2.15Corrosion of Ceramic Materials
Mathias Herrmann and Hagen Klemm,Fraunhofer-Institut für Keramische Technologien und Systeme IKTS,
(www.ikts.fraunhofer.de)Dresden,Germany
ó2014Elsevier Ltd.All rights reserved.
2.15.1Introduction 4132.15.2Corrosion in Gases 4152.15.2.1
Oxidation 4162.15.2.2
Reactions in Humid Atmospheres 4212.15.3Corrosion in Aqueous Solutions 4232.15.3.1
Basic Processes 4232.15.3.2
Corrosion of Different Ceramics in Aqueous Solutions 427
2.15.4Final Remarks 440
References 441
2.15.1Introduction
The term corrosion is de ?ned as localized or large-scale reaction of a material with the surrounding media,
resulting in degradation or even in destruction of the material or component.Corrosion behavior is therefore a
property not of the material,but of the system including the material,the media and conditions such as
temperature,pressure,medium type and volume or ?ow rate,and tribological as well as mechanical loads.
Therefore,a simple statement concerning corrosion resistance of a material cannot be given because the material
may be stable under one set of conditions,but unstable under another set of conditions (Jacobson,1986;
Klemm,2010;Nickel &Gogotsi,2000;Nickel,Quirmbach,&P?tschke,2010;Petzow &Herrmann,2002;
Schmalzried &Schwetz,2010).
Fundamentally two distinctly different types of corrosion can occur,namely,active or passive.
If the corrosion products are removed from the surface,i.e.if species with high vapor pressures or compo-
nents soluble in the corrosion media are formed,the corrosion reaction is characterized by removal of the
corrosion products and hence reduction in size and mass of the ceramic material.This type of corrosion is called
active corrosion .Active corrosion is usually characterized by a linear time dependence of the mass loss or the
decrease in dimensions (Figure 1(a)).
D x ?Kt (1)
where x is the mass or dimensions and K ,the rate constant.
If the reaction product of the corrosion reaction is a solid or a high-viscosity liquid (e.g.a silicate)that is
insoluble in the corrosion media,the corrosion is often controlled by the properties of the formed surface layer.
If the surface layer is dense and the rate of diffusion of the reactants or reaction products through this layer is
low,the formed layer acts as a corrosion barrier and the corrosion is controlled by this barrier.This case is called
passive corrosion (Figure 1(b)).
For times longer than the time necessary for the formation of the passive layer,the change in mass or di-
mensions is proportional to the square root of time:
D x ?k ??t p tC 1;(2)
where D x is the thickness of the layer and the constant k is the rate constant,C 1includes the processes up to
formation of a stable layer.The layer thickness and mass change can be recalculated using the equation of the
chemical reaction and the component densities.The equation has the physical meaning that the diffusion through the barrier is rate-controlling and as a result,the thickness of the barrier increases with ??t p .More
complicated equations have been derived for short reaction times (formation of the stable oxide layer)(Nickel
et al.,2010;Nickel &Gogotsi,2000).The above equation is valid for steady-state systems,i.e.in which the
material surfaces and surface layer properties can be considered to be constant.If any of these parameters is
Comprehensive Hard Materials,Volume 2https://www.doczj.com/doc/545720842.html,/10.1016/B978-0-08-096527-7.00034-9413
Figure 1Schematics of different types of corrosion:(a)active (b)and (c)passive with amorphous and crystallized oxide layer
respectively,in silicon carbide ceramics (d)paralinear (active)behavior in boron carbide ceramics.
414Corrosion of Ceramic Materials
changed,more complicated equations must be used to describe the process (Nickel et al.,2010;Nickel &
Gogotsi,2000).It was shown that if the layer crystallizes and the diffusion through the crystals is slow,the
equation changes to D x ?A tB log (t ),where A and B are constants (Figure 1(c)).
The active and passive corrosion mechanisms are shown schematically in Figure 1for the oxidation of SiC.
A detailed derivation of the equations depending on the mechanism and the sample geometry is given in the
literature (Hou &Chou,2009;Nickel &Gogotsi,2000;Nickel et al.,2010;Persson &Nygren,1994;Herrmann,2013).
Besides large-scale homogeneous corrosion,more intense corrosion can take place locally (pitting).Pitting
can be caused by inhomogeneities in the ceramic (pores,cracks or segregated secondary phases with lower
corrosion resistivity)or by locally damaged corrosion layers (through gas bubble formation or impurities from
the corroding atmospheres).Pitting is mainly responsible for the decrease in strength of ceramics due to
corrosion (Figure 2).
A material ’s corrosion behavior is often distinguished by the surrounding media:
l
Corrosion in gases l Corrosion in liquid media.
This classi ?cation is based on the differences in media,transport mechanisms and experimental methods of
investigation.Gas corrosion often occurs at higher temperatures and plays a signi ?cant role in high-
temperature applications,especially for nonoxide materials.Water-or organic-based systems play an
important role in industrial processes in which ceramics and hard materials are used,e.g.as seals,bearings or
valves.These processes take place near ambient temperature.Nevertheless,if the interaction with metal or
glass melts is taken into account,high temperatures are also involved.However,corrosion in these systems is
very speci ?c and therefore beyond the scope of this chapter.This chapter is focused on corrosion in air,
combustion gases and water vapor-containing gases as well as in acidic and basic solutions and under hy-
drothermal conditions.
2.15.2Corrosion in Gases
This chapter concentrates on corrosion in air,combustion gases and water vapor-containing gases due to the
practical importance of these processes.Corrosion in halogenides and SO 2/SO 3is not treated (see Jacobson &
Fox,1988;Jacobson,1993;Marra,Kreidler,Jacobson,&Fox,1988;Nickel &Gogotsi,2000;Nickel et al.,2010;
Presser,Heon,&Gogotsi,2011;Readey,1998;Van der Biest,Barnes,Corish,&Norton,1987).Presser and
co-workers (Presser et al.,2011)provide an overview of the reaction of different carbides with Cl 2.The halo-
genides d e.g.Cl 2and HCl d extract the metal from the carbon,leaving a porous carbon material.The goal of the
investigations of the interaction was to gain an understanding of the process of formation of porous carbon
(carbon derived from carbides,or CDC materials),not of the corrosion behavior.
For unknown systems,an initial estimate of the corrosion behavior can be made by means of the gas
reactions and the associated thermodynamic data.A corrosion reaction generally becomes possible when the
Gibbs free energy (D G reaction )of the corresponding reaction is negative.If condensed phases are formed,
passive corrosion can occur depending on the properties of the formed phases.Active corrosion is likely if the
thermodynamic calculations predict the formation of gaseous phases only.In this case,the reaction can also
take place if D G reaction is positive.This only means that the partial pressure of the gaseous product has
a
Figure 2Pits formed in Si 3N 4ceramics during oxidation (Klemm,Taut,&W?tting,2003).
Corrosion of Ceramic Materials 415
partial pressure of <1atm.For example,under gas turbine conditions a partial pressure of the reaction
products of 10à7MPa results in a degradation rate of Si 3N 4ceramics of approximately 400m m per 1000h
(Fritsch,2008).A 100times higher pressure would result in approximately 100times higher recession rate.
For gas reactions (active corrosion),the lower the partial pressure of the reaction products,the lower the
corrosion rate.
The basic principles of the interaction of nonoxide ceramics with air or combustion gases will be outlined in
the following chapter using the examples of SiC and Si 3N 4ceramics due to the abundance of studies performed
on them and their predominance in high-temperature applications.Table 1gives a summary of important
literature in which the behavior of the materials is explained in detail.Presser and Nickel (2008)gives a
comprehensive overview concerning the oxidation of SiC materials and single crystals.
2.15.2.1Oxidation
All nonoxide ceramics are thermodynamically unstable in air,exhibiting passive oxidation behavior up to high
temperatures.Therefore,their stability is connected with the stability of the oxide layer and diffusion of the
Table 1
Overview of corrosion data for nonoxide ceramics (EN12923,2006)Material Mechanism/Remarks Literature
Overview of corrosion of ceramics Jacobson,1993;Nickel &Gogotsi,2000;Nickel et al.,2010;Opila,2003
Testing procedures Advanced,2006;dos Santos e Lucato,Sudre,&Marshall,2011;
Fritsch,2008;Jacobson,1993;Nickel &Gogotsi,2000;
Nickel et al.,2010;Opila,2003
Si 3N 4Passive oxidation,in ?uence of material properties Backhaus-Ricoult,Guerin,&Urbanovich,2002;Klemm et al.,2003;
Klemm,2002,2010;Klemm,Herrmann,&Schubert,1998;
Nickel &Gogotsi,2000;Nickel et al.,2010;Petzow &Herrmann,2002
Gas turbine conditions Fritsch,2008;Fritsch,Klemm,Herrmann,Michaelis,&Schenk,2010;
Klemm,2002;Klemm,2010;Opila,2003;Parthasarathy,
Rapp,Opeka,&Kerans,2009
SiC Passive/transition from passive to active Balat,1996;Balat,Berjoan,Pichelin,&Rochmann,1998;Charpentier,
Balat-Pichelin,&Audubert,2010;Charpentier,Balat-Pichelin,
Glénat,et al.,2010;Charpentier,Ma?tre,Balat-Pichelin,et al.,2009;
Costello &Tressler,1986;Courtright,1991;Dawi,Balat-Pichelin,
Charpentier,et al.,2012;dos Santos e Lucato et al.,2011;Heuer
&Lou,1990;Kim &Moorhead,1990a,1990b;More,
Tortorelli,Walker,et al.,2003;Narushima,Goto,Yokoyama,
et al.,1994a,1994b;Narushima,Goto,Yokoyama,Iguchi,&Hirai,
1993;Nickel &Gogotsi,2000;Nickel et al.,2010;Opila &Serra,
2011;Osada,Nakao,Takahashi,&Ando,2009;Presser &Nickel,
2008;Presser,Loges,Hemberger,et al.,2009;Presser,Loges,
Wirth,et al.,2009;Ramberg &Worrell,2001;Schmalzried &
Schwetz,2010;Schneider,Guette,Naslain,et al.,1998;
Vaughn &Maahs,1990;Wang,Zhang,Zeng,Vignoles,&Guette,2008
Gas turbine conditions Fritsch et al.,2010;Fritsch,2008;Hisamatsu,Etori,&
Yamamoto,2003;Jacobson &Farmer,1999;Jacobson,1993;
Nickel &Gogotsi,2000;Opila &Myers,2004;Opila &Serra,2011;
Opila,2003;Opila,Smialek,Robinson,Fox,&Jacobson,1999;
Roode,2010
EBC for Si 3N 4and SiC and oxide ceramics Environmental barrier coatings Fritsch &Klemm,2006;Fritsch &Klemm,2008;Fritsch,2008;
Klemm,2002;Klemm,2010;Roode,2010
BN/B 4C/borides Passive/active,in ?uence of moisture Eichler &Lesniak,2008;Fahrenholtz,Hilmas,Talmy,&Zaykoski,
2007;Hu,Zhang,Han,Guang,&Du,2010;Jacobson &Farmer,
1999;Nickel &Gogotsi,2000;Nickel et al.,2010;Parthasarathy
et al.,2009;Schmalzried &Schwetz,2010;Sciti et al.,2005
AlN
Dutta,Mitra,&Rabenberg,1992416
Corrosion of Ceramic Materials
Corrosion of Ceramic Materials417 oxygen through the formed oxide?lms.At ambient temperatures,nanometer-thick or even thinner oxide?lms are suf?cient for stabilizing the nonoxide material(passive oxidation).At higher temperatures,the?lm thickness increases due to faster diffusion and oxidation reactions.The diffusion coef?cients of the oxides and the resulting typical parabolic oxidation rates for selected ceramics are given in Figure3.The data reveal that SiO2is superior to other oxides as an oxidation barrier.SiO2has an additional advantage in that it forms amorphous layers up to high temperatures,thus preventing the formation of grain boundaries(with accord-ingly higher diffusion coef?cients)in the oxide scale and the destruction of the oxide scale due to the volume change during crystallization.The highly viscous character of the silica in the layer also allows the healing of cracks and,at least above the glass transition temperature,the relaxation of stresses between the oxide layer and the matrix.These simple principles are responsible for the high oxidation resistance of silica-forming systems (SiC,Si3N4and MoSi2)(Figure3).
The data also indicate that the oxidation resistance of transition metal carbides,nitrides and borides alike (ZrB2,TiC,ZrC,ZrN,and WC)is poor due to the high oxygen diffusion coef?cients of the https://www.doczj.com/doc/545720842.html,posites with SiC are often used to improve the oxidation behavior of these materials.SiO2forms as an oxidation product of SiC,followed by a protective layer which includes the oxides or silicates of the other components. This method is used for example to improve the stability of the so-called ultrahigh-temperature materials (Fahrenholtz et al.,2007;Hu et al.,2010;Parthasarathy et al.,2009;Sciti,Brach,&Bellosi,2005).
The properties of the protective oxide scales also depend on factors other than the main component of the material.Secondary phases such as those found in liquid phase-sintered materials can react with the oxide scale, usually reducing the viscosity and increasing the diffusion coef?cients in the oxide scale.This was investigated in detail for Si3N4materials.The oxidation stability of Si3N4ceramics with different sintering additives at tem-peratures above1200 C was found to increase in the following order:
MgO,MgO/Al2O3,MgO/R2O3 Oxidation at high temperatures does not take place only at the surface of the component if the diffusion along the grain boundaries is faster than the oxidation reaction.This is the case in liquid phase-sintered ma-terials that have amorphous grain boundaries that allow relatively fast process of oxygen transport into the bulk (Klemm et al.,1998;Klemm et al.,2003;Petzow&Herrmann,2002). The differences between the chemical potentials of the components in the surface oxide layer and the grain boundary in the bulk also result in the diffusion of the additives or impurities toward the surface and in diffusion of unreacted oxygen and oxides formed by oxidation into the material.These processes lead to damage in the bulk of the material due to segregation of the grain boundaries and pore formation and ul-timately to degradation of the material(Klemm et al.,2003).This can be alleviated by crystallization of the grain boundaries as well as at least partial crystallization of the formed oxides.The high oxidation resistance and remarkable increase in long-term stability of Si3N4/SiC and Si3N4/MoSi2composite materials result from in situ crystallization of Si2N2O in the near-surface area(Klemm et al.,1998;Klemm,2010).These processes are shown in Figure4. Solid phase-sintered materials such as SiC and Si3N4with minimal additive contents(Si3N4HIPed without additives),have a higher oxidation resistance than the analogous liquid phase-sintered materials due to the low extent of diffusion of oxygen into the bulk of these ceramics,oxidation taking place only on the outer surface (Figure4(a)). Small amounts of alkaline oxide or?uorine impurities strongly reduce the viscosity of the amorphous grain boundary phase and hence the oxidation and creep resistance in Si3N4materials.Therefore for high-temperature materials,pure raw materials must be used.Impurities in the gas phase can also change the diffusion coef?cients in the oxide scale.Alkaline,sulphate and vanadium impurities in combustion gases have a signi?cant negative effect on the oxidation stability of Si3N4and SiC(Jacobson,1993;Klemm,2010;Nickel et al.,2010;Nickel&Gogotsi,2000;Petzow&Herrmann,2002). Si3N4ceramics with nitrogen-rich grain boundary phases exhibit accelerated oxidation,so-called catastrophic oxidation,in the range of900–1100 C due to the absence of a dense oxide layer.Stresses caused by the volume increase during oxidation result in formation of microcracks and ultimately in rapid destruction of the material (Sciti et al.,2005;Petzow&Herrmann,2002).“Pest oxidation”of MoSi2is another example of incomplete for-mation of a protective oxidation scale at intermediate temperatures(electric heaters at temperatures<1000 C). Oxidation of nitrides and carbides also results in gaseous reaction products(N2and CO/CO2respectively).If the diffusion of these gases is much lower than the diffusion of oxygen through the layer,bubbles can be formed in the oxide layer,resulting in locally increased oxidation rates and pitting(Figure2).These pores/bubbles in the oxide layer were found in Si3N4materials at oxidation temperatures above1200–1300 C due to the low 4.5 5.0 5.5 6.0 6.5 7.07.5 8.01.0 x 10–71.0 x 10–81.0 x 10–91.0 x 10–101.0 x 10–111.0 x 10–12 1.0 x 10–13 1.0 x 10–14 HfO 2 10Y 2O 3P e r m i a b i l i t y , g O 2/(c m s e c )104/Temperature (K –1) Al 2O 3SiO 2Y 2O 3CaZrO 3ZrO 2 10Y 2O 3 1800 1600 140012001000 Temperature (°C) 4.0 4.5 5.0 5.5 6.0 6.5 7.07.5 8.01 x 10 1 x 101 x 101 x 101 x 101 x 10O x i d a t i o n r a t e , (μm 2 h ?1)104/Temperature (K –1) AlN Temperature (°C) SiC Al l A N Figure 3Oxygen permeability in oxides (Courtright,1991)and typical parabolic oxidation constants (Courtright,1991;Jacobson & Farmer,1999;Petzow &Herrmann,2002). 418Corrosion of Ceramic Materials solubility and low diffusion rate of the nitrogen formed as a reaction product of oxidation (Backhaus-Ricoult et al.,2002;Jacobson,1986;Klemm,2010;Klemm et al.,1998;).Bubbles can also be formed by impurities with higher oxidation rates (e.g.carbon in SiC)(Nickel et al.,2010;Nickel &Gogotsi,2000;Presser &Nickel, 2008;Schmalzried &Schwetz,2010). Oxidation is strongly in ?uenced by the porosity in the material.All open pores provide sites for oxidation and hence porous materials oxidize faster than dense materials.Depending on the pore structure and the oxidation rate,small pores can be closed by the oxidation product due to the volume increase usually observed Figure 4SEM micrographs of cross-oxidized sections of at 1500 C.(a)Si 3N 4without sintering additives oxidized for 2500h (b)Si 3N 4 material with Y 2O 3/Al 2O 3additives oxidized for 1000h.(c)Si 3N 4material with Y 2O 3and MoSi 2additives oxidized for 2500h. Corrosion of Ceramic Materials 419 during oxidation,thus reducing or preventing internal oxidation(oxidation in the bulk).For example,the rate of oxidation of porous reaction-bonded Si3N4and of recrystallized SiC materials decreases with increasing temperature in the range between900and1200 C due to faster pore closure.This process is described in detail in the literature(Jennings,1983). Depending on the oxygen partial pressure and the temperature,the oxide layers can become unstable, resulting in a change from passive to active oxidation. The theory of active oxidation was?rst developed by Wagner for Si and then modi?ed by different authors for SiC and Si3N4(Table1).The idea behind the theory was that during active oxidation,the?ux of the oxygen or water to the surface must be as high as the?uxes of the reaction products away from the surface(Figure1(b)) and the partial pressure of the reaction products must be lower than the equilibrium concentration necessary for the formation of the oxide layer.Based on these ideas,combining thermodynamic equilibrium and transport equations in the gas phase,the oxygen partial pressure at which the change from active to passive oxidation takes place can be calculated as a function of temperature.The transition boundary between active and passive oxidation for Si3N4and SiC in air is shown in Figure5.In the literature,different equilibria determining the critical partial pressure are proposed for SiC,e.g.Heuer and Lou(1990)proposed the condition where SiO2 smoke is formed near the surface: SiOtO20SiO2esmokeT(3) (For silicon-based ceramics,the main silicon-containing species in the gas phase in the region of active oxidation in dry atmospheres is silicon monoxide(SiO)(Heuer&Lou,1990)). Based on the consideration of zero weight change during oxidation,Wang et al.(2008)proposed another condition,according to the following reaction: SiCt4=3O252=3SiO2econd:Tt1=3SiOegTtCOegT (4) Figure5Dependence of the transition from active to passive oxidation on temperature and oxygen partial pressure in air for Si3N4-and SiC ceramics. 420Corrosion of Ceramic Materials Corrosion of Ceramic Materials421 Nevertheless,all these equations result in similar values for the boundaries(e.g.oxygen partial pressure as a function of temperature).Additional uncertainty is introduced by the fact that the precise values of the diffusion coef?cients of the gaseous species and the thickness of the diffusion layer are not known exactly.On the other hand,the experimental data concerning the transition point for the change from active to passive oxidation exhibit a certain amount of scatter,making it dif?cult for the most precise boundary conditions to be identi?ed (Presser&Nickel,2008). The change in the activity of SiO2in the oxide scale by formation of silica melts due to diffusion of additives into the surface layer(rare earth,Al2O3in Si3N4or LPSSiC materials or impurities in the gas phase)also in-?uences the theoretical boundary(Charpentier et al.,2009;Klemm,2010). For Si3N4-based materials,the boundary depends on both the oxygen partial pressure and the nitrogen pressure in the system(increasing the nitrogen pressure suppresses the active oxidation process).For SiC-based materials,the CO/CO2pressure in the atmosphere has an effect on the boundary.A higher CO pressure sta-bilizes the oxide,thus suppressing the change to active oxidation.Kim and Moorhead(1990a)showed that the strength of SSiC decreases linearly with mass loss during active oxidation. The stability regime of the oxide layer also depends on the gas velocity,with a high gas velocity expanding the active oxidation temperature/pressure region.In addition,water vapor in?uences the decomposition process. Besides the described region of active oxidation,a second region exists for SiC.The transition from passive to active oxidation takes place at high temperature nearly irrespective of the oxygen pressure if the interaction of the SiO2surface layer with the SiC results in a partial pressure which is higher than or equal to the overall pressure.Therefore,the reaction SiCt3=2O20SiO2tCO(5) results in the formation of large bubbles in the oxide layer on the surfaces of the SiC components and a transition from passive to active oxidation(active II)(Jacobson,1993;Narushima et al.,1994b)(Figure5).The same mechanism is also known for Si3N4ceramics Above the oxide scale decomposition temperature,simple decomposition and evaporation reactions of SiC into Si and carbon and of Si3N4materials into Si and N can also take place. The same active oxidation mechanism described here is also active in humid atmospheres,especially in combustion atmospheres with high water vapor pressures. 2.15.2.2Reactions in Humid Atmospheres In humid atmospheres,corrosion is usually accelerated even in the region of passive oxidation due to the higher reactivity of water vapor and higher diffusion coef?cients.Water vapor can also react to form hydroxides which can evaporate at high temperatures.For the common boride ceramic materials,H3BO3or HBO2has the highest partial pressure(Figure6). Therefore boride,BN and B4C materials are moisture-sensitive much below1000 C.For boride systems, the oxidation law can be changed from parabolic for passive oxidation in dry air to paralinear,indicative of active oxidation(Figure1(d)).The mechanism behind this is that the oxidation process determined by the diffusion through the oxide layer has the same rate as the evaporation process and hence the thickness of the oxide layer remains constant with time,but the material dimensions decrease.Hydroxides of Si,Al,Mg and of some of the transition metals have low partial pressures even at high temperatures.In static(non?owing) atmospheres,the evaporation of hydroxides is of little signi?cance,but the situation is completely different in atmospheres with high gas stream velocities and high water vapor pressures such as those found in gas turbine environments(Fritsch,2008;Hisamatsu et al.,2003;Jacobson,1993;Klemm et al.,1998;Klemm,2010; Opila et al.,1999;Opila,2003).In these conditions,even alumina,SiC and Si3N4materials can undergo severe degradation(Fritsch&Klemm,2008;Fritsch et al.,2010;Fritsch,2008;Hisamatsu et al.,2003; Jacobson&Farmer,1999;Jacobson,1993;Klemm et al.,1998;Klemm,2010;Opila&Myers,2004;Opila et al.,1999;Opila,2003).Table2gives the dependencies of the corrosion mechanism on the?ow rate of the hot gas.Measured regression rates of different nonoxide and oxide materials are compiled in Figure7. Therefore,for application of these materials in gas turbine environments,environmental barrier coatings (EBCs)must be used.These coatings have the function of suppressing or preventing the evaporation of the hydroxides.Up to now the best results have been observed with compounds of the transition metals(ZrO2, HfO2,Y2O3and Yb2O3).Besides possessing this chemical function,these materials must have similar thermal expansion coef ?cients to that of the substrate and must be stable in relation to the oxide scale and the substrate material.In the ideal case,the coating forms directly from the bulk to enable https://www.doczj.com/doc/545720842.html,yered systems are also being considered to achieve the complex functionalities required for these coatings.A detailed overview of the current status of EBCs for Si 3N 4and other nonoxides is given by Klemm (Fritsch &Klemm,2006,2008; Fritsch,2008;Hong-fei &Klemm,2011;Roode,2010). The functionality of an EBC in nonoxide (Si 3N 4)and oxide (Al 2O 3)materials is demonstrated in Figure 8.The micrograph show polished cross-sections of the surface region after hot gas testing.Corrosion was not evident in the surface region protected by the EBC,but material loss was found in the unprotected region. Table 2Principle categories of corrosion attack of structural ceramics in water vapor-rich hot gas environments (tests performed at 1200–1500 C,7.5–100%water vapor,1–18bar total pressure and 100–5000h exposure times;a detailed compilation of literature results is given in Fritsch et al.(2010)) Type Test equipment Flow rate (m s à1)Corrosion value K w (mg cm à2h à1)Passive corrosion/oxidation Furnace 10à4–10à2Si 3N 4,SiC w weight gain,Al 2O 3stable Paralinear corrosion Thermogravimetry 10à2–10à1Si 3N 4,SiC,Al 2O 3w 10à3–10à2 Active corrosion Burner rig/test turbine 20–300Si 3N 4,SiC,Al 2O 3w 10à2–10à 1 Figure 6Partial pressure of different hydroxides at 1bar pressure (0.1bar oxide pressure and 0.1bar water pressure)as a function of the temperature (Fritsch,2008and data calculated using SGTE database). 422Corrosion of Ceramic Materials 2.15.3 Corrosion in Aqueous Solutions 2.15.3.1Basic Processes Ceramic materials exhibit a unique combination of properties such as hardness,wear and corrosion resistance, enabling them to be used in pumps and seals (mainly SiC and alumina),ball bearings (mainly Si 3N 4ceramics), chemical apparatus,valves and a wide variety of other applications.Despite the high corrosion resistance in comparison with that of many metals,the suitable material for the given application must be chosen carefully with respect to mechanical load,tribological conditions and corrosion. Therefore,a detailed understanding of the corrosion behavior is necessary.In contrast to metals,which undergo redox reactions (oxidation of metal)during corrosion,ceramics undergo acid –base reactions in cor- rosive conditions: M x O y t2y H t0x Me e2y =x Tteaq :Tty H 2O (6) Figure 7Ranking of ceramic materials in terms of hot-gas-corrosion recession with linear weight loss rate measured in a gas burner test at 1450 C at ?ow rate of 100m s à1,P H 2O ?0:28atm and overall pressure of 1atm (Fritsch et al.,2010 ). Figure 8Functionality of EBC on Si 3N 4ceramics after hot gas testing at 1450 C for 100h. Corrosion of Ceramic Materials 423 or hydration of metal oxide M x O ytn H2O0M x O y$n H2O(7) or hydrolysis of covalent bonds(shown below for AlN) AlNt3H2O0AleOHT3tNH3(8) The few electrically conductive ceramic materials,e.g.SiC,TiN,TiC,MoSi2,hardmetals MAX phases and conductive composites,can undergo electrochemically driven redox reactions like metals.This can change the corrosion behavior strongly and will be explained at the end of this chapter.For a better understanding of the corrosion stability,it is convenient to distinguish solid phase-and liquid phase-sintered materials.The solid phase-sintered materials are usually single-phase materials and do not contain continuous grain boundary phases;examples include high-purity Al2O3,ZrO2and SiC.The stability of the material is hence determined by the stability of the main ceramic component.Liquid phase-sintered materials(e.g.sintered Si3N4-ceramics, liquid phase-sintered SiC(LPSSiC),porcelain,mullite and Al2O3with glassy phase)or materials produced by in?ltration(e.g.Si-in?ltrated SiC)contain continuous grain boundary phase skeletons that can be leached out of the ceramics even under conditions in which the main components are stable.Therefore the stability of the grain boundary phase is often the parameter determining the stability of the ceramic.Alumina ceramics can be either solid-or liquid phase sintered depending on the silica content of the starting composition.The weight gain of alumina as a function of the silica content in HCl at150 C is given in Figure9(Genthe&Hausner, 1989).The glassy grain boundary phase was less stable than alumina in the acid and strongly reduced the stability of the alumina ceramics.A similar strong change in the stability in acids as a function of the grain boundary composition was observed for Si3N4materials(Figure10).A change in weight loss of more than two orders of magnitude was found for certain compositions.The two examples illustrate the strong dependence of the corrosion resistance on composition and microstructure. In order to assess the corrosion behavior of ceramics in advance,it is necessary to evaluate their thermo-dynamic and kinetic stabilities in aqueous media.To achieve a high corrosion resistance,it is advantageous to have the lowest possible solubility of the ceramic or its most unstable component.Generally corrosion reaction only becomes possible when the Gibbs free energy(D G reaction)of the corresponding dissolution reaction is negative.These parameters can be assessed at least by pH-dependent activities of the metal ions in equilibrium with the solids,e.g.of the oxides(Conradt,2008;Franks&Gan,2007;Iler,1982;Schilm,2004). Information Figure9Dependence of the weight loss of Al2O3ceramics in1M HCl as a function of the silica content of the alumina ceramics(MgO content approximately500ppm(Genthe&Hausner,1989)). 424Corrosion of Ceramic Materials about glass stability in aqueous media obtained from extensive studies in the ?eld of glass corrosion can also be applied to ceramic materials with glassy grain boundary phases (Clark,Dilmore,Ethridge,&Hench,1976; Conradt,2008;Freiman,Wiederhorn,&Mecholsky,2009;Iler,1982;Risbud,1981;Schilm,2004;Schilm, Herrmann,&Michael,2004b;Scholze,1991).For example,the low solubility of glasses with high SiO 2contents at low pH values (Conradt,2008;Iler,1982)corresponds to a high stability of Si 3N 4ceramics with SiO 2-rich grain boundary phases in concentrated mineral acids (except HF)up to 100 C (Herrmann,2005;Schilm,2004; Schilm,Herrmann,&Michael,2007;Herrmann,2013). However,if solubility limits are reached during the corrosion process,precipitation of solid phases,i.e. formation of compounds with low solubility,occurs.These phases deposit inside the ceramic material or on its surface,resulting in the formation of protective layers.These layers reduce the rate or completely prevent further corrosion reactions. Whereas thermodynamics provides basic information about the possibility (D G reaction <0)or impossibility (D G reaction >>0)of corrosive attack,kinetic examinations yield information about the reaction rates.Thus,for example,the thermodynamic instability of Al 2O 3ceramics in acids is countered by high activation energy for the dissolution reaction,which is responsible for the high-corrosion stability.In general,corrosive attack in- volves several reactions or material transport processes depending on the ambient parameters (temperature, concentration ratios in corrosive media,composition and grain boundary phase content).The individual processes overlap each other,often resulting in complex corrosion behavior determined by the slowest and thus rate-limiting process.Figure 11schematically illustrates three common types of corrosion in ceramics interfacial (reaction)controlled,limited by the diffusion of the species or passivating due to the formation of a nonsoluble reaction product.The corrosion behavior of Si 3N 4ceramics in 1N H 2SO 4is a good example (Figure 11(b))for the illustration of the different kinetics.In this case,a media temperature change of just 30K is suf ?cient to realize the different behaviors.A detailed discussion of the corrosion equation is given in the literature (Herrmann &Schilm,2009;Herrmann,Schilm,Hermel,&Michaelis,2006;Schilm,2004;Schilm,Gruner, Herrmann,&Michael,2006;Seipel &Nickel,2003;Herrmann,2013). The locally increased attack and resultant damage in the ceramics is called pitting and is the main factor determining the strength of the materials after corrosion (residual strength).A pronounced reduction in strength is typically observed in the initial stage of corrosion.This is caused by the fact that in the initial period,the corrosion is accelerated at existing inhomogeneities.Also the relation between strength (s )and defect size (a ) s w 1???a p (9) Figure 10Dependence of the linear corrosion rate of Si 3N 4materials and oxynitride glasses (with similar composition as the grain boundary phase of silicon nitride ceramics)as a function of the structure of the glass network (after Herrmann,2013). Corrosion of Ceramic Materials 425 directly results in a stronger dependence of strength on defect size for small defect sizes,strongly growing in the initial period.The mechanisms of pitting have been poorly studied thus far and it is very speci ?c for the different materials.They presumably involve growth of existing inhomogeneities (pores,chemical impurities,cracks and local stress). Apart from chemically caused corrosive degradation,stress occurring in the ceramics may signi ?cantly in- ?uence the stability.The low stability of yttria-stabilized tetragonal zirconia (Y-TZP)ceramics in hot acids and under hydrothermal conditions is mainly caused by the chemically induced transformation of zirconia from the metastable tetragonal phase (t-ZrO 2)to the monoclinic phase (m-ZrO 2)(see below). Subcritical crack growth is accelerated if the external tensile stress below the fracture stress is accompanied by a corrosion process.Local chemical corrosion at the crack tip may increase the crack growth rate by several orders Figure 11(a)Schematic view of the different corrosion kinetics,(b)Time dependence of the thickness of the corrosion layer of a Si 3N 4 ceramic as a function of temperature in 0.5mol H 2SO 4(Si 3N 4material with 6wt%Y 2O 3and 4wt%Al 2O 3)(Herrmann,2013). 426Corrosion of Ceramic Materials Corrosion of Ceramic Materials427 of magnitudes,resulting in a signi?cant reduction in lifetime(Barinov,Ivanov,Orlov,&Shevchenko,1998; Chevalier,Olagnon,&Fantozzi,1999;Freiman et al.,2009;Lawson,1995;Lughi&Sergo,2010;Salmang& Scholze,2007;Schneider et al.,2008).Corrosive attack in suspensions combined with abrasive wear may result in a signi?cant increase in the corrosion rate(Fang,Sidky,&Hocking,1997;Presser,Berthold,Wirth,&Nickel, 2008;Kitaoka,Toshidhide,Toshio,Yamaguchi,&Kashiwagi,1992,1994a,1994b;Presser,Nickel,Krumm-hauer,&Kailer,2009).Table3gives an overview of the corrosion behavior of different ceramics under various conditions and Figure12gives the strengths of various ceramic materials in different media.Because the corrosion depends strongly on microstructure and impurities,these data can only serve as a guideline for the corrosion behavior of the materials. The corrosion behavior of different thermally sprayed coatings in bases and acids was investigated by Berger et al.(Stahr,Berger,Herrmann,&Deska,2008;Toma et al.,2010;Herrmann&Toma,2014).Despite having similar compositions to those of the ceramics,the coatings were much less stable than the ceramics.This reveals the strong in?uence of the microstructure on the corrosion behavior.A detailed derivation of the equations depending on the mechanism and the sample geometry is given in the literature(Hou&Chou,2009;Nickel& Gogotsi,2000;Nickel et al.,2010;Herrmann,2013). Additional results concerning the corrosion of the main structural ceramics are given below in more detail. 2.15. 3.2Corrosion of Different Ceramics in Aqueous Solutions Pure alumina ceramics have a high-corrosion resistance in bases and acids and under hydrothermal conditions. Even in supercritical water,they exhibit a high-corrosion resistance(Franks&Gan,2007;Galuskova et al., 2011a;Genthe&Hausner,1989;Genthe&Hausner,1992;Hirata et al.,2003;Hoppert,2010;Kitaoka et al., 1992;Mikeska et al.,2000;Mikeska,1999;Oda&Yoshio,1997;Sato et al.,1991).Silica and alkaline additives in alumina often used to reduce the sintering temperature are leached out in acids and under hydrothermal conditions(Figures9and13).MgO results in the formation of spinel phases which are chemically stable and do not degrade.Therefore these materials are more stable than the alumina ceramics with silica impurities (Figure13b)(Hoppert,2010;Genthe&Hausner,1989;Genthe&Hausner,1992). Zirconium oxide(ZrO2)has different crystallographic modi?cations.The cubic modi?cation(?uorite structure)stable at high temperatures transforms to the tetragonal modi?cation at2370 C.The tetragonal modi?cation transforms to the monoclinic modi?cation at1170 C.The tetragonal-to-monoclinic phase transformation is associated with a volume expansion of nearly5%,resulting in cracking of the material. Therefore,pure ZrO2is of no practical use;the tetragonal and cubic modi?cations can be stabilized through the addition of rare-earth or earth alkali oxides.The following types of zirconia exist(organized according to the degree of stabilization)(Chevalier et al.,2009;Iio,Okada,Asano,&Yoshimura,1992; Lughi&Sergo,2010): l Fully stabilized(cubic)zirconia has moderate strength and toughness and is mostly used as an oxide conductor,e.g.in sensors or solid oxide fuel cells.Very few results concerning the corrosion stability of this material are available.In general,it is highly stable in solutions and in humid air.Fully stabilized ZrO2is also used as thermal barrier coatings in gas turbine applications,making use of its high stability in water vapor (Chevalier et al.,2009;Fritsch et al.,2010;Yoshimura et al.,1986).Yoshimura(Yoshimura et al.,1986) investigated the stability of yttrium stabilized zirconia in different media and at different temperatures. l Partially stabilized zirconia(PSZ)exhibits a cubic matrix with?ne tetragonal precipitates(typically w200nm)formed during cooling.Typically these materials are prepared with MgO as the stabilizer.If a load is applied,the tetragonal phase can transform to the monoclinic phase,resulting in transformation toughening.These materials are used as wear parts and in chemical equipment and have a higher stability than and similar corrosion mechanisms to those of Y-TZP materials(Chen&Lu,2003;Chevalier et al.,2009; Herrmann et al.,2003;Schacht et al.,1998;Tan et al.,1996). l Tetragonal zirconia polycrystalline(TZP)ceramics consist of metastable tetragonal grains which when loaded can transform to the tetragonal phase,resulting in transformation toughening.The typical material is2–3mol yttria-stabilized ZrO2which can reach strengths of>1GPa and a fracture toughness of!6MPa m1/2. CeO2-stabilized materials can reach even higher fracture toughness,but lower strength,levels.Besides the described zirconia ceramics,several composites are used,with the most prominent being zirconia-toughened alumina containing10–20vol%ZrO2(ZTA)and alumina-toughened zirconia(ATZ).Y-TZP is widely used in cutting applications and dental implants and hence the hydrothermal stability of this material has been Figure 12Strengths of different ceramic materials after corrosion in 1N NaOH,H 2SO 4and water at elevated temperatures (temperature is given in the graph)after 200h (Herrmann,Schilm,&Michael,2003). thoroughly investigated (Bartolome et al.,2004;Chevalier et al.,2009;Kimel &Adair,2002;Lawson,1995;Lughi &Sergo,2010). Transformation toughening of the zirconia ceramics is based on stress-induced phase transformation of the metastable tetragonal phase to the stable monoclinic phase accompanied by a volume increase at the crack tip.This volume increase results in compressive stress at the crack tip.The phase transformation can be initiated by mechanical loading as well as by corrosion.The same mechanism that causes toughening results in accelerated aging/corrosion of ZrO 2ceramics:water or even water vapor can destabilize t-ZrO 2.If the monoclinic phase content is high,the arising stresses result in the formation of microcracks and grain lifting (spalling)(Bartolome et al.,2004;Chevalier et al.,2009;Lawson,1995;Li &Watanabe,1998;Lughi &Sergo,2010;Marro et al.,2009;Tan et al.,1996).This process starts on the surface,increasing the surface roughness and in ?uencing the wear behavior.The formed microcracks create pathways for water penetration into the ceramic,resulting in further transformation,microcracking and ultimately formation of macrocracks.Thus the phase transformation leads to accelerated aging of the material.The interrelation between aging behavior,stresses and wear and the effect on the integrity of zirconia devices are illustrated in Figure 14.The same mechanism that results in toughening,i.e.improvement of the mechanical behavior,also results in accelerated aging/corrosion of ZrO 2. Details of the destabilization mechanism in ZrO 2are still under discussion.The main process is the water adsorption and diffusion of OH àinto the ZrO 2lattice,resulting in ?lling of the vacancies in the oxygen sublattice by OH à(Chevalier et al.,2009;Guo &Schober,2004;Yoshimura et al.,1986)or O 2à(Chevalier et al.,2009).Incorporation of water strongly depends on the partial pressure of the water vapor (Yoshimura et al.,1986).The microstructure and the corrosion conditions mainly control the kinetics.Most investigations were carried out under hydrothermal conditions (sterilization of medical products at 135 C in water for 5h).Additionally,Y-TZP ceramics have the lowest stability in the temperature range between 200and 300 C (Bartolome et al.,2004;Chevalier et al.,2009;Guo &Schober,2004;Lawson,1995;Lughi &Sergo,2010;Yashima et al.,1995).The stability under hydrothermal conditions can be increased by different factors: l Reduction of the grain size results in an increase in the stability of t-ZrO 2.Above the critical grain size of approximately 0.3–0.5m m,the corrosion is strongly accelerated.This makes precise temperature control during sintering necessary.Nanocrystalline materials show an strongly improved corrosion stability (Johannes &Schneider,2012) l Increasing of the stabilizer content results in reduced transformation toughening and therefore reduced fracture toughness and strength of the material.Therefore an optimum has to be found.It was proposed that by inhomogeneous yttria distribution (higher yttria content in the outer shells of the grains),the stability could be increased without a reduction in toughness.Corrosion of Ceramic Materials 429 l Additional doping with other oxides (Chevalier et al.,2009;Lawson,1995;Lughi &Sergo,2010;Schacht et al.,1998),mainly CeO 2(Chevalier et al.,2009;Lawson,1995;Lughi &Sergo,2010;Schacht et al.,1998),increases the stability.The higher stability can be explained by the different solubilities of CeO 2and Y 2O 3as well as by the different concentrations of oxygen vacancies (no vacancies in CeO 2in CeO 2-stabilized ZrO 2)which play an important role in the corrosion mechanism. l Increasing the Al 2O 3content in Y-TZP reduces the extent of phase transformation during corrosion and therefore increases the stability.Al 2O 3/ZrO 2have also been observed to show improved corrosion resistance Figure 13Corrosion rate and change in residual strength during corrosion (Hoppert,2010).(a)Relative corrosion volume of a 92%Al 2O 3ceramic after 121days at 20 C in different acids results normalized with respect to the corrosion of the ceramics in 96%H 2SO 4).(b)Residual strength of different Al 2O 3ceramics in 5%H 2SO 4at 100 C (96K Al 2O 3:96%Al 2O 3with crystalline secondary phase;99Al 2O 3;92Al 2O 3:Al 2O 3ceramic with 99%and 92%purity and glassy grain boundary phase). 430Corrosion of Ceramic Materials in comparison with that of pure TZP (Johannes &Schneider,2012).MgO,spinel and transition metal oxide additives exhibit similar effects (Lawson,1995). l Use of pore-free microstructures and materials also results in improved stability. The Mg-PSZ ceramics are more stable than the Y-TZP ceramics are under hydrothermal conditions.Direct comparison of Ce-TZP,Mg/Y-PSZ,and Mg-PSZ in different acids (HCl,H 2SO 4and H 3PO 4)at 390 C was carried out by Schacht (Schacht et al.,1998).The results yielded an increase in stability in the order Mg-PSZ Subcritical crack growth and phase transformation in Y-TZP ceramics were investigated in detail to predict the lifetime of ZrO 2implants (Bartolome et al.,2004;Chevalier et al.,1999;Yashima et al.,1995).Schneider carried out detailed studies of the phase transformation of alumina-toughened ZrO 2(Schneider et al.,2008)and found a much lower extent of aging in humid atmospheres for these materials than for 3Y-TZP ceramics.A trans-formation of approximately 50%of the ZrO 2fraction was calculated to take place in only about 50years (extrapolated from higher temperatures)at 37 C and was observed to take place after <100h at 134 C (Schneider et al.,2008). Thus transformation-toughened ZrO 2materials can only be used in solutions or humid air at higher tem-peratures if a detailed selection process has been carried out to determine the right material,microstructure and processing. Silicon nitride materials are usually liquid phase-sintered materials containing amorphous grain boundary phases.In Si 3N 4ceramics,the grain boundary phase is distributed among the triple junctions and the thin ?lms between the grains.The triple junctions form a three-dimensional network and have cross-sectional diameters of <1–2m m (Figure 15).The thin grain boundary ?lms between adjacent grains have thicknesses typically in the range of 1–2nm,strongly depending on the grain boundary composition (Petzow &Herrmann,2002;Kleebe et al.,1993).In materials with 5–10vol%additives more than 90%of the grain boundary phase is concentrated in the triple junctions.These microstructural features must be taken into account in the inter-pretation of the corrosion resistance. Typical sintering additives are rare-earth oxides and Al 2O 3/AlN or MgO or MgO/Al 2O 3(Petzow &Herrmann,2002).Because of their different additive contents and processing/sintering,the ceramics have different grain boundary phase amounts and compositions.Studies of the corrosion resistance of Si 3N 4materials revealed a strong relationship between the stability of the grain boundary and the corrosion resistance of the ceramic material (Galuskova et al.,2011b;Herrmann &Schilm,2009;Herrmann et al.,2003;Herrmann et al.,2006;Herrmann,2005;Herrmann,2012;Kitaoka et al.,1994;Kleebe et al.,1993;Nagae,Koyama,et al.,2006; Sato Figure 14Potential effect of corrosion on the integrity of zirconia components (after Chevalier et al.,2009). Corrosion of Ceramic Materials 431 et al.,1988a,1988b;Sato et al.,1992;Schilm et al.,2003;Schilm et al.,2004a;Schilm et al.,2006;Schilm et al.,2007;Schilm,2004;Seipel &Nickel,2003;Shimada &Sato,1989;Somiya,2001). Materials sintered conventionally with Y 2O 3/Al 2O 3have much lower strengths after corrosion in acids at elevated temperatures due to grain boundary phase dissolution in the acids.This dissolution of the grain boundary phase can occur to depths of several micrometers without the three-dimensional network of the Si 3N 4grains being destroyed (Figures 11(b)and 16(a)).Even materials with completely dissolved grain boundaries exhibit strengths of 400–500MPa. Comprehensive investigations of the relationship between grain boundary phase composition and corrosion behavior were carried out by Herrmann and Schilm et al.(Herrmann,2005;Herrmann,2012;Herrmann et al.,2003;Herrmann et al.,2006;Herrmann &Schilm,2009;Schilm,2004;Schilm et al.,2003;Schilm et al.,2004a;Schilm et al.,2006;Schilm et al.,2007;Seipel &Nickel,2003)who found that the corrosion behavior of silicon nitride ceramics with amorphous grain boundary phases exposed to H 2SO 4,HCl,other mineral acids except HF (Monteverde et al.,2001;Schilm et al.,2004a;Sharkawy &El-Aslabi,1998;Shimada &Sato,1989)and bases at temperatures to at least 100–130 C depends on the stability of the grain boundary phase:under these Figure 15FESEM micrographs of polished sections (a,c and e)with Y 2O 3/Al 2O 3additives and (b,d and f)with Y 2O 3/MgO/Al 2O 3additives before and after corrosion (Herrmann,2005).(a and b)initial state,(c and d)corroded in 1N H 2SO 4at 90 C,and (e and f)corroded in 1N NaOH at 90 C. 432Corrosion of Ceramic Materials 第二章有理数及其运算 12．用计算器进行运算 一、学生知识状况分析 在上节课的基础上，学生能够非常有兴趣来学习计算器的使用方法。关键要照顾好不能准确记忆每个键功能的学生，教师及时帮扶，通过动手能力强的学生带动弱势群体来学习本节课知识。 二、教学任务分析 计算器和计算机的逐步普及，对数学教育产生了深刻的影响。因此《标准》强调，“把现代信息技术作为学生学习数学和解决问题的强有力工具，致力于改变学生的学习方式，使学生乐意并有更多的精力投入到现实的、探索性的数学活动中去”。一方面计算器可以使学生从繁琐的纸笔计算中解放出来，也为解决实际问题提供了有力的工具；另一方面，计算器和计算机对学生的数学学习方式也有很大的影响.计算器可以帮助学生探索数学规律，理解数学概念和法则。学生刚学了有理数的运算法则，可以将纸笔计算与计算器计算的结果相对照，因此学好本节内容对于学生的发展起着举足轻重的作用，在探索现实问题和需要进行复杂的运算时，应当鼓励学生使用计算器，慢慢养成像使用纸笔那样使用计算器的习惯。根据本节课的内容及学生的特点，设置教学目标及重难点如下：1经历探索计算器使用方法的过程，了解计算器按键功能，会使用计算进行有理数的加、减、乘、除、乘方运算.掌握按键顺序， 2经历运用计算器探索数学规律的活动，培养合情推理能力，能运用计算器进行实际问题的复杂运算. 3在合作交流的学习过程中，培养合作能力和动手操作的实践能力。 本节课的重点是计算器的使用及技巧。. 本节课难点是难点是运用计算器进行较为繁琐的运算和探索规律，关键是熟练准确的运用计算器进行计算。 三、教学过程分析 本节课设计了五个环节：动手操作掌握运用；例题讲解熟能生巧；尝试练 小学四年级数学“用计算器计算”教案 【教学目标】： 1、让学生初步认识计算器，了解计算器的基本功能，会使用计算器进行大数目的一两步连续运算，并通过计算探索发现一些简单数学规律。 2、让学生体验计算器计算的方便与快捷，进一步培养对数学学习的兴趣，感受计算器在人们生活和工作中的价值。【教学重点、难点】：通过计算发现一些简单的数学规律。【教学准备】：课件、练习纸、计算器 【教学过程】： 一、游戏导入，激发兴趣。 谈话：同学们，你们玩过快乐联想的游戏吗？还想玩吗？课件依次出示四个提示 提示一 提示二 提示三 提示四 完美 基督教 医院 三三两两 师：你能想到什么？ 生1：我猜是十字架。 生2：我想可能是。 出示提示四 生3：我猜是十。 答对的同学，给予肯定。 师：还想玩吗？ 课件依次出示提示 提示一 提示二 提示三 提示四 知错能改 小巧 学习用品 计算工具 生1：我猜是橡皮 生2：我也认为是橡皮。 出示了提示四后 生3：计算器。 表扬答对的同学。 今天我们来学习用计算器计算。课件出示课题，并板书。 二、自主探究，解决问题。 1、认识计算器。 同学们，你们在哪里见过计算器？（根据同学回答，依次出示课件中的图片） 表述：看来计算器已经深入我们生活中。瞧，老师手中就有一个计算器，你们观察过计算器吗？看老师手中的计算器，你们看到了什么？（根据学生回答，依次板书数字键、符号键、功能键、键盘、显示器） 指出：有些功能键由于我们所学知识有限，现在还不需要用，今后我们可以再慢慢认识它们。 2、认识开机键、关机键。 用计算器前，先按什么键？（ON键，根据学生回答指出开机键） 用完后呢？（OFF键，指出关机键） 3、尝试用计算器计算。 有多少同学会用计算器？真会?那我们来试着瞧瞧。 (课件出示38 ＋27 = 3018 = ) 指名说第一题计算过程。 师：你是怎么输入的? （先输入3和8，再输入加号键，输入3和7和等号键,等于65。） 追问：想知道得数，需要输入什么键？（等号键） 12用计算器进行运算 测试时间:25分钟 一、选择题 1.在计算器的键盘中,表示开启电源的键是( ) A.OFF B.AC/ON C.MODE D.SHIFT 2.在计算器的键盘中,表示关闭电源的键是( ) A.OFF B.AC/ON C.MODE D.SHIFT 3.用计算器求35+12的按键顺序正确的是( ) ①输入数据35依次按数字键12依次按数字键 A.①②③④ B.①③②④ C.①④②③ D.①③④② 4.下列说法正确的是( ) A.用计算器进行混合运算时,应先按键进行乘方运算,再按键进行乘除运算,最后按键进行加减运算 B.输入0.58的按键顺序是 C.输入-5.8 D.输入-3.7 5.用计算器计算-42的按键顺序是( ) 6.用科学计算器计算,若按键顺序是则结果为( ) A.512 B.511 C.513 D.500 二、填空题 7.如果进行加、减、乘、除和乘方的混合运算时,只要按算式的顺序输入,计算器就会按要求算出结果. 8.小芳在用计算器计算“14.9×73”时,发现计算器的小数点键坏了,你还能用这个计算器把正确的结果算出来吗?请把你想到的方法用算式表示出来: . 三、解答题 9.用计算器求下列各式的值: (1)36×3-28÷2;(2)-25×0.36÷(-1.2); . (3)-12÷6-(-2)5;(4)(7.3-8.9)×1 8 10.使用计算器计算各 式:6×7=;66×67=;666×667=;6666×6667=. (1)根据以上结果,你发现了什么规律? (2)依照你发现的规律,不用计算器,你能直接写出666666×666667的结果吗?请你试一试. 单击此处编辑母版标题样式 虚拟 “实验”（分子模拟技术） Materials Studio是整合的计算模拟平台 Materials Studio? 3.5利用计算器进行简单的计算教学案 个性化设计： 一、教与学目标： 1、知识与能力 会使用计算器进行有理数的加、减、乘、除、乘方运算；会运用计算器进行实际问题 的复杂运算。 2、过程与方法 通过运用计算器探求规律的活动，发展合理推理的能力。 3、情感、态度与价值观 通过学生动手操作，培养学生的动手能力。 二、教与学重点难点： 重点：会使用计算器进行有理数的加、减、乘、除、乘方运算。 难点：会运用计算器进行实际问题的复杂运算。 三、教与学方法： 合作探究小组交流 四、教与学过程： (一)、情境导入： 1、一根底面直径为12.5厘米的圆钢，长为230厘米，它的体积是多少啊？ 你能很快的得出答案吗？ 2、在20秒内计算出下列算式的结果。 8.5+13.65-35.35 1.26-0.78-5.03 56÷4+32×2 51×11÷17-19 同学们想知道怎样才能做到这件事吗？ 通过设置两个问题情境，一方面让学生感受到数学来源于生活，又应用于生活，另一 方面激发学生的学习兴趣，热爱数学。 (二)、探究新知： 1、问题导读： 阅读课本68页文字部分，了解计算器的使用方法，找出你存在的疑问。 2、合作交流： (1)让学生介绍自己手中的计算器的构造。 显示计算过程中输入的数据和计算的结果。显示屏因计算器的种类 不同，有单行显示的也有双行显示的。键盘上的每一个键都表明了 这个键的功能。一般的，计算器上的ON 是开机和清屏键。使用计 算器时，先按这个键，可以清除显示屏上的数与符号。需要关机时， 依次按第二功能键SHIFT 和关机键OFF(及AC的第二功能)，就可以 切断电源。不同的计算器上的功能符号不同，使用计算器前，应先 阅读使用说明书，了解各个按键的功能和按键的方法，以免使用中出现计算错误。对于加 减乘除四种运算，各个计算器的按键功能通常是一样的。 3、精讲点拨： (1)、用计算器计算 15﹢3.2﹣9.5 解析：按键的顺序为1 5 ﹢ 3 . 2 ﹣ 9 . 5 =显示屏最后结果为8.7。 所以15﹢3.2﹣9.5=8.7 (2)、用计算器计算 168÷(7﹣14×12.5) Materials studio简介 1、诞生背景美国Accelrys公司的前身为四家世界领先的科学软件公司――美国Molecular Simulations Inc.(MSI)公司、Genetics Computer Group(GCG)公司、英国Synopsys Scient ific系统公司以及Oxford Molecular Group(OMG)公司，由这四家软件公司于2001年6月1日合并组建的Accelrys公司，是目前全球范围内唯一能够提供分子模拟、材料设计以及化学信息学和生物信息学全面解决方案和相关服务的软件供应商。 Accelrys材料科学软件产品提供了全面完善的模拟环境，可以帮助研究者构建、显示和分析分子、固体及表面的结构模型，并研究、预测材料的相关性质。Accelrys的软件是高度模块化的集成产品，用户可以自由定制、购买自己的软件系统，以满足研究工作的不同需要。Accelrys软件用于材料科学研究的主要产品包括运行于UNIX工作站系统上的Cerius2软件，以及全新开发的基于PC平台的Materials Studio软件。Accelrys材料科学软件被广泛应用于石化、化工、制药、食品、石油、电子、汽车和航空航天等工业及教育研究部门，在上述领域中具有较大影响的世界各主要跨国公司及著名研究机构几乎都是Accelrys产品的用户。 2、软件概况 Materials Studio是专门为材料科学领域研究者开发的一款可运行在PC上的模拟软件。它可以帮助你解决当今化学、材料工业中的一系列重要问题。支持Windows 98、2000、NT、Unix以及Linux等多种操作平台的Materials Studio使化学及材料科学的研究者们能更方便地建立三维结构模型，并对各种晶体、无定型以及高分子材料的性质及相关过程进行深入的研究。 多种先进算法的综合应用使Materials Studio成为一个强有力的模拟工具。无论构型优化、性质预测和X射线衍射分析，以及复杂的动力学模拟和量子力学计算，我们都可以通过一些简单易学的操作来得到切实可靠的数据。 Materials Studio软件采用灵活的Client-Server结构。其核心模块Visualizer运行于客户端PC，支持的操作系统包括Windows 98、2000、NT；计算模块（如Discover，Amorphous，Equilibria，DMol3，CASTEP等）运行于服务器端，支持的系统包括Windows2000、NT、SGIIRIX以及Red Hat Linux。浮动许可（Floating License）机制允许用户将计算作业提交到网络上的任何一台服务器上，并将结果返回到客户端进行分析，从而最大限度地利用了网络资源。 任何一个研究者，无论是否是计算机方面的专家，都能充分享用Materials Studio软件所带来的先进技术。Materials Studio生成的结构、图表及视频片断等数据可以及时地与其它PC软件共享，方便与其他同事交流，并能使你的讲演和报告更加引人入胜。 Materials Studio软件能使任何研究者达到与世界一流研究部门相一致的材料模拟的能力。模拟的内容包括了催化剂、聚合物、固体及表面、晶体与衍射、化学反应等材料和化学研究领域的主要课题。 3、模块简介 Materials Studio采用了大家非常熟悉的Microsoft标准用户界面，允许用户通过各种控制面板直接对计算参数和计算结果进行设置和分析。目前，Materials Studio软件包括如下功能模块： Materials Visualizer: 提供了搭建分子、晶体及高分子材料结构模型所需要的所有工具，可以操作、观察及分析结构模型，处理图表、表格或文本等形式的数据，并提供软件的基本环境和分析工具以及支持Materials Studio的其他产品。是Materials Studio产品系列的核心模块。 七年级数学一教学教案-课时训练 2.12.计算器的使用 一、计算题 1. 用计算器计算 (1) 35 + 18X 19;( 2)—6 —126X 27; (3) 49 —( 52.3 + 78.9 );( 4) 31.5 —2.5 X〔27.3 —(—36.5 )〕 2. 用计算器计算 (1) -2xO.Fx(-0,2r-(-d8)-0.02 (保留两位小数) -3- [-5+(1-0.2'x-)^ (-2)'] (2) 5 二、解答题 1. 三、综合创新题 1. 有理数氐k C在数轴上的对应点如图所示，下面式子中正确的是（ b -3- 2 亠1*0* I 2 3 （-6）+ 8+（— 4）,并且用数轴上一点 P 运动的过程来反应这个式子 3. 如图是一个由棱长为 3的小 正方体摆成的几何体的三视图， 试求出该几何体的体积. 4. 观察图，把你观察到的数学信息写下来，并提出三个以上的数学问题予以解答. 5?如图，i 和C 的位置由图给出，请根据下面的算式来确定 d 的位置：（1）d+b+E 二0, （2）a-i+c = 0 ? 6.如图，下面是由火柴拼出的一列图形，观察这些图形计算像这样的摆法当摆出十五 个正方形时需要多少根火柴. 7.从2001年2月21日0时起，中国电信执行新的电话收费标准，其中本地网营业区 内通话费是：前三分钟为 0.2元（不足3分钟按3分钟计算），以后每分钟加收 足1分钟按1分钟计算）.上星期天，一位学生调查了甲、乙、丙、丁、戊五位同学某天打 本地网营业区内电话的通话时间情况如下表： 甲 乙 丙 丁 戊 第一次通话时间 3分 3分45秒 3分55秒 3分20秒 6分 第二次通话时间 0 4分 3分40秒 4分50秒 0 第三次通话时间 0 5分 2分 0 电话费（元） 请分别计算出五位同学这一天的电话费填在表内. 1.判断题 （1）有理数fl 和0，如果 axhO ,且空+b 》0, 则?（ 主现图 左視图 俯挟图 A. i+c>0 B ? C ? aoic D ?血》饥 2.计算：2 + 在数轴上的意义. □I 0.1元（不 课题：用计算器进行计算●教学目标： 一、知识与技能目标： 1. 会使用计算器进行有理数的加、减、乘、除、乘方的混合运算. 二、过程与方法目标： 1经历运用计算器探求规律的活动，发展合情推理能力. 2.培养自主探究的能力 三、情感态度与价值观目标： 能运用计算器进行实际问题的复杂运算. ●重点： 利用计算器进行有理数的加、减、乘、除、乘方的混合运算. ●难点 用计算器探求规律的活动. ●教学流程： 一、回顾旧知，情景导入 如图为科学计算器的面板。 显示器用来显示输入的数据和计算结果，有单行和双行显示。 计算器的键盘上面标有这个键的功能。 如是开启计算器键，按下之后，计算器处于开机状态 是清除键，按下可以清除当前显示的数和符号 的功能是完成运算或执行指令 是加法运算键，按下这个键，计算器就执行加法运算。 有些键的上边还标注着其他功能，我们称它为第二功能。通常用不同颜色标明以区别于这个键的第一功能。 如：直接按下键，计算机执行第一功能，即清除显示器显示的所有符号和数； 先按键，再按键，执行第二功能，即关闭计算器。 二、解答困惑，讲授新知 如何用计算器进行有理数运算。 . 三、实例演练深化认识 例用计算器计算： （1）（3.2-4.5）×32- （2）[3×（-2）3+1]÷（-） 解：（1）按键顺序为： 计算器显示结果为-，可以按键切换为小数格式-12.1，所以（3.2-4.5）×32- =-12.1 （2）按键顺序为： 计算器显示结果为 此时，若按键，则结果切换为小数格式19.16666667.这一结果显然不是准确值，而是一个近似数。在用计算器计算时，所得到的结果有时候是近似数。为了得到所需精确度的近似数，常采用四舍五入法。 2.12 用科学计算器进行运算 教学目标： 1、会使用计算器进行有理数的加、减、乘、除、乘方的混合运算。 2、经历运用计算器探求规律的活动，发展合情推理能力。 3、能运用计算器进行实际问题的复杂运算。 教学重点: 使用计算器进行有理数的加、减、乘、除、乘方的混合运算。 教学难点: 用计算器探求规律的活动。 教学过程： 一、创设情境、导入课题 师：同学们，大家都去过乐客多吧？它每天都有很多顾客，特别是到了节假日，那更是人山人海。当顾客推着满满一车物品去付款时，营业员总是能在很短的时间内告诉他应该付多少钱，为什么营业员会算得那么快呢，你知道吗？ 生：因为是用计算器计算的。 师：对，今天这节课我们就来一起学习用“计算器计算”。（出示课题） 二、学习用计算器计算 1、认识计算器 师：你知道在我们日常生活中还有哪些地方用到了计算器吗？ 生1：在菜场买菜时。 生2：在书店买书付帐时用到了计算器。 生3：工人在拿工资时也用到过计算器。 …… 师：你了解计算器吗？今天假如你是一位计算器的推销员，你打算怎样向大家介绍你手中的这款计算器的构造？（同桌之间相互说一说后再全班交流） 生（边指边说）：我的计算器是英文牌子的，还有一个R，这说明是经过国家质量验证过的。这是显示器，下面是键盘，有数字键，运算符号键和功能键，它们是用三种不同的颜色来表示的。 …… 说明：各种不同的计算器的功能和操作方法也不完全相同，因此在使用前一定要先看使用说明书。但对于一些简单的操作，方法还是相同的，象开机按？关机按？ 生：开机按ON/C，关机按OFF 2、用计算器计算 师：大家已经认识了计算器，你会操作他吗？现在咱们就用计算器来算一些题目，请把计算器准备好，准备好了吗？ 小黑板出示： 75+47= 24×7.6= 62.8-0.95= 师：现在请你们同桌之间说说你是怎样用计算器计算器这三题的。（同桌交流） 生1：75+47我是这样操作的，先按75再按“+”再按47，最后按“=”，显示器上就出现了结果，是112。 生2：24×7.6我是这样操作的，先按24再按“×”再按7.6，再按一下“=”结果就出来了，是182.4。 生3：62.8-0.95我是这样操作的，先按62.8再按“-”再按0.95再按“=”结果是61.85。生4：62.8-0.95我的操作和他不一样，在按0.95时，我是先按小数点，再按9按5的。师：是吗？我们按照这种方法试一试，看看能得到0.95吗？（学生齐操作） 师：通过计算这三题，我们可以发现，用计算器计算时只要从左往右依次按键就可以了。现在我们要来比一比谁算的最快，请准备好，开始：出示0.092÷1.15×25= 生1：我是这样操作的，先按小数点，再依次按0、9、2，再按“÷”再按1.15再按“×”再按25，最后按“=”，结果是2。 生2：我的操作方法和他基本相似，就是一开始先按0再按的小数点，结果也是2。 三、介绍计算工具的发展史 师：通过用计算器计算上面这些题目，你有什么体会？你觉得用计算器计算怎么样啊？ 生1：我觉得用计算器计算很快。 生2：我觉得用计算器计算不容易出错。 生3：我觉得用计算器计算又对有快。 师：那么同学们有没有想过在计算器还没发明之前，我们的先辈们都用过哪些计算工具呢？你能不能将你课前收集的资料联系书本上的介绍来说一说？（小组交流后再全班交流） 生1：在远古时期人们是用的小石子，还有小棒。 生2：还有竹签，筷子和算盘。 Materials Studio是Accelrys专为材料科学领域开发的可运行于PC机上的新一代材料计算软件，可帮助研究人员解决当今化学及材料工业中的许多重要问题。Materials Studio 软件采用Client/Server结构，客户端可以是Windows 98、2000或NT系统，计算服务器可以是本机的Windows 2000或NT，也可以是网络上的Windows 2000、Windows NT、Linux或UNIX系统。使得任何的材料研究人员可以轻易获得与世界一流研究机构相一致的材料模拟能力。 Materials Studio 由分子模拟软件界的领先者--美国ACCELRYS公司在2000年初推出的新一代的模拟软件Materials Studio,将高质量的材料模拟带入了个人电脑（PC）的时代。 Materials Studio是ACCELRYS 公司专门为材料科学领域研究者所涉及的一款可运行在PC上的模拟软件。他可以帮助你解决当今化学、材料工业中的一系列重要问题。支持Windows98、NT、Unix以及Linux等多种操作平台的Materials Studio使化学及材料科学的研究者们能更方便的建立三维分子模型，深入的分析有机、无机晶体、无定形材料以及聚合物。 任何一个研究者，无论他是否是计算机方面的专家，都能充分享用该软件所使用的高新技术，他所生成的高质量的图片能使你的讲演和报告更引人入胜。同时他还能处理各种不同来源的图形、文本以及数据表格。 多种先进算法的综合运用使Material Studio成为一个强有力的模拟工具。无论是性质预测、聚合物建模还是X射线衍射模拟，我们都可以通过一些简单易学的操作来得到切实可靠的数据。灵活方便的Client-Server结构还是的计算机可以在网络中任何一台装有NT、Linux或Unix操作系统的计算机上进行，从而最大限度的运用了网络资源。 ACCELRYS的软件使任何的研究者都能达到和世界一流工业研究部门相一致的材料模拟的能力。模拟的内容囊括了催化剂、聚合物、固体化学、结晶学、晶粉衍射以及材料特性等材料科学研究领域的主要课题。 Materials Studio采用了大家非常熟悉Microsoft标准用户界面，它允许你通过各种控制面板直接对计算参数和计算结构进行设置和分析。 模块简介： 基本环境 MS.Materials Visualizer 分子力学与分子动力学 MS.DISCOVER https://www.doczj.com/doc/545720842.html,PASS 计算器的使用教案 教学目标 1．知识目标：指导学生学会应用计算器进行实数的加、减、乘、除、乘方运算及混合运算。 2．能力目标：用计算器完成较为繁杂的计算，鼓励学生用计算器进行探索规律的活动。 3．情感态度：使学生了解计算工具的发展历史，进一步认识到数学来源于生活服务于生活的道理，通过类比认识到现代信息技术是学习数学和解决问题的强有力的工具。 教材分析 1．地位与作用：计算器和计算机的逐步普及，对数学教育产生了深刻的影响。因此《标准》强调，“把现代信息技术作为学生学习数学和解决问题的强有力工具，致力于改变学生的学习方式，使学生乐意并有更多的精力投入到现实的、探索性的数学活动中去”。一方面计算器可以使学生从繁琐的纸笔计算中解放出来，也为解决实际问题提供了有力的工具。另一方面，计算器和计算机对学生的数学学习方式也有很大的影响。计算器可以帮助学生探索数学规律，理解数学概念和法则。 学生刚学了有理数的运算法则，可以将纸笔计算与计算器计算的结果相对照，对于数值（绝对值）较为复杂的运算鼓励学生使用计算器，因此学好本节内容对于学生的发展起着举足轻重的作用，在探索现实问题和需要进行复杂的运算时，应当鼓励学生使用计算器，慢慢养成像使用纸笔那样使用计算器的习惯。 2．重点与难点：重点是计算器的使用及技巧，难点是运用计算器进行较为繁琐的运算和探索规律，关键是熟练准确的运用计算器进行计算。 教学准备 教具：算盘、计算器、（简单计算器、科学技术器、图形计算器）、多媒体展示台、计算机。 广泛的计算工材料： 1、扩展资料: ①计算器的历史：说起计算器，值得我们骄傲的是，最早的计算工具诞生在中国。中国古代最早采用的一种计算工具叫筹策，又被叫做算筹。这种算筹多用竹子制成，也有用木头，兽骨充当材料的。约二百七十枚一束，放在布袋里可随身携带。直到今天仍在使用的珠算盘，是中国古代计算工具领域中的另一项发明，明代时的珠算盘已经与现代的珠算盘几乎相同。17世纪初，西方国家的计算工具有了较大的发展，英国数学家纳皮尔发明的"纳皮尔算筹"，英国牧师奥却德发明了圆柱型对数计算尺，这种计算尺不仅能做加减乘除、乘方、开方运算，甚至可以计算三角函数，指数函数和对数函数，这些计算工具不仅带动了计算器的发展，也为现代计算器发展奠定了良好的基础，成为现代社会应用具。 ②电子计算器的特殊键 在使用电子计算器进行四则运算的时候，一般要用到数字键，四则运算键和清除数据键。除了这些按键，还有一些特殊键，可以使计算更加简便迅速。 2．图形计算器的发展：图形计算器技术动态 背景资料：1995年，美国德克萨斯州仪器公司(TI)将图形计算器(Graphing 2.12用计算器进行运算 1．用计算器求下列各式的值： （1）（－345）+421=________；（2）（12.236）÷（－2.3）=_______； （3）23×1=________；（4）－1553=________；（5）（3.2－4.5）×32－=_______． 2．用计算器求出棱长为56cm的正方体体积为_______． 3．用计算器计算：在比例尺是1：300 000的地图上，甲、乙两地相距2.6厘米，?则它们之间的实际距离是______千米． 4．利用计算器探索规律．任选1，2，3，…，9中的一个数字，将这个数乘7，再将结果乘15 873，你发现了什么规律？能试着解释一下理由吗？ 5．用计算器补充完整下表： 从表中你发现3的n次方幂的个位数有何规律？3的个位数是什么数字？为什么？ 6．计算下列各式（可以使用计算器）： 6×7= 66×67= 666×667= 6 666×6 667= 66 666×66 667= 观察上述结果，你发现了什么规律？能尝试说明理由吗？ 7．用计算器计算下列各式，将结果填写在横线上． 99 999×11=____________；99 999×12=____________； 99 999×13=____________；99 999×14=____________． （1）你发现了什么？ （2）不用计算器，你能直接写出99 999×19的结果吗？ 8．用计算器计算并观察． 1.22=？ 0.122=？ 0.0122=？ 122=？ 1202=？ 你发现了什么规律？ 参考答案 1．（1）76 （2）－5.32 （3）27.6 （4）－3 723 875 （5）12.1 2．175 616cm3 分析：?因为正方体的棱长为56cm，?所以正方体的体积为563=175616cm3． 12 用计算器进行运算 测试时间:25分钟 一、选择题 1.在计算器的键盘中,表示开启电源的键是( ) A.OFF B.AC/ON C.MODE D.SHIFT 2.在计算器的键盘中,表示关闭电源的键是( ) A.OFF B.AC/ON C.MODE D.SHIFT 3.用计算器求35+12的按键顺序正确的是( ) ①输入数据35依次按数字键35;②输入数据12依次按数字键12;③按+键;④按ENTER. A.①②③④ B.①③②④ C.①④②③ D.①③④② 4.下列说法正确的是( ) A.用计算器进行混合运算时,应先按键进行乘方运算,再按键进行乘除运算,最后按键进行加减运算 B.输入0.58的按键顺序是0·58 C.输入-5.8的按键顺序是(-)+5·8 D.输入-3.7的按键顺序是3·7- 5.用计算器计算-42的按键顺序是( ) A.4x 2(-)= B.(-)x 24= C.(-)4=x 2 D.(-)4x 2= 6.用科学计算器计算,若按键顺序是8x y 3=,则结果为( ) A.512 B.511 C.513 D.500 二、填空题 7.如果进行加、减、乘、除和乘方的混合运算时,只要按算式的 顺序输入,计算器就会按要求算出结果. 8.小芳在用计算器计算“14.9×73”时,发现计算器的小数点键坏了,你还能用这个计算器把正确的结果算出来吗?请把你想到的方法用算式表示出来: . 三、解答题 9.用计算器求下列各式的值: (1)36×3-28÷2;(2)-25×0.36÷(-1.2); (3)-12÷6-(-2)5;(4)(7.3-8.9)×. 18 10.使用计算器计算各 式:6×7= ;66×67= ;666×667= ;6666×6667= . (1)根据以上结果,你发现了什么规律? (2)依照你发现的规律,不用计算器,你能直接写出666666×666667的结果吗?请你试一试. 2．15 用计算器进行计算 教学目标 1．会使用计算器进行有理数的加、减、乘、除、乘方运算. 2．通过运用计算器探求规律的活动，发展合情推理的能力. 3．能运用计算器进行实际问题的复杂运算． 重点 用计算器进行有理数的混合运算． 难点 能用计算器进行有理数的乘方的运算． 一、创设情境，导入新课 教师出示：已知一个圆柱的底面半径为2.32 cm，它的高为7.06 cm， 求这个圆柱的体积． 学生经过合作讨论，列出算式：π×2.322×7.06，然后在学生做题结 果的基础上，教师利用计算器进行计算，使学生初步感受利用计算器计算， 既准确又快速． 二、合作交流，探究新知 活动1：介绍计算器的使用方法 出示幻灯片显示计算器的面板示意图． 教师结合示意图介绍按键的使用方法． 学生根据教师的介绍，使用计算器进行实际操作. 通过训练，使学生 掌握计算器的按键操作，熟悉计算器的程序设计模式． 活动2：用计算器进行运算 师：用计算器进行加、减、乘、除四则运算及其混合运算，只要将算式按书写顺序输入计算器就会正确算出结果，但在输入负数时，应注意．另外在进行乘方运算时，也要注意按键顺序． 学生分组完成教材例2、例3、例4的计算，通过小组和课本中介绍的步骤进行错误纠正，然后完成各例题相对应的“做一做”，进一步熟练用计算器进行计算． 三、运用新知，深化理解 例1 用计算器计算：0.5＋(－2)×6÷(－4)－3. 分析：从左到右依次输入各数字及运算符号． 按键顺序为0·5＋（－）2×6÷（（－）4）－3＝，显示结果为0.5，所以0.5＋(－2)×6÷(－4)－3＝0.5. 注意：计算器输入顺序与算式的书写顺序相同．输入0.5时，也可以省去小数点前的0，按.5即可． 例2 若运用教材上使用的某种电子计算器进行计算，则按键5x2＋2xＫ3＝的结果为( ) A．16 B．33 C．37 D．36 分析：5x2表示52，2xＫ3中表示2xＫ表示2的乘方，3表示2的指数，所以按照5x2＋2xＫ3这个顺序按键，得到的算式为52＋23，结果为33. 注意：用计算器求一个数的正整数次幂，不同的计算器可能会有不同的按键方式． 2.12计算器的使用 1．用计算器求下列各式的值： （1）（－345）+421=________；（2）（12.236）÷（－2.3）=_______； =_______．（3）23×1=________；（4）－1553=________；（5）（3.2－4.5）×32－2 5 2．用计算器求出棱长为56cm的正方体体积为_______． 3．用计算器计算：在比例尺是1：300 000的地图上，甲、乙两地相距2.6厘米，?则它们之间的实际距离是______千米． 4．利用计算器探索规律．任选1，2，3，…，9中的一个数字，将这个数乘7，再将结果乘15 873，你发现了什么规律？能试着解释一下理由吗？ 5．用计算器补充完整下表： 从表中你发现3的n次方幂的个位数有何规律？3225的个位数是什么数字？为什么？ 6．计算下列各式（可以使用计算器）： 6×7= 66×67= 666×667= 6 666×6 667= 66 666×66 667= 观察上述结果，你发现了什么规律？能尝试说明理由吗？ 7．用计算器计算下列各式，将结果填写在横线上． 99 999×11=____________；99 999×12=____________； 99 999×13=____________；99 999×14=____________．（1）你发现了什么？ （2）不用计算器，你能直接写出99 999×19的结果吗？ 8．用计算器计算并观察． 1.22=？ 0.122=？ 0.0122=？ 122=？ 1202=？ 你发现了什么规律？ 参考答案 1．（1）76 （2）－5.32 （3）27.6 （4）－3 723 875 （5）12.1 2．175 616cm3分析：?因为正方体的棱长为56cm，?所以正方体的体积为563=175616cm3． 3．7.8 分析：因为图上距离：实际距离=比例尺， 所以实际距离=图上距离 比例尺= 2.6÷1 300000 =2.6 ×300 000=780 000（厘米） =7 800（米）=7.8（千米），注意单位换算． 4．解：取数字3，乘7，再将结果乘15 873得：（3×7）×15 873=21 ×15 873=333 333． 取数字5，乘7，再将结果乘15 873，得：（5×7）×15 873=35×15 ?873=?555555． 取数字8，乘7，再将结果乘15 873，得（8×7）×15 873=56×15 873=888 888．?通过观察发现，任选1，2，3，…，9中的一个数字n，将这个数乘7，再将结果乘15 873，均得到一个6位数，每位上的数字相同，都是n，即（n×7）×15 873=nnn nnn．?因为7 ×15873=111 111．所以（n×7）×15 873=n×（7×15 873）=n×111 111=nnn nnn． 点拨：通过探索规律可以发现，数学真奇妙，数学中存在一些具有特殊作用的数字，如本题7与15 873的积就具有神奇的“复印”功能，你能将任意 一个1，2，3，…，9中的数字连续“复印”6次，你还能发现其他具有 “特异功能”的数字吗？ 5．解： 1、诞生背景美国Accelrys公司的前身为四家世界领先的科学软件公司――美国Molecular Simulations Inc.(MSI)公司、Genetics Computer Group(GCG)公司、英国Synopsys Scient ific 系统公司以及Oxford Molecular Group(OMG)公司，由这四家软件公司于2001年6月1日合并组建的Accelrys公司，是目前全球范围内唯一能够提供分子模拟、材料设计以及化学信息学和生物信息学全面解决方案和相关服务的软件供应商。 Accelrys材料科学软件产品提供了全面完善的模拟环境，可以帮助研究者构建、显示和分析分子、固体及表面的结构模型，并研究、预测材料的相关性质。Accelrys的软件是高度模块化的集成产品，用户可以自由定制、购买自己的软件系统，以满足研究工作的不同需要。Accelrys软件用于材料科学研究的主要产品包括运行于UNIX工作站系统上的Cerius2软件，以及全新开发的基于PC平台的Materials Studio软件。Accelrys材料科学软件被广泛应用于石化、化工、制药、食品、石油、电子、汽车和航空航天等工业及教育研究部门，在上述领域中具有较大影响的世界各主要跨国公司及著名研究机构几乎都是Accelrys产品的用户。 2、软件概况 Materials Studio是专门为材料科学领域研究者开发的一款可运行在PC上的模拟软件。它可以帮助你解决当今化学、材料工业中的一系列重要问题。支持Windows 98、2000、NT、Unix以及Linux等多种操作平台的Materials Studio使化学及材料科学的研究者们能更方便地建立三维结构模型，并对各种晶体、无定型以及高分子材料的性质及相关过程进行深入的研究。 多种先进算法的综合应用使Materials Studio成为一个强有力的模拟工具。无论构型优化、性质预测和X射线衍射分析，以及复杂的动力学模拟和量子力学计算，我们都可以通过一些简单易学的操作来得到切实可靠的数据。 Materials Studio软件采用灵活的Client-Server结构。其核心模块Visualizer运行于客户端PC，支持的操作系统包括Windows 98、2000、NT；计算模块（如Discover，Amorphous，Equilibria，DMol3，CASTEP等）运行于服务器端，支持的系统包括Windows2000、NT、SGIIRIX以及Red Hat Linux。浮动许可（Floating License）机制允许用户将计算作业提交到网络上的任何一台服务器上，并将结果返回到客户端进行分析，从而最大限度地利用了网络资源。 任何一个研究者，无论是否是计算机方面的专家，都能充分享用Materials Studio软件所带来的先进技术。Materials Studio生成的结构、图表及视频片断等数据可以及时地与其它PC软件共享，方便与其他同事交流，并能使你的讲演和报告更加引人入胜。 Materials Studio软件能使任何研究者达到与世界一流研究部门相一致的材料模拟的能力。模拟的内容包括了催化剂、聚合物、固体及表面、晶体与衍射、化学反应等材料和化学研究领域的主要课题。 3、模块简介 Materials Studio采用了大家非常熟悉的Microsoft标准用户界面，允许用户通过各种控制面板直接对计算参数和计算结果进行设置和分析。目前，Materials Studio软件包括如下功能模块： Materials Visualizer: 提供了搭建分子、晶体及高分子材料结构模型所需要的所有工具，可以操作、观察及分析结构模型，处理图表、表格或文本等形式的数据，并提供软件的基本环境和分析工具以及支持Materials Studio的其他产品。是Materials Studio产品系列的核心模块。 2.12 用计算器进行运算 教学内容： 2.12用计算器进行数的简单运算。 教学目的和要求： 1．进一步熟练掌握有理数的运算。 2．培养学生的运用计算器的能力及正确、熟练地运用计算器解决问题。 教学重点和难点： 重点：培养学生的运用计算器的能力及正确、熟练地运用计算器解决问题。 难点：培养学生的运用计算器的能力及正确、熟练地运用计算器解决问题。 教学工具和方法： 工具：应用投影仪，投影片。 方法：分层次教学，讲授、练习相结合。 教学过程： 一、复习引入： 问题： 已知一个圆柱的底面半径长2.32cm，高为7.06cm，求这个圆柱的体积。 我们知道，圆柱的体积＝底面积×高。因此，计算这个圆柱的体积就要做一个较复杂的运算： π，这种计算，我们可以利用电子计算器(简称计算器)来完成。计算器是一.22? ? 32 06 .7 种常用的计算工具，利用计算器可以进行许多种复杂的运算。 二、讲授新课： 1．例题： 例1：①用计算器求345＋21.3。 用计算器进行四则运算，只要按算式的书写顺序按键，输入算式，再按等号键，显示器上就显示出计算结果。 解：用计算器求345＋21.3的过程为： 键入，显示器显示运算式子345+21.3 在第二行显示运算结果366.3，∴345＋21.3=366.3。 ②做一做按例1的方法，用计算器求105.3－243. 例2：①用计算器求31.2÷(－0.4)。 解：用计算器求31.2÷(－0.4) 78，∴31.2÷(－0.4)=78。 注意：(1)31.2÷(－0.4)不能按成3 1. 2 ÷－ 0.4 ＝，那样计算器会按31.2－0.4进行计算的。 (2)输入0.4时可以省去小数点前的0，按成 .4 。 ②做一做按例2的方法，用计算器求 8.2×(－4.3) ÷2.5。 例3：①用计算器求62.2－4×(－7.8)。 这是减法和乘法的混合运算.对于加、减、乘、除法和乘方的混合运算.只要按算式的书写顺 序输入，计算器会按要求算出结果.因此，本题的按键顺序是： 。∴ 62.2－4×(－7.8)＝93.4。 ②做一做按例3的方法，用计算器求 (－59)×2÷4.2÷(－7)。 例4：①用计算器求2.73。 用计算器求一个数的正整数次幂，一般要用乘幂运算键 y x。 解：用计算器求 2.73的按键顺序是 ∴ 2.73＝19.683。 注意：一般地，求一个正数的n次方都可以按上面的步骤进行.求一个负数的n次方，可以先 求这个负数的相反数的n次方，如果n是奇数，那么再在所得结果的前面加上负号。 ②做一做： (1)按例4的方法求53.6 (2)用计算器求出本节开头的圆柱的体积(结果精确到mm， 取3.14)。 三、课堂小结： 《计算材料学》实验讲义 实验一：Materials Studio软件简介及基本操作 一、前言 1.计算材料学概述 随着科学技术的不断发展，科学研究的体系越来越复杂，理论研究往往不能给出复杂体系解析表达，或者即使能够给出解析表达也常常不能求解，传统的解析推导方法已不敷应用，也就失去了对实验研究的指导意义。反之，失去了理论指导的实验研究，也只能在原有的工作基础上，根据科研人员的经验理解、分析与判断，在各种工艺条件下反复摸索，反复实验，最终造成理论研究和实验研究相互脱节。近年来，随着计算机科学的发展和计算机运算能力的不断提高，为复杂体系的研究提供了新的手段。 在材料学领域，随着对材料性能的要求不断的提高，材料学研究对象的空间尺度在不断变小，纳米结构、原子像已成为材料研究的内容，对功能材料甚至要研究到电子层次，仅仅依靠实验室的实验来进行材料研究已难以满足现代新材料研究和发展的要求。然而计算机模拟技术可以根据有关的基本理论，在计算机虚拟环境下从纳观、微观、介观、宏观尺度对材料进行多层次研究，进而实现材料服役性能的改善和材料设计。因此，计算材料学应运而生，并得到迅速发展，目前已成为与实验室实验具有同样重要地位的研究手段。 计算材料学是材料科学与计算机科学的交叉学科，是一门正在快速发展的新兴学科，是关于材料组成、结构、性能、服役性能的计算机模拟与设计的学科，是材料科学研究里的“计算机实验”。计算材料学主要包括两个方面的内容：一方面是计算模拟，即从实验数据出发，通过建立数学模型及数值计算，模拟实际过程；另一方面是材料的计算机设计，即直接通过理论模型和计算，预测或设计材料结构与性能。计算材料科学是材料研究领域理论研究与实验研究的桥梁，不仅为理论研究提供了新途径，而且使实验研究进入了一个新的阶段。 计算材料学的发展是与计算机科学与技术的迅猛发展密切相关的。从前，即便使用大型计算机也极为困难的一些材料计算，如材料的量子力学计算等，现在使用微机就能够完成，可以预见，将来计算材料学必将有更加迅速的发展。另外，随着计算材料学的不断进步与成熟，材料的计算机模拟与设计已不仅仅是材料物理以及材料计算理论学家的热门研究课题，更将成为一般材料研究人员的一个重要研究工具。由于模型与算法的成熟，通用软件的出现,北师大版7年级数学上册2.12.用计算器进行计算教学设计
小学四年级数学“用计算器计算”教案
15-第二章12用计算器进行运算
Material studio软件介绍
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? 可兼顾科研和教学需求 ? 可在大规模机群上进行并行计算 ? 客户端-服务器 计算方式 – Windows Linux Windows, – 最大限度的使用已有IT资源 – – – – – – – – DFT及半经验量子力学 线形标度量子力学 分子力学 QM/MM方法 介观模拟 统计方法 分析仪器模拟 …… ? 全面的应用领域 - 固体物理与表面化学 - 催化、分离与化学反应 - 半导体功能材料 - 金属与合金材料 - 特种陶瓷材料 - 高分子与软材料 - 纳米材料 - 材料表征与仪器分析 - 晶体与结晶 - 构效关系研究与配方设计 - ……
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