2D Lattice Direction for Lattice Points Solution

STEP 0: Pre-Calculation Summary
Formula Used
Lattice Direction = (X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b)
r = (u*alattice)+(v*b)
This formula uses 5 Variables
Variables Used
Lattice Direction - (Measured in Meter) - The Lattice Direction is a crystal direction [uvw] which is parallel to the direction joining the origin of the crystal lattice with the point with coordinates (ua, vb, wc) Crystal directions.
X-coordinate of lattice point - The X-coordinate of lattice point is the first element in an ordered pair (u,v,w) representing a lattice point.
Lattice Constant a - (Measured in Meter) - The Lattice Constant a refers to the physical dimension of unit cells in a crystal lattice along x-axis.
Y-coordinate of lattice point - The Y-coordinate of lattice point is the second element in an ordered pair (u,v,w) representing a lattice point.
Lattice Constant b - (Measured in Meter) - The Lattice Constant b refers to the physical dimension of unit cells in a crystal lattice along y-axis.
STEP 1: Convert Input(s) to Base Unit
X-coordinate of lattice point: 2 --> No Conversion Required
Lattice Constant a: 14 Angstrom --> 1.4E-09 Meter (Check conversion here)
Y-coordinate of lattice point: 7 --> No Conversion Required
Lattice Constant b: 12 Angstrom --> 1.2E-09 Meter (Check conversion here)
STEP 2: Evaluate Formula
Substituting Input Values in Formula
r = (u*alattice)+(v*b) --> (2*1.4E-09)+(7*1.2E-09)
Evaluating ... ...
r = 1.12E-08
STEP 3: Convert Result to Output's Unit
1.12E-08 Meter -->112 Angstrom (Check conversion here)
FINAL ANSWER
112 Angstrom <-- Lattice Direction
(Calculation completed in 00.004 seconds)

Credits

Created by Prerana Bakli
University of Hawaiʻi at Mānoa (UH Manoa), Hawaii, USA
Prerana Bakli has created this Calculator and 800+ more calculators!
Verified by Akshada Kulkarni
National Institute of Information Technology (NIIT), Neemrana
Akshada Kulkarni has verified this Calculator and 900+ more calculators!

5 Lattice Direction Calculators

3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points
Go Lattice Direction = ((Integer along X-axis*Lattice Constant a)+(Integer Along Y-axis*Lattice Constant b)+(Integer along Z-axis*Lattice Constant c))+(X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b)+(Z-coordinate of Lattice Point*Lattice Constant c)
3D Lattice Direction for points in space which are not Lattice Points
Go Lattice Direction = (X-coordinate of Point in Space*Lattice Constant a)+(Y-coordinate of Point in Space*Lattice Constant b)+(Z-coordinate of Point in Space*Lattice Constant c)
3D Lattice Direction for Lattice Points
Go Lattice Direction = (X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b)+(Z-coordinate of Lattice Point*Lattice Constant c)
2D Lattice Direction for Lattice Points
Go Lattice Direction = (X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b)
1D Lattice Direction for Lattice Points
Go Lattice Direction = (X-coordinate of lattice point*Lattice Constant a)

2D Lattice Direction for Lattice Points Formula

Lattice Direction = (X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b)
r = (u*alattice)+(v*b)

What are Bravais Lattices?

Bravais Lattice refers to the 14 different 3-dimensional configurations into which atoms can be arranged in crystals. The smallest group of symmetrically aligned atoms which can be repeated in an array to make up the entire crystal is called a unit cell.
There are several ways to describe a lattice. The most fundamental description is known as the Bravais lattice. In words, a Bravais lattice is an array of discrete points with an arrangement and orientation that look exactly the same from any of the discrete points, that is the lattice points are indistinguishable from one another.
Out of 14 types of Bravais lattices some 7 types of Bravais lattices in three-dimensional space are listed in this subsection. Note that the letters a, b, and c have been used to denote the dimensions of the unit cells whereas the letters 𝛂, 𝞫, and 𝝲 denote the corresponding angles in the unit cells.

How to Calculate 2D Lattice Direction for Lattice Points?

2D Lattice Direction for Lattice Points calculator uses Lattice Direction = (X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b) to calculate the Lattice Direction, The 2D Lattice Direction for Lattice Points is a crystal direction (u,v) which is parallel to the direction joining the origin of the crystal lattice with the point with coordinates (ua, vb) Crystal directions. Lattice Direction is denoted by r symbol.

How to calculate 2D Lattice Direction for Lattice Points using this online calculator? To use this online calculator for 2D Lattice Direction for Lattice Points, enter X-coordinate of lattice point (u), Lattice Constant a (alattice), Y-coordinate of lattice point (v) & Lattice Constant b (b) and hit the calculate button. Here is how the 2D Lattice Direction for Lattice Points calculation can be explained with given input values -> 1.1E+12 = (2*1.4E-09)+(7*1.2E-09).

FAQ

What is 2D Lattice Direction for Lattice Points?
The 2D Lattice Direction for Lattice Points is a crystal direction (u,v) which is parallel to the direction joining the origin of the crystal lattice with the point with coordinates (ua, vb) Crystal directions and is represented as r = (u*alattice)+(v*b) or Lattice Direction = (X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b). The X-coordinate of lattice point is the first element in an ordered pair (u,v,w) representing a lattice point, The Lattice Constant a refers to the physical dimension of unit cells in a crystal lattice along x-axis, The Y-coordinate of lattice point is the second element in an ordered pair (u,v,w) representing a lattice point & The Lattice Constant b refers to the physical dimension of unit cells in a crystal lattice along y-axis.
How to calculate 2D Lattice Direction for Lattice Points?
The 2D Lattice Direction for Lattice Points is a crystal direction (u,v) which is parallel to the direction joining the origin of the crystal lattice with the point with coordinates (ua, vb) Crystal directions is calculated using Lattice Direction = (X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b). To calculate 2D Lattice Direction for Lattice Points, you need X-coordinate of lattice point (u), Lattice Constant a (alattice), Y-coordinate of lattice point (v) & Lattice Constant b (b). With our tool, you need to enter the respective value for X-coordinate of lattice point, Lattice Constant a, Y-coordinate of lattice point & Lattice Constant b and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.
How many ways are there to calculate Lattice Direction?
In this formula, Lattice Direction uses X-coordinate of lattice point, Lattice Constant a, Y-coordinate of lattice point & Lattice Constant b. We can use 4 other way(s) to calculate the same, which is/are as follows -
  • Lattice Direction = (X-coordinate of lattice point*Lattice Constant a)
  • Lattice Direction = (X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b)+(Z-coordinate of Lattice Point*Lattice Constant c)
  • Lattice Direction = (X-coordinate of Point in Space*Lattice Constant a)+(Y-coordinate of Point in Space*Lattice Constant b)+(Z-coordinate of Point in Space*Lattice Constant c)
  • Lattice Direction = ((Integer along X-axis*Lattice Constant a)+(Integer Along Y-axis*Lattice Constant b)+(Integer along Z-axis*Lattice Constant c))+(X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b)+(Z-coordinate of Lattice Point*Lattice Constant c)
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