Ferromagnetism and magnetomechanics of ferromagnetic thermoelastic martensites

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Ferromagnetism and magnetomechanics of
ferromagnetic thermoelastic martensites
Lecture 2

• V.A. Chernenko
• Institute of Magnetism, Kiev, Ukraine

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In collaboration with

• Lvov V.A. ,Taras Shevchenko University, Kiev,
  Ukraine
• Muellner P., Boise State University, Boise, USA
• Kostorz G.K., ETH, Zuerich, Switzerland
• Takagi T., Tohoku University, Sendai, Japan

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MAGNETOELASTIC MODEL OF FERROMAGNETIC MARTENSITE
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MAGNETIC CHARACTERISTICS OF MARTENSITE (theory)
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MAGNETIC CHARACTERISTICS OF MARTENSITE (theory)
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MAGNETIZATION VS TEMPERATURE(case TmTc)

• Ni53.1Mn26.6Ga20.3

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MAGNETIZATION VS TEMPERATURE(case TmltTc)

• Ni52.6Mn23.5Ga23.9

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MAGNETIZATION VS TEMPERATURE(case TmgtTc)

• Ni51.2Mn31.1Ga17.7

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(i)Magnetic-field-induced superelasticity of
ferromagnetic martensite(ii)Strain-induced
change magnetization of ferromagnetic martensite
(100)-oriented
(ii)
(i)
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MAGNETOMECHANICS OF SINGLE VARIANT Ni-Mn-Ga
MARTENSITE EXPERIMENT AND MODELLING

• The aim precise determination of magneto-stress
  as function of H
• and comparison with magnetoelastic model
• PART I
• Modeling of stress-strain curves under H is based
  on statistical approach developed by Lvov et
  al.,2003 for description of magnetostrain
  behavior

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• reorientation of variants is caused by total
• effective stress which is sum of mechanical and
  magnetic-field-induced stresses,tensile if
  positive, compressive if negative, it is acting
  in x direction in each twin variant.
• two-stage of twin boundary rearrangement
• critical stress is different for
  twin variants
• statistical distribution of critical stresses
  around certain sc

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For each stress value, N of disappeared twins
(boundaries jumps) is found from the condition
which gives rise with
(ii) to  
According to (i)
On stress-strain curve at H  x during
compression, ay is
During unloading
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All above equations need
function which is deduced from magnetoelastic
model as follows
s 3 is invariant to x y permutation s 2
only initiates any motion of twin boundaries
When H//x, it induces in y-variant
For x-variant s2(H)0
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• is negative, so s2(H) is compression along
  x-axis or tension along y-axis produced by H
• Compression along y ( ) for
  x-variant is equivalent to its elongation under
  stress because either
  stress results in same s2 value,so

For simultaneous H and syy
Most indicative is equivalent stress
Experiment tetragonal Ni52.0Mn24.4Ga23.6
martensite ( c/alt1), Texp293 K
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CALCULATED AND EXPERIMENTAL CURVES
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Experiment open circles Fitting solid line
Thermoelastic model dash X-variant
fractiondash-dot
Magnetoelastic nature of magneto- strain in
martensite !
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Conclusive remarks
In our model, magnetoelastic stress is
responsible for both ordinary magnetostriction
and detwinning.
(i) Illustratively, H.E. for ferromagnetic
martensite
Eqs. show that neither MA energy nor ZE cannot
contribute to stress. In contrast
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(ii) Illustration why the consideration of MA
energy instead of magnetoelastic can lead to the
reasonable physical estimations.
Substitution of spontaneous tetragonal
deformation into F
shows, that this deformation creates
magnetoelastic energy about
which is anisotropy energy
with
This energy is approximately equal to mechanical
work performed by magnetoelastic stress in
the course of detwinning of martensite.
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• How ordinary magnetostriction can induce twin
  boundary motion?
• If it is disregarded we are forced to state that
  on microscopic scale rotation of M-vector under
  H does not change atom positions neither in x-
  nor in y-variants so, no reason exists for twin
  boundary motion.
• Magnetostriction is sufficient to trigger
  detwinning
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  A.
• From Fig.(a) stress 1.8 MPa, causing complete
  detwinning, induces small elastic strain
• According to WLR this deformation exceeds
  sustainable misfit.
• Ordinary magnetostriction is
  .

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B.
If ,
magnetostrictive displacements of atoms near
pinning centers exceed value of c so,
magnetostriction is able to tear twin boundary
away from such centers

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Interdependence between magnetic properties and
lattice parameters of Ni-Mn-Ga martensiteResearc
h line followed scheme (i) measurements of
Hs(T)(ii) determination of c/a(T) according to
our phenomenological theory(iii) comparison
with c/a(T) function obtained by X-rays
measurements.
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Ni49,5 Mn25,4Ga25,1 (A1) TM 170 K, TA 180
K , TC 381 K Ni52,6Mn23,6Ga23,8 (A2) TM
284 K, TA 297 K,TC 363 K
A2
A1
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A
B
From X-rays (squares) From M(T) (circles)
So, validity of Eq. c/a vs Hs is confirmed!