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固体物理基础答案解析吴代鸣.pdf

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1、1.试证理想六方密堆结构中c/a=.证明：如图所示，六方密堆结构的两个晶格常数为a 和c。右边为底面的俯视图。而三个正三角形构成的立体结构，其高度为2若晶胞基矢cba,互相垂直，试求晶面族（hkl）的面间距。解：cba,互相垂直，可令kccjbbiaa,晶胞体积abccbav)(倒格子基矢：kcjbiaabcbavbjbiakcabcacvbiakcj babccbvb2)(2)(22)(2)(22)(2)(2321而与（hkl）晶面族垂直的倒格矢222321)()()(2)(2clbkahGkcljbkiahblbkbhG故（hkl）晶面族的面间距222222)()()(1)()()(222

2、clbkahclbkahGd3若在体心立方晶胞的每个面中心处加一个同类原子，试说明这种晶体的原胞应如何选择每个原胞含有几个原子答：通过分析我们知道，原胞可选为简单立方，每个原胞中含有5 个原子。体心，八个顶点中取一个，对面面心各取一个原子（即三个）作为基元。布拉菲晶格是简单立方格子。4试求面心立方结构的（111）和（110）面的原子面密度。解：（111）面平均每个（111）面有2213613个原子。（111）面面积222232322)22()2(221aaaaaa所以原子面密度22)111(34232aa（110）面平均每个（110）面有2212414个原子。（110）面面积222aaa所以（

3、110）面原子面密度22)110(222aa5设二维矩形格子的基矢为j aaiaa2,21，试画出第一、二、三、布里渊区。解：倒格子基矢：jbjajajaxxaaaavbkxaiaxiaxaaaavb11323321212212222)(2)(2222)(2所以倒格子也是二维矩形格子。2b方向短一半。最近邻;,22bb次近邻;2,2,2211bbbb再次近邻;,12122121bbbbbbbb再再次近邻;3,322bb做所有这些点与原点间连线的垂直平分线，围成布里渊区。再按各布里渊区的判断原则进行判断，得：第一布里渊区是一个扁长方形；第二布里渊区是2 块梯形和2块三角形组成；第三布里渊区是2

4、对对角三角和4 个小三角以及2 个等腰梯形组成。6六方密堆结构的原胞基矢为：kcajaiaajai aa32123212321试求倒格子基矢并画出第一布里渊区。文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1

5、R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3

6、文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1

7、R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3

8、文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1

9、R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3

10、文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3解：原胞为简单六方结构。原胞体积：cajijicaijacjiakcjiajiaaaav2232123)3()3(41)3(21)3(21)3(21)3(21)(倒格子基矢：kcaavbjiajiak

11、ccaaavbjiakcjiacaaavb2)(2)3(2)3(21232)(2)3(32)3(21232)(221321322321由此看到，倒格子同原胞一样，只是长度不同，因此倒格子仍是简单六方结构。（注意：倒格子是简单六方，而不是六方密堆）选六边形面心处格点为原点，则最近邻为六个角顶点，各自倒格矢的垂直平分面构成一个六面柱体。次近邻为上下底面中心，其垂直平分面为上下平行平面。再次近邻是上下面六个顶角，其垂直平分面不截上面由最近邻和次近邻垂直平分面构成的六角柱体。所以第一布里渊区是一个六角柱体。比倒格子六方要小。7略8、证明一维NaCl 晶体的马德隆常数为2ln2证明：，则左右两侧对称分布

12、任选一参考离子i最近距离）为晶格常数（正负离子；这里令aaarjij.为其中，异号为；同号;.4131211121那么，有：jja文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T

13、5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R

14、7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T

15、5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R

16、7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T

17、5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R

18、7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3.432)1ln(利用展开式：432xxxxx.41312112ln，得：1令x2ln29、若离子间的排斥势用re来表示，只考虑最近邻离子间的排斥作用，试导出离子晶体结合能的表达式，并讨论参数和应如何决定。解：离子为原点）（以，则

19、设最近邻离子间距离为irarrjij，（最近邻以外）4），（最近邻，4)(0202/ijijijrijrerrreeruij最近邻/)(02142总相互作用能为：rNijjeareNU为最近邻离子数其中)1.(.；42/02ZeZreNUr)2.(.4；得：0由平衡条件：/200200rrreZrerU)3.(.142得：0002rreNU)(结合能0rUEc)4.(.91等离子晶体：对于0220rrrUNrKNaCl)5.(.142181/2300200reZrerK文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V

20、9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编

21、码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V

22、9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编

23、码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V

24、9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编

25、码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V

26、9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3)6.(.1442181得：)5(代入)2(将200230020rererK)7.(.722400202Krere)8.(.4得：)2(由/20020reZre10、如果 NaCl 结构晶体中离子的电荷增加一倍，假定排斥势不变，试估计晶体的结合能及离子间的平衡距离将产生多大变化。解：)1.(42总相互作用能02nrBreNU)2.(.0421020020nrrrnBreNrU)2.(.4得：11200nenBr)3.(.4得：)2(由1002nrneB)4.(118)(得：)1(代

27、入)3(0020nreNrU111004)()2(4)()2(可知：)4(和)2(时，由2变为当电荷由nnneUeUereree11、在一维单原子晶格中，若考虑每一院子于其余所有原子都有作用，在简谐近似下求格波的色散关系。jiijijjiijijuUuxU20041)(21解：在简谐近似下：)(41个原子的运动方程：第222jiijijnnnuuuUdtudmn文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8

28、Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 H

29、J1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8

30、Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 H

31、J1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8

32、Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 H

33、J1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8

34、Y3)(41右边)(2)(2njnjnjniininnuuu)()(41)(2)(2njnjnjniininnuuuuu)()(21)()(njnjnjniininuuuu)()(niniinuupnpnpnpuuu)2(pnaqpntiaqpntipnaqtinaqtinuAeAeAemAeu)2(代入上式得：设)()()(2)(pppaqm)cos1(2整理，得：212、设有一维双原子晶格，两种院子的质量相等，最近邻原子间的力常数交错地等于1和2，试求格波的色散关系。nnnnnnnnuuudtudm)()()(解：2121121122nnnnnnnnuuuudtdm)()()(211121

35、1222)()(;试探解：tnaqintnaqinBeAeuBAAeBmABBeAmiaqiaq)()(代入方程，得：2121221212文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH

36、4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z

37、4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH

38、4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z

39、4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH

40、4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z

41、4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y30)()()(2121221221meemiaqiaqmaqcos2经计算，得：21222121213、已知一维单原子晶格的格波色散关系为)cos1(2)(2qaMq试求：(1)格波的模密度g();(2)低温下晶格热容与温

42、度的比例关系。)(2)(解：一维时，模密度qdqlgaqdqMadMaqsin22;21cos由色散关系，得：22/142224MMMaddqmqMqMMaqqdqlg02/14222)(4)()()()(22)(2/142224MMMalmTkdgTTECB01)/exp()(晶格热容：）1项，（因为低温，略去4mBTkedMMalTC01文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4

43、B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3

44、 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4

45、B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3

46、 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4

47、B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3

48、 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y301deTMal

49、TkB)似为无穷大主要，所以上限可以近因为低温，频率低的占(0222)1(dxeexTkMalxxB3经计算，上面积分2TMalkCB3214、将 Debye 模型用于一维晶格，求低温下晶格热容与温度的关系，并和上题的结果进行比较，讨论 Debye模型的合理性。cq色散关系：解：对于德拜模型，有cdqd)(2)(qdqlg0)(1qdcl01)(TkBegdTC0222)1(dxeexTkclxxB3上面积分2TcklCB32温的情况下。有其合理性，尤其是低成正比，说明德拜模型与上题结果比较，都与T文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4

50、B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3 ZH4D9T5F8Y3文档编码:CO4B2Z4L6R7 HJ1R5V9H4T3

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