The
Physics
Department
at Boston
College,
Higgins Hall
When a Good Martensite Metal… Goes Bad!
C. P. Opeil1, J. C. Lashley2, R. A. Fisher3, R. K. Schulze2,B. Mihaila2,
J. L. Smith2, P. Riseborough4, L. Mañosa5 and A. Planes5
1Boston
College, Physics Department, Chestnut Hill, MA, USA
2Los Alamos National Laboratory, Los Alamos, NM, USA
3Univ. of California, Berkeley-Lawrence/Berkeley Laboratory, CA,
USA
4Temple University, Physics Department, Philadelphia, PA, USA
5 Universitat de Barcelona, Departament d Estructura i Constituents
de la Matèria, Facultat de Física, Diagonal 647, E-08028 Barcelona,
Catalonia, Spain
Work sponsored by: Dept. of Energy and Boston College
Boston C
ollege
Fr. Opeil s
Low Temperature
Laboratory
Hey George, do you know how a
good martensite metal…
turns bad?
Barman, et al., PRB 72, 184410 (2005).
HIGH T:
Heusler, L21 (Fm3m)
•
•
•
•
austenitic
cubic
Magnetic moment on
Mn atoms: µ≈ 4.2µB
Coupling RKKY
Ferromagnetic order
Weak magnetic anisotropy.
martensitic
tetragonal
distortion
Martensitic Transition…… and related properties
Solid state transition: first-order, diffusionless,
driven by shear mechanisms.
High-symmetry
Phase (cubic)
Low-symmetry
phase.
(degenerate)
Shape-Memory effect
CUBIC PHASE
MARTENSITE
Strain
Ni2MnGa Single Crystal
Low Energy Electron
Diffraction (LEED)
at T=293 K
Back Scatter Laue, T = 293K
Ni2MnGa (100)
Cubic
Fm-3m
a = 5.825 Ang.
Vol = 192.34 Ang.3
Ni (0.25,0.25,0.25)
Mn (0.5,0.5,0.5)
Ga (0, 0, 0)
ρ(T) (close up):
ρ(T):
martensite
crystallographic
changes
Abe, what s this?
Is our martensite metal
good or is it… going bad?
ρ(T):
martensite
crystallographic
changes
Jason C. Lashley
Jason C. Lashley
Resistivity? Well, what
the heck is resistivity?
Resistance and Resistivity: Electrical Transport
i
i
Resistance and Resistivity: Electrical Transport
i
i
Resistance and Resistivity: Electrical Transport
i
i
Volts
Resistance
R [ohms]= V [volts] / i [amps]
Ohm s Law
Resistance and Resistivity: Electrical Transport
d
i
i
Volts
A
Resistance
R [ohms]= V [volts] / i [amps]
ρ [ohms-cm] = R [ohms] x A [cm-cm]/d [cm]
Ohm s Law
Resistivity
Resistance and Resistivity: Electrical Transport
d
i
i
Volts
A
Resistance
R [ohms]= V [volts] / i [amps]
Ohm s Law
ρ [ohms-cm] = R [ohms] x A [cm-cm]/d [cm]
Resistivity
ρ [ohms-cm] = V [volts] x A [cm-cm] / i [amps] x d [cm]
Resistance and Resistivity: Electrical Transport
d
i
i
Volts
A
Resistance
R [ohms]= V [volts] / i [amps]
ρ [ohms-cm] = R [ohms] x A [cm-cm]/d [cm]
Ohm s Law
Resistivity
ρ [ohms-cm] = {V [volts] x A [cm-cm]}/{ i [amps] x d [cm]}
ρ (T) = {V x A}/{ i x d}
ρ
[ohms-cm]
normal metallic behavior
Temperature (K)
Resistivity (AC Transport)
Resistivity (AC Transport), ρ(T):
non-monotonic
behavior
sudden
energy shifts
Pre-Martensite Transition Resistivity (H = 0 T):
7.40 K
Magneto-resistance (H = +1 to -1 T) & H⊥ [1,0,0]:
Magneto-resistance (H = +1 to -1 T) & H⊥ [1,0,0]:
Dilatometry
MT
197 K
MT is field independent
FCC to Monoclinic at MT
PMT
214 K
Dilatometry: This technique measures the length change in a sample over changes in temperature and magnetic 5ield (5-­‐350 K, 0-­‐9 T). This dilatometer made of OFHC copper utilizes a capacitive technique that compares a capacitor gap to the expansion or contraction of a sample. Further design details of this dilatometer can be found in G. Schmiedeshoff, et al., Rev. of Sci. Inst. 77, 123907 (2006) see below. This technique enables measurement of linear and volumetric coef5icients of expansion, Grüenisen parameters and indications of sudden changes in crystal symmetry. Specific Heat:
How much heat energy can you
stuff in or take out
of a little sample in a certain amount of time?
Heat
Heat
Energy
Energy
sample
Specific Heat:
Specific Heat:
Specific Heat:
Vacuum
Specific Heat:
on
T [K]
off
t [sec]
on
T [K]
t [sec]
off
Specific Heat:
T [K]
T1 = A1 exp{+B1/τ1}
T2 = A2 exp{-B2/τ2}
t [sec]
Specific Heat
T = 2 - 300 K, B = 0 g
Specific Heat
T = 2 - 300 K, B = 10000 g
Specific Heat
T = 2 - 300 K, B = 0 to 90000 g
TM = 202 K
Specific Heat (H = 0 g)
C/T = γ + B3T2
Trange = 2 - 30 K
H=
0
100
250
500
1,000
5,000
7,500
10,000
90,000 (g)
Specific Heat
C/T = γ + B3T2
(H = 90,000 g)
Trange = 2 - 30 K
H=
0
100
250
500
1,000
5,000
7,500
10,000
90,000 (g)
Specific Heat: Global Data (H = 0 to 90,000 g)
Specific Heat Analysis of Ni2MnGa:
global
Normative for
Magnetic
Materials
C/T = γ + B3T2
Comparable
to Cu
Trange = 2 - 30 K
ΔSM = Entropy Change due to M Transistions
ΔHM = Enthalpy Change
ΔSL = Entropy Change (Latent) due to PM Transistion
ΔHL = Enthalpy Change (Latent)
Photoemission,
Electrons and Gaps
Fundamentals of Photoemission:
The big three names:
Photoelectric
effect
H. Hertz
Observed
P.E.E. first
in 1887
A. Einstein
Nobel 21
K. Siegbahn
Nobel 81
ARPES: Angle
Resolved
Photoemission
Spectroscopy
e-
Ekinetic = h" # e$ # Ebinding
!
Brillouin
zone
orientation
!
[100]
kX
kII =
kZ
Z
ARPES - choose azimuthal
analyzer
2meEkinetic
2
h
θ to specify k-vector to
probe, and then vary polar
φ to collect DOS at various
kII and observe dispersion
of bands along k-vector
surface normal
φ
α-U(001) surface
" sin#
θ
[001]
kY
[010]
(100) plane
Energy Levels or Bands
1s2, 2s2, 2p6, 3s2, 3p6,
4s2, 4p6....6d, 7f
Outer shell
Valence band
Fermi
Energy
N
Inner shell
or energy band
Outer shell
Valence band
Energy Levels or Bands
1s2,
2s2,
2p6,
3s2,
3p6,
Fermi
Energy
What happens at
the Fermi energy
determines the type
of energy gap.
4s2, 4p6....6d, 7f
As distance
changes from the
nucleus, electron
energy and
density change
until the Fermi
energy is
reached.
Inner shell
or energy band
N
Energy Levels or Bands
1s2,
2s2,
2p6,
3s2,
Outer shell
Valence band
Fermi
Energy
What happens at
the Fermi energy
determines the type
of gap.
3p6,
4s2, 4p6....6d, 7f
Just before the Fermi
Energy we can have
three kinds of gaps,
Band Gaps:
1) No Gap
2) Full Gap
3) Pseudo-Gap
Think of a Gap as the
ability for outer
electrons to reach the
Fermi Energy.
Inner shell
or energy band
N
Density of states
Densities of States
and Gaps
No Gap
Density of states
Energy (eV)
Fermi Energy
Gap between
last energy state
and the FE
Energy (eV)
Fermi Energy
Density of states
A Gap becomes…
Energy (eV)
Fermi Energy
Density of states
A Gap becomes a Pseudo-Gap:
Energy (eV)
Pseudo-Gap – Distinct changes
around the Fermi Energy. No
excluded density of states, but
fluctuations in the density of states
due to temperature or field.
Fermi Energy
Band Gaps:
1) No Gap - No excluded density of
states, a good metal.
2) Full Gap - Some excluded density of
states, a very, very bad metal, in
reality an insulator.
3) Pseudo-Gap – No excluded density of
states, but fluctuations in the
density of states due to temperature
or field.
Temperature Dependent UV-Spectroscopy (hν=21.21eV)
Normal Incidence
Temperature Dependent UV-Spectroscopy (hν=21.21eV)
Normal Incidence
ARPES-295 K
Contour height
color key
ARPES-219 K
ARPES-219 K
Contour height
color key
ARPES-173 K
Energy Dispersion Curves:
normal incidence
normal incidence
-2.5
-2.0
-1.5
-1.0
-0.5
Eb [eV]
0.0
0.5
The story of data on a martensite metal
going bad
does not end there…
Life as a theorical physicist.
3-D Fermi Surface Map:
Fermi Surface Map
Lee, et al., Phys. Rev. B 66 (2002).
Surely you were aware when you accepted the position,
Professor, that it was publish or perish.
Surely you were aware when you accepted the position,
Father, that it was publish or parish.
Special thanks to some of my collaborators:
James L. Smith
Jason Captain Lashley
Your
name
here!
Thank you for listening,
none of these guys
ever listen to me!