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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. Check FAQs
r=((n⋅alattice)+(p⋅b)+(q⋅c))+(u⋅alattice)+(v⋅b)+(w⋅c)
r - Lattice Direction?n - Integer along X-axis?alattice - Lattice Constant a?p - Integer Along Y-axis?b - Lattice Constant b?q - Integer along Z-axis?c - Lattice Constant c?u - X-coordinate of lattice point?v - Y-coordinate of lattice point?w - Z-coordinate of Lattice Point?

3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points Example

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Here is how the 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points equation looks like with Values.

Here is how the 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points equation looks like with Units.

Here is how the 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points equation looks like.

436Edit=((6Edit⋅14Edit)+(5Edit⋅12Edit)+(4Edit⋅15Edit))+(2Edit⋅14Edit)+(7Edit⋅12Edit)+(8Edit⋅15Edit)
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3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points Solution

Follow our step by step solution on how to calculate 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points?

FIRST Step Consider the formula
r=((n⋅alattice)+(p⋅b)+(q⋅c))+(u⋅alattice)+(v⋅b)+(w⋅c)
Next Step Substitute values of Variables
∴ r=((6⋅14A)+(5⋅12A)+(4⋅15A))+(2⋅14A)+(7⋅12A)+(8⋅15A)
Next Step Convert Units
∴ r=((6⋅1.4E-9m)+(5⋅1.2E-9m)+(4⋅1.5E-9m))+(2⋅1.4E-9m)+(7⋅1.2E-9m)+(8⋅1.5E-9m)
Next Step Prepare to Evaluate
∴ r=((6⋅1.4E-9)+(5⋅1.2E-9)+(4⋅1.5E-9))+(2⋅1.4E-9)+(7⋅1.2E-9)+(8⋅1.5E-9)
Next Step Evaluate
∴r=4.36E-08m
LAST Step Convert to Output's Unit
∴r=436A

3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points Formula Elements

Variables
Lattice Direction
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.
Symbol: r
Measurement: LengthUnit: A
Note: Value can be positive or negative.
Formulas to find Lattice DirectionOpen Variable
Integer along X-axis
Integer along X-axis is add-on with respect to a point in space which is not a lattice point.
Symbol: n
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Integer along X-axisOpen Variable
Lattice Constant a
The Lattice Constant a refers to the physical dimension of unit cells in a crystal lattice along x-axis.
Symbol: alattice
Measurement: LengthUnit: A
Note: Value can be positive or negative.
Formulas to find Lattice Constant aOpen Variable
Integer Along Y-axis
Integer along Y-axis is add-on with respect to a point in space which is not a lattice point.
Symbol: p
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Integer Along Y-axisOpen Variable
Lattice Constant b
The Lattice Constant b refers to the physical dimension of unit cells in a crystal lattice along y-axis.
Symbol: b
Measurement: LengthUnit: A
Note: Value can be positive or negative.
Formulas to find Lattice Constant bOpen Variable
Integer along Z-axis
Integer along Z-axis is add-on with respect to a point in space which is not a lattice point.
Symbol: q
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Integer along Z-axisOpen Variable
Lattice Constant c
The Lattice Constant c refers to the physical dimension of unit cells in a crystal lattice along z-axis.
Symbol: c
Measurement: LengthUnit: A
Note: Value can be positive or negative.
Formulas to find Lattice Constant cOpen Variable
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.
Symbol: u
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find X-coordinate of lattice pointOpen Variable
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.
Symbol: v
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Y-coordinate of lattice pointOpen Variable
Z-coordinate of Lattice Point
The Z-coordinate of lattice point is the third element in an ordered pair (u,v,w) representing a lattice point.
Symbol: w
Measurement: NAUnit: Unitless
Note: Value can be positive or negative.
Formulas to find Z-coordinate of Lattice PointOpen Variable

Other Formulas to find Lattice Direction

​Go 1D Lattice Direction for Lattice Points
r=(u⋅alattice)
​Go 2D Lattice Direction for Lattice Points
r=(u⋅alattice)+(v⋅b)

How to Evaluate 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points?

3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points evaluator uses 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) to evaluate the Lattice Direction, The 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points 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. Lattice Direction is denoted by r symbol.

How to evaluate 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points using this online evaluator? To use this online evaluator for 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points, enter Integer along X-axis (n), Lattice Constant a (alattice), Integer Along Y-axis (p), Lattice Constant b (b), Integer along Z-axis (q), Lattice Constant c (c), X-coordinate of lattice point (u), Y-coordinate of lattice point (v) & Z-coordinate of Lattice Point (w) and hit the calculate button.

FAQs on 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points

What is the formula to find 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points?
The formula of 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points is expressed as 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). Here is an example- 4.4E+12 = ((6*1.4E-09)+(5*1.2E-09)+(4*1.5E-09))+(2*1.4E-09)+(7*1.2E-09)+(8*1.5E-09).
How to calculate 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points?
With Integer along X-axis (n), Lattice Constant a (alattice), Integer Along Y-axis (p), Lattice Constant b (b), Integer along Z-axis (q), Lattice Constant c (c), X-coordinate of lattice point (u), Y-coordinate of lattice point (v) & Z-coordinate of Lattice Point (w) we can find 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points using the formula - 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).
What are the other ways to Calculate Lattice Direction?
Here are the different ways to Calculate Lattice Direction-
  • Lattice Direction=(X-coordinate of lattice point*Lattice Constant a)OpenImg
  • Lattice Direction=(X-coordinate of lattice point*Lattice Constant a)+(Y-coordinate of lattice point*Lattice Constant b)OpenImg
  • 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)OpenImg
Can the 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points be negative?
Yes, the 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points, measured in Length can be negative.
Which unit is used to measure 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points?
3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points is usually measured using the Angstrom[A] for Length. Meter[A], Millimeter[A], Kilometer[A] are the few other units in which 3D Lattice Direction for points in space which are not Lattice Points with respect to lattice points can be measured.
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