School of Applied and Engineering Physics , Cornell University , Ithaca , New York 14853 , United States.
Physics and Astronomy Department , Stony Brook University , Stony Brook , New York 11794-3800 , United States.
J Phys Chem B. 2018 May 31;122(21):5694-5706. doi: 10.1021/acs.jpcb.8b00110. Epub 2018 Mar 27.
Nuclear quantum effects lead to an anomalous shift of the volume of hexagonal ice; heavy ice has a larger volume than light ice. Furthermore, this anomaly in ice increases with temperature and persists in liquid water up to the boiling point. To gain more insight, we study nuclear quantum effects on the density and compressibility of several ice-like structures and crystalline ice phases. By calculating the anisotropic contributions to the stain tensor, we analyze how the compressibility changes along different directions in hexagonal ice, and find that hexagonal ice is softer along the x- y plane than the z-direction. Furthermore, by performing ab initio density functional theory calculations with a van der Waals functional and with the quasiharmonic approximation, we find an anomalous isotope effect in the bulk modulus of hexagonal ice: heavy ice has a smaller bulk modulus than light ice. In agreement with the experiments, we also obtain an anomalous isotope effect for clathrate hydrate structure I. For the rest of the ice polymorphs, the isotope effect is (i) anomalous for ice IX, Ih, Ic, clathrate, and low density liquid-like (LDL-like) amorphous ice; (ii) normal at T = 0 K and becomes anomalous with increasing temperature for ice IX, II, high density liquid-like (HDL-like) amorphous ices, and ice XV; and (iii) normal for ice VIII up to the melting point. There is a transition from an anomalous isotope effect to a normal isotope effect for both the volume and bulk modulus, as the density (compressibility) of the structures increases (decreases). This result can explain the anomalous isotope effect in liquid water: as the compressibility decreases from the melting point to the compressibility minimum temperature, the difference between the volumes of the heavy and light water rapidly decreases, but the effect stays anomalous up to the boiling temperature as the hydrogen bond network is never completely broken by fully filling all of the interstitial sites.
核量子效应对六方冰的体积产生异常位移；重冰的体积大于轻冰。此外，这种冰的异常现象随着温度的升高而增加，并在液态水中持续到沸点。为了获得更多的认识，我们研究了核量子效应对几种冰状结构和结晶冰相的密度和压缩率的影响。通过计算应变张量的各向异性贡献，我们分析了六方冰在不同方向上的压缩率如何变化，发现六方冰在 xy 平面上比 z 方向上更软。此外，通过使用范德华泛函和准谐近似进行第一性原理密度泛函理论计算，我们发现六方冰的体弹模量存在异常同位素效应：重冰的体弹模量小于轻冰。与实验结果一致，我们还发现笼形水合物结构 I 存在异常同位素效应。对于其余的冰多晶型物，同位素效应为 (i)冰 IX、Ih、Ic、笼形水合物和低密度液态样（LDL-样）非晶冰为异常；(ii)在 T = 0 K 时为正常，对于冰 IX、II、高密度液态样（HDL-样）非晶冰和冰 XV，随着温度的升高变为异常；(iii)冰 VIII 在熔点之前为正常。随着结构的密度（压缩率）增加（降低），从体积和体弹模量的异常同位素效应转变为正常同位素效应。这一结果可以解释液态水中的异常同位素效应：随着从熔点到压缩率最小温度的压缩率降低，重水和轻水的体积差异迅速减小，但由于氢键网络从未完全通过完全填充所有的间隙位置而被打破，因此这种效应在沸点之前仍然是异常的。
