Accelerated search for materials with targeted properties by adaptive design

Abstract

Finding new materials with targeted properties has traditionally been guided by intuition, and trial and error. With increasing chemical complexity, the combinatorial possibilities are too large for an Edisonian approach to be practical. Here we show how an adaptive design strategy, tightly coupled with experiments, can accelerate the discovery process by sequentially identifying the next experiments or calculations, to effectively navigate the complex search space. Our strategy uses inference and global optimization to balance the trade-off between exploitation and exploration of the search space. We demonstrate this by finding very low thermal hysteresis (ΔT) NiTi-based shape memory alloys, with Ti50.0Ni46.7Cu0.8Fe2.3Pd0.2 possessing the smallest ΔT (1.84 K). We synthesize and characterize 36 predicted compositions (9 feedback loops) from a potential space of ∼800,000 compositions. Of these, 14 had smaller ΔT than any of the 22 in the original data set.

Figure 1. Our adaptive design loop.

(a) Prior knowledge, including data from previous experiments and physical models, and relevant features are used to describe the materials. This information is used within a machine learning framework to make predictions that include error estimates. The results are used by an experimental design tool (for example, Global optimization) that suggests new experiments (synthesis and characterization) performed in this work, with the dual goals of model improvement and materials discovery. The results feed into a database, which provides input for the next iteration of the design loop. The green arrows represent the step-wise approach of the state-of-art using experiments or calculations, although few studies have demonstrated feedback. The red star shows that although sample number 3 is not the best predicted choice relative to sample 4, the ‘expected improvement' by selecting it is greater than other choices due to the large uncertainty. (b) Our loop, as executed in practice specific to the design problem featured in this work, is as follows: (i) an initial alloy experimental data set with known thermal dissipation ΔT and features or materials descriptors serves as input to the inference model. (ii) The model is trained and cross-validated with the initial alloy data. (iii) A data set of unexplored alloys defines the total search space of probable candidates. The trained model in (ii) is applied to all the alloys in (iii), to predict their ΔT. (iv) The design chooses the ‘best' four candidates for synthesis and characterization. (v) The new alloys, with their measured ΔT, augment the initial data set to further improve the inference and design. The four alloys for experiments are chosen iteratively by augmenting four times the initial data set with each new predicted alloy from the inference and design.

Figure 2. Inference and design combination.

The relative performance of various regressor:selector combinations on the NiTi SMA training data set. On the abscissa, we plot the number of initial random picks, taken from the training set, for building the statistical inference model. On the ordinate, we plot the average number of picks required to find the alloy in the training set with the lowest thermal hysteresis (ΔT). The best regressor:selector finds the optimal alloy in as few picks as possible. We conclude that SVR_rbf:KG (continuous red line) is the best regressor:selector combination for the NiTi SMA problem. Random picks are given as continuous blue line.

Figure 3. Results and insights from inference and global optimization.

(a) The experimental measurements for thermal hysteresis ΔT as a function of the number of iterations of the loop of Fig. 1 compared with the predictions (inset). Iteration 0 is the original training set of 22 alloys. At each iteration (from 1 onwards), four new predicted alloys are synthesized. The difference between the predicted and measured values of ΔT is large for iterations 1 and 2, drops significantly for iterations 3–6 and then increases beyond iteration 7. We interpret this as illustrating exploration in the early iterations, finding a reasonable minimum in the middle iterations and then exploring new areas in later iterations. (b) The ΔT as a function of the VEN feature shows that the exploration after iteration 3 is confined to an apparent minimum in the narrow interval (6.9:7; inset), favouring the B2→R transformation that is known to have the smallest ΔT (global minimum) compared with B19 and B19' transformations. (c) The average valence electron number of the four synthesized alloys as a function of the number of iterations, showing the exploratory nature (large standard deviation (s.d.)/error bars during iterations 1–2 and from 7 onwards) of the adaptive design in this feature space. The error bars denote standard deviations for VEN over the four samples. The tenth iteration indicates that the design is drifting away from the apparent global minimum (∼6.96 in the y axis).

Figure 4. Experimental measurements for the predicted Ti_50.0Ni_46.7Cu_0.8Fe_2.3Pd_0.2 alloy.

(a) Resistivity measurements for the new alloy, Ti_50.0Ni_46.7Cu_0.8Fe_2.3Pd_0.2 , compared with NiTi (inset) emphasize the very small hysteresis (0.84 K). (b) DSC curves for Ti_50.0Ni_46.7Cu_0.8Fe_2.3Pd_0.2 , whose peak-to-peak ΔT is measured as 1.84 K, which is the lowest among related NiTi-based SMAs. Thermal cycles (60 heating and cooling cycles) also show very small shift (∼0.02 K in the inset), indicating excellent thermal fatigue resistance.