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  • 2022-10-26
    在近邻近似下，用紧束缚近似导出体心立方晶体S能带的[tex=2.357x1.571]hu6ZoXP/tQ3Updruu73M6bthxQlY8XEF/V907jS9ovU=[/tex]），试画出沿Kx方向（[tex=5.643x1.286]lnFJvh1qWQ+fq4KQLv3Ahw==[/tex]）的散射关系曲线，并计算能带宽度。→a a、a
    • 解：选体心原子为参考点，最近邻原子的2位置[p=align:center][tex=12.143x2.143]e/oaP50ZzRZdjBmjkkHKyctFkUefNiwmATEXWnKPFBIHo2apQYlNVa3xiNLXRwP9X4Exo2si1mI3iM2py8Gw49o5jE+SVtu21z4IHMOAX7iFP62fmZzxYlnNQ0j3YcyS[/tex] (共八个)则[p=align:center][tex=30.143x2.214]PbGXNH/KGxoAl/26XCo9eu/Gn1cFJH4/l4EoK6XIcCDHmYubdrdPc+6gDmTIN/IzflgzbEVTS/ZVE957hQPF1XNnlTQPDxAdh5xnldGVeaJqMtSLFeQSal3Bog0u//1gz03dY/PSXOtOFNmJNC26rbjvI69rWBtoKnXSZgZkYz5cepufB+cOgFIloSkjx4lAdo/SOZPS6aSmFOuKaIo3zqu7yH/egFWOfRakOwBRUd2K7GR8Wf92S3f1SfKPJtyRAVIHWYd956fUQGeia5VnXhCwv//W+X4JkJgbvl5KxU49GAgfK+Lf0A8qO+xbVmnfnwZqk9VhMYpXfpsaDx2xRYM/rJfQVFQ/8b3EWY/raGB01nIq724Hg1Pex1PvrIHIhIarSLTZnsJDsllaoCXflw==[/tex][tex=31.143x2.214]34RT8VLiSbgwZMRLB/LdKH3AP05TxU6NPXfgkwaoLeKmRQyx+CVhgeZzedvmJhQeEbUsMdSD5qN4TkkI1orFN/IJgYRs/lwR2DDifGZZvdVv2Q7TJP8Pvbxo6kfE67hSR1KxXbv4azRIxCaEF+cvoFm/fcMfFWPl91lbDXgJu+zE4FiClE9YG417dZSGRjWIEd0AwyG2CiF46JHcZB1FQgiVEsMAumt1sqO2BMUTxHiVs91omObKvTNnWl78Z6AX8hBdf3oVRTu0zWjEvcRXMND7v1zqGuT+zYgtSZW5sQ83/ZQa/QRbMH7yqqL+X7aglPF0FkrouU0vdpb9KJtzzw==[/tex][tex=32.857x2.214]AxoacmXg52yBjgf+5Uh/l322XcueVcAHNQa+I+shVIcOtr4c0pJ8HnWhR7dbBu+QPIW3u5gVYsspyrcNUwFD5fvT2nv5+P4jgHRW/eelW129F/IGr4rIlcXD2cVdfCbChoOQdvYme+0FhWtPn/j9v9RQRRkhNw0FWYH1SArwpar4icRBl1XL0Wfo3eeQ1KKrfwBmyOE2604EGF2/UCnFhqeYUq7V5j5yMS1QZYVR1buHIq3QPQAw3xOSOl9jO2IyUl5lLnn5kt5Q82EWQhnSl2pUIY8xsHR/dLA3xnStRDn/X3KQDVfAhloDx6qg3WdmXHo/GU+dlYTTSzKIPS0mekpmDej0UpqlLv+2JqwZgGQ=[/tex][tex=25.714x7.5]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[/tex]同时 [tex=3.0x1.214]3xQMuPhF0GGEYFjBBuxK4afo7jTOaHSFWxeaoVOdb+4=[/tex] 时 [tex=8.786x1.429]PbGXNH/KGxoAl/26XCo9etrFTozhxI/k8owT6Tbx8UFECgDC6vkDE/YPmLL37jUufQsOqbUUa1MVGBzkYNWc/rtAz51+rRceWomYahdGuWY=[/tex]当 [tex=9.786x1.357]/OjPJqrRD7tlxDFOkMnLBLN0tvCpVRjZPUs8aeK2wAc=[/tex] 或 [tex=9.714x1.357]EPbLPllTB+pcnCzq/BUCPyJf141Le0XIS/yANd27WPfkuu6N9fdYnB8CxPG81uOl[/tex] 时 [tex=9.286x1.429]X7LYvZ1l+6rqbldoFexWQ9sgxIonghck/e4gBftuy3c=[/tex]能帯宽度 [tex=8.714x1.214]Ihbi+R4AC48DiQ7kowx6X42AZ2+eDw4+5nEAg9lIXDXxnzKi4U2Rug6P80l1iA8qXepf6SJ8P0fCHMNFKSLbgw==[/tex]
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    内容

    • 0

      [tex=3.0x1.214]okauwYSs8zbVDQ2n7FpSpQ==[/tex]晶体为简单立方点阵结构,晶胞中包含 1 个[tex=2.357x1.429]pyyu0BzHf4Ha3iwrjTcrBw==[/tex]和 1 个[tex=1.643x1.143]ZcmpEX+ZwRM8FE5sRM0eBQ==[/tex],晶胞参数 [tex=4.214x1.214]6E3wisjNoHpQNrE5txtfFA==[/tex].(1) 若[tex=2.357x1.429]pyyu0BzHf4Ha3iwrjTcrBw==[/tex]热运动呈球形,试画出晶胞结构示意图;(2) 已知[tex=1.643x1.143]ZcmpEX+ZwRM8FE5sRM0eBQ==[/tex]半径为[tex=2.929x1.214]msbP1nxmdWumj8NR3aEpnQ==[/tex], 求球形[tex=2.357x1.429]pyyu0BzHf4Ha3iwrjTcrBw==[/tex]的半径;(3) 计算晶体密度;(4) 计算平面点阵族[tex=2.286x1.357]k968LmdN4QP2n2erOW6xuQ==[/tex]相邻两点阵面的间距;(5) 用[tex=2.786x1.0]ahLGM/LKr2AkacTUqkyk6w==[/tex]射线进行衍射,计算衍射指标 330 的衍射角[tex=1.286x1.357]zzh2m2PmGj0mj8ZqeFa3Lw==[/tex];(6) 若[tex=2.357x1.429]pyyu0BzHf4Ha3iwrjTcrBw==[/tex]不因热运动而转动,[tex=0.857x1.0]aPLFPHMGSKDwulHSwLWugg==[/tex]为有序分布,请讨论晶体所属的点群.

    • 1

      向量[tex=5.643x1.286]UOUVlYY3Owd/9Y+4aGhD2Q==[/tex]在[tex=4.786x1.286]x/DRKltwGOjd6FFY9joZ6Q==[/tex]上的投影[tex=3.214x1.286]HwD6aHO6Qt0l6J++EPGgPBkdil9ILD3xu4YblbhvSoE=[/tex][input=type:blank,size:6][/input] ，[tex=0.5x1.286]PGyKeLDo0qv9T0n29ldi6w==[/tex]在[tex=0.571x1.286]mRKL/orzOudCEARA8qn3Kw==[/tex]上的投影[tex=3.143x1.286]HwD6aHO6Qt0l6J++EPGgPJ4STKvTqeKlzMVUIz66NNQ=[/tex][input=type:blank,size:6][/input] . 

    • 2

      在紧束缚近似下，简单立方晶体s态原子能带宽度为 A: 6J B: 8J C: 12J D: 16J

    • 3

      已知[tex=7.714x2.786]VayJAJ4dPoPvWvsG3JDU0vw7vChCzZ3AwX+Zo2PMQEu+bRX6raxVRNsM2x2DiAjMt/2V1YC7ENJQ1SgVqw9NgQ==[/tex]，试把积分区间[tex=2.0x1.357]pL+9s9nh77uX8/Gl5SRykA==[/tex][tex=1.0x1.0]5ll/4oTq8VGGY6gN6eTenQ==[/tex]等分，分别用矩形近似公式、梯形近似公式、抛物线近似公式计算 [tex=0.571x0.786]l57IXZOdm4C+U7oqJ3rVIQ==[/tex]的近似值.

    • 4

      试证明面心立方晶格的八面体间隙半径x[tex=4.786x1.286]MqUFxONbob4o1yKqMi7QTA==[/tex]，四面体间隙半径[tex=4.786x1.286]J0vikukpnonuUlGTFHnWHw==[/tex]；体心立方晶格的八面体间隙半径：[tex=2.857x1.286]dHYD1m+bDuhwLtE72Qqvkw==[/tex]晶向的[tex=4.786x1.286]ViQ+jyuSQtiwk8ql5cferQ==[/tex]，[tex=2.857x1.286]eMNNz2RXQfgnS5JFMuh3mQ==[/tex]晶向的[tex=4.786x1.286]oLSidi3mQUPIqmoUCFVnsg==[/tex]，四面体间隙半径[tex=4.786x1.286]wYtd7Go0xGu8z4hV/HQNyA==[/tex]。（[tex=0.786x1.286]yokTf2U2Z7kNGUXMm22GjQ==[/tex]为原子半径）