<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@vertical+block@78321ae608374391bdbcea28d2707789" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">Question 1: Diffusion</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@58abc650ebd54b2b902e1a17dde823fa">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@58abc650ebd54b2b902e1a17dde823fa" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_58abc650ebd54b2b902e1a17dde823fa" class="problems-wrapper" role="group"
aria-labelledby="58abc650ebd54b2b902e1a17dde823fa-problem-title"
data-problem-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@58abc650ebd54b2b902e1a17dde823fa" data-url="/courses/course-v1:MITx+3.012S.3x+1T2019/xblock/block-v1:MITx+3.012S.3x+1T2019+type@problem+block@58abc650ebd54b2b902e1a17dde823fa/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="3.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="58abc650ebd54b2b902e1a17dde823fa-problem-title" aria-describedby="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@58abc650ebd54b2b902e1a17dde823fa-problem-progress" tabindex="-1">
Problem 1.1
</h3>
<div class="problem-progress" id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@58abc650ebd54b2b902e1a17dde823fa-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>Carbon is allowed to diffuse through a steel plate \(15 \; mm\) thick. The concentrations of carbon at the two faces are \(0.65\) and \(0.3 \; kg/m^3\), which are maintained constant. If the diffusivity pre-exponential, \(D_0\), and the activation energy, \(Q\), are \(6.2 \times 10^{-7}\; m^2/s\) and \(80,000 \; J/mol\), respectively, compute the temperature at which the diffusion flux is \(1.43 \times 10^{-9} \;kg/m^2s\).</p>
<p>\(T\) (in degrees \(C\))</p>
<div id="formulaequationinput_58abc650ebd54b2b902e1a17dde823fa_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_58abc650ebd54b2b902e1a17dde823fa_2_1" id="input_58abc650ebd54b2b902e1a17dde823fa_2_1" data-input-id="58abc650ebd54b2b902e1a17dde823fa_2_1" value="" aria-describedby="status_58abc650ebd54b2b902e1a17dde823fa_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_58abc650ebd54b2b902e1a17dde823fa_2_1"/>
<span class="status unanswered" id="status_58abc650ebd54b2b902e1a17dde823fa_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_58abc650ebd54b2b902e1a17dde823fa_2_1" class="answer"/>
<div id="input_58abc650ebd54b2b902e1a17dde823fa_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 1.1" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_58abc650ebd54b2b902e1a17dde823fa" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_58abc650ebd54b2b902e1a17dde823fa">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="58abc650ebd54b2b902e1a17dde823fa-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="58abc650ebd54b2b902e1a17dde823fa-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="58abc650ebd54b2b902e1a17dde823fa-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@18f75b04300c48f8aeb4ba2f86dc7d20">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@18f75b04300c48f8aeb4ba2f86dc7d20" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_18f75b04300c48f8aeb4ba2f86dc7d20" class="problems-wrapper" role="group"
aria-labelledby="18f75b04300c48f8aeb4ba2f86dc7d20-problem-title"
data-problem-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@18f75b04300c48f8aeb4ba2f86dc7d20" data-url="/courses/course-v1:MITx+3.012S.3x+1T2019/xblock/block-v1:MITx+3.012S.3x+1T2019+type@problem+block@18f75b04300c48f8aeb4ba2f86dc7d20/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="3.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="18f75b04300c48f8aeb4ba2f86dc7d20-problem-title" aria-describedby="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@18f75b04300c48f8aeb4ba2f86dc7d20-problem-progress" tabindex="-1">
Problem 1.2
</h3>
<div class="problem-progress" id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@18f75b04300c48f8aeb4ba2f86dc7d20-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>A sheet of BCC iron \(1 \; mm\) thick was exposed to a carburizing gas atomosphere on one side and a decarburizing atmosphere on the other side at \(725^{\circ}C\). After having reached steady state, the iron was quickly cooled to room temperature. The carbon concentrations at the two surfaces of the sheet were determined to be \(0.012\) and \(0.0075 \; wt \%\). Compute the diffusion coefficient if the diffusion flux is \(1.4 \times 10^{-8}\;kg/m^2 \cdot s\). Assume the density of the BCC iron is \(7.87 g/cm^3\).</p>
<p>\(D\) (in \(m^2/s\)):</p>
<div id="formulaequationinput_18f75b04300c48f8aeb4ba2f86dc7d20_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_18f75b04300c48f8aeb4ba2f86dc7d20_2_1" id="input_18f75b04300c48f8aeb4ba2f86dc7d20_2_1" data-input-id="18f75b04300c48f8aeb4ba2f86dc7d20_2_1" value="" aria-describedby="status_18f75b04300c48f8aeb4ba2f86dc7d20_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_18f75b04300c48f8aeb4ba2f86dc7d20_2_1"/>
<span class="status unanswered" id="status_18f75b04300c48f8aeb4ba2f86dc7d20_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_18f75b04300c48f8aeb4ba2f86dc7d20_2_1" class="answer"/>
<div id="input_18f75b04300c48f8aeb4ba2f86dc7d20_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 1.2" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_18f75b04300c48f8aeb4ba2f86dc7d20" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_18f75b04300c48f8aeb4ba2f86dc7d20">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="18f75b04300c48f8aeb4ba2f86dc7d20-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="18f75b04300c48f8aeb4ba2f86dc7d20-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="18f75b04300c48f8aeb4ba2f86dc7d20-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@vertical+block@329393c22c854710a7000cea8bf495aa" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">Question 2: Defect Reactions</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@4f2e267373244543838b216f2e10e3a2">
<div class="xblock xblock-public_view xblock-public_view-drag-and-drop-v2" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@4f2e267373244543838b216f2e10e3a2" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="drag-and-drop-v2" data-init="DragAndDropBlock" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"problem_text": "Use the drag and drop tool to write out the defect reaction for the following: CdO is introduced in a \nBi\u003csub\u003e2\u003c/sub\u003e\u0026nbsp;O\u003csub\u003e3\u003c/sub\u003e lattice, resulting in a large number of anion vacancies.", "display_name": "Problem 2.1", "target_img_expanded_url": "/assets/courseware/v1/db1a456afd15b1f8edf82a0637c08a45/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_background.jpg", "url_name": "4f2e267373244543838b216f2e10e3a2", "show_title": true, "display_zone_borders": false, "type": "drag-and-drop-v2", "weight": 1.0, "display_zone_labels": false, "has_deadline_passed": false, "max_attempts": 0, "target_img_description": "A schematic of a chemical reaction. There is one box (Box 1) on the left side, an arrow with Bi2O3 written above, and three boxes on the right side Box 2 + Box 3 + Box 4", "block_id": "block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@4f2e267373244543838b216f2e10e3a2", "title": "Problem 2.1", "item_text_color": null, "weighted_max_score": 1.0, "max_items_per_zone": 1, "mode": "assessment", "graded": true, "show_problem_header": true, "is_anonymous_user": true, "zones": [{"height": "125", "align": "center", "title": "Box 1", "width": 196, "x": "10", "y": "50", "uid": "top", "description": "Box 1"}, {"height": "125", "align": "center", "title": "Box 2", "width": "196", "x": "360", "y": "50", "uid": "middle", "description": "Box 2"}, {"height": "125", "align": "center", "title": "Box 3", "width": "196", "x": "620", "y": "50", "uid": "bottom", "description": "Box 3"}, {"height": "125", "align": "center", "title": "Box 4", "width": "196", "x": "871", "y": "50", "uid": "zone-1", "description": "Box 4"}], "item_background_color": "white", "items": [{"expandedImageURL": "/assets/courseware/v1/92aa1333914c2f003f1d5841070661b0/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_A.jpg", "widthPercent": "17", "imageDescription": "CdO", "displayName": "", "imageURL": "/assets/courseware/v1/92aa1333914c2f003f1d5841070661b0/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_A.jpg", "id": 0}, {"expandedImageURL": "/assets/courseware/v1/f8dbc13e205b50cdbaf854fa0421dc60/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_B.jpg", "widthPercent": "17", "imageDescription": "2CdO", "displayName": "", "imageURL": "/assets/courseware/v1/f8dbc13e205b50cdbaf854fa0421dc60/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_B.jpg", "id": 1}, {"expandedImageURL": "/assets/courseware/v1/21355087b271cabe0a342ed828b197fc/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_C.jpg", "widthPercent": "17", "imageDescription": "3CdO", "displayName": "", "imageURL": "/assets/courseware/v1/21355087b271cabe0a342ed828b197fc/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_C.jpg", "id": 2}, {"expandedImageURL": "/assets/courseware/v1/7ccea5cf8b30653fb6d1c906537786bf/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_D.jpg", "widthPercent": "17", "imageDescription": "Cd^{'}_{Bi}", "displayName": "", "imageURL": "/assets/courseware/v1/7ccea5cf8b30653fb6d1c906537786bf/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_D.jpg", "id": 3}, {"expandedImageURL": "/assets/courseware/v1/f93c26074d6c91762b8d5913e5755804/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_E.jpg", "widthPercent": "17", "imageDescription": "2Cd^{'}_{Bi}", "displayName": "", "imageURL": "/assets/courseware/v1/f93c26074d6c91762b8d5913e5755804/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_E.jpg", "id": 4}, {"expandedImageURL": "/assets/courseware/v1/4d0885831c7a482421fa69838e41e122/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_F.jpg", "widthPercent": "17", "imageDescription": "3Cd^{'}_{Bi}", "displayName": "", "imageURL": "/assets/courseware/v1/4d0885831c7a482421fa69838e41e122/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_F.jpg", "id": 5}, {"expandedImageURL": "/assets/courseware/v1/1d105d894f55b474f842166a8eefbe3c/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_G.jpg", "widthPercent": "17", "imageDescription": "Bi^{+}_{Cd}", "displayName": "", "imageURL": "/assets/courseware/v1/1d105d894f55b474f842166a8eefbe3c/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_G.jpg", "id": 6}, {"expandedImageURL": "/assets/courseware/v1/83dce4eeaaec2924a122229fc25dbd5c/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_H.jpg", "widthPercent": "17", "imageDescription": "2Bi^{+}_{Cd}", "displayName": "", "imageURL": "/assets/courseware/v1/83dce4eeaaec2924a122229fc25dbd5c/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_H.jpg", "id": 7}, {"expandedImageURL": "/assets/courseware/v1/adc79fae3d19a1ec84dfd70a98f49c62/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_I.jpg", "widthPercent": "17", "imageDescription": "3Bi^{+}_{Cd}", "displayName": "", "imageURL": "/assets/courseware/v1/adc79fae3d19a1ec84dfd70a98f49c62/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_I.jpg", "id": 8}, {"expandedImageURL": "/assets/courseware/v1/f0dc1228e2adc7e75da689df87a9cdd8/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_S.jpg", "widthPercent": "17", "imageDescription": "O_{O}^{x}", "displayName": "", "imageURL": "/assets/courseware/v1/f0dc1228e2adc7e75da689df87a9cdd8/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_S.jpg", "id": 9}, {"expandedImageURL": "/assets/courseware/v1/8068ef458d1e2b35c933c9c2a89243aa/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_K.jpg", "widthPercent": "17", "imageDescription": "2O_{O}^{x}", "displayName": "", "imageURL": "/assets/courseware/v1/8068ef458d1e2b35c933c9c2a89243aa/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_K.jpg", "id": 10}, {"expandedImageURL": "/assets/courseware/v1/4ca9163740b3ddf762622cb1e5b0c555/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_L.jpg", "widthPercent": "17", "imageDescription": "3O_{O}^{x}", "displayName": "", "imageURL": "/assets/courseware/v1/4ca9163740b3ddf762622cb1e5b0c555/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_L.jpg", "id": 11}, {"expandedImageURL": "/assets/courseware/v1/9c732f601320d2f81450782974446ab0/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_M.jpg", "widthPercent": "17", "imageDescription": "V_{O}^{++}", "displayName": "", "imageURL": "/assets/courseware/v1/9c732f601320d2f81450782974446ab0/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_M.jpg", "id": 12}, {"expandedImageURL": "/assets/courseware/v1/8f88028bfc0371c47f88ebe78b1e4ab4/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_N.jpg", "widthPercent": "17", "imageDescription": "2V_{O}^{++}", "displayName": "", "imageURL": "/assets/courseware/v1/8f88028bfc0371c47f88ebe78b1e4ab4/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_N.jpg", "id": 13}, {"expandedImageURL": "/assets/courseware/v1/2e22a66adbdf3fe9ba48b3b862f6f63d/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_O.jpg", "widthPercent": "17", "imageDescription": "3V_{O}^{++}", "displayName": "", "imageURL": "/assets/courseware/v1/2e22a66adbdf3fe9ba48b3b862f6f63d/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_O.jpg", "id": 14}, {"expandedImageURL": "/assets/courseware/v1/da9d945b911b96a9f63c3db099e8ea53/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_P.jpg", "widthPercent": "17", "imageDescription": "V_{O}^{''}", "displayName": "", "imageURL": "/assets/courseware/v1/da9d945b911b96a9f63c3db099e8ea53/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_P.jpg", "id": 15}, {"expandedImageURL": "/assets/courseware/v1/9b15b784ecb9421017c10d33ed582052/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_Q.jpg", "widthPercent": "17", "imageDescription": "2V_{O}^{''}", "displayName": "", "imageURL": "/assets/courseware/v1/9b15b784ecb9421017c10d33ed582052/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_Q.jpg", "id": 16}, {"expandedImageURL": "/assets/courseware/v1/a78b2a897dc5589a1220d7620a5cbca9/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_R.jpg", "widthPercent": "17", "imageDescription": "3V_{O}^{''}", "displayName": "", "imageURL": "/assets/courseware/v1/a78b2a897dc5589a1220d7620a5cbca9/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_R.jpg", "id": 17}]}
</script>
<div class="themed-xblock xblock--drag-and-drop">
<span class="fa fa-spin fa-spinner initial-load-spinner" aria-hidden="true"></span>
Loading drag and drop problem.
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@1ee77aa2dd85430f891ceb408eef0a3f">
<div class="xblock xblock-public_view xblock-public_view-drag-and-drop-v2" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@1ee77aa2dd85430f891ceb408eef0a3f" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="drag-and-drop-v2" data-init="DragAndDropBlock" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"problem_text": "Use the drag and drop tool to write out the defect reaction for the following: Ca\u0026nbsp;Cl\u003csub\u003e2\u003c/sub\u003e is added as impurity to CaO. Assume Cl substitutes for O. ", "display_name": "Problem 2.2", "target_img_expanded_url": "/assets/courseware/v1/1520e3993d6dcf8ed0b451f3a3f2e8c8/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2background.jpg", "url_name": "1ee77aa2dd85430f891ceb408eef0a3f", "show_title": true, "display_zone_borders": false, "type": "drag-and-drop-v2", "weight": 1.0, "display_zone_labels": false, "has_deadline_passed": false, "max_attempts": 0, "target_img_description": "A schematic of a chemical reaction. There is one box (Box 1) on the left side, an arrow with 2CaO written above, and three boxes on the right side Box 2 + Box 3 + Box 4", "block_id": "block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@1ee77aa2dd85430f891ceb408eef0a3f", "title": "Problem 2.2", "item_text_color": null, "weighted_max_score": 1.0, "max_items_per_zone": 1, "mode": "assessment", "graded": true, "show_problem_header": true, "is_anonymous_user": true, "zones": [{"height": "110", "align": "center", "title": "Box 1", "width": 196, "x": "12", "y": "20", "uid": "top", "description": "Box 1"}, {"height": "110", "align": "center", "title": "Box 2", "width": "196", "x": "365", "y": "20", "uid": "middle", "description": "Box 2"}, {"height": "110", "align": "center", "title": "Box 3", "width": "196", "x": "625", "y": "20", "uid": "bottom", "description": "Box 3"}, {"height": "110", "align": "center", "title": "Box 4", "width": "196", "x": "876", "y": "20", "uid": "zone-1", "description": "Box 4"}], "item_background_color": "white", "items": [{"expandedImageURL": "/assets/courseware/v1/3c324b2fa86ee40e1cbe40c0a0e19fd9/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2A.jpg", "widthPercent": "17.3", "imageDescription": "CaCl_2", "displayName": "", "imageURL": "/assets/courseware/v1/3c324b2fa86ee40e1cbe40c0a0e19fd9/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2A.jpg", "id": 0}, {"expandedImageURL": "/assets/courseware/v1/b3346b4d3ec638c074aa4bb52a1bebb8/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2B.jpg", "widthPercent": "17.3", "imageDescription": "2CaCl_2", "displayName": "", "imageURL": "/assets/courseware/v1/b3346b4d3ec638c074aa4bb52a1bebb8/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2B.jpg", "id": 1}, {"expandedImageURL": "/assets/courseware/v1/d8283a57bbe1fe90f74a8f2e9ec0b2c3/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2C.jpg", "widthPercent": "17.3", "imageDescription": "3CaCl_2", "displayName": "", "imageURL": "/assets/courseware/v1/d8283a57bbe1fe90f74a8f2e9ec0b2c3/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2C.jpg", "id": 2}, {"expandedImageURL": "/assets/courseware/v1/ce2ccc8751512c17c4e5a0fd2d721fd7/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2D.jpg", "widthPercent": "17.3", "imageDescription": "Ca^x_{Ca}", "displayName": "", "imageURL": "/assets/courseware/v1/ce2ccc8751512c17c4e5a0fd2d721fd7/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2D.jpg", "id": 3}, {"expandedImageURL": "/assets/courseware/v1/fcd19d8c238965800b4484b704fa53d0/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2E.jpg", "widthPercent": "17.3", "imageDescription": "2Ca^x_{Ca}", "displayName": "", "imageURL": "/assets/courseware/v1/fcd19d8c238965800b4484b704fa53d0/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2E.jpg", "id": 4}, {"expandedImageURL": "/assets/courseware/v1/2806e739194125b855e37e022e8a36f5/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2F.jpg", "widthPercent": "17.3", "imageDescription": "3Ca^x_{Ca}", "displayName": "", "imageURL": "/assets/courseware/v1/2806e739194125b855e37e022e8a36f5/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2F.jpg", "id": 5}, {"expandedImageURL": "/assets/courseware/v1/744a02a50c9dc92400a5b13cea18362d/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2G.jpg", "widthPercent": "17.3", "imageDescription": "Cl^{+}_{O}", "displayName": "", "imageURL": "/assets/courseware/v1/744a02a50c9dc92400a5b13cea18362d/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2G.jpg", "id": 6}, {"expandedImageURL": "/assets/courseware/v1/e4d8d6b0ae8ec662465c450e4eb72bc1/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2H.jpg", "widthPercent": "17.3", "imageDescription": "2Cl^{+}_{O}", "displayName": "", "imageURL": "/assets/courseware/v1/e4d8d6b0ae8ec662465c450e4eb72bc1/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2H.jpg", "id": 7}, {"expandedImageURL": "/assets/courseware/v1/3ed18498b675c78772fc89cfbcaea1fa/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2I.jpg", "widthPercent": "17.3", "imageDescription": "3Cl^{+}_{O}", "displayName": "", "imageURL": "/assets/courseware/v1/3ed18498b675c78772fc89cfbcaea1fa/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2I.jpg", "id": 8}, {"expandedImageURL": "/assets/courseware/v1/f3c9ea9074e92352a3ff687974cf6078/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2J.jpg", "widthPercent": "17.3", "imageDescription": "Cl_O+^{'}", "displayName": "", "imageURL": "/assets/courseware/v1/f3c9ea9074e92352a3ff687974cf6078/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2J.jpg", "id": 9}, {"expandedImageURL": "/assets/courseware/v1/a622a210963db709d9feb74c00247eb3/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2K.jpg", "widthPercent": "17.3", "imageDescription": "2Cl_O+^{'}", "displayName": "", "imageURL": "/assets/courseware/v1/a622a210963db709d9feb74c00247eb3/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2K.jpg", "id": 10}, {"expandedImageURL": "/assets/courseware/v1/1eb6a38384d02cc1c3a002fbde6598de/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2L.jpg", "widthPercent": "17.3", "imageDescription": "3Cl_O+^{'}", "displayName": "", "imageURL": "/assets/courseware/v1/1eb6a38384d02cc1c3a002fbde6598de/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2L.jpg", "id": 11}, {"expandedImageURL": "/assets/courseware/v1/1371925000af760242c38236e71d8951/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2M.jpg", "widthPercent": "17.3", "imageDescription": "V_{Ca}^{''}", "displayName": "", "imageURL": "/assets/courseware/v1/1371925000af760242c38236e71d8951/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2M.jpg", "id": 12}, {"expandedImageURL": "/assets/courseware/v1/0d5d60c697f378644fadef8b09b69c40/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2N.jpg", "widthPercent": "17.3", "imageDescription": "2V_{Ca}^{''}", "displayName": "", "imageURL": "/assets/courseware/v1/0d5d60c697f378644fadef8b09b69c40/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2N.jpg", "id": 13}, {"expandedImageURL": "/assets/courseware/v1/ffebf33c061ca77c6af94cd548f7ec4f/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2O.jpg", "widthPercent": "17.3", "imageDescription": "3V_{Ca}^{''}", "displayName": "", "imageURL": "/assets/courseware/v1/ffebf33c061ca77c6af94cd548f7ec4f/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2O.jpg", "id": 14}, {"expandedImageURL": "/assets/courseware/v1/44aa8d26a197e6f607dc9c5e0e7ca1ea/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2P.jpg", "widthPercent": "17.3", "imageDescription": "V_O^{''}", "displayName": "", "imageURL": "/assets/courseware/v1/44aa8d26a197e6f607dc9c5e0e7ca1ea/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2P.jpg", "id": 15}, {"expandedImageURL": "/assets/courseware/v1/c9be4edc0012ab36b6f0c2d3647565d8/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2Q.jpg", "widthPercent": "17.3", "imageDescription": "2V_O^{''}", "displayName": "", "imageURL": "/assets/courseware/v1/c9be4edc0012ab36b6f0c2d3647565d8/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2Q.jpg", "id": 16}, {"expandedImageURL": "/assets/courseware/v1/34dee809a66e01fa44475a8c962c0706/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2R.jpg", "widthPercent": "17.3", "imageDescription": "3V_O^{''}", "displayName": "", "imageURL": "/assets/courseware/v1/34dee809a66e01fa44475a8c962c0706/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Quiz3_P3_2R.jpg", "id": 17}]}
</script>
<div class="themed-xblock xblock--drag-and-drop">
<span class="fa fa-spin fa-spinner initial-load-spinner" aria-hidden="true"></span>
Loading drag and drop problem.
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@vertical+block@1338c6f4c7c441c5ba75219b12f7cbb2" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">Question 3: Slip Systems</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@e9cc58dbbd2542cab317d9c965c69a47">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@e9cc58dbbd2542cab317d9c965c69a47" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_e9cc58dbbd2542cab317d9c965c69a47" class="problems-wrapper" role="group"
aria-labelledby="e9cc58dbbd2542cab317d9c965c69a47-problem-title"
data-problem-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@e9cc58dbbd2542cab317d9c965c69a47" data-url="/courses/course-v1:MITx+3.012S.3x+1T2019/xblock/block-v1:MITx+3.012S.3x+1T2019+type@problem+block@e9cc58dbbd2542cab317d9c965c69a47/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="1"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="e9cc58dbbd2542cab317d9c965c69a47-problem-title" aria-describedby="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@e9cc58dbbd2542cab317d9c965c69a47-problem-progress" tabindex="-1">
Problem 3.1
</h3>
<div class="problem-progress" id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@e9cc58dbbd2542cab317d9c965c69a47-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>You now look at a single crystal sample of \(Al\). It is oriented for a tensile test such tht its slip plane normal makes an angle of \(28.1^{\circ}\) with the tensile axis. Three possible slip directions make angles of \(62.4^{\circ}\), \(72.0^{\circ}\), and \(81.1^{\circ}\) with the same tensile axis. Which of these three slip directions is most favored?</p>
<div class="choicegroup capa_inputtype" id="inputtype_e9cc58dbbd2542cab317d9c965c69a47_2_1">
<fieldset aria-describedby="status_e9cc58dbbd2542cab317d9c965c69a47_2_1">
<div class="field">
<input type="radio" name="input_e9cc58dbbd2542cab317d9c965c69a47_2_1" id="input_e9cc58dbbd2542cab317d9c965c69a47_2_1_choice_0" class="field-input input-radio" value="choice_0"/><label id="e9cc58dbbd2542cab317d9c965c69a47_2_1-choice_0-label" for="input_e9cc58dbbd2542cab317d9c965c69a47_2_1_choice_0" class="response-label field-label label-inline" aria-describedby="status_e9cc58dbbd2542cab317d9c965c69a47_2_1"> \(62.4^{\circ}\) to the tensile axis
</label>
</div>
<div class="field">
<input type="radio" name="input_e9cc58dbbd2542cab317d9c965c69a47_2_1" id="input_e9cc58dbbd2542cab317d9c965c69a47_2_1_choice_1" class="field-input input-radio" value="choice_1"/><label id="e9cc58dbbd2542cab317d9c965c69a47_2_1-choice_1-label" for="input_e9cc58dbbd2542cab317d9c965c69a47_2_1_choice_1" class="response-label field-label label-inline" aria-describedby="status_e9cc58dbbd2542cab317d9c965c69a47_2_1"> \(72.0^{"\circ}\) to the tensile axis
</label>
</div>
<div class="field">
<input type="radio" name="input_e9cc58dbbd2542cab317d9c965c69a47_2_1" id="input_e9cc58dbbd2542cab317d9c965c69a47_2_1_choice_2" class="field-input input-radio" value="choice_2"/><label id="e9cc58dbbd2542cab317d9c965c69a47_2_1-choice_2-label" for="input_e9cc58dbbd2542cab317d9c965c69a47_2_1_choice_2" class="response-label field-label label-inline" aria-describedby="status_e9cc58dbbd2542cab317d9c965c69a47_2_1"> \(81.1^{\circ}\) to the tensile axis
</label>
</div>
<span id="answer_e9cc58dbbd2542cab317d9c965c69a47_2_1"/>
</fieldset>
<div class="indicator-container">
<span class="status unanswered" id="status_e9cc58dbbd2542cab317d9c965c69a47_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
</div>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 3.1" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_e9cc58dbbd2542cab317d9c965c69a47" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_e9cc58dbbd2542cab317d9c965c69a47">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="e9cc58dbbd2542cab317d9c965c69a47-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="e9cc58dbbd2542cab317d9c965c69a47-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="e9cc58dbbd2542cab317d9c965c69a47-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@9e27091932394ccd845945b41eb55eaa">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@9e27091932394ccd845945b41eb55eaa" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_9e27091932394ccd845945b41eb55eaa" class="problems-wrapper" role="group"
aria-labelledby="9e27091932394ccd845945b41eb55eaa-problem-title"
data-problem-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@9e27091932394ccd845945b41eb55eaa" data-url="/courses/course-v1:MITx+3.012S.3x+1T2019/xblock/block-v1:MITx+3.012S.3x+1T2019+type@problem+block@9e27091932394ccd845945b41eb55eaa/handler/xmodule_handler"
data-problem-score="0.0"
data-problem-total-possible="3.0"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="9e27091932394ccd845945b41eb55eaa-problem-title" aria-describedby="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@9e27091932394ccd845945b41eb55eaa-problem-progress" tabindex="-1">
Problem 3.2
</h3>
<div class="problem-progress" id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@9e27091932394ccd845945b41eb55eaa-problem-progress"></div>
<div class="problem">
<div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><p>If plastic deformations begin at a tensile stress of \(1.95 \;MPa\), determine the critical resolved shear stress for the \(Al\) sample in Part 1.</p>
<p>\(\tau_{crss}\) (in \(MPa\)):</p>
<div id="formulaequationinput_9e27091932394ccd845945b41eb55eaa_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<input type="text" name="input_9e27091932394ccd845945b41eb55eaa_2_1" id="input_9e27091932394ccd845945b41eb55eaa_2_1" data-input-id="9e27091932394ccd845945b41eb55eaa_2_1" value="" aria-describedby="status_9e27091932394ccd845945b41eb55eaa_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_9e27091932394ccd845945b41eb55eaa_2_1"/>
<span class="status unanswered" id="status_9e27091932394ccd845945b41eb55eaa_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_9e27091932394ccd845945b41eb55eaa_2_1" class="answer"/>
<div id="input_9e27091932394ccd845945b41eb55eaa_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
</div>
<div class="action">
<input type="hidden" name="problem_id" value="Problem 3.2" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_9e27091932394ccd845945b41eb55eaa" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_9e27091932394ccd845945b41eb55eaa">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="9e27091932394ccd845945b41eb55eaa-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="9e27091932394ccd845945b41eb55eaa-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="9e27091932394ccd845945b41eb55eaa-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@vertical+block@59f6e78b4df84c398787157653a27755" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">Question 4: Dislocations</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@2ed2fb9c0bb84688a32054c09fc46a0d">
<div class="xblock xblock-public_view xblock-public_view-problem xmodule_display xmodule_ProblemBlock" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@2ed2fb9c0bb84688a32054c09fc46a0d" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="problem" data-init="XBlockToXModuleShim" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"xmodule-type": "Problem"}
</script>
<div id="problem_2ed2fb9c0bb84688a32054c09fc46a0d" class="problems-wrapper" role="group"
aria-labelledby="2ed2fb9c0bb84688a32054c09fc46a0d-problem-title"
data-problem-id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@2ed2fb9c0bb84688a32054c09fc46a0d" data-url="/courses/course-v1:MITx+3.012S.3x+1T2019/xblock/block-v1:MITx+3.012S.3x+1T2019+type@problem+block@2ed2fb9c0bb84688a32054c09fc46a0d/handler/xmodule_handler"
data-problem-score="0"
data-problem-total-possible="3"
data-attempts-used="0"
data-content="
<h3 class="hd hd-3 problem-header" id="2ed2fb9c0bb84688a32054c09fc46a0d-problem-title" aria-describedby="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@2ed2fb9c0bb84688a32054c09fc46a0d-problem-progress" tabindex="-1">
Burgers Vector
</h3>
<div class="problem-progress" id="block-v1:MITx+3.012S.3x+1T2019+type@problem+block@2ed2fb9c0bb84688a32054c09fc46a0d-problem-progress"></div>
<div class="problem">
<div>
<p>Calculate the magnitude of the Burgers vector for aluminum, chromium, and iron in Angstroms.</p>
<p>The Burgers vectors typically from in the closest packed directions. For FCC metals, this leads to dislocations of the type,
\[
b = \frac{a}{2} (1,1,0)
\]
BCC metals typically have dislocations of the type
\[
b = \frac{a}{2} (1,1,1)
\]
The lattice constant for aluminum is 4.05 Angstroms; iron is 2.87 Angstroms; chromium is 2.88 Angstroms.
</p>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 1" role="group"><div id="formulaequationinput_2ed2fb9c0bb84688a32054c09fc46a0d_2_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_2ed2fb9c0bb84688a32054c09fc46a0d_2_1" id="label_2ed2fb9c0bb84688a32054c09fc46a0d_2_1">Aluminum (in \(&#197;\))</label>
<input type="text" name="input_2ed2fb9c0bb84688a32054c09fc46a0d_2_1" id="input_2ed2fb9c0bb84688a32054c09fc46a0d_2_1" data-input-id="2ed2fb9c0bb84688a32054c09fc46a0d_2_1" value="" aria-describedby="status_2ed2fb9c0bb84688a32054c09fc46a0d_2_1" size="20"/>
<span class="trailing_text" id="trailing_text_2ed2fb9c0bb84688a32054c09fc46a0d_2_1"/>
<span class="status unanswered" id="status_2ed2fb9c0bb84688a32054c09fc46a0d_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_2ed2fb9c0bb84688a32054c09fc46a0d_2_1" class="answer"/>
<div id="input_2ed2fb9c0bb84688a32054c09fc46a0d_2_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 2" role="group"><div id="formulaequationinput_2ed2fb9c0bb84688a32054c09fc46a0d_3_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_2ed2fb9c0bb84688a32054c09fc46a0d_3_1" id="label_2ed2fb9c0bb84688a32054c09fc46a0d_3_1">Iron (in \(&#197;\))</label>
<input type="text" name="input_2ed2fb9c0bb84688a32054c09fc46a0d_3_1" id="input_2ed2fb9c0bb84688a32054c09fc46a0d_3_1" data-input-id="2ed2fb9c0bb84688a32054c09fc46a0d_3_1" value="" aria-describedby="status_2ed2fb9c0bb84688a32054c09fc46a0d_3_1" size="20"/>
<span class="trailing_text" id="trailing_text_2ed2fb9c0bb84688a32054c09fc46a0d_3_1"/>
<span class="status unanswered" id="status_2ed2fb9c0bb84688a32054c09fc46a0d_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_2ed2fb9c0bb84688a32054c09fc46a0d_3_1" class="answer"/>
<div id="input_2ed2fb9c0bb84688a32054c09fc46a0d_3_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="wrapper-problem-response" tabindex="-1" aria-label="Question 3" role="group"><div id="formulaequationinput_2ed2fb9c0bb84688a32054c09fc46a0d_4_1" class="inputtype formulaequationinput">
<div class="unanswered">
<label class="problem-group-label" for="input_2ed2fb9c0bb84688a32054c09fc46a0d_4_1" id="label_2ed2fb9c0bb84688a32054c09fc46a0d_4_1">Chromium (in \(&#197;\))</label>
<input type="text" name="input_2ed2fb9c0bb84688a32054c09fc46a0d_4_1" id="input_2ed2fb9c0bb84688a32054c09fc46a0d_4_1" data-input-id="2ed2fb9c0bb84688a32054c09fc46a0d_4_1" value="" aria-describedby="status_2ed2fb9c0bb84688a32054c09fc46a0d_4_1" size="20"/>
<span class="trailing_text" id="trailing_text_2ed2fb9c0bb84688a32054c09fc46a0d_4_1"/>
<span class="status unanswered" id="status_2ed2fb9c0bb84688a32054c09fc46a0d_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_2ed2fb9c0bb84688a32054c09fc46a0d_4_1" class="answer"/>
<div id="input_2ed2fb9c0bb84688a32054c09fc46a0d_4_1_preview" class="equation">
\(\)
<img src="/static/images/spinner.bc34f953403f.gif" class="loading" alt="Loading"/>
</div>
</div>
<div class="script_placeholder" data-src="/static/js/capa/src/formula_equation_preview.b1967ab28c31.js"/>
</div></div>
<div class="solution-span">
<span id="solution_2ed2fb9c0bb84688a32054c09fc46a0d_solution_1"/>
</div></div>
<div class="action">
<input type="hidden" name="problem_id" value="Burgers Vector" />
<div class="submit-attempt-container">
<button type="button" class="submit btn-brand" data-submitting="Submitting" data-value="Submit" data-should-enable-submit-button="True" aria-describedby="submission_feedback_2ed2fb9c0bb84688a32054c09fc46a0d" >
<span class="submit-label">Submit</span>
</button>
<div class="submission-feedback" id="submission_feedback_2ed2fb9c0bb84688a32054c09fc46a0d">
<span class="sr">Some problems have options such as save, reset, hints, or show answer. These options follow the Submit button.</span>
</div>
</div>
<div class="problem-action-buttons-wrapper">
</div>
</div>
<div class="notification warning notification-gentle-alert
is-hidden"
tabindex="-1">
<span class="icon fa fa-exclamation-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="2ed2fb9c0bb84688a32054c09fc46a0d-problem-title">
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification warning notification-save
is-hidden"
tabindex="-1">
<span class="icon fa fa-save" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="2ed2fb9c0bb84688a32054c09fc46a0d-problem-title">None
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
<div class="notification general notification-show-answer
is-hidden"
tabindex="-1">
<span class="icon fa fa-info-circle" aria-hidden="true"></span>
<span class="notification-message" aria-describedby="2ed2fb9c0bb84688a32054c09fc46a0d-problem-title">Answers are displayed within the problem
</span>
<div class="notification-btn-wrapper">
<button type="button" class="btn btn-default btn-small notification-btn review-btn sr">Review</button>
</div>
</div>
</div>
"
data-graded="True">
<p class="loading-spinner">
<i class="fa fa-spinner fa-pulse fa-2x fa-fw"></i>
<span class="sr">Loading…</span>
</p>
</div>
</div>
</div>
</div>
</div>
<div class="xblock xblock-public_view xblock-public_view-vertical" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@vertical+block@459cc13854274b31883642f512134c60" data-graded="True" data-has-score="False" data-runtime-version="1" data-block-type="vertical" data-init="VerticalStudentView" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<h2 class="hd hd-2 unit-title">Question 5: Liquid Crystals</h2>
<div class="vert-mod">
<div class="vert vert-0" data-id="block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@f85af8ceeb62413aa75e498afc3d17cc">
<div class="xblock xblock-public_view xblock-public_view-drag-and-drop-v2" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@f85af8ceeb62413aa75e498afc3d17cc" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="drag-and-drop-v2" data-init="DragAndDropBlock" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"problem_text": "A solution of rod-shaped mesogens is found to exhibit four different structural states on cooling: isotropic liquid, nematic liquid crystal, smectic liquid crystal, and crystalline solid. Rank the degree of translational order that characterize each of these four states.", "display_name": "Question 5A", "target_img_expanded_url": "/assets/courseware/v1/3366f9d104034fbea99e3dfb66479941/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Final_5A.jpg", "url_name": "f85af8ceeb62413aa75e498afc3d17cc", "show_title": true, "display_zone_borders": false, "type": "drag-and-drop-v2", "weight": 1.0, "display_zone_labels": false, "has_deadline_passed": false, "max_attempts": 0, "target_img_description": "Four zones that represent increasing translational order.", "block_id": "block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@f85af8ceeb62413aa75e498afc3d17cc", "title": "Question 5A", "item_text_color": "white", "weighted_max_score": 1.0, "max_items_per_zone": 1, "mode": "assessment", "graded": true, "show_problem_header": true, "is_anonymous_user": true, "zones": [{"height": "100", "align": "center", "title": "Highest translational order", "width": "263", "x": "85", "y": "38", "uid": "top", "description": "Zone representing the highest translational order"}, {"height": "95", "align": "center", "title": "Second-highest translational order", "width": "263", "x": "85", "y": "138", "uid": "zone-1", "description": "Zone representing second-highest translational order"}, {"height": "90", "align": "center", "title": "Second-lowest translational order", "width": "263", "x": "85", "y": "229", "uid": "zone-2", "description": "Zone representing the second-lowest translational order"}, {"height": "95", "align": "center", "title": "Lowest translational order", "width": "263", "x": "85", "y": "329", "uid": "zone-3", "description": "Zone representing the lowest translational order"}], "item_background_color": "orange", "items": [{"expandedImageURL": "", "imageDescription": "", "imageURL": "", "displayName": "Isotropic liquid", "id": 0}, {"expandedImageURL": "", "imageDescription": "", "imageURL": "", "displayName": "Nematic liquid crystal", "id": 1}, {"expandedImageURL": "", "imageDescription": "", "imageURL": "", "displayName": "Crystalline solid", "id": 2}, {"expandedImageURL": "", "imageDescription": "", "imageURL": "", "displayName": "Smectic liquid cyrstal", "id": 3}]}
</script>
<div class="themed-xblock xblock--drag-and-drop">
<span class="fa fa-spin fa-spinner initial-load-spinner" aria-hidden="true"></span>
Loading drag and drop problem.
</div>
</div>
</div>
<div class="vert vert-1" data-id="block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@9ff0d189946a47528203e87b8d258e53">
<div class="xblock xblock-public_view xblock-public_view-drag-and-drop-v2" data-request-token="0ae295a8e99f11efb7c70e0e3c45b88f" data-usage-id="block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@9ff0d189946a47528203e87b8d258e53" data-graded="True" data-has-score="True" data-runtime-version="1" data-block-type="drag-and-drop-v2" data-init="DragAndDropBlock" data-course-id="course-v1:MITx+3.012S.3x+1T2019" data-runtime-class="LmsRuntime">
<script type="json/xblock-args" class="xblock-json-init-args">
{"problem_text": " Rank the degree of rotational order that characterize each of the states below.", "display_name": "Question 5B", "target_img_expanded_url": "/assets/courseware/v1/7c800ddf3653c3ec4b4c8231cd5b3288/asset-v1:MITx+3.012S.3x+1T2019+type@asset+block/3012_Final5B.jpg", "url_name": "9ff0d189946a47528203e87b8d258e53", "show_title": true, "display_zone_borders": false, "type": "drag-and-drop-v2", "weight": 1.0, "display_zone_labels": false, "has_deadline_passed": false, "max_attempts": 0, "target_img_description": "Four zones that represent increasing rotational order.", "block_id": "block-v1:MITx+3.012S.3x+1T2019+type@drag-and-drop-v2+block@9ff0d189946a47528203e87b8d258e53", "title": "Question 5B", "item_text_color": "white", "weighted_max_score": 1.0, "max_items_per_zone": 1, "mode": "assessment", "graded": true, "show_problem_header": true, "is_anonymous_user": true, "zones": [{"height": "135", "align": "center", "title": "Highest rotational", "width": "263", "x": "85", "y": "38", "uid": "top", "description": "Zone representing the highest rotational order"}, {"height": "130", "align": "center", "title": "Second-highest rotational order", "width": "263", "x": "85", "y": "173", "uid": "zone-1", "description": "Zone representing second-highest rotational order"}, {"height": "130", "align": "center", "title": "Lowest rotational order", "width": "263", "x": "85", "y": "300", "uid": "zone-2", "description": "Zone representing lowest rotational order"}], "item_background_color": "orange", "items": [{"expandedImageURL": "", "imageDescription": "", "imageURL": "", "displayName": "Isotropic liquid", "id": 0}, {"expandedImageURL": "", "imageDescription": "", "imageURL": "", "displayName": "Liquid crystal", "id": 1}, {"expandedImageURL": "", "imageDescription": "", "imageURL": "", "displayName": "Crystalline solid", "id": 2}]}
</script>
<div class="themed-xblock xblock--drag-and-drop">
<span class="fa fa-spin fa-spinner initial-load-spinner" aria-hidden="true"></span>
Loading drag and drop problem.
</div>
</div>
</div>
</div>
</div>
© All Rights Reserved