Composites with extremal or unusual thermal expansion coefficients are designed using a three-phase topology optimization method. The composites are made of two different material phases and a void phase. The topology optimization method consists in finding the distribution of material phases that optimizes an objective function (e.g. thermoelastic properties) subject to certain constraints, such as elastic symmetry or volume fractions of the constituent phases, within a periodic base cell. The effective properties of the material structures are found using the numerical homogenization method based on a finite-element discretization of the base cell. The optimization problem is solved using sequential linear programming. To benchmark the design method we first consider two-phase designs. Our optimal two-phase microstructures are in fine agreement with rigorous bounds and the so-called Vigdergauz microstructures that realize the bounds. For three phases, the optimal microstructures are also compared with new rigorous bounds and again it is shown that the method yields designed materials with thermoelastic properties that are close to the bounds. The three-phase design method is illustrated by designing materials having maximum directional thermal expansion (thermal actuators), zero isotropic thermal expansion, and negative isotropic thermal expansion. It is shown that materials with effective negative thermal expansion coefficients can be obtained by mixing two phases with positive thermal expansion coefficients and void.

Design of materials with extreme thermal expansion using a three-phase topology optimization method

Negative thermal expansion (NTE) is an intriguing physical property of solids, which is a consequence of a complex interplay among the lattice, phonons, and electrons. Interestingly, a large number of NTE materials have been found in various types of functional materials. In the last two decades good progress has been achieved to discover new phenomena and mechanisms of NTE. In the present review article, NTE is reviewed in functional materials of ferroelectrics, magnetics, multiferroics, superconductors, temperature-induced electron configuration change and so on. Zero thermal expansion (ZTE) of functional materials is emphasized due to the importance for practical applications. The NTE functional materials present a general physical picture to reveal a strong coupling role between physical properties and NTE. There is a general nature of NTE for both ferroelectrics and magnetics, in which NTE is determined by either ferroelectric order or magnetic one. In NTE functional materials, a multi-way to control thermal expansion can be established through the coupling roles of ferroelectricity-NTE, magnetism-NTE, change of electron configuration-NTE, open-framework-NTE, and so on. Chemical modification has been proved to be an effective method to control thermal expansion. Finally, challenges and questions are discussed for the development of NTE materials. There remains a challenge to discover a “perfect” NTE material for each specific application for chemists. The future studies on NTE functional materials will definitely promote the development of NTE materials.

Negative thermal expansion in functional materials: controllable thermal expansion by chemical modifications

New Al-based amorphous alloys were formed in Al-Ce-M (M=Nb, V, Cr, Mn, Fe, Co, Ni or Cu) ternary systems by melt spinning. The compositional range is the widest for Al-Ce-Ni alloys and extends from 2 to 15 at% Ce and below 30%Ni. The Al-Ce-M (M=Nb, Fe, Co, Ni or Cu) alloys containing over 80%Al have good bending ductility. The crystallization temperature (Tx) and hardness (Hv) of the ductile alloys increase to 625 K and 400 DPN with increasing M and Ce content and the highest tensile strength reaches 935 MPa. The effect of M elements on Tx and Hv is interpreted by taking the bonding nature of Ce and M atoms into consideration.

New Amorphous Alloys with Good Ductility in Al-Ce-M (M=Nb, Fe, Co, Ni or Cu) Systems : Condensed Matter

It is experimentally shown that an anomalously high negative magnetoresistance is observed in silicon with manganese-atom complexes [Mn]4 at room temperature. It is established that the negative magnetoresistance has the largest value at T = 230–240 K, while its value decreases with temperature, and the inversion of the magnetoresistance sign takes place at T < 170 K; i.e., the positive magnetoresistance is observed. It is established that the negative magnetoresistance and its temperature dependence are substantially affected by the intensity of both integrated and monochromatic light.

Negative magnetoresistance in silicon with manganese-atom complexes [Mn] 4

Structural rearrangement in SrRuO3 near the magnetic critical point

Using a low-temperature stage X-ray diffractometer, we have investigated the temperature dependence of the lattice parameters of single crystal superconductors Bi2Sr1.8CaCu2Ox. The experimental results show that (i) the lattice constants increase linearly with increasing temperature above about 100 K; (ii) thec-axis lattice parameter shows a kink in the superconducting transition region, while thea, b-axis parameters do not show any anomalous behavior in this region; (iii) botha, b, andc show negative thermal expansion coefficients below 40–50 K, which may be related to the characteristics of the Cu-O bond.

Thermal expansion of Bi2.2Sr1.8CaCu2Ox superconductor single crystals

The transverse magnetoresistance has been measured for the newly discovered magnetically ordered icosahedral quasicrystals Al70−xPd15Mn15Bx (x=0,2,4,6,8,10). Experiments were conducted at 4.2 K in magnetic fields up to 5.5 T. The results showed a systematic change as a function of boron concentration. The magnetoresistance for x=0,2,4,6 showed a negative field dependence which became weak with increasing x. The samples with x=8,10 showed a negative magnetoresistance at low fields, which became positive for higher applied fields. The minimum in the magnetoresistance shifted to lower field value with increasing boron content (to about 0.5 T for 10 at. %B). The analysis of the results has been based on the theory of three‐dimensional weak localization, with a strong influence of spin‐orbit scattering. The magnetoresistance is negative for low boron concentration due to weak spin‐orbit scattering, and is positive for high boron concentration due to strong spin‐orbit scattering.

Magnetoresistance of the magnetically ordered icosahedral quasicrystals Al‐Pd‐Mn‐B

Amorphous AlYNi alloys, prepared by rapid solidification from the melt, have shown a unique combination of low density and high tensile strength. In the present work amorphous alloys of the composition Al 87 Y 8 Ni 5− x Fe x (2≤ x ≤5) have been studied using room temperature 57 Fe Mossbauer effect spectroscopy. These alloys show a mean quadrupole splitting which increases slightly with increasing Fe content. The mean isomer shift remains essentially constant as a function of x . All spectra are very nearly symmetric, indicating a weak correlation between the isomer shift and quadrupole splitting. The mean isomer shift is approximately +0.17 mm/s relative to α-Fe and is consistent with Fe probe atoms in a close-packed Al environment.

Mössbauer effect studies of amorphous AlYNiFe alloys

The magnetic and electrical transport properties of amorphous Fe‐Zr based alloys with compositions near 10 at. % Zr with various elements substituted for Fe are of particular interest. In the case of Mn substitutions the Curie temperature and the average magnetic moment decrease monotonically with increasing Mn content and the temperature dependence of the magnetization is significantly modified. The electrical transport properties of amorphous Fe90−xMnxZr10 (for x=0, 4, 8, and 12) over the temperature range of 4.2–300 K and the magnetoresistance for fields up to 4.0 T at 4.2 K are reported in the present work. A broad minimum in the resistivity is observed at around 255, 235, 200, and 180 K for the four compositions, respectively. In the case of the x=8 sample a second minimum occurs at around 50 K. The magnetoresistance of all samples shows a sharp increase for small fields and a linear field relationship for fields above about 0.1 T.

M.H. Yewondwossen

Papers

Thermal expansion of Bi2.2Sr1.8CaCu2Ox superconductor single crystals

Magnetoresistance of the magnetically ordered icosahedral quasicrystals Al‐Pd‐Mn‐B

Mössbauer effect studies of amorphous AlYNiFe alloys

Electrical transport in amorphous Fe‐Mn‐Zr alloys