Physical Chemistry – The Solid State – Cubic Crystals – Face Corners, Edge ,Diagonal, center- part-5.<\/p>\n
[fvplayer id=”777″]<\/p>\n
In solid-state chemistry<\/strong>, cubic crystals are a key concept in understanding crystal structures. Let’s break down the important elements: Face, Corners, Edges, Diagonal, and Center<\/strong> in cubic crystals.<\/p>\n Cubic crystals exist in three main forms<\/strong>: Important:<\/strong> The number of atoms per unit cell differs for each type: Total corner atoms in a unit cell =<\/strong><\/p>\n 8\u00d718=18 \\times \\frac{1}{8} = 1<\/span>8<\/span>\u00d7<\/span><\/span>81<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>1<\/span><\/span><\/span><\/span><\/span><\/p>\n Total face atoms in FCC unit cell =<\/strong><\/p>\n 6\u00d712=36 \\times \\frac{1}{2} = 3<\/span>6<\/span>\u00d7<\/span><\/span>21<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/p>\n Total edge atoms =<\/strong><\/p>\n 12\u00d714=312 \\times \\frac{1}{4} = 3<\/span>12<\/span>\u00d7<\/span><\/span>41<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>3<\/span><\/span><\/span><\/span><\/span><\/p>\n Where a = edge length of the cube<\/strong><\/p>\n Used in calculating atomic radius (r)<\/strong> Total atoms in BCC unit cell =<\/strong><\/p>\n 1(corner\u00a0atoms)+1(body-centered\u00a0atom)=21 (\\text{corner atoms}) + 1 (\\text{body-centered atom}) = 2<\/span>1<\/span>(<\/span>corner\u00a0atoms<\/span><\/span>)<\/span>+<\/span><\/span>1<\/span>(<\/span>body-centered\u00a0atom<\/span><\/span>\u00a01. Types of Cubic Crystals<\/strong><\/h3>\n
1\ufe0f\u20e3 Simple Cubic (SC)<\/strong> \u2013 Atoms at corners only
2\ufe0f\u20e3 Body-Centered Cubic (BCC)<\/strong> \u2013 Atoms at corners + one atom at the center
3\ufe0f\u20e3 Face-Centered Cubic (FCC)<\/strong> \u2013 Atoms at corners + one atom at the center of each face<\/p>\n
SC:<\/strong> 1 atom
BCC:<\/strong> 2 atoms
FCC:<\/strong> 4 atoms<\/p>\n\u00a02. Face, Corners, Edge, Diagonal, and Center in Cubic Crystals<\/strong><\/h3>\n
\u00a0(A) Corners<\/strong><\/h3>\n
\n
\u00a0(B) Faces<\/strong><\/h3>\n
\n
\u00a0(C) Edges<\/strong><\/h3>\n
\n
\u00a0(D) Diagonal<\/strong><\/h3>\n
\n
\u2714 SC:<\/strong> r=a2r = \\frac{a}{2}<\/span>r<\/span>=<\/span><\/span>2<\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\u2714 BCC:<\/strong> r=3a4r = \\frac{\\sqrt{3}a}{4}<\/span>r<\/span>=<\/span><\/span>4<\/span><\/span>3<\/span>\u200b<\/span><\/span>a<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>
\u2714 FCC:<\/strong> r=2a4r = \\frac{\\sqrt{2}a}{4}<\/span>r<\/span>=<\/span><\/span>4<\/span><\/span>2<\/span>\u200b<\/span><\/span>a<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n\u00a0(E) Center<\/strong><\/h3>\n
\n