Solids, Its Properties, and the Intermolecular Forces | Crystalline Solids and Amorphous Solids

Summary

This video script explores the properties of solids, distinguishing between crystalline and amorphous solids. Crystalline solids have a regular, repeating structure, like diamond and ice, while amorphous solids lack long-range order, such as glass and rubber. The script delves into the concept of crystal lattices and unit cells, explaining how they dictate a material's properties. It also touches on the significance of atomic packing and the use of X-ray diffraction to determine crystal structures, providing a comprehensive foundation for understanding solid-state chemistry.

Takeaways

• 🧊 Solids have a rigid structure distinguishing them from liquids and gases, where atoms, ions, or molecules are usually locked into place.
• 🔍 The arrangement of particles in a solid can be either crystalline, with a regular repeating pattern, or amorphous, with no particular order.
• 💎 Crystalline solids like diamond and graphite demonstrate how different properties arise from the same elemental composition due to different arrangements of atoms.
• 🌐 Crystalline solids are characterized by long-range order, which affects their physical properties and how they change when heated.
• 🔥 Amorphous solids lack long-range order and soften over a range of temperatures, unlike crystalline solids that have a specific melting point.
• 🏺 Examples of amorphous solids include glass, plastic, coal, and rubber, which are more like supercooled liquids.
• 📊 Crystalline structures are built from repeating units called crystal lattices, which dictate the physical properties of the solid.
• 🔬 The unit cell is the smallest repeating unit in a crystal lattice, and different types of unit cells (cubic, hexagonal, etc.) determine the crystal structure.
• 🔄 There are different types of packing in crystals, such as simple cubic, body-centered cubic, and face-centered cubic, each with different coordination numbers.
• 🔬 X-ray diffraction is a technique used to determine the atomic and molecular structure of crystals by analyzing how x-rays scatter off the crystal's atoms.
• 🔑 The arrangement of atoms in a crystalline solid affects properties like atomic coordination numbers, inter-atomic distances, and bonding types.

Q & A

What is the main difference between crystalline and amorphous solids?

Crystalline solids have a regular repeating three-dimensional structure called a crystal lattice, while amorphous solids have a random orientation of particles with no particular order.

What is the significance of long-range order in crystalline solids?

Long-range order in crystalline solids refers to the repetition of structural units over long atomic distances, which results in distinct physical properties and behaviors compared to amorphous solids.

How do crystalline solids behave when heated?

Crystalline solids have a specific melting point where they transition from solid to liquid, and this change in physical properties is sharp and occurs at a specific temperature.

What is the difference between amorphous solids and liquids?

Amorphous solids are like liquids in that they do not have long-range order, but they have limited localized order in their structure, whereas liquids have no fixed order at all.

Why are crystalline solids considered incompressible?

Crystalline solids are considered incompressible because their ordered arrangement of units maximizes the space they occupy, and the strong intermolecular forces make them resistant to compression.

What are the common examples of crystalline and amorphous solids mentioned in the script?

Examples of crystalline solids include ice, sodium chloride, diamond, graphite, and sugar. Amorphous solids include glass, plastic, coal, and rubber.

What are the different types of unit cells in crystalline solids?

The script mentions seven fundamentally different kinds of unit cells that differ in the relative lengths of the edges and the angles between them. The focus is primarily on cubic unit cells, which include primitive cubic, body-centered cubic, and face-centered cubic.

How does the coordination number in a crystal lattice affect the properties of a material?

The coordination number, which is the number of atoms or particles surrounding an atom in a crystal lattice, affects atomic coordination numbers, inter-atomic distances, and the types and strengths of bonding within a solid, influencing the physical, chemical, electrical, and mechanical properties of the material.

What is the significance of the crystal lattice in determining the properties of a crystalline solid?

The crystal lattice is significant because it determines the arrangement of atoms, ions, or molecules in a crystalline solid, which in turn affects the atomic coordination numbers, inter-atomic distances, and bonding types, leading to specific physical and chemical properties.

How is the structure of crystals determined?

The structure of crystals is determined using X-ray diffraction, a technique that analyzes the patterns formed by the elastic scattering of X-rays off the atoms in a crystal.

What is the Bragg equation and how is it used in X-ray diffraction?

The Bragg equation, nλ = 2d sinθ, is used in X-ray diffraction to calculate the distance between planes of atoms in a crystal from the angles at which the X-rays are diffracted, where n is an integer, λ is the wavelength of the X-rays, d is the distance between crystal planes, and θ is the angle of incidence.

Outlines

00:00

🔬 Introduction to Solids and Their Properties

This paragraph introduces the topic of solids and their properties. The focus is on the distinction between crystalline and amorphous solids. Crystalline solids have a regular, repeating three-dimensional structure known as a crystal lattice, while amorphous solids lack this long-range order and have a random arrangement of particles. Examples of crystalline solids include ice, sodium chloride, diamond, graphite, and sugar, whereas glass, plastic, coal, and rubber are cited as amorphous solids. The difference in properties between these two types of solids stems from the presence or absence of long-range order in their atomic arrangements.

05:01

🌡 Behavior of Amorphous Solids Under Heat

The paragraph discusses the behavior of amorphous solids when heated. Unlike crystalline solids, which have a sharp change in physical properties at a specific melting point, amorphous solids soften gradually and melt over a wide range of temperatures. This is due to the random arrangement of particles in their structure, which causes some parts to melt before others. Examples such as coal and plastics illustrate this behavior. The paragraph also introduces the concept of amorphous solids lacking long-range order and having only limited localized order, similar to liquids.

10:04

🔬 Crystal Lattice and Unit Cells in Crystalline Solids

This section delves into the concept of the crystal lattice, which is the structural framework of crystalline solids. It explains that the lattice structure depends on the nature and size of the particles involved, as well as the intramolecular and intermolecular forces present. The forces that contribute to the stability of crystalline solids include ionic forces, covalent bonds, metallic bonds, and hydrogen bonds. The paragraph introduces the idea of a unit cell, which is the smallest repeating unit in a crystal lattice, and compares it to a Rubik's cube made up of smaller interconnected cubes. The description also covers the seven fundamental types of unit cells and their characteristics, focusing on cubic unit cells and their properties.

15:07

🔍 Types of Cubic Unit Cells and Their Packing

The paragraph explores the different types of cubic unit cells: primitive cubic, body-centered cubic (BCC), and face-centered cubic (FCC). It describes how these unit cells are arranged and the number of particles they contain. The discussion includes the concept of packing, where atoms are arranged to form an ordered three-dimensional structure. The paragraph also explains open and closed packing, with examples of how these packing types appear in different crystalline structures. The coordination number, which is the number of nearest neighbors surrounding a particle in a crystal lattice, is introduced as a key feature of crystal structures.

20:07

🔬 Close Packed Lattices and Their Importance

This section discusses close packed lattices, which allow for the maximum amount of interaction between atoms, leading to more energetically stable structures. The paragraph explains the hexagonal close packing (hcp) and face-centered cubic (fcc) or cubic closest packing (ccp) arrangements, detailing how they are formed and their respective unit cell compositions. The importance of understanding atomic packing in a unit cell and crystal lattice is emphasized, as it affects atomic coordination numbers, inter-atomic distances, and the types and strengths of bonding within a solid, which in turn influence the material's physical, chemical, electrical, and mechanical properties.

25:09

🔬 Determining Crystal Structures Through X-ray Diffraction

The final paragraph explains how the structures of crystals are determined using x-ray diffraction, a technique that reveals the atomic and molecular structure of a crystal. It describes the process of creating a diffraction pattern by passing x-rays through a powdered crystal sample and how the angles at which the rays are diffracted can be used to calculate the distance between planes of atoms in the crystal. The Bragg equation, which relates the angles of diffraction to the crystal structure, is introduced. The paragraph concludes with a historical note on one of the first x-ray diffraction photographs and a look at modern x-ray diffraction projections.

Keywords

💡Solids

Solids are one of the three primary states of matter, characterized by a rigid structure where component atoms, ions, or molecules are typically locked into place. In the video, this concept is foundational as it sets the stage for discussing the properties of different types of solids. Examples given include diamond and graphite, which are both forms of carbon but have vastly different properties due to their atomic arrangements.

💡Crystalline Solids

Crystalline solids are a type of solid where atoms, molecules, or ions are arranged in a regular, repeating three-dimensional pattern called a crystal lattice. This ordered structure is what gives crystalline solids their characteristic properties, such as fixed geometric shapes and sharp melting points. The video uses examples like ice, sodium chloride, and diamond to illustrate crystalline solids.

💡Amorphous Solids

Amorphous solids are solids that lack a long-range order, meaning their particles are arranged in a random manner. This randomness leads to different physical properties compared to crystalline solids, such as a tendency to soften over a range of temperatures rather than melting at a specific point. The video mentions glass, plastic, coal, and rubber as examples of amorphous solids.

💡Crystal Lattice

A crystal lattice is the repeating three-dimensional pattern that forms the structure of a crystalline solid. It is the fundamental concept in solid-state chemistry and is used to describe the arrangement of particles in a crystalline solid. The video explains that the crystal lattice can take different forms, such as simple cubic, body-centered cubic, and face-centered cubic.

💡Long-range Order

Long-range order refers to the repetition of structural units of a substance over long atomic distances. This concept is crucial for distinguishing crystalline solids from amorphous solids. The video explains that more than 90% of naturally occurring and artificially prepared solids are crystalline, which exhibit long-range order, unlike amorphous solids like glass.

💡Unit Cell

The unit cell is the smallest repeating unit in a crystal lattice that can be used to describe the entire structure of a crystalline solid. It is the basic building block of a crystal lattice. The video discusses different types of unit cells, such as simple cubic, body-centered cubic, and face-centered cubic, and their significance in determining the properties of crystalline solids.

💡Coordination Number

Coordination number is the number of nearest neighbors surrounding an atom in a crystal lattice. It indicates how tightly the atoms are packed together. The video explains that different unit cell structures have different coordination numbers, which can affect the physical properties of the material. For example, face-centered cubic has a coordination number of 12, indicating a tightly packed structure.

💡Packing

Packing in the context of the video refers to how atoms are arranged in a crystal lattice. The two main types of packing discussed are open packing and close packing. The video explains that close packing allows for the maximum amount of interaction between atoms, which can lead to more energetically stable structures. This is important for understanding the physical properties of crystalline materials.

💡X-ray Diffraction

X-ray diffraction is a technique used to determine the atomic and molecular structure of a crystal. The video describes how x-rays are scattered by a crystal's atoms, creating a diffraction pattern that can be analyzed to determine the crystal's structure. This technique is crucial for understanding the arrangement of atoms in crystalline solids and is illustrated with examples from the video.

💡Bragg Equation

The Bragg equation is a fundamental principle used in x-ray crystallography to determine the distances between planes of atoms in a crystal from the angles at which x-rays are diffracted. The video explains the concept using a simple geometric model and mentions that the equation is essential for deriving the structure of crystals from x-ray diffraction data.

Highlights

Solids have a rigid structure with component atoms, ions, or molecules usually locked into place.

Crystalline solids are arranged in fixed geometric patterns or lattices, like ice and sodium chloride.

Amorphous solids have a random orientation of particles, such as glass, plastic, coal, and rubber.

More than 90% of naturally occurring and artificially prepared solids are crystalline.

Crystalline solids have long-range order, while amorphous solids lack it.

Crystalline solids become liquids at a specific temperature, known as the melting point.

Amorphous solids soften gradually when heated and can melt over a wide range of temperatures.

Glass is an amorphous solid, composed mainly by mixing molten silicon dioxide with other components.

Crystal lattice is the fundamental concept in solid-state chemistry, representing the smallest structure of a crystal.

There are seven fundamentally different kinds of unit cells that differ in the relative lengths of their edges.

Cubic unit cells are the simplest and have structural particles centered only at their corners.

The arrangement of atoms in a crystalline solid is called packing, which can be open or closed.

The three types of cubic unit cells are primitive cubic, body-centered cubic, and face-centered cubic.

Coordination number is the number of atoms surrounding an atom in a crystal lattice.

Close-packed lattices allow the maximum amount of interaction between atoms, leading to a more stable structure.

Hexagonal closest packing (HCP) and face-centered cubic (FCC) are two common close-packed arrangements.

Understanding atomic packing in a unit cell and crystal lattice can provide insight into the properties of a crystalline material.

X-ray diffraction is a technique used to determine the atomic and molecular structure of a crystal.

The Bragg equation is used to calculate the distance between planes of atoms in a crystal from the angles at which the rays are diffracted.

Transcripts

in this

video we're going to talk about solids

and its properties

the learning competency for this video

is to describe the difference between

the two

and the specific learning outcome is to

compare the properties of crystalline

and

amorphous solids the solid state is

distinguished

from gas and liquid states by a rigid

structure

in which the component atoms ions or

molecules are usually locked

into place in many solids the components

are arranged

in extended three-dimensional patterns

producing a wide range of properties

that can often be tailored to specific

functions

thus a diamond an allotrope of elemental

carbon

is one of the hardest materials known

yet graphite

another allotrope of carbon is a soft

slippery material used in pencil lead

and

as lubricant therefore when we discuss

solids we consider the positions of the

atoms

molecules or ions which are essentially

fixed in space rather than their motions

which are important

in liquids and gases so the constituents

of a solid can be arranged

in two general ways they can form a

regular repeating three-dimensional

structure

called a crystal lattice thus producing

a crystalline solid or they can

aggregate with no particular order

in which case they form an amorphous

solid so it's from the greek word

amorphous

meaning shapeless now the differences in

properties of these two groups

arise from the presence or absence of

long-range order of arrangements

in the solid so what are the differences

crystalline solids are arranged in fixed

geometric patterns or lattices

examples are ice and sodium chloride

other examples include copper sulfate

diamond

graphite and sugar now the ordered

arrangement of their units

maximizes the space they occupy

and are essentially incompressible

amorphous solids on the other hand

have a random orientation of particles

examples include glass plastic

coal and rubber so they are considered

super cooled liquids where molecules

are arranged in a random manner similar

to the liquid state

now more than 90 percent of naturally

occurring and artificially prepared

solids are crystalline minerals

sand clay all have crystalline

structures

now the repetition of structural units

of the substance over long atomic

distances

is referred to as long range order

okay so amorphous solids such as glass

are like liquids they do not have long

range order

but have limited localized order

in their structure so the presence or

absence of

long-range order in the structure of

solids

results in the difference in the

behavior of the solid

when heated okay so as i have said

the structures of crystalline solids are

built from repeating units

called crystal lattices the surroundings

of particles in the structure

are unit form and attractive forces

experienced

by the particles are of similar types

and strands so these attractive forces

are broken by the same

amount of energy and thus crystals

become liquids at a specific

temperature which what we call the

melting point

at the melting point physical properties

of the crystalline solids

change sharply examples are pyrite

or the fool's gold or fluorite

now amorphous solids they soften

gradually when they

are heated they have the tendency to

melt

over a wide range of temperature this

behavior is a result of the variation

in the arrangement of particles in their

structures

causing some parts of the solid to melt

ahead

of other parts this behavior is

noticeable in substances

such as coal and plastics

which are both amorphous solids

so i want to start this discussion with

amorphous solids

because it's easier and less tedious

than crystalline solids amorphous solids

lack

regular arrangement of atoms so we say

that the molecules in an amorphous solid

are

arranged in a random motion

or manner and that we say that this kind

of solid

has no long range further amorphous

solids

also do not diffract glass

is a familiar and important amorphous

solid

they are optically transparent fusion

product of

inorganic materials that has cooled

to a rigid state without crystallization

so glasses are composed mainly by mixing

molten silicon dioxide with other

components such as

sodium oxide boric anhydride and certain

transition

metal oxides so they behave more as a

liquid

than a solid now this figure

shows a crystalline silicon dioxide or

what we call

quartz just by observation

you will already know the difference

between amorphous

silicon dioxide and crystalline

silicon dioxide so what are the

distinguishing feature

of crystalline solids to answer that

we have to further talk about the

crystal lattice

you have to remember that the lattice

structure of a crystal solid

depends on the nature and size of the

particles involved it also depends on

the intramolecular and

intermolecular forces present to be

specific

the force is responsible for the

stability of crystalline solids are the

following

we have ionic forces covalent bonds

thunder valves forces and hydrogen bonds

or a combination of some of them now i

have mentioned

crystal lattice a lot of times but what

exactly

is a crystal lattice

keep in mind that each crystalline solid

is represented by a crystal lattice

now think of crystalline solid as this

rubik's cube

okay so this rubik's cube

is made up of smaller cubes connected

to each other each cube is what we call

a unit cell now the arrangement

or structure of these connected cells

or cubes is what we call a crystal

lattice so basically the crystal lattice

is like a scaffolding for the solid

okay now the unit cell is the

fundamental concept

in solid-state chemistry it is the

smallest representation of structure

which carries all the information

necessary to construct

an ambiguously infinite lattice

okay on a molecular level it looks like

this

so the edge of each unit is what we call

a lattice point

at the lattice point you can see the

atoms

the molecules or ions so this one is a

cubic cell

and it is the simplest unit cell and has

structural particles

centered only at its corners

so if you're going to look at this

figure there are seven fundamentally

different

kinds of unit cells which differ in the

relative

lengths of the edges which are

indicated by a b and c

and the angles between them so alpha is

the angle between b

and c beta is the angle between

a and c and gamma is the angle between

a and b so each unit cell has six

sides and each side is a parallelogram

so we focus primarily on the cubic unit

cells

in which all sides have the same length

and

all angles are 90 degrees but

the concepts that we introduce also

apply to the substances

whose unit cells are not cubic okay

so the way atoms are arranged to form an

ordered three-dimensional structure is

called

packing okay remember that the type of

unit cell is determined

by the way atoms are packed or

arranged in layers so we have two kinds

of packing

open packing and the closed packing by

observation you will see that the open

packing has larger voids in between

particles

compared to close packed crystals

now in some books or references they

call open packing

as square packing because if you notice

you will have four points touching

here one two

three four

okay and they call close packing as

hexagonal packing because you have

six points okay

so you're touching six other atoms

four five six

so we have three types of cubic unit

cells as shown in this figure

we have primitive cubic body centered

cubic

and face centered cubic it's a primitive

cubic when the lattice points

are at the corners only it is a body

centered cubic or bcc when the lattice

point

also occurs at the center of the unit

cell

now it will be called as face centered

cubic or

fcc when the cell has lattice points

at the center of each face as well as

at each corner to make it easier to

visualize i will show you a video

from the user yusuf nasihi

so he makes chemistry physics and other

scientific videos

so if you want you may check his youtube

channel

the video that you will see will discuss

the types of cubic cell

the video the video that you will see

will discuss the types of cubic unit

cells

and their origins okay

if you could travel within a crystalline

solid

you would see the particles atoms ions

or molecules arranged in a regular array

here the spaces are greatly exaggerated

but in reality

the particles are packed close together

the unit cell of a crystal structure is

the smallest

portion that defines the structure

stacking

unit cells next to each other in all

three directions

gives the structure many elements and

simple compounds have unit cells from

the cubic crystal system

let's examine the three types of cubic

unit cells

all cubic unit cells have particles at

the corners of a cube

the simple or primitive cubic unit cell

has particles at the corners

only in reality the particles lie as

close to each other as possible

note that the particles touch along the

cube

edges but not along a diagonal in the

face

or along a diagonal through the body

by slicing away parts that belong to

neighboring unit cells we see that the

actual unit cell consists

of portions of the particles

when the cells pack next to each other

in all three dimensions we obtain the

crystal

if we fade the others out you can see

the original group of eight particles

within the array

and the unit cell within that group we

find the number of particles in one unit

cell by

combining all the particles portions

in the simple cubic unit cell eight

corners

each of which is one eighth of a

particle combine

to give one particle a key feature of a

crystal structure

is its coordination number the number of

the nearest

neighbors surrounding each particle in a

simple cubic array

any given particle has a neighboring

particle above

below to the right to the left in front

and in back of it for a total of

six nearest neighbors the body-centered

cubic unit cell has a particle at each

corner

and one in the center which is colored

pink to make it easier to see

with full size spheres you can see that

the particles don't touch along the

edges of the cube

but each corner particle does touch the

one

in the center the actual unit cell

consists of portions of the corner

particles and the whole one in the

center

eight eighths give one particle and the

one in the center gives

another for a total of two particles

in this tiny portion of a body-centered

cubic array

you can see that any given particle has

four

nearest neighbors above and four below

for a total of eight

nearest neighbors the face-centered

cubic unit cell has a particle at each

corner

and in each face which are colored

yellow here

but none in the center the corner

particles don't touch each other

but each corner does touch a particle in

the face

and those in the faces touch each other

as well

the actual unit cell consists of

portions of particles at the corners

and in the faces eight eighths at the

corners gives one particle

and half a particle in each of six faces

gives

three more for a total of four particles

in this tiny portion of a face-centered

cubic array

notice that a given particle has four

nearest

neighbors around it four more above and

four more below for a total of twelve

nearest neighbors stacking spheres shows

how the three

cubic unit cells arise arrange a layer

of spheres in

horizontal and vertical rows note the

large

diamond-shaped space among the particles

placing the next layer directly over the

first

gives a structure based on the simple

cubic unit cell

those larger spaces mean an inefficient

use of space

in fact only 52 percent of the available

volume

is actually occupied by spheres

because of this inefficiency the simple

cubic unit cell is seen

rarely in nature a more efficient

stacking occurs if we place the second

layer over the spaces formed by the

first layer

and the third layer over the space is

formed by the second

that simple change leads to 68 percent

of the available volume occupied by the

spheres

and a structure based on the body

centered cubic unit cell

many metals including all the alkali

metals adopt

this arrangement for the most efficient

stacking

shift every other row in the first layer

so the large

diamond shaped spaces become smaller

triangular spaces

and place the second layer over them

then the third layer goes over the holes

visible through the first

and second layers in this arrangement

called cubic closest packing spheres

occupy

74 of the volume note that it is based

on the face

centered cubic unit cell okay so again

from the video you have seen the concept

of coordination

number coordination number is the number

of atoms or particles

surrounding an atom in a crystal lattice

or simply the number of atoms touching

it

so coordination numbers indicate how

tightly the atoms pack the larger

coordination numbers

the tighter the packing is so face

centered cubic here has 12

right so now let's talk about the close

packed lattice

in 3d so close packed lattices

allow the maximum amount of interaction

between

atoms so if these interactions

are mainly attractive then close

packing usually leads to a more

energetically

stable structure as we pointed a while

ago

hexagonal packing of a single layer

is more efficient than square packing

so this is where we begin in the first

layer the spheres are arranged

in a hexagonal pattern where each

sphere is being surrounded by six

others okay so we call it layer a

then a second layer b with the same

structure

is added but the layer is slightly

shifted

hence just feeling the gaps off the

first

layer now in a third step another

equivalent

layer is added filling the gaps

just as before but now there are two

opportunities

either this layer lies exactly above the

first

one or so so layer

a again so we'll have a pattern

a b a or it is

shifted with respect to both a

and b and thus has its own

position c so we will have the pattern

c b a this aba pattern is called the

hexagonal closest

backing or hcp while this

cba or abc pattern

is called fcc

or the face centered cubic or some

references they call it ccp

cubic closest back in so let's have a

closer view

this one so a ccp arrangement has a

total of four spheres

per unit cell okay so a ccp

arrangement or a fcc arrangement

has a total of 4 spheres per unit cell

and an hcp arrangement has 8 spheres

per unit cell however both

configurations

have coordination number of wealth

so why is it important to know all of

these

what's the importance of the packing

the arrangement of atoms in a

crystalline solid affects

atomic coordination numbers inter-atomic

distances

and the types and strengths of bonding

that occur

within a solid so an understanding of

atomic packing in a unit cell

and crystal lattice can give insight to

the physical

chemical electrical and mechanical

properties

of a given crystalline material

now we're not going to talk about the

relationship between the edge

length and atomic radius so that would

be for another topic

and for your higher chemistry so how

are the structures of crystals

determined

structures of crystals are determined by

x-ray diffraction x-ray diffraction

is a technique used to determine the

atomic and molecular structure of

a crystal wherein atoms cause beams of

incident x-rays to diffract

into many specific directions

here is an image of a diffraction

pattern

produced by an electron beam incident on

graphite crystal so how does

this work okay so first a sample is

powdered and it is placed

here then x-rays of single wavelength is

used

so from the x-ray tube it will pass

a led screen

then this beam will heat the crystal

sample

diffracting it it means that the wave

scatters

in an elastic manner so we call it

elastic scattering

this is a type of scattering where the

wave

interacting with a particle bounces

off in some direction without changing

its wavelength so this will produce

patterns or spots

from diffracted x-ray okay

now this big circle in the middle is a

spot

from the incident beam that's why you

have here

the shield okay so the distance between

planes of atoms in the crystals

are calculated from the angles at which

the rays are diffracted

using brag equation okay so

here you have two layers okay

layer one and layer two

okay so the incident ray one

will heat atom a and b reflected

at a certain angle so this reflected ray

will be measured by an x-ray detector

okay so and this incident ray 2

will heat atom c then it will be

reflected okay but if you notice

in this figure incident rays

one and two have different path lengths

okay they are only the same

at this point from a to b

and in terms of reflected race it's the

same from

a to d

okay so you have some extra distance

to get the length of the extra distance

s

we need to use some trigonometry

concepts

so from a to c this

will be your hypotenuse d okay

and you will have right angles here

here and angle here

theta so to get the distance from b

to c you will have

d sine theta

and from c to d you will have

d sine

theta so the extra distance

traveled by the lower ray is equal to

bc plus cd

which is equal to n

times lambda where n

is an integer and lambda is the

wavelength of the x-rays

so this will be equal to

2 d sine

theta okay so this

is what we call the bragg equation

now i'm going to leave the solving part

to your higher chem subjects

but this is one of the ways to derive

brag

equation this figure shows one of the

first

x-ray diffraction photographs so the

figure on the left

is one of the first x-ray diffraction

photograph

and on the right is a modern x-ray

diffraction

projection okay so in the next video

we're going to talk about the types of

crystals