Lecture 3
Properties of diamond films
● Thermal conductivity
● Isotopic effect
● Impurities
● Optical properties
● Stress
● Fracture strength
Thermal conductivity of diamond and some optical
and electronic materials at room temperature
bulk materials
Thermal conductivity (W/m*K)
2000
CVD Diamond
1500
3 GHz, 50 W transistor on
CVD diamond heat spreader.
“Pulsar” company, Moscow
1000
500
4H-SiC
Cu
BeO
0
AlN
Si
GaN
GaAs Al O
2 3
● thermal conductivity of diamond:
5 times higher than for copper, and 50 times higher than for sapphire.
● ultimate bulk material for thermal management and high power optics.
Anisotropy of thermal conductivity
in polycrystalline CVD diamond
Phonon scattering on grain boundaries.
Columnar grain structure  TC anisotropy.
Depth inhomogeneity due to crystal size variation.
Perpendicular values k should higher than the in-plane values k.
J. Graebner, et al., J. Appl. Phys. 71 (1992) 5353.
Measurements of thermal diffusivity by Laser Flash Technique (LFT)
Method: heating of the front
side by short laser pulse and
tracing the T(t) on rear side.
● Delivery of laser pulse through an optical fiber to improve
uniformity of irradiation on the sample.
● Software for automatic evaluation of thermal diffusivity and TC.
● Vacuum Cryostat. Measurements thermal diffusivity in the
temperature range 180 – 430 К.
IR
detector
laser beam
sample
metal film
(absorber)
Temperature evolution (T(t)
on rear side of the film
● LFT measures perpendicular thermal diffusivity D.
Transient thermal grating technique
measures parallel thermal diffusivity D
He - Ne
0 ,0 8
D iffraction intensity, a.u.
Nd:YAG
0 ,1 0
0 ,0 6
0 ,0 4
1 0 6 4 nm
0 ,0 2
0 ,0 0
-2
-1
0
1
2
3
4
5
T im e, m icroseconds
● thermal grating formation due to
refraction coefficient modulation by
two interfering laser (Nd:YAG) beams.
● diffraction of probe He-Ne laser beam
on the transient grating with period Λ.
Diffraction signal decay due to thermal
dissipation
 

2
4 D II
2
Set-up for DII measurement using thermal grating technique
A custo-op tic g ate
63 3 nm
H e-N e laser
H arm on ics g en erator
YA G :N d laser
10 64, 532 , 35 5,
26 6, 2 13 nm
1
Trigg errin g
D iffractio nal
beam sp litter
S patial filter
PM T
S am ple
Period of thermal
grating 30-120 µm
S patial filter
D igital osciloscope
and P C
O ptical
fiber
E.V. Ivakin, Quantum Electronics (Moscow), 32 (2002) 367.
Thermal conductivity at room temperature
sensitive to content of hydrogen impurity in diamond
● Bonded hydrogen (C-H) decorates defects and grain boundaries.
● Hydrogen concentration as an indicator the defect abundance in CVD diamond.
22
K II
20
K
k , W /c m К
18
K┴
16
14
12
10
K║
8
0
200
400
600
800
1000
H yd ro g e n co n ce n tra tio n in d ia m o n d , p p m
● Thermal conductivity as high as 2100 W/mK.
● anisotropy: k (perpendicular ) > k (in-plane); Δk/k=10-15%.
A.V. Sukhadolau et al. Diamond Relat. Mater. 14 (2005) 589
Thermal conductivity k┴ vs hydrogen impurity in diamond
T h e rm a l c o n d u c tiv ity, W /c m K
25
20
15
10
5
10
100
1000
H yd ro g e n c o n c e n tra tio n , p p m
Open squares – samples from Element Six [S.E. Coe, Diamond Relat. Mater. 9 (2000) 1726];
full squares – GPI samples.
V. Ralchenko, in Hydrogen Materials Science and Chemistry of Metal Hydrides, Kluwer, 2002, p. 203.
Thermal conductivity along diamond wafer
as measured by LFT at room temperature
disk diameter 63 mm, thickness 1.28 mm
k, W/cmK
Distance along disk diameter, mm
Correlation of optical absorption and
parallel thermal conductivity
 =
18
5 0 0 nm
T h e rm a l c o n d u c tiv ity W c m
-1
K
-1
Absorption spectra in the visible
100
 , cm
-1
75
50
7 . 9 W cm
-1
K
-1
1 1 .3
16
14
12
10
8
0
5
10
15
20
1 2 .4
A b s o rp tio n , c m
25
30
35
1 2 .5
1 5 .3
1 7 .4
200
25
-1
300
400
500
600
700
In agreement with the correlation found by
J. Graebner, DRM, 4 (1995) 1196 for white
light absorption and k.
W av el en g t h , n m
At least a part of defects contribute both in enhanced absorption and in thermal resistance.
A.V. Sukhadolau et al. Diamond Relat. Mater. 14 (2005) 589
Thermal conductivity kII at elevated temperatures
The decrease of thermal conductivity with T
is mostly due to phonon-phonon scattering
mechanism (phonon population increases
with T).
Well fitted with the relationship k ~ T –n
(solid lines).
T h erm al c o n d u c tiv ity, W /c m K
22
ty pe IIa
B -d op e C V D
u nd op ed C V D
20
18
16
14
Samples compared:
- undoped diamond film (poly),
-B-doped film poly);
- type IIa single crystal diamond
[T.D. Ositinskaya, Superhard Materials
(Kiev), No. 4 (1980) 13].
12
10
8
6
2 50
30 0
35 0
40 0
45 0
50 0
550
Te m p e ratu re , K
60 0
65 0
k(T) : general form for an insulator
Heat is transferred by phonons
k = ⅓ C(T)· v· λ(T)
C is the heat capacity per unit volume, v is the average phonon velocity,
λ is the mean free path of phonons between collisions.
Any phonon scattering mechanism reducing λ decreases the thermal conductivity.
scattering
on boundary
defects
phonon-phonon
scattering
● The peak in k occurs at a temperature about 10% of Debye temperature, D.
● At low T: λ is constant, and k ~ C(T) ~ T3.
● Phonon-phonon scattering dominates at high T (k ~ T-1).
● Scattering on defects is essential at intermediate temperatures.
Temperature dependence of thermal conductivity
for certain crystals
k, W/mK
Occurrence a maximum in k(T) at
low temperatures (80-100 K).
Diamond – not the champion in the
value of maximum TC,
but its k is uniquely high at high
temperatures (T>70K), particularly
at room temperature.
This is the consequence of record
high Debye temperature θD =1860K
for diamond (very high phonon
frequencies are excited).
R. Berman, Diamond. Res. (1976)
Thermal conductivity kII at elevated temperatures
T = 293-460 K
Exponent n = 0.17 – 1.02
increases with diamond quality
Approximation k ~ T –n
36
is o to p ic a lly p u re [O ls o n , 1 9 9 3 ]
32
28
22
20
20
[H ] = 1 5 0 p p m
16
50
18
CVD
16
K II (W c m /K )
K II (W c m /K )
24
250
12
690
10
14
12
10
8
8
620
6
T yp e Ia [5 ]
4
300
360
420
480
T e m p e ra tu re (K )
0 .2
0 .4
0 .6
0 .8
1 .0
1 .2
1 .4
n
● Concentration of H impurity (in ppm) is indicated for
each sample.
● Comparison with data for single crystal natural
diamonds [ Burgemeister, Physica, 1978].
● The data for isotopically pure (12C) synthetic HPHT
single crystal diamond [Olson PB’1993] give n=1.36, the
highest slope for any diamond.
● Weak temperature dependence for highly
defective CVD diamond.
A.V. Sukhadolau et al. Diamond Relat. Mater. 14 (2005) 589
Defects in transparent CVD diamond (poly)
GB - grain boundaries
T - twins
SF - stacking faults
D - dislocations
L. Nistor et al, Phys. Stat. Sol.(a), 174 (1999) 5.
Typical dimensions of defects
Defects present in polycrystalline
CVD diamond and their scale
K.J. Gray, Diamond Relat. Mater. (1999)
Point defects are atomic scale defects:
- isolated foreign atoms;
- different isotopes;
- vacancies
Nitrogen ~ 1 ppm or less
Boron << 1ppm
Hydrogen 20 -1000 ppm (poly)
Vacancies - few ppm (?)
Isotope 13C ~10,000 ppm (main
impurity!)
Scattering rate of phonons with
frequency ω on isotopic atom with
mass m +Δm:
1/τiso = Ãisoω4
Ãiso = Ciso(V0/4πv3)[Δm/m]2
Ciso is isotope concentration, V0 is
atomic volume, v is sound velocity.
For diamond Δm=1 :
Aiso (nat) = 4.045 × 10-3 c-1K-1.
Thermal conductivity of isotopically “pure” diamond
Is it possible to increase K for diamond above 2400 W/mK at
room temperature?
Natural and synthetic diamonds (and any carbon material) contain 1.1%
of isotope 13C. The 13C atoms are scattering centers for phonons –
carriers of heat, thus restricting the thermal conductivity of diamond.
Concentration of 13C isotope is much higher than other impurities–point
defects.
Solution – eliminate 13C isotope from CVD diamond.
Isotopic composition of C, Si and Ge
Element
C
Si
Ge
Isotopes content, %
12C
13C
98.93
1.07
28Si
29Si
30Si
92.23
4.68
3.09
70Ge
72Ge
73Ge
74Ge
76Ge
20.38
27.31
7.76
36.72
7.83
Isotopic effect on thermal conductivity of diamond
The ultimate opportunity to achieve TC values > 2400 W/mK relays on
purification of isotopic composition of diamond.
The natural isotope content in diamond is 98.93% 12C and 1.07% 13C.
Phonon scattering on 13C atoms results in thermal resistance.
Previous works
Si
diamond
Isotopically modified 12C (99.90%)
single crystal HPHT diamond, General
Electric (1990-1993)
k=33.2 W/cmK
50% increase vs “normal” diamond.
L. Wei, PRL, 70 (1993) 3764
28Si.
Highly enriched (99.98%)
At room temperature:
thermal conductivity enhancement of 10%
compared to k = 140 W/mK for natural Si.
In the maximum at 26K the TC gain is 8 times.
R.K. Kremer et al. Sol. State Comm. 131 (2004) 499.
12C-enriched
polycrystalline CVD diamond films:
k = 21,8 W/cmK; k = 26 W/cmK
G.E. Graebner, Appl. Phys. Lett. 64 (1994) 2549.
Growth of isotopically enriched poly 12C CVD diamond
12
45
C
1
1
Thermal conductivity (W cm K )
● production of 12CO with purity 12C 99.96%
● conversion to 12CH4
● diamond deposition by MPCVD (purity is preserved)
● cutting to 12x2x0.46 mm3 bar
● TC measurements, steady state method
CO isotope separation by diffusion.
“Colonna” system,
Kourchatov Institute, Moscow.
40
35
25.1 W/cm K
30
25
20
natur
C (poly)
15
19.0 W/cm K
10
100
200
300
400
Temperature (K)
k = 2510 W/mK at 298K for
12C
diamond (higher than for type IIa single crystals) - isotopic effect of 32%.
k = 1900 W/mK for 0.5 mm thick film with natural isotope abundance.
k=2600 W/mK - perpendicularly to the film plane.
The isotopic effect increases with temperature decrease - the maximum TC of 4700 W/mK at T=160K.
A. Inyushkin et al. Bull. Lebedev Phys. Inst. 34 (2007) 329
The further increase in TC for 12C diamond is limited by defects, impurities, grain boundaries.
► single crystals
Measurement cell to determine thermal conductivity at T = 4 - 450K
Steady state method of constant thermal gradient.
Sample – polycrystalline CVD diamond.
The cryostat in vacuum lower 10-5 Torr.
Multilayer thermal radiation shield (at T>200K).
Copper
block
Diamond bar
14x2x0.5 mm3
Measurement accuracy of k is better 3%
(primarily due to an error in distance between
thermometers).
Resistor thermometer
(Cernox, LakeShore
Cryotronics)
Heater
(resistor)
Kourchatov Institute, Moscow
Applications of isotopically modified diamonds
with extraordinary thermal conductivity
● Heat spreaders for high power electronic devices
● Single crystals and nanocrystals with nitrogen-vacancy (NV)
fluorescent color centers for quantum computing and cryptography isotope 13C with nuclear spin should be eliminated to increase spin
relaxation (coherence) time of NV centers to µs level.
● Reflecting and transmission X-ray optics for high intensity beams
(synchrotron sources)
a combination of high TC, low atomic number Z and structure
perfection is required.
● Laser optics (including diamond Raman lasers) with increased damage
threshold.
Thermal conductivity of UNCD
measured by a laser flash technique
0 ,0 7 0
0.12
0.11
2
T h e rm a l d iffu s iv ity, c m /s
0 ,0 6 0
0 ,0 5 5
0.1
0 ,0 5 0
0.09
0 ,0 4 5
0.08
0 ,0 4 0
0.07
0 ,0 3 5
0.06
0 ,0 3 0
0.05
0
5
10
15
20
25
N 2, %
Thermal conductivity vs N2%
T h e rm a l c o n d u c tiv ity, W /c m *К
0 ,0 6 5
● k = 0.06-0.10 W/cmK at RT is 200 times
lower than for single crystal diamond, but
still higher than for amorphous sp3 carbon
ta-C ka-C = 0.035 W/cmK.
● Thermal conductivity decreases with
nitrogen “doping”.
● k = 1/3 C*V*L, where C – heat
capacity, V – sound velocity, L – phonon
free path. For single crystal L=240 nm;
for NCD L2 nm (of the order of grain
size).
V. Ralchenko, et al. DRM, 16 (2007) 2067
Thermal conductivity of UNCD
Temperature dependences measured by “3 Omega” method
W.L. Liu et al. APL 89 (2006) 171915
2
Thermal Conductivity (W/cmK)
10
Bulk Diamond: Callaway Model
1
10
Poly
NCD_25
NCD_0
Hopping Model (2m, t=0.9)
0
10
Hopping Model (22nm, t=0.32)
-1
10
Hopping Model (26nm, t=0.2)
a-C
-2
10
Minimum K for Carbon
-3
10
200
400
Temperature (K)
● kNCD is between polycrystalline diamond and amorphous carbon;
● slow and monotonic temperature dependence;
● in a phonon-hopping model (PHM) the reduction in thermal conductivity is
due to decrease in phonon transparency parameter (t) through grain boundaries:
t=0.2-0.32 for UNCD, t=0.9 for polycrystalline film.
Nitrogen and hydrogen impurities in CVD diamond
N and H content evaluation from optical absorption spectra
N-induced UV absorption
270 nm
25
A
600
C-H stretch absorption bands
2800-3100 cm-1
150
A
500
-1
A b so rb a n ce , cm
400
50
70
60
0
250
300
300
350
400
W a v ele n g th, n m
50
B
T, %
A b s o rb a n c e , c m
-1
 , cm
-1
100
20
200
D
C
40
30
E
2-phonon
absorptio
n
20
100
10
200
300
400
500
W a ve le n g th , n m
600
700
4000
3500
3000
2500
2000
1500
Wavenumber, cm
1000
500
-1
15
10
D
5
B
E
C
2800
2900
3000
W a ve n u m b e r, cm
Diamond samples of different qualities A - E
S. Nistor et al. J. Appl. Phys. 87 (2000) 8741.
-1
3100
Correlation of (bonded) H and N impurities
B o n d e d h yd ro g e n co n ce n tra tio n , p p m
Hydrogen and nitrogen concentrations are determined from IR and UV absorption
600
500
400
300
200
100
0
2
4
6
8
10
12
14
16
18
S u b stitu tio n a l n itro g e n co n ce n tra tio n , p p m
V. Ralchenko et al. in Hydrogen Materials Science and Chemistry of Metal Hydrides,
Kluwer, 2002, p. 203;
A.V. Sukhadolau et al. Diamond Relat. Mater. 14 (2005) 589.
Luminescent nitrogen-vacancy (N-V) and nitrogen-vacancy (Si-V)
color centers in diamond
350
(N-V)
575 nm
(N-V)
637 nm
200
150
2-nd order
250
daimond
Intensity, arb. units
-
0
300
Si-V
738 nm
PL spectrum on moderate quality of
polycrystalline diamond film.
100
● Bright PL lines на 637 nm (1,945
эВ) from NV- and 575 nm from NV0.
50
0
500
600
700
Wavelenght, nm
800
● PL lines на 738 nm from SiV.
● All these centers are stable at room
temperature.
● Doping during growth process
Si impurity in CVD diamond: depth mapping
V. Ralchenko, in Nanostructured Thin Films and Nanodispersion Strengthened Coatings, 2004, p. 209.
Mapping PL in cross section
50
Intensity, a.u.
40
30
o
Si, 800 C
20
o
Si, 700 C
10
o
M o, 700 C
0
0
10
20
30
40
50
60
distance from substrate surface,  m
Si-diamond interface
The diamond films were deposited on Si
substrate at temperature 700ºC (squares) and
800ºC (triangles), and on Mo substrate at 700ºC
(circles).
Si impurity extends to 20-60 μm in depth.
Optical transmission
Extremely broad transparency window: from UV to RF,
including THz range
1
80
Window 27_02_2009
# 109
1 5 0  m t hick
40
Transmittance
T ra n s m itta n c e , %
60
20
1
10
0
10
W a ve le n g th ,  m
● Cut-off wavelength 225 nm.
● 2-phonon absorption band at 2.5- 6.3 µm
● Loss tangent 10-5 at 170 GHz.
100
Wavenumber, cm
1000
-1
Optical transmission in UV and visible range for natural
IIa type single crystal diamond and poly CVD film
80
S in g le crysta l
70
C V D d ia m o n d
T ra n s m is s io n , %
60
50
40
absorption and scattering on
defects and grain boundaries
30
20
10
0
200
300
400
500
600
W a v e le n g th , n m
700
800
Polycrystalline CVD diamond as material for high power CO2
laser windows
Non-contact phase photothermal method to absolute measurements of optical
absorption coefficient
The absorption of heating CO2 laser (λ=10.6 μm) leads to local variable (at
the modulation frequency) heating and to changes in the refractive index,
which, in turn, caused the change in the phase difference between two probe
beams of He-Ne laser (633 nm) detected by the probe interferometer.
Diamond type
HPHT single crystal (yellow)
Natural single crystal (white)
CVD polydiamond (GPI)
CVD polydiamond (Element Six)
Theoretical limit
(due to two phonon absorption tail)
α, cm-1 (10.6 μm)
0.09 – 0.50
0.086
0.057
0.03
0.03
Simulation and experiment show that the level of low
absorption achieved is enough for use of CVD diamond
as window of multi-kilowatt cw CO2 lasers.
A.Yu. Luk’yanov, Quantum Electronics (Moscow) 38 (2008) 1171
Dielectric losses in CVD diamond (170 GHz)
● Far infrared (Microwave) absorption of dielectrics is due to lattice absorption owing to
unharmonism (two phonon absorption - TPA). Diamond has very low TPA, hence low
loss tangent.
● Theory: tgδ ~109 for λ=2 mm (150 GHz) [B. Garin, JTP Lett. 1994, No. 21, p.56] –
record low for any material. Compare with tgδ ~105 for Si.
● Experiment: best result tgδ ~ 3106 @ 140 GHz for Element Six polydiamond.
Sample: GPI 0.74 mm thick diamond film
tgδ ~105 stable up to 400ºC
6
ta n  [1 0
]
35
ta n  [1 0
30
5
]
5
25
4
20
3
1
15
2
2
10
1
50
5
100
150
200
f [G H z]
0
100
200
300
400
500
600
o
T e m p e ra tu re , C
B. Garin et al. Techn. Phys. Lett. 25 (1999) 288
MicroRaman mapping of stress in diamond films
The confocal optical scheme – high spatial resolution
1 3 3 2 .5 c m
-1
◄ no stress
a
Intensity, a.u.
b
1320
c
1330
R am an shift, cm
d
◄ compressive stress
e
◄ tensile stress
1340
-1
Raman spectra taken at 5 different locations on the surface of diamond film
within one grain (≈100x100 µm). The shift of the peak from 1332. 5 cm-1
position is the evidence of stress.
MicroRaman stress mapping on a surface over
a selected 160x160 μm grain in the diamond film
local stress regions
E
Ki
Ks
Ei
{1 1 0 }
[1
10
-1
4
 , c m
A
D
6
C
]
2
_
[0 0 1 ]
[110]
{110}
[001]
 [cm-1] = -2.2 [GPa] stress along (111);
 [cm-1] = -0,7 [GPa] stress along (100).
max  ≈ 6 cm-1
S plitting
[1 1 0 ]
B
0
max  ≈ 3 GPa
I.I. Vlasov, Appl. Phys. Lett. 71 (1997) 1789.
MicroRaman Stress mapping around grain boundary
laser beam scanning in depth and along the surface
1332.5 cm
tension (-)
in-depth, grain B
in-depth, grain A
lateral, from A to B
-1
1332.5 c m
com pression (+ )
tens ion (-)
1332.5 cm
-1
c om pres s ion (+ )
tension (-)
-1
com pression (+ )
-60  m
0 m
-40  m
0 m
20  m
Intensity, a.u.
-20  m
Intensity, a.u.
Intensity, a.u.
0 m
20  m
40  m
20  m
1320
1330
1340
R a m a n s hift, c m
40  m
60  m
40  m
1320
1330
1340
-1
R a m a n s h ift, c m
-1
1320
1330
1340
R a m a n s h ift, c m
-1
I. Vlasov, Physica Status Solidi (a), 174 (1999) 11.
Fracture strength by 3-point measurement techniques
Advantage of 3 point method: ability to handle with small size samples
Observation: the fracture happens
close to the central part of the bars (in
locations of maximum stress)
Testing apparatus at Fraunhofer
Institute IAF, Friburg
Fracture strength
Young’s modulus
 
E 
3
l
2 h b
2
l
 F frac (1)
3
4 b h
3

F
(2)
D
b and h are the specimen width and thickness,
Fс is critical load value,
l = 7.8 mm is distance between supports,
D is displacement of the bar under load
(measured by an inductive sensor with a resolution
~ 1µm).
two supporting cylinders 3mm diameter.
Similar principle at USTB (Beijing) DF-100 test unit
bar thickness of 0.5 mm only
L = 8 mm, loading rate 0.5 N/s
V.G. Ralchenko et al. Diamond and Related Materials 23 (2012) 172.
Fracture strength vs film thickness
white diamond
2500
300
Grain Size, m
Fracture strength f, MPa
250
2000
200
150
100
50
1500
0
0
500
1000
1500
Film Thickness, m
2000
Grain size ranges with thickness
from 10 µm to ~ 200 µm
substrate side
1000
σfr = 400 - 1400 MPa
for 0.5 mm thick plate
500
growth side
0
0
300
600
900
1200
Film thickness, m
● Rapid increase in strength towards small thickness h:
σ = 600 MPa @ h ≈ 1000 µm ► 2.2 GPa @ h = 60 µm (nucleation side in tension).
● Similar tendency for growth side.
● Compatible with Hall-Petch relation if the length of critical cracks is proportional to grain size.
● Results similar to Element Six data.
● The Young’ modulus of Е=1072 ± 153 GPa measured from the bending tests is only 10% lower
compared to therotetical Young’ modulus of polycrystalline diamond.
Fracture strength vs grain size
Hall-Petch relation σf = σ0 +Kd-1/2
400
Fracture strength f , MPa
2400
Grain size d, m
100
44
25
16
11
substrate side
2000
1600
1200
800
400
0
growth side
0
0.05
0.10
0.15
(Grain size d)
0.20
- 1/2
, m
0.25
0.30
- 1/2
Growth side and substrate side are under tensile load. White diamond.
The plate side under
0, MPa
K, MPa·cm1/2
41±36
3900±270
197±105
6910±780
tension
growth side (21 samples)
substrate side (21 samples)
Fracture patterns close to growth and nucleation sides
white diamond
Growth side, top view –
evidence of transgrain fracture
Growth side
Cleavage steps
Nucleation side
●Transcrystallite fracture over entire film thickness
● Strong grain boundaries
Fractures statistics. Weibull analysis for white diamond
P(σ) = 1 – exp[– (σ)/σN)m]
m is Weibull modulus, can found from slope of eq. or ln[–ln(1 – P)] = – mln(σN) + mln(σ)
High m value means more narrow strength interval (more predictable behavior).
2
ln (-ln(1-P))
1 growth side
0
m = 6.4
-1
substrate side
-2
m = 4.5
-3
-4
5.7
(a)
Failure Probability
1.0
0.8
0.6
0.4
6.3
6.6
6.9
7.2
substrate side
0.2
0
6.0
growth side
(b)
0
ln , MPa
Nominal strength
σN = 550 MPa for growth side in tension
σN =1060 MPa for substrate side in tension
Higher modulus m for growth side
300
600
900
, MPa
1200
1500
Comparison of fracture strength of white and black diamond
film thickness 0.5 mm
diamond
grade
black
white
thickness t, grain size,
μm
μm
538±39
490±10
10
60
σfg,
MPa
σfn,
MPa
141±10
312±33
316±109
812±86
Independent on what side is under tension, a factor of 2 – 2.5 lower σ for
opaque material in spite of the smaller grain size.
Black diamond. Fracture surface
Cleavage along GB ►smooth surface planes along boundaries of columnar grains
► reduced bending strength
intergranular fracture
transgranular
fracture
Growth side
Nucleation side
Area in the middle of the cross- section
Columnar structure is seen even in a few
microns thin layer adjacent to the substrate.