金属学-北科大-2003年考研真题

北京科技⼤学材科基考研（名词解释汇总及课后重要习题）北京科技⼤学攻读硕⼠学位《⾦属学》复习⼤纲（适⽤专业：材料加⼯⼯程、材料学、材料科学与⼯程、材料物理与化学）⼀、⾦属与合⾦的晶体结构1. 原⼦间的键合1)⾦属键, 2)离⼦键, 3)共价键2．晶体学基础1）空间点阵， 2）晶系及布喇菲点阵， 3）晶向指数与晶⾯指数3．⾦属的晶体结构1）典型的⾦属晶体结构，2）原⼦的堆垛⽅式，3）晶体结构中的间隙，4）晶体缺陷4．合⾦相结构1）置换固溶体，2）间隙固溶体，3）影响固溶体溶解度的主要因素4）中间相5．晶体缺陷1）点缺陷, 2)晶体缺陷的基本类型和特征, 3)⾯缺陷⼆、⾦属与合⾦的凝固1．⾦属凝固的热⼒学条件2．形核1）均匀形核，2）⾮均匀形核3．晶体⽣长1）液-固界⾯的微观结构，2）⾦属与合⾦凝固时的⽣长形态，3）成分过冷4．凝固宏观组织与缺陷三、⾦属与合⾦中的扩散1．扩散机制2．扩散第⼀定律3．扩散第⼆定律4．影响扩散的主要因素四、⼆元相图1．合⾦的相平衡条件2．相律3．相图的热⼒学基础4．⼆元相图的类型与分析五、⾦属与合⾦的塑性变形1．单晶体的塑性变形1）滑移，2）临界分切应⼒,3）孪⽣，4）纽折2．多晶体的塑性变形1）多晶体塑性变形的特点，2）晶界的影响，3.塑性变形对组织与性能的影响1）屈服现象,2)应⼒-应变曲线及加⼯硬化现象,3)形变织构等六、回复和再结晶1．回复和再结晶的基本概念2．冷变形⾦属在加热过程中的组织与性能变化3．再结晶动⼒学4．影响再结晶的主要因素5．晶粒正常长⼤和⼆次再结晶七、铁碳相图与铁碳合⾦1．铁碳相图2．铁碳合⾦3．铁碳合⾦在缓慢冷却时组织转变⼋、固态相变1．固态相变的基本特点2．固态相变的分类3．扩散型相变1）合⾦脱溶，2）共析转变，3）调幅分解4．⾮扩散型相变参考书：1.⾦属学（修订版）, 宋维锡主编, 冶⾦⼯业出版社，1998；2.材料科学基础, 余永宁主编, ⾼等教育出出版社，2006；3.材料科学基础（第⼆版）, 胡赓祥等主编, ⾼等教育出出版社，2006；4.任何⾼等学校材料科学与⼯程专业《⾦属学》或《材料科学基础》教学参考书。

北京科技大学2010年硕士学位研究生入学考试试题试题编号： ________________________ 试题名称：___________ （共2页）适用专业：材料科学与工程______________________________________________________________说明：所有答案必须写在答题纸上，做在试题或草稿纸上无效.一、分析发生下列现象的原因（30分）1. 低碳钢应力-应变曲线的屈服现象（10分）2. 金属及合金凝固时形成树枝状晶（10分）3. 上坡扩散（5分）4. 二次再结晶（5分）二、在面心立方结构的金属中（111）面上运动着柏氏矢量为6=a/2［110］的位错，位错线方向也是［110］,请在单胞中画出（ill）晶面和山0］晶向，并说明该位错属于什么类型？如果该位错的运动受到阻碍后，请判断是否有可能转移到（ill）, （ill）, （ill）各晶面上继续运动？说明为什么？（15分）三、以含Al-4wt%Cu合金为例，给出其经过不同固溶时效工艺处理后的脱溶贯序；定性说明各阶段脱溶相的尺寸及分布特点、与母相的界面匹配关系及其强化效果等.（20分）四、讨论晶体结构和空间点阵之间的关系。

（15分）五、与液态结晶过程相比，固态相变有什么特点？这些特点对固态相变后形成的组织有什么影响？（15分）六、叙述离子晶体的结构规则（15分）七、分析形成下列不同铸态组织的可能原因，并说明要得到细小的等轴晶，可采取哪些办法？（20分）八、参考下面提供的示意图，画出按组织分区的Fe-Fe’C相图，写出各三相反应,并说明分别为1. Owt%C和3. Owt%C的铁碳合金经过缓慢冷却在相关三相反应完成后形成的各组织特点（20分）。

2010答案:一、1.低碳钢在一定条件下形变时，应力-应变曲线的大致规律是首先发生线性弹性变形，达到屈服时发生塑性变形直至断裂。

特殊的地方在于应力-应变曲线上常常出现上下屈服点，这与C间隙原子对位错的钉扎作用有关。

2003年全国硕士研究生入学统一考试数学一试题一、填空题:本题共6小题,每小题4分,共24分,请将答案写在答题纸指定位置上.(1)21ln(1)0lim(cos )x x x +→=(2) 曲面22y x z +=与平面042=-+z y x 平行的切平面的方程是.(3) 设)(cos 02ππ≤≤-=∑∞=x nx ax n n,则2a = .(4) 从2R 的基⎪⎪⎭⎫ ⎝⎛-=⎪⎪⎭⎫ ⎝⎛=11,0121αα到基⎪⎪⎭⎫⎝⎛=⎪⎪⎭⎫ ⎝⎛=21,1121ββ的过渡矩阵为.(5) 设二维随机变量(,)X Y 的概率密度为，y x x y x f 其他,10,0,6),(≤≤≤⎩⎨⎧=则=≤+}1{Y X P.(6) 已知一批零件的长度X (单位:cm cm)服从正态分布)1,(μN ,从中随机地抽取16个 零件,得到长度的平均值为40 (cm ),则μ的置信度为0.95的置信区间是.(注:标准正态分布函数值.)95.0)645.1(,975.0)96.1(=Φ=Φ二、选择题:本题共6小题,每小题4分,共24分,下列每小题给出的四个选项中,只有一项符合题目要求,把所选项前的字母填在题后的括号内.(1) 设函数()f x 在),(+∞-∞内连续,其导函数的图形如图所示, 则()f x 有( )(A)一个极小值点和两个极大值点. (B)两个极小值点和一个极大值点. (C)两个极小值点和两个极大值点. (D)三个极小值点和一个极大值点.(2) 设}{},{},{n n n c b a 均为非负数列,且0lim =∞→n n a ,1lim =∞→n n b ,∞=∞→n n c lim ,则必有( )(A) n n b a <对任意n 成立. (B) n n c b <对任意n 成立. (C) 极限n n n c a ∞→lim 不存在. (D) 极限n n n c b ∞→lim 不存在.(3) 已知函数(,)f x y 在点(0,0)的某个邻域内连续,且1)(),(lim2220,0=+-→→y x xyy x f y x ,则( ) (A) 点(0,0)不是(,)f x y 的极值点. (B) 点(0,0)是(,)f x y 的极大值点. (C) 点(0,0)是(,)f x y 的极小值点.(D) 根据所给条件无法判断点(0,0)是否为(,)f x y 的极值点.(4) 设向量组I:r ααα,,,21 可由向量组II:s βββ,,,21 线性表示,则( )(A) 当s r <时,向量组II 必线性相关. (B) 当s r >时,向量组II 必线性相关. (C) 当s r <时,向量组I 必线性相关. (D) 当s r >时,向量组I 必线性相关.(5) 设有齐次线性方程组0Ax =和0Bx =, 其中,A B 均为n m ⨯矩阵,现有4个命题:① 若0Ax =的解均是0Bx =的解,则秩(A )≥秩(B )； ② 若秩(A )≥秩(B ),则0Ax =的解均是0Bx =的解； ③ 若0Ax =与0Bx =同解,则秩(A )=秩(B )； ④ 若秩(A )=秩(B ), 则0Ax =与0Bx =同解. 以上命题中正确的是( )(A) ① ②. (B) ① ③.(C) ② ④. (D) ③ ④.(6) 设随机变量21),1)((~X Y n n t X =>,则( ) (A) )(~2n Y χ. (B) )1(~2-n Y χ.(C) )1,(~n F Y . (D) ),1(~n F Y .三 、(本题满分10分)过坐标原点作曲线ln y x =的切线,该切线与曲线ln y x =及x 轴围成平面图形D . (1) 求D 的面积A ;(2) 求D 绕直线x e =旋转一周所得旋转体的体积V .四 、(本题满分12分)将函数x x x f 2121arctan )(+-=展开成x 的幂级数,并求级数∑∞=+-012)1(n nn 的和.已知平面区域}0,0),{(ππ≤≤≤≤=y x y x D ,L 为D 的正向边界. 试证: (1) dx ye dy xe dx ye dy xex Ly x L ysin sin sin sin -=-⎰⎰--;(2).22sin sin π≥--⎰dx ye dy xe x Ly六 、(本题满分10分)某建筑工程打地基时,需用汽锤将桩打进土层. 汽锤每次击打,都将克服土层对桩的阻力而作功. 设土层对桩的阻力的大小与桩被打进地下的深度成正比(比例系数为,0k k >).汽锤第一次击打将桩打进地下a m . 根据设计方案,要求汽锤每次击打桩时所作的功与前一次击打时所作的功之比为常数(01)r r <<. 问(1) 汽锤击打桩3次后,可将桩打进地下多深？(2) 若击打次数不限,汽锤至多能将桩打进地下多深？ (注:m 表示长度单位米.)七 、(本题满分12分)设函数()y y x =)在),(+∞-∞内具有二阶导数,且)(,0y x x y =≠'是()y y x =的反函数.(1) 试将()x x y =所满足的微分方程0))(sin (322=++dy dx x y dyx d 变换为()y y x =满足的微分方程；(2) 求变换后的微分方程满足初始条件23)0(,0)0(='=y y 的解.八 、(本题满分12分)设函数()f x 连续且恒大于零,⎰⎰⎰⎰⎰+++=Ω)(22)(222)()()(t D t d y xf dvz y x f t F σ,⎰⎰⎰-+=tt D dxx f d y x f t G 12)(22)()()(σ,其中}),,{()(2222t z y x z y x t ≤++=Ω,}.),{()(222t y x y x t D ≤+=(1) 讨论()F t 在区间),0(+∞内的单调性. (2) 证明当0t >时,).(2)(t G t F π>设矩阵⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=322232223A ,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=100101010P ,P A P B *1-=,求2B E +的特征值与特征向量,其中*A 为A 的伴随矩阵,E 为3阶单位矩阵.十 、(本题满分8分)已知平面上三条不同直线的方程分别为1:230l ax by c ++=,2:230l bx cy a ++=,3:230l cx ay b ++=.试证: 这三条直线交于一点的充分必要条件为.0=++c b a十一 、(本题满分10分)已知甲、乙两箱中装有同种产品,其中甲箱中装有3件合格品和3件次品,乙箱中仅装有3件合格品. 从甲箱中任取3件产品放入乙箱后,求:(1) 乙箱中次品件数X 的数学期望； (2) 从乙箱中任取一件产品是次品的概率.十二 、(本题满分8分)设总体X 的概率密度为⎩⎨⎧≤>=--,,,0,2)()(2θθθx x e x f x其中0>θ是未知参数. 从总体X 中抽取简单随机样本n X X X ,,,21 ,记).,,,min(ˆ21nX X X =θ (1) 求总体X 的分布函数()F x ; (2) 求统计量θˆ的分布函数)(ˆx F θ；(3) 如果用θˆ作为θ的估计量,讨论它是否具有无偏性.2003年全国硕士研究生入学统一考试数学一试题解析一、填空题 (1)【详解】方法1:求()lim ()v x u x 型极限,一般先化为指数形式()()ln ()lim ()lim v x v x u x u x e =然后求lim ()ln ()v x u x ,再回到指数上去．)1ln(12)(cos lim x x x +→=220ln cos ln cos limln(1)ln(1)lim x xxx x x e e→++→=,而2200ln cos ln(1cos 1)limlim ln(1)ln(1)x x x x x x →→+-=++20cos 1lim x x x →-=(等价无穷小替换ln(1)x x +) 220112lim 2x x x →-==-(等价无穷小替换211cos 2x x -) 故 原式=.121ee=-方法2:令21ln(1)(cos )x y x +=,有2ln cos ln ln(1)xy x =+,以下同方法1．(2)【答案】542=-+z y x【详解】由题意,只要满足所求切平面的法向量与已知平面的法向量平行即可．平面042=-+z y x 的法向量:1{2,4,1}n =-；曲面22y x z +=在点),,(000z y x 的法向量:20000{(,),(,),1}x y n z x y z x y =-00{2,2,1}x y =- 由于12//n n ,因此有00221241x y -==- 可解得,2,100==y x ,相应地有.520200=+=y x z所求切平面过点(1,2,5),法向量为:2{2,4,1}n =-,故所求的切平面方程为0)5()2(4)1(2=---+-z y x ,即 542=-+z y x(3)【答案】1【详解】将)()(2ππ≤≤-=x x x f 展开为余弦级数2()cos ()n n f x x a nx x ππ∞===-≤≤∑,其中⎰=ππcos )(2nxdx x f a n ．所以 x d x xdx x a 2sin 12cos 2222⎰⎰=⋅=ππππ21[sin2sin22]x xx xdx πππ=-⋅⎰1cos2xd x ππ=⎰001[cos2cos2]x x xdx πππ=-⎰1=(4)【答案】⎪⎪⎭⎫ ⎝⎛--2132【详解】n 维向量空间中,从基n ααα,,,21 到基n βββ,,,21 的过渡矩阵P 满足[n βββ,,,21 ]=[n ααα,,,21 ]P ,因此过渡矩阵P 为:P =[121],,,-n ααα [],,,21n βββ ．根据定义,从2R 的基⎪⎪⎭⎫ ⎝⎛-=⎪⎪⎭⎫ ⎝⎛=11,0121αα到基⎪⎪⎭⎫⎝⎛=⎪⎪⎭⎫ ⎝⎛=21,1121ββ的过渡矩阵为P =[121],-αα[⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡-=-21111011],121ββ=.213221111011⎥⎦⎤⎢⎣⎡--=⎥⎦⎤⎢⎣⎡⎥⎦⎤⎢⎣⎡-(5)【答案】14． 【分析】本题为已知二维随机变量(,)X Y 的概率密度(,)f x y ,求满足一定条件的概率}),({0z Y X g P ≤．连续型二维随机变量(,)X Y 概率的求解方法(,)(,),y xF x y f u v dudv -∞-∞=⎰⎰此题可转化为二重积分}),({0z Y X g P ≤0(,)(,)g x y z f x y dxdy ≤=⎰⎰进行计算．【详解】图中阴影区域为积分区域. 由题设,有=≤+}1{Y X P 1(,)x y f x y dxdy +≤⎰⎰11206xxdx xdy -=⎰⎰1220(612)x x dx =-⎰14=(6)【答案】)49.40,51.39(． 【分析】可以用两种方法求解:(1) 已知方差12=σ,对正态总体的数学期望μ进行估计. 因为(,1)X N μ,设有n 个样本,样本均值11ni i X X n ==∑,则1(,)XN n μ,将其标准化,由公式~(0,1)X N 得:)1,0(~1N nX μ- 由正态分布分为点的定义αμα-=<-1}1{2u nX P 可确定临界值2αu ,进而确定相应的置信区间22(x u x u αα-+．(2)本题是在单个正态总体方差已知条件下,求期望值μ的置信区间问题．由教材上已经求出的置信区间22(x u x u αα-+,其中2{}1,(0,1)P U u UN αα<=-,可以直接得出答案．【详解】方法1:由题设,95.01=-α,可见.05.0=α 查标准正态分布表知分位点.96.12=αu 本题16n =, 40=x .根据 1.96}0.95P <=,有 1.96}0.95P <=,即{39.5140.49}0.95P μ<<=,故μ的置信度为0．95的置信区间是)49.40,51.39(．方法2:由题设,95.01=-α,22222{}{}2()10.95,()0.975P U u P u U u u u ααααα<=-<<=Φ-=Φ=查得.96.12=αu 将1σ=,16n =, 40=x代入22(x u x u αα-+得置信区间)49.40,51.39(二、选择题(1)【答案】()Cy【分析】函数的极值点可能是驻点(一阶导数为零) 或导数不存在的点,极值点是极大值点还是极小值 点可进一步由取极值的第一或第二充分条件判定． 【详解】根据导函数的图形可知,一阶导数为零的 点有3个(导函数与x 轴交点的个数)；0x =是导数 不存在的点．对3个一阶导数为零的点左右两侧导数符号均 不一致,故必为极值点,其中第一个交点左右两侧导数符号由正变为负,是极大值点；第二个交点和第三个交点左右两侧导数符号由负变为正,是极小值点,则三个驻点中有两个极小值点,一个极大值点；对导数不存在的点:0x =．左侧一阶导数为正,右侧一阶导数为负,可见0x =为极大值点．故()f x 共有两个极小值点和两个极大值点,应选(C)．(2)【答案】()D 【详解】方法1:推理法由题设lim 1n n b →∞=,假设lim n n n b c →∞存在并记为A ,则lim limn nn n n nb c c A b →∞→∞==,这与lim n n c →∞=∞矛盾,故假设不成立,lim n n n b c →∞不存在． 所以选项()D 正确．方法2:排除法取1n a n =,1n n b n-=,满足0lim =∞→n n a ,1lim =∞→n n b , 而11111,0,a b a b ==>,()A 不正确；取1n n b n-=,2n c n =-,满足1lim =∞→n n b ,∞=∞→n n c lim ,而1101b c =>-=,()B 不正确；取1n a n=,2n c n =-,满足0lim =∞→n n a ,∞=∞→n n c lim ,而lim 1n n n a c →∞=,()C 不正确．(3)【答案】()A 【详解】由2220,0(,)lim1()x y f x y xyx y →→-=+222(,)(1)()f x y xy x y α⇒-=++,其中00lim 0x y α→→=． 由(,)f x y 在点(0,0)连续知,(0,0)0f =．取y x =,x 充分小,0x ≠,有222(,)(1)(2)0f x y x x α=++>； 取y x =-,x 充分小,0x ≠,有222(,)(1)(2)0f x y x x α=-++<故点(0,0)不是(,)f x y 的极值点,应选()A ． (极值的定义)(4)【分析】 本题为一般教材上均有的比较两组向量个数的定理:若向量组I:r ααα,,,21 可由向量组II:s βββ,,,21 线性表示,则当s r >时,向量组I 必线性相关． 或其逆否命题:若向量组I:r ααα,,,21 可由向量组II:s βββ,,,21 线性表示,且向量组I 线性无关,则必有s r ≤． 可见正确选项为(D)． 本题也可通过举反例用排除法找到答案．【详解】 用排除法:⎪⎪⎭⎫⎝⎛=⎪⎪⎭⎫ ⎝⎛=⎪⎪⎭⎫ ⎝⎛=10,01,00211ββα,则21100ββα⋅+⋅=,但21,ββ线性无关,排除(A)；⎪⎪⎭⎫ ⎝⎛=⎪⎪⎭⎫ ⎝⎛=⎪⎪⎭⎫ ⎝⎛=01,01,00121βαα,则21,αα可由1β线性表示,但1β线性无关,排除(B)；⎪⎪⎭⎫⎝⎛=⎪⎪⎭⎫ ⎝⎛=⎪⎪⎭⎫ ⎝⎛=10,01,01211ββα,1α可由21,ββ线性表示,但1α线性无关,排除(C)．(5)【答案】(B)【分析】本题可找反例用排除法进行分析,但①、②两个命题的反例比较复杂一些,关键是抓住③、④,迅速排除不正确的选项．【详解】若0AX =与0BX =同解,则它们的解空间中的基础解系所含向量个数相同,即n -秩(A )=n -秩(B ), 得秩(A )=秩(B ),命题③成立,可排除(A), (C)；但反过来,若秩(A )=秩(B ),则不能推出0AX =与0BX =同解,通过举一反例证明,若⎥⎦⎤⎢⎣⎡=0001A ,⎥⎦⎤⎢⎣⎡=1000B ,则秩(A )=秩(B )=1,但0AX =与0BX =不同解,可见命题④不成立,排除(D). 故正确选项为(B)．(6)【答案】(C)．【分析】求解这类问题关键在于了解产生2χ变量、t 变量、F 变量的典型模式．(1)2χ分布:设12,,,n X X X 相互独立且均服从标准正态分布,则随机变量21ni i Z X ==∑服从自由度为n 的2χ分布．记做2().Zn χ(2)t 分布:设1(0,1)X N ,22~()X n χ,且12,X X 相互独立,则随机变量Z =从自由度为n 的t 分布．记做()Zt n(3)F 分布:设2212(),(),Xn Y n χχ且,X Y 相互独立,则随机变量12X n Z Y n =服从F 分布,其第一、二自由度分别为12,.n n 记做12(,).ZF n n【详解】其实,由F 分布的性质以及t 分布和F 分布的关系得,(1) 如果统计量 ()T t n ,则有2(1,)T F n ；(2) 如果统计量12(,)FF n n ,则有211(,)F n n F．由以上两条性质可以直接得出本题的答案为(C)．先由t分布的定义知()X t n =,其中)(~),1,0(~2n V N U χ,于是 21XY ==122U n V U n V =,分母中只含有一个标准正态分布的平方,所以)1(~22χU . 由F 分布的定义知~(,1).Y F n故应选(C)．三【分析】圆锥体体积公式:213V r h π=⋅；旋转体的体积:(1) 连续曲线()y f x =,直线x a =、x b =所围成的图形绕直线0x x =旋转一周而成的立体的体积[]210()ba V f x x dx π=-⎰(2) 连续曲线()x g x =,直线y c =、y d =所围成的图形绕直线0y y =旋转一周而成的立体的体积[]220()dc V g y y dy π=-⎰【详解】为了求D 的面积,首先要求出切点的坐标,设切点的横坐标为0x ,则曲线ln y x =在点)ln ,(00x x 处的切线方程是:).(1ln 000x x x x y -+= 切线的斜率为01x y x '=,由于该切线过原点,将(0,0)点代入切线方程,得01ln 0=-x ,从而.0e x = 所以该切线的方程为.1x ey =(1) 利用平面图形D 的面积公式()()S y y dy βαϕψ=-⎰,得⎰-=-=1.121)(e dy ey e A y (2) 旋转体体积可用一大立体(圆锥)体积减去一小立体体积进行计算,为了帮助理解,可画一草图．切线x ey 1=与x 轴及直线x e =所围成的三角形绕直线x e =旋转所得的圆锥体积为: 122101().3V e ey dy e ππ=-=⎰曲线ln y x =与x 轴及直线x e =所围成的图形绕直线x e =旋转所得的旋转体体积为:dy e e V y 212)(⎰-=π1220(2)y y e e e e dy π=-⋅+⎰12201(2)2yy e y e e e π=-⋅+211(2)22e e π=-+-因此所求旋转体的体积为).3125(6)(312102221+-=--=-=⎰e e dy e e e V V V y πππ四【分析】幂级数展开有直接法与间接法,一般考查间接法展开,即通过适当的恒等变形、求导或积分等,转化为可利用已知幂级数展开的情形．另外,由于函数展开成的幂级数,经两边求导或积分(其中一边是逐项求导或逐项积分)后,其新的展开式收敛区间不变,但在收敛区间端点处,求导(积分)后的展开式成立与否,要另行单独处理,设已有00()()n n n f x a x x ∞==-∑收敛区间为00(,)x R x R -+． 如果在0x x R =+处级数收敛,并且()f x (左)连续,则展开式成立的范围可扩大到0x x R =+处,在0x x R =-处亦有类似的结论,不过此时()f x (左)连续应改称(右)连续．【详解】本题可先求导,()f x '()2222(12)2(12)1212121212111212x x x x x x x x x '-+---⎛⎫ ⎪++⎝⎭==--⎛⎫⎛⎫++ ⎪ ⎪++⎝⎭⎝⎭基本求导公式 22422(14)14x x --==++21214x=-+ 对于函数2114x+,可以利用我们所熟悉的函数x -11的幂级数展开: 2011(11)1nnn x x x x x x ∞==+++++=-<<-∑所以 2222001(4)(1)414114n n n nn n x x x x ∞∞===-=--<-<+∑∑ (把x 换成24x -) 有 22111()22(1)4,(,).1422n n n n f x x x x ∞='=-=--∈-+∑对上式两边求积分,得200()(0)()2(1)4xxn n n n f x f f t dt t dt ∞=⎛⎫'-==-- ⎪⎝⎭∑⎰⎰221000(1)4112(1)42,(,)2122n n x nnnn n n t dt x x n ∞∞+==-=--=-∈-+∑∑⎰,又因为04f π=（）,所以()(0)()xf x f f t dt '=+⎰=).21,21(,124)1(24120-∈+--+∞=∑x x n n n nn π即 21012(1)411arctan 2,(,).1242122n n n n x x x x n π∞+=--=-∈-++∑ (*)在21=x 处,右边级数成为0(1)1212n n n ∞=-⋅+∑,收敛(利用莱布尼茨定理),左边函数()f x 连续,所以成立范围可扩大到21=x 处．而在12x =-处,右边级数虽然收敛,但左边函数()f x 不连续,所以成立范围只能是11(,]22x ∈-．为了求∑∞=+-012)1(n nn ,令21=x 代入(*)得∑∑∞=+∞=+--=⋅+--=012012)1(4]21124)1([24)21(n nn n n n n f ππ,再由0)21(=f ,得.4)21(412)1(0ππ=-=+-∑∞=f n n n五【详解】(1) 方法1:用格林公式证明. 由曲线为正向封闭曲线,自然想到用格林公式L D Q P Pdx Qdy dxdy x y ⎛⎫∂∂+=- ⎪∂∂⎝⎭⎰⎰⎰． 所以 ⎰⎰⎰--+=-D x y x L ydxdy e e dx ye dy xe)(sin sin sin sin所以⎰⎰⎰+=---Dx y x Ly dxdy e e dx ye dy xe )(sin sin sin sin 因为积分区域D 关于y x =对称,所以sin sin sin sin ()()x y yxyx DDeedxdyee dxdy --+=+⎰⎰⎰⎰与互换故dx ye dy xe dx ye dy xe x Ly x Ly sin sin sin sin -=-⎰⎰-- 方法2:化为定积分证明左边sin sin y x LLxe dy ye dx -=-⎰⎰=dx edy exy⎰⎰--0sin 0sin ππππ=⎰-+ππ0sin sin )(dx e e x x右边sin sin y x LLxe dy ye dx -=-⎰⎰=⎰⎰--ππππ00sin sin dx e dy e x y =⎰-+ππ0sin sin )(dx e e x x所以dx ye dy xe dx ye dy xe x Ly x Ly sin sin sin sin -=-⎰⎰--． (2) 方法1:用格林公式证明⎰⎰⎰--+=-Dx y x Ly dxdy e e dx ye dy xe )(sin sin sin sin =dxdy e dxdy eDDx y⎰⎰⎰⎰-+sin sin =dxdy e dxdy e DDx x ⎰⎰⎰⎰-+sin sin 利用轮换对称性=sin sin ()2x x DDe e dxdy dxdy -+≥⎰⎰⎰⎰22π=(因为0,0a b a b +≥>>)方法2:由(1)知,sin sin sin sin 0()2y x x x Lxe dy ye dx e e dx dx ππππ---=+≥⎰⎰⎰22π=六【详解】(1) 建立坐标系,地面作为坐标原点,向下为x 轴正向,设第n 次击打后,桩被打进地下n x ,第n 次击打时,汽锤所作的功为),3,2,1( =n W n ．由题设,当桩被打进地下的深度为x 时,土层对桩的阻力的大小为kx ,汽锤所作的功等于克服阻力所做的功．121102x k W kxdx x ==⎰,2122221()2x x k W kxdx x x ==-⎰,3222332()2x x k W kxdx x x ==-⎰,1x a =从而 212332k W W W x ++=又 12rW W =,2321W rW r W ==, 从而222231231(1)(1)22k k x W W W r r W r r a =++=++=++于是 3x =(2) 第n 次击打后,桩被打进地下n x ,第n 次击打时,汽锤所作的功为),3,2,1( =n W n ． 则汽锤前n 次所功的和等于克服桩被打进地下n x m 所做的功．11210(1)nx n n kxdx W W W r r W -=+++=+++⎰而 2102a kW kxdx a ==⎰ 牛-莱公式所以212(1)22n n k k x r r a -=+++从而 n x == 等比数列求和公式由于01r <<,所以1lim n n x +→∞．七【详解】 (1) 将题中的dy dx 与22d xdy变换成以x 为自变量y 为因变量的导数dx dy 与22d y dx 来表示(即通常所说的反函数变量变换),有dy dx =y dxdy '=11,)(22dy dx dy d dy x d ==dy dx y dx d ⋅')1(=32)(1y y y y y '''-='⋅'''-． 代入原方程,得 .sin x y y =-'' ( * )(2) 方程( * )所对应的齐次方程为0=-''y y ,特征方程为210r -=,根1,21r =±,因此通解为.21xxe C e C Y -+= 由于i λω+不是特征方程得根,所以设方程( * )的特解为x B x A y sin cos *+=则 *sin cos y A x B x '=-+,*cos sin y A x B x ''=--代入方程( * ),得:cos sin cos sin 2cos 2sin sin A x B x A x B x A x B x x ----=--= 解得21,0-==B A ,故x y sin 21*-=. 从而x y y sin =-''的通解为 .sin 2121*x e C e C y Y y x x -+=+=-由23)0(,0)0(='=y y ,得1,121-==C C ．故变换后的微分方程满足初始条件23)0(,0)0(='=y y 的解为.sin 21x e e y x x --=-且()y x 的导函数1()cos 02x x y x e e x -'=+->,满足题设0y '≠条件．八【详解】(1) 首先对()F t 进行化简,三重积分转化为在球面坐标系中的计算；二重积分转化为在极坐标系中的计算．222222220()()()sin 2sin ()t tt f x y z dv d d f r r dr d f r r dr πππθϕϕπϕϕΩ++==⎰⎰⎰⎰⎰⎰⎰⎰()2222002()cos 4()t tf r r dr f r r dr ππϕπ=⋅-=⎰⎰ (球面坐标)222220()()()2()t tD t f x y d d f r rdr f r rdr πσθπ+==⎰⎰⎰⎰⎰ (极坐标)所以222220000222()sin 4()()()2()ttttd d f r r drf r r drF t d f r rdrf r rdrπππθϕϕπθπ==⎰⎰⎰⎰⎰⎰⎰22022()()ttf r r drf r rdr=⎰⎰为了讨论()F t 在区间),0(+∞内的单调性,对()F t 求导:222222022()()()()()2[()]t ttt f t f r rdr f r r dr f t tF t f r rdr ⋅-⋅'=⎰⎰⎰22022()()()2[()]tttf t f r r t r drf r rdr ⋅-=⎰⎰由于()0,0,0f t r t r >>->,所以2()()0f r r t r ->. 再利用定积分的性质:若在区间[,]a b 上()0f x >,则()0baf x dx >⎰. 所以()0F t '>,所以()F t 在区间),0(+∞内严格单调增加．(2) 将待证的不等式作适当的恒等变形后,构造辅助函数,再用单调性进行证明即可． 因为 2220()2()2()tt ttf x dx f x dx f r dr -==⎰⎰⎰,所以2222()0022200()2()()()()2()()ttD t ttttf x y d f r rdr f r rdrG t f x dxf r drf r drσππ-+===⎰⎰⎰⎰⎰⎰⎰要证明0t >时)(2)(t G t F π>,只需证明0t >时,0)(2)(>-t G t F π,即22200222()2()2()()()()t tttf r r drf r rdrF tG t f r rdrf r drπ-=-⎰⎰⎰⎰()()()()()222222202()()()()()tt tttf r r dr f r dr f r rdr f r rdr f r dr⎡⎤⋅-⎢⎥⎣⎦=⋅⎰⎰⎰⎰⎰令 ()()()22222()()()()tt tg t f r r dr f r dr f r rdr =⋅-⎰⎰⎰222222220222()()()()()2()()()()()0t t ttg t f t t f r dr f t f r r dr f t t f r rdrf t f r t r dr t '=+-=->>⎰⎰⎰⎰故()g t 在),0(+∞内单调增加,又因为(0)0g =,所以当0t >时,有()0)0g t g>=（, 从而0t >时,).(2)(t G t F π>九【分析】 法1:可先求出*1,A P -,进而确定P A P B *1-=及2B E +,再按通常方法确定其特征值和特征向量；法2:先求出A 的特征值与特征向量,再相应地确定*A 的特征值与特征向量,最终根据2B E +与*2A E +相似求出其特征值与特征向量． 【详解】方法1:经计算可得⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡------=522252225*A ,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=-1000011101P ,所以 P A P B *1-==⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡----322452007,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡----=+5224720092E B ． 令 2900(2)274(9)(3)0225E B E λλλλλλ--+=-=--=-,故2B E +的特征值为.3,9321===λλλ当921==λλ时,解0)9(=-x A E ,得线性无关的特征向量为,0111⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=η ,1022⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=η所以属于特征值921==λλ的所有特征向量为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-+⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=+102011212211k k k k ηη,其中21,k k 是不全为零的任意常数．当33=λ时,解0)3(=-x A E ,得线性无关的特征向量为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=1103η,所以属于特征值33=λ的所有特征向量为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=110333k k η,其中03≠k 为任意常数． 方法2:设A 的特征值为λ,对应的特征向量为η,即ληη=A ．由于07≠=A ,所以.0≠λ所以 ***()()A A A E A A A E A A A E ηηηη=⇒=⇒=***()AA A A A A ληηληηηηλ⇒=⇒=⇒=,于是 11*11()()()AB P P A P P P ηηηλ----==,.)2()2(11ηλη--+=+P AP E B因此,2+λA为2B E +的特征值,对应的特征向量为.1η-P由于)7()1(3222322232--=---------=-λλλλλλA E ,故A 的特征值为1231,7λλλ===当121==λλ时,对应的线性无关特征向量可取为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=0111η, .1012⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=η当73=λ时,对应的一个特征向量为.1113⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=η 由⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=-1000011101P,得⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=-01111ηP ,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡--=-11121ηP ,⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=-11031ηP ．因此,2B E +的三个特征值分别为9,9,3．对应于特征值9的全部特征向量为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡--+⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡-=+--11101121212111k k P k P k ηη,其中21,k k 是不全为零的任意常数；对应于特征值3的全部特征向量为⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=-1103313k P k η,其中3k 是不为零的任意常数．十【分析】三条直线相交于一点,相当于对应线性方程组有唯一解,进而转化为系数矩阵与增广矩阵的秩均为2．【详解】方法1:“必要性”. 设三条直线321,,l l l 交于一点,则线性方程组⎪⎩⎪⎨⎧-=+-=+-=+,32,32,32b ay cx a cy bx c by ax (*) 有唯一解,故系数矩阵⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=a c c b b a A 222与增广矩阵⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡---=b a c a c b c b a A 323232的秩均为2,于是.0=A232()3()23232323a b c a b c b c a c a b A bca b c a c a bc ab -++++-++=-=---123111()236()23a b c b ca abc b ca c abc a b-=++-=-++-1006()6()c b a ba b c b c b a b a b c a c b cc a c b c--=-++--=-++----6()[()()()()]a b c c b b c a b a c =-++-----2226()()a b c bc c b bc a ac ab bc =-++--+-++- 2226()()a b c a b c ac ab bc =++++--- 2223()[()()()]a b c a b b c c a =++-+-+-,由于三条直线互不相同,所以0)()()(222≠-+-+-a c c b b a ,故.0=++c b a“充分性”. 由0=++c b a ,则从必要性的证明可知,0=A ,故秩.3)(<A由于])([2)(22222b b a a b ac cb b a ++-=-==0]43)21[(222≠++-b b a ,故秩()2A =．于是,秩(A )=秩)(A =2．因此方程组(*)有唯一解,即三直线321,,l l l 交于一点．方法2:“必要性”设三直线交于一点),(00y x ,则⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡100y x 为0BX =的非零解,其中2323.23a b c B b c a c a b ⎡⎤⎢⎥=⎢⎥⎢⎥⎣⎦ 所以||0B =．而232323232323a b c a b cB bc a bca A c a bca b-==--=-- 2223()[()()()]a b c a b b c c a =-++-+-+-,(解法同方法1)但根据题设 0)()()(222≠-+-+-a c c b b a ,故.0=++c b a“充分性”:考虑线性方程组⎪⎩⎪⎨⎧-=+-=+-=+,32,32,32b ay cx a cy bx c by ax (*)将方程组(*)的三个方程相加,并由.0=++c b a 可知,方程组(*)等价于方程组⎩⎨⎧-=+-=+.32,32a cy bx c by ax (* *) 因为])([2)(22222b b a a b ac cb ba ++-=-==222[()]0ab a b -+++≠,故方程组(* *)有唯一解,所以方程组(*)有唯一解,即三直线321,,l l l 交于一点．十一【详解】乙箱中可能的次品件数为0,1,2,3,分别求出其概率,再按定义求数学期望即可；而求从乙箱中任取一件产品是次品的概率,涉及到两次试验,是典型的用全概率公式的情形,第一次试验的各种可能结果(取到的次品数)就是要找的完备事件组．(1) 方法1:X 的可能取值为0,1,2,3, 取出k 件次品()0,1,2,3k =的取法有333k kC C -种；样本空间即从两个箱子中取出3件产品的总的取法数为36C ．所以有,X 的概率分布为36333}{C C C k X P kk -==, k 0,1,2,3.= 即 X 0 1 2 3 P201 209 209 201 因此,由离散型数学期望的定义{}1()nk k k E X x P X x ==⋅=∑易得 19913()0123.202020202E X =⨯+⨯+⨯+⨯= 方法2:本题对数学期望的计算也可用分解法:设0, ,1,i i X i ⎧=⎨⎩从甲箱中取出的第件产品是合格品从甲箱中取出的第件产品是次品. 则i X 的概率分布为i X 0 1P21 21.3,2,1=i 因为321X X X X ++=,所以由数学期望的线性可加性,有200321 ()()()()1233.2E X E X E X E X =++= (2) 设A 表示事件“从乙箱中任取一件产品是次品”,由于}0{=X ,}1{=X ,}2{=X ,}3{=X 构成完备事件组,因此根据全概率公式,有∑====30}{}{)(k k X A P k X P A P =33001{}{}66k k k P X k k P X k ===⋅=⋅=∑∑ ()1131.6624E X ==⋅=十二【分析】本题表面上是一数理统计问题,实际上考查了求分布函数、随机变量的函数求分布和概率密度以及数学期望的计算等多个知识点．将数理统计的概念与随机变量求分布与数字特征结合起来是一种典型的命题形式．求分布函数()F X 是基本题型:求统计量θˆ的分布函数)(ˆx F θ,可作为多维相互独立且同分布的随机变量函数求分布函数,直接用定义即可；是否具有无偏性,只需检验θθ=ˆE 是否成立．【详解】(1) 由连续型随机变量分布函数的定义,有.,,0,1)()()(2θθθ≤>⎩⎨⎧-==⎰∞---x x e dt t f x F xx (2) 由题给).,,,min(ˆ21nX X X =θ,有 }),,,{min(}ˆ{)(21ˆx X X X P x P x F n≤=≤= θθ 121{min(,,,)}n P X X X x =->121{,,,}n P X x X x X x =->>> 1[1()]n F x =--2(),1,.0,n x x e x θθθ-->⎧-=⎨≤⎩(3) 由连续型随机变量概率密度是分布函数在相应区间上的微分得θˆ概率密度为.,,0,2)()()(2ˆˆθθθθθ≤>⎩⎨⎧==--x x ne dxx dF x f x n 因为 2()ˆˆ()()2n x E xf x dx nxe dx θθθθ+∞+∞---∞==⎰⎰12nθθ=+≠, 所以θˆ作为θ的估计量不具有无偏性．。

2001北京科技大学攻读硕士研究生入学考试试题考试科目：金属学A适用专业：科学技术史，冶金物理化学，钢铁冶金，有色金属，材料加工工程。

说明：1.试题必须写在答题纸上。

2.统考生做1--10题；单考生做1--7题和11--13题。

1.名词解释：（每小题2分，共10分）（1）单胞和复合单胞（2）金属键（3）代位固溶体（4）位错（5）偏聚和有序化2.判断对错：（10分）3.以液态无限互溶、固态有限溶解并具有共晶反应的二元相图为例说明二元相图是制作方法和二元相图的一般几何规律。

（10分）4.结晶后的组织中产生显微偏析的原因是什么？采用什么措施能减少和消除偏析。

（10分）5.什么是晶界？讨论晶界在多晶体形变过程中的作用。

（10分）6.什么是相界面？复合合金形变的特点是什么？（10分）7.说明使多晶体晶粒细化能使材料的强度提高、韧性增加的原因。

（10分）8.简要叙述马氏体转变的一般特点。

（10分）9.要想获得粗大的再结晶晶粒可采取什么措施，说明原因。

（10分）10.简述固态相变在相变阻力、新相形核、新相成长方面的特点。

（10分）11.什么叫再结晶？什么是再结晶温度？简要描述再结晶过程。

（10分）2002北京科技大学攻读硕士研究生入学考试试题考试科目：金属学A适用专业：科学技术史，冶金物理化学，钢铁冶金，有色金属，材料加工工程。

说明：1.试题必须写在答题纸上。

2.统考生做1--9题；单考生做1--6题和10--12题。

一.名词解释（20分，每个2.5分）（1）点阵畸变（2）柏氏矢量（3）相图（4）过冷度（5）形变织构（6）二次再结晶（7）滑移系（8）孪生二.画出立方晶系中（111）面、（435）面。

写出立方晶系空间点阵特征。

（10分）三.铸锭的一般组织可分为哪几个区域？写出其名称。

并简述影响铸锭结晶组织的因素。

（10分）四.画图并简述形变过程中位错增殖的机制。

（10分）五.写出菲克第一定律的数学表达式，并说明其意义。

2003年东北大学博士研究生入学考试试题Part ⅡVocabulary & Structure (20%)Directions:There are 40 incomplete sentences in this part. For each of the sentence, there are four choices. Choose the one that best completes the sentence and cover the corresponding letter on the Answer Sheet with●．21．The design of the gymnasium shows a great deal of______ We have never seen a building of such a type before．A．solidarity B．originality C．invention D．fascination22．The psychiatrist say that a person with inferiority feelings can be very______．A．disgraceful B．disrespectful C．disapproval D．disagreeable23．The Secretary of State______to being astonished at this unexpected statement．A．complied B．confirmed C．confessed D．conformed24．When the doctor proposed to him long walks in the fresh air, Mr. Park admitted______ for a long walk for years．A．not having been B．not being C．being not D．having not been25．Agriculture was a step in human progress______subsequently there was nothing comparable until our own machine age．A．to which B．with which______ C．from which D．in which26．The change in the treatment of his characters is a significant______to Shakespeare's growth as a dramatist．A．label B．signal C．mark D．index27．Chaucer has been called the Father Poetry by______generations．A．aggressive B．progressive C．successive D．comprehensive28．After______on a merry-go-round, she started to feel dizzy and had to lie down．A．to have ridden B．redden C．riding D．to ride29．Experience leads me to think that it is not always good to get______ with strangers．A．tolerant B．confidential C．enthusiastic D．agreeable30．Each plant and animal be natural tendency,______far more seeds and eggs and seedlings and young, than is necessary to maintain______population．A．is to produce..．their B．produces..．itsC．produces..．their D．produce..．their31．Someone who gives an expensive gift often feels that he should receive more praise than if he______ a less expensive gift．A．gave B．gives C．had given D．has given32．The doctor said that it would take a month for her fractured wrist toA．recover B．heal C．remedy D．cure33．Although she did not look back she could tell that he was still following. Let______a streetcar, she thought, and really there was one．A．there were B．there beC．there being D．there has been34．During the famine of 1943, millions of Chinese peasants______to the cities because they could not survive in the rural areas．A．migrated B．emigrated C．immigrated D．mobilized35．The waltz and the tango seem to be out of fashion today. Things like the twist and jerk seem to be _____young people are really interested in．A．all that about B．about that all C．about all that D．all about that 36．In his culture,______ it was, this exchange of manes on pieces of paper was probably a formal polit eness, like saying “thank you”．A．all that B．whatever C．whichever D．what37．The survival______of some wild animals is not very high as they are ruthlessly hunted for their skins．A．standard B．scale______ C．ratio D．rate38．The leaders of the two countries feel it desirable to______ funds from armaments to health and education．A．derive B．change C．convert D．divert39．The Home Secretary has been asked to______because the union leaders and their employers cannot agree on a course of action．A．intervene B．negotiate C．meditate D．reconcile40．The neighbors do not considered him quite______as most evenings he awakens them with his drunken singing．A．respected B．respectable C．respective D．respectful41．The sun is very large in comparison with its nine______planets which, in turn, are circled by a total of thirty-three satellite．A．surrounding B．cycling C．orbiting D．whirling42．When I emerged from the telephone box, I come face to face with a little man, who was looking as______ as a stray dog．A．humble B．pathetic C．dreadful D．merciful43．I found seated at the table opposite to mine another guest. He was a decently unsociable man, anxious to______alone．A．leave B．be leaving C．be left D．have left44．The house they have bought is in very bad repair. The old boiler in the kitchen needs A．to see B．to be seen C．seeing D．seeing to45．As to the lost world of Egypt, we know nearly everything______to know．A．there is B．it is C．which is D．what is46．Mark Evens, who had failed the physics test, was sitting on a bench in the corner______over his disappointment．A．complaining B．meditating C．brooding D．apologizing47．Some researchers have undertaken some psychological studies which prove that many children develop fears of______dangers．A．imagination B．imaginary C．imaginable D．imaginative48．The mother separated the quarreling children, and gave each of them a sharp______．A．punch B．pinch C．puppy D．pumpkin49．Soccer is the most truly international team sport, but there is still some question______whether it should be called a game or open warfare．A．as to B．due to C．in addition to D．owing to50．______but I still like him．A．Selfish though he is B．Selfish as he isC．Whether he is selfish or not D．Selfish he may be51．It was so incredible to her that I should have made the highest score in the class______she was trying to test me again, personally.A．that B．therefore C．when D．because52．I think it was all fixed up by lawyers or______arranges adoptions．A．someone B．anyone C．whoever D．those53．With a weather worn face, Ted is______a very old man but in fact he is only fifty．A．obviously B．evidently C．apparently D．sufficiently54．They don't want to be involved in the dispute, so they exhibit______on such matters．A．integrity B．reserve C．morality D．justice55．I'd just do as soon as you______the research yourself．A．do B．will do C．would do D．did56．I don't know______it was that answered the phone this morningA．who B．why C．how D．that57．If any law and order______not maintained, neither the citizen nor his property is safe．A．be B．are C．were D．is58．In New York City______has highly restrictive guidelines for______police may use their guns, the number of people shot by local cops soared in the past three years from 68 to 108．A．there, where B．there, when C．it, where D．which, when59．Thousands of children nowadays prefer doing their homework to a background of popmusic______it in a quite room．A．rather than doing B．to doingC．rather than to do D．to do60．Five score years ago, a great American, ______symbolic shadow we stand, signed the Emancipation Proclamation．A．with his B．in whose C．by him D．of whomPart ⅢReading Comprehension (35 %)Directions:There are seven passages in this part. Each is followed by five questions or unfinished statements. Choose the one out of the choices marked by A, B, C, and D．and mark your answer on the Answer Sheet with●．Passage 1Researchers disagree whether the “use it or lose it” philosophy holds for cognitive aging, but there is one evidence that keeping mentally active can slow age—related declines．At Pennsylvania State University, Sherry Willis and her husband, K. Warner Schaie, have studied 5,000 people, some since 1956．People lucky enough to avoid chronic diseases may also fare better in intellectual function, they find, perhaps because chronic diseases can restrict lifestyle and reduce mental stimulation. Similarly, those lucky enough to be relatively affluent also fare better, perhaps because money can buy intellectually stimulating things like travel．Education helps, too, researchers say because in instills the conviction that you can always learn something new. The Schaie-Willis team also has some other observations. Being in a stable marriage with a stimulating spouse, they say, helps maintain intellectual vigor．Flexibility counts too. People who stay mentally vibrant are often those who do not insist that “they must do things today as they did before” Schaie says. In neuropsychological terms, the ability to see problems in new ways often yields higher scores on tests of mental function. Andpeople satisfied with life also stay more mentally fit, he says．If you find your mental skills sagging, consider working on specific deficits. When Willis gave 5-hour tutorials on inductive reasoning or spatial skills to about 200 people whose skills had declined in the previous 14 years, 40 percent regained lost abilities. That advantage held up seven years late when they were retested.Other ways to stay sharp, Schaie says, are doing jigsaw puzzles to hone visual-spatial skills, working crossword puzzles for verbal skills, playing bridge for memory and simply matching wits at home with players on TV game shows．Finally, remember this. Even though you may lose some mental skills with normal aging, you also gain in one key area: wisdom. The growth of wisdom continues throughout the 40s, 50s and even 60s．Questions 61 to 65 are based on the passage．61．In the passage, the author mainly discuss______．A．the role mental stimulation in preventing mental agingB．gradual loss of mental skills with normal agingC．the relationship between mental function and spatial skillsD．effective ways to keep intellectual vigor62．The word “it” in the saying “use it or lose it” (paragraph 1) refer to______．A．brain power B．cognitive developmentC．mental stimulating D．intellectual function63．According to the researchers, which of the following factors affects cognitive aging?A．Education. B．Chronic illness．C．Standard of living. D．All of the above．64．From this passage we may safely infer that______might help prevent mental declines．A．physical exercises B．social interconnectionsC．rigid daily routines D．a healthy diet65．According to the author, all of the following can truly be said about wisdom EXCEPT that ______．A．wisdom may be thought of as a special form of abilities and knowledge completely developed with life experienceB．wisdom may still grow even when the process of mental aging startedC．wisdom is superior in importance to mental skills such as inductive reasoning and spatial skillsD．wisdom makes up an important part of brain powerPassage 2Generation gaps are nothing new. Imperfect communication between age groups plagued the ancient Greeks and current works alike．Many an older worker chafes at an under-30 colleague who surfs the Internet, listens to his Sony Walkman and chats on the phone or with his desk mate-all while working on a project due in an hour．Sometimes, of course, he isn't corking, and that's a whole different issue. But sometimes he is getting lots of great stuff done. In the meantime, the different work styles create a case of “Would you please shut up” vs. “Lighten up. Get a life.”Marc Prensky, vice president of Bankers Trust and founder of its interactive learningsubsidiary, Corporate Gameware, was on point in Across the Board, a publication of the conference board. The business research organizatio n titled Prensky's article “Twitch Speed”, a reference to the fast pace of video game play．Today under-30 workers likely grew up in a multimedia, technology—rich, twitch speed environment. Prensky says they simultaneously did homework, watched TV and listened to music; this exposure changed the ways they receive and process information．Baby boomers and older workers may or may not have done homework by TV, but much else has changed. Sociologists say the over-30s are more likely to want room doors close, TV off. One thing happening at a time. Quiet, please!When the two heritages clash in the workplace, it pits comfort with speed and “multitasking” against comfort with deliberation and focused concentration．Sound familiar? If the gap has become a chasm in your workplace, it's time to talk．Both work styles can be productive, but both sides need to make accommodations so the other's productivity isn't impaired．Questions 66 to 70 are based on the passage．66．This passage is mainly talking about______．A．generation gapsB．work styles of different age groupsC．lack of mutual understanding between the old and the youngD．imperfect communication between old and young workers67．From the context we may figure out that the word “plagued” (p aragraph 1) means______．A．annoyed B．infected C．damaged D．affected68．According to the passage, which of the following is NOT true?A．Older workers often feel annoyed about their young colleagues' attitudes towards work．B．Younger workers always do a good job of their work though they prefer to listen to music or chat with others while working．C．The different work styles may sometimes lead to an unnecessary argument．D．Older workers are used to working in a comfortable and quiet environment so that they can fully concentrate on what they are doing．69．The author agrees with Marc Prensky on the point that younger workers prefer a “multitasking” style because______．A．they are smart and energeticB．they have the special ability to perform several tasks at the same timeC．brought up in a special cultural background, they have developed a behavioral pattern different form that of their older colleaguesD．they have been trained to receive and process information in a special way70．The author maintains that both sides should______if the two pattern work styles clash headlong．A．be patientB．realize that both work styles are productiveC．make efforts to avoid doing damage to the other's productivityD．make compromise to bridge the gulf between themPassage 3A child who has once been pleased with a tale likes, as a rule, to have it retold in identically the same words, but this should not lead parents to treat printed fairy stories as sacred texts. It is always much better to tell a story than read it out of a book, and if a parent can produce what, in the actual circumstances of the time and the individual child, is an improvement on the printed test, so much the better．A charge made against fairy tales is that they harm the child by frightening him or arousing his sadistic impulses. To prove the latter, one would have to show in a controlled experiment that children who have read fairy stories were more often guilty of cruelty than those who had not. Aggressive, destructive, sadistic impulses every child has and, on the whole, their symbolic verbal discharge seems to be rather a safety valve than an incitement to overt action. As to fears, there are I think, well-authenticated cases of children being dangerously terrified by some fairy story. Often, however, this arises from the child having heard the story once. familiarity with the story by repetition turns the pain of fear into other pleasure of the fear faced and mastered．There are also people who object fairy stories on the grounds that they are not objectively true, that faints. Witches, two-headed dragons, magic carpets, etc, do not exist; and that, instead of indulging his fantasies in fairy tales. The child should be taught how to adapt to reality by studying history and mechanics. I find such people, I must confess, so unsympathetic and peculiar that I do not know how to argue with them. If their case were sound, the word should be full of madmen attempting to fly from New York to Philadelphia on a broomstick or covering a telephone with kissed in the belief that it was their enchanted girlfriend．No fairy story ever claimed to be a description of the external work and a sane child had ever believed that it was．Questions 71 to 75 are based on the passage．71．The author considers that a fairy story is more effective when it is______．A．repeated without variationB．treated with reverenceC．adapted by the parentD．set in the present72．Some people dislike fairy stories they feel that they______．A．tempt people to be cruel to childrenB．show the primitive cruelty in childrenC．lend themselves to undesirable experiments with childrenD．increase a tendency by which children's impulses may be73．Fairy stories are a means by which children's impulses may beA．beneficially channeledB．given a destructive tendencyC．held back until maturityD．effectively suppressed74．The advantage claimed for repeating fairy stories to young children is that it______．A．makes them come to terms with their fearsB．develops their power of memoryC．convinces them there is nothing to be afraid ofD．encourages them not to have ridiculous beliefs75．The author's mention of broomsticks and telephones is meant to suggest that______．A．fairy stories are still being made upB．there is confusion about different kinds of truthC．people try to modernize old fairy storiesD．there is more concern for children's fears nowadaysPassage 4No other country spends what we do per capita for medical care. The care available is among the best technically, even if used too lavishly and thus dangerously, but none of the countries that stand above us unhealth status have such a high proportion of medically disenfranchised persons. Given the evidence that medical care is not that valuable and access to care not that bad, it seems most unlikely that our bad showing is caused by the significant proportion who are poorly served. Other hypotheses have greater explanatory power: excessive poverty, both actual and relative, and excessive affluence．Excessive poverty is probably more prevalent in the U. S. than in any of the countries that have a better infant mortality rate and female life expectancy at birth. This is probably true also for all but four or five of the countries with a longer male life expectancy. In the notably poor countries that exceed us in male survival, difficult living conditions are a more accepted way of life and in several of them, a good basic diet, basic medical care and basic education, and lifelong employment oportunities are an everyday fact of life. In the U. S. a motional unemployment level of 10 percent may be 40 percent in the ghetto while less than 4 percent elsewhere. The countries that have surpassed us in health do not have such severe or entrenched problems. Nor are such a high proportion of their people involve in them．Excessive affluence is not so obvious a cause of ill health, but, at least until recently, few other nations could afford such unhealthful ways of living. Excessive intake of animal protein and fats, dangerous intake of alcohol and use of tobacco and drugs (prescribed and proscribed), and dangerous recreational sports and driving habits are all possible only because of affluence. Our heritage, desires, opportunities, and our machism, combined with the relatively low cost of bad foods and speedy vehicles, make us particularly vulnerable to our affluence. And those who are not affluent try harder. Our unacceptable health status, then, will not be improved appreciably by expanded medical resources nor by their redistribution so much as by a general at tempt to improve the quality of life for all．Questions 76 to 80 are based on the passage．76．All of the following are mentioned in the passage as factors affecting the health of the population EXCEPT_______．A．the availability of medical care servicesB．the genetic endowment of individualsC．the nation's relative position in health statusD．an individual's own behavior77．The author is primarily concerned withA．condemning the U.S. for its failure to provide better medical care to the poorB．evaluating the relative significance of factors contributing to the poor health status in the U. S．C．comparing the general health of the U.S. population with world averagesD．advocating specific measures designed to improve the health of U. S. population78．The passage best supports which of the following conclusions about the relationshipbetween per capita expenditure of the health of a population?A．The per capita expenditure for medical care has relatively little effect on the total amount of medical care available to a population．B．The genetic makeup of a population is a more powerful determinant of the health of a population than the per capita expenditure for medical care．C．A population may have very high per capita expenditures for medical care and yet have a lower health status than other populations with lower per capita expenditures．D．The higher the per capita expenditure on medical care, the more advanced is the medical technology; and the more advanced the technology, the better is the health of the population．79．The author refers to the excessive intake of alcohol and tobacco and drug use in order to ______．A．show that some heath problems cannot be attacked by better medical careB．demonstrate that use of tobacco and intoxicants is detrimental to healthC．cite examples of individual behavior that have adverse consequences for health status D．illustrate ways in which affluence may contribute to poor health status80．The passage provides information to answer which of the following questions?A．Which is the most powerful influence on the health status of a population?B．Which nation in the world leads in health status?C．Is the life expectancy of males in the U. S. longer than of females?D．What are the most important genetic factors influencing the health of an individual?Passage 5In the 1960s, medical researchers Thomas Holmes and Richard Rahe developed a checklist of stressful events. They appreciated the tricky point that any major change can be stressful. Negative events like “serious illness of a family member” were high on the list but so were some positive life-changing events like marriage. When you take the Holmes-Rahe test you must remember that the score does not reflect how you deal with stress-it only shows how much you have chances of staying healthy. By the early 1970s, hundreds of similar studies had followed Holmes and Rahe. And millions of Americans who work and live under stress worried over the reports. Somehow the research got boiled down to a memorable message, women's magazines ran headlines like “Stress causes illness.” “If you want to stay physically and mentally healthy,” the articles said, “avoid stressful events.” But such simplistic advice is impossible to follow. Even if stressful events are dangerous, many-like the death of a loved one-are impossible to avoid. Moreover, any warning to avoid all stressful events is a prescription for staying away from opportunities as well as trouble. Since any change can be stressful, a person who wanted to be completely free of stress would never marry, have a child, take a new job or move. The notion that all stress makes you sick also ignores a lot of what we know about people. It assumes we're all vulnerable and passive in the face of adversity. But what about human initiative and creativity? Many come through periods of stress with more physical and mental vigor than they had before. We also know that a long time without change or challenge can lead to boredom and mental strain．Questions 81 to 85 are based on the passage．81．The result of Holmes-Rahe's medical research tell us______．A．the way you handle major events may cause stressB．what should be done to avoid stressC．what kind of event would cause stressD．how to cope with sudden changes in life82．The studies on stress in the early 1970's led to______．A．widespread concern over its harmful effectsB．great panic over the mental disorder it could causeC．intensive research into stress-related illnessesD．popular avoidance of stressful jobs83．The score of the Holmes-Rahe test shows______．A．how much pressure you are underB．how positive events can change you lifeC．how stressful a major event can beD．how you can deal with life-changing events84．Why is “such simplistic advice” (Line 10．Para. 1) impossible to follow?A．No one can stay on the same job for long．B．No prescription is effective in relieving stress．C．People have to get married someday．D．You could be missing opportunities as well．85．According to the passage people who have experienced ups and downs may become______．A．nervous when faced with difficultiesB．physically and mentally strainedC．more capable of coping with adversityD．indifferent toward what happens to themPassage 6“Most episodes of absent-mindedness-forgetting where you lift something or wondering why you just entered a room-are caused by a simple lack of attention,” says Schacter. “You are supposed to remember something but you haven't encoded deeply.” Encoding, Schacter explains, is a special way of paying attention to an event that has a major impact on recalling it later. Failure to encode properly can create annoying situations. If you put your mobile phone in a pocket, for example, and don't pay attention to what you did because you are involved in a conversation, you'll probably forget that the pho ne is in the jacket now hanging in your wardrobe. “Your memory itself isn't failing you,” says Schacter,“rather you didn't give your memory system the information it needed.”Lack of interest can also lead to absent-mindedness. “A man who can recite spo rts statistics from 30 years ago,” says Zelinski, “may not remember to drop a letter in the mailbox.” Women have slightly better memories than men possibly because they pay more attention to their environment and memory relies on just that. “Visual cues ca n help prevent absent-mindedness.” says Schacter. “But be sure the cue is clear and available,” he cautions. If you want to remember to take a medication with lunch, put the pill bottle on the kitchen table-don't leave it in the medicine chest and write yourself a note that you keep in a pocket. Another common episode of absent-mindedness like walking into a room and wondering why you're there is most likely because you were thinking about something else. “Everyone does this from time to time,” says Zelinski. The best thing to do is to return to where you were before entering the room and you will likely remember．Questions 86 to 90 are based on the passage．86．Why does the author think that encoding properly is very important?A．It helps us understand our memory system better．B．It enables us to recall something from our memory．C．It expands our memory capacity considerably．D．It slows down the process of losing our memory．87．One possible reason why women have better memories than men is that______．A．they have a wider range of interestsB．they are more reliant on the environmentC．they have an unusual power of focusing their attentionD．they are more interested in what's happening around them88．A note in the pocket can hardly serve as a reminder because______．A．it will easily get lostB．it's not clear enough for you to readC．it's out of your sightD．it might get mixed up with other things89．What do we learn from the last paragraph?A．If we focus our attention on one thing, we might forget another．B．Memory depends to a certain extent on the environment．C．Repetition helps improve our memory．D．If we keep forgetting things, we'd better return to where we were．90．What is the passage mainly about?A．The process of gradual memory loss．B．The causes of absent-mindedness．C．The impact of the environment on memory．D．A way of encoding and recalling．Passage 7It is hard to track the blue whale, the ocean's largest creature, which has almost been killed off by commercial whaling and is now listed as an endangered species. Attaching radio devices to it is difficult and visual sightings are too unreliable to give real insight into its behavior．So biologists were delighted early this year when with the help of the Navy they were able to track a particular blue whale for 43 days monitoring its sounds. This was possible because of the Navy's formerly top-secret system of underwater listening devices spanning the oceans. Tracking whales is but one example of a exciting new world just opening to civilian scientists after the cold war as the Navy starts to share and partly uncover its global network of underwater listening system built over the decades to track the ships of potential enemies．Earth scientists announced at a news conference recently that they had used the system for closely monitoring a deep-sea volcanic eruption for the first time and that they plan similar studies. Other scientists have proposed to use the network for tracking ocean currents and measuring changes in ocean and global temperatures. The speed of sound in water is roughly one mile a second-slower than through land but faster than through air. What is most important, different layers of ocean water can act as channels for sounds, focusing them in the same way a stethoscope (听诊器) does when it carries faint noises from a patient's chest to a doctor's ear. This focusing is the main reason that even relatively weak sounds in the ocean, especially low-frequency ones can often travel thousands of miles．。

一：大纲分析：北京科技大学2009年攻读硕士学位《金属学》复习大纲（适用专业：材料加工工程、材料学、材料科学与工程、材料物理与化学）一、金属与合金的晶体结构1.原子间的键合1)金属键, 2)离子键, 3)共价键2．晶体学基础1）空间点阵， 2）晶系及布喇菲点阵， 3）晶向指数与晶面指数3．金属的晶体结构1）典型的金属晶体结构，2）原子的堆垛方式，3）晶体结构中的间隙，4）晶体缺陷4．合金相结构1）置换固溶体，2）间隙固溶体，3）影响固溶体溶解度的主要因素4）中间相5．晶体缺陷1）点缺陷, 2)晶体缺陷的基本类型和特征, 3)面缺陷二、金属与合金的凝固1．金属凝固的热力学条件2．形核1）均匀形核，2）非均匀形核3．晶体生长1）液-固界面的微观结构，2）金属与合金凝固时的生长形态，3）成分过冷4．凝固宏观组织与缺陷三、金属与合金中的扩散1．扩散机制2．扩散第一定律3．扩散第二定律4．影响扩散的主要因素四、二元相图1．合金的相平衡条件2．相律3．相图的热力学基础4．二元相图的类型与分析五、金属与合金的塑性变形1．单晶体的塑性变形1）滑移，2）临界分切应力,3）孪生，4）纽折2．多晶体的塑性变形1）多晶体塑性变形的特点，2）晶界的影响，3.塑性变形对组织与性能的影响1）屈服现象,2)应力-应变曲线及加工硬化现象,3)形变织构等六、回复和再结晶1．回复和再结晶的基本概念2．冷变形金属在加热过程中的组织与性能变化3．再结晶动力学4．影响再结晶的主要因素5．晶粒正常长大和二次再结晶七、铁碳相图与铁碳合金1．铁碳相图2．铁碳合金3．铁碳合金在缓慢冷却时组织转变八、固态相变1．固态相变的基本特点2．固态相变的分类3．扩散型相变1）合金脱溶，2）共析转变，3）调幅分解4．非扩散型相变参考书：1.金属学（修订版）, 宋维锡主编, 冶金工业出版社，1998；2.材料科学基础, 余永宁主编, 高等教育出出版社，2006；3.材料科学基础（第二版）, 胡赓祥等主编, 高等教育出出版社，2006；4.任何高等学校材料科学与工程专业《金属学》或《材料科学基础》教学参考书。

2001北京科技大学攻读硕士研究生入学考试试题考试科目：金属学A适用专业：科学技术史，冶金物理化学，钢铁冶金，有色金属，材料加工工程。

说明：1.试题必须写在答题纸上。

2.统考生做1--10题；单考生做1--7题和11--13题。

1.名词解释：（每小题2分，共10分）（1）单胞和复合单胞（2）金属键（3）代位固溶体（4）位错（5）偏聚和有序化2.判断对错：（10分）3.以液态无限互溶、固态有限溶解并具有共晶反应的二元相图为例说明二元相图是制作方法和二元相图的一般几何规律。

（10分）4.结晶后的组织中产生显微偏析的原因是什么？采用什么措施能减少和消除偏析。

（10分）5.什么是晶界？讨论晶界在多晶体形变过程中的作用。

（10分）6.什么是相界面？复合合金形变的特点是什么？（10分）7.说明使多晶体晶粒细化能使材料的强度提高、韧性增加的原因。

（10分）8.简要叙述马氏体转变的一般特点。

（10分）9.要想获得粗大的再结晶晶粒可采取什么措施，说明原因。

（10分）10.简述固态相变在相变阻力、新相形核、新相成长方面的特点。

（10分）11.什么叫再结晶？什么是再结晶温度？简要描述再结晶过程。

（10分）2002北京科技大学攻读硕士研究生入学考试试题考试科目：金属学A适用专业：科学技术史，冶金物理化学，钢铁冶金，有色金属，材料加工工程。

说明：1.试题必须写在答题纸上。

2.统考生做1--9题；单考生做1--6题和10--12题。

一.名词解释（20分，每个2.5分）（1）点阵畸变（2）柏氏矢量（3）相图（4）过冷度（5）形变织构（6）二次再结晶（7）滑移系（8）孪生二.画出立方晶系中（111）面、（435）面。

写出立方晶系空间点阵特征。

（10分）三.铸锭的一般组织可分为哪几个区域？写出其名称。

并简述影响铸锭结晶组织的因素。

（10分）四.画图并简述形变过程中位错增殖的机制。

（10分）五.写出菲克第一定律的数学表达式，并说明其意义。