickness of200?m shows a slight decrease of lifetime.For all the coatings with YSZ thickness larger than150?m,the cracks often occur at the interface of the YSZ layer and the bond coat(Fig.8B–D).

To rationalize these results,the stress state in TBCs is consid-ered.The stress distribution of TBCs has strong in?uence on the performance indicators of the coatings,such as spallation and delamination resistance,fatigue life,bonding strength,etc.[16]. Generally,these stresses are the results of:(1)rapid contraction of the sprayed splats during plasma spray(i.e.quenching stress), (2)the mismatch of thermal expansions between the ceramic layer and the bond coat(i.e.thermal stress),(3)growth stress (i.e.bond coat oxidation)[17].The quenching stress can be released or avoided by preheating the substrate during plasma spraying.

The interfacial thermal stress is the main factor of crack initia-tion and extension.Moreover,if the stress state exceeds the adhe-sive or cohesive bonding forces of the coating,delamination and spallation may occur[18].For the single-layer LZ coating,the interfacial thermal stress is much higher than that of the single-layer YSZ coating because of the low thermal expansion coef?-cient.Moreover,the fracture toughness of LZ(1.2MPa m1/2)is evidently lower than that of YSZ(2.4MPa m1/2),implying that the crack initiation and growth will occur even with lower stress levels.This is why the single-layer LZ coating has a thermal cycling life of only a few cycles.YSZ has large thermal expan-sion coef?cient and extremely high fracture toughness,but the high thermal conductivity and phase transition below1200?C are the intrinsic shortcomings of YSZ,which restrict its long-term application at temperatures higher than1200?C.Based on the discussion above,the DCL structure was developed,which could protect YSZ against high temperatures and minimize the thermal mismatch at the interface of the ceramic and the bond coat.

The coating with YSZ thickness of100?m has much shorter thermal cycling life than those with YSZ thickness larger than 100?m and even more interesting is the crack occurring in the LZ layer close to the interface of LZ layer and YSZ layer.As far as we know,there are some reasons that may lead to this kind of failure as described above.The Initial imperfection at the inter-face of ceramic layers may be one critical factor in determining the failure mechanism.However,as can be seen in Fig.3B,the ceramic layer interface of the DCL coating with YSZ thick-ness of100?m was quite perfect.Moreover,it was reported in Ref.[11]that the thermal expansion mismatch between the ceramic layers would lead to the coating crack at the interface.As discussed above,the failure of DCL coatings with YSZ thick-ness larger than100?m mainly occurs at the interface of the YSZ layer and the bond coat.In additional,Fig.9shows the microstructure of the ceramic layer interface of DCL coating with YSZ thickness of150?m before and after thermal cycling, and the corresponding element maps of La,Zr and Y by EDS. After thermal cycling,the interface part of the DCL coating is still perfect and adheres to each other.No signi?cant difference is observed between the microstructure of the interface before

and Fig.8.Microstructures of the cross-sections of DLC coatings:(A)LZ/YSZ200/100?m,(B)LZ/YSZ150/150?m,(C)LZ/YSZ100/200?m,(D)YSZ310?m,rim part of the coating after thermal cycling.

6H.Dai et al./Materials Science and Engineering A 433(2006)

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Fig.9.EDS map scanning of interface of LZ layer and YSZ layer before (A)and after (B)thermal cycling.

after thermal cycling.As shown in EDS maps,a strip of YSZ was found in the LZ layer close to the interface,which may ascribe to the penetration of YSZ through the interconnected pores in the coating.Those observations indicate that thermal expansion mismatch between LZ and YSZ is not the main factor for the DCL coating failure.

Based on the results in our experiments,a plausible explana-tion is put forward as follows.The introduction of YSZ coating as the interlayer between the LZ coating and the bond coat may contribute to the improvement of thermal cycling performance,because:the ?rst,the thermal stress can be reduced,and the sec-ond the driving force for crack extension and the stress intensity factor can be reduced.On the other hand,it is believed that the reduction of thermal stress and stress intensity factor depend strongly on the thickness of the interlayer [19].The thin YSZ contributes only negligibly to the change of the severe stress state in the LZ layer.Therefore,the cracking reason for the coating with YSZ thickness of 100?m in the LZ layer could be that the stress between LZ and bond coat due to thermal expansion mismatch is not effectively relieved.

From Fig.5,it is evident that the lives of DCL coatings have obviously increased when the thickness of YSZ layer is larger than 150?m,implying that the severe stress state in the LZ layer has been reduced to a low level.For the DCL coatings with YSZ thickness larger than 150?m,due to the thermal protection of the LZ layer,the surface temperature of the YSZ layer was reduced.The calculation of the surface temperature is based on the thermal conductivity of LZ (1.56W m ?1K ?1,relative den-sity ～97%,layer thickness)and YSZ (2.5W m ?1K ?1,relative density ～99%,layer thickness).The steady state heat conduc-tion obeys the following equation:J =?λ

d T d l

(1)

where J is the heat ?ux,λthe thermal conductivity,T the temper-ature and l is the thickness of the coating.During thermal cycling,the mean temperatures of the surface and substrate of DLC coat-ings are T Surf =1250?C and T Sub =970?C.For the DCL coating with YSZ thickness of 150?m,the surface temperature of the

YSZ layer is below 1080?C,which is about 90?C lower than its phase transformation temperature and about 200?C lower than its sintering temperature (coating).When it comes to the DCL coating with YSZ thickness of 200?m,the surface temperature (1125?C)increases because of the reducing thickness of LZ layer,indicating that the advantage of LZ layer to protect YSZ against higher temperatures are reduced.This may be the reason of the slightly decreasing lifetime of the DCL coating with YSZ thickness of 200?m.

For the DCL coatings with YSZ thickness larger than 150?m,an additional failure mechanism seems to be dominant.The major factors that contribute to the stress growth in TBCs are:(1)the oxidation of bond coat results in the growth of Al 2O 3scale between the bond coat and the ceramic top coat [20,21],(2)phase transformation of YSZ [6,7],(3)the sintering of the ceramic coating combined with the increase of Young’s modu-lus [22].As discussed above,due to the thermal protection of the LZ layer,the temperature of the YSZ layer is reduced,and the growth stress by the bond coat oxidation becomes the main failure factor for the DCL coatings with YSZ thickness larger than 150?m.The successive chipping of the YSZ layer along the bond coat interface can be obviously observed as shown in Fig.8B–D.4.Summary

The DCL coatings of LZ and YSZ with various thickness ratios were produced by the atmospheric plasma spraying.The cycling lives of the DCL coatings depend strongly on the thick-ness of YSZ.When its thickness is between 150and 200?m,the DCL coating has a longer thermal cycling life than the single-layer YSZ coating,indicating that DCL structure is an ef?cient way to use the advantages and overcome the disadvantages of different coating materials,giving promise to the application of the TBCs at temperatures higher than 1250?C.Since no single material that has been studied so far satis?es all the require-ments for high temperature TBCs,the DCL coating may be an important development direction.

H.Dai et al./Materials Science and Engineering A433(2006)1–77

Acknowledgements

The authors thank Dr.Q.S.Wang(Beijing Institute of Tech-nology)for the invaluable assistance during plasma spraying, and great thanks also to Dr.R.Vassen(Forschungszentrum Juelich GmbH,Deutschland)for the vacuum plasma spraying of the bond coat and the support of YSZ powder.This work was ?nancially supported by NSFC-20471058.

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第七章、统计热力学基础习题和答案

统计热力学基础 一、选择题 1. 下面有关统计热力学的描述，正确的是：( ) A. 统计热力学研究的是大量分子的微观平衡体系 B. 统计热力学研究的是大量分子的宏观平衡体系 C. 统计热力学是热力学的理论基础 D. 统计热力学和热力学是相互独立互不相关的两门学科B 2. 在研究N、V、U有确定值的粒子体系的统计分布时，令刀n i = N,刀n i & i = U , 这是因为所研究的体系是：( ) A. 体系是封闭的，粒子是独立的 B 体系是孤立的，粒子是相依的 C. 体系是孤立的，粒子是独立的 D. 体系是封闭的，粒子是相依的C 3. 假定某种分子的许可能级是0、&、2 ￡和3 &,简并度分别为1、1、2、3四个这样的分子构成的定域体系，其总能量为3￡时，体系的微观状态数为：() A. 40 B. 24 C. 20 D. 28 A 4. 使用麦克斯韦-波尔兹曼分布定律，要求粒子数N 很大，这是因为在推出该定律时：( ) . 假定粒子是可别的 B. 应用了斯特林近似公式 C. 忽略了粒子之间的相互作用 D. 应用拉氏待定乘因子法A 5. 对于玻尔兹曼分布定律n i =(N/q) ? g i ? exp( - ￡ i/kT)的说法：(1) n i是第i能级上的粒子分布数; (2) 随着能级升高，￡ i 增大，n i 总是减少的; (3) 它只适用于可区分的独立粒子体系; (4) 它适用于任何的大量粒子体系其中正确的是：( ) A. (1)(3) B. (3)(4) C. (1)(2) D. (2)(4) C 6. 对于分布在某一能级￡ i上的粒子数n i，下列说法中正确是：() A. n i 与能级的简并度无关 B. ￡ i 值越小，n i 值就越大 C. n i 称为一种分布 D. 任何分布的n i 都可以用波尔兹曼分布公式求出B 7. 15?在已知温度T时，某种粒子的能级￡ j = 2 ￡ i，简并度g i = 2g j，则「和￡ i上 分布的粒子数之比为：( ) A. 0.5exp( j/2￡kT) B. 2exp(- ￡j/2kT) C. 0.5exp( -￡j/kT) D. 2exp( 2 j/k￡T) C 8. I2的振动特征温度? v= 307K，相邻两振动能级上粒子数之n(v + 1)/n(v) = 1/2的温度是：( ) A. 306 K B. 443 K C. 760 K D. 556 K B 9. 下面哪组热力学性质的配分函数表达式与体系中粒子的可别与否无关：( ) A. S、G、F、C v B. U、H、P、C v C. G、F、H、U D. S、U、H、G B 10. 分子运动的振动特征温度?v是物质的重要性质之一，下列正确的说法是： ( ) A. ? v越高，表示温度越高 B. ?v越高，表示分子振动能越小 C. ?越高，表示分子处于激发态的百分数越小 D. ?越高，表示分子处于基态的百分数越小 C 11. 下列几种运动中哪些运动对热力学函数G与

第七章、统计热力学基础习题和答案

统计热力学基础 题 择 一、选 1. 下面有关统计热力学的描述，正确的是：( ) A. 统计热力学研究的是大量分子的微观平衡体系 B. 统计热力学研究的是大量分子的宏观平衡体系 C. 统计热力学是热力学的理论基础 D. 统计热力学和热力学是相互独立互不相关的两门学科B 2.在研究N、V、U 有确定值的粒子体系的统计分布时，令∑n i = N，∑n iεi = U， 3.这是因为所研究的体系是：( ) A. 体系是封闭的，粒子是独立的 B 体系是孤立的，粒子是相依的 C. 体系是孤立的，粒子是独立的 D. 体系是封闭的，粒子是相依的 C 4.假定某种分子的许可能级是0、ε、2ε和3ε，简并度分别为1、1、2、3 四个这样的分子构成的定域体系，其总能量为3ε时，体系的微观状态数为：( ) A. 40 B. 24 C. 20 D. 28 A 5. 使用麦克斯韦-波尔兹曼分布定律，要求粒子数N 很大，这是因为在推出该定律 6.时：( ) . 假定粒子是可别的 B. 应用了斯特林近似公式 C. 忽略了粒子之间的相互作用 D. 应用拉氏待定乘因子法 A 7.对于玻尔兹曼分布定律n i =(N/q) ·g i·exp( -εi/kT)的说法：(1) n i 是第i 能级上的 粒子分布数; (2) 随着能级升高，εi 增大，n i 总是减少的; (3) 它只适用于可区分的独 8.立粒子体系; (4) 它适用于任何的大量粒子体系其中正确的是：( ) A. (1)(3) B. (3)(4) C. (1)(2) D. (2)(4) C 9.对于分布在某一能级εi 上的粒子数n i ，下列说法中正确是：( ) 10.A. n i 与能级的简并度无关 B. εi 值越小，n i 值就越大 C. n i 称为一种分布 D.任何分布的n i 都可以用波尔兹曼分布公式求出 B 11. 15．在已知温度T 时，某种粒子的能级εj = 2εi，简并度g i = 2g j，则εj 和εi 上分布的粒子数之比为：( ) A. 0.5exp( j/2εk T) B. 2exp(- εj/2kT) C. 0.5exp( -εj/kT) D. 2exp( 2 j/kεT) C 12. I2 的振动特征温度Θv= 307K，相邻两振动能级上粒子数之n(v + 1)/n(v) = 1/2 的温度 13.是：( ) A. 306 K B. 443 K C. 760 K D. 556 K B 14.下面哪组热力学性质的配分函数表达式与体系中粒子的可别与否无关：( ) A. S、G、F、C v B. U、H、P、C v C. G、F、H、U D. S、U、H、G B 15. 分子运动的振动特征温度Θv 是物质的重要性质之一，下列正确的说法是： ( ) A.Θv 越高，表示温度越高 B.Θv 越高，表示分子振动能越小 C. Θv 越高，表示分子处于激发态的百分数越小 D. Θv 越高，表示分子处于基态的百分数越小 C 16.下列几种运动中哪些运动对热力学函数G 与A 贡献是不同的：( ) A. 转动运动 B. 电子运动 C. 振动运动 D. 平动运动 D 17.三维平动子的平动能为εt = 7h 2 /(4mV2/ 3 )，能级的简并度为：( )

第七章 统计热力学基础

第七章统计热力学基础 一、单选题 1．统计热力学主要研究（）。 (A) 平衡体系(B) 近平衡体系(C) 非平衡体系 (D) 耗散结构(E) 单个粒子的行为 2．体系的微观性质和宏观性质是通过（）联系起来的。 (A) 热力学(B) 化学动力学(C) 统计力学(D) 经典力学(E) 量子力学 3．统计热力学研究的主要对象是：（） (A) 微观粒子的各种变化规律(B) 宏观体系的各种性质 (C) 微观粒子的运动规律(D) 宏观系统的平衡性质 (E) 体系的宏观性质与微观结构的关系 4．下述诸体系中，属独粒子体系的是：（） (A) 纯液体(B) 理想液态溶液(C) 理想的原子晶体 (D) 理想气体(E) 真实气体 5．对于一个U，N，V确定的体系，其微观状态数最大的分布就是最可几分布，得出这一结论的理论依据是：（） (A) 玻兹曼分布定律(B) 等几率假设(C) 分子运动论 (D) 统计学原理(E) 能量均分原理

6．在台称上有7个砝码，质量分别为1g、2g、5g、10g、50g、100g，则能够称量的质量共有：（） (A) 5040 种(B) 127 种(C) 106 种(D) 126 种 7．在节目单上共有20个节目序号，只知其中独唱节目和独舞节目各占10个，每人可以在节目单上任意挑选两个不同的节目序号，则两次都选上独唱节目的几率是：（） (A) 9/38 (B) 1/4 (C) 1/180 (D) 10/38 8．以0到9这十个数字组成不重复的三位数共有（） (A) 648个(B) 720个(C) 504个(D) 495个 9．各种不同运动状态的能级间隔是不同的，对于同一种气体分子，其平动、转动、振动和电子运动的能级间隔的大小顺序是：（） (A)△e t >△e r >△e v >△e e(B)△e t <△e r <△e v <△e e (C) △e e >△e v >△e t >△e r(D)△e v >△e e >△e t >△e r (E)△e r >△e t >△e e >△e v 10．在统计热力学中，对物系的分类按其组成的粒子能否被分辨来进行，按此原则：（） (A) 气体和晶体皆属定域子体系(C) 气体属离域子体系而晶体属定域子体系 (B) 气体和晶体皆属离域子体系(D) 气体属定域子体系而晶体属离域子体系 11．对于定位系统分布X所拥有的微观状态t x为：（B） (A)(B)