Unified High-Pressure Phase-Transition Sequence in the f -Electron Metals: oF16→oF8 Transition in Terbium

The lanthanide elements have long been reported as having a common series of structural phase transitions on compression, but recent diffraction studies have revealed series of transitions: one in the low-Z lanthanides (Nd and Sm) involving an 8-atom orthorhombic structure (<a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mi>o</a:mi><a:mi>F</a:mi><a:mn>8</a:mn></a:math>), also seen in some actinide elements, and another in the high-Z lanthanides (Gd, Tb, Dy, and Ho) involving an isosymmetric 16-atom structure (<c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>o</c:mi><c:mi>F</c:mi><c:mn>16</c:mn></c:math>), unique to the lanthanides. No element has yet been found to exhibit both structures. We have followed the structural evolution of Tb to 308 GPa and find that <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:mi>o</e:mi><e:mi>F</e:mi><e:mn>16</e:mn></e:math>-Tb transforms to <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:mi>o</g:mi><g:mi>F</g:mi><g:mn>8</g:mn></g:math>-Tb at 234 GPa, which is stable to at least 308 GPa. This transition is confirmed by theoretical results which show the <i:math xmlns:i="http://www.w3.org/1998/Math/MathML" display="inline"><i:mi>o</i:mi><i:mi>F</i:mi><i:mn>8</i:mn></i:math> phase becoming energetically favorable above 280 GPa. This observation of the <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>o</k:mi><k:mi>F</k:mi><k:mn>16</k:mn><k:mo stretchy="false">→</k:mo><k:mi>o</k:mi><k:mi>F</k:mi><k:mn>8</k:mn></k:math> transition unites the two phase-transition sequences and suggests that there is a common <n:math xmlns:n="http://www.w3.org/1998/Math/MathML" display="inline"><n:mi>o</n:mi><n:mi>F</n:mi><n:mn>16</n:mn><n:mo stretchy="false">→</n:mo><n:mi>o</n:mi><n:mi>F</n:mi><n:mn>8</n:mn><n:mo stretchy="false">→</n:mo><n:mi>o</n:mi><n:mi>C</n:mi><n:mn>4</n:mn><n:mo stretchy="false">→</n:mo><n:mi>t</n:mi><n:mi>I</n:mi><n:mn>2</n:mn></n:math> transition sequence in the lanthanide elements under pressure.