The Linear Density for BCC [110] direction formula is defined as the number of atoms per unit length of the direction vector is calculated using linear_density = 0.306/ Radius of Constituent Particle.To calculate Linear Density for BCC [110] direction, you need Radius of Constituent Particle (R).With our tool, you need to enter the respective value for Radius of Constituent Particle and hit. * Calculate the planar density of the (110) plane of a BCC unit cell*. 2. Calculate the planar density of the (110) plane of a FCC unit cell. 3. Calculate the planar density of the (111) plane of a SC unit cell. 4. Calculate the planar density of the (111) plane of a BCC unit cel

- #potentialg #gatephysics #csirnetjrfphysics In this video we will discuss about Planer density ,number of atoms ,Sc Bcc Fcc for (100) (110) (111) planes and.
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- (a) derive planar density expressions for BCC (100) and (110) planes interms of the atomic radius R. (b) Compute and compare planardensity values for these same two planes for molybdenum
- (b) Compare planar densities (Problem 3.55) for the (100), (110), and (111) planes for BCC. Solution (a) For the FCC crystal structure, the planar density for the (110) plane is given in Equation 3.11 as PD110(FCC)= 1 4R22 = 0.177 R2 Furthermore, the planar densities of the (100) and (111) planes are calculated in Homework Problem 3.54
- e the planar density (atoms/nm2) in terms of atomic radius R. (c) Out of the {100}, {110}, and {111} direction families, which direction families fall within the plane? PD[Natoms_,Aplane_]:=Natoms/Aplane; aBCC=4*r/Sqrt[3]; (100) (a) See sol'n 1 (1 pt) (b) (1 pt.
- (0 1 0) plane for BCC and Planar Density x z y Body-centered Cubic Crystal Structure (BCC) = # = 1 4 + 1 4 + 1 4 + 1 4 2 = 1 4 3 2= 3 162 1 4 1 4 1 4 1 4

- 3.53 (a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R. (b) Compute and compare linear density values for these same two directions for tungsten. Solution (a) In the figure below is shown a [110] direction within a BCC unit cell
- Calculate the planar density of {110} planes in a-Fe (BCC) crystal. a = 0.287 nm. Crystallographic Planes And Planar Density: Crystallography is the study of crystalline solids and their cell..
- 1 Answer to (a) Derive planar density expressions for BCC (100) and (110) planes in terms of the atomic radius R. (b) Compute and compare planar density values for these same two planes for vanadium
- planar density BCC <111> NO, but {110} has highest planar density FCC <110> {111} Chapter 3 - Close Packed Direction & Planes of Highest Planar Density in Cubic Crystals 8 y x y y x x z z z Simple Cubic BCC FCC Close Packed Direction <100> Plane with Highest Planar Density
- What is Planar Density for FCC (110) plane? The Planar Density for FCC (110) plane formula is defined as number of atoms per unit area that are centered on a particular crystallographic plane and is represented as P.D = 0.177/ (R^2) or planar_density = 0.177/ (Radius of Constituent Particle^2)
- e the planar density and packing fraction for BCC lithium in the (100), (110), and (111) planes. Which, if any, of these planes are close packed
- Answer to: Calculate the numerical planar density for a BCC crystal structure in the {100}, {110}, and {111} planes. By signing up, you'll get..

Hence, the planar density for this (100) plane is 100 = No. of atoms centered on (100)plane Area of (100)plane = 1 atom 162/3 = 3 162 A BCC (110) plane is shown in the figure. (x = a, y= √2 a n= 2 atoms, area = a √2 a = √2 (√3)2 = 16√2 2 3 Thus, the planar density is 110 = No. of atoms centered on (110)plane Area of (110)plane = 2 atoms 16√22/3 = 3 8√22 (b) Given that the atomic radius of vanadium is 0.132 nm Linear density (example) a [110] Linear density of Al in [110] direction a = 0.405 nm # atoms length 3.5 nm 1 2a 2 LD = − Planar Density of (100) Iron Solution: At T < 912°C iron has the BCC structure. (100) Radius of iron R = 0.1241 nm R 3 4 3 a = Adapted from Fig. 3.2(c), Callister 7e. 2D repeat unit Planar Density = = a2 1 atoms 2D repeat. * P 3*.53 (a): Linear Density for BCC Calculate the linear density for the following directions in terms of R: [100] [110] [111] * Planar Density of (100) Iron Solution: At T < 912ºC iron has the BCC structure. (100) Radius of iron R = 0.1241 nm R 3 3 4 a = Adapted from Fig. 3.2(c), Callister & Rethwisch 8e. 2D repeat unit = Planar Density = a 2.

Calculate the planar density for the (110) plane in (bcc) Fe. The lattice parameter for this structure is 0.124 nm Hence, the **planar** **density** for this (100) plane is just A **BCC** unit cell within which is drawn a **(110)** plane is shown below. For this **(110)** plane there is one atom at each of the four cube corners through which it passes, each of which is shared with four adjacent unit cells, while the center atom lies entirely within the unit cell

** In-Class Exercise 2: Determine planar density and packing fraction**. Determine the planar density and packing fraction for BCC lithium in the (100), (110), and the (111) planes. Which, if any, of these planes is close packed? 24. Solution for plane (100) First, find atomic radius for Nickel from Appendix 2, page 797 of Textbook (6th Ed 1 Answer to (a) derive planar density expressions for BCC (100) and (110) planes interms of the atomic radius R.(b) Compute and compare planar density values for these same two planes for molybdenum 3.73 Calculate the planar atomic density in atoms per square millimeter for the following crystal planes in BCC chromium, which has a lattice constant of 0.28846 nm: (a) (100), (b) (110), (c) (111). (a) (b) (c) a a a Smith Foundations of Materials Science and Engineering Solution Manual 4 a) Derive planar density expressions for BCC (100) and (110) planes in terms of the atomic radius R. (b) Compute and compare planar density values for these same two planes for vanadium. View Answer In terms of the factors that determine market liquidity, why do investors consider real estate to be a relatively illiquid asset

Planar density Planar density = # of atoms/area of plane Planar density of (110) for BCC Iron? Radius of iron R = 0.1241 nm Q1. Determine the Planar Density of (110) for BCC Iron ? A. 1.7 x 10 18 atoms/m 2 B. 2.7 x 10 18 atoms/m 2 C. 1.7 x 10 19 atoms/m 2 D. 2.7 x 10 19 atoms/m Fig.2b shows the atomic arrangement of {110} planes in a BCC structure which are the planes of highest atomic density. There are 6 planes of this type, and each contains two close packed directions. Consideration of fig. 1b and 2b shows the closed packed direction joins diagonally opposite corners of the BCC unit cell

a) Derive planar density expressions for BCC (100) and (110) planes in terms of the atomic radius R. (b) Compute and compare planar density values for these same two planes for vanadium. View Answer Inter planar separation consider a plane hkl in a crystal lattice Planar density, atoms per area To do this you should draw the plane an FCC would make from (1, 1, 0) in a 111 cube. When you draw this you will see that for the FCC structure, that each of the. an BCC (110) plane . Chapter 3 - Atomic arrangements • Atomic planar density: number of atoms centered on a plane/area of plane • Linear Density of Atoms ≡ LD = Unit length of direction vector Number of atoms Planar Density = #atoms Area(2D repeat unit) Chapter 3 - 1 Derive planar density expressions for BCC (110) planes in terms of the atomic radius For this (110) plane there is one atom at each of the four cube corners through which it passes, each of which is shared with four adjacent unit cells, while the center atom lies entirely within the unit cell Determine The Planar Density Of (110) In A BCC Crystal, Then Compare This Value With The Planar Density Of (111) Plane In The FCC Crystal. Assume Same Atomic Radius In Both Crystal Structures. What is weight per unit length? The mass per unit length is the linear density of a one-dimensional substance such as a wire or thread

Solved: (a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R. (b) Compute and compare linear density values for these same two directions for iron (Fe). - Slade Chegg.com Calculate the planar density of the (110) plane of a BCC unit cell. 2. Calculate the planar density of the (110) plane of a FCC unit cell. 3. Calculate the planar density of the (111) plane of a SC unit cell. 4. Calculate the planar density of the (111) plane of a BCC unit cell

Calcualte the number of atoms per unit area in an Iron crystal on the (111), (110) and (100) planes. Fe is bcc and the lattice parameter of Fe is 2.87 Å. Hence, the number of atoms per unit area of the (100), (110) and (111) planes of Fe are 7 ××10 18, 1.72×1019 and 1.21 ×10 19 First of all please do not use Diamond lattice we should call it Diamond Cubic crystal structure (Lattice of this structure is FCC). Within the unit cell atoms sit on corners, face centres and four extra atoms, one each on each body diagonals. I.. a) Derive linear density expression for BCC [110] direction in terms of the atomic radius R. Compute linear density value for the same direction for tungsten. In the figure below is shown a [110] direction within a BCC unit cell. For this [110] direction there is one atom at each of the two unit cell corners, and, thus, there is the equivalenc Hence, the planar density for this (100) plane is just PD 100 = number of atoms centered on (100) plane. area of (100) plane 1 atom. 16 R 2 3 3 16 R 2 A BCC unit cell within which is drawn a (110) plane is shown below. For this (110) plane there is one atom at each of the four cube corners throug

The planar atomic density of (110) plane in Al with lattice parameter 0.423 nm. (Al is FCC). 7.90 atom/nm2 - DO CALCULATION. The linear atomic density of [110] direction in a BCC unit cell, with atomic radius R = 0.132 nm is; (In BCC atom touch along [111] direction. 2.32 atom/nm - DO CALCULATION solution to Problem 3.55, the planar densities for BCC (100) and (110) are 3 16 R2 and 3 8R2 2, respectively—that is 0.19 R2 and 0.27 R2. Thus, since the planar density for (110) is greater, it will have the lower surface energy. 4.33 (a) Employing the intercept technique, determine the average grain size for the steel specimen whos Packing fraction = Linear **density** x 2 r = 3.91 x 2 x 0.12781 = 1.0 . In FCC, [**110**] is the close packed direction and atoms touch each other. Problem 2: Simple cubic polonium has lattice parameter, 0.334 nm. Calculate the **planar** **density** and **planar** packing fraction for (010) and (020) planes. Solution: Both planes are shown this BCC (100) plane. The planar section represented in the above figure is a square, wherein the side lengths are equal to the unit cell edge length, √ and, thus, Area of this square is just √ = . Hence, the planar density for this (100) plane is just = = = A BCC unit cell within which is drawn a (110) plane is shown below For each of these three alloys we need, by trial and error, to calculate the density using Equation 4.8, and compare it to the value cited in the problem. For SC, BCC, and FCC crystal structures, the respective values of n are 1, 2, and 34, whereas the expressions for a (since V C = a) are 2R, 2 R, and 3 4R

Packing Density When the lattice points are inflated gradually, at some point they start to touch each other along the diagonals of the cube. One can now interpret the atoms as close packed spheres with a radius defined geometrically by ${4r = \sqrt{3}a}$ ${\Leftrightarrow \; r = \frac{\sqrt{3}}{4}a}$ b 1 b 2 b 3 A A A A A A C B C C B B Face Centered Cubic Slip Systems FCC (eg. Cu, Ag, Au, Al, and Ni) Slip Planes {111} Slip Directions [110] The shortest lattice vectors are ½[110] and [001] According to Frank's rule, the energy of a dislocation is proportional to the square of th highest atomic planar density Slip directions: <110> direction family in FCC possesses the highest atomic density {111}: eight octahedral planes in a cube, only 4 of them need to be considered (the other 4 are parallel planes). <110>: total six, but, only three lie in each of the {111} slip plane. Ex: (111) slip plane contains the [011], [101.

the planar density and packing fraction for BCC lithium in the (100), (110), and (111) planes. Which, if any, of these planes are close packed? 2. Suppose that FCC rhodium is produced as a 1 mm-thick sheet, with the (111) plane parallel to the surface of the sheet • What is the total area of atoms that lie on the (110) plane? • The planar density is defined as PD= # atoms with their center in the plane / Area of plane (i.e. 2D repeat unit) BCC (110) Plane. Book Section 3.11. Chapter 3 - 15 Slip System - Slip plane - plane on which easiest slippage occur ** 3**.59 (a) Derive planar density expressions for BCC (100) and (110) planes in terms of the atomic radius R. (b) Compute and compare planar density values for these same two planes for vanadium (V).** 3**.64 Using the data for aluminum in Table** 3**.1, compute the interplanar spacing f or the (110) and (221) set of planes

linear density = = ××-10 1 atom 1 a2 5.08 10 2 = 1.39 x 109 atoms/m Problem #4 For aluminum at 300K, calculate the planar packing fraction (fractional area occupied by atoms) of the (110) plane and the linear packing density (atoms/cm) of the [100] direction. Solution Aluminum at 300K has FCC structure: Volume unit of a cell: ×× × 3 2 It is the closest pack plane in the BCC, but it is not as closely packed as it is in the FCC. It turns out that there are a total of three different types of planes where you can have slip in body-centered cubic. So for example, we'eve been describing slip in the (110) plane on the (110) plane in the <111> direction Example: linear density of Al in [110] direction a = 0.405 nm Linear Density of Atoms LD= a [110] Unit length of direction vector Number of atoms centered on direction vector # atoms length 3.5 nm 1 2a 2 LD = =-Recall: Linear and Planar Densities Planar Density of Atoms PD = Area of plane (001) 7 Number of atoms centered on a plan • Rare due to poor packing (only Po [84] has this structure) • Close-packed directions are cube edges. Coordination number = 6 Simple Cubic (SC) Structure •Coordination number is the number of nearest neighbors •Linear density (LD) is the number of atoms per unit length along a specific crystallographic direction a1 a2 a3 . . . L * The areal fraction (area occupied by atoms: area of the plane) of the (111) plane in BCC crystal is 3 /16 = 0*.34 (→ taking into account the atoms whose centre of mass lie on the (111) plane). However the (111) plane partially intersects the atom in the body centre position (as shown in the figure below)

The planar density (=1/(2sqrt3 r²) in the (111) plane of FCC is higher than the densest packed plane (110) in the BCC structure. What is the distinction between the structure of a liquid and a crystalline solid BCC (100) and (110) planes in terms of the atomic radius R. (b) Compute and compare planar density val- ues for these same two planes for molybdenum. 3.55 (a) Derive the planar density expression for the HCP (0001) plane in terms of the atomic radius R. (b) Compute the planar density value for this same plane for titanium. Polycrystalline Material Planar Atomic Density Formula planar atomic density: 40 p = Equivalent number of atoms whose centers are intersected by selected area Selected area 41. Example:In Iron (BCC, a=0.287 nm), the (110) plane intersects center of 5 atoms (four ¼ and 1 full atom). Calculate the planar atomic density. 41 42

density (Section 3.11)]—that is, the higher the packing density, the greater the number of nearest-neighbor atoms, and the more atomic bonds in that plane that are satisfied, and, consequently, the lower the surface energy. From the solution to Problem 3.54, the planar densities for BCC (100) and (110) are 3 16R2 and 3 8R2 2, respectively. The 100 plane of an FCC structure is the plane of the unit cell in the zy direction. This face has 1 whole face atom and 4*1/4 corner atoms = 2 atoms. The unit cell length of an FCC structure in. Calculate the planar density of atoms on each of the planes in problem 1. (Use units of atoms/nm 2 .) Answer: The (111) in the unit cube is an equilateral triangle whose area is This area contains two atoms since the 3 atoms in the centers of the edges are each shared between two triangles and the 3 corner atoms are each shared between 6 triangles Correct answer to the question (a) Calculate planar densities for the (100), (110), and (111) planes for FCC. (b) Calculate planar densities for the (100) and (110) planes for BCC. (a) (100) plane (FCC) planar density - e-eduanswers.co Solved: 1.Calculate The Planar Density Of The (110) Plane Chegg.com Calculate the planar density of the (110) plane of a BCC unit cell. 2. Calculate the planar density of the (110) plane of a FCC unit cell. 3. Calculate the planar density of the (111) plane of a SC unit cell. 4. Calculate the planar density of the (111) plane of a BCC unit cel

Get the detailed answer: Determine the planar density and packing fraction for BCC lithium in the (100), (110), and (111) planes. Which, if any, of these And, thus, the planar density is Of plane arca of (l I l) planc 2 That portion of an FCC (1 1 1) plane contained within a unit cell is shown . Author: Concordia university Created Date * Linear and Planar Densities 3*.80 (a) Derive linear density expressions for FCC [100] and [111] directions in terms of the atomic radius R. (b) Compute and compare linear density values for these same two directions for copper (Cu). 3.81 (a) Derive linear density expressions for BCC [110] and [111] directions in terms of the atomic radius R. (b. Linear and Planar Densities 3.52 (a) Derive linear density expressions for FCC [100] and [111] directions in terms of the atomic radius R. 11120 211101 2 (001) 0.30 nm 0 .4 0 n m (110) 0.35 nm 0 .5 0 n m (101) 0.40 nm 0 .4 6 n m (a) To what crystal system does the unit cell belong? (b) What would this crystal structure be called

e.g. Pure iron has a BCC crystal structure at room temperature which changes to FCC at 912 C. [110] •A direction and its multiple is identical, [100] is identical to Calculate the planar density and planar packing factor 1/4 1/4 1/4 1/4 1 a Planar density is the number of atoms centered on a plane, divided by the area of that plane. (0001) in HCP is a close-packed plane in which every atom is surrounded by (and touching) six neighbors. Their centers therefore create a hexagon whose sides are each of length 2R. The six surrounding neighbors each contribute 2/6 of their area to the.

(a) Compare planar densities (Section 3.11 and Problem 3.53 ) for the (100),(110), and (111) planes for FCC. (b) Compare planar densities (Problem 3.54 ) for t Join our Discord to get your questions answered by experts, meet other students and be entered to win a PS5 Therefore, the linear density is equal toLD 110 = number of atoms centered on [110] direction vector length of [110] direction vector = 1 atom 4 R 2 3 = 3 4 R 2 A BCC unit cell within which is drawn a [111] direction is shown below formation is 1.08 eV/atom. Furthermore, the density and atomic weight for Fe are 7.65 g/cm3 and 55.85 g/mol, respectively. e. Calculate the linear density for the [110] direction, and the planar density for the (110) plane for BCC unit cell. f. Differentiate between the different types of cast iron. g. State the types of diffusion mechanism • What is the area of the (110) plane in terms of the atomic radius? • What is the total area of atoms that lie on the (110) plane? • The planar density is defined as PD= # atoms with their center in the plane / Area of plane (i.e. 2D repeat unit) • Concept Check - What is the PD for (110) in a SC unit cell?

Contributors and Attributions; A number of important metals ( e.g. Fe, W, Mo ) have the bcc structure. As a result of the low packing density of the bulk structure, the surfaces also tend to be of a rather open nature with surface atoms often exhibiting rather low coordination numbers Planar density of hcp structure of Cr2N at different orientations I am trying to calculate which orientation from 110, 111 and 113 has higher planar density in case of Cr2N Atomi

Crystallographic planes that are equivalent have the same atomic planar density. The plane of interest is positioned so as to pass through atom centers. Planar density is the fraction of total crystallographic plane area that is occupied by atoms. Linear and planar densities are one- and two-dimensional analogs of the atomic packing factor 1) Planar density ot (110) plane in BCC lattice is 16v'9 No, the answer is incorrect. Score: O Accepted Answers: 1 point 1 point 1 point 1 point 1 point 1 point 1 point 1 point 1 point 1 point 1 point 2) In a BCC lattice, arrange the planes (100), (110) and (111) in the descending order as per their planar density. (110) > (111) > (100

planar atomic density equiv. no. of atoms whose centers are intersected by selected area ρp = ———————————— selected area ex. calculate planar atomic density ρp on (110) plane of the α-Fe in BCC lattice in atoms/mm2. (lattice constant a = 0.287 nm The planar density of the (112) plane in BCC iron is 9.94 x 1014 atoms/cm2. Calculate (l) the planar density of the (110) plane and (2) the interplanar spacings for both the (112) and (110) planes Planar Atomic Density • Planar atomic density= • Example:- In Iron (BCC, a=0.287), The (110) plane intersects center of 5 atoms (Four ¼ and 1 full atom). ¾Equivalent number of atoms = (4 x ¼ ) + 1 = 2 atoms Area of 110 plane = ρ p Equivalent number of atoms whose centers are intersected by selected area Selected area ρ p 2()0.287 2 2. that V has a BCC crystal structure, a density of 5.96 g/cm3, and an atomic weight of 50.9 g/mol Derive linear density expressions for BCC [110] and [111] Q10. (a) Derive planar density expressions for FCC (100) and (111) planes in terms of the atomic radius R. (b) Compute and compare planar density values for these same two planes for. And, finally, the planar density for this (111) plane is PD111(BCC) = 0.5 atom 8R2 3 = 3 16R2 = 0.11 R2 8.7 Below is shown the atomic packing for a BCC {110} type plane. The arrows indicate two different <111> type directions. 8.8 Below is shown the atomic packing for an HCP {0001} type plane. The arrows indicate three different <112 0 > type.

110 = (d 110,sc) = 2 a d 111 = 21 (d 111,sc) = 2 3 and d 100: d 110: d 111= 1: 2: 3 1 For bcc d 100 = 21 (d 100,sc) = 2 a a d 110 = (d 110,sc) = 2 ad 111 = 21 (d 111,sc) = 2 3 and d 100: d 110: d 111= 1: 1 2: 3 2 Ex: Determine the Miller Indices of a plane which is parallel to x-axis and cuts intercepts of 2 and 2 1. * Determine the planar the (111) plane of FCC structure*. (a) 0.1743 x 1015 points/cm 2 What is the theoretical density (tuv) and linear density ((twx) along [110] of Cr. Assume transformationin a pure metal from the FCC to BCC crystal structure. Assume the hard

BCC crystals have 48 slip systems but only 5 are independent (5 is the minimum requirement for ductility). However, the 5 independent slip systems may not be activated at all temperatures, so some BCC metals are ductile while others are brittle. The 48 BCC slip systems are {110}<111>, {112}<111>, and {123}<111> in order of ease of activation The surface energy for a crystallographic plane will depend on its packing density [i.e., the planar density (Section 3.11)]—that is, the higher the packing density, the greater the number of nearest-neighbor atoms, and the more atomic bonds in that plane that are satisfied, and, consequently, the lower the surface energy

So both FCC and BCC have the highest possible. For FCC this is the <110> family of directions and for BCC it is the <111> family Any plane that contains the hex arrangement (bot h HCP and FCC do) is the highest possible planer density. BCC does not have this sort of arrangement. Therefore, the greatest planer density in FCC is greater. APF of BCC • APF for a body-centered cubic structure = 0.68 Close-packed directions: length = 4R = 3 a Unit cell contains: 1 + 8 x 1/8 = 2 atoms/unit cell APF = a3 4 3 • Planar Density PD = number of atoms centered on a plane area of plane. Materials Scienc9 3 1 r e t p a h eC X-ray Diffraction Diffraction Phenomeno

Formation of a dense and planar Li metal anode with preferential growth along the (110) facet is explained by the lattice matching between Ti 3 C 2 T x and hcp‐Li and then with bcc‐Li, as well as preferred thermodynamic factors including the large dendrite formation energy and small migration barrier for Li 110 Figure 3.26 Notation for lattice positions. 121 . Atomic Planar density, PD (number of atoms/unit area) Slip plane (more later) Calculate PD if cube is BCC Chapter 3- Calculate PD if is FCC Chapter 3- Atomic Volume density, VD — Calculate VD if cube is BCC (number of atoms/unit volume) Chapter 3- Atomic Volume density, VD Volume dencity of bcc is 2/a³ (that is two atoms per cell a³) Planar density of each layer = (volume density) * (thickeness of (111) planes) = 2√3 / a² 0 Calculate the radius of one atom, given the density of Mo is 10.28 g /cm 3. Solution: 1) Determine mass of two atoms in a bcc cell: 95.96 g/mol / 6.022 x 10 23 mol¯ 1 = 1.59349 x 10¯ 22 g (this is the average mass of one atom of Mo) (2) (1.59349 x 10¯ 22 g) = 3.18698 x 10¯ 22 g. 2) Determine the volume of the unit cell

The planar density (PD) is the number of atoms per unit area measured in reciprocal area (e.g. m^-2 or radius ^ -2), where PD = (number of atoms centered on a plane) / (area of plane). For the FCC unit cell, calculate PD for the (100), (110), or (111) plane in terms of the atom radius r 1 pt Natoms, 1 pt Aplane answer (100) (110) (111 The (110) planes are not necessarily (220) planes! For cubic crystals: Miller Indices provide you easy measure of distance between planes. d110 = a 1 2+1 +02 = a 2 = a 2 2 Distance between (110) planes MSE 280: Introduction to Engineering Materials ©D.D. Johnson 2004, 2006-08 Directions in HCP Crystals 1. To emphasize that they are equal, a. Planar density is the atomic area per plane area where the plane must pass through an atom's center for that particular atom to be included. The calculations of linear density for [100], [110] and [111] directions and planar density for (100), (110) and (111) planes are shown