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Radius Ratio Calculator

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✖The Radius of Cation is the radius of the positively charged ion in the crystal structure.ⓘ Radius of Cation [R_c]			+10% -10%
✖The Radius of Anion is the radius of negatively charged ion in the crystal.ⓘ Radius of Anion [R_a]			+10% -10%

✖The Radius Ratio is the ratio of radius of cation to radius of anion.ⓘ Radius Ratio [R_ratio]

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Formula

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Radius Ratio

Formula

`"R"_{"ratio"} = "R"_{"c"}/"R"_{"a"}`

Example

`"1.262136"="65A"/"51.5A"`

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Radius Ratio Solution

STEP 0: Pre-Calculation Summary

Formula Used

Radius Ratio = Radius of Cation/Radius of Anion
R_ratio = R_c/R_a
This formula uses 3 Variables

Variables Used

Radius Ratio - The Radius Ratio is the ratio of radius of cation to radius of anion.
Radius of Cation - (Measured in Meter) - The Radius of Cation is the radius of the positively charged ion in the crystal structure.
Radius of Anion - (Measured in Meter) - The Radius of Anion is the radius of negatively charged ion in the crystal.

STEP 1: Convert Input(s) to Base Unit

Radius of Cation: 65 Angstrom --> 6.5E-09 Meter (Check conversion here)
Radius of Anion: 51.5 Angstrom --> 5.15E-09 Meter (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

R_ratio = R_c/R_a --> 6.5E-09/5.15E-09

Evaluating ... ...

R_ratio = 1.2621359223301

STEP 3: Convert Result to Output's Unit

1.2621359223301 --> No Conversion Required

FINAL ANSWER

1.2621359223301 ≈ 1.262136 <-- Radius Ratio

(Calculation completed in 00.006 seconds)

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Created by Pragati Jaju

College Of Engineering (COEP), Pune

Pragati Jaju has created this Calculator and 50+ more calculators!

Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

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< 24 Lattice Calculators

Miller index along X-axis using Weiss Indices

Go Miller Index along x-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along x-axis

Miller index along Y-axis using Weiss Indices

Go Miller Index along y-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index along y-axis

Miller index along Z-axis using Weiss Indices

Go Miller Index along z-axis = lcm(Weiss Index along x-axis,Weiss Index along y-axis,Weiss Index Along z-axis)/Weiss Index Along z-axis

Edge Length using Interplanar Distance of Cubic Crystal

Go Edge Length = Interplanar Spacing*sqrt((Miller Index along x-axis^2)+(Miller Index along y-axis^2)+(Miller Index along z-axis^2))

Fraction of impurity in lattice terms of Energy

Go Fraction of Impurities = exp(-Energy required per impurity/([R]*Temperature))

Energy per impurity

Go Energy required per impurity = -ln(Fraction of Impurities)*[R]*Temperature

Fraction of Vacancy in lattice terms of Energy

Go Fraction of Vacancy = exp(-Energy Required per Vacancy/([R]*Temperature))

Energy per vacancy

Go Energy Required per Vacancy = -ln(Fraction of Vacancy)*[R]*Temperature

Packing Efficiency

Go Packing Efficiency = (Volume Occupied by Spheres in Unit Cell/Total Volume of Unit Cell)*100

Number of lattice containing impurities

Go No. of Lattice Occupied by Impurities = Fraction of Impurities*Total no. of lattice points

Fraction of impurity in lattice

Go Fraction of Impurities = No. of Lattice Occupied by Impurities/Total no. of lattice points

Fraction of Vacancy in lattice

Go Fraction of Vacancy = Number of Vacant Lattice/Total no. of lattice points

Number of vacant lattice

Go Number of Vacant Lattice = Fraction of Vacancy*Total no. of lattice points

Weiss Index along X-axis using Miller Indices

Go Weiss Index along x-axis = LCM of Weiss Indices/Miller Index along x-axis

Weiss Index along Y-axis using Miller Indices

Go Weiss Index along y-axis = LCM of Weiss Indices/Miller Index along y-axis

Weiss Index along Z-axis using Miller Indices

Go Weiss Index Along z-axis = LCM of Weiss Indices/Miller Index along z-axis

Radius of Constituent Particle in BCC lattice

Go Radius of Constituent Particle = 3*sqrt(3)*Edge Length/4

Edge length of Body Centered Unit Cell

Go Edge Length = 4*Radius of Constituent Particle/sqrt(3)

Edge Length of Face Centered Unit Cell

Go Edge Length = 2*sqrt(2)*Radius of Constituent Particle

Radius Ratio

Go Radius Ratio = Radius of Cation/Radius of Anion

Number of Tetrahedral Voids

Go Number of Tetrahedral Voids = 2*Number of Closed Packed Spheres

Radius of Constituent Particle in FCC lattice

Go Radius of Constituent Particle = Edge Length/2.83

Radius of Constituent particle in Simple Cubic Unit Cell

Go Radius of Constituent Particle = Edge Length/2

Edge length of Simple cubic unit cell

Go Edge Length = 2*Radius of Constituent Particle

Radius Ratio Formula

Radius Ratio = Radius of Cation/Radius of Anion
R_ratio = R_c/R_a

What is Radius Ratio?

The ratio of the radius of the smaller ion to that of the larger; commonly cation to anion. Radius ratios are used to predict coordination numbers of anions about cations in ionic crystal structures.

How to Calculate Radius Ratio?

Radius Ratio calculator uses Radius Ratio = Radius of Cation/Radius of Anion to calculate the Radius Ratio, The Radius Ratio formula is defined as the ratio of radius of cation to the radius of anion. It is used to predict the coordination number. Radius Ratio is denoted by R_ratio symbol.

How to calculate Radius Ratio using this online calculator? To use this online calculator for Radius Ratio, enter Radius of Cation (R_c) & Radius of Anion (R_a) and hit the calculate button. Here is how the Radius Ratio calculation can be explained with given input values -> 1.262136 = 6.5E-09/5.15E-09.

FAQ

What is Radius Ratio?

The Radius Ratio formula is defined as the ratio of radius of cation to the radius of anion. It is used to predict the coordination number and is represented as R_ratio = R_c/R_a or Radius Ratio = Radius of Cation/Radius of Anion. The Radius of Cation is the radius of the positively charged ion in the crystal structure & The Radius of Anion is the radius of negatively charged ion in the crystal.

How to calculate Radius Ratio?

The Radius Ratio formula is defined as the ratio of radius of cation to the radius of anion. It is used to predict the coordination number is calculated using Radius Ratio = Radius of Cation/Radius of Anion. To calculate Radius Ratio, you need Radius of Cation (R_c) & Radius of Anion (R_a). With our tool, you need to enter the respective value for Radius of Cation & Radius of Anion and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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