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Caption : fig. s1 the rdf for the alo (a) and yo (b) pairs in yag melt (2000 k) with different concentration (at.%) of er3+.

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Caption : fig. s2 the rdf for the alo (a) and yo (b) pairs in yag melt (2600 k) with different concentration (at.%) of er3+.

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Caption : fig. 3s rdf between alal, yy and aly ionic pair in the yag (2000 k) with 0, 3, 6, 9, 12, 15, 20, 30, 40 and 50 at.% er.

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Caption : fig. 4s rdf between alal, yy and aly ionic pair in the yag (2600 k) with 0, 3, 6, 9, 12, 15, 20, 30, 40 and 50 at.% er.

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Caption : fig. s5 rdf between aly and aler cation pairs in the melt (2000 k) with 3, 6, 9, 12, 15, 20, 30, 40, and 50 at.% doping concentration.

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Caption : fig. s6 rdf between aly and aler cation pairs in the melt (2600 k) with 3, 6, 9, 12, 15, 20, 30, 40, and 50 at.% doping concentration.

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Caption : fig. s7 rdf between yy and yer cation pairs in the melt (2000 k) with 3, 6, 9, 12, 15, 20, 30, 40, and 50 at.% doping concentration.

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Caption : fig. s8 rdf between yy and yer cation pairs in the melt (2600 k) with 3, 6, 9, 12, 15, 20, 30, 40, and 50 at.% doping concentration.

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Caption : fig. s9 rdf between yo and ero cation pairs in the melt (2000 k) with 3, 6, 9, 12, 15, 20, 30, 40, and 50 at.% doping concentration.

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Caption : fig. s10 rdf between yo and ero cation pairs in the melt (2600 k) with 3, 6, 9, 12, 15, 20, 30, 40, and 50 at.% doping concentration.

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Caption : fig. s11 (a), (b) and (c) represent the detailed first peak of ero and yo rdf in systems with 3 , 20 and 50 at. % doping concentration respectively. (d) show the relationship between coordination number for y3+ and er3+ and temperature at these three doping concentrations.

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Caption : fig. s12 function of mean square displacement with time for o2-, al3+, y3+, and er3+, which include three different dynamic stages in er:yag (3 at.%) melt at different temperature.

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Caption : fig. s13 function of mean square displacement with time for o2-, al3+, y3+, and er3+, which include three different dynamic stages in er:yag (15 at.%) melt at different temperature.