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STRUCTURE OF MATERIALSSTRUCTURE OF MATERIALS
The Key to its PropertiesAAMultiscaleMultiscale PerspectivePerspective
Anandh Subramaniam
Materials and Metallurgical Engineering
INDIAN INSTITUTE OF TECHNOLOGY KANPURINDIAN INSTITUTE OF TECHNOLOGY KANPUR
Kanpur-
208016
Email: [email protected]
http://home.iitk.ac.in/~anandh
Jan 2009
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Properties of Materials
The Scale of Microstructures
Crystal Structures
+ Defects
Microstructure
With Examples from the Materials World
OUTLINEOUTLINE
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PROPERTIES
Structure sensitive Structure Insensitive
E.g. Yield stress, Fracture toughness E.g. Density, Elastic Modulus
Structure Microstructure
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What determines the properties?
Cannot just be the composition!
Few 10s of ppm
of Oxygen in Cu can degrade its conductivity
Cannot just be the amount of phases present!
A small amount of cementite
along grain boundaries can cause thematerial to have poor impact toughness
Cannot just be the distribution of phases!
Dislocations can severely weaken a crystal
Cannot just be the defect structure in the phases present!
The presence of surface compressive stress toughens glass
Composition
Phases &
TheirDistribution
Defect Structure
Residual Stress
[1]
[1] Metals Handbook, Vol.8, 8thEdition, ASM, 1973
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Nucleus Atom Crystal Microstructure Component
Defects
Length Scales Involved
Unit Cell* Crystalline Defects Microstructure Component
*Simple Unit Cells
Angstroms
Dislocation Stress fields
Nanometers Microns Centimeters
Grain Size
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Atom Structure
Crystal
Electro-magnetic
Microstructure Component
Thermo-mechanicalTreatments
Phases Defects+
Casting Metal Forming Welding Powder Processing Machining
Vacancies Dislocations Twins
Stacking Faults Grain Boundaries Voids Cracks
+
Residual
Stress
Processing determines shape and microstructure of a component
Crystalline Quasicrystalline
Amorphous
Ferromagnetic Ferroelectric
Superconducting
Property
based
Structure
based
Avoid Stress Concentrators Good Surface Finish
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Atom Structure
Crystal
Electro-magnetic
Microstructure Component
Thermo-mechanicalTreatments
Phases Defects+
Casting Metal Forming Welding Powder Processing Machining
Vacancies Dislocations Twins
Stacking Faults Grain Boundaries Voids Cracks
+
Residual
Stress
Processing determines shape and microstructure of a component
Crystalline Quasicrystalline
Amorphous
Ferromagnetic Ferroelectric
Superconducting
Property
based
Structure
based
Avoid Stress Concentrators Good Surface Finish
& their distribution
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METALSEMI-METAL
SEMI-CONDUCTORINSULATOR
GAS
BAND STRUCTURE
AMORPHOUS
ATOMIC
STATE / VISCOSITY
SOLID LIQUID LIQUIDCRYSTALS
QUASICRYSTALS CRYSTALSRATIONALAPPROXIMANTS
STRUCTURE
NANO-QUASICRYSTALS NANOCRYSTALS
SIZE
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Atom Structure
Crystal
Electro-
magnetic
Microstructure Component
Why is BCC Iron the stable form of Iron at room temperature and not the FCCform of Iron?
1 Atm
G vs
T showing regions of stability of FCC andBCC Iron(Computed using thermo-calc software and database developed at
the Royal Institute of Technology, Stockholm)The Structure of Materials, S.M. Allen & E.L. Thomas, John Wiley & Sons, Inc. New York, 1999.
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Microstructure
Phases Defects+
Vacancies Dislocations Twins
Stacking Faults Grain Boundaries Voids Cracks
+
Residual
Stress
This functional definitionof microstructure
includes all lengthscales
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Microstructure
Phases Defects+
Vacancies Dislocations Twins
Stacking Faults Grain Boundaries Voids Cracks
+Residual
Stress
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Microstructure
Phases Defects+
Vacancies Dislocations
Twins Stacking Faults Grain Boundaries Voids Cracks
+
Residual
Stress
Microstructural
Defects (Crystalline)
Component
Vacancies Dislocations
Phase Transformation Voids
Cracks
Stress corrosion cracking
+ Residual SurfaceCompressive Stress
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CRYSTAL STRUCTURESCRYSTAL STRUCTURES
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Crystal =
Lattice (Where to repeat)+Motif (What to repeat)
Crystal =Space group
(how to repeat)
+Asymmetric unit (Motif: what to repeat)
+ =
Unit cell of BCC lattice
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Cubic
Tetragonal
Triclinic
Monoclinic
Orthorhombic
Progressive lowering of symmetry amongst the 7 crystal systems
Hexagonal
Trigonal
I
ncreasing
symmetry
Arrow marks lead from supergroups to subgroups
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1.
Cubic Crystals
a = b= c
=
=
= 90
Simple Cubic (P)
Body Centred
Cubic (I)
BCC
Face Centred
Cubic (F) -
FCC
FluoriteOctahedron
PyriteCube
m23
m4432,,3m3m,423,groupsPoint
[1] http://www.yourgemologist.com/crystalsystems.html
[2] L.E. Muir, Interfacial Phenomenon in Metals, Addison-Wesley Publ. co.
[1] [1]Garnet
Dodecahedron
[1]
Vapor grown NiO crystal
[2]
Tetrakaidecahedron(Truncated Octahedron)
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(The symmetry of) Any physical property of a crystal has at least thesymmetry of the crystal
Crystals are anisotropic with respect to most properties
The growth shape of a (well grown) crystal has the internal symmetry ofthe crystal
Polycrystalline materials or aggregates of crystals may have isotropicproperties (due to averaging of may randomly oriented grains)
The properties of a crystal can be drastically altered in the presence ofdefects (starting with crystal defects)
Crystals and Properties
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0D(Point defects)
CLASSIFICATION OF DEFECTS BASED ON DIMENSIONALITY
1D(Line defects)
2D(Surface / Interface)
3D(Volume defects)
Vacancy
Impurity
Frenkel
defect
Schottky
defect
Dislocation SurfaceInterphase
boundary
Grain
boundary
Twin
boundary
Twins
Precipitate
Faulted
region
Voids /
Cracks
Stacking
faults
Disclination
Dispiration
Thermal
vibration
Anti-phase
boundaries
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0D
(Point defects)
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0D
(Point defects)
Vacancy
Impurity
Frenkel
defect
Schottky
defect
Non-ionic
crystals
Ionic
crystals
Imperfect point-like regions in the crystal about the size of 1-2 atomic
diameters
Interstitial
Substitutional
Other ~
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Vacancy
Missing atom from an atomic site Atoms around the vacancy displaced
Tensile stress field produced in the vicinity
Tensile Stress
Fields
R l ti
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Impurity
Interstitial
Substitutional
SUBSTITUTIONAL IMPURITY
Foreign atom replacing the parent atom in the crystal
E.g. Cu sitting in the lattice site of FCC-Ni
INTERSTITIAL IMPURITY
Foreign atom sitting in the void of a crystal
E.g. C sitting in the octahedral void in HT FCC-Fe
Compressive stress
fields
Tensile StressFields
CompressiveStress
Fields
Relative
size
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Interstitial C sitting in the octahedral void in HT FCC-Fe
rOctahedral
void
/ rFCC
atom
= 0.414 rFe-FCC
= 1.29
rOctahedral
void
= 0.414 x 1.29 = 0.53
rC
= 0.71
Compressive strains around the C atom
Solubility limited to 2
wt% (9.3 at%)
Interstitial C sitting in the octahedral void in LT BCC-Fe
rTetrahedral
void
/ rBCC
atom
= 0.29
rC
= 0.71
rFe-BCC
= 1.258
rTetrahedral
void
= 0.29 x 1.258 = 0.364
But C sits in smaller octahedral void-
displaces fewer atoms
Severe
compressive strains around the C atom Solubility limited to 0.008 wt% (0.037 at%)
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Equilibrium Concentration of Vacancies
Formation of a vacancy leads to missing bonds and distortion of
the
lattice
The potential energy (Enthalpy) of the system increases
Work required for the formaion
of a point defect
Enthalpy of formation (Hf
)
[kJ/mol or eV/defect]
Though it costs energy to form a vacancy its formation leads to
increase in configurational entropy
above zero Kelvin there is an equilibrium number of vacancies
Crystal Kr Cd Pb Zn Mg Al Ag Cu Ni
kJ / mol 7.7 38 48 49 56 68 106 120 168eV / vacancy 0.08 0.39 0.5 0.51 0.58 0.70 1.1 1.24 1.74
G = H
T S ln( )ConfigS k
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T (C) n/N
500 1 x 1010
1000 1 x 105
1500 5 x 104
2000 3 x 103
Hf
= 1 eV/vacancy
= 0.16 x 1018
J/vacancyG(
Gibbsfre
eenergy)
n (number of vacancies)
Gmin
Equilibrium
concentration
G (perfect crystal)
Certain equilibrium number of vacancies are preferred at T > 0K
Vacancies play a role in:
Diffusion
Climb
Electrical conductivity
Creep etc.
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1D
(Line defects)
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2
Gm
The shear modulus of metals is in the range 20
150 GPa
DISLOCATIONS
Actual shear stress is 0.5
10 MPa
I.e. (Shear stress)theoretical
> 100 * (Shear stress)experimental
!!!!
The theoretical shear stress will bein the range 3
30 GPa
Dislocations weaken the crystal
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EDGE
DISLOCATIONS
MIXED SCREW
Usually dislocations have a mixed character andEdge and Screwdislocations are the ideal extremes
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Motion of
Edgedislocation
Conservative(Glide)
Non-conservative
(Climb)
For edge dislocation: as b
t they define a plane the slip plane
Climb involves addition or subtraction of a row of atoms below the
half plane
+ve
climb = climb
up removal of a plane of atoms
ve
climb = climb
down addition of a plane of atoms
Motion of dislocations
On the slip plane
Motion of dislocation
to the slip plane
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Mixed dislocations
b
tb
Pure EdgePure screw
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Slip
Role of Dislocations
FractureFatigue
CreepDiffusion
(Pipe)
Structural
Grain boundary
(low angle)
Incoherent Twin
Semicoherent
InterfacesDisc of vacancies~ edge dislocationCreep
mechanisms in
crystalline
materials
Dislocation climb
Vacancy diffusion
Cross-slip
Grain boundary sliding
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2D
(Surface / Interface)
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Grain Boundary
The grain boundary region may be distorted with atoms belonging toneither crystal
The thickness may be of the order of few atomic diameters
The crystal orientation changes abruptly at the grain boundary
In an low angle boundary the orientation difference is < 10
In the low angle boundary the distortion is not so drastic as thehigh-angle boundary can be described as an array of
dislocations Grain boundary energy is responsible for grain growth on heating
~ (>0.5Tm
)
Large grains grow at the expense of smaller ones The average no. of nearest neighbours
for an atom in the grain
boundary of a close packed crystal is 11
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Type of boundary Energy (J/m2)
Grain boundary between BCC crystals 0.89
Grain boundary between FCC crystals 0.85
Interface between BCC and FCC crystals 0.63
Grain boundaries in
SrTiO3
T i B d
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Twin Boundary
The atomic arrangement on one side of the twin boundary is related to
the other side by a symmetry operation (usually a mirror)
Mirror twin boundaries usually occur in pairs such that the orientationdifference introduced by one is restored by the other
The region between the regions is called the twinned region
Annealing twins (formed during recrystallization)
Deformation twins (formed during plastic deformation)
Twin
[1] Transformations in Metals, Paul G. Shewmon,McGraw-Hill Book Company, New York, 1969.
Annealing twins in Austenitic StainlessSteel
[1]
T i b d i F d d S TiO bi t l ( ifi i ll d)
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Twin boundary in Fe doped SrTiO3
bicrystals
(artificially prepared)
[1] S. Hutt, O. Kienzle, F. Ernst and M. Rhle, Z Metallkd, 92 (2001) 2
Twin plane
Mirror related
variants
High-resolution micrograph
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Grain size and strength
dk
iy y
Yield stress
i
Stress to move a dislocation in single crystal
k Locking parameter (measure of the relative
hardening contribution of grain boundaries)
d
Grain diameterHall-Petch
Relation
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Defects:Defects:
Further EnquiryFurther Enquiry
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Random
DEFECTS
Structural
Based on
origin
Vacancies Dislocations Ledges
The role played by a random defect is very different from the role played by astructural defect in various phenomenon
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b
2h2
Low Angle Grain Boundaries
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No visibleGrain
Boundary
2.761
Fourier filtered image
Dislocationstructures atthe Grain
boundary
~8
TILT BOUNDARY IN SrTiO3
POLYCRYSTAL
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Random
DEFECTS
Ordered
Based on
position
Ordered defects become part of the structure and hence affect the basic symmetryof the structure
Vacancies Stacking Faults
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Crystal with vacancies
Vacancy ordering
E.g. V6
C5
, V8
C7
Effect of Atomic Level Residual Stress
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Effect of Atomic Level Residual Stress
Yield Point Phenomenon
(GPa)
x ()
y(
)
Interaction of the stress fields ofdislocations
with Interstitial atoms
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3D
(Volume defects)
&
MICROSTRUCTURES
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T.J. Konno, K. Hiraga and M. Kawasaki, Scripta mater. 44 (2001) 23032307
HAADF
micrographs of the GP zones:
(a) Intercalated monatomic Cu layers several nm in width are clearly resolved,(b) a GP-zone two Cu layers thick can chemically
be identified.
Bright field TEM micrograph of an Al-
3.3% Cu alloy, aged at room temperaturefor 100 days, showing the GP-I zones.
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Precipitate particleb
b
Hardening effect Part of the dislocation line segment (inside theprecipitate) could face a higher PN stress
Increase in surface area due to particle shearing
Pi i ff t f th i it t
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Pinning effect of the precipitate
Can act like a Frank-Reed source
rGb2~
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Controlling microstructures:Controlling microstructures:
Examples
EutecticFe-Cementite diagram
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%C
T
Fe Fe3
C
6.74.30.80.16
2.06
PeritecticL +
Eutectic
L
+ Fe3
C
Eutectoid
+ Fe3
C
L
L +
+ Fe3C
1493C
1147C
723C
Fe-Cementite
diagram
Austenite () FCC
Ferrite () BCC
Cementite
(Fe3
C) Orthorhombic
Fe3C
[1] rruff.geo.arizona.edu/doclib/zk/vol74/ZK74_534.pdf
[1]
Time- Temperature-Transformation (TTT) Curves Isothermal Transformation
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Austenite
Austenite
Pearlite
Pearlite + Bainite
Bainite
Martensite100
200
300
400
600500
800
723
0.1 1 10 102 103 104 105
Eutectoid temperature
Ms
Mf
Coarse
Fine
t (s)
T
Eutectoid steel (0.8%C)
[1] Physical Metallurgy for Engineers, D S Clark and W R Varney, Affiliated EastWest Press Pvt. Ltd., New Delhi, 1962
[1]348C
[1]278C
Metals Handbook, Vol.8, 8th
edition, ASM, Metals Park, Ohio
[2] Introduction to Physical Metallurgy, S.H. Avner, McGraw-Hill Book Company, 1974
[2]
[2]
Time- Temperature-Transformation (TTT) Curves Isothermal Transformation
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AustenitePearlite
Pearlite + Bainite
Bainite
Martensite100
200
300
400
600
500
800
723
0.1 1 10 102 103 104 105
Eutectoid temperature
Ms
Mf
t (s)
T
Eutectoid steel (0.8%C)
+ Fe3C
Eutectoid steel (0 8%C)Different cooling treatments
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Eutectoid steel (0.8%C)
100
200
300
400
600
500
800
723
0.1 1 10 102 103 104 105t (s)
T
Waterq
uench O
ilquench
Norm
alizing
Fulla
nnea
l
e e t coo g t eat e ts
M = Martensite
P = Pearlite
Coarse P
PM M + Fine P
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% Carbon Hardness(R
c)
20
40
60
0.2 0.4 0.6
Harness of Martensite
as afunction of Carbon content
Properties of 0.8% C steel
Constituent Hardness (R c
) Tensile strength (MN / m2)
Coarse pearlite 16 710Fine pearlite 30 990
Bainite 45 1470
Martensite 65 -Martensite tempered at 250 oC 55 1990
Cooling
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C1 C2
%C
T
0.80.02
Eutectoid
+ Fe3
C
+ Fe3C
+
+ Fe3C
Fe
C3
[1] Materials Science and Engineering, W.D.Callister, Wiley India (P) Ltd., 2007.
Pro-eutectoid
Cementite
Pearlite
1.4%C [1]
3.4%C, 0.7% Si, 0.6% Mn 2.5% C, 1.0% Si, 0.55% Mn
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White CI
Grey CI
Fully Malleabilized10 m
Ferrite (White)
Graphite (black)
Malleable CI
10 m Ferritic
Matrix Ferrite
Graphite nodules
Nodular CI Ductile
3Fe C Graphite NodulesHeatTreatment
3.4% C,1.8% Si, 0.5% Mn
3.4% C, 0.1% P, 0.4% Mn,1.0% Ni, 0.06%Mg
3 3 3L ( ) ( )Ledeburite Pearlite
Fe C Fe C Fe C
Chang
e
Comp
ositio
n
0%
0.5%
12%
18%
Anisotropy in Material Properties: an example
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Texture can reintroduce anisotropy in material properties
py p p
11E
12E
1
11 12244 E EE
Cubic Crystal
(3 Elastic Moduli)
PolycrystalAnisotropic Isotropic Anisotropic
Texture
Rolling/
Extrusion
Cold Worked
Moly Permalloy: 4% Mo, 79% Ni, 17% Fe
Annealed
Textured samples
EquiaxedElongated
[1] Metals Handbook, Vol.8, 8thEdition, ASM, 1973
[1]
[1]
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CONCLUSIONCONCLUSION
To understand the properties of materials theTo understand the properties of materials the
structurestructure at many differentat many different lengthscaleslengthscales mustmust
be viewedbe viewed
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Ionic Crystals
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Ionic Crystals
Overall electrical neutrality has to be maintained
Frenkel
defect
Cation
(being smaller get displaced to interstitial voids
E.g. AgI, CaF2
Schottky defect
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Schottky
defect
Pair of anion and cation
vacancies E.g. Alkali halides
Other defects due to charge balance
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g
If Cd2+
replaces Na+
one cation
vacancy is created
Defects due to off stiochiometry
ZnO
heated in Zn vapour
Zny
O
(y >1)
The excess cations
occupy interstitial voids
The electrons (2e) released stay associated to the interstitial cation
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FeO
heated in oxygen atmosphere Fex
O
(x
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Cubic48
Tetragonal16
Triclinic2
Monoclinic4
Orthorhombic8
Progressive lowering of symmetry amongst the 7 crystal systems
Hexagonal24
Trigonal12
Increasing
symmetry
Superscript to the crystal system is the order of the lattice point group
Arrow marks lead from supergroups to subgroups
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