Supplementary material for
Giant negative thermal expansion covering room temperature in nanocrystalline GaNxMn3
J. C. Lin,1 P. Tong,1,a) X. J. Zhou,2 H. Lin,2,b) Y. W. Ding,3 Y. X. Bai,3 L. Chen,1 X. G. Guo,1 C.
Yang,1 B. Song,1 Y. Wu,1 S. Lin,1 W. H. Song,1 and Y. P. Sun 4,1,5,c)
1
Key Laboratory of Materials Physics, Institute of Solid State Physics, Chinese Academy of
Sciences, Hefei 230031, China
2
Shanghai Institute of Applied Physics, Chinese Academy of Sciences, Shanghai 200120, China
3
Hefei National Laboratory for Physical Sciences at Microscale, University of Science and
Technology of China, Hefei 230026, China
4
High Magnetic Field Laboratory, Chinese Academy of Sciences, Hefei 230031, China
5
Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing
210093, China
Email addresses: a) tongpeng@issp.ac.cn (P. Tong), b) linhe@sinap.ac.cn (H. Lin), c)
ypsun@issp.ac.cn (Y. P. Sun)
1
1. Analysis of temperature-dependent X-ray diffraction data.
Temperature evolutions of (111) X-ray diffraction peak for N09 series of samples were
plotted in Fig. S1.
For non-milled samples, N10-BM0 (see Fig. 1 in the main text) and N09-BM0 (Fig. S1), the
clear-cut diffraction peaks allow us to fit the diffraction patterns using two cubic phases. The
refined lattice constant (a0) and phase fraction were plotted in Fig. S2(a)-(d). It is obvious that the
overall lattice expands upon cooling because the large-lattice phase (ph1) grows at the expense of
the small-lattice one (ph2). After ball milling, the diffraction peaks become wider (Fig. 1 and Fig.
S1). Consequently, the double X-ray diffraction peaks belong to the two phases are hard to be
distinguished (Fig. 1 and Fig. S1) and thus treated as a single peak during structure refinement.
Fig. S1. The (111) peak in XRD patterns at different temperatures for samples including (a) nonmilled (N09-BM0), (b) 10-hours milled (N09-BM10), (c) 22-hours milled (N09-BM22), (d) 35hours milled (N09-BM35) samples, respectively. The data corresponding to the temperature
range of negative thermal expansion were plotted in red for each sample. The dotted lines trace
the shift of peak as temperature changes.
2
Fig. S2. Coexistence of two cubic phases at the antiferromagnetic to paramagnetic transition in
GaN0.9Mn3 (N09) and GaNMn3 (N10) series of samples. For non-milled samples (N09-BM0 and
N10-BM0), the refined lattice constant and phase fraction are plotted in (a)-(d). Full Width at
Half Maximum (FWHM) of (111) X-ray diffraction was plotted in (e) and (f) for milled N09
(N09-BM10, N09-BM22 and N09-BM35) and N10 (N10-BM10, N10-BM25 and N10-BM35)
samples, respectively.
2. Particle and grain sizes of nanocrystalline GaNxMn3.
Particle size was significantly reduced after ball milling as demonstrated in the SEM patterns
(Fig. S3). The average grain size (<D>) was estimated using the (111) X-ray diffraction peak by
means of the well-known Scherrer formula [1]: <D> = 0.93λ/(BCosθ), where λ is the wavelength
of the X-ray radiation, θ the diffraction angle position of the (111) peak, and B is the full width at
3
half-maximum of the peak after taking into account the instrumental broadening. We choosed the
data at 163 K abd 403 K at which the samplses are in single phase.
Fig. S3. The FE-SEM images for the GaNMn3 (N10) samples subjected to ball-milling for 10
hours (N10-BM10) (a), 25 hours (N10-BM25) (b), and 35 hours (N10-BM35) (c).
4
Fig. S4. The average grain size at 163 K and 403 K deduced from the (111) X-ray diffraction
peak as a function of milling time for the samples GaNMn3 (N10) and GaN0.9Mn3 (N09).
3. Modeling of pair distribution function, G(r).
Temperature dependent G(r)s were plotted in Fig. S5.
We tested the G(r)s at 198 K and 373 K for both N10-BM0 and N10-BM25 samples using
the average cubic model (space group, Pm-3m). The r range for fitting is 1.5 Å - 9 Å. It is found
that the Pm-3m model describe the G(r)s well. The fitting profiles at 373 K were plotted in Fig.
S6(a) and (b) as an example. The obtained atomic displacements and lattice constant were listed
in Table S1. For Pm-3m symmetry, the atomic displacements is isotropic at both the Ga and N
sites (U11 = U22 = U33), but could be anisotropic at the Mn site [2]. However, the refined U11 (U22)
at Mn sites is very close to U33, no matter whether the sample was milled or not. The atomic
displacements at Mn and Ga sites are enhanced after ball milling, while those at N sites are
decreased. The atomic displacements for N site may be less accurate than those for Mn and Ga
sites because the X-ray atomic scattering factor for N is much smaller than that of Mn and Ga.
Assuming Mn deficiencies exist, the nearest Mn-Mn bond should split into three parts, two
longer ones and a shorter one [3]. So an anisotropic broadening of G(r) peak is expected.
However, the G(r) peaks at 2.7 Å and 3.85 Å arising from Mn-Mn and Mn-Ga bonds show a clear
Gaussian shape (Fig. S6(c) for N10-BM25 at 373K). This indicates there is no Mn-Mn bond
5
splitting. Furthermore, introducing Mn vacancies (e.g., 10% Mn vacancies, as shown in Fig.
S6(d)) to the Pm-3m symmetry gives a worse fit to the experimental G(r).
Fig. S5. Pair distribution functions, G(r)s, for non-milled (N10-BM0) (a) and 25-hours milled
(N10-BM25) (c) GaNMn3 samples at different temperatures. The magnified pattern of the G(r)
peak at 7.3 Å for N10-BM0 (b) and N10-BM25 (d).
6
Fig. S6. Modeling of G(r)s. Calculated G(r)s using cubic Pm-3m model (the red line) together
with the experimental G(r) (circle) at 373 K for non-milled (N10-BM0) (a) and 25-hours milled
(N10-BM25) (b) GaNMn3 samples. (c) A Gaussian fit (the red line) to the experimental G(r) (i.e.,
the data of (b)) peaks at 2.7 Å and 3.85 Å. (d) Calculated G(r) using cubic Pm-3m model
assuming 10% Mn vacancies (red line) and the experimental G(r) (circle). The difference
between calculated and experimental G(r)s is shown at the bottoms of (a), (b) and (d).
7
Table S1. The refined lattice constant, atomic displacements (U11, U22 and U33) and the agreement
factor (Rw) obtained by fitting the G(r) data for non-milled samples (N10-BM0) and 25-hours
milled samples (N10-BM25) with the cubic model (space group, Pm-3m).
Lattice constant (Å)
Ga(U11,U22,U33) (Å2)
N10-BM0
3.911
0.0060
N(U11,U22,U33) (Å2)
Mn(U11, U22) (Å2)
Mn(U33) (Å2)
Rw
0.0099
0.0080
0.0081
8.8%
373K
N10-BM25
3.887
0.00675
0.0079
0.0091
0.0089
10.4%
198K
N10-BM0
3.922
0.00314
N10-BM25
3.902
0.0045
0.01
0.00588
0.00592
8.3%
0.0067
0.00622
0.00625
9.8%
References:
[1] A. L. Patterson, Phys. Rev. 56, 978-982 (1939).
[2] P. Tong, D. Louca, G. King, A. Llobet, J. C. Lin, Y. P. Sun, Appl. Phys. Lett. 102, 041908
(2013).
[3] Z. H. Sun, X. Y. Song, J. Mater Sci. Technol. 30, 903-909 (2014).
8