Volume of Triclinic cell Calculator

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Inter-planar distance and inter-planar angle

✖The Lattice Constant a refers to the physical dimension of unit cells in a crystal lattice along x-axis.ⓘ Lattice Constant a [a_lattice]			+10% -10%
✖The Lattice Constant b refers to the physical dimension of unit cells in a crystal lattice along y-axis.ⓘ Lattice Constant b [b]			+10% -10%
✖The Lattice Constant c refers to the physical dimension of unit cells in a crystal lattice along z-axis.ⓘ Lattice Constant c [c]			+10% -10%
✖The Lattice parameter alpha is the angle between lattice constants b and c.ⓘ Lattice parameter alpha [α]			+10% -10%
✖The Lattice Parameter Beta is the angle between lattice constants a and c.ⓘ Lattice Parameter Beta [β]			+10% -10%
✖The Lattice Parameter gamma is the angle between lattice constants a and b.ⓘ Lattice Parameter gamma [γ]			+10% -10%

✖Volume is the amount of space that a substance or object occupies or that is enclosed within a container.ⓘ Volume of Triclinic cell [V_T]

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Formula

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Volume of Triclinic cell

Formula

`"V"_{"T"} = ("a"_{"lattice"}*"b"*"c")*sqrt(1-(cos("α")^2)-(cos("β")^2)-(cos("γ")^2)+(2*cos("α")*cos("β")*cos("γ")))`

Example

`"7E^-28m³"=("14A"*"12A"*"15A")*sqrt(1-(cos("30°")^2)-(cos("35°")^2)-(cos("38°")^2)+(2*cos("30°")*cos("35°")*cos("38°")))`

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Volume of Triclinic cell Solution

STEP 0: Pre-Calculation Summary

Formula Used

Volume = (Lattice Constant a*Lattice Constant b*Lattice Constant c)*sqrt(1-(cos(Lattice parameter alpha)^2)-(cos(Lattice Parameter Beta)^2)-(cos(Lattice Parameter gamma)^2)+(2*cos(Lattice parameter alpha)*cos(Lattice Parameter Beta)*cos(Lattice Parameter gamma)))
V_T = (a_lattice*b*c)*sqrt(1-(cos(α)^2)-(cos(β)^2)-(cos(γ)^2)+(2*cos(α)*cos(β)*cos(γ)))
This formula uses 2 Functions, 7 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Volume - (Measured in Cubic Meter) - Volume is the amount of space that a substance or object occupies or that is enclosed within a container.
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.
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.
Lattice Constant c - (Measured in Meter) - The Lattice Constant c refers to the physical dimension of unit cells in a crystal lattice along z-axis.
Lattice parameter alpha - (Measured in Radian) - The Lattice parameter alpha is the angle between lattice constants b and c.
Lattice Parameter Beta - (Measured in Radian) - The Lattice Parameter Beta is the angle between lattice constants a and c.
Lattice Parameter gamma - (Measured in Radian) - The Lattice Parameter gamma is the angle between lattice constants a and b.

STEP 1: Convert Input(s) to Base Unit

Lattice Constant a: 14 Angstrom --> 1.4E-09 Meter (Check conversion here)
Lattice Constant b: 12 Angstrom --> 1.2E-09 Meter (Check conversion here)
Lattice Constant c: 15 Angstrom --> 1.5E-09 Meter (Check conversion here)
Lattice parameter alpha: 30 Degree --> 0.5235987755982 Radian (Check conversion here)
Lattice Parameter Beta: 35 Degree --> 0.610865238197901 Radian (Check conversion here)
Lattice Parameter gamma: 38 Degree --> 0.66322511575772 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

V_T = (a_lattice*b*c)*sqrt(1-(cos(α)^2)-(cos(β)^2)-(cos(γ)^2)+(2*cos(α)*cos(β)*cos(γ))) --> (1.4E-09*1.2E-09*1.5E-09)*sqrt(1-(cos(0.5235987755982)^2)-(cos(0.610865238197901)^2)-(cos(0.66322511575772)^2)+(2*cos(0.5235987755982)*cos(0.610865238197901)*cos(0.66322511575772)))

Evaluating ... ...

V_T = 6.95030665924782E-28

STEP 3: Convert Result to Output's Unit

6.95030665924782E-28 Cubic Meter --> No Conversion Required

FINAL ANSWER

6.95030665924782E-28 ≈ 7E-28 Cubic Meter <-- Volume

(Calculation completed in 00.004 seconds)

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< 11 Volume of Different Cubic Cell Calculators

Volume of Triclinic cell

Go Volume = (Lattice Constant a*Lattice Constant b*Lattice Constant c)*sqrt(1-(cos(Lattice parameter alpha)^2)-(cos(Lattice Parameter Beta)^2)-(cos(Lattice Parameter gamma)^2)+(2*cos(Lattice parameter alpha)*cos(Lattice Parameter Beta)*cos(Lattice Parameter gamma)))

Volume of Rhombohedral cell

Go Volume = (Lattice Constant a^3)*sqrt(1-(3*(cos(Lattice parameter alpha)^2))+(2*(cos(Lattice parameter alpha)^3)))

Volume of Monoclinic cell

Go Volume = Lattice Constant a*Lattice Constant b*Lattice Constant c*sin(Lattice Parameter Beta)

Volume of Orthorhombic cell

Go Volume = Lattice Constant a*Lattice Constant b*Lattice Constant c

Volume of Hexagonal cell

Go Volume = (Lattice Constant a^2)*Lattice Constant c*0.866

Volume of Body Centered Unit Cell

Go Volume = (4*Radius of Constituent Particle/sqrt(3))^3

Volume of face Centered Unit Cell

Go Volume = (2*sqrt(2)*Radius of Constituent Particle)^3

Volume of Tetragonal cell

Go Volume = (Lattice Constant a^2)*Lattice Constant c

Volume of Simple Cubic Unit Cell

Go Volume = (2*Radius of Constituent Particle)^3

Volume of cubic cell

Go Volume = (Lattice Constant a^3)

Volume of Unit cell

Go Volume = Edge Length^3

Volume of Triclinic cell Formula

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 Volume of Triclinic cell?

Volume of Triclinic cell calculator uses Volume = (Lattice Constant a*Lattice Constant b*Lattice Constant c)*sqrt(1-(cos(Lattice parameter alpha)^2)-(cos(Lattice Parameter Beta)^2)-(cos(Lattice Parameter gamma)^2)+(2*cos(Lattice parameter alpha)*cos(Lattice Parameter Beta)*cos(Lattice Parameter gamma))) to calculate the Volume, The Volume of Triclinic cell formula is defined as the space occupied by an Triclinic crystal lattice. Volume is denoted by V_T symbol.

How to calculate Volume of Triclinic cell using this online calculator? To use this online calculator for Volume of Triclinic cell, enter Lattice Constant a (a_lattice), Lattice Constant b (b), Lattice Constant c (c), Lattice parameter alpha (α), Lattice Parameter Beta (β) & Lattice Parameter gamma (γ) and hit the calculate button. Here is how the Volume of Triclinic cell calculation can be explained with given input values -> 7E-28 = (1.4E-09*1.2E-09*1.5E-09)*sqrt(1-(cos(0.5235987755982)^2)-(cos(0.610865238197901)^2)-(cos(0.66322511575772)^2)+(2*cos(0.5235987755982)*cos(0.610865238197901)*cos(0.66322511575772))).

FAQ

What is Volume of Triclinic cell?

The Volume of Triclinic cell formula is defined as the space occupied by an Triclinic crystal lattice and is represented as V_T = (a_lattice*b*c)*sqrt(1-(cos(α)^2)-(cos(β)^2)-(cos(γ)^2)+(2*cos(α)*cos(β)*cos(γ))) or Volume = (Lattice Constant a*Lattice Constant b*Lattice Constant c)*sqrt(1-(cos(Lattice parameter alpha)^2)-(cos(Lattice Parameter Beta)^2)-(cos(Lattice Parameter gamma)^2)+(2*cos(Lattice parameter alpha)*cos(Lattice Parameter Beta)*cos(Lattice Parameter gamma))). The Lattice Constant a refers to the physical dimension of unit cells in a crystal lattice along x-axis, The Lattice Constant b refers to the physical dimension of unit cells in a crystal lattice along y-axis, The Lattice Constant c refers to the physical dimension of unit cells in a crystal lattice along z-axis, The Lattice parameter alpha is the angle between lattice constants b and c, The Lattice Parameter Beta is the angle between lattice constants a and c & The Lattice Parameter gamma is the angle between lattice constants a and b.

How to calculate Volume of Triclinic cell?

The Volume of Triclinic cell formula is defined as the space occupied by an Triclinic crystal lattice is calculated using Volume = (Lattice Constant a*Lattice Constant b*Lattice Constant c)*sqrt(1-(cos(Lattice parameter alpha)^2)-(cos(Lattice Parameter Beta)^2)-(cos(Lattice Parameter gamma)^2)+(2*cos(Lattice parameter alpha)*cos(Lattice Parameter Beta)*cos(Lattice Parameter gamma))). To calculate Volume of Triclinic cell, you need Lattice Constant a (a_lattice), Lattice Constant b (b), Lattice Constant c (c), Lattice parameter alpha (α), Lattice Parameter Beta (β) & Lattice Parameter gamma (γ). With our tool, you need to enter the respective value for Lattice Constant a, Lattice Constant b, Lattice Constant c, Lattice parameter alpha, Lattice Parameter Beta & Lattice Parameter gamma 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 Volume?

In this formula, Volume uses Lattice Constant a, Lattice Constant b, Lattice Constant c, Lattice parameter alpha, Lattice Parameter Beta & Lattice Parameter gamma. We can use 10 other way(s) to calculate the same, which is/are as follows -

Volume = Edge Length^3
Volume = (2*Radius of Constituent Particle)^3
Volume = (4*Radius of Constituent Particle/sqrt(3))^3
Volume = (2*sqrt(2)*Radius of Constituent Particle)^3
Volume = (Lattice Constant a^3)
Volume = (Lattice Constant a^2)*Lattice Constant c
Volume = (Lattice Constant a^2)*Lattice Constant c*0.866
Volume = Lattice Constant a*Lattice Constant b*Lattice Constant c
Volume = (Lattice Constant a^3)*sqrt(1-(3*(cos(Lattice parameter alpha)^2))+(2*(cos(Lattice parameter alpha)^3)))
Volume = Lattice Constant a*Lattice Constant b*Lattice Constant c*sin(Lattice Parameter Beta)

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