2.A Frenkel defect<\/strong> forms when an ion moves to an interstitial site.(\u5f53\u4e00\u4e2a\u79bb\u5b50\u79fb\u52a8\u5230\u95f4\u9699\u4f4d\u7f6e\u65f6\uff0c\u5c31\u4f1a\u5f62\u6210\u5f17\u4f26\u514b\u5c14\u7f3a\u9677\u3002)<\/p>\n\n\n\n 3.Atom exchange can also give rise to a point defect<\/strong> as in CuAu.(\u539f\u5b50\u4ea4\u6362\u4e5f\u4f1a\u4ea7\u751f\u70b9\u7f3a\u9677\uff0c\u4f8b\u5982\u5728\u94dc\u91d1\u5408\u91d1\uff08CuAu\uff09\u4e2d\u3002)<\/p>\n\n\n\n Bonding electrons: 2 (in \u03c3(2s)) +4 (in \u03c0(2p)) +2 (in \u03c3(2p)) =8 \uff1bAntibonding electrons: 2 (in \u03c3\u2217(2s)) =2<\/p>\n\n\n\n BO = 1\/2 x ( 8-2) = 3.All electrons in the MO configuration are paired.<\/p>\n\n\n\n So,the cyanide ion (CN-) has a bond order of 3<\/strong> and 0 unpaired electrons<\/strong>.<\/p>\n\n\n\n BO = 1\/2 x ( 2-0) = 1.All electrons in the MO configuration are paired.<\/p>\n\n\n\n So,the cyanide ion (CN-) has a bond order of 1<\/strong> and 0 unpaired electrons<\/strong>.<\/p>\n\n\n\n a) Which cation do you think occupies each hole and why? (5p) Ag+ occupies octahedral holes, while Sb3+<\/sup> occupies tetrahedral holes.<\/p>\n\n\n\n The radius ratio of Ag+<\/sup> \/ S2-<\/sup> is 115\/184 \u2248 0.625, which matches the range for octahedral coordination (0.414\u20130.732).<\/p>\n\n\n\n The radius ratio of Sb3+ <\/sup>\/ S2-<\/sup> is 58\/184 \u2248 0.315, which fits the tetrahedral coordination range (0.225\u20130.414).<\/p>\n<\/div>\n<\/div>\n<\/div>\n\n\n\n b) What fraction of octahedral holes would be occupied with your model of what is happening? (3p) In close-packed structures, the number of octahedral holes is equal to the number of anions.<\/p>\n\n\n\n There are 3 S2-<\/sup> ions and 3 octahedral holes, fully occupied by 3 Ag+<\/sup> ions.<\/p>\n\n\n\n Fraction of occupied octahedral holes = 3\/3 = 1<\/p>\n<\/div>\n\n\n\n c) What fraction of tetrahedral holes would be occupied with your model of what is happening? (3p)\u6839\u636e\u4f60\u7684\u6a21\u578b\uff0c\u56db\u9762\u4f53\u7a7a\u9699\u88ab\u5360\u636e\u7684\u6bd4\u4f8b\u662f\u591a\u5c11\uff1f<\/strong><\/p>\n\n\n\n In close-packed structures, tetrahedral holes are twice the number of anions.<\/p>\n\n\n\n For 3 S2- <\/sup>ions, total tetrahedral holes = 6, with only 1 Sb3+<\/sup> occupying one tetrahedral hole.<\/p>\n\n\n\n Fraction of occupied tetrahedral holes = 1\/6<\/p>\n<\/div>\n<\/div>\n\n\n\n The two figures above depict the cubic unit cell of the Cu\u2082O crystal. The lattice constant of the structure is 427.0 pm.(\u56fe\u4e2d\u6240\u793a\u4e3a Cu\u2082O \u6676\u4f53\u7684\u7acb\u65b9\u6676\u80de\uff0c\u8be5\u7ed3\u6784\u7684\u6676\u683c\u5e38\u6570\u4e3a427.0 pm)<\/p>\n\n\n\n a) Which of the atoms (A or B) is copper? Which basic structure (primitive cubic, face centered cubic, body centered cubic, diamond) is formed by the A atoms and which structure is formed by the B atoms? What are the coordination numbers of the atoms? (\u539f\u5b50 A \u548c\u539f\u5b50 B \u4e2d\uff0c\u54ea\u4e00\u4e2a\u662f\u94dc\u539f\u5b50\uff1fA \u539f\u5b50\u5f62\u6210\u7684\u57fa\u672c\u7ed3\u6784\uff08\u7b80\u5355\u7acb\u65b9\u3001\u9762\u5fc3\u7acb\u65b9\u3001\u4f53\u5fc3\u7acb\u65b9\u3001\u91d1\u521a\u77f3\u578b\uff09\u662f\u4ec0\u4e48\uff1fB \u539f\u5b50\u5f62\u6210\u7684\u7ed3\u6784\u53c8\u662f\u4ec0\u4e48\uff1f\u4e24\u79cd\u539f\u5b50\u7684\u914d\u4f4d\u6570\u5404\u662f\u591a\u5c11\uff1f)(7p)<\/strong><\/p>\n<\/div>\n\n\n\n There are 2A atoms and 4B atoms in the cell. Cu:B b) Calculate the smallest O-O, Cu-O and Cu-Cu distances in the structure.(\u8ba1\u7b97\u8be5\u7ed3\u6784\u4e2d O-O\u3001Cu-O \u548c Cu-Cu \u7684\u6700\u5c0f\u539f\u5b50\u95f4\u8ddd) (6p)<\/strong><\/p>\n\n\n\n dO-O<\/sub> :half of the cell body diagonal 1\/2*427.0pm*\u221a<\/strong>3 = 369.8pm c) What is the density of pure copper(I) oxide? (\u7eaf\u6c27\u5316\u4e9a\u94dc\u7684\u5bc6\u5ea6\u662f\u591a\u5c11)(2p)<\/strong><\/p>\n\n\n\n The volume of the unit cell is (427.0pm)3<\/sup> d)A common defect in this crystal is some copper atoms missing with the oxygen lattice unchanged. The composition of one such crystal sample was studied, and 0.2% of all copper atoms were found to be in oxidation state +2. What percentage of normal copper sites are empty in the crystal sample? What is x in the empirical formula Cu\u2082\u208b\u2093O of the crystal?(\u8be5\u6676\u4f53\u4e2d\u4e00\u79cd\u5e38\u89c1\u7f3a\u9677\u662f\u90e8\u5206\u94dc\u539f\u5b50\u7f3a\u5931\uff0c\u800c\u6c27\u539f\u5b50\u6676\u683c\u4fdd\u6301\u4e0d\u53d8\u3002\u5bf9\u67d0\u4e00\u6837\u54c1\u8fdb\u884c\u6210\u5206\u5206\u6790\u540e\u53d1\u73b0\uff0c0.2% \u7684\u94dc\u539f\u5b50\u5904\u4e8e + 2 \u6c27\u5316\u6001\u3002\u8bf7\u95ee\u8be5\u6676\u4f53\u6837\u54c1\u4e2d\uff0c\u6b63\u5e38\u94dc\u539f\u5b50\u4f4d\u7f6e\u7684\u7a7a\u4f4d\u5360\u6bd4\u662f\u591a\u5c11\uff1f\u7ecf\u9a8c\u5f0fCu2-x<\/sub>O\u4e2d\u7684x\u503c\u662f\u591a\u5c11(4p)<\/strong><\/p>\n\n\n\n a) How many formula units (ZnS) are there in the unit cell of sphalerite? (\u95ea\u950c\u77ff\u6676\u80de\u4e2d\u5305\u542b\u591a\u5c11\u4e2a ZnS \u7ed3\u6784\u5355\u5143<\/strong>)(2p)<\/strong><\/p>\n\n\n\n b) Heavier elements of group IV (i.e. group 14), silicon and germanium, also adopt the structure of diamond. The radius of elemental germanium is r(Ge)=1.23\u00a0A\u02da. Calculate the density of solid germanium. (\u7b2c 14 \u65cf\uff08\u78b3\u65cf\uff09\u7684\u8f83\u91cd\u5143\u7d20\uff08\u5982\u7845\u3001\u9517\uff09\u4e5f\u4f1a\u5f62\u6210\u91d1\u521a\u77f3\u578b\u7ed3\u6784\u3002\u5df2\u77e5\u91d1\u5c5e\u9517\u7684\u539f\u5b50\u534a\u5f84r(Ge)=1.23\u00a0A\u02da\uff0c\u8ba1\u7b97\u56fa\u6001\u9517\u7684\u5bc6\u5ea6<\/strong>)(4p)<\/strong><\/p>\n\n\n\n c) Germanium is a semiconductor similar to silicon. It is used in electro-technology and similarly to silicon, it is also very fragile. Therefore, more flexible isoelectronic gallium arsenide, GaAs, is used in some practical applications. This compound belongs to semiconductors of III-V type (compounds of elements from groups III and V, i.e. groups 13 and 15, respectively) and adopts the structure of sphalerite. The lattice constants of Ge and GaAs are very similar, and a(GaAs)=5.65\u00a0A\u02da. An analogous compound GaP also adopts the structure of sphalerite, but has a smaller unit cell with a(GaP)=5.45\u00a0A\u02da. Calculate the difference between the radii of P and As in the respective compounds with gallium (GaP versus GaAs).(\u9517\u662f\u4e00\u79cd\u548c\u7845\u7c7b\u4f3c\u7684\u534a\u5bfc\u4f53\uff0c\u5728\u7535\u5b50\u6280\u672f\u4e2d\u5e94\u7528\u5e7f\u6cdb\uff0c\u4f46\u548c\u7845\u4e00\u6837\u8d28\u5730\u5f88\u8106\u3002\u56e0\u6b64\uff0c\u5728\u4e00\u4e9b\u5b9e\u9645\u5e94\u7528\u4e2d\u4f1a\u4f7f\u7528\u66f4\u67d4\u97e7\u7684 III-V \u65cf\u534a\u5bfc\u4f53\u7837\u5316\u9553\uff08GaAs\uff09\uff0c\u8fd9\u7c7b\u534a\u5bfc\u4f53\u7531\u7b2c 13 \u65cf\u548c\u7b2c 15 \u65cf\u5143\u7d20\u7ec4\u6210\uff0c\u540c\u6837\u91c7\u7528\u95ea\u950c\u77ff\u7ed3\u6784\u3002\u9517\u548c\u7837\u5316\u9553\u7684\u6676\u683c\u5e38\u6570\u975e\u5e38\u63a5\u8fd1\uff0ca(GaAs)=5.65\u00a0A\u02da\u3002\u7c7b\u4f3c\u5730\uff0c\u78f7\u5316\u9553\uff08GaP\uff09\u4e5f\u91c7\u7528\u95ea\u950c\u77ff\u7ed3\u6784\uff0c\u4f46\u6676\u80de\u66f4\u5c0f\uff0c\u6676\u683c\u5e38\u6570a(GaP)=5.45\u00a0A\u02da\u3002\u8ba1\u7b97\u5728\u8fd9\u4e24\u79cd\u5316\u5408\u7269\u4e2d\uff0c\u78f7\uff08P\uff09\u548c\u7837\uff08As\uff09\u7684\u79bb\u5b50\u534a\u5f84\u5dee\uff08GaP \u4e0e GaAs \u5bf9\u6bd4\uff09) (7p)<\/strong><\/p>\n\n\n\n 1)List three types of intrinsic point defects for crystalline mat …<\/p>\n","protected":false},"author":1,"featured_media":132,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-118","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/posts\/118","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/comments?post=118"}],"version-history":[{"count":8,"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/posts\/118\/revisions"}],"predecessor-version":[{"id":143,"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/posts\/118\/revisions\/143"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/media\/132"}],"wp:attachment":[{"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/media?parent=118"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/categories?post=118"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/kongling.xin\/index.php\/wp-json\/wp\/v2\/tags?post=118"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}2) a) Prepare a molecular orbital (MO) energy-level diagram for the cyanide ion (CN-). Use sketches to show clearly how the atomic orbitals interact to form MOs. Please calculate the bond order and unpaired electrons. \uff08\u7ed8\u5236\u6c30\u6839\u79bb\u5b50\uff08CN-\uff09\u7684\u5206\u5b50\u8f68\u9053\uff08MO\uff09\u80fd\u7ea7\u56fe\u3002\u8bf7\u7528\u8f68\u9053\u793a\u610f\u56fe\u6e05\u6670\u8bf4\u660e\u539f\u5b50\u8f68\u9053\u5982\u4f55\u76f8\u4e92\u4f5c\u7528\u5f62\u6210\u5206\u5b50\u8f68\u9053\uff0c\u5e76\u8ba1\u7b97\u5176\u952e\u7ea7\u548c\u672a\u6210\u5bf9\u7535\u5b50\u6570\u3002(4p)<\/h2>\n\n\n\n
![\"\"](\"https:\/\/kongling.xin\/wp-content\/uploads\/2026\/05\/1779180205-8d5d2a9f4dc169b3f3298104d8131e7b-1024x962.jpeg\")
<\/figure>\n\n\n\n2)b)) Prepare a molecular orbital energy-level diagram for linear ion,H3+.Use sketches to show clearly how the atomic orbitals interact to form MOs. Please calculate the bond order and unpaired electrons. (\u7ed8\u5236\u7ebf\u6027\u79bb\u5b50H3+\u7684\u5206\u5b50\u8f68\u9053\u80fd\u7ea7\u56fe\u3002\u8bf7\u7528\u8f68\u9053\u793a\u610f\u56fe\u6e05\u6670\u8bf4\u660e\u539f\u5b50\u8f68\u9053\u5982\u4f55\u76f8\u4e92\u4f5c\u7528\u5f62\u6210\u5206\u5b50\u8f68\u9053\uff0c\u5e76\u8ba1\u7b97\u5176\u952e\u7ea7\u548c\u672a\u6210\u5bf9\u7535\u5b50\u6570)(6p)<\/h2>\n\n\n\n
![\"\"](\"https:\/\/kongling.xin\/wp-content\/uploads\/2026\/05\/1779183621-e4a83c1f306328d62f5d22eae0064473-951x1024.jpg\"){kind=spacer}
<\/figure>\n\n\n\n3) Determine the point group for each of the following molecules or molecular ions. Neglect all hydrogen atoms and assume conjugated systems are fully delocalized. (\u786e\u5b9a\u4e0b\u5217\u6bcf\u4e2a\u5206\u5b50\u6216\u5206\u5b50\u79bb\u5b50\u7684\u70b9\u7fa4\u3002\u5ffd\u7565\u6240\u6709\u6c22\u539f\u5b50\uff0c\u5e76\u5047\u8bbe\u5171\u8f6d\u4f53\u7cfb\u5b8c\u5168\u79bb\u57df)(12p)<\/h2>\n\n\n\n
![\"\"](\"https:\/\/kongling.xin\/wp-content\/uploads\/2026\/05\/1779184018-f4731972d087c4290d9572029ed63d4d-907x1024.jpg\")
<\/figure>\n\n\n![\"\"](\"https:\/\/kongling.xin\/wp-content\/uploads\/2026\/05\/1779185293-1.png\")
<\/figure>\n<\/div>\n\n\na.<\/h4>\n\n\n\n
\n
b. <\/strong><\/h4>\n\n\n\n
\n
c. <\/h4>\n\n\n\n
\n
d.<\/h4>\n\n\n\n
\n
e. <\/h4>\n\n\n\n
\n
f. <\/h4>\n\n\n\n
\n
4) The mineral pyrargyrite,Ag3<\/sub>SbS3<\/sub>, utilizes the hexagonal lattice system. The sulfides are space-filling and the Ag+ ions occupy one sort of hole (either octahedral or tetrahedral) while the Sb3+ ions occupy the other sort of hole. (\u77ff\u7269\u786b\u9511\u94f6\u77ff\u91c7\u7528\u516d\u65b9\u6676\u7cfb\u6676\u683c\u3002\u786b\u79bb\u5b50\u505a\u5bc6\u5806\u79ef\uff0cAg+<\/sup>\u79bb\u5b50\u5360\u636e\u4e00\u79cd\u7a7a\u9699\uff08\u516b\u9762\u4f53\u6216\u56db\u9762\u4f53\u7a7a\u9699\uff09\uff0cSb3+<\/sup>\u79bb\u5b50\u5360\u636e\u53e6\u4e00\u79cd\u7a7a\u9699)(11p)<\/h2>\n\n\n\n
\u4f60\u8ba4\u4e3a\u54ea\u79cd\u9633\u79bb\u5b50\u5360\u636e\u54ea\u79cd\u7a7a\u9699\uff1f\u4e3a\u4ec0\u4e48\uff1f<\/strong><\/p>\n\n\n\n
\u6839\u636e\u4f60\u7684\u6a21\u578b\uff0c\u516b\u9762\u4f53\u7a7a\u9699\u88ab\u5360\u636e\u7684\u6bd4\u4f8b\u662f\u591a\u5c11\uff1f<\/strong><\/p>\n<\/div>\n\n\n\n5)One of the first materials used in solid state electronics was red copper(I) oxide. Interest is renewed nowadays because it could be a non-toxic and cheap component of solar cells. (\u56fa\u6001\u7535\u5b50\u5b66\u4e2d\u6700\u65e9\u4f7f\u7528\u7684\u6750\u6599\u4e4b\u4e00\u662f\u6c27\u5316\u4e9a\u94dc\uff08Cu\u2082O\uff09<\/strong>\u3002\u5982\u4eca\u4eba\u4eec\u5bf9\u5b83\u7684\u5174\u8da3\u91cd\u65b0\u9ad8\u6da8\uff0c\u56e0\u4e3a\u5b83\u6709\u671b\u6210\u4e3a\u592a\u9633\u80fd\u7535\u6c60\u4e2d\u4e00\u79cd\u65e0\u6bd2\u4e14\u5ec9\u4ef7\u7684\u7ec4\u4ef6)(19p)<\/h2>\n\n\n\n
![\"\"](\"https:\/\/kongling.xin\/wp-content\/uploads\/2026\/05\/1779206529-image.png\")
<\/figure>\n\n\n\n
B:fcc A:bcc
B:2 A:4<\/p>\n\n\n\n
dCu-O<\/sub>:1\/4th<\/sup> of the cell body diagonal 1\/4*427.0pm*\u221a<\/strong>3 =184.0pm
dCu-Cu<\/sub>:half of the face diagonal:1\/2*427.0pm*\u221a<\/strong>2 =301.9pm
1p each, no penalty for Cu and O switched<\/p>\n\n\n\n
The mass of a unit cell is (4MCu<\/sub>+2MO<\/sub>)\/NA<\/sub>.The density is 6.106g\/cm3<\/sup><\/p>\n\n\n\n6)Zinc blende (sphalerite, ZnS) crystallizes in a different crystal structure type, which is closely related to the structure of diamond. Both types of structures are shown in Figure below(\u95ea\u950c\u77ff\uff08\u7acb\u65b9\u786b\u5316\u950c\uff0cZnS\uff09\u7684\u6676\u4f53\u7ed3\u6784\u4e0e\u91d1\u521a\u77f3\u7ed3\u6784\u5bc6\u5207\u76f8\u5173\uff0c\u4e24\u79cd\u7ed3\u6784\u5982\u4e0b\u56fe\u6240\u793a) (13p):<\/h2>\n\n\n\n
![\"\"](\"https:\/\/kongling.xin\/wp-content\/uploads\/2026\/05\/1779209007-image.png\")
<\/figure>\n\n\n\n7)The bond lengths inO2<\/sub>,O2<\/sub>+<\/sup>andO2<\/sub>2-<\/sup>are 121, 112, and 149 pm,respectively. Please rationalize the differences in bond lengths. (6p)
<\/h2>\n\n\n\n![\"\"](\"https:\/\/kongling.xin\/wp-content\/uploads\/2026\/05\/1779209379-image.png\")
<\/figure>\n","protected":false},"excerpt":{"rendered":"