Photon Factory Activity Report 2022 #40 (2023)

Metallic bonds and thermal vibration in brass

BL-9C/2022G017

Toshihiko YOKOYAMA1,*1

Institute for Molecular Science, Myodaiji-cho, Okazaki, Aichi 444-8585, Japan

1 Introduction
The CuZn alloy called brass is one of the most familiar
alloys. Cu and Zn exhibit significantly different
thermodynamical properties in elemental metals such as
the boiling point, the melting point, the adhesive energy,
the bulk modulus, and the interatomic distance. In thepresent study, local structural and thermal vibrational
properties of the brass alloy were investigated by analysing
temperature dependent Cu and Zn K-edge EXAFS(extended x-ray absorption fine structure) spectra andconducting the theoretical PIECP (path integral effectiveclassical potential) simulations. For details of the present
study, see the already published reference [1].

temperatures of ΘD(Cu) = 295 K and ΘD(Zn) = 302 K. ThePIECP results agree with the EXAFS ones at least
qualitatively [ΘD(Cu) = 329 K and ΘD(Zn) = 348 K]. Thisfinding is rather surprising since it seems to be essentiallycontradictory to the simple prediction based on thepotential stiffness (Cu should be much stiffer than Zn).
Figure 2 shows temperature dependence of theinteratomic distance R [Fig. 2(a)], the third- and fourthorder cumulants, C3 [Fig. 2(b)] and C4 [Fig. 2(c)], for the
first-NN shells. In Fig. 2(b), although the PIECP
simulation slightly underestimates the C3 values, theagreement in C3 between the EXAFS and PIECP results is2 Experiment
The Cu and Zn K-edge EXAFS spectra of acommercially available brass foil Cu64.7Zn35.3 with 10 µm
thickness were recorded at BL9C with the transmission
mode for the temperature range of 20-300 K.
3 Results and Discussion
Figure 1 shows the mean square relative displacements
C2 for the first-NN (nearest neighbor) shells obtained by
the experimental EXAFS analysis and the theoretical
PIECP simulation. It is found that the absolute C2 values
are noticeably larger in the EXAFS results than in thePIECP simulation, indicating much larger static disorder inthe real alloy sample. More importantly, the EXAFS
results show slightly smaller temperature dependence
around Zn than around Cu, this yielding the Debye

Fig. 1 Mean square relative displacements C2 for thefirst-NN pairs obtained by the one-shell EXAFS
analysis (with error bars; Cu: red; Zn: green) and thePIECP simulations (average Cu: magenta; average Zn:
light blue; solid line: quantum; dashed line: classical),respectively. The corresponding Debye temperatures
are also given in the figure.

Fig. 2 Temperature dependence of (a) the interatomic
distance R, (b) third- and (c) fourth-order cumulants, C3and C4, for the first-NN pairs obtained by the EXAFS
analysis (with error bars; Cu: red; Zn: green) and thePIECP simulations (average Cu: magenta; average Zn:light blue). The lattice constant (a0/√2) are also plottedin (a), where the experimental thermal expansion
coefficient was referred to from the literature.

Photon Factory Activity Report 2022 #40 (2023)

Fig. 3 (a) Two-body interatomic potentials of Cu–Cu,Cu–Zn, and Zn–Zn pairs estimated the EAM(embedded atom method). Numerical potential
indicators are given in the figure. (b) Frequency
distribution of the first-NN Cu–Cu, Cu–Zn, and Zn–Znforce constants in ten types Cu171Zn85 superlattices.
The average force constant values for the Cu–Cu, Cu–Zn, and Zn–Zn pairs are given in the figure.
fairly good. The EXAFS C3(Zn) seems to be a little smaller
than C3(Cu), and temperature dependence of PIECP
C3(Zn) also looks slightly smaller than the PIECP C3(Cu),
implying consistency between the EXAFS and PIECP
results at least qualitatively.
Figure 3(a) shows the two-body interatomic potential
for each atom pair, employed in the present PIECP
simulations. As expected, the Zn–Zn potential is actually
the shallowest, while the Cu–Cu potential is the deepest.
On the contrary, Fig. 3(b) shows the frequency distributionof the first-NN force constants in the present Cu171Zn85

superlattices, and it is clearly found that the Zn–Zn atompair gives a larger force constant than the Cu–Cu pair. The
reason for a larger force constant in Zn–Zn atom pair isprobably ascribed to a steeper repulsive potential at ashorter distance side in the Zn–Zn pair. When the system
is really diatomic, the Zn–Zn distance is hardly contracted
due to the steep repulsive potential and is easily elongated,
resulting in large anharmonic vibrational amplitude in thediatomic Zn2 molecule. On the contrary, in a closed packed
solid like fcc, the Zn–Zn distance is hardly elongated dueto the existence of other atoms at the opposite side, leading
to confinement of the Zn atom. This is coincident to theinteratomic distance determined by the EXAFS analysis. It
is expected that the first-NN interatomic distance aroundZn would be significantly larger than that around Cu, while
the EXAFS analysis reveals that the first-NN interatomicdistances are not very different from each other [only ~0.01Å difference between Cu and Zn. See Fig. 2(a)]. This
indicates that the Zn atoms in brass are likely to be
confined in a space that is a little too small for Zn and are
hardly movable.
In summary, local thermal vibration in brass wasinvestigated by the temperature dependent Cu and Zn Kedge EXAFS measurements and the theoretical PIECP
simulation. It is unexpectedly found that the thermal
vibrational amplitude around Zn is meaningfully smaller
than that around Cu and that the first-NN interatomic
distances are nearly equivalent between Zn and Cu.
Although brass is one of the most familiar alloys, thefundamental thermal properties are still not easily
predicted. The experimental EXAFS and theoretical
PIECP techniques have successfully settle the problem inthe present work and will remain useful techniques forfuture works.
References[1] T. Yokoyama, Phys. Chem. Chem. Phys. 25, 3413
(2023); DOI: 10.1039/D2CP05035H.
* yokoyama@ims.ac.jp