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Ductile High-Entropy Alloys
February 25, 2019
It's
playtime at the
elementary school, and the
teacher marches her
children outside to the
playground. There are
rules of decorum inside the school, and all the children have learned to march in a
single file out the door. Once out the door, it's the usual
chaos at the playground until the teacher signals that it's time to return to the classroom, The children
queue at the door for their march back to class. Their arrangement, however, is not the same as when they arrived. That's an example of
entropy.
While the
idea of entropy was known from
Carnot's 1824 work on the
efficiency of
heat engines, now codified in the
second law of thermodynamics, it was given a
statistical interpretation by
Ludwig Boltzmann (1844-1906) around 1875.
Boltzmann's entropy formula is easily written:
where
S is the
configurational entropy,
KB is
Boltzmann's constant of 1.38065 x 10
23 joule/
kelvin (J/K), and
Ω is the number of
states accessible to a system; that is, the ways in which
atoms can be differently arranged.
Austrian physicist, Ludwig Boltzmann (1844-1906), in a 1902 photo.
As Seneca the Younger (c. 4 BC - 65 AD) quoted Aristotle in his De Tranquillitate Animi (On Tranquility of the Mind),[1] "No great genius has existed without an element of madness (Nullum magnum ingenium sine mixtura dementiae fuit)," and Boltzmann was an example of this.
Boltzmann appears to have been a manic depressive, with intense work in physics interrupted by periods of depression. This condition was exacerbated by the rejection of his ideas by his physics peers. He committed suicide in 1906 while on holiday with his family.
(Wikimedia Commons image, modified for artistic effect.)
If we form a
crystal of a
pure element, there's no entropy involved, since all the
atoms are the same.
Elements have
isotopes that make some atoms distinguishable from others, but such isotopes behave identically as far as
chemistry is concerned. In the case of combining atoms of
i different elements of
mole fractions Xi, the entropy is easily calculated:
where
R is the
gas constant of 8.314
joule/
kelvin/
mol. While we can imagine such a crystal forming with the different atoms populating the
regular lattice sites in a
crystal structure, it's the nature of atoms that they prefer to
bond together in different ways. That's why a
mixture of
metal atoms typically results in a
solid of different
polycrystals. In most cases, formation of secondary
phases is encouraged by the addition of certain elements to provide additional
strength. That's why pure
iron is soft, but iron with the addition of
carbon forms
steel strengthened by an iron-
carbide phase (
cementite).
Alloy design has always been about the creation secondary phases in a base metal to improve
physical properties such as strength,
fracture toughness, and
ductility, and also chemical properties such as
oxidation resistance and
corrosion resistance. That mindset was broken with the 2004
publication by
scientists at the
Oxford University Department of Materials of a single phase
alloy made from equal portions of five components.[2] This alloy was
Fe20Cr20Mn20Ni20Co20, which forms a
face-centered cubic solid solution. The entropy of such a material is high, since the five different atom types can be distributed in many arrangements. Alloys of this type are called
high-entropy alloys (HEAs).
Atomic structure model of the Oxford University FeCrMnNiCo alloy.
In this image, magenta = Fe, green = Co, blue = Cr, cyan = Ni, and yellow = Mn. Aside from slight differences in atomic size, swapping colors would serve just as well, since the composition is equi-atomic.
(Image by Shaoqing Wang, via Wikimedia Commons.)
Aside from being a
thermodynamic curiosity, do HEAs have any beneficial
properties? Equi-atomic multicomponent alloys have good resistance to
radiation damage, since they are more
tolerant to having their atoms displaced by
energetic particles such as
neutrons. It's been observed that HEAs with the
body-centered cubic crystal structure have high strength and low ductility, while the converse is true for face-centered cubic HEAs; however, the
statistical sample size is too small at this time to call this a
rule.
A recent
paper by
Chinese scientists presents their
research on the
cryogenic ductility of the face-centered cubic high-entropy alloy,
CoCrFeNi. As numerous
YouTube videos of
immersing various objects into
liquid nitrogen have demonstrated, most
materials become
brittle (less ductile) at
low temperatures. While most of these demonstrations are a
cheat, since the objects contain
water, this is a
phenomenon that happens for some alloys. Certain
steels will become brittle at temperatures below about -50 °C, and this was only discovered after many
World War II "
liberty ships" were lost in the cold waters of the
North Atlantic Ocean.
We need ductile metals that sustain their
fracture toughness at cryogenic temperatures for such applications as
spacecraft and
containment vessels for
Superconducting magnets. A good target would be an
ultimate tensile strength greater than 1
GPa, and a
strain at fracture greater than 60%.[4] This is difficult at cryogenic temperatures in most alloys, since the motion of
dislocations is limited.[3] The CoCrFeNi
high-entropy alloy was demonstrated to have a strength of 1.25 GPa and a strain at fracture of as large as 62% at
liquid helium temperature (4.2 K).[3-4]
Tensile tests of the CoCrFeNi high-entropy alloy at different temperatures.
An interesting feature is the serration (saw tooth) feature that appears in the stress-strain curve.
Deformation twinning produces strain-hardening that sustains plastic flow at stresses, resulting in the serration feature.[3]
(Image © Science China Press.)
The
researchers conjecture that the high strength and ductility of the alloys arises from the low
stacking fault energy at extremely low temperatures and a resulting deformation twinning.[3]
Ultimate tensile strength vs elongation for different materials at liquid helium temperature (4.2K). The CoCrFeNi high-entropy alloy shows superior properties. (Image © Science China Press.)
In a recent publication, the high entropy alloy concept has been extended to
oxide ceramics containing equi-molar ratios of multiple
transition metals and/or
rare earth elements.[5] These oxides have been shown to exhibit a strong tendency to crystallize in simple single phase structures, as would be expected from the high degree of configurational entropy.[5] One studied high entropy oxide (HEO) was X(
Co0.2Cr0.2Fe0.2Mn0.2Ni0.2)
O3 in which X was
Gd,
La,
Nd,
Sm, or
Y.[5]
References:
- L. Annaei Senecae, "Ad Serenvm de Tranquillitate Animi," from the Latin Library.
- B. Cantor, I.T.H. Chang, , P. Knight, and A.J.B. Vincent, "Microstructural development in equiatomic multicomponent alloys," Materials Science and Engineering, vols. 375-377 (July 2004), pp. 213-218, doi:10.1016/j.msea.2003.10.257.
- Junpeng Liu, Xiaoxiang Guo, Qingyun Lin, Zhanbing He, Xianghai An, Laifeng Li, Peter K. Liaw, Xiaozhou Liao, Liping Yu, Junpin Lin, Lu Xie, and Jingli Ren, "Excellent ductility and serration feature of metastable CoCrFeNi high-entropy alloy at extremely low temperatures," Science China Materials (December 6, 2018), pp. 1-11, https://doi.org/10.1007/s40843-018-9373-y.
- A high-performance material at extremely low temperatures: High-entropy alloy, Science China Press Press Release, January 4, 2019.
- Ralf Witte, Abhishek Sarkar, Robert Kruk, Benedikt Eggert, Richard A. Brand, Heiko Wende, and Horst Hahn, "High entropy oxides: An emerging prospect for magnetic rare earth - transition metal perovskites," arXiv, January 8, 2019.
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